Research on high precision flow control technology of low speed wind tunnel air supply system

Aiming at the shortcomings of traditional analog control valves and digital valves, a high-pressure air supply system with accurate flow control is designed. Firstly, the ER5000 controller and pilot proportional valve drive several diaphragm reducing valves to achieve the preliminary adjustment of air pressure. Secondly, a needle valve based on the PCM digital valve and equal percentage flow characteristics is used to achieve accurate control of gas flow. Then, the Venturi flow meter with a honeycomb and damping network is used to accurately measure the airflow. Finally, a PID flow control algorithm based on nonlinear self-tuning is proposed. The results show that the flow regulation range of the system reaches 0.1∼8 kg/s, the absolute control accuracy is better than ±3 g/s, and the relative control accuracy is better than ±0.04%. Moreover, the system has the characteristics of short regulation time, small overshoot, and good dynamic performance, which can achieve strong support for wind tunnel air supply tests.


Introduction
Wind tunnel tests on items such as inlet, flow control, dynamic simulation, and thrust vector provide important performance parameters for the design and improvement of the aerodynamic force of engine inlets in China and the optimization of the aerodynamic layout components of aircraft [1] .With the deepening of experimental technology research, the refinement level of the high-pressure air supply system, which is the most basic and important part of wind tunnel tests, directly affects the accuracy of test data [2] .
At present, the comprehensive error of the traditional analog control valve is 0.5%, and the actual adjustable ratio is usually lower than the design value (usually 30~60) [3][4] .In addition, the control valve has the problems of dead zone control, regulation lag, and easy wear and tear of seals, so it can hardly meet the test requirements of newly developed flow control valves-high-precision, wide-range, and high-reliability PWM, PCM, and other digital valves, which have been widely used in various industries and played an important role [5][6][7][8] .However, they still have some shortcomings.The solenoid valve used by PWM digital valves has always been in a high-frequency switching state, so the parts are easy to wear, and the flow rate is relatively small, which leads to loud high-frequency noises, and the need for large flow rates cannot be met.The PCM digital valve is a kind of step control, and the output flow is discrete.The machining error of the nozzle will lead to oscillation when the step is advanced and backward.In addition, the response time of solenoid valves with different diameters is also different, which will reduce the synchronization of the switch and reduce the control accuracy.
To solve the above problems, a high-pressure air supply system with accurate flow control is designed, which can effectively compensate for the shortcomings of analog control valves and digital

Working principle
The high-pressure air supply system adopts a two-stage adjustment scheme, and its working principle is shown in Figure 1.In the first stage, the ER5000 controller and pilot proportional valve are used to driving two thin film pressure relief valves to reduce the 13 ~ 22 MPa high-pressure gas source to 6 ~ 10 MPa.The adjustment pressure is set according to the demand so that the pressure can remain constant while sufficient flow capacity is ensured.In the second stage, the flow regulating device composed of a PCM digital valve and a needle valve with equal percentage flow characteristics is used to achieve accurate flow control.At the second stage of the flow regulation process, the PCM digital valve provides reference flow, which is the basis for needle valve fine-tuning.Therefore, it is not necessary to design many nozzles with small valve positions and throat areas for the digital valve.During a certain flow regulation interval, the switching state of all solenoid valves remains unchanged, which can avoid the control oscillation caused by frequent switching.Due to the poor adjustment performance of the needle valve in the two transitional stages of the opening moment and full opening, the adjustment range is compressed to 30% ~ 80% during the design, which is the best adjustment range of the control valve, yielding the best performance [9] .Both the digital valve and the needle valve adopt a critical flow Venturi nozzle to achieve accurate flow regulation by controlling the total throat area.
In order to prevent large fluctuation of the pressure behind the valve of the high-pressure relief valve caused by the wide range adjustment of flow in the test process, an air buffer with a large capacity is added between the relief valve and the flow adjustment device, which can effectively filter and improve the stability of flow control.In order to adjust the outlet temperature of the airflow, two pneumatic control valves are added at the back end of the flow regulating device.The airflow is divided into two branches, one of which has a heat exchanger to heat the airflow, and the airflow temperature after mixing is quickly adjusted by controlling the airflow ratio of the two branches.
The flowmeter is mainly composed of a honeycomb and damping network, a throat, a total pressure probe, a static pressure probe, and so on.Its structure is shown in Figure 2.Among the components, the rectification device composed of honeycomb and damping networks can achieve the purpose of airflow guidance and vortex breaking to improve the flow field quality and the flow measurement accuracy.Due to the need to take into account the accuracy requirements of different measurement ranges and to meet the conditions of the throat to achieve sound speed under different test conditions, a number of flowmeters with different throat areas are designed to switch and match, which can ensure better measurement accuracy in different intervals.

High-Pressure relief valve
The working principle of the high-pressure relief valve is shown in Figure 3, the remote controller sends the set value of the pressure signal to the electronic pressure controller ER5269, which convert the electrical signal into the pressure signal, and then amplify the pressure to 6 ~ 10 MPa through the pilot proportional valve 26-2065, and then output it to the control chamber of the two thin film pressure relief valves 26-1261, respectively.The gap between the pressure regulating valve core and the valve seat increases or decreases the pressure behind the valve.At the same time, the feedback chamber of the regulating valve applies an effect opposite to that of the control chamber.When the two functions are balanced, the pressure behind the valve is stable.
Because of the large-capacity air buffer at the back end of the pressure relief valve 26-1261, the pressure regulation will be delayed.Therefore, the pressure relief valve adopts the way of external pressure.The pressure at the top of the air buffer is measured and used as the feedback pressure of the regulating valve.At the same time, the pressure signal is collected in real time by the pressure sensor, and the PID control is carried out by the remote controller.The outlet pressure of the valve can be accurately adjusted.In order to ensure the safety of the system and equipment, the high-pressure pneumatic ball valve is equipped before the pressure relief valve to quickly cut off the upstream pressure.The adopted nozzle of the digital valve is a critical flow Venturi nozzle with a diffusion tube.Compared with the standard nozzle, the critical outlet pressure can be significantly restored to avoid excessive pressure loss.According to Wu and Liu [10] , the ratio of diffusion section area to throat area in the selected nozzle is 4, and the critical pressure ratio can be increased from 0.528 to 0.89, that is when the outlet pressure of the digital valve is less than 0.89 times the inlet pressure, the critical state can be achieved.The flow rate of the nozzle throat is the sound velocity.In the ideal state, the flow rate is only determined by the inlet pressure, inlet temperature, and throat area.The calculation method is shown in Formula (1).
where P0 is the nozzle inlet pressure (Pa), T0 is the nozzle inlet temperature (K), and A * is the throat area (m 2 ).
The PCM digital valve consists of four branches, and its throat area is arranged in a binary sequence.Under the design conditions of inlet pressure 10 MPa, inlet temperature 20°C, and total flow 7.5 kg/s, the throat area of each nozzle can be obtained by four-bit binary calculation, as shown in Table 1.

Needle valve
The needle valve structure, as shown in Figure 5, mainly includes a cavity, an actuator, an orifice plate, a sleeve, a throat, a valve core, and so on.The flow control of the needle valve is realized by changing the throttling area of the throat, which is completed by the linear motion of the valve core.Therefore, the surface design and effective stroke of the valve core are directly related to the resolution and control accuracy of the flow.In addition, in order to improve the stability of the valve core operation, a cylinder orifice plate is used to rectify the upstream of the valve core, which can effectively reduce the unevenness of the airflow in the cavity.In order to avoid the installation of the actuator and other components in the pipeline, which will increase the difficulty of installation and maintenance, the inlet and outlet of the needle valve are misaligned.The actuator is installed outside the pipeline, connected to the tail of the valve core through the sleeve, and sealed with a double-layer O-ring.The flow characteristics of the control valve usually refer to the relationship between the relative flow of the valve and the relative displacement of the valve core, as shown in Formula (2).Compared with other flow characteristics such as parabola and straight line, the regulation performance of equal percentage characteristics is stable and the effect is better [11] .Its main feature is that the flow change caused at each point is proportional to the flow at that point, and the percentage of flow change is equal.When the flow is small, the flow change is small, and when the flow is large, the flow change is large.Therefore, the flow characteristics with an equal percentage have the same adjustment accuracy at different openings, which suits the design requirements of needle valves well where qV/qVmax is the ratio of the flow rate of the control valve in a certain opening state to that in a full opening state, l/L is the ratio of the core displacement of the control valve in a certain opening state to that in a full opening state, and R is the ideal adjustable ratio of the valve.
Since the throttling area of the needle valve is the difference between the throat area and the cross-sectional area of the valve core at the throat, the surface curve of the valve core can be designed as: where D is the throat diameter (mm), and r is the radius (mm) of the valve core at a certain opening.

MCAI-2023 Journal of Physics: Conference Series 2724 (2024) 012007
The maximum flow rate of the needle valve is 1 kg/s, and the throat diameter is calculated at 7.34 mm by Formula (1).The design effective stroke of the valve core should not be too small, otherwise, the resolution will be reduced.Also, it should not be too large, as a stroke too large will increase the overall size of the valve.After comprehensive consideration, the length of 10 times the throat diameter is selected as the effective stroke of the valve core in practical application.

Flow control principle
The control principle of the high-pressure air supply system is shown in Figure 6.The remote controller gives the regulating pressure signal of the high-pressure relief valve and the flow signal required by the test.The pressure regulator realizes the closed-loop control of the regulating pressure of the relief valve.The flow regulator realizes the opening and closing of each valve position of the PCM digital valve and the precise control of the opening of the needle valve.When the test requires the system to provide a stable outlet pressure, the pressure can be converted to a flow, so that the pressure can be controlled by controlling the flow.In the flow control, firstly, the flow value is directly given or converted from the pressure value; secondly, the difference between the actual flow measured by the flowmeter and the flow value is calculated; thirdly, the control value is output by the flow regulator; finally, according to the specified needle valve regulation interval of 30% ~ 80%, the flow of the PCM digital valve and needle valve is determined.Under the design conditions, when the flow control value is less than 0.8 kg/s, the digital valve should be fully closed, and only the needle valve should be adjusted.When the flow control value is higher than 0.8 kg/s, the digital valve controls each valve position according to different flow ranges without advanced or backward operation and then adjusts the opening of the needle valve on this basis.If the flow rate required by the test is less than 0.3 kg/s, the output pressure of the high-pressure relief valve can be reduced to ensure that the needle valve can also be in the optimal adjustment range.Due to the needle valve in the same position, the front pressure is reduced, and the flow will be proportionally reduced, so the accuracy requirements of small flows can be met.

Flow Control Algorithm
By analyzing the principle and structure of the high-pressure air supply system and the flow response curve, the transfer function of the flow control object can be simplified as a first-order inertial plus pure lag link, and its time constant is related to the length and volume of the pipeline and the heat exchanger, filter, and flowmeter at the back end.Due to the wide range of flow regulation, pressure, and flow rate have a great influence on the parameters of the transfer function, and the change of load during the test will also bring great disturbance, so it is difficult to accurately establish the control model.
In order to meet the test requirements for a fast, accurate flow with a wide range, a nonlinear self-tuning PID control algorithm is designed for the system, which can realize the self-tuning of the three parameters of proportional, integral, and differential in a certain range.The basic principle of the control algorithm is as follows: (1) Proportional gain parameter kp: when the deviation is large, kp is also large, which can improve the response speed; when the deviation is small, kp is also small, which can reduce overshoot.Therefore, according to the above variation law, the nonlinear function of kp is constructed as follows: exp( ( ) exp( ( ) 4) where kp1, kp2, and kp3 are positive real constants, the maximum value of kp is kp1 + kp2, and the minimum value is kp1.kp3 determines the change rate of kp.
(2) Integral gain parameter ki: when the deviation is large, ki should not be too large so that integral saturation can be prevented and the impact on dynamic performance and stability can be reduced; when the deviation is small, ki increases appropriately, which can effectively eliminate the steady-state error.Therefore, according to the above variation law, the nonlinear function of ki is constructed as follows: where ki1 and ki2 are positive real constants, and the maximum value of ki is ki1.ki2 determines the change rate of ki.
(3) Differential gain parameter kd: when the negative deviation is large, kd should gradually increase without affecting the response speed, which can inhibit the generation of overshoot; when the positive deviation is large, and kd should be slowly reduced and limited.Therefore, according to the above variation law, the nonlinear function of kd is constructed as follows: where kd1, kd2, kd3, and kd4 are positive real constants, the maximum value of kd is kd1 + kd2, and the minimum value is kd1.kd4 determines the change rate of kd.The nonlinear self-tuning control algorithm involves many parameters and needs some experience and debugging ability.If the parameters are selected properly, the control system can have a faster response speed and stronger anti-interference ability to effectively improve the flow control accuracy and dynamic performance.

Performance Testing
After the installation and commissioning of the high-pressure air supply system in the FL-12 wind tunnel, a comprehensive performance test was carried out.Figures 7 and 8 show the characteristic curves of dynamic and steady flow regulation, respectively.
It can be seen from Figure 7 that the flow regulation range of the air supply system is 0.1 ~ 8 kg/s, the regulation time is within 15 s, the overshoot is small, and there is no control oscillation phenomenon.It can be seen from Figure 8 that the flow steady-state performance is good.Under the given flow rate of 7 kg/s, the absolute control accuracy is better than ±3 g/s, and the relative control accuracy is better than 0.04%.

Conclusions
(1) The design of the high-pressure air supply system is successful.It has the characteristics of a wide flow regulation range, high control accuracy, and good dynamic characteristics.At present, it has been successfully applied to many wind tunnel tests, such as tests on inlets and dynamic simulation, which provide reliable experimental data and strong support for the design and optimization of inlets and aerodynamic layouts in China.
(2) The two-stage control scheme is used to comprehensively utilize the accurate pressure regulating the ability of the high-pressure relief valve, the flow expansion ability of the PCM digital valve, and the flow control ability of the needle valve in the middle area, which can effectively compensate for the shortcomings of the single traditional control valve, PWM digital valve, and PCM digital valve.
(3) The regulating interval of the needle valve is limited to 30% ~ 80%, which belongs to the optimal regulating interval of regulating valves and can avoid the adverse effects of the valve in the two transitional stages of the opening moment and full opening.In addition, the equal percentage flow characteristics can ensure high flow control accuracy at different valve core positions.
(4) It is not necessary to consider the influence of the response time difference of different types of solenoid valves and throat machining accuracy.By continuing to increase the digital valve position, the flow adjustment range can be further widened, which has great application prospects.

Figure 1 .
Figure 1.Diagram of the working principle of the high-pressure air supply system.At the second stage of the flow regulation process, the PCM digital valve provides reference flow, which is the basis for needle valve fine-tuning.Therefore, it is not necessary to design many nozzles with small valve positions and throat areas for the digital valve.During a certain flow regulation interval, the switching state of all solenoid valves remains unchanged, which can avoid the control oscillation caused by frequent switching.Due to the poor adjustment performance of the needle valve in the two transitional stages of the opening moment and full opening, the adjustment range is compressed to 30% ~ 80% during the design, which is the best adjustment range of the control valve, yielding the best performance[9] .Both the digital valve and the needle valve adopt a critical flow Venturi nozzle to achieve accurate flow regulation by controlling the total throat area.In order to prevent large fluctuation of the pressure behind the valve of the high-pressure relief valve caused by the wide range adjustment of flow in the test process, an air buffer with a large capacity is added between the relief valve and the flow adjustment device, which can effectively filter and improve the stability of flow control.In order to adjust the outlet temperature of the airflow, two pneumatic control valves are added at the back end of the flow regulating device.The airflow is divided into two branches, one of which has a heat exchanger to heat the airflow, and the airflow temperature after mixing is quickly adjusted by controlling the airflow ratio of the two branches.The flowmeter is mainly composed of a honeycomb and damping network, a throat, a total pressure probe, a static pressure probe, and so on.Its structure is shown in Figure2.Among the components, the rectification device composed of honeycomb and damping networks can achieve the purpose of airflow guidance and vortex breaking to improve the flow field quality and the flow measurement accuracy.Due to the need to take into account the accuracy requirements of different measurement ranges and to meet the conditions of the throat to achieve sound speed under different test conditions, a number of flowmeters with different throat areas are designed to switch and match, which can ensure better measurement accuracy in different intervals.

Figure 2 .
Figure 2. Diagram of the Venturi flow meter structure.

Figure 3 .
Figure 3. Diagram of the working principle of the high-pressure relief valve.

Figure 4 .
Figure 4. Diagram of the digital valve branch structure.

Figure 5 .
Figure 5. Diagram of the needle valve structure.

Figure 6 .
Figure 6.Schematic diagram of the control principle of the air supply system.

Table 1 .
Throat area distribution of the digital valve.