Fluid-structure interaction analysis method for pressure compensating emitter

Abstract: Pressure compensating emitter (PCE) can maintain a constant flow rate over a wide range of working pressures, and has extensive application prospect in mountain regions where there are often great changes of hydraulic pressure in conduit pipe. The rapid design method for non-pressure-compensating emitter based on CFD is a quite mature technology at present. However, as there is two-way coupled interaction between fluid flow and elastic diaphragm in the PCE, the common CFD method is not suitable for the flow rate prediction in the design of PCE. In order to improve the design accuracy and efficiency of PCE, the fluid-structure interaction (FSI) analysis method was studied in this paper. In addition, hydraulic performance tests were carried out to verify the FSI analysis results with the test samples by rapid prototyping and manufacturing (RP&M). There are two major difficulties in the FSI analysis of PCE: 1) Distortion of the fluid mesh in a confined space caused by the deformation of diaphragm may lead to termination of the analysis; 2) It is difficult to obtain the convergent result because of the nonlinearity including the material nonlinearity of the rubber diaphragm, the geometric nonlinearity of the diaphragm's large deformation and the state nonlinearity of the contact between diaphragm and emitter's main body. And moreover, the coupled fluid-structure equation is a nonlinear system. Thus an adaptive mesh repair technique was adopted to refine the distorted fluid mesh and incremental method and displacement-pressure finite element formulation was used for the nonlinear analysis of the incompressible material. In this paper, SST K-ω turbulence model was used for the fluid analysis, contact analysis method and Neo-Hookean Mooney-Rivlin rubber material model was adopted for the structure analysis. The working process of PCE can be obtained through the FSI analysis result. The results shows that when the distance between the diaphragm and the outlet of pressure-compensating (PC) chamber is small enough (smaller than 0.03mm in this paper), the flow rate of PCE tends to be stable with increasing the working pressure, which means that the flow rate will be adjusted by a very small deformation of the diaphragm to reach a steady state. The flow rate is so sensitive to the deformation of diaphragm that high calculating accuracy for the displacement of the structure analysis is required and element sizes in the region between diaphragm and outlet of PC chamber must be small enough. The displacement tolerance that controls the convergence of the coupled system is also required to be small enough (the relative residual is smaller than 0.0005 in this paper). So the design accuracy of PCE can be ensured by the high accuracy analysis results and indicates that diaphragm with good quality is necessary in PCE design. At last, compared with the test results, the analyzed flow rates were a little larger with the maximum relative deviation smaller than 2.5%. This research verifies that the FSI analysis method could predict the flow rate of PCE accurately under working pressures and the FSI analysis method can improve the design accuracy and reduce test times for rapid design of PCE.