Design and Analysis of New Hydrogen Oxygen Pneumatic Proportional Reducing Pressure Valve

The pneumatic proportional pressure reducing valve is the main pressure control component in the fuel cell gas supply system, which directly affects the performance of the entire fuel cell system. Based on the research background of the hydrogen oxygen fuel cell gas supply system, a set of pneumatic proportional pressure reducing valves suitable for hydrogen oxygen gas environments was designed. Through structural design and multi-parameter analysis, the structural parameter design optimization and characteristic analysis of the proportional valve were proposed. It can provide high-precision and high stability gas control capabilities for fuel cell systems, and provide support for engineering applications.


Introduction
Hydrogen-oxygen proton exchange membrane fuel cell is an electrochemical power generation device that uses pure hydrogen and pure oxygen as reaction fuel [1][2][3].The fuel cell gas supply system is composed of multiple subsystems, including a variety of regulating valves, sensors, water, gas, and heat control devices.The pneumatic proportional pressure valve is one of the main pressure control elements in the fuel cell gas supply system, and the performance of voltage stabilization directly affects the performance of the whole fuel cell system which is an important link to ensure fuel cell supply and safe operation [4].
At present, many pneumatic manufacturers have realized productization and serialization, and most of them has stable product performance [5].Representative products include SMC's ITV, VY1 series, and Festo's VPPM, MPPES.The control accuracy can reach 0.5%~2%.The research on the characteristics of the proportional pressure valve is mainly aimed at the structural design of the pressure reducing valve, flow field simulation, control strategy and so on [6][7][8][9].
Most of the researches on the existing proportional pressure reducing valves are directed to air or inert gas, and there are few studies on the proportional pressure valves that can be applied to the hydrogen-oxygen medium [10][11][12][13].In this paper, the gas supply system of hydrogen-oxygen fuel cells is used as the research background, and a group of suitable design is applied.The new type of pneumatic proportional pressure reducing valve in the gas hydrogen-oxygen environment.

Structure Design Formatting the Title
In the fuel cell system, the pneumatic proportional pressure reducing valve is the main component to control the gas supply pressure of the system.The accuracy of the gas control directly determines the gas supply pressure regulation accuracy of the whole system.
The following technical specification are proposed for the hydrogen-oxygen pneumatic proportional pressure reducing valve: 1. Hydrogen valve: flow rate ≥600SL/min, when the inlet pressure is 0.3~0.6MPa, the outlet pressure is adjustable from 0.05 to 0.2MPa, and the voltage stabilization accuracy is ±4kPa.Rated working condition: inlet pressure is 0.4MPa, outlet pressure is 0.2MPa.
2. Oxygen valve: flow rate ≥300SL/min, when the inlet pressure is 0.3~0.6MPa, the outlet pressure is adjustable from 0.05~0.2MPa,and the voltage regulation accuracy is ±4kPa.Rated operating conditions: inlet pressure is 0.4MPa, outlet pressure is 0.2MPa.
Based on the above design scheme, the overall structure of the designed pneumatic proportional pressure reducing valve is shown in figure 1.The proportional pressure reducing valve is mainly composed of a proportional electromagnet, a bellows feedback cavity assembly, a valve stem, a main valve body, a valve core and a return spring in the figure, port a is the air inlet and port b is the decompression port.

Analysis of Working Principle
The following analyses the working principle of the proportional pressure reducing valve.When the pressure reducing valve is not working, the proportional solenoid has no signal input, and the pressure reducing valve is normally closed.When the proportional electromagnet receives the electrical signal, the proportional electromagnet converts the electrical signal into an acting force, acting on the top of the feedback cavity bellows, thereby pushing the valve spool.When the acting force is greater than the return spring preload and the valve system damping force, the valve turn on.
The high-pressure gas flows in from the air inlet a, achieves pressure reduction through the throttle effect of the valve port, and flows to the pressure relief port b and the feedback cavity of the bellows.At this time, the pressure of the bellows feedback cavity acts on the effective area of the bellows to form a feedback force opposite to the output force of the electromagnet.The outlet pressure value of the pressure reducing valve is set by the proportional solenoid.When the outlet pressure changes, the pressure in the feedback cavity changes, the force balance is broken, and the opening of the valve port changes.When the force of the spool reaches equilibrium here, the pressure regulation effect is achieved.

Preliminary Structural Parameter
According to the engineering experience, the structural parameters are initially determined as follows.

Assumption
In order to facilitate the analysis of the gas flow characteristics in the valve, the following assumptions are made for the system: a).The working medium is satisfied by ideal gas, and the flow of gas through the valve port or orifice is isentropic flow; b).The temperature and pressure fields in each chamber are uniform, the constant pressure specific heat and constant volume heat remain constant, and gas leakage caused by poor sealing in the system is ignored.c).Ignore the effect of gravity field.

Mathematics Model
The internal structure of the pressure reducing valve can be simplified into a series combination of multiple air resistances and air capacities, and a variable orifice is used to simplify the work of simulating the system load.The simplified gas resistance and gas capacity model is shown in figure 2   There are three main throttle functions during the operation of the pressure reducing valve, which are the main valve port, the feedback chamber throttle port, and the variable load throttle port.To simplify the calculation, the valve orifice is equivalent to one or more constricting nozzles, and the flow in the nozzle is regarded as one-dimensional isentropic motion.According to the Sanville flow pressure formula, the main valve port is equivalent to a single contracting nozzle, and the flow equation of the main valve port is expressed as 0 () where qs is the main valve port mass flow rate (kg/s); Cd is the flow coefficient; Av is the main valve port flow area (mm 2 ); Po is the outlet pressure (MPa); Ps is the upstream inlet pressure (MPa); Ts is the upstream temperature (K); γ is the gas adiabatic index; b is the critical pressure ratio, and it can be set as 0.528.
When the inlet and outlet pressure ratio is po/ps<b, the gas is in a choked flow state.The gas flow rate is sonic, and the flow rate is not related to the downstream pressure.On the contrary, it is a subsonic flow, and the flow rate changes with the upstream and downstream pressure changes.where Av is the flow area of the valve port.Based on the above considerations, the over-flow is modelled more finely when the valve is slightly opened.Assuming that the leakage area is 1/10 of the area comparing with the positive displacement, and based on engineering experience, assuming that the negative displacement is -0.2mm, the overflow area of the valve port is expressed as The flow coefficient of the feedback chamber damping hole can be expressed as o f0 ( ) where qf is the mass flow rate through the feedback cavity (kg/s); Avf is the feedback cavity damping orifice flow area (mm 2 ); Pf is the feedback cavity pressure (MPa); Tf is the feedback cavity temperature (K).
The load downstream of the proportional pressure reducing valve is simplified into a variable load orifice, and the load flow can be expressed as l () where ql is the mass flow rate of the load (kg/s); Ao is the equivalent area of the load damping hole (mm 2 ); pl is the load pressure (MPa), here it is set to the atmospheric pressure 1.013MPa; To is the temperature of the outlet cavity (K).
The opening system in the pressure reducing valve mainly includes the outlet cavity and the feedback cavity of the main valve, and the thermodynamic equation of the outlet cavity can be expressed as where Cp is the isobaric specific heat capacity J/(kg•K); Cv is the isometric specific heat capacity J/(kg•K); ms is the gas mass of the inlet chamber (kg); ml is the gas mass of the load chamber (kg); mf is the gas mass of the feedback cavity (kg).
The thermodynamic equations of the feedback cavity need to be divided into two situations for discussion.When the pressure value of the outlet cavity of the main valve is higher than or equal to the pressure of the feedback cavity, po≥pf, gas flows from the outlet cavity into the feedback cavity; when the pressure value of the outlet cavity of the main valve is less than the pressure of the feedback cavity, po<pf, the gas flows into the oral cavity from the feedback cavity, and the thermodynamic equation of the feedback cavity can be expressed as where dd ii m q t = , qi is the mass flow through the cavity (kg/s).In the working process of the pressure reducing valve, the main spool assembly and the pneumatic piston assembly are regarded as a whole for force analysis.The schematic diagram of the force is shown in figure 4.
where Fy is the spool preload force (N); F  is the spool damping force (N); mz is the spool component mass (kg); Kb, Ky is the stiffness of the bellows and return spring (N/m).

Static Characteristics Analysis
This article mainly explores the characteristics and pressure characteristics of proportional pressure reducing valves.According to the mathematical model of pressure reducing valves established above, a simulation model of static characteristics of pressure reducing valves is built to analyse the valve statically.The force of the spool in the static process can be expressed as follows.
The static characteristics of the pressure reducing valve are mainly affected by the key structural parameters such as the diaphragm area and the equivalent additional rigidity of the diaphragm and the return spring.The actual effects of the two key parameters are explored below.
The flow characteristics and pressure characteristics under different feedback cavity diameters are shown in the figure 5. Increasing the diaphragm area can improve the static flow characteristics and pressure characteristics of the valve.The changes in upstream pressure and load flow affect the opening of the valve port.Changes are the main cause of the static output pressure of the valve.Increasing the diaphragm area will reduce the gain value of the valve opening change, and improving the static characteristics of the system.

Static Characteristics Analysis
According to the mathematical model of the proportional pressure reducing valve, a nonlinear simulation model is built, including the moving parts of the diaphragm, the flow of the valve port and the thermodynamic and dynamic processes of the gas in the controlled cavity, which lays the foundation for the theoretical study of the dynamic characteristics, taking the hydrogen pressure reducing valve as an example , Under the rated operating conditions, the key structural parameters of the valve body (feedback cavity orifice, main spool diameter, friction resistance of the spool assembly, spring stiffness, diameter of the feedback cavity diaphragm, maximum allowable valve opening) are analysed.The influence of dynamic characteristics provides guidance for the optimization of valve structure parameters.

Feedback Cavity Orifice.
The dynamic response characteristics of the valve under different feedback cavity damping hole diameters are shown in the figure 7. The simulation results show that the size of the feedback cavity orifice has a great influence on the dynamic characteristics of the pressure reducing valve.The feedback cavity orifice mainly serves as a pressure buffer, damping the size of the hole will affect the response change time of the pressure in the cavity.When the size of orifice is too small, the pressure change of the cavity cannot be reasonably matched with the pressure response of the outlet cavity, resulting in a larger response overshoot and a longer adjustment time.10.The spring stiffness mainly affects the stability of the system.When the spring stiffness is too small, the system stability becomes worse.

Optimization Parameters and Characteristics Analysis
In the above, the influence of key structural characteristics of valves on the dynamic and static characteristics of proportional pressure reducing valves was explored through the parameter method.Now, through the comprehensive matching of key valve parameters, the optimized valve parameter combination is obtained.

Conclusion 1)
Designed a new type of non-overflow pneumatic proportional pressure reducing valve with bellows instead of feedback cavity with fully considering the characteristics of the hydrogenoxygen medium, and completed the overall structural design and optimized selection of highly compatible materials.
2) The mathematical model of the electromagnet part and the main valve body part of the valve was established, the nonlinear simulation model of the pneumatic proportional pressure reducing valve was built, and the static and dynamic characteristics of the proportional pressure reducing valve were carried out.
3) The influence of key structural parameters (feedback cavity diameter, feedback cavity damping hole, valve port diameter, equivalent spring stiffness, etc.) on the dynamic and static characteristics was analysed, and the valve structure parameters are optimized through the parameter method to obtain the better voltage stabilization characteristics and response characteristics.Finally, through experiments, the feasibility and accuracy of the design were verified.

Figure 1 .
Figure 1.Structure of the pneumatic proportional pressure reducing valve.

Figure 3 .
Figure 3. Simplified gas resistance and gas capacity model.

Figure 4 .
Figure 4.The schematic diagram of the force.

Figure 5 .
Figure 5. Static characteristics with different feedback cavity diameters.The flow characteristics and pressure characteristics under different equivalent additional stiffness are shown in the figure6.Reducing the additional stiffness can improve the static characteristics of the valve.When the external pressure and flow change, the opening of the valve port will change accordingly.When the spring stiffness becomes smaller, the deviation of the outlet pressure will be smaller accordingly due to the change in the opening of the valve port.

Figure 6 .
Figure 6.Static characteristics with different equivalent additional stiffness.
Diameter.The dynamic response characteristics of the valve at different valve spool diameters are shown in the figure 8.The size of the valve spool diameter directly affects the flow gain during valve opening.Increasing the valve spool opening system response becomes faster but the overshoot increases.The flow rate is reasonable to choose the diameter of the valve port.

Figure 7 .
Figure 7. Dynamic characteristics with different feedback cavity orifice.

Figure 8 .
Figure 8. Dynamic characteristics with different feedback cavity diameters.

4. 2 . 3 .
Friction Resistance.The dynamic response characteristics of the valve under different friction resistance are shown in the figure 9.The friction force affects the stability and adjustment time of the system.When designing and processing the valve, the system friction force should be reduced as much as possible.4.2.4.Spring Stiffness.The dynamic response characteristics of the valve under different spring stiffness are shown in the figure

Figure 9 .
Figure 9. Dynamic characteristics with different friction resistance.

Figure 10 .
Figure 10.Dynamic characteristics with different spring stiffness.4.2.5.Diameter of the Feedback Cavity Diaphragm.The dynamic response characteristics of the valve under different feedback cavity diameters are shown in the figure 11.The diameter of the feedback cavity affects the overshoot of the system.When the diaphragm area of the feedback cavity of the valve increases, the gain of the feedback cavity to the pressure changes increases.At the same time, the response speed is accelerated, and the overshoot increases.

4. 2 . 6 .
Maximum Allowable Opening of Valve Port.The dynamic response characteristics of the valve at the maximum allowable opening of different valve ports are shown in the figure12.The maximum allowable opening of the valve port will affect the response speed and overshoot of the pressure reducing valve.While ensuring the system response speed, the valve port is limited.The opening size can effectively reduce the overshoot when the valve is opened.

Figure 11 .
Figure 11.Dynamic characteristics with different diameter of the feedback cavity diaphragm.

Figure 12 .
Figure 12.Dynamic characteristics with different maximum allowable opening.

4. 3 . 1 .
Static Characteristics.The static characteristics of the hydrogen valve and the oxygen valve after parameter optimization are shown in the figure13.The characteristics of the hydrogenoxygen proportional pressure reducing valve are basically the same.Within the scope of technical indicators, the pressure deviation under the optimized static flow characteristic is less than ±8kPa, and the pressure characteristic deviation is less than ±5kPa.

Figure 13 .
Figure 13.Static characteristics of hydrogen and oxygen valve.

4. 3 . 2 .
Dynamic Characteristics.The static characteristics of the hydrogen valve and the oxygen valve after parameter optimization are shown in the Figure14.The response characteristics of the hydrogen and oxygen proportional pressure reducing valve are basically synchronized.The response time of the optimized hydrogen valve is about 35ms, and the overshoot is 23kPa; the response of the oxygen valve.The time is about 42ms and the overshoot is about 18kPa.Within the scope of technical requirements, the pressure-reducing valves can work normally, and have better stability and response characteristics.

Table 1 .
Hydrogen and oxygen valve preliminary structure parameter

Table 2 .
Hydrogen and oxygen valve optimization structure parameter