Simulation of compressibility of entrapped air in an incompressible free surface flow using a pressure‐based method for unified equations

Abstract

Summary A pressure‐based method is developed to solve the unified conservation laws for incompressible and compressible fluids. A polytropic law is used to model the compressibility of a gas and decouple the energy equation. The pressure field is calculated by solving a single‐pressure Poisson equation for the entire flow domain. The effects of the compressibility of the gas are reflected in the source term of the Poisson equation. The continuities of pressure and normal velocity across a material interface are achieved without any additional treatment along the interface. To validate the developed method, the oscillation of a water column in a closed tube due to the compression and expansion of air in the tube is simulated. The computed time history of the pressure at the end wall of the tube is in good agreement with other computational results. The free drop of a water column in a closed tank is simulated. The time history of the pressure at the center of the bottom of the tank shows good agreement with other reported results. The developed code is applied to simulate the air cushion effect of entrapped air in a dam break flow. The computed result is in good agreement with other experimental and computational results until the air is entrapped. As the entrapped air pocket undergoes rapid pulsation, the pressure field of water around the air pocket oscillates synchronously.

A pressure‐based numerical scheme for compressible–incompressible two‐phase flows

“…Figure 7(B) gives the comparison of the time history of pressure at the bottom center with the works of Ma et al, 3 Sun et al, 16 and Shin. 25 The peak pressure occurs at about 0.65 s. Among those works, the present peak value is closest to that of Shin's. Shin 25 uses a similar unified method, in which the pressure equation is omitted rather than the density equation.…”

“…25 The peak pressure occurs at about 0.65 s. Among those works, the present peak value is closest to that of Shin's. Shin 25 uses a similar unified method, in which the pressure equation is omitted rather than the density equation. In addition, the WENO scheme is also adopted to solve the advection terms.…”

“…The same phenomenon has been observed in Shin's work. 25 The compression and expansion of the air pocket verify the scheme's capacity to take the gas's compressibility into consideration.…”

Numerical Analysis of Turbulent Flow around an Irregularly Shaped Airfoil

“…The flow is considered steady with a constant velocity and 2-D space planar. Incompressibility [16] is another of this flow's characteristics. To comprehend the deviation of its characteristics, varying Mach numbers [17] have also been used.…”