Numerical Simulation Of Compressible Flow Research Articles

Modelling aerodynamic forces and torques of spheroid particles in compressible flows

In the present study, we conduct numerical simulations of compressible flows around spheroid particles, for the purpose of refining empirical formulas for drag force, lift force, and pitching torque acting on them. Through an analysis of approximately a thousand numerical simulation cases spanning a wide range of Mach numbers, Reynolds numbers and particle aspect ratios, we first identify the crucial parameters that are strongly correlated with the forces and torques via Spearman correlation analysis, based on which the empirical formulas for the drag force, lift force and pitching torque coefficients are refined. The novel formulas developed for compressible flows exhibit consistency with their incompressible counterparts at low Mach number limits and, moreover, yield accurate predictions with average relative errors of less than 5%. This underscores their robustness and reliability in predicting aerodynamic loads on spheroidal particles under various flow conditions.

Lagrangian Voronoï meshes and particle dynamics with shocks

We present a new first order particle method on lagrangian and moving Voronoï meshes for the numerical simulation of compressible flows with shocks and internal interfaces between different gas. The method is based on the closed form formula of the partial derivative of the volume of Voronoï cells with respect to the generators. The mathematical proof of the formula seems original with respect to the literature. A corollary is that the volume of Voronoï cells is generically of class C1 with respect to the generators. The final scheme is conservative in local mass, total momentum and total energy, and it is endowed with an entropy inequality which insures the correctness of shocks calculations. Numerical illustrations in dimension d=2 are displayed for basic problems on coarse meshes. The implementation developed to obtain the numerical illustrations uses a freely available library for the generation of the Voronoï cells at all time steps.

A novel compressible enstrophy transport equation-based analysis of instability during Magnus–Robins effects for high rotation rates

The effects of compressibility on the instability of a two-dimensional flow past a rotating cylinder executing high rotation rates are investigated, in detail, using a novel analysis based on the compressible enstrophy transport equation (CETE). Accurate analysis of the instability necessitates the generation of high fidelity numerical solutions, and this is achieved by employing optimized numerical methods that enable high accuracy direct numerical simulation of compressible flows. To study the effects of compressibility induced by rotation alone, a low free stream Mach number and two high rotation rates are considered, as compared to that reported in the literature. Results demonstrate single-sided vortex shedding, the presence of significant compressibility in the flow field confirmed by local Mach number, and temperature and density gradient fields with transient formation of supersonic pockets noted for the higher rotation speed cases. The temporal instability is studied by analyzing the relative contributions of different terms in the CETE to the growth of enstrophy. As per the authors' knowledge, this is the first such research effort demonstrating an application of the CETE for instabilities. Analysis shows that viscous diffusion is the dominant mechanism in creating the flow instability with a secondary role played by the baroclinic mechanism.

Characteristic Based Volume Penalization Method for Numerical Simulation of Compressible Flows on Unstructured Meshes

Characteristic Based Volume Penalization Method for Numerical Simulation of Compressible Flows on Unstructured Meshes

An efficient targeted ENO scheme with local adaptive dissipation for compressible flow simulation

High fidelity numerical simulation of compressible flow requires the numerical method being used to have both stable shock-capturing capability and high spectral resolution. Recently, a family of Targeted Essentially Non-Oscillatory (TENO) schemes is developed to fulfill such requirements. Although TENO has very low dissipation for smooth flow, it introduces a cutoff value CT to maintain the non-oscillatory shock-capturing property. As CT actually controls the dissipation property of TENO, the choice of CT for better shock-capturing capability also means higher dissipation for small structures. To overcome this, in this paper, a new local adaptive method is proposed for the choice of CT. By introducing a novel adaptive function based on the WENO smoothness indicators, CT is dynamically adjusted from 1.0×10−10 for lower dissipation to 1.0×10−4 for stable capturing of shock according to the smoothness of the reconstruction stencil. The numerical results of the new method are compared with those of the original TENO method and an adaptive TENO method in Fu et al. (2019) [49]. It reveals that the new method is capable of suppressing numerical oscillations near discontinuities while further improving the resolution of TENO at a low extra computational cost.

Optimal explicit Runge-Kutta methods for compressible Navier-Stokes equations

We focus our attention on the numerical simulations of compressible flows obtained by using Finite Difference in time /Finite Element in space approximation. In particular, we determine optimal explicit Runge-Kutta methods capable to maximize the stability features of the resulting numerical scheme. Two different regimes characterized by low and moderate Mach numbers have been taken into account. In the former regime, we have determined an explicit Runge-Kutta method of fourth order that is approximately 15% more efficient than classical ERK(4,4) schemes. For moderate Mach numbers, Ma≈0.4, and transitional Reynolds numbers we have determined ERK schemes that outperform classic ERK(3,3) or ERK(4,4). Optimal ERK have a reduced CFL approximatively four or five times larger than classical ones. These optimized ERK schemes are then promising for the study of transitional flows for global stability or transient growth analyses.

Numerical simulation of compressible flows by lattice Boltzmann method

In this article, we propose a numerical framework based on multiple relaxation time lattice Boltzmann (LB) model and novel discretization techniques for simulating compressible flows. Highly efficient finite difference lattice Boltzmann methods are employed to simulate one- and two-dimensional compressible flows. These numerical techniques are applied on the single- and multiple-relaxation-time on the 16-discrete-velocity (Kataoka and Tsutahara, Phys. Rev. E, 69(5):056702, 2004) compressible lattice Boltzmann model. The Boltzmann equation is discretized via modified Lax-Wendroff and modified total variation diminishing schemes which have ability to damps oscillations at discontinuities, effectively. The results of compressible models are compared and validated with the well-known inviscid compressible flow benchmark test cases, so called Riemann problems. The proposed method shows its superiority over available techniques when compared to the analytical solutions. It is then used to solve two-dimensional inviscid compressible flow benchmarks, including regular shock reflection and Richtmyer–Meshkov instability problems to ensure its applicability for more complex problems. It is found that, the applied discretization techniques improve the stability of original LB models and enhance the robustness of compressible flow problems by preventing the formation of oscillation.

Numerical Investigation of the Hub-Seal Mass Flow Rate Effect on the Axial Turbine Stage Efficiency

The contribution deals with numerical simulation of compressible flow through the axial turbine stage equipped with the hub-seal. The current flowing from the hub-seal has a major impact on the secondary flow in the hub-region of the blade span. The aim of this work is to found a dependency of the efficiency-drop on the hub-seal mass flow rate. Numerical simulation has been made for configuration of experimental axial single-stage reaction turbine.

A pressure-corrected Immersed Boundary Method for the numerical simulation of compressible flows

The development of an improved IBM method is proposed in the present article. This method roots in efficient proposals developed for the simulation of incompressible flows, and it is expanded for compressible configurations. The main feature of this model is the integration of a pressure-based correction of the IBM forcing which is analytically derived from the set of dynamic equations. The resulting IBM method has been integrated in various flow solvers available in the CFD platform OpenFOAM. A rigorous validation has been performed considering different test cases of increasing complexity. The results have been compared with a large number of references available in the literature of experimental and numerical nature. This analysis highlights numerous favorable characteristics of the IBM method, such as precision, flexibility and computational cost efficiency.

3D model of flow in micro channels

The micro channels are important components in many micro - electro - mechanical systems (MEMS) and technical systems. They are used to transport a gas or a liquid into devices and the systems. In our work, the gas flows into a micro channel have been studied for various shapes and sizes of the micro channels. Numerical simulations of compressible flows through a micro channel are performed by solving the Navier–Stokes equations and the quasigasdynamic equations (QGD). The numerical approaches are realized on hybrid parallel computer systems. The software includes the Domain Decomposition technique, the Message Passing Interface (MPI) for organization of interprocess data exchange and an application programming interface Open Multi-Processing (OpenMP). The calculations are performed on the Heterogeneous Computer Systems with Video Processing Units (VPU) and the classical microprocessors - Central Processing Unit (CPU).

Numerical simulations of compressible flows using multi-fluid models

Numerical simulations of two-fluid flow models based on the full Navier–Stokes equations are presented. The models include six and seven partial differential equations, namely, six- and seven-equation models. The seven-equation model consists of a non-conservative equation for volume fraction evolution of one of the fluids and two sets of balance equations. Each set describes the motion of the corresponding fluid, which has its own pressure, velocity, and temperature. The closure is achieved by two stiffened gas equations of state. Instantaneous relaxation towards equilibrium is achieved by velocity and pressure relaxation terms. The six-equation model is deduced from the seven-equation model by assuming an infinite rate of velocity relaxation. In this model, a single velocity is used for both fluids. The numerical solutions are obtained by applying the Strang splitting technique. The numerical solutions are examined in a set of one, two, and three dimensions for both the six- and seven-equation models. The results indicate very good agreement with the experimental results. There is an insignificant difference between the results of the two models, but the six-equation model is much more economical compared to the seven-equation model.

Simulation of Secondary and Separated Flow in Diffusing S Ducts

The focus of this paper is on the numerical simulation of compressible flow in diffusing S-ducts; this flow is characterized by secondary flow as well as regions of boundary-layer separation. The S-duct geometry produces streamline curvature and an adverse pressure gradient resulting in these flow characteristics. Two S-duct geometries are employed in this investigation: one was used in an experimental study conducted at NASA John H. Glenn Research Center at Lewis Field in the early 1990s, and the other is a benchmark configuration proposed by AIAA Propulsion Aerodynamics Workshop to assess the accuracy and best practices of computational fluid dynamics solvers. The computational fluid dynamics flow solver ANSYS-FLUENT is employed in the investigation of compressible turbulent flow through the S duct. A second-order accurate, steady, density-based solver is employed in a finite-volume framework. The three-dimensional Reynolds-averaged Navier–Stokes equations are solved on a structured mesh with a number of turbulence models, namely, the Spalart–Allmaras, , shear stress transport, and transition shear stress transport models, and the results are compared with the available experimental data. The computed results capture the flowfield and pressure recovery with acceptable accuracy when compared to the experimental data. The turbulence model giving the best results is identified.

101 解適合直交格子を用いた衝撃波を伴う流れの数値シミュレーション(GS01 計算力学)

101 解適合直交格子を用いた衝撃波を伴う流れの数値シミュレーション(GS01 計算力学)

An assessment of compact schemes combined with compact filters for a numerical simulation of compressible flow

An assessment of compact schemes combined with compact filters for a numerical simulation of compressible flow

Simulation of secondary and separated flow in a diffusing S-duct using four different turbulence models

The focus of this article is on the numerical simulation of compressible flow in a diffusing S-duct inlet; this flow is characterized by secondary flow as well as regions of boundary layer separation. The S-duct geometry produces streamline curvature and an adverse pressure gradient resulting in these flow characteristics. The geometry used in this investigation is based on a NASA Glenn Research Center experimental diffusing S-duct that was studied in the early 1990s. The computational fluid dynamics flow solver ANSYS - FLUENT is employed in the investigation of compressible flow through the S-duct. A second-order accurate, steady, density-based solver is employed in a finite-volume framework. The three-dimensional Reynolds-Averaged Navier-Stokes equations are solved on a structured mesh with a number of turbulence models, namely the Spalart–Allmaras (SA), k-ɛ, k-ω SST, and Transition SST models, and the results are compared with the experimental data. The computed results capture the flow field and pressure recovery with acceptable accuracy when compared with the experimental data. The turbulence model giving the best results is identified.

A NOVEL LESS DISSIPATION FINITE-DIFFERENCE LATTICE BOLTZMANN SCHEME FOR COMPRESSIBLE FLOWS

In this paper, a new smoothness indicator is proposed to improve the finite-difference lattice Boltzmann method (FDLBM). The necessary and sufficient conditions for convergence are derived. A detailed analysis reveals that the convergence order is higher than that of the previous finite-difference scheme. The coupled double distribution function (DDF) model is used to describe discontinuity flows and verify the improvement. Numerical simulations of compressible flows with shock wave show that the improved finite-difference lattice Boltzmann scheme is accurate and has less dissipation. The numerical results are found to be in good agreement with the analytical results and better than those of the previous scheme.

Staggered schemes for all speed flows

We review in this paper a class of schemes for the numerical simulation of compressible flows. In order to ensure the stability of the discretizations in a wide range of Mach numbers and introduce sufficient decoupling for the numerical resolution, we choose to implement and study pressure correction schemes on staggered meshes. The implicit version of the schemes is also considered for the theoretical study. We give both algorithms for the barotropic Navier-Stokes equations, for the full Navier-Stokes equations and for the Euler equations. In each case, we summarize the theoretical results that were recently obtained concerning the stability and consistency of the schemes and present some numerical results which confirm their good performance.

801 0penFOAMによる圧縮性流れの数値シミュレーション(0s.2 圧縮性流れの基礎と応用1)

801 0penFOAMによる圧縮性流れの数値シミュレーション(0s.2 圧縮性流れの基礎と応用1)

An effective limiting algorithm for particle-based numerical simulations of compressible flows

Eulerian computational fluid dynamics (CFD) and Lagrangian computational structural dynamics (CSD) are used extensively in the aerospace industry. Combined mesh-based Eulerian and particle-based Lagrangian algorithms arevery effective for modelling and simulation due to the increased efficiency of combining the two numerical simulations. However, when compressible flows are simulated using a particle-based algorithm, calculations of strong discontinuity, such as a shock wave, may become unstable. In the present study, a numerical limiter is integrated with a particle-based CFD code to remedy this instability. The limiting algorithm incorporates an ‘averaging’ technique which calculates average values using the properties of neighbouring particles (also known as material points), including mass, momentum and energy. These averaged values are then input to a min-mode limiter to eliminate numerical noise and incur dissipation in the flow in areas with steep property gradients. The results of this algorithm show very stable solutions with minimal oscillations when applied to the one-dimensional shock tube problem and an increased accuracy with reduced oscillations for a two-dimensional cylinder cross-flow problem.

Artificial boundary conditions for the numerical solution of the Euler equations by the discontinuous galerkin method

We present artificial boundary conditions for the numerical simulation of compressible flows using high-order accurate discretizations with the discontinuous Galerkin (DG) finite element method. The construction of the proposed boundary conditions is based on characteristic analysis and applied for boundaries with arbitrary shape and orientation. Numerical experiments demonstrate that the proposed boundary treatment enables to convect out of the computational domain complex flow features with little distortion. In addition, it is shown that small-amplitude acoustic disturbances could be convected out of the computational domain, with no significant deterioration of the overall accuracy of the method. Furthermore, it was found that application of the proposed boundary treatment for viscous flow over a cylinder yields superior performance compared to simple extrapolation methods.