Application of Preconditioning Method to Gas-Liquid Two-Phase Flow Computations
33
Citation
25
Reference
10
Related Paper
Citation Trend
Abstract:
A preconditioned numerical method for gas-liquid two-phase flows is applied to solve cavitating flow. The present method employs a finite-difference method of the dual time-stepping integration procedure and Roe’s flux difference splitting approximation with the MUSCL-TVD scheme. A homogeneous equilibrium cavitation model is used. The present density-based numerical method permits simple treatment of the whole gas-liquid two-phase flow field, including wave propagation, large density changes and incompressible flow characteristics at low Mach number. Two-dimensional internal flows through a backward-facing step duct, convergent-divergent nozzles and decelerating cascades are computed using this method. Comparisons of predicted and experimental results are provided and discussed.Keywords:
Compressible flow
Real gas
Roe solver
Abstract Due to its attractive properties in computing compressible flows, such as sharp capturing of discontinuities, satisfying entropy condition and positivity preservation, the HLLEM approximate Riemann solver has been widely applied for simulations of many compressible flow problems. However, when it comes to weakly compressible or incompressible flows, the HLLEM scheme cannot give physically correct solutions. In the current study, a simple low Mach number fix is applied to improve the accuracy and stability of HLLEM approximate Riemann solver in the low Mach limit. As a result, a modified HLLEM scheme called LM-HLLEM scheme is proposed. Numerical results demonstrate that the proposed LM-HLLEM scheme is able to compute various flow problems accurately and robustly ranging from compressible to low Mach incompressible flows.
Roe solver
Compressible flow
Solver
Euler system
Classification of discontinuities
Cite
Citations (3)
In the present study improvements to numerical algorithms for the solution of the compressible Euler equations at low Mach numbers are investigated. To solve flow problems for a wide range of Mach numbers, from the incompressible limit to supersonic speeds, preconditioning techniques are frequently employed. On the other hand, one can achieve the same aim by using a suitably modified acoustic damping method. The solution algorithm presently under consideration is based on Roe's approximate Riemann solver [Roe PL. Approximate Riemann solvers, parameter vectors and difference schemes. Journal of Computational Physics 1981; 43: 357–372] for non-structured meshes. The numerical flux functions are modified by using Turkel's preconditioning technique proposed by Viozat [Implicit upwind schemes for low Mach number compressible flows. INRIA, Rapport de Recherche No. 3084, January 1997] for compressible Euler equations and by using a modified acoustic damping of the stabilization term proposed in the present study. These methods allow the compressible Euler equations at low-Mach number flows to be solved, and they are consistent in time. The efficiency and accuracy of the proposed modifications have been assessed by comparison with experimental data and other numerical results in the literature. Copyright © 2000 John Wiley & Sons, Ltd.
Compressible flow
Roe solver
Cite
Citations (0)
Numerical simulation of compressible nozzle flows of real gas with or without the addition of heat is presented. A generalized real gas method, using an upwind scheme and curvilinear coordinates, is applied to solve the unsteady compressible Euler equations in axisymmetric form. The present method is an extension of a previous 2D method, which was developed to solve the problem for a gas having the general equation of state in the form p = p(ρ, i). In the present work the method is generalized for an arbitrary P-V-T equation of state introducing an iterative procedure for the determination of the temperature from the specific internal energy and the flow variables. The solution procedure is applied for the study of real gas effects in an axisymmetric nozzle flow.
Compressible flow
Perfect gas
Real gas
Cite
Citations (24)
Conservation of mass
Compressible flow
Cite
Citations (7)
Roe solver
Solver
Perfect gas
Real gas
Cite
Citations (59)
Real gas
Ideal gas
Compressible flow
Solver
Organic Rankine Cycle
Critical point (mathematics)
Cite
Citations (0)
Compressible flow
Roe solver
Cite
Citations (11)
A method for calculating accelerational pressure drop in two-phase compressible gas-liquid flow has been developed. Knowing this pressure drop is important in the design and analysis of high-velocity compressible flow systems such as flare networks where critical two-phase flow may occur. This article sets out a simple relationship between critical mass flux and accelerational pressure drop for single phase and two-phase compressible flow in oil and natural gas pipelines. Based on this relationship and on the Moody model for critical flow, the new method for calculating acceleration pressure drop was developed.
Compressible flow
Flow coefficient
Mass flux
Isothermal flow
Flare
Cite
Citations (8)
A cell-centered spatiotemporal coupled method is developed to solve the compressible Euler equations. The spatial discretization is performed using an improved weighted essentially non-oscillation scheme, where the Harten–Lax–van Leer–contact approximate Riemann solver is used for computing the numerical fluxes. A two-stage fourth-order scheme is adopted to carry out time advancement for unsteady problems. The proposed method is featured by spatiotemporal coupling time-stepping that can be generalized without using the case-dependent generalized Riemann problem solver. A number of one- and two-dimensional test cases are presented to demonstrate the performance of the proposed method for solving the compressible Euler equations on structured grids. The numerical results indicate that the novel method can achieve relatively large Courant–Friedrichs–Lewy (CFL) number compared to other studies that implement the two-stage fourth-order scheme, and that it is more capable of capturing small-scale flow structures than the Runge–Kutta (RK) method.
Compressible flow
Roe solver
Solver
Oscillation (cell signaling)
Cite
Citations (1)
Godunov's scheme
Compressible flow
Component (thermodynamics)
Conservation law
Roe solver
Conservation of mass
Cite
Citations (261)