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23 pages, 17032 KiB  
Article
Experimental Investigation of Rotor Noise in Reverse Non-Axial Inflow
by Liam Hanson, Leone Trascinelli, Bin Zang and Mahdi Azarpeyvand
Aerospace 2024, 11(9), 730; https://doi.org/10.3390/aerospace11090730 - 6 Sep 2024
Viewed by 1213
Abstract
This paper experimentally characterises the far-field noise emissions of a rotor operating in reverse non-axial inflow conditions. Specifically, experiments were undertaken at a range of rotor tilting angles and inflow velocities to investigate the effects of negative tilting on rotor acoustics and their [...] Read more.
This paper experimentally characterises the far-field noise emissions of a rotor operating in reverse non-axial inflow conditions. Specifically, experiments were undertaken at a range of rotor tilting angles and inflow velocities to investigate the effects of negative tilting on rotor acoustics and their correlation with aerodynamic performance. The results show that the forces and moments experienced by the rotor blades change significantly with increasing inflow velocity and increasing negative tilting angle. Correspondingly, distinct modifications to the far-field acoustic spectra are observed for the negatively tilted rotor when compared to the edgewise condition, with the broadband noise content notably increasing. Moreover, for a given tilting angle, the broadband noise component is accentuated with increasing inflow velocity, similar to when the negative tilting angle is increased. With reference to the flow-field surveys conducted in the literature and a preliminary in-house flow measurement, the increase in broadband content can possibly be attributed to the heightened level of ingestion of blade self-turbulence, i.e., the ingestion of turbulent wake generated by the upstream portion of the rotor by the downstream portion. At lower inflow velocities, the magnitude of the blade passing frequency at each of the observer angles is found to change minimally with negative tilt. In contrast, at higher inflow velocities, the directivity pattern and intensity of both the blade passing frequency and the overall sound pressure level are shown to change with increases in magnitude, particularly at downstream observer locations with negative tilt. These findings have important ramifications for the design and suitable operational profile of aerial vehicles for future urban air mobility applications. Full article
Show Figures

Figure 1

Figure 1
<p>Schematic showing an eVTOL flight path in an urban environment. Reverse non-axial inflow conditions are likely to be experienced by eVTOL rotors during landing transition maneuvers. The asterisk indicates the flight conditions being investigated in the current paper.</p>
Full article ">Figure 2
<p>Details of the rotor assembly showing (<b>a</b>) the definition of tilting angle (<math display="inline"><semantics> <mi>α</mi> </semantics></math>) and coordinate system and (<b>b</b>) the different components annotated on the test rig.</p>
Full article ">Figure 3
<p>Chord length and pitch angle distribution of the 12″ × 6″ rotor used in the present study.</p>
Full article ">Figure 4
<p>Schematic representation of the experimental setup in the wind tunnel showing (<b>a</b>) the side-view of the setup with top polar microphone arc and (<b>b</b>) the back-view of the setup with the distance-corrected polar side array.</p>
Full article ">Figure 5
<p>Interpretation of the flow field of the rotor at a negative tilting orientation for (<b>a</b>) low inflow velocity and (<b>b</b>) high inflow velocity based on previous findings [<a href="#B18-aerospace-11-00730" class="html-bibr">18</a>,<a href="#B21-aerospace-11-00730" class="html-bibr">21</a>] and an in-house PIV experiment [<a href="#B23-aerospace-11-00730" class="html-bibr">23</a>].</p>
Full article ">Figure 6
<p>Time-averaged aerodynamic coefficients for a rotor operating at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> </mrow> </semantics></math> RPM presented as a function of the advance ratio (<math display="inline"><semantics> <mi>μ</mi> </semantics></math>) at different tilting angles. The following coefficients are presented: mean thrust coefficient (<math display="inline"><semantics> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">T</mi> </msub> </semantics></math>) variation (<b>a</b>), mean power coefficient (<math display="inline"><semantics> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">P</mi> </msub> </semantics></math>) variation (<b>b</b>), mean yaw force coefficient (<math display="inline"><semantics> <msub> <mi mathvariant="normal">C</mi> <mi>Fy</mi> </msub> </semantics></math>) variation (<b>c</b>) and mean yawing moment coefficient (<math display="inline"><semantics> <msub> <mi mathvariant="normal">C</mi> <mi>My</mi> </msub> </semantics></math>) variation (<b>d</b>).</p>
Full article ">Figure 7
<p>Sound pressure level spectra of a rotor operating at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> measured from three observer locations of <math display="inline"><semantics> <mrow> <mi>θ</mi> <mo>=</mo> <msup> <mn>60</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <msup> <mn>90</mn> <mo>∘</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>120</mn> <mo>∘</mo> </msup> </semantics></math> at inflow velocities of (<b>a</b>–<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">U</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>d</b>–<b>f</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>g</b>–<b>i</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>j</b>–<b>l</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles from <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>. The blue and red vertical lines in each sub-figure indicate both the rotor shaft tones (<math display="inline"><semantics> <mrow> <mi>m</mi> <mo>=</mo> <mn>0.5</mn> <mo>,</mo> <mn>1.5</mn> </mrow> </semantics></math>) and blade passing frequency tones (<span class="html-italic">m</span> = 1–3) respectively. The grey, red and blue shaded regions in (<b>c</b>) indicate three frequency bands: LF (<math display="inline"><semantics> <mrow> <mn>160</mn> <mspace width="3.33333pt"/> <mi>Hz</mi> <mo>≤</mo> <mi>f</mi> <mo>&lt;</mo> <mn>3</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> </mrow> </semantics></math>), MF (<math display="inline"><semantics> <mrow> <mn>3</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> <mo>≤</mo> <mi>f</mi> <mo>&lt;</mo> <mn>10</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> </mrow> </semantics></math>) and HF (<math display="inline"><semantics> <mrow> <mi>f</mi> <mo>≥</mo> <mn>10</mn> <mspace width="3.33333pt"/> <mi>kHz</mi> </mrow> </semantics></math>).</p>
Full article ">Figure 8
<p>Sound pressure level spectra of a rotor operating at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> measured from three observer locations of <math display="inline"><semantics> <mrow> <mi>ϕ</mi> <mo>=</mo> <msup> <mn>74</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, <math display="inline"><semantics> <msup> <mn>90</mn> <mo>∘</mo> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mn>107</mn> <mo>∘</mo> </msup> </semantics></math> at inflow velocities of (<b>a</b>–<b>c</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">U</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>d</b>–<b>f</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>g</b>–<b>i</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>j</b>–<b>l</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles from <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>. The blue and red vertical lines in each sub-figure indicate both the rotor shaft tones (<span class="html-italic">m</span> = 0.5, 1.5) and blade passing frequency tones (<span class="html-italic">m</span> = 1–3) respectively. The grey, red and blue shaded regions in (<b>c</b>) indicate three frequency bands: LF (160 Hz ≤ <span class="html-italic">f</span> &lt; 3 kHz), MF (3 kHz ≤ <span class="html-italic">f</span> &lt; 10 kHz) and HF ( <span class="html-italic">f</span> ≥ 10 kHz).</p>
Full article ">Figure 9
<p>Far- field noise directivity pattern at the fundamental BPF (<math display="inline"><semantics> <msub> <mi>SPL</mi> <mrow> <mi mathvariant="normal">m</mi> <mo>=</mo> <mn>1</mn> </mrow> </msub> </semantics></math>) on the top array (<math display="inline"><semantics> <mi>θ</mi> </semantics></math>) at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> for inflow velocities of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">U</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles of <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
Full article ">Figure 10
<p>Far- field noise directivity pattern at the fundamental BPF (<math display="inline"><semantics> <msub> <mi>SPL</mi> <mrow> <mi mathvariant="normal">m</mi> <mo>=</mo> <mn>1</mn> </mrow> </msub> </semantics></math>) on the side array (<math display="inline"><semantics> <mi>ϕ</mi> </semantics></math>) at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> for inflow velocities of (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="normal">U</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> over tilting angles of <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
Full article ">Figure 11
<p>Overall sound pressure level and directivity pattern of the rotor on the top array (<math display="inline"><semantics> <mi>θ</mi> </semantics></math>) at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> for inflow velocities of (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles of <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
Full article ">Figure 12
<p>Overall sound pressure level and directivity pattern of a rotor on the side array (<math display="inline"><semantics> <mi>ϕ</mi> </semantics></math>) at <math display="inline"><semantics> <mrow> <mo>Ω</mo> <mo>=</mo> <mn>9000</mn> <mspace width="3.33333pt"/> <mi>RPM</mi> </mrow> </semantics></math> for inflow velocities of (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>8.7</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>15.6</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>20.0</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>26.5</mn> <mspace width="3.33333pt"/> <msup> <mi>ms</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </semantics></math> and tilting angles of <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> to <math display="inline"><semantics> <mrow> <mo>−</mo> <msup> <mn>12</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
Full article ">
16 pages, 8028 KiB  
Article
Investigation of Non-Uniform Inflow Effects on Impeller Forces in Axial-Flow Pumps Operating as Turbines
by Kan Kan, Qingying Zhang, Hui Xu, Jiangang Feng, Zhenguo Song, Jianping Cheng and Maxime Binama
Water 2024, 16(10), 1428; https://doi.org/10.3390/w16101428 - 17 May 2024
Cited by 1 | Viewed by 1217
Abstract
Due to the existence of an inlet elbow, transmission shaft, and other structural components, the inflow of axial-flow pumps as turbines (PATs) becomes non-uniform, resulting in the complexity of internal flow and adverse effects such as structural vibration. In this paper, numerical methods [...] Read more.
Due to the existence of an inlet elbow, transmission shaft, and other structural components, the inflow of axial-flow pumps as turbines (PATs) becomes non-uniform, resulting in the complexity of internal flow and adverse effects such as structural vibration. In this paper, numerical methods were employed to explore the non-uniform inflow effects on impeller forces and internal flow field characteristics within an axial-flow PAT. The study results indicated that non-uniform inflow caused uneven pressure distribution inside the impeller, which leads to an imbalance in radial forces and offsetting the center of radial forces. With an increasing flow rate, the asymmetry of radial forces as well as the amplitude of their fluctuations increased. Non-uniform inflow was found to induce unstable flow structures inside the impeller, leading to low-frequency, high-amplitude pressure fluctuations near the hub. Using the enstrophy transport equation, it was shown that the relative vortex generation term played a major part in the spatiotemporal evolution of vortices, with minimal viscous effects. Full article
(This article belongs to the Special Issue Design and Optimization of Fluid Machinery)
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Figure 1

Figure 1
<p>Geometric model of the PAT.</p>
Full article ">Figure 2
<p>Local refinement mesh of the impeller blade.</p>
Full article ">Figure 3
<p>Comparison between the experimental and simulation results.</p>
Full article ">Figure 4
<p>Pressure distribution at the guide vane inlet.</p>
Full article ">Figure 5
<p>Pressure distribution on the impeller blade: (<b>a</b>) 0.8 <span class="html-italic">Q</span><sub>BEP</sub>; (<b>b</b>) <span class="html-italic">Q</span><sub>BEP</sub>; and (<b>c</b>) 1.2 <span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">Figure 6
<p>Three-dimensional forces distribution characteristics of impeller: (<b>a</b>) 0.8 <span class="html-italic">Q</span><sub>BEP</sub>; (<b>b</b>) <span class="html-italic">Q</span><sub>BEP</sub>; and (<b>c</b>) 1.2 <span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">Figure 7
<p>The variation laws of axial force and total radial force of the impeller with time under three flow rate conditions: (<b>a</b>) axial force <span class="html-italic">F<sub>x</sub></span>; (<b>b</b>) total radial force <span class="html-italic">F<sub>r</sub></span>.</p>
Full article ">Figure 8
<p>The pulsation characteristics of the axial and radial forces of the impeller under three flow rate conditions; (<b>a</b>) axial force <span class="html-italic">C<sub>Fx</sub></span>; (<b>b</b>) radial force <span class="html-italic">C<sub>Fy</sub></span>; and (<b>c</b>) radial force <span class="html-italic">C<sub>Fz</sub></span>.</p>
Full article ">Figure 9
<p>Schematic diagram of pressure pulsation monitoring points of impeller blade; (<b>a</b>) pressure surface; (<b>b</b>) suction surface.</p>
Full article ">Figure 10
<p>Frequency domain of pressure fluctuation on pressure surface: (<b>a</b>) 0.8 <span class="html-italic">Q</span><sub>BEP</sub>; (<b>b</b>) <span class="html-italic">Q</span><sub>BEP</sub>; and (<b>c</b>) 1.2 <span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">Figure 10 Cont.
<p>Frequency domain of pressure fluctuation on pressure surface: (<b>a</b>) 0.8 <span class="html-italic">Q</span><sub>BEP</sub>; (<b>b</b>) <span class="html-italic">Q</span><sub>BEP</sub>; and (<b>c</b>) 1.2 <span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">Figure 11
<p>Frequency domain of pressure fluctuation on the suction surface: (<b>a</b>) 0.8 <span class="html-italic">Q</span><sub>BEP</sub>; (<b>b</b>) <span class="html-italic">Q</span><sub>BEP</sub>; and (<b>c</b>) 1.2 <span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">Figure 12
<p>Enstrophy distribution on the blade-to-blade surface: (<b>a</b>) 0.8 <span class="html-italic">Q</span><sub>BEP</sub>; (<b>b</b>) <span class="html-italic">Q</span><sub>BEP</sub>; and (<b>c</b>) 1.2 <span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">Figure 12 Cont.
<p>Enstrophy distribution on the blade-to-blade surface: (<b>a</b>) 0.8 <span class="html-italic">Q</span><sub>BEP</sub>; (<b>b</b>) <span class="html-italic">Q</span><sub>BEP</sub>; and (<b>c</b>) 1.2 <span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">Figure 13
<p>Distribution of each term of the enstrophy transport equation on the blade-to-blade surface under 0.8<span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">Figure 14
<p>Distribution of each term of the enstrophy transport equation on the blade-to-blade surface under <span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">Figure 15
<p>Distribution of each term of the enstrophy transport equation on the blade-to-blade surface under 1.2<span class="html-italic">Q</span><sub>BEP</sub>.</p>
Full article ">
18 pages, 8358 KiB  
Article
Wind Tunnel Investigation of Transient Propeller Loads for Non-Axial Inflow Conditions
by Catharina Moreira, Nikolai Herzog and Christian Breitsamter
Aerospace 2024, 11(4), 274; https://doi.org/10.3390/aerospace11040274 - 30 Mar 2024
Cited by 3 | Viewed by 1841
Abstract
Recent developments in electrical Vertical Take-off and Landing (eVTOL) vehicles show the need for a better understanding of transient aero-mechanical propeller loads for non-axial inflow conditions. The variety of vehicle configurations conceptualized with different propellers in terms of blade geometry, number of blades, [...] Read more.
Recent developments in electrical Vertical Take-off and Landing (eVTOL) vehicles show the need for a better understanding of transient aero-mechanical propeller loads for non-axial inflow conditions. The variety of vehicle configurations conceptualized with different propellers in terms of blade geometry, number of blades, and their general integration concept results in aerodynamic loads on the propellers which are different from those on conventional fixed-wing aircraft propellers or helicopter rotors. Such varying aerodynamic loads have to be considered in the vehicle design as a whole and also in the detailed design of their respective electric propulsion systems. Therefore, an experimental approach is conducted on two different propeller blade geometries and a varying number of blades with the objective to explore the characteristics at non-axial inflow conditions. Experimental data are compared with calculated results of a low-fidelity Blade Element Momentum Theory (BEMT) approach. Average thrust and side force coefficients are shown to increase with inflow angle, and this trend is captured by the implemented numerical method. Measured thrust and in-plane forces are shown to oscillate at the blade passing frequency and its harmonics, with higher amplitudes at higher angles of inflow or lower number of blades. Full article
(This article belongs to the Special Issue Gust Influences on Aerospace)
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Figure 1

Figure 1
<p>Components of the experimental propeller test bench for the wind tunnel campaign. Propeller blades (not shown on this picture) attached to the rotor fixture on the left.</p>
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<p>(<b>a</b>) Test bench with Type A (APC) propeller blades positioned on the rotating platform in the wind tunnel, including axes adopted for load measurements. (<b>b</b>) Outside view of the TUM-AER Wind Tunnel A which was used for these experiments.</p>
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<p>Different propeller types investigated. Type B (Ramoser) propeller enabled the measurement of the same blade geometry in 2-, 3-, 4-, and 5-bladed configurations.</p>
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<p>Comparison of radial blade geometry of APC 18×8E, APC 18×12E, and RAM 18×12 for extracted and published (pub) data by APC; In the figure, (<b>a</b>) radial pitch-to-diameter ratio, (<b>b</b>) radial blade twist, and (<b>c</b>) chord-to-diameter ratio; all data over non-dimensional blade radius <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>/</mo> <mi>R</mi> </mrow> </semantics></math>; published data for chord-to-diameter ratio of both APC blades overlap.</p>
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<p>Three representative airfoil sections of APC 18×8E blade shape.</p>
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<p>Section-wise polar input obtained from 2D-RANS simulations for different Reynolds Numbers for APC 18×8E blade.</p>
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<p>Thrust and power coefficients (<math display="inline"><semantics> <msub> <mi>C</mi> <mi>T</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>C</mi> <mi>P</mi> </msub> </semantics></math>) over advance ratio <span class="html-italic">J</span>; REF data from [<a href="#B23-aerospace-11-00274" class="html-bibr">23</a>].</p>
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<p>Thrust and power coefficients, <math display="inline"><semantics> <msub> <mi>C</mi> <mi>T</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>C</mi> <mi>P</mi> </msub> </semantics></math>, over <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>o</mi> <mi>A</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math> and 25 m/s with 5000 RPM; Type B propellers with 2, 3, and 4 blades.</p>
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<p>Experimental force coefficients <math display="inline"><semantics> <msub> <mi>C</mi> <mi>x</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>C</mi> <mi>y</mi> </msub> </semantics></math> over <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>o</mi> <mi>I</mi> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mo>∞</mo> </msub> <mo>=</mo> <mrow> <mo>[</mo> <mn>10</mn> <mo>,</mo> <mn>25</mn> <mo>]</mo> </mrow> </mrow> </semantics></math> m/s at 5000 RPM. Type B propellers with 2, 3, and 4 blades.</p>
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<p>Lateral force coefficients <math display="inline"><semantics> <msub> <mi>C</mi> <mi>X</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>C</mi> <mi>Y</mi> </msub> </semantics></math> for Type B (Ramoser) propeller blades, including variations in pitch, RPM, wind speed, and blade count. Experimental data.</p>
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<p>Experimental forces over one rotation for two Type B propellers at different incidence angles.</p>
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<p>Experimental and BEMT results recorded over a single rotation for in-plane side force coefficient <math display="inline"><semantics> <msub> <mi>C</mi> <msub> <mi>F</mi> <mi>x</mi> </msub> </msub> </semantics></math> and roll moment coefficient <math display="inline"><semantics> <msub> <mi>C</mi> <msub> <mi>M</mi> <mi>x</mi> </msub> </msub> </semantics></math> for Type B propeller as a two-bladed variant (<b>left</b>) and a three-bladed variant (<b>right</b>); 5000 RPM at an inflow of <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mo>∞</mo> </msub> <mo>=</mo> <mn>25</mn> </mrow> </semantics></math> m/s; (<b>a</b>,<b>b</b>) at <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>o</mi> <mi>I</mi> <mo>=</mo> <msup> <mn>15</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>; (<b>c</b>,<b>d</b>) at <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>o</mi> <mi>I</mi> <mo>=</mo> <msup> <mn>45</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Experimental RMS values for the forces acting on the RAM propeller; measured for different propeller blade count and varying <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>o</mi> <mi>I</mi> </mrow> </semantics></math>, colored by experimental mean <math display="inline"><semantics> <msub> <mi>C</mi> <mi>T</mi> </msub> </semantics></math>. Results include different RPM, <math display="inline"><semantics> <msub> <mi>V</mi> <mo>∞</mo> </msub> </semantics></math> and blade pitch configurations.</p>
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<p>Power Spectral Density of lateral force <math display="inline"><semantics> <msub> <mi>F</mi> <mi>y</mi> </msub> </semantics></math> for Type B propeller with 3 blades, pitch 12 inches, 5000 RPM. Experimental data.</p>
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<p>Type B (Ramoser) with two blades, 5000 RPM, pitch 12 inches, wind speed 25 m/s.</p>
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<p>Type B (Ramoser) with three blades, 5000 RPM, pitch 12 inches, wind speed 25 m/s.</p>
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17 pages, 20600 KiB  
Article
Design of Sinusoidal Leading Edge for Low-Speed Axial Fans Operating under Inflow Distortion
by Lorenzo Tieghi, Giovanni Delibra, Johan Van der Spuy and Alessandro Corsini
Energies 2024, 17(5), 1150; https://doi.org/10.3390/en17051150 - 28 Feb 2024
Viewed by 1355
Abstract
Axial fans may be equipped with passive flow control devices to enhance rotor efficiency or minimize noise emissions. In this regard, blade designs influenced by biomimicry, such as rotors with sinusoidal leading edges (LEs), have gained popularity in recent years. However, their design [...] Read more.
Axial fans may be equipped with passive flow control devices to enhance rotor efficiency or minimize noise emissions. In this regard, blade designs influenced by biomimicry, such as rotors with sinusoidal leading edges (LEs), have gained popularity in recent years. However, their design is predominantly driven by a trial-and-error approach, with limited systematic studies on the influence of rotor performance. Furthermore, their effectiveness is typically evaluated under controlled conditions that may significantly differ from operations in real installation layouts. In this work, a systematic review of the design process for sinusoidal LE axial fan rotors is provided, aiming to summarize previous design experiences. Then, a modified sinusoidal LE is designed and fitted to a 7.3 m low-speed axial fan for air-cooled condensers (ACCs). These fans operate at environmental conditions, providing a quasi-zero static pressure rise, often with inflow non-uniformities. A series of RANS computations were run to simulate the performance of the baseline fan and that of the sinusoidal leading edge, considering a real installation setup at Stellenbosh University, where the ACC is constrained between buildings and has a channel running on the ground below the fan inlet. The aim is to explore the nonbalanced inflow condition effects in both rotor geometries and to test the effect of the installation layout on fan performance. The results show that the modification to the rotor allows for a more even distribution of flow in the blade-to-blade passages with respect to the baseline geometry. Full article
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Figure 1

Figure 1
<p>Modification of the straight leading edge (dashed line) using a sinusoidal function.</p>
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<p>Front view of the fan and blade numbering.</p>
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<p>Comparison between the tip leak vortex dynamics for baseline and modified blades. The relative velocity streamlines are colored using relative velocity magnitude, <span class="html-italic">W</span>.</p>
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<p>Static pressure distribution on the suction and pressure surfaces for the baseline rotor.</p>
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<p>Scheme of the numerical model of the experimental facility (computational domain).</p>
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<p>Total-to-static pressure rise and electric power absorption versus volumetric flow rate for the two rotors, and a power comparison using the available measurements.</p>
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<p>Electric power absorption and total-to-static efficiency versus volumetric flow rate for the two rotors at different inflow balances.</p>
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<p>Scheme of air intake, and a comparison between the inflow velocities in the bellmouth section for the three scenarios. Axial velocity is normalized with respect to bulk velocity, <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>V</mi> <mo>^</mo> </mover> <mo>/</mo> <msub> <mi>U</mi> <mi>b</mi> </msub> </mrow> </semantics></math>. The black lines represent the inflow channel reported in <a href="#energies-17-01150-f005" class="html-fig">Figure 5</a>.</p>
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<p>Lateral, bottom, and three-dimensional view of the flow streamlines, colored according to the inflow direction; baseline geometry.</p>
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<p>Lateral, bottom, and three-dimensional view of the flow streamlines, colored according to the inflow direction; sinusoidal LE geometry.</p>
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<p>Cascade projection of the relative velocity contour at 50% of the span for the two rotors. The blades are numbered according to <a href="#energies-17-01150-f002" class="html-fig">Figure 2</a>.</p>
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<p>Cascade projection of the relative velocity contour at 95% of the span for the two rotors. The blades are numbered according to <a href="#energies-17-01150-f002" class="html-fig">Figure 2</a>.</p>
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14 pages, 4686 KiB  
Article
A Turbulent Inflow Generation Method for the LES of High Re Flow by Scaling Low Re Flow Data
by Lei Luo and Honghu Ji
Aerospace 2023, 10(9), 808; https://doi.org/10.3390/aerospace10090808 - 15 Sep 2023
Cited by 1 | Viewed by 1225
Abstract
The rescaling–recycling method (RRM) is usually used to generate turbulent inflow for the LES of compressible wall-bounded flows, which can lead to relatively high computational cost for high Re flows since the mesh resolution increases exponentially with Re number. A turbulent inflow generation [...] Read more.
The rescaling–recycling method (RRM) is usually used to generate turbulent inflow for the LES of compressible wall-bounded flows, which can lead to relatively high computational cost for high Re flows since the mesh resolution increases exponentially with Re number. A turbulent inflow generation method based on the scaling of low Re flow, referred as TIG-LowRe, is proposed, aiming at reducing the computational cost when applying the RRM. To validate the proposed method, the TIG-LowRe method was applied to generate turbulent inflow for the LES of a non-isothermal round jet flow at Re = 86,000. Two cases were carried out with the inflow generated based on two round pipe flows at Re = 10,000 and 24,000. The results show that the mean and fluctuating temperatures of the two cases agree well with the experimental data. In the case of low Re flow at Re = 10,000, the jet flow decays too fast along the axial direction, the mean and fluctuating axial velocities are over-predicted and the radial fluctuating velocity is under-predicted. By increasing the Re of the low Re flow to 24,000, the decay rate of the jet flow decreases and the accuracies of the mean and fluctuating axial velocities are obviously improved, while the radial fluctuating velocity shifts further away from the experimental data. The main reason for the difference between the two cases is that more fine turbulent structure of the inflow in case-Re10000 is lost than in case-Re24000 during the turbulence generation process. Full article
(This article belongs to the Section Aeronautics)
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Figure 1
<p>Schematic of the TIG-LowRe method.</p>
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<p>Schematic of the jet flow.</p>
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<p>Simulation domain of the LES of jet flow.</p>
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<p>Mesh size in axial and radial directions.</p>
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<p>Radial profiles of the RMS of normalized fluctuating axial, circumferential and radial velocities of the inflow generated by the TIG-LowRe.</p>
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<p>Distributions on the jet flow centerline of the normalized (<b>a</b>) mean axial velocity and (<b>b</b>) mean temperature.</p>
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<p>Radial profiles of the normalized mean axial velocity at <span class="html-italic">x/D</span> = 3.</p>
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<p>Distributions on the jet flow centerline of the normalized fluctuations of the (<b>a</b>) axial velocity; (<b>b</b>) radial velocity; and (<b>c</b>) temperature.</p>
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<p>Radial profiles at <span class="html-italic">x/D</span> = 3 of the normalized fluctuating: (<b>a</b>) axial velocity; (<b>b</b>) radial velocity; and (<b>c</b>) temperature.</p>
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<p>Turbulent structure of the jet flow in the form of the instantaneous iso-surfaces of the Q criterion (<b>a</b>) case-Re10000 and (<b>b</b>) case-Re24000.</p>
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<p>Iso-lines of the instantaneous vorticity magnitudes of (<b>a</b>) case-Re10000 and (<b>b</b>) case-Re24000.</p>
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15 pages, 6136 KiB  
Article
Study on Inflow Distortion Mechanism and Energy Characteristics in Bidirectional Axial Flow Pumping Station
by Jia Chen, Huiyan Zhang, Yanjun Li, Fan Meng and Yunhao Zheng
Machines 2022, 10(11), 1014; https://doi.org/10.3390/machines10111014 - 2 Nov 2022
Cited by 2 | Viewed by 1654
Abstract
In the present work, unsteady flow solved by the Reynolds time-averaged Navier–Stokes equation was investigated to determine the inflow distortion mechanism and the spatial distribution of hydraulic loss in a bidirectional axial flow pumping station (Case 1) based on the entropy production theory. [...] Read more.
In the present work, unsteady flow solved by the Reynolds time-averaged Navier–Stokes equation was investigated to determine the inflow distortion mechanism and the spatial distribution of hydraulic loss in a bidirectional axial flow pumping station (Case 1) based on the entropy production theory. A laboratory-scale performance experiment was also employed for the accuracy verification of the simulation approach, and an axial flow pump with pipe passages (Case 2) accompanying uniform inflow was utilized for analysis comparison. The results show that the non-uniform inflow causes a noticeable reduction in head and efficiency, as high as 27% and 21%, respectively, and the best efficiency point with uniform inflow shifts to the point with a larger flow rate. The axial velocity of the impeller inlet in Case 2 changes more smoothly along the Span compared with that in Case 1, which further indicates a more uniform inflow at the impeller inlet. The total entropy production (TEP) of each domain in Case 1 is always higher than that in Case 2, and the TEP of the whole domain in Case 1 increased by 18.68%, 30.50%, and 29.67% with flow rates of 0.8Qdes, 1.0Qdes, and 1.2Qdes, respectively, compared with that in Case 2. In the inlet passage, the larger TEPR regions in Case 1 are mainly located in the horn passage, which is far away from the inlet side, and are also distributed in the suction side of impeller blades and guide vanes. Therefore, this work may provide an optimal design reference for pumping stations in practical application. Full article
(This article belongs to the Section Turbomachinery)
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Figure 1
<p>Calculation models: (<b>a</b>) with X-shaped flow channel; (<b>b</b>) with pipe passages.</p>
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<p>Meshes of the computational domain: (<b>a</b>) the guide vanes, (<b>b</b>) the impeller, (<b>c</b>) the X-shaped intake, and (<b>d</b>) the X-shaped outlet passage.</p>
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<p>Distribution of Y+ value for the impeller and guide vanes.</p>
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<p>Schematic of the closed test bench.</p>
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<p>Comparison of hydraulic performance between test and CFD results.</p>
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<p>Comparison of head and efficiency between uniform and non-uniform inflow.</p>
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<p>Axial velocity of impeller inlet for each case with different flow rates.</p>
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<p>TEP distribution for Cases 1 and 2 with different flow rates.</p>
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<p>Total entropy production rate of the inflow passage for each case with different flow rates: (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>Velocity distribution of the inflow passage for each case with different flow rates: (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>Total entropy production rate on the turbo surface with Span = 0.5 of impeller for each case with different flow rates: (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>Velocity distribution on the turbo surface with Span = 0.5 of impeller for each case with different flow rates: (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>Total entropy production on the turbo surface with Span = 0.5 of guide vanes for each case with different flow rates: (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>Velocity streamline on the turbo surface with Span = 0.5 of guide vanes for each case with different flow rates: (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>The location of the vertical mid-section of the outlet passage in each case.</p>
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<p>Total entropy production rate distribution of the outlet passage for each case with different flow rates: (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>Velocity streamlined distribution of the outlet passage for each case with different flow rates: (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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17 pages, 16802 KiB  
Article
Investigation of Energy Losses Induced by Non-Uniform Inflow in a Coastal Axial-Flow Pump
by Fan Meng, Yanjun Li and Jia Chen
J. Mar. Sci. Eng. 2022, 10(9), 1283; https://doi.org/10.3390/jmse10091283 - 11 Sep 2022
Cited by 6 | Viewed by 2110
Abstract
A non-uniform velocity profile occurs at the inlet of a coastal axial-flow pump which is placed downstream of the forebay with side-intake. As a result, the actual efficiency and head of the pump is dissimilar to the design parameters, and the lack of [...] Read more.
A non-uniform velocity profile occurs at the inlet of a coastal axial-flow pump which is placed downstream of the forebay with side-intake. As a result, the actual efficiency and head of the pump is dissimilar to the design parameters, and the lack of the theoretical investigation on the relationship between inflow distortion and energy losses restricts the application of the coastal axial-flow pump in the drainage project. In this paper, the unsteady numerical simulation and entropy production theory are employed to obtain the internal flow structure and quantify energy losses, respectively, with three inflow deflection angles (θ = 0°, 15°, or 30°). It is reported that the best efficiency point (BEP) shifts to large flow rate with θ increasing, due to the decline of the velocity component in axial direction at the impeller inlet. Therefore, the total entropy production (TEP) of the coastal axial-flow pump rises with θ increasing under small flow rates, but it decreases with θ increasing under large flow rates. The high total entropy production rate (TEPR) in the vicinity of the tailing edge of the impeller and guide vanes rises with θ increasing, caused by the enhanced wake vortex strength. In addition, the high TEPR area near the inlet of outflow conduit rises with θ increasing, originated from the improvement of secondary vortices intensity. Full article
(This article belongs to the Special Issue CFD Analysis in Ocean Engineering)
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Figure 1
<p>Geometry structure of a coastal axial-flow pump.</p>
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<p>Mesh of the coastal axial-flow pump.</p>
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<p>Grid independence analysis.</p>
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<p>Definition of the inflow deflection angle.</p>
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<p>Test bench photo.</p>
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<p>The external characteristic parameters of CFD and test at <math display="inline"><semantics> <mi>θ</mi> </semantics></math> = 0°.</p>
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<p>The (<b>a</b>) efficiency and (<b>b</b>) head curves under three inflow deflection angles.</p>
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<p>The axial velocity at the impeller inlet with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>TEP distribution with three inflow deflection angles under 0.8<span class="html-italic">Q</span><sub>des</sub>, 1.0<span class="html-italic">Q</span><sub>des</sub>, and 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>TEP percentage of hydraulic components with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>The division diagram of (<b>a</b>) turbo surface and (<b>b</b>) part of impeller.</p>
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<p>The volume-averaged TEPR in the impeller with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>The TEPR distribution on the turbo surface of the impeller with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>. (<span class="html-italic">R</span>* = 0.95).</p>
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<p>The division diagram of (<b>a</b>) turbo surface and (<b>b</b>) part of guide vanes.</p>
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<p>The volume-averaged TEPR in the guide vanes with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>The TEPR distribution on the turbo surface of the guide vanes with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>. (<span class="html-italic">R</span>* = 0.1).</p>
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<p>The radial distribution of the circumferential velocity of the guide vanes outlet under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>TEPR distribution in the outlet of guide vanes with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
Full article ">Figure 18 Cont.
<p>TEPR distribution in the outlet of guide vanes with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>The position of vertical mid section of the outflow conduit.</p>
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<p>The TEPR distibution and velocity vector in the vertical mid section of the outflow conduit with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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<p>The TEPR distibution and velocity vector in the vertical mid section of the outflow conduit with three inflow deflection angles under (<b>a</b>) 0.8<span class="html-italic">Q</span><sub>des</sub>, (<b>b</b>) 1.0<span class="html-italic">Q</span><sub>des</sub>, and (<b>c</b>) 1.2<span class="html-italic">Q</span><sub>des</sub>.</p>
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26 pages, 61733 KiB  
Article
Numerical Investigations of a Non-Uniform Stator Dihedral Design Strategy for a Boundary Layer Ingestion (BLI) Fan
by Tianyu Pan, Kaikai Shi, Hanan Lu, Zhiping Li and Jian Zhang
Energies 2022, 15(16), 5791; https://doi.org/10.3390/en15165791 - 10 Aug 2022
Cited by 2 | Viewed by 2071
Abstract
A distributed propulsion system has the advantage of saving 5–15% fuel burn through ingesting the fuselage boundary layer of an aircraft by fan or compressor. However, due to boundary layer ingestion (BLI), the fan stage will continuously operate under serious inlet distortion. This [...] Read more.
A distributed propulsion system has the advantage of saving 5–15% fuel burn through ingesting the fuselage boundary layer of an aircraft by fan or compressor. However, due to boundary layer ingestion (BLI), the fan stage will continuously operate under serious inlet distortion. This will lead to a circumferentially non-uniform flow separation distribution on the stator blade suction surface along the annulus, which significantly decreases the fan’s adiabatic efficiency. To solve this problem, a non-uniform stator dihedral design strategy has been developed to explore its potential of improving BLI fan performance. First, the stator full-annulus blade passages were divided into blade dihedral design regions and baseline design regions on the basis of the additional aerodynamic loss distributions caused by BLI inlet distortion. Then, to find the appropriate dihedral design parameters, the full-annulus BLI fan was discretized into several portions according to the rotor blade number and the dihedral design parameter investigations for dihedral depth and dihedral angle were conducted at the portion with the largest inflow distortion through a single-blade-passage computational model. The optimal combinational dihedral design parameter (dihedral depth 0.3, dihedral angle 6 deg) was applied to the blade passages with notable flow loss which were mainly located in the annulus positions from −120 to 60 degrees suffering from inlet distortion, while the blades in the low-loss annulus locations were unchanged. In this way, a non-uniform stator dihedral design scheme was achieved. In the end, the effectiveness of the non-uniform stator dihedral design was validated by analyzing the internal flow fields of the BLI fan. The results show that the stator dihedral design in distorted regions can increase the inlet axial velocity and reduce the aerodynamic load near the blade trailing edge, which are beneficial for suppressing the flow separations and reducing aerodynamic loss. Specifically, compared with the baseline design, the non-uniform stator dihedral design has achieved a reduction of aerodynamic loss of about 7.7%. The fan stage has presented an improvement of adiabatic efficiency of about 0.48% at the redesigned point without sacrificing the total pressure ratio. In the entire operating range, the redesigned fan has also shown a higher adiabatic efficiency than the baseline design with no reduction of the total pressure ratio, which provides a probable guideline for future BLI distortion-tolerant fan design. Full article
(This article belongs to the Special Issue Flow and Heat Transfer in Turbomachinery)
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<p>Meridional geometry of the investigated fan stage.</p>
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<p>Computational domain and inlet total pressure distribution.</p>
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<p>Computational grid in the transonic fan stage. (<b>a</b>) Rotor mesh; (<b>b</b>) Stator mesh.</p>
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<p>The results of the grid independence study.</p>
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<p>Comparison of performance maps between CFD results and experimental data.</p>
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<p>Absolute velocity contours on the blade-to-blade plane in the stator passage at the design point at 50% span. (<b>a</b>) CFD results; (<b>b</b>) Experimental data.</p>
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<p>Distribution of incidence angle at the stator inlet.</p>
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<p>Comparisons of total pressure loss distributions at 10%, 50%, and 90% span under BLI inlet distortion and clean inflow conditions.</p>
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<p>Parameterization of a blade airfoil section. (<b>a</b>) Blade airfoil; (<b>b</b>) Camber line; (<b>c</b>) Suction surface.</p>
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<p>Schematic graph of tangential stacking line for the dihedral blade.</p>
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<p>Comparison of the baseline stator blade (<b>left</b>) and the dihedral-designed stator blade (<b>right</b>).</p>
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<p>Scheme of dividing the full-annulus BLI fan.</p>
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<p>Numerical simulation scheme of stator blade dihedral design.</p>
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<p>Effects of dihedral depth and dihedral angle on stator loss.</p>
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<p>The effects of dihedral angle and dihedral depth on fan stage efficiency. (<b>a</b>) Dihedral angle and depth on fan efficiency; (<b>b</b>) Dihedral angle on fan efficiency with dihedral depth 0.3.</p>
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<p>The efficiency variation with the dihedral angle at different inflow portions (dihedral depth = 0.3).</p>
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<p>The efficiency variation with the dihedral angle at different mass flow operating conditions (dihedral depth = 0.3).</p>
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<p>Scheme of non-uniform stator dihedral design.</p>
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<p>Radial distributions of pitch-averaged axial and tangential velocities at the inlet of baseline and dihedral stators for different annulus positions. (<b>a</b>) −180 deg; (<b>b</b>) 90 deg; (<b>c</b>) 0 deg; (<b>d</b>) −90 deg.</p>
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<p>Static pressure distributions along the chordwise direction at different annulus positions at a 90% span for the baseline stator and dihedral stator. (<b>a</b>) −180 deg; (<b>b</b>) 90 deg; (<b>c</b>) 0 deg; (<b>d</b>) −90 deg.</p>
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<p>Comparisons of flow separations in stator blade passages between the baseline design and dihedral design at different annulus positions. (<b>a</b>) Baseline design, (<b>b</b>) Dihedral design.</p>
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<p>Comparisons of flow separations in stator blade passages between the baseline design and dihedral design at different annulus positions. (<b>a</b>) Baseline design, (<b>b</b>) Dihedral design.</p>
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<p>Comparisons of radial distributions of stator loss between the baseline design and the dihedral design at different annulus positions. (<b>a</b>) −180 deg; (<b>b</b>) 90 deg; (<b>c</b>) 0 deg; (<b>d</b>) −90 deg.</p>
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<p>Comparison of entropy contours on the blade-to-blade surface at 90% span in stator blade passage between the baseline design and the dihedral design.</p>
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<p>Circumferential distributions of stator loss at 90% span for the baseline and dihedral designs.</p>
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<p>Comparison of the stator loss between the baseline design and the non-uniform dihedral design over the whole operating range.</p>
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<p>Comparisons of overall performance maps between the baseline design and the non-uniform stator dihedral design.</p>
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19 pages, 6765 KiB  
Article
Predictions of Vortex Flow in a Diesel Multi-Hole Injector Using the RANS Modelling Approach
by Aishvarya Kumar, Jamshid Nouri and Ali Ghobadian
Fluids 2021, 6(12), 421; https://doi.org/10.3390/fluids6120421 - 23 Nov 2021
Cited by 1 | Viewed by 3271
Abstract
The occurrence of vortices in the sac volume of automotive multi-hole fuel injectors plays an important role in the development of vortex cavitation, which directly influences the flow structure and emerging sprays that, in turn, influence the engine performance and emissions. In this [...] Read more.
The occurrence of vortices in the sac volume of automotive multi-hole fuel injectors plays an important role in the development of vortex cavitation, which directly influences the flow structure and emerging sprays that, in turn, influence the engine performance and emissions. In this study, the RANS-based turbulence modelling approach was used to predict the internal flow in a vertical axis-symmetrical multi-hole (6) diesel fuel injector under non-cavitating conditions. The project aimed to predict the aforementioned vortical structures accurately at two different needle lifts in order to form a correct opinion about their occurrence. The accuracy of the simulations was assessed by comparing the predicted mean axial velocity and RMS velocity of LDV measurements, which showed good agreement. The flow field analysis predicted a complex, 3D, vortical flow structure with the presence of different types of vortices in the sac volume and the nozzle hole. Two main types of vortex were detected: the “hole-to-hole” connecting vortex, and double “counter-rotating” vortices emerging from the needle wall and entering the injector hole facing it. Different flow patterns in the rotational direction of the “hole-to-hole” vortices have been observed at the low needle lift (anticlockwise) and full needle lift (clockwise), due to their different flow passages in the sac, causing a much higher momentum inflow at the lower lift with its much narrower flow passage. Full article
(This article belongs to the Collection Advances in Turbulence)
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Graphical abstract

Graphical abstract
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<p>Representation of the simulated 3D model geometry of the injector and the needle/injector assembly at different needle lifts.</p>
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<p>(<b>a</b>) Sketch of the needle and injector assembly, and the positions where the predictions of mean and RMS velocity were made; (<b>b</b>) recorded locations in the experimental data [<a href="#B8-fluids-06-00421" class="html-bibr">8</a>].</p>
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<p>(<b>a</b>) One-sixth of the flow domain at the full needle lift, with periodic (cyclic) boundary conditions (the numbers represent the boundaries of flow domains: (1) inlet flow, (2) outlet flow, (3) injector and needle walls, and (4) periodic (cyclic) interface); (<b>b</b>) mesh of the flow domain; (<b>c</b>) axial plane mesh of the nozzle and sac volume flow domain.</p>
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<p>Normalised mean axial velocity (<b>left</b> column) component and the corresponding RMS velocity (<b>right</b> column) of non-cavitating nozzle flow at low lift (1.6 mm) CN = 0.44 and full lift (6.0 mm) CN = 0.45, and at x = 10.5 mm from the nozzle entrance; experimental data from [<a href="#B8-fluids-06-00421" class="html-bibr">8</a>].</p>
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<p>Planes and surfaces in the flow domain for flow-field analysis.</p>
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<p>Distribution of velocity vectors on plane 1 for the (<b>a</b>) low lift and (<b>b</b>) full lift; the vortices are encircled.</p>
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<p>Distribution of velocity vectors on plane 2 for the (<b>a</b>) low lift and (<b>b</b>) full lift; the vortices are encircled.</p>
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<p>(<b>a</b>) Distribution of velocity vectors on cyclic interface 1 for the (<b>a</b>) low lift and (<b>b</b>) full lift; the 3D isosurface of vorticity (1% of the vorticity magnitude) is also plotted.</p>
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<p>(<b>a</b>) Distribution of velocity vectors on cyclic interface 1 for the (<b>a</b>) low lift and (<b>b</b>) full lift; the 3D isosurface of vorticity (1% of the vorticity magnitude) is also plotted.</p>
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<p>(<b>a</b>) Zoomed 3D isosurface of vorticity (1% of the vorticity magnitude) of the sac region at low needle lift, generated to detect the presence of vortices; (<b>b</b>) 2D vectors of velocity are also plotted on the cyclic interface, in order to further detect vortices.</p>
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<p>High-speed digital images of cavitation in the fuel injector: (<b>a</b>) from the bottom, showing ‘‘hole-to-hole’’ connecting string cavitation and vortex cavitation structures emerging from the needle wall [<a href="#B7-fluids-06-00421" class="html-bibr">7</a>]; (<b>b</b>) from the side of the nozzle hole, showing two “counter-rotating strings cavities” inside the nozzle at full lift [<a href="#B11-fluids-06-00421" class="html-bibr">11</a>].</p>
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<p>Distribution of velocity vectors on plane 4 and cyclic1 and -2 for the (<b>a</b>) low lift and (<b>b</b>) full lift.</p>
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<p>Isosurface of vorticity (1% of the vorticity magnitude) viewed from the bottom of the injector to show the formation of the double-rotating vortices emerging from the needle wall and entering the injector hole at the (<b>a</b>) lower needle lift and (<b>b</b>) full needle lift.</p>
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<p>Normalised mean axial velocity (<b>left</b> column) component and the corresponding RMS velocity (<b>right</b> column) of non-cavitating nozzle flow at CN = 0.44: (<b>a</b>) x = 9.5 mm and (<b>b</b>) x = 10.5 mm from the entrance.</p>
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<p>Normalised mean axial velocity (<b>left</b> column) component and the corresponding RMS velocity (<b>right</b> column) of non-cavitating nozzle flow at CN = 0.44: (<b>a</b>) x = 13.5 mm and (<b>b</b>) x = 16.5 mm from the entrance.</p>
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15 pages, 7092 KiB  
Technical Note
Improvement of the Parallel Compressor Model and Application to Inlet Flow Distortion
by Emmanuel Benichou, Nicolas Binder, Yannick Bousquet and Xavier Carbonneau
Int. J. Turbomach. Propuls. Power 2021, 6(3), 34; https://doi.org/10.3390/ijtpp6030034 - 25 Aug 2021
Cited by 4 | Viewed by 4110
Abstract
This paper introduces a semi-analytical approach which enables one to deal with distorted inflow in axial fans or compressors. It is inspired by the classical parallel compressor (PC) theory but relies on a local flow-loading coefficient formalism. It is applied to non-uniform flow [...] Read more.
This paper introduces a semi-analytical approach which enables one to deal with distorted inflow in axial fans or compressors. It is inspired by the classical parallel compressor (PC) theory but relies on a local flow-loading coefficient formalism. It is applied to non-uniform flow conditions to study the aerodynamic behavior of a low-speed fan in response to upstream flow distortion. Experimental measurements and 3D RANS simulations are used to evaluate the prediction of fan performance obtained with the local PC method. The comparison proves that, despite its simplicity, the present approach enables to correctly capture first order phenomena, offering interesting perspectives for an early design phase if different fan geometries are to be tested and if the upstream distortion maps are available. Full article
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<p>Performance curve plotted in the <math display="inline"><semantics> <mi>ϕ</mi> </semantics></math>–<math display="inline"><semantics> <mi>ψ</mi> </semantics></math> framework.</p>
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<p>Loss correlation (<b>left</b>) and modified MacKenzie’s law at rotor TE (<b>right</b>).</p>
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<p>Velocity triangles upstream and downstream of the rotor row.</p>
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<p>Example of coarsened mesh used for PC calculation.</p>
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<p>Local parallel compressor workflow.</p>
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<p>3D view of the fan stage.</p>
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<p>Distortion grids and example of measured total pressure pattern.</p>
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<p>(<b>a</b>–<b>c</b>) Boundary conditions used in PC model for the compressor operating point (<math display="inline"><semantics> <msub> <mi>T</mi> <mi>i</mi> </msub> </semantics></math> is uniform).</p>
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<p>(<b>a</b>–<b>c</b>) Boundary conditions used in PC model at free windmill (<math display="inline"><semantics> <msub> <mi>T</mi> <mi>i</mi> </msub> </semantics></math> is uniform).</p>
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<p>Swirl angle measured at rotor LE: compressor (<b>a</b>) and free windmill (<b>b</b>).</p>
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<p>Total pressure (<b>top</b>) and total temperature (<b>bottom</b>) downstream of the rotor.</p>
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<p>Total pressure (<b>left</b>) and total temperature (<b>right</b>) downstream of the stator.</p>
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<p>Total pressure (<b>top</b>) and total temperature (<b>bottom</b>) downstream of the rotor.</p>
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<p>Total pressure (<b>left</b>) and total temperature (<b>right</b>) downstream of the stator.</p>
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<p>Axial velocity downstream of the stator: compressor (<b>a</b>) and free windmill (<b>b</b>).</p>
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<p>Total pressure and total temperature downstream of the rotor, assuming the same <math display="inline"><semantics> <msub> <mi>V</mi> <mi>z</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>P</mi> <mi>i</mi> </msub> </semantics></math>, <math display="inline"><semantics> <msub> <mi>T</mi> <mi>i</mi> </msub> </semantics></math> conditions from URANS and uniform zero swirl angle: compressor (<b>a</b>) and free windmill (<b>b</b>).</p>
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23 pages, 935 KiB  
Article
Power Maximization and Turbulence Intensity Management through Axial Induction-Based Optimization and Efficient Static Turbine Deployment
by Mfon Charles, David T. O. Oyedokun and Mqhele Dlodlo
Energies 2021, 14(16), 4943; https://doi.org/10.3390/en14164943 - 12 Aug 2021
Cited by 2 | Viewed by 1718
Abstract
Layout optimization is capable of increasing turbine density and reducing wake effects in wind plants. However, such optimized layouts do not guarantee fixed T-2-T distances in any direction and would be disadvantageous if reduction in computational costs due to turbine set-point updates is [...] Read more.
Layout optimization is capable of increasing turbine density and reducing wake effects in wind plants. However, such optimized layouts do not guarantee fixed T-2-T distances in any direction and would be disadvantageous if reduction in computational costs due to turbine set-point updates is also a priority. Regular turbine layouts are considered basic because turbine coordinates can be determined intuitively without the application of any optimization algorithms. However, such layouts can be used to intentionally create directions of large T-2-T distances, hence, achieve the gains of standard/non-optimized operations in these directions, while also having close T-2-T distances in other directions from which the gains of optimized operations can be enjoyed. In this study, a regular hexagonal turbine layout is used to deploy turbines within a fixed area dimension, and a turbulence intensity-constrained axial induction-based plant-wide optimization is carried out using particle swarm, artificial bee colony, and differential evolution optimization techniques. Optimized plant power for three close turbine deployments (4D, 5D, and 6D) are compared to a non-optimized 7D deployment using three mean wind inflows. Results suggest that a plant power increase of up to 37% is possible with a 4D deployment, with this increment decreasing as deployment distance increases and as mean wind inflow increases. Full article
(This article belongs to the Special Issue Selected Papers from ENERGYCON 2020 Conference)
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<p>A regular hexagonal layout of turbines with hexagonal side = 7<span class="html-italic">D</span>.</p>
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<p>The Princess Amalia wind plant showing a regular hexagonal turbine layout [<a href="#B43-energies-14-04943" class="html-bibr">43</a>].</p>
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<p>Turbine Power and Thrust Curve: Power (kW) and thrust coefficient (<math display="inline"><semantics> <msub> <mi>C</mi> <mi>t</mi> </msub> </semantics></math>) versus wind speed (m/s) of the Bonus 300 kW MkIII wind turbine generator with <math display="inline"><semantics> <msub> <mi>U</mi> <mrow> <mi>i</mi> <mi>n</mi> </mrow> </msub> </semantics></math> = 3 m/s, <math display="inline"><semantics> <msub> <mi>U</mi> <mi>r</mi> </msub> </semantics></math> = 14 m/s, <math display="inline"><semantics> <msub> <mi>U</mi> <mrow> <mi>o</mi> <mi>u</mi> <mi>t</mi> </mrow> </msub> </semantics></math> = 25 m/s, <span class="html-italic">D</span> = 31 m, and <math display="inline"><semantics> <msub> <mi>z</mi> <mrow> <mi>h</mi> <mi>u</mi> <mi>b</mi> </mrow> </msub> </semantics></math> = 30 m, <math display="inline"><semantics> <msup> <mrow> <msub> <mi>C</mi> <mi>p</mi> </msub> </mrow> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msup> </semantics></math> = 0.5923 [<a href="#B44-energies-14-04943" class="html-bibr">44</a>].</p>
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<p>A regular hexagonal layout with hexagonal side of 4<span class="html-italic">D</span>, showing direction of inflow.</p>
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<p>Convergence plot for 5D at 10 m/s mean wind speed.</p>
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<p>Convergence plot for 6D at 10 m/s mean wind speed.</p>
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<p>4<span class="html-italic">D</span> deployment distance at 7 m/s mean wind speed.</p>
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<p>5<span class="html-italic">D</span> deployment distance at 7 m/s mean wind speed.</p>
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<p>6<span class="html-italic">D</span> deployment distance at 7 m/s mean wind speed.</p>
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<p>7<span class="html-italic">D</span> deployment distance at 7 m/s mean wind speed.</p>
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<p>Total plant power for all deployment distances, at 7 m/s mean wind speed.</p>
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<p>4<span class="html-italic">D</span> deployment distance at 8 m/s mean wind speed.</p>
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<p>5<span class="html-italic">D</span> deployment distance at 8 m/s mean wind speed.</p>
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<p>6<span class="html-italic">D</span> deployment distance at 8 m/s mean wind speed.</p>
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<p>7<span class="html-italic">D</span> deployment distance at 8 m/s mean wind speed.</p>
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<p>Total plant power for all deployment distances, at 8 m/s mean wind speed.</p>
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<p>Total plant power for all deployment distances, at 10 m/s mean wind speed.</p>
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<p>Plant efficiency variation for a 7 m/s inflow.</p>
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<p>Plant efficiency variation for a 8 m/s inflow.</p>
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<p>Twelve-bin wind rose for WM10 Butterworth at 60 m above ground level.</p>
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<p>Wind speed distribution for WM10 Butterworth at 60 m above ground level.</p>
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18 pages, 4661 KiB  
Article
Radial Turbine Design for Solar Chimney Power Plants
by Paul Caicedo, David Wood and Craig Johansen
Energies 2021, 14(3), 674; https://doi.org/10.3390/en14030674 - 28 Jan 2021
Cited by 9 | Viewed by 2822
Abstract
Solar chimney power plants (SCPPs) collect air heated over a large area on the ground and exhaust it through a turbine or turbines located near the base of a tall chimney to produce renewable electricity. SCPP design in practice is likely to be [...] Read more.
Solar chimney power plants (SCPPs) collect air heated over a large area on the ground and exhaust it through a turbine or turbines located near the base of a tall chimney to produce renewable electricity. SCPP design in practice is likely to be specific to the site and of variable size, both of which require a purpose-built turbine. If SCPP turbines cannot be mass produced, unlike wind turbines, for example, they should be as cheap as possible to manufacture as their design changes. It is argued that a radial inflow turbine with blades made from metal sheets, or similar material, is likely to achieve this objective. This turbine type has not previously been considered for SCPPs. This article presents the design of a radial turbine to be placed hypothetically at the bottom of the Manzanares SCPP, the only large prototype to be built. Three-dimensional computational fluid dynamics (CFD) simulations were used to assess the turbine’s performance when installed in the SCPP. Multiple reference frames with the renormalization group k-? turbulence model, and a discrete ordinates non-gray radiation model were used in the CFD simulations. Three radial turbines were designed and simulated. The largest power output was 77.7 kW at a shaft speed of 15 rpm for a solar radiation of 850 W/m2 which exceeds by more than 40 kW the original axial turbine used in Manzanares. Further, the efficiency of this turbine matches the highest efficiency of competing turbine designs in the literature. Full article
(This article belongs to the Section A: Sustainable Energy)
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<p>Sectional view of a solar chimney power plant (SCPP) with an axial turbine in the chimney, adapted from [<a href="#B6-energies-14-00674" class="html-bibr">6</a>]. The dimensions are: D<math display="inline"><semantics> <msub> <mrow/> <mn>1</mn> </msub> </semantics></math> = D<math display="inline"><semantics> <msub> <mrow/> <mn>2</mn> </msub> </semantics></math> = 10 m, H<math display="inline"><semantics> <msub> <mrow/> <mn>1</mn> </msub> </semantics></math> = H<math display="inline"><semantics> <msub> <mrow/> <mn>2</mn> </msub> </semantics></math> = 1.85 m, and H<math display="inline"><semantics> <msub> <mrow/> <mi>C</mi> </msub> </semantics></math> = 194.6 m.</p>
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<p>Configurations of axial turbines in an SCPP; (<b>a</b>) single vertical axis (VA) turbine, (<b>b</b>) multiple VA turbines, and (<b>c</b>) multiple horizontal axis (HA) turbines from Fluri [<a href="#B2-energies-14-00674" class="html-bibr">2</a>].</p>
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<p>Schematic drawing of turbine layouts, adapted from [<a href="#B11-energies-14-00674" class="html-bibr">11</a>].</p>
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<p>Schematic of the proposed radial turbine using Manzanares SCPP dimensions.</p>
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<p>Main geometrical features of the radial inflow (RIF) blade.</p>
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<p>Velocity triangles for an RIF turbine with radial inlet flow and axial outlet flow adapted from [<a href="#B29-energies-14-00674" class="html-bibr">29</a>]. <math display="inline"><semantics> <msub> <mi>C</mi> <mn>0</mn> </msub> </semantics></math> is the radial flow into the turbine located at the base of the chimney. The numbers on the left indicate the turbine sections.</p>
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<p>3D model of the stator and rotor completed in CFturbo for the three designs. Direction of rotation—counterclockwise. (<b>a</b>) First design; (<b>b</b>) second design; (<b>c</b>) third design.</p>
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<p>Grid completed in ANSYS Meshing using the 3D turbine model.</p>
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<p>Variation in the power output with the turbine rotational speed for the first design.</p>
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<p>Streamlines in rotating co-ordinates for the first and third designs. Direction of rotation—counterclockwise. (<b>a</b>) Streamlines for the first design; (<b>b</b>) streamlines for the third design.</p>
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24 pages, 35340 KiB  
Article
Effects of Mean Inflow Velocity and Droplet Diameter on the Propagation of Turbulent V-Shaped Flames in Droplet-Laden Mixtures
by Gulcan Ozel Erol and Nilanjan Chakraborty
Fluids 2021, 6(1), 1; https://doi.org/10.3390/fluids6010001 - 22 Dec 2020
Cited by 2 | Viewed by 2772
Abstract
Three-dimensional carrier phase Direct Numerical Simulations of V-shaped n-heptane spray flames have been performed for different initially mono-sized droplet diameters to investigate the influence of mean flow velocity on the burning rate and flame structure at different axial locations from the flame holder. [...] Read more.
Three-dimensional carrier phase Direct Numerical Simulations of V-shaped n-heptane spray flames have been performed for different initially mono-sized droplet diameters to investigate the influence of mean flow velocity on the burning rate and flame structure at different axial locations from the flame holder. The fuel is supplied as liquid droplets through the inlet and an overall (i.e., liquid + gaseous) equivalence ratio of unity is retained in the unburned gas. Additionally, turbulent premixed stoichiometric V-shaped n-heptane flames under the same turbulent flow conditions have been simulated to distinguish the differences in combustion behaviour of the pure gaseous phase premixed combustion in comparison to the corresponding behaviour in the presence of liquid n-heptane droplets. It has been found that reacting gaseous mixture burns predominantly under fuel-lean mode and the availability of having fuel-lean mixture increases with increasing mean flow velocity. The extent of flame wrinkling for droplet cases has been found to be greater than the corresponding gaseous premixed flames due to flame-droplet-interaction, which is manifested by dimples on the flame surface, and this trend strengthens with increasing droplet diameter. As the residence time of the droplets within the flame decreases with increasing mean inflow velocity, the droplets can survive for larger axial distances before the completion of their evaporation for the cases with higher mean inflow velocity and this leads to greater extents of flame-droplet interaction and droplet-induced flame wrinkling. Mean inflow velocity, droplet diameter and the axial distance affect the flame brush thickness. The flame brush thickens with increasing droplet diameter for the cases with higher mean inflow velocity due to the predominance of fuel-lean gaseous mixture within the flame. However, an opposite behaviour has been observed for the cases with lower mean inflow velocity where the smaller extent of flame wrinkling due to smaller values of integral length scale to flame thickness ratio arising from higher likelihood of fuel-lean combustion for larger droplets dominates over the thickening of the flame front. It has been found that the major part of the heat release arises due to premixed mode of combustion for all cases but the contribution of non-premixed mode of combustion to the total heat release has been found to increase with increasing mean inflow velocity and droplet diameter. The increase in the mean inflow velocity yields an increase in the mean values of consumption and density-weighted displacement speed for the droplet cases but leads to a decrease in turbulent burning velocity. By contrast, an increase in droplet diameter gives rise to decreases in turbulent burning velocity, and the mean values of consumption and density-weighted displacement speeds. Detailed physical explanations have been provided to explain the observed mean inflow velocity and droplet diameter dependences of the flame propagation behaviour. Full article
(This article belongs to the Special Issue Modelling of Reactive and Non-reactive Multiphase Flows)
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Figure 1

Figure 1
<p>Instantaneous fields of gaseous equivalence ratio, <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>g</mi> </msub> </mrow> </semantics></math> on the central x-y midplane for initial <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> <mo>,</mo> <mtext> </mtext> <mn>0.05</mn> <mo>,</mo> <mtext> </mtext> <mn>0.06</mn> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (1st row) and 10 (2nd row) at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>2.0</mn> <msub> <mi>t</mi> <mrow> <mi>f</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mrow> </semantics></math>. White lines illustrate <math display="inline"><semantics> <mi>c</mi> </semantics></math> = 0.1, 0.5 and 0.9 contours from outer to inner periphery and the droplets residing on the plane are indicated by grey dots (not to the scale).</p>
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<p>PDFs of <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>g</mi> </msub> </mrow> </semantics></math> in the region corresponding to 0.01 <math display="inline"><semantics> <mrow> <mo>≤</mo> <mi>c</mi> <mo>≤</mo> </mrow> </semantics></math> 0.99 at different locations A, B and C (top to bottom) for initial <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> </mrow> </semantics></math> (<span class="html-fig-inline" id="fluids-06-00001-i001"> <img alt="Fluids 06 00001 i001" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i001.png"/></span>), 0.05 (<span class="html-fig-inline" id="fluids-06-00001-i002"> <img alt="Fluids 06 00001 i002" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i002.png"/></span>) and 0.06 (<span class="html-fig-inline" id="fluids-06-00001-i003"> <img alt="Fluids 06 00001 i003" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i003.png"/></span>) with <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (continuous line) and 10.0 (dashed line).</p>
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<p>PDFs of <math display="inline"><semantics> <mi>c</mi> </semantics></math> conditional on <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>c</mi> <mo stretchy="false">˜</mo> </mover> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.5</mn> <mo> </mo> <mo>,</mo> <mn>0.9</mn> </mrow> </semantics></math> at different locations A, B and C (top to bottom) for initial <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> </mrow> </semantics></math> (<span class="html-fig-inline" id="fluids-06-00001-i004"> <img alt="Fluids 06 00001 i004" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i004.png"/></span>), 0.05 (<span class="html-fig-inline" id="fluids-06-00001-i005"> <img alt="Fluids 06 00001 i005" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i005.png"/></span>) and 0.06 (<span class="html-fig-inline" id="fluids-06-00001-i006"> <img alt="Fluids 06 00001 i006" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i006.png"/></span>) with <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (solid line) and 10.0 (dashed line).</p>
Full article ">Figure 4
<p>Contours of <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>c</mi> <mo stretchy="false">˜</mo> </mover> <mo>=</mo> </mrow> </semantics></math> 0.1 (solid line), 0.5 (dashed line) and 0.9 (dotted line) contours for gaseous premixed (<span class="html-fig-inline" id="fluids-06-00001-i007"> <img alt="Fluids 06 00001 i007" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i007.png"/></span>) case and droplet cases with initial droplet diameter <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> </mrow> </semantics></math> (<span class="html-fig-inline" id="fluids-06-00001-i008"> <img alt="Fluids 06 00001 i008" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i008.png"/></span>), 0.05 (<span class="html-fig-inline" id="fluids-06-00001-i009"> <img alt="Fluids 06 00001 i009" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i009.png"/></span>) and 0.06 (<span class="html-fig-inline" id="fluids-06-00001-i010"> <img alt="Fluids 06 00001 i010" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i010.png"/></span>) with <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (<b>left</b>) and 10.0 (<b>right</b>). The dashed grey lines show the sampling locations (A, B, C from left to <b>right</b>), and the dotted black line shows the flame centre.</p>
Full article ">Figure 5
<p>PDFs of <math display="inline"><semantics> <mrow> <msub> <mi>ϕ</mi> <mi>g</mi> </msub> </mrow> </semantics></math> conditional on <math display="inline"><semantics> <mrow> <mover accent="true"> <mi>c</mi> <mo stretchy="false">˜</mo> </mover> <mo>=</mo> <mn>0.1</mn> <mo>,</mo> <mn>0.5</mn> <mo> </mo> <mo>,</mo> <mn>0.9</mn> </mrow> </semantics></math> isosurfaces at different locations A, B and C (top to bottom) for initial <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> </mrow> </semantics></math> (<span class="html-fig-inline" id="fluids-06-00001-i011"> <img alt="Fluids 06 00001 i011" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i011.png"/></span>), 0.05 (<span class="html-fig-inline" id="fluids-06-00001-i012"> <img alt="Fluids 06 00001 i012" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i012.png"/></span>) and 0.06 (<span class="html-fig-inline" id="fluids-06-00001-i013"> <img alt="Fluids 06 00001 i013" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i013.png"/></span>) with <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (solid line) and 10.0 (dashed line).</p>
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<p>Instantaneous views of <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> isosurface coloured with <math display="inline"><semantics> <mrow> <msub> <mi>κ</mi> <mi>m</mi> </msub> <mo>×</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> values for gaseous premixed and spray flames with initial <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> <mo>,</mo> <mo> </mo> <mn>0.05</mn> <mo>,</mo> <mo> </mo> <mn>0.06</mn> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (1st row) and 10.0 (2nd row) at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>2.0</mn> <msub> <mi>t</mi> <mrow> <mi>f</mi> <mi>l</mi> <mi>o</mi> <mi>w</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>PDFs of <math display="inline"><semantics> <mrow> <msub> <mi>κ</mi> <mi>m</mi> </msub> <mo>×</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> of the <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> isosurface at locations A, B and C (top to bottom) for gaseous premixed (<span class="html-fig-inline" id="fluids-06-00001-i014"> <img alt="Fluids 06 00001 i014" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i014.png"/></span>) and V-shaped spray flames with initial <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> </mrow> </semantics></math> (<span class="html-fig-inline" id="fluids-06-00001-i015"> <img alt="Fluids 06 00001 i015" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i015.png"/></span>), 0.05 (<span class="html-fig-inline" id="fluids-06-00001-i016"> <img alt="Fluids 06 00001 i016" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i016.png"/></span>) and 0.06 (<span class="html-fig-inline" id="fluids-06-00001-i017"> <img alt="Fluids 06 00001 i017" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i017.png"/></span>) for <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (continuous line) and 10.0 (dashed line). The y-axis is shown in log-scale.</p>
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<p>Percentage of heat release arising from premixed (for initial <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> </mrow> </semantics></math> (<span class="html-fig-inline" id="fluids-06-00001-i018"> <img alt="Fluids 06 00001 i018" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i018.png"/></span>), 0.05 (<span class="html-fig-inline" id="fluids-06-00001-i019"> <img alt="Fluids 06 00001 i019" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i019.png"/></span>), 0.06 (<span class="html-fig-inline" id="fluids-06-00001-i020"> <img alt="Fluids 06 00001 i020" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i020.png"/></span>)) and non-premixed (for initial <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> </mrow> </semantics></math> (<span class="html-fig-inline" id="fluids-06-00001-i021"> <img alt="Fluids 06 00001 i021" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i021.png"/></span>), 0.05 (<span class="html-fig-inline" id="fluids-06-00001-i022"> <img alt="Fluids 06 00001 i022" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i022.png"/></span>), 0.06 (<span class="html-fig-inline" id="fluids-06-00001-i023"> <img alt="Fluids 06 00001 i023" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i023.png"/></span>)) modes of combustion for <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (1st row) and 10.0 (2nd row) at locations A, B and C (left to right).</p>
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<p>Variations of mean values of <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>w</mi> <mo>˙</mo> </mover> <mi>c</mi> </msub> </mrow> </semantics></math> (solid line), <math display="inline"><semantics> <mrow> <mo>∇</mo> <mo>·</mo> <mrow> <mo>(</mo> <mrow> <mi>ρ</mi> <mi>D</mi> <mo>∇</mo> <mi>c</mi> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> (line with circle marker), <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>A</mi> <mo>˙</mo> </mover> <mi>c</mi> </msub> </mrow> </semantics></math> (dotted line), <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>S</mi> <mo>˙</mo> </mover> <mrow> <mi>l</mi> <mi>i</mi> <mi>q</mi> <mo>,</mo> <mi>c</mi> </mrow> </msub> </mrow> </semantics></math> (triangle marker), <math display="inline"><semantics> <mrow> <mi>ρ</mi> <msub> <mi>S</mi> <mi>d</mi> </msub> <mrow> <mo>|</mo> <mrow> <mo>∇</mo> <mi>c</mi> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> (dashed line) and <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mrow> <mo>|</mo> <mrow> <mo>∇</mo> <mi>c</mi> </mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> (cross) conditional on <math display="inline"><semantics> <mrow> <mi>c</mi> </mrow> </semantics></math> for premixed gaseous (<span class="html-fig-inline" id="fluids-06-00001-i024"> <img alt="Fluids 06 00001 i024" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i024.png"/></span>) and droplet cases with initial <math display="inline"><semantics> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>/</mo> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mn>0.04</mn> </mrow> </semantics></math> (<span class="html-fig-inline" id="fluids-06-00001-i025"> <img alt="Fluids 06 00001 i025" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i025.png"/></span>), 0.05 (<span class="html-fig-inline" id="fluids-06-00001-i026"> <img alt="Fluids 06 00001 i026" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i026.png"/></span>) and 0.06 (<span class="html-fig-inline" id="fluids-06-00001-i027"> <img alt="Fluids 06 00001 i027" src="/fluids/fluids-06-00001/article_deploy/html/images/fluids-06-00001-i027.png"/></span>) for <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (1st column) and 10.0 (2nd column) at locations A, B, C (top to bottom). All terms are normalised by <math display="inline"><semantics> <mrow> <msub> <mi>δ</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>ρ</mi> <mn>0</mn> </msub> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
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<p>The mean values of <math display="inline"><semantics> <mrow> <msub> <mi>S</mi> <mi>c</mi> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msubsup> <mi>S</mi> <mi>d</mi> <mo>*</mo> </msubsup> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mrow> <mo>(</mo> <mrow> <mo>〈</mo> <msub> <mi>ϕ</mi> <mi>g</mi> </msub> <mo>〉</mo> </mrow> <mo>)</mo> </mrow> </mrow> </msub> </mrow> </semantics></math> on the <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math> isosurface at locations A–C for the cases with <math display="inline"><semantics> <mrow> <msub> <mi>u</mi> <mrow> <mi>m</mi> <mi>e</mi> <mi>a</mi> <mi>n</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>S</mi> <mrow> <mi>b</mi> <mo>,</mo> <mi>s</mi> <mi>t</mi> </mrow> </msub> <mo>=</mo> </mrow> </semantics></math> 5.0 (1st column) and 10.0 (2nd column).</p>
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24 pages, 10037 KiB  
Article
A Comparison of Isolated and Ducted Fixed-Pitch Propellers under Non-Axial Inflow Conditions
by Michael Cerny and Christian Breitsamter
Aerospace 2020, 7(8), 112; https://doi.org/10.3390/aerospace7080112 - 3 Aug 2020
Cited by 10 | Viewed by 8114
Abstract
A strong interest in highly-efficient, small-scale propeller configurations can be recognized, especially due to the currently growing number of and usage possibilities for unmanned aerial vehicles (UAVs). Although a variety of different propulsion concepts already exist on the market or are discussed in [...] Read more.
A strong interest in highly-efficient, small-scale propeller configurations can be recognized, especially due to the currently growing number of and usage possibilities for unmanned aerial vehicles (UAVs). Although a variety of different propulsion concepts already exist on the market or are discussed in the literature, there is still a demand for a systematic investigation to compare such configurations, in particular, small-scale propellers with a fixed pitch, which are analyzed in this work. Therefore, different configurations of small-scale propellers with a fixed pitch are analyzed in this paper. They were operated as isolated single propellers and as ducted propellers in a cylindrical wing. Furthermore, due to their flight envelope, UAVs are likely to operate at highly inclined inflow conditions and even under reverse inflow. These non-axial inflow conditions have a major influence on the flow field around a propeller. In order to investigate this influence, all analyses were performed at a range of inflow angles in relation to the propeller axis from αdisc=0° to 180°. Full article
Show Figures

Figure 1

Figure 1
<p>Definition of the coordinate system. From [<a href="#B12-aerospace-07-00112" class="html-bibr">12</a>].</p>
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<p>Flow phenomena of a propeller under non-axial inflow. (<b>a</b>) Illustration of the inflow, the rotational speed and the induced velocities, the flow around the blade tip, the radial flow and the vortex structures. (<b>b</b>) Illustration of the resulting three-components’ pressure distributions and forces.</p>
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<p>Inflow characteristics of a propeller’s blade section under non-axial inflow. The non-axial inflow influences the local lift <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>L</mi> </mrow> </semantics></math> and drag <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>D</mi> </mrow> </semantics></math>, and furthermore, the local thrust <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>T</mi> </mrow> </semantics></math> and portion of propeller torque <math display="inline"><semantics> <mrow> <mi>d</mi> <mi>Q</mi> <mo>/</mo> <mi>r</mi> </mrow> </semantics></math> [<a href="#B12-aerospace-07-00112" class="html-bibr">12</a>].</p>
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<p>(<b>a</b>) Size, (<b>b</b>) twist angle and chord length distribution of the applied APC 18x8E propeller.</p>
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<p>Dimensions of the applied duct.</p>
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<p>(<b>a</b>) Rotatable wind tunnel support with mounted propeller. (<b>b</b>) Instrumentation of the support with a one-sided illustration of the duct.</p>
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<p>(<b>a</b>) Stereo-PIV setup. The laser and the cameras were mounted on uniformly moving traverse systems. (<b>b</b>) The laser illuminated the vertically aligned plane of measurement.</p>
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<p>Mesh convergence study.</p>
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<p>Computational grid. (<b>a</b>) Blocking of the rotational propeller domain, (<b>b</b>) grid around the airfoil at <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>/</mo> <mi>R</mi> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>, (<b>c</b>) grid of propeller and outer domain at the symmetry plane (<math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>).</p>
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<p>Validation of the numerical setup by the thrust coefficient <math display="inline"><semantics> <msub> <mi>c</mi> <mi>T</mi> </msub> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>.</p>
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<p>Ratio of thrust coefficient to power coefficient <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mi>T</mi> </msub> <mo>/</mo> <msub> <mi>c</mi> <mi>P</mi> </msub> </mrow> </semantics></math>. (<b>a</b>) Static thrust conditions (<math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>), (<b>b</b>) polar over the advance ratio <span class="html-italic">J</span> with <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>4000</mn> </mrow> </semantics></math> rpm. Wind tunnel data.</p>
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<p>Thrust coefficient distribution. Polar over the advance ratio <span class="html-italic">J</span>, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>4000</mn> </mrow> </semantics></math> rpm. URANS results.</p>
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<p>(<b>a</b>,<b>b</b>) Thrust coefficient <math display="inline"><semantics> <msub> <mi>c</mi> <mi>T</mi> </msub> </semantics></math> and (<b>c</b>,<b>d</b>) effective thrust coefficient <math display="inline"><semantics> <msub> <mi>c</mi> <mrow> <mi>T</mi> <mo>,</mo> <mi>e</mi> <mi>f</mi> <mi>f</mi> </mrow> </msub> </semantics></math>. (<b>a</b>,<b>c</b>) <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>; black: open propeller; red: ducted propeller configuration. (<b>b</b>,<b>d</b>) Plot of total loads of the ducted configuration over <math display="inline"><semantics> <mi>μ</mi> </semantics></math> and <math display="inline"><semantics> <mi>κ</mi> </semantics></math>. Wind tunnel data.</p>
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<p>(<b>a</b>,<b>b</b>) Lift coefficient <math display="inline"><semantics> <msub> <mi>c</mi> <mi>L</mi> </msub> </semantics></math>. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>; black: open propelle; red: ducted propeller configuration. (<b>b</b>) Plot of total loads of the ducted configuration over <math display="inline"><semantics> <mi>μ</mi> </semantics></math> and <math display="inline"><semantics> <mi>κ</mi> </semantics></math>. Wind tunnel data.</p>
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<p>Pitching moment coefficient <math display="inline"><semantics> <msub> <mi>c</mi> <mi>m</mi> </msub> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, URANS results.</p>
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<p>Time-resolved relative (<b>a</b>) propeller and (<b>b</b>) duct thrust coefficients over one propeller revolution for different inflow angles. Plotted in relation to their individual averaged thrust magnitudes. <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, URANS calculation.</p>
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<p>Normalized induced axial velocity component <math display="inline"><semantics> <msub> <mi>U</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> </mrow> </msub> </semantics></math>. (<b>a</b>) Open propeller, (<b>b</b>) ducted propeller. URANS calculation. <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Pressure coefficient distribution on the duct contour. <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>4000</mn> </mrow> </semantics></math> rpm, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math>. URANS calculation.</p>
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<p>Normalized vorticity components perpendicular to two intersecting planes. (<b>a</b>) Open propeller, (<b>b</b>) ducted configuration. URANS calculation, <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Normalized induced axial velocity component <math display="inline"><semantics> <msub> <mi>U</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> </mrow> </msub> </semantics></math> of the ducted propeller. (<b>a</b>) PIV measurement with blanked areas due to shading of the PIV laser sheet. (<b>b</b>) URANS calculation. <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Normalized vorticity components perpendicular to two intersecting planes. URANS calculation, <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Formation of the central duct vortices. Derived from URANS calculation, <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>30</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Normalized induced axial velocity component <math display="inline"><semantics> <msub> <mi>U</mi> <mrow> <mi>x</mi> <mo>,</mo> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> </mrow> </msub> </semantics></math>. (<b>a</b>) Open propeller, (<b>b</b>) ducted propeller. URANS calculation. <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>60</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Pressure distribution around the duct contour at the propeller’s cross-section (<math display="inline"><semantics> <mrow> <mi>z</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>). URANS calculation, <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>60</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Normalized vorticity components perpendicular to two intersecting planes. URANS calculation, <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>60</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Formation of the outer duct vortices. Derived from URANS calculation, <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>60</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Three-dimensional illustration of the vortex structures under high inflow angles and reverse inflow, respectively. Normalized vorticity components perpendicular to two intersecting planes. URANS calculation, <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mrow> <mi>d</mi> <mi>i</mi> <mi>s</mi> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mn>90</mn> <mo>–</mo> <mn>180</mn> <mo>°</mo> </mrow> </semantics></math>.</p>
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<p>Area-averaged velocity components at the duct throat. URANS calculation, <math display="inline"><semantics> <mrow> <mi>J</mi> <mo>=</mo> <mn>0.33</mn> </mrow> </semantics></math>.</p>
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23 pages, 14080 KiB  
Article
An Induction Curve Model for Prediction of Power Output of Wind Turbines in Complex Conditions
by Mohsen Vahidzadeh and Corey D. Markfort
Energies 2020, 13(4), 891; https://doi.org/10.3390/en13040891 - 17 Feb 2020
Cited by 6 | Viewed by 3024
Abstract
Power generation from wind farms is traditionally modeled using power curves. These models are used for assessment of wind resources or for forecasting energy production from existing wind farms. However, prediction of power using power curves is not accurate since power curves are [...] Read more.
Power generation from wind farms is traditionally modeled using power curves. These models are used for assessment of wind resources or for forecasting energy production from existing wind farms. However, prediction of power using power curves is not accurate since power curves are based on ideal uniform inflow wind, which do not apply to wind turbines installed in complex and heterogeneous terrains and in wind farms. Therefore, there is a need for new models that account for the effect of non-ideal operating conditions. In this work, we propose a model for effective axial induction factor of wind turbines that can be used for power prediction. The proposed model is tested and compared to traditional power curve for a 2.5 MW horizontal axis wind turbine. Data from supervisory control and data acquisition (SCADA) system along with wind speed measurements from a nacelle-mounted sonic anemometer and turbulence measurements from a nearby meteorological tower are used in the models. The results for a period of four months showed an improvement of 51% in power prediction accuracy, compared to the standard power curve. Full article
(This article belongs to the Special Issue Fluid Mechanics and Turbulence in Wind Farms)
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Graphical abstract

Graphical abstract
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<p>A power curve derived for the 2.5 MW study turbine, using ten-minute data during the period of study, spanning from 20 February to 18 June 2018 and bins of 1 m s<sup>−1</sup>. Cut-in region (I), operational region (II) and rated region (III) are also shown.</p>
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<p>(<b>a</b>) Two-dimensional binning of wind power in terms of rotor equivalent wind speed and density and (<b>b</b>) the resulting power surface.</p>
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<p>A schematic of the wind turbine, the associated control volume within the ABL, and the variables required in Equation (<a href="#FD7-energies-13-00891" class="html-disp-formula">7</a>). The dashed rectangle depicts the control volume containing the wind turbine rotor.</p>
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<p>The stream-tube containing the wind turbine expands in the axial direction due to the fact that wind speed decreases gradually from the inflow towards the far wake.</p>
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<p>An example induction curve for the 2.5 MW turbine in this study, derived using bins of 0.5 m s<sup>−1</sup>. The boxes show the interquartile range for each bin, the lower and upper quartiles are shown with dashed lines, and values outside the lower and upper qartiles are shown with red plus marks.</p>
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<p>Satellite image of the location of the 106 m tall met tower and the stand-alone wind turbine in relation to each other and the City of Cedar Rapids. Image: Google.</p>
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<p>A schematic of the sensors installed on the 106 m tall met tower at the site. The instruments are installed on seven booms, at six different heights. Six booms are extended towards the west while Boom 7 extends easterly.</p>
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<p>Distribution of wind and generated energy during the four-month period of study: (<b>a</b>) wind rose from SCADA data and (<b>b</b>) energy rose from SCADA data in MWh, only for periods when the turbine was operating. The energy rose is generated by considering bins of 10°, and integrating the total amount of energy generated for each bin in MWh.</p>
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<p>Comparison of ten-minute averaged hub-height wind speed measurements at the met tower and at the nacelle. The diagonal represents a 1:1 relationship.</p>
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<p>Observed distribution of ten-minute averaged atmospheric variables, including: (<b>a</b>) hub-height wind speed (m s<sup>−1</sup>), (<b>b</b>) hub-height turbulence intensity (<math display="inline"><semantics> <mrow> <mi>T</mi> <mi>I</mi> </mrow> </semantics></math>), (<b>c</b>) shear exponent, (<b>d</b>) hub-height air density (kg m<sup>−3</sup>).</p>
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<p>Variation of induction factor with wind speed and density, as derived from Equation (<a href="#FD23-energies-13-00891" class="html-disp-formula">23</a>), based on 10 min mean wind speed and turbulent flux data. An Induction curve is obtained using bins of 0.5 m s<sup>−1</sup> for <math display="inline"><semantics> <msub> <mi>U</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>q</mi> </mrow> </msub> </semantics></math>.</p>
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<p>Classification of stability regimes based on distribution of <math display="inline"><semantics> <msub> <mi>R</mi> <mi>B</mi> </msub> </semantics></math>.</p>
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<p>The effect of <math display="inline"><semantics> <msub> <mi>C</mi> <mi>z</mi> </msub> </semantics></math> on <math display="inline"><semantics> <mrow> <mi>R</mi> <mi>M</mi> <mi>S</mi> <mi>E</mi> </mrow> </semantics></math> of power prediction showing optimum values for: (<b>a</b>) stable regime, (<b>b</b>) neutral regime, (<b>c</b>) unstable regime, normalized by <math display="inline"><semantics> <msup> <mi>D</mi> <mn>2</mn> </msup> </semantics></math>, where <span class="html-italic">D</span> is the diameter of the wind turbine.</p>
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<p>(<b>a</b>) Induction curve resulting from values of <math display="inline"><semantics> <msub> <mi>C</mi> <mi>z</mi> </msub> </semantics></math> found for different stability regimes and then dividing axial flow induction factor values into bins of 0.5 m s<sup>−1</sup> for <math display="inline"><semantics> <msub> <mi>U</mi> <mrow> <mi>r</mi> <mi>e</mi> <mi>q</mi> </mrow> </msub> </semantics></math> and (<b>b</b>) two induction curves resulting from division of data into two smaller sets based on air density.</p>
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<p>Performance of: (<b>a</b>) standard power curve, (<b>b</b>) power surface, (<b>c</b>) induction curve, and (<b>d</b>) double induction curve, for predicting power generation of the wind turbine.</p>
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<p>Time series of error reduction in power prediction during a sample twelve-hour period on 16 February 2018 from 3:00 a.m. to 3:00 p.m., resulting from (<b>a</b>) double induction curve, and (<b>b</b>) power surface, compared to the standard power curve.</p>
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<p>The linear relation between <math display="inline"><semantics> <msubsup> <mi>σ</mi> <mi>u</mi> <mn>2</mn> </msubsup> </semantics></math> and <math display="inline"><semantics> <msup> <mrow> <msub> <mi>u</mi> <mo>*</mo> </msub> </mrow> <mn>2</mn> </msup> </semantics></math> while setting the intercept to the origin, and for the sonic anemometers on (<b>a</b>) boom 4 (32 m), (<b>b</b>) boom 5 (80 m), and (<b>c</b>) boom 6 (106 m).</p>
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<p>Performance of: (<b>a</b>) induction curve using approximated values of turbulent fluxes, and (<b>b</b>) double induction curve using approximated values of turbulent fluxes, for predicting power generation of the wind turbine.</p>
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