RU2786749C1 - A method for determining the unsteady pressure of a gas flow and a device for its implementation - Google Patents

Abstract

FIELD: measurement of non-stationary (time-varying) pressure in gas and liquid flows.

SUBSTANCE: invention relates to measurement of non-stationary (time-varying) pressure in gas and liquid flows. The invention is intended to determine the unsteady pressure in a gas or liquid stream in the presence of particles in it. A method for determining the unsteady pressure of a gas flow using a pressure receiver in which there is a cavity and a receiving hole connecting the cavity to the outer space is based on the readings of a pressure sensor installed in the cavity. The damping coefficient and the natural frequency of gas vibrations in the intake opening of the nozzle, without taking into account damping (resonant frequency), are determined by the method for free damped oscillations or by the method of steady harmonic oscillations.

EFFECT: expansion of the operating frequency range of the nozzle, including the resonant frequency of the resonator, due to the possibility of reducing the size of the internal cavity, increasing the accuracy of determining the unsteady pressure in the flow according to the readings of the sensor installed in the internal cavity of the nozzle, and increasing the survivability of the sensor during experimental studies.

2 cl, 6 dwg

Description

The invention relates to the field of measurement of non-stationary (time-varying) pressure in gas and liquid flows. The invention is intended to determine the non-stationary pressure in a gas or liquid flow in the presence of particles in it.

The invention can be used to measure non-stationary gas-dynamic flow parameters in wind tunnels, combustion chambers, bladed compressors, pumps, pipelines, diffusers, hydraulic systems, as well as in experimental studies using high-speed aerodynamic carts. In all these installations there is a natural dustiness of the flow. Steam and gas condensate in the form of drops and ice particles, products of incomplete combustion of fuel, metal particles, paint, scale, plastics, etc. can be added to the natural dustiness of the flow. At high flow rates, these particles can damage miniature sensors that measure pressure pulsations. Damage is most likely to occur when flow is perpendicular to the sensor element, such as in the case of total pressure measurement. The invention can be applied in the design of sensors and receivers for measuring gas pressure (for example, Kulite Semiconductor products, Inc, Leonia, NJ, USA).

A miniature nozzle for measuring non-stationary pressure FAP-250 (Kulite Semiconductor products, Inc, Leonia, NJ, USA) is known. The sensitive elements of the sensors are located flush with the surface of the packing, which significantly reduces the survivability of the sensors in a flow with an admixture of particles. A difficult technical problem arises, how to protect the sensors from damage.

, где a - скорость звука, V - объем полости приемника давления, S - площадь приемного отверстия, l=l₀+2Δ, l₀ - глубина приемного отверстия, Δ - концевая поправка, связанная с вовлечением в движение газа с одной стороны отверстия. Наличие резонанса искажает результаты измерений нестационарного давления датчиком, установленным в полости. Из литературы известны приемники такой конструкции для измерения полного давления:One solution to this problem is to create an extended cavity (buffer region) inside the nozzle between the sensor and the flow, when a particle moving in the flow does not reach the pressure sensor when it enters the buffer region. This buffer region consists of a cavity and a receiving hole and is a well-known Helmholtz resonator, which is characterized by its own resonant frequency. The resonant frequency of the gas in the hole, according to Rayleigh (JWS Strutt (Lord Rayleigh), The Theory of Sound, second ed., Macmillan, London, 1926), is determined by the formula:

, where a is the speed of sound, V is the volume of the cavity of the pressure receiver, S is the area of the receiving hole, l=l ₀ +2Δ, l ₀ is the depth of the receiving hole, Δ is the end correction associated with the involvement of gas from one side of the hole. The presence of resonance distorts the results of measurements of non-stationary pressure by a sensor installed in the cavity. Receivers of this design are known from the literature for measuring the total pressure:

1.J.P. Giovanangeli, A new method for measuring static pressure fluctuations with application to wind-wave interaction. Experiments in Fluids 6 (1988) 156-164. https://doi.org/10.1007/BF00230727.

2. Seifert, L.T. Pack, 1999. Oscillatory excitation of unsteady compressible flows over airfoils at flight Reynolds numbers. AIAA 99-0925. https://doi.org/10.2514/6.1999-925.

3. G. Grossir, S. Paris, K. Bensassi, P. Rambaud, 2013. Experimental characterization of hypersonic nozzle boundary layers and free-stream noise levels. AIAA 2013-1130. https://doi.org/10.2514/6.2013-1130.

4. Patent "Prandtl probe for non-stationary speed measurement" (DE 3421515 A1).

In the total pressure receivers described in the literature, the transient pressure transducer is located inside the nozzle. There is a cavity between the sensor and the receiving opening. The sensor is located on the geometric axis of the receiving hole. The presence of a cavity in the nozzle leads to a limitation of the pressure frequency range by the resonant frequency of the resonator.

The prototype of the invention for the device is the device described in the patent "Prandtl probe for non-stationary speed measurements (DE 3421515 A1). The device consists of an elongated ogival body with a cylindrical hole in the nose and one or more holes on the side surface, which are connected to a small differential sensor connected to the holes in the nose and side surface. The disadvantage considered in the prototype of the device is that the sensor is placed on the axis of the receiving hole located in the nose of the device. To expand the operating frequency range, the sensor is brought closer to the receiving hole, which increases the likelihood that a particle flying through the hole will damage the sensor.

There is a known method for correcting the amplitude of oscillations in the external flow according to the amplitude of oscillations measured by a sensor installed in a Pitot full pressure receiver (A. Seifert, L.T. Pack, 1999. Oscillatory excitation of unsteady compressible flows over airfoils at flight Reynolds numbers. AIAA 99-0925. https ://doi.org/10.2514/6.1999-925). Seifert and Pack acted on a sensor installed in a Pitot total pressure receiver and on a nearby microphone with sound in the form of discrete tones. They determined the ratio of the amplitudes of the sensor and microphone readings. Based on the results obtained, the authors constructed a polynomial of the 2nd degree from the frequency of the given sound. They correct the pressure amplitude in the outer area according to the readings of the sensor installed in the nozzle, using this polynomial. The disadvantage of this method is the limitation of the operating frequency range: no more than 95% of the resonant oscillation frequency in the receiving hole.

Known adopted for the prototype method for measuring the parameters of unsteady flow (patent RU 2559566 "Method for measuring the parameters of a pulsating flow"), which consists in the fact that they measure and record the instantaneous values of the three components of the flow velocity, pulsations of the total and static pressures in any plane relative to the nozzle, while use a nozzle receiver with at least four pressure pulsation sensors, collect, digitally convert and record analog data coming from the sensors, process the sensor readings using calibration curves, visually monitor the operation of each of the sensors, conduct a spectral analysis of the measured data , determine instantaneous flow directions, Mach number values, values of the angle of attack and slip angle in the flow, and the pressure coefficient using approximating coefficients determined from the measured pressures.

The disadvantage considered in the prototype (patent RU 2559566) of the method is that it does not take into account the influence of gas fluctuations in the hole of the nozzle located in front of the pressure sensor. This leads to a decrease in the accuracy of measuring non-stationary pressure.

An important and difficult problem arises - how to measure non-stationary pressure when there is a cavity with a small hole between the sensor and the flow, which is a typical Helmholtz resonator. The Helmholtz resonator is a dynamic system. This is the reason for the complexity of the problem being solved: the dynamic pressure is measured by a dynamic system.

The technical result of the invention is to increase the survivability of the sensor during experimental studies, to increase the accuracy of determining the non-stationary pressure in the flow according to the readings of the sensor installed in the internal cavity of the nozzle, to expand the operating frequency range of the nozzle, including the resonant frequency of the resonator due to the possibility of reducing the size of the internal cavity.

The technical result is achieved by the fact that in the method for determining the non-stationary pressure of a gas flow using a pressure receiver, in which there is a cavity and a receiving hole connecting the cavity with the external space, a pressure sensor is installed inside the cavity, pressure sensor readings are obtained, during installation the pressure sensor is displaced relative to the axis intake opening, and to determine the desired pressure in the outer space, the following formulas are used:

>

>

5

five

where P is the pressure measured by the sensor;

P _e - pressure in the outer space;

и

- первая и вторая производные по времени показаний датчика давления;

and

- the first and second time derivatives of the pressure sensor readings;

P ^a - amplitude of pressure fluctuations in the hole, measured by the sensor;

- амплитуда колебаний искомого давления во внешнем пространстве;

- amplitude of fluctuations of the desired pressure in the outer space;

β - damping factor;

ω ₀ - natural circular frequency of gas oscillations in the hole in the absence of damping, i.e. resonant frequency;

ω - circular frequency of gas oscillations in the hole.

The technical result is also achieved by the fact that in a device for determining the non-stationary pressure of a gas flow, containing a pressure receiver with an internal cavity and an opening connecting the cavity with the external space, a pressure sensor is installed inside the cavity, the pressure sensor is displaced relative to the axis of the receiving opening, and the transverse size of the cavity is , at least the sum of the transverse dimensions of the hole and the sensing element of the sensor when the sensor and the hole are coaxially located, or the sum of the depth of the hole and the transverse dimension of the sensing element of the sensor when they are installed perpendicularly.

List of figures illustrating the proposed method and device.

In FIG. 1 shows a diagram of a nozzle for measuring non-stationary total and static pressure with small-sized sensors installed inside.

In FIG. 2. shows a photograph of the installation for determining the resonant frequency and damping coefficient of total and static pressure receivers by the method of free damped oscillations.

In FIG. Figure 3 shows the dependences of the relative amplitude of the sensor readings in the total and static pressure receivers on time, by which the damping coefficient is determined, with free damped oscillations.

In FIG. 4 shows the dependence for determining the resonant frequency of gas oscillations in the receiving hole by the method of steady harmonic oscillations.

In FIG. 5 shows the dependence for determining the damping factor by the method of steady harmonic oscillations.

In FIG. 6 shows the time dependences of the static pressure measured by the reference sensor and the sensor installed in the nozzle, as well as the result of pressure correction by the method proposed in this invention.

The following designations are adopted on the diagrams and conditionally shown:

1 - receiving opening of full pressure;

2 - static pressure inlet;

3 - small-sized sensor for measuring non-stationary pressure;

4 - reference sensor for measuring static pressure;

5 - reference sensor for measuring total pressure;

6 - ball to create pressure fluctuations;

7 - measuring system;

The method on which the present invention is based is implemented as follows:

1. In a device for determining the non-stationary pressure of a gas flow, containing a pressure receiver with an internal cavity and an opening 1, 2 connecting the cavity with the external space, a pressure sensor 3 is installed inside the cavity, the pressure sensor 3 is displaced relative to the axis of the receiving opening 1, 2. Pressure sensor can be displaced relative to the axis of the receiving hole in such a way that the transverse size of the cavity is at least the sum of the transverse dimensions of the hole 1, 2 and the sensitive element of the sensor 3 when the sensor and the hole 1, 2 are coaxially located, or the sum of the depth of the hole 1, 2 and the transverse dimension of the sensing element of the sensor 3 when they are installed perpendicularly. To create oscillations in the hole of the pressure receiver, the ball 6, located near the nozzle, is torn. The sensor is connected by an electric cable to the measuring system 7.

2. Determine the damping coefficient β and the natural frequency of gas oscillations in the nozzle inlet without taking into account damping ω ₀ (resonant frequency). These parameters can be determined in two ways: by the method of free damped oscillations and steady harmonic ones.

a) The method of free damped oscillations of the gas in the hole, arising when a pressure pulse is applied to the receiver, for example, when the ball breaks 6. The damping coefficient β is determined from the expression

where T is the oscillation period;

- амплитуда давления, измеренного датчиком;

- amplitude of the pressure measured by the sensor;

- начальная амплитуда давления, измеренного датчиком;

- initial amplitude of the pressure measured by the sensor;

n=0, 1, 2, …

,The resonant circular frequency of pressure oscillations in the hole is determined from the expression

,

where ω is the circular frequency of gas pressure oscillations, determined from the sensor readings.

b) The method of steady harmonic oscillations. The vibrations are set by the sound generator. The resonant frequency is determined using the expression

where ε is the phase difference between the readings of the exemplary sensor and the sensor installed in the nozzle.

The damping coefficient is determined from the expression

3. The desired pressure in the outer space is determined by the following formulas:

where P is the pressure measured by the sensor;

P _e - pressure in the outer space;

и

- первая и вторая производные по времени показаний датчика давления;

and

- the first and second time derivatives of the pressure sensor readings;

P ^a - amplitude of pressure fluctuations in the hole, measured by the sensor;

- амплитуда колебаний искомого давления во внешнем пространстве;

- amplitude of fluctuations of the desired pressure in the outer space;

β - damping factor;

ω ₀ - natural circular frequency of gas oscillations in the hole in the absence of damping, i.e. resonant frequency;

ω - circular frequency of gas oscillations in the hole.

The device on which the invention is based is implemented as follows. In the pressure receiver, which consists of a body, an internal cavity, an inlet 1, 2 connecting the cavity with the outer space, a pressure sensor 3 is installed inside the cavity so that the sensor membrane 3 is displaced relative to the inlet 1, 2. The pressure sensor 3 can be displaced relative to axes of the receiving hole 1, 2 so that the transverse dimension of the cavity is at least the sum of the transverse dimensions of the hole and the sensitive element of the sensor when the sensor and the hole are coaxially located, or the sum of the depth of the hole and the transverse dimension of the sensitive element of the sensor when they are installed perpendicularly.

The advantages of the proposed method for determining the non-stationary pressure of a gas flow and the device that implements it are as follows:

1. The non-stationary pressure in front of the inlet is determined from the readings of the sensor installed in the nozzle, using an ordinary non-uniform second-order differential equation at any arbitrary moment in time. This requires only the results of measurements in the vicinity of this point in time to calculate the first and second time derivatives of the sensor readings.

2. The method makes it possible to take into account the influence of the cavity located between the sensor and the receiving opening when measuring non-stationary pressure.

3. The method makes it possible to determine non-stationary pressure from the readings of a sensor installed in the cavity inside the nozzle in a wide frequency range, including the natural frequency of gas oscillations in the inlet.

4. The device significantly increases the survivability of sensors for measuring non-stationary pressure in a gas flow with solid and liquid impurities.

5. The displacement of the sensor relative to the axis of the receiving hole allows you to reduce the size of the internal cavity of the pressure receiver.

The presence of the advantages listed above of the proposed method for determining non-stationary pressure and the proposed device increases the accuracy of determining the parameters of a non-stationary flow with particles of impurities and increases the survivability of the sensor, extends the operating frequency range of the nozzle. Confirmation is obtained by the results of experimental studies.

Claims (12)

1. A method for determining the non-stationary pressure of a gas flow using a pressure receiver in which there is a cavity and a receiving hole connecting the cavity with the external space, a pressure sensor is installed inside the cavity, pressure sensor readings are obtained, characterized in that during installation the pressure sensor is displaced relative to the axis of the receiving holes, and to determine the desired pressure in the external space, the following formulas are used:

,

, where P is the pressure measured by the sensor; P _e - pressure in the outer space;

and

- the first and second time derivatives of the pressure sensor readings; P ^a - amplitude of pressure fluctuations in the hole, measured by the sensor;

- amplitude of fluctuations of the desired pressure in the outer space; β - damping factor; ω ₀ - natural circular frequency of gas oscillations in the hole in the absence of damping, i.e. resonant frequency; ω - circular frequency of gas oscillations in the hole. 2. A device for determining the non-stationary pressure of a gas flow, containing a pressure receiver with an internal cavity and an opening connecting the cavity with the external space, a pressure sensor is installed inside the cavity, characterized in that the pressure sensor is displaced relative to the axis of the receiving opening, and the transverse size of the cavity is, according to at least the sum of the transverse dimensions of the hole and the sensing element of the sensor when the sensor and the hole are coaxially located, or the sum of the depth of the hole and the transverse dimension of the sensing element of the sensor when they are installed perpendicularly.

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