Visualization and analysis on the thrust vectoring control in three-dimensional dual-throat nozzles

The dual-throat vectoring nozzle is an efficient technique utilizing less high-pressure secondary streams to control mainstream deflections flexibly. In this article, three-dimensional Reynolds-averaged Navier–Stokes simulations were performed using a commercial computational fluid dynamics program, and the numerical methods applied in this study were validated through comparison with the experimental results. Two parameters of the slot injector have been investigated, namely the incident angle of the secondary stream and the slot length-to-width ratio. Critical performance parameters have been quantitatively analyzed, involving the pitching angle, injected mass flow ratio, system resultant thrust ratio, and resultant pitching thrust efficiency. Furthermore, visual flow-field features are expounded using Mach number contours on the center-plane, Mach number contours on various slices, and streaklines. Some meaningful conclusions are drawn herein. The flow field in this three-dimensional dual-throat nozzle is not fully symmetric based on the reference of the center-plane. Consequently, a full domain is essential to capture the flow characteristics accurately, instead of a half domain. Although the pitching angle for the secondary stream incidence angle of 120° is the highest, comprehensive characteristics in terms of resultant pitching thrust efficiency and system resultant thrust ratio for 150° are more outstanding. The pitching angle, system resultant thrust ratio, and resultant pitching thrust efficiency increase with an increase in the slot length-to-width ratio for a constant secondary stream mass flow rate. Under the circumstance of a constant injection pressure ratio, the pitching angle increases with an increase in the slot length, whereas system resultant thrust ratio and resultant pitching thrust efficiency decline with an increasing slot length.

Graphic abstract

A _e :

Nozzle exit area (mm²)

C _r :

Resultant pitching thrust efficiency (°/%)

C _s :

System resultant thrust ratio

D :

Slot width (mm)

F _i :

Ideally isentropic thrust force (N)

F _{i ,p} :

Ideally isentropic thrust force of the mainstream (N)

F _{i ,s} :

Ideally isentropic thrust force of the secondary stream (N)

F _x :

X-Component of the thrust force (N)

F _y :

Y-Component of the thrust force (N)

F _z :

Z-Component of the thrust force (N)

H _ut :

Upstream minimum throat height (mm)

H _dt :

Downstream minimum throat height (mm)

IPR :

Injection pressure ratio, IPR = P_i/P_atm

L :

Slot length (mm)

L _c :

Length of the recessed cavity (mm)

m ₀ :

Mass flow rate of the mainstream (kg/s)

m _i :

Mass flow rate of the secondary stream (kg/s)

NPR :

Nozzle pressure ratio, NPR = P₀/P_atm

P :

Static pressure (Pa)

P ₀ :

Total pressure of the nozzle inlet (Pa)

P _i :

Total pressure of the slot injector inlet (Pa)

P _atm :

Standard ambient pressure (Pa)

P _e :

Area-weighted average pressure on the dual-throat nozzle exit (Pa)

\(P_{uw}\) :

Static pressure along the centerline on the upper cavity surface (Pa)

R _g :

Gas constant

T :

Static temperature (K)

T ₀ :

Total temperature (K)

V :

Velocity (m/s)

V _ex :

X-Component of the nozzle exit velocity (m/s)

V _ey :

Y-Component of the nozzle exit velocity (m/s)

V _ez :

Z-Component of the nozzle exit velocity (m/s)

W :

Nozzle width (mm)

X :

X-Component

Y :

Y-Component

Z :

Z-Component

ρ :

Density (kg/m³)

γ :

Specific heat ratio (γ = 1.4 for air)

δ _β :

Pitching angle (°)

μ :

Dynamic viscosity (kg/m⋅s)

μ _t :

Turbulent viscosity (kg/m⋅s)

θ ₁ :

Cavity divergence angle (°)

θ ₂ :

Cavity convergence angle (°)

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. NRF-2016R1A2B3016436).

Authors and Affiliations

1. Department of Mechanical Engineering, Andong National University, Andong, Gyeongsangbuk-do, 760-749, Republic of Korea

   Kexin Wu, Tae Ho Kim & Heuy Dong Kim

Corresponding author

Correspondence to Heuy Dong Kim.

Conflict of interest

The author declares that they have no conflict of interest.

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