# Dynamic Modeling and Full-Process Simulation of the Core Engine Test Rig Main Test System
## 1 Introduction
[18] discovered that the surface roughness may result in a big difference between the flow coefficient obtained by simulation without friction and the actual flow coefficient. The second type of research [24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42] focuses on the whole system rather than the valve, and thus generally uses the traditional 0D throttling flow-rate equation instead of the momentum equation to describe the dynamic throttling effect of the valve spool. In order to accurately describe the throttling effect, this simplified modeling method must take flow-rate equation, flow coefficient calculation, and valve-spool opening and closing rule into full consideration. Firstly, as the core of the throttling model, the valve-spool or orifice throttling flow-rate equation is a semi-theoretical and semi-empirical formula. By the form of relationship between the flow rate and the upstream and downstream pressures, it can be roughly divided into the pressure ratio-based form [15; 24; 25] and the pressure difference-based form [15; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42]. The former generally applies to the condition of gas flow medium while the latter usually applies to the condition of liquid flow medium. In addition, to avoid the flow-rate distortion of the foresaid approach in the case of slight differential pressure in front of and behind the valve spool, the local loss model [25] returning to the momentum equation may be used. Secondly, in the case that the pressures and densities at the upstream and downstream of the spool or orifice are known, the calculation value of the flow rate at the throttling point depends on values of the flow cross-sectional area and the flow coefficient, where the flow area is a one-variable function of the spool opening, and the relation between the flow area and the opening can be obtained by mathematical derivation once the shapes of the valve spool and valve seat are determined, whereas the flow coefficient is a function of many factors such as opening, fluid properties, and throttling form, and it is a very complicated challenge to determine the relation between the flow coefficient and the opening which is generally obtained by interpolating or fitting the experimental data of spool characteristics. By treatment method for the flow area and the flow coefficient, the second type of research can be further divided into four cases: (1) both are calculated by their respective relations with the opening; (2) both are integrated into one variable and deemed as the function of opening; (3) the flow coefficient is an empirical constant; (4) both flow coefficient and flow area are constant. For example, in [15], the pressure ratio-based injector orifice model uses the first type of method, while the pressure difference-based orifice model uses the second type of method. [PERSON] et al. [42] investigated the temperature control of a vehicle climate chamber, and the flow coefficient of adjusting valves in the chilled water system also adopted the second type of method. As for the third type of method, [PERSON] et al. [26] used a nozzle model with variable area for the modeling of the pressure reducer valve when simulating the liquid propellant engine pressurization systems, where the flow area is function of the opening and the flow coefficient is constant; the same treating method also occurred in the modeling of the first and second throttling orifices of a class of three-way pressure reducing valve by [PERSON] [27]. The fourth type of method usually applies to the full open valve or the constant-flow-area orifice. When conducting the modeling for the three-way pressure-reducing valve, [PERSON] [27] considered the flow coefficient as constant for the loading orifice with constant flow area. [PERSON] et al. [28] also set the flow coefficient of the pilot metering orifice in the control valve as constant in their numerical research on a two-stage proportional flow control valve with pilot digital pressure compensator.