A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves

This paper is focused on the numerical simulation of the interaction of an ultrasound wave with a bubble. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects. As the volume oscillation of the bubble occurs in a low Mach number regime, a specific care must be paid to the effectiveness of the numerical method which is chosen to solve the compressible Euler equations. Three different numerical solvers, an explicit HLLC (Harten–Lax–van Leer-Contact) solver [48], a preconditioning explicit HLLC solver [14] and the compressible projection method , and , are described and assessed with a one dimensional spherical benchmark. From this preliminary test, we can conclude that the compressible projection method outclasses the other two, whether the spatial accuracy or the time step stability are considered. Multidimensional numerical simulations are next performed. As a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities, a specific velocity/pressure time splitting is proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided, since both the accuracy and the stability of the overall algorithm are enhanced if this new time splitting is used. Finally, the numerical simulation of the interaction of a moving and deformable bubble with a plane wave is presented in order to bring out the ability of the new method in a more complex situation

Preconditioning methods for ideal and multiphase fluid flows

The objective of this study is to develop a preconditioning method for ideal and multiphase multispecies compressible fluid flow solver using homogeneous equilibrium mixture model. The mathematical model for fluid flow going through phase change uses density and temperature in the formulation, where the density represents the multiphase mixture density. The change of phase of the fluid is then explicitly determined using the equation of state of the fluid, which only requires temperature and mixture density. The method developed is based on a finite-volume framework in which the numerical fluxes are computed using Roe’s [1] approximate Riemann solver and the modified Harten, Lax and Van-leer scheme (HLLC) [2]. All speed Roe and HLLC flux based schemes have been developed either by using preconditioning or by directly modifying dissipation to reduce the effect of acoustic speed in its numerical dissipation when Mach number decreases. Preconditioning proposed by Briley, Taylor and Whitfield [3], Eriksson [4] and Turkel [5] are studied in this research, where as low dissipation schemes proposed by Rieper [6] and Thornber, Mosedale, Drikakis, Youngs and Williams [7] are also considered. Various preconditioners are evaluated in terms of development, performance, accuracy and limitations in simulations at various Mach numbers. A generalized preconditioner is derived which possesses well conditioned eigensystem for multiphase multispecies flow simulations. Validation and verification of the solution procedure are carried out on several small model problems with comparison to experimental, theoretical, and other numerical results. Preconditioning methods are evaluated using three basic geometries; 1) bump in a channel 2) flow over a NACA0012 airfoil and 3) flow over a cylinder, which are then compared with theoretical and numerical results. Multiphase capabilities of the solver are evaluated in cryogenic and non-cryogenic conditions. For cryogenic conditions the solver is evaluated by predicting cavitation on two basic geometries for which experimental data are available, that is, flow over simple foil and a quarter caliber hydrofoil in a tunnel using liquid nitrogen as a fluid. For non-cryogenic conditions, water near boiling conditions is used to predict cavitation on two simple geometries, that is, flow over simple foil in a tunnel and flow over a one caliber ogive. Cavitation predictions in both cryogenic and non-cryogenic cases are shows to agree well with available experimental data

All-speed Two-phase Computations for General Equation of State with Preconditioning Techniques and Scaling of Numerical Dissipations

학위논문 (석사)-- 서울대학교 대학원 : 기계항공공학부, 2015. 2. 김종암.The present research focuses on the system preconditioning and the scaling of numerical dissipations of RoeM and AUSMPW+ methods to enable more efficient and accurate computations of all-speed two-phase flows. Previous all-speed two-phase RoeM and AUSMPW+ methods have applied only steady system preconditioning technique while unsteady system preconditioning is essential for the convergence acceleration of unsteady low Mach number flows. In this study, unsteady system preconditioning is achieved by the consideration of Strouhal number in preconditioning parameter. Unlike existing preconditioning techniques, scaling factors in numerical dissipations are treated separately with preconditioning parameter in system so that the numerical instability and the accuracy degradation issues in low Mach number regions are resolved regardless of the convergence. The extension of two-phase RoeM and AUSMPW+ methods to general equation of state (EOS) is completed through the modification of shock discontinuity sensing term (SDST) to be independent on EOS. The performance of the modified SDST is confirmed to be as stable as the previous SDST which works well, but is compatible only with specific forms of EOS.1.Introduction 1 1.1 Computation of All-speed Two-phase Flows 1 1.2 Thesis Objectives 3 2 Governing Equations 5 2.1 Homogeneous Mixture Equations 5 2.1.1 Two-phase Navier-Stokes Equations 5 2.1.2 Determination of Mixture Properties 7 2.2 Preconditioning Techniques 7 3 Numerical Methods 11 3.1 Extension of Two-phase RoeM and AUSMPW+ to General EOS 11 3.1.1 Original Two-phase All-speed RoeM 12 3.1.2 Original Two-phase All-speed AUSMPW+ 13 3.1.3 Generalization of SDST 15 3.2 System Preconditioning for Unsteady Flows 20 3.3 Scaling of Numerical Dissipations 22 3.3.1 Properly Scaled Two-phase All-speed RoeM 26 3.3.2 Properly Scaled Two-phase All-speed AUSMPW+ 28 4 Numerical Results 30 4.1 Single-phase Flow Computation 31 4.1.1 Steady Inviscid Flow over a NACA0012 Airfoil 31 4.1.2 Steady Viscous Flow over a RAE2822 Airfoil 31 4.1.3 Steady Inviscid Flow around a Cylinder 34 4.1.4 Unsteady Inviscid Vortex Propagation 38 4.2 Two-phase Flow Computation 42 4.2.1 Two-phase Shocktube 42 4.2.2 Shock/Water-Column Interaction 45 4.2.3 Cryogenic cavitation 48 5 Conclusions 50Maste

Rescaling of the Roe Scheme in Low Mach-Number Flow Regions II: Artificial Speed of Sound and Low Mach Number Fix

We look at two simple modifications of the Roe scheme in the incompressible limit, based on different ideas: the Rossow's artificial speed of sound and the Rieper's low Mach number fix. Both schemes modify the eigenspaces of the dissipation matrix. The analysis emphasizes the properties of the dissipation matrix for the Von Neumann stability, the asymptotic behaviour and the solution accuracy in the incompressible limit. Numerical results in the very low-speed limit are discussed for robustness, consistency and accuracy issues of the numerical procedure. Possible occurrence of checkerboard pressure modes, when using a collocated arrangement for velocity components and pressure in the finite-volume scheme, and spurious acoustic modes, is also illustrated for both schemes

Computations of Cryogenic Cavitating Flows around Turbopump Inducer

This paper deals with the numerical computations of cryogenic cavitating flows around turbopump inducer in liquid rocket. The baseline numerical fluxes for the computations of all-speed two-phase flows (two-phase RoeM and AUSMPW+ schemes) are extended for treating general equation of states, and improved preconditioning techniques are developed for robust and efficient computations in low-speed region. As a validation step for such progress, cryogenic cavitating flows around hydrofoil and ogive are computed. Finally, numerical simulations of three-dimensional KARI turbopump inducer are carried out under various flow conditions with water and cryogenic fluids, and the difference in inducer flow physics depending on the working fluids are examined.OAIID:oai:osos.snu.ac.kr:snu2014-01/104/0000004648/19SEQ:19PERF_CD:SNU2014-01EVAL_ITEM_CD:104USER_ID:0000004648ADJUST_YN:NEMP_ID:A001138DEPT_CD:446CITE_RATE:0FILENAME:김종암_국제학술대회_20140717_김형준.pdfDEPT_NM:기계항공공학부CONFIRM:

Artificial Compressibility Approaches in Flux Reconstruction for Incompressible Viscous Flow Simulations

Copyright © 2021 The Author(s). Several competing artificial compressibility methods for the incompressible flow equations are examined using the high-order flux reconstruction method. The established artificial compressibility method (ACM) of \citet{Chorin1967} is compared to the alternative entropically damped (EDAC) method of \citet{Clausen2013}, as well as an ACM formulation with hyperbolised diffusion. While the former requires the solution to be converged to a divergence free state at each physical time step through pseudo iterations, the latter can be applied explicitly. We examine the sensitivity of both methods to the parameterisation for a series of test cases over a range of Reynolds numbers. As the compressibility is reduced, EDAC is found to give linear improvements in divergence whereas ACM yields diminishing returns. For the Taylor--Green vortex, EDAC is found to perform well; however on the more challenging circular cylinder at $Re=3900$, EDAC gives rise to early transition of the free shear-layer and over-production of the turbulence kinetic energy. This is attributed to the spatial pressure fluctuations of the method. Similar behaviour is observed for an aerofoil at $Re=60,000$ with an attached transitional boundary layer. It is concluded that hyperbolic diffusion of ACM can be beneficial but at the cost of case setup time, and EDAC can be an efficient method for incompressible flow. However, care must be taken as pressure fluctuations can have a significant impact on physics and the remedy causes the governing equation to become overly stiff.https://arxiv.org/abs/2111.07915v

Numerical Simulation of Shock Wave Propagation in Ducts with Grooves

The pressure attenuation of moving shocks when they propagate in ducts, is of great importance in a wide variety of applications, such as health, safety, and transportation. The objective of this research is to simulate the propagation of shock waves in ducts with roughness. The roughness is added in the form of grooves as in an existing experiment. Different shapes are considered in order to better understand the physics behind the evolution of the complex shock patterns resulting from diffraction, reflection and refraction of the primary moving shock. The contribution of grooves and duct shape on these phenomena and pressure attenuation is investigated. The numerical method is validated through several test cases, and the results are compared against the theory and the experimental measurements. Good agreement between high resolution computations and the experiment is obtained for the shock speeds and complex wave patterns created by the grooves. Time histories of pressure at various locations are also compared. It is found that accurate pressure history agreement requires a close representation of the full experimental setup to fully capture boundary layer development, and pressure losses associated with unsteady moving shocks in long ducts. Different groove geometries have been tested in the numerical computation in order to identify the shape that will diminish shock strength, hence pressure extrema more effectively. Analysis and animations of the computed results are employed to reveal salient features of the unsteady flowfield

Reacting plume inversion on urban geometries through gradient based design methodologies

An increased focus on domestic security in recent years has brought attention to several important application areas where computational fluid dynamics (CFD) has the ability to make a significant impact. In particular, disaster mitigation and post-event forensic activities are of interest. This work investigates a procedure built on gradient based design methods to allow for the solution of the so-called inverse chemistry problem in urban environments. The inverse chemistry problem consists of computing a release location based on the sensing of chemical byproducts of the release and the ability to compute an accurate flow field on the geometry of interest. In this study, Washington DC is simulated under conditions of a hazardous plume. A CFD solver is implemented which allows for the solution of the preconditioned finite-rate Navier-Stokes equations as well as the in situ computation of design gradients