Numerical Simulation Of Compressible Flow Research Articles

1302 格子ボルツマン法を用いたトンネル内における鉄道車両周り流れ解析(GS-5 CFDなど(1))

1302 格子ボルツマン法を用いたトンネル内における鉄道車両周り流れ解析(GS-5 CFDなど(1))

Direct numerical simulation of transitional flow at high Mach number coupled with a thermal wall model

In transitional and turbulent high speed boundary-layer flows the wall thermal boundary conditions play an important role and in many cases an assumption of a constant temperature or a specified heat flux may not be appropriate for numerical simulations. In this paper we extend a formulation for direct numerical simulation of compressible flows to include a thin plate that is thermally fully coupled to the flow. Even without such thermal coupling compressible flows with shock waves and turbulence represent a challenge for numerical methods. In this paper we review the scaling properties of algorithms, based on explicit high-order finite differencing combined with shock capturing, that are suitable for dealing with such flows. An application is then considered in which an isolated roughness element is of sufficient height to trigger transition in the presence of acoustic forcing. With the thermal wall model included it is observed that the plate heats up sufficiently during the simulation for the transition process to be halted and the flow consequently re-laminarises.

Flat-Plate Interaction with the Near Wake of a Square Cylinder

B LUFF bodies are integral components of aircraft, high-speed trains, automobiles, and many forms of industrial equipment. The minimization of mean and fluctuating force levels generated by bluff bodieswhen placed in afluid streamhas the benefits of reducing drag, vibration, and radiated sound. It is therefore very important that a good understanding of the flowfield about bluff bodies be obtained to achieve these aims. This Note explores how lowReynolds number bluff-body wake interference can affect the generation of unsteady flowand force. The case chosen for study is the interaction of a square cylinder and an infinitely thin flat plate. A rigid square cylinder is one of the most basic forms of a bluff body and when placed in a uniform fluid stream has been shown to exhibit strong vortex shedding, resulting in fluctuating forces and the radiation of sound in the form of an aeolian tone. Previous fluid dynamic experimental studies [1,2] exhibit this strong vortex shedding over a wide range of Reynolds number (10–10). Numerical studies investigating the fluid dynamics [3–6] also confirm this behavior. Despite the wealth of experimental data available for circular cylinders, experimental or numerical data for square cylinders are rare. Available studies include the work of Inoue [7], who performs a numerical simulation of compressible flow about a square cylinder at Re 150. Zhou et al. [8] use an upstream plate to suppress fluctuating lift on a square cylinder. They find that there is an optimal position and size for the upstream plate for effective lift suppression. Studies concerning the control of noise from a circular cylinder are more common. Recent numerical studies [9,10] investigate the use of a splitter plate attached to the base of a circular cylinder. These studies show that vortex shedding can disappear once the splitter plate achieves a certain length. Numerical solutions of the compressible unsteady Navier–Stokes equations for tandem square cylinders [11] show that significant force and noise reduction can occur if the cylinders are placed at a critical spacing in a region in which vortex shedding from the upstream cylinder is suppressed. If this separation distance is increased, the force and noise increase rapidly, due to the reestablishment of upstream vortex shedding and the associated vortex impingement on the downstream cylinder. Other work includes the experimental time-resolved force measurements of tandem bluff bodies by Sakamoto et al. [12] and Alam and Zhou [13], which were used to investigate the phase difference between the aerodynamic forces of each body in the vortex-shedding regime (i.e., the interbody spacing was such that vortex shedding was allowed to occur from each body). In each case, the phase varied linearly with separation distance. Further, Alam and Zhou developed a theoretical model based on the convective properties of isolated bluff-body wakes that agrees reasonably with experimental results. This Note will consider the case of an infinitely thin flat plate placed in the near wake of a square cylinder at a Reynolds number of Re 150. To the author’s knowledge, there have been no previous investigations of the interaction of a thin flat plate with the near wake of a square cylinder. The Note is structured as follows. After outlining the numerical approach (Sec. II), a solution of the incompressible Navier–Stokes equations for the single square cylinder case is presented and validated against available experimental and numerical results (Sec. III). A second solution is then presented that includes the downstream plate (Sec. IV), and the flow and force results are analyzed. The Note concludes with a summary of the key results.

Gas flows in microchannels and microtubes

This study analyses compressible gas flows through microchannels or microtubes, and develops two complete sets of asymptotic solutions. It is a natural extension of the previous work by Arkilicet al. on compressible flows through microchannels. First, by comparing the magnitudes of different forces in the compressible gas flow, we obtain proper estimations for the Reynolds and Mach numbers at the outlets. Second, based on these estimations, we obtain asymptotic analytical solutions of velocities, pressure and temperature distributions of compressible gas flow inside the microchannels and microtubes with a relaxation of the isothermal assumption, which was previously used in many studies. Numerical simulations of compressible flows through a microchannel and a microtube are performed by solving the compressible Navier–Stokes equations, with velocity slip and temperature jump wall boundary conditions. The numerical simulation results validate the analytical results from this study.

Compressible Gas Flow Inside a Two Dimensional Uniform Microchannel

DOI: 10.2514/1.29362 This paper analyzes a compressible gas flow through a microchannel, and reports a complete set of first-order analyticalsolutions.ThisworkrepresentsanextensionofthepreviousworkofArkiliconcompressible flowsthrough amicrochannel.First,bycomparingthemagnitudesofdifferentforcesinthecompressiblegas flow,weobtainproper estimations for the Reynolds and Mach numbers at the channel exit. Second, based on these estimations, we obtain asymptotic analytical solutions of velocities, pressure, and temperature distributions of compressible gas flow inside the microchannel with a relaxation of the isothermal assumption, which was previously used by many researchers. Numerical simulations of compressible flows through microchannels with a compressible Navier–Stokes equation solver are performed and combined with velocity slip and temperature jump wall boundary conditions. The numerical simulation results validate the analytical results from this study.

Numerical Simulation of Compressible Flow with Phase Change of Filling Stage in Injection Molding

The filling stage in injection molding has important effects on the final properties and quality of the parts. It is significant to predict the history of flow and heat transfer in the filling stage accurately and thus predict the part properties and quality. The modeling is based on the generalized Hele–Shaw flow of a compressible viscous fluid under non-isothermal conditions with consideration of the effects of compressibility and phase change. A hybrid FEM/FDM method combined with a control volume method was adopted to simulate the filling stage in plastics injection molding. A program was developed and compressible flow analysis of the filling stage was implemented using Visual C++. Comparison of numerical and experimental results verified the numerical algorithm and program of the compressible filling simulation. The numerical analysis also indicated that the compressibility of the material had important effects on flow field of imbalance molds.

On the discontinuous Galerkin method for the simulation of compressible flow with wide range of Mach numbers

The paper is concerned with the numerical simulation of compressible flow with wide range of Mach numbers. We present a new technique which combines the discontinuous Galerkin space discretization, a semi-implicit time discretization and a special treatment of boundary conditions in inviscid convective terms. It is applicable to the solution of steady and unsteady compressible flow with high Mach numbers as well as low Mach number flow at incompressible limit without any modification of the Euler or Navier–Stokes equations.

Statistical description of the free-space propagation of highly aberrated optical beams

The free-space propagation of initially aberrated optical beams is considered with an emphasis on aero-optical applications. An exact statistical solution of the paraxial wave equation is derived that can be used to obtain statistics of the beam such as beam center, spread, and higher-order statistics as algebraic functions of propagation distance, wavelength, and statistics of the initial wavefront. Correlations between the proposed description and intensity-based statistics, such as the Strehl ratio, are investigated. It is found that the root-mean-square (rms) of the gradient of the wavefront plays an important role in causing coherence degradation and that the rms of the wavefront error is not always an appropriate measure of the degradation. To illustrate the use of this statistical tool, index of refraction data from a numerical simulation of compressible flow over a cylinder are employed to perform an aero-optical analysis.

Finite element/volume solution to axisymmetric conservation laws

Conservation laws in axisymmetric geometries are discretized for the first time according to the node-pair framework of Selmin [Comput. Methods Appl. Mech. Eng. 102 (1993) 107–138]. A relation is found linking the node-pair finite element discretization to the finite volume scheme, opening the way to the use of standard finite volume stabilization techniques and high-resolution schemes in the computation of axisymmetric problems. By construction, the treatment of the axis is naturally built-in inside the basic structural elements of the spatial discretization. Numerical results are presented and compared to the exact solution for scalar advection in a source flow, considering both continuous and discontinuous initial profiles. Numerical simulations of compressible flows include the complex dynamical interaction and propagation of waves in a shock-tube experiment and the steady flow at the exit of under-expanded and sonic nozzles. Numerical results are found to agree fairly well with experimental data, demonstrating the validity of the proposed approach.

A stable gradient reconstruction for the MUSCL schemes applied to systems of conservation laws

The numerical simulations of compressible flows need more and more accuracy. Several approaches can be used to increase the order of the scheme. One of the most popular has been introduced by [11]: the so-called MUSCL scheme. In the present work, we focus our attention on the robustness of this method. We propose a relevant CFL restriction and a new gradient reconstruction strategy to enforce stability of the method. The novelty stays in the fact that non conservation argument is involved in the gradient reconstruction. Numerical results are performed using this new variant of the MUSCL scheme.

Compact finite difference schemes on non-uniform meshes. Application to direct numerical simulations of compressible flows

In this paper, the development of a fourth- (respectively third-) order compact scheme for the approximation of first (respectively second) derivatives on non-uniform meshes is studied. A full inclusion of metrics in the coefficients of the compact scheme is proposed, instead of methods using Jacobian transformation. In the second part, an analysis of the numerical scheme is presented. A numerical analysis of truncation errors, a Fourier analysis completed by stability calculations in terms of both semi- and fully discrete eigenvalue problems are presented. In those eigenvalue problems, the pure convection equation for the first derivative, and the pure diffusion equation for the second derivative are considered. The last part of this paper is dedicated to an application of the numerical method to the simulation of a compressible flow requiring variable mesh size: the direct numerical simulation of compressible turbulent channel flow. Present results are compared with both experimental and other numerical (DNS) data in the literature. The effects of compressibility and acoustic waves on the turbulent flow structure are discussed. Copyright © 1999 John Wiley & Sons, Ltd.

Outflow Boundary Conditions for Direct Numerical Simulation of Compressible Flows.

Outflow boundary conditions for direct numerical simulation of compressible flow are proposed. In the newly developed boundary conditions, flow field near the outflow boundary is decomposed into compressible and incompressible parts by Hehnholtz decomposition. Navier Stokes Characteristic Boundary Conditions (NSCBC) are used for compressible part. Convective-viscous boundary conditions with transport equation for pressure (CVBCTP) which produce very accurate results in incompressible flows are applied for incompressible part. Both boundary conditions are superposed to define final one. The new boundary conditions are applied to three test cases which are acoustic wave propagation, a single vortex passing through boundary and a single vortex with acoustic wave propagation. The results show that the present boundary conditions provide a significant improvement over the conventional boundary conditions.

Simulation of steady compressible flows based on Cauchy/Riemann equations and Crocco's relation

SUMMARY In this paper, alternative formulations of the steady Euler equations for conservation of mass, momentum and energy are adopted for the numerical simulation of compressible flows with shock waves. The total enthalpy is assumed to be constant and hence an isentropic density is calculated in terms of the velocity components. Also, the x- and y-momentum equations written in conservation form are combined to yield the tangential and normal momentum equations. For smooth flows the tangential momentum equation reduces to the entropy transport equation, while the normal momentum equation gives the vorticity in terms of the entropy gradient normal to the flow direction (Crocco’s relation). Hence the velocity components can be obtained from the continuity equation and normal momentum equation (Cauchy=Riemann equations), while the entropy correction for the density is obtained from the tangential momentum equation (this correction is not needed in the isentropic flow regions). The present formulation can be easily extended to handle variable total enthalpy. Preliminary results are presented for transonic and supersonic flows over aerofoils and the entropy and vorticity effects are clearly identified. # 1998 John Wiley & Sons, Ltd. Int. J. Numer. Meth. Fluids, 27: 127‐138 (1998)

Numerical simulation of compressible flow induced by a heat and mass source in a partially—open cavity

A numerical analysis is given for the prediction of unsteady, two‐dimensional fluid flow induced by a heat and mass source in an initially closed cavity which is vented when the internal overpressure reaches a certain level. A modified ICE technique is used for solving the Navier–Stokes equations governing a compressible flow at a low Mach number and high temperature. Particular attention is focused on the treatment of the boundary conditions on the vent surface. This has been treated by an original procedure using the resolution of a Riemann problem. The configuration investigated may be viewed as a test problem which allows simulation of the ventilation and cooling of such cavities. The injection of hot gases is found to play a key role on the temperature field in the enclosure, whereas the vent seems to produce a distortion of the dynamic flow‐field only. When the injection of hot gases is stopped, the enclosure heat transfer is strongly influenced by the vent. A comparison with the results obtained when the radiative heat transfer between the walls of the enclosure is considered, indicate that radiation dominates the heat transfer in the enclosure and alters the flow patterns significantly.

Large eddy simulation and direct simulation of compressible turbulence and combusting flows in engines based on the BI-SCALES method

Physical features of turbulence and vortex-flame interaction in engines are investigated by performing large eddy simulation and direct numerical simulation of compressible flows. A BI-SCALES (Boundary-Inner Smoothly Coupled, Alternating multi-Level Equations System) is proposed, which is a mathematical formulation of the system of governing equations suitable for computations of compressible flows. A numerical method based on the proposed formulation is developed. Using the method, the transition to turbulence in the compression process and the cyclic variations are examined. Then, the vortex-flame interaction is studied, mainly on the relation between the flame structure and the Kalvoritz- and turbulent Reynolds number effect. Finally, the large wrinkle simulation (LWS) of engine combusting flow is performed.

Numerical Simulation of Shock Wave Behavior Induced by Arc Discharge.

Shock wave and transient flow induced by thermal release such as combustion, detonation or electric discharge are of special interest in research on combustion phenomena of gas turbines and shock wave propagation in gas laser oscillators. In MHD power generation, excessive Joule heat due to Faraday and Hall current, and abnormal phenomena such as arc discharge disturb supersonic flow in the generator. In this paper, numerical simulation of compressible flow involving thermal release is executed by means of the Euler implicit method, in which Neumann-type artificial viscosity is appended in order to calculate the behavior of physical discontinuities such as shock waves in pressurized gas. In terms of gas pressure and energy density, the Mach number of the shock wave due to arc discharge is investigated here, where the pressurized gas is argon (Ar) at room temperature. Furthermore, the behavior of the thermal wave as the boundary of the high-temperature region, which follows after a shock wave with a velocity much lower than that of the shock wave, is also clarified.