An SPH multi‐fluid model based on quasi buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios

• Published in: International journal for numerical methods in fluids Vol. 87; no. 10; pp. 487 - 507
• Main Authors: Kruisbrink, A.C.H., Pearce, F.R., Yue, T., Morvan, H.P.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.08.2018
• Subjects: Air; Air flow; Approximation; Buoyancy; Case studies; Coefficients; Compressibility; Computational fluid dynamics; Density; Density corrections; Fluid flow; Fluid pressure; Fluids; Gas turbine engines; Gas turbines; Gravitational waves; Gravity; Gravity waves; Heat transfer; Hydrodynamics; Instability; interface treatment; Internal waves; Mathematical models; Modelling; Momentum; Momentum equation; multi‐fluid; Nondestructive testing; Pressure; Pressure gradients; Ratios; Smooth particle hydrodynamics; smoothed particle hydrodynamics; Stability; Stabilization; Taylor instability; Turbine engines; Velocity; Wave propagation
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4498

Summary We introduce a smoothed particle hydrodynamics (SPH) concept for the stabilization of the interface between 2 fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implicit to SPH. To stabilize the interface, a pressure gradient correction is proposed. In this approach, the multi‐fluid pressure gradients are related to the (gravitational and fluid) accelerations. This leads to a quasi‐buoyancy correction for hydrostatic (stratified) flows, which is extended to nonhydrostatic flows. The result is a simple density correction that involves no parameters or coefficients. This correction is included as an extra term in the SPH momentum equation. The new concept for the stabilization of the interface is explored in 5 case studies and compared with other multi‐fluid models. The first case is the stagnant flow in a tank: The interface remains stable up to density ratios of 1:1000 (typical for water and air), in combination with artificial wave speed ratios up to 1:4. The second and third cases are the Rayleigh‐Taylor instability and the rising bubble, where a reasonable agreement between SPH and level‐set models is achieved. The fourth case is an air flow across a water surface up to density ratios of 1:100, artificial wave speed ratios of 1:4, and high air velocities. The fifth case is about the propagation of internal gravity waves up to density ratios of 1:100 and artificial wave speed ratios of 1:4. It is demonstrated that the quasi‐buoyancy model may be used to stabilize the interface between 2 fluids up to high density ratios, with real (low) viscosities and more realistic wave speed ratios than achieved by other weakly compressible SPH multi‐fluid models. Real wave speed ratios can be achieved as long as the fluid velocities are not very high. Although the wave speeds may be artificial in many cases, correct and realistic wave speed ratios are essential in the modelling of heat transfer between 2 fluids (eg, in engineering applications such as gas turbines). With standard SPH the interface between two fluids is unstable, due to the change of pressure gradient, causing an error in the particle approximation. A novel SPH concept, without parameters or coefficients, is presented to stabilize the interface up to high density ratios of 1000 and realistic wave speed ratios. The latter is essential in the modelling of heat transfer. It allows for more robust modeling of liquid‐gas flows in a wide variety of applications, including free surface flows.