Analysis of wave propagation and pulsation in an elastic tube using a diaphragm pump

Abstract

In this research, the flow wave propagation, speed, and suppression of pulsation through an elastic tube were studied by using a diaphragm pump. The flow fluctuations with shocking pressure fluctuations occur through the elastic tube because the check ball is blocked to prevent reverse flow. Thus, the check ball is one of the causes of pulsating flow in diaphragm pumps, but only a few studies have analyzed the relationship among the check ball movement, pressure, and flow fluctuations. In this study, we constructed several elastic tube experiments: (i) single-tube model; (ii) two-tube model. To predict the flow wave propagation and pulsation through an elastic tube, we developed an axisymmetric theoretical model and compared it with the experimental results. Based on our study, the main results are as follows: The relationship among the check ball movement, pressure, and flow fluctuations shows that the pressure and flow rate pulsation is caused by the asymmetry of the check ball movement. Additionally, we observed that the theoretical flow wave propagation trend had good agreement with the experimental results although the flow wave speed in the urethane-tube experiment differed significantly from the theoretical prediction. Furthermore, the amplitude of the pulsation increased significantly because of the reflected wave at the tube exit, but it did not increase when the resistance was added at the exit. We also observed that the pulsation is reduced more in the silicon tubes compared with urethane tubes because the deformation of the silicon tubes is larger than that of urethane tubes.

Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method

“…The numerical approach known as the method of lines involves solving partial differential equations by discretizing all dimensions except one and then integrating the semi-discrete problem as a system of ordinary differential equations (ODEs) [1][2][3][4][5][6]. An advantage of this method is it allows the solution to take advantage of the sophisticated general-purpose methods and software that have been developed for numerically integrating ODEs.…”

“…The Method of Lines is a semi-discrete computational approach that estimates space derivatives by converting the problem into a system of initial value ordinary differential equations (ODEs). This method involves to solve the ODE system, allowing for efficient and accurate solutions [1][2][3][4][5][6]. To enhance accuracy, highly efficient initial value ODE solvers can be employed, allowing for corresponding orders of accuracy in time integration without the requirement for incredibly short time steps.…”

“…In existing applications, partial differential equations play a crucial role in various fields, with a focus on the sciences and engineering [6][7][8]. Many studies in scientific and engineering domains are modeled using partial differential equations, including studies in thermoelasticity [8,9], fluid flow [10,11], and so on. There is a growing emphasis on the development, analysis, and implementation of numerical methods to solve these problems.…”