Magnetohydrodynamic Simulations of Hypersonic Flow over a Cylinder Using Axial- and Transverse-Oriented Magnetic Dipoles

Numerical simulations of magnetohydrodynamic (MHD) hypersonic flow over a cylinder are presented for axial- and transverse-oriented dipoles with different strengths. ANSYS CFX is used to carry out calculations for steady, laminar flows at a Mach number of 6.1, with a model for electrical conductivity as a function of temperature and pressure. The low magnetic Reynolds number (≪1) calculated based on the velocity and length scales in this problem justifies the quasistatic approximation, which assumes negligible effect of velocity on magnetic fields. Therefore, the governing equations employed in the simulations are the compressible Navier-Stokes and the energy equations with MHD-related source terms such as Lorentz force and Joule dissipation. The results demonstrate the ability of the magnetic field to affect the flowfield around the cylinder, which results in an increase in shock stand-off distance and reduction in overall temperature. Also, it is observed that there is a noticeable decrease in drag with the addition of the magnetic field

Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions

We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. Parallel scaling analysis and grid-independent results including contours and isosurfaces of density and velocity and magnetic field vectors are shown in this study, confirming the ability of these types of solvers to approximate the solutions of hyperbolic equations efficiently and accurately

Evaluation of eddy viscosity-based models in decaying rotating stratified turbulence

The results of large eddy simulation (LES) using three sub-grid scale models, namely: constant coefficient Smagorinsky, dynamic Smagorinsky, and a dynamic Clark model, for rotating stratified turbulence in the absence of forcing using large-scale isotropic initial condition, are reported here. The LES results are compared to in-house direct numerical simulation (DNS) for establishing grid-independence requirements. Three cases with varying ratios of Brunt-Vaisala frequency to the inertial wave frequency, N / f, have been chosen to evaluate the performance of LES models. The Reynolds number and N / f are chosen as (a) Case 1: Re = 3704, N / f = 5, (b) Case 2: Re = 6667, N / f = 40, and, (c) Case 3: Re = 6667, N / f = 138. This framework is used to illustrate the relative magnitudes of the stratification and rotation which is observed in geophysical flows. Various quantities including turbulent kinetic energy (tke), turbulent potential energy (tpe), total dissipation, potential and total energy spectra, and their fluxes, are analyzed to understand the predictive capability of the various LES models. Results show that all the SGS model predictions are very similar, with the classical Smagorinsky model displaying the highest deviation compared to DNS. The effect of an increase in the value of N / f is also seen in the results of LES with an increase in the oscillations observed in the evolution of tke and tpe and a reduction in dissipation. The spectral analysis shows that the dynamic Clark and Smagorinsky models predict the large-scale physics (\kappa < 10), while the small scales (10 < \kappa < 64) energy is under-predicted.Comment: 12 pages, 10 figure

Magnetohydrodynamic Simulations of Hypersonic Flow over a Cylinder Using Axial- and Transverse-Oriented Magnetic Dipoles

Numerical simulations of magnetohydrodynamic (MHD) hypersonic flow over a cylinder are presented for axial- and transverse-oriented dipoles with different strengths. ANSYS CFX is used to carry out calculations for steady, laminar flows at a Mach number of 6.1, with a model for electrical conductivity as a function of temperature and pressure. The low magnetic Reynolds number (≪1) calculated based on the velocity and length scales in this problem justifies the quasistatic approximation, which assumes negligible effect of velocity on magnetic fields. Therefore, the governing equations employed in the simulations are the compressible Navier-Stokes and the energy equations with MHD-related source terms such as Lorentz force and Joule dissipation. The results demonstrate the ability of the magnetic field to affect the flowfield around the cylinder, which results in an increase in shock stand-off distance and reduction in overall temperature. Also, it is observed that there is a noticeable decrease in drag with the addition of the magnetic field

Large eddy simulations of turbulence -chemistry -radiation interactions in diffusion flames

The efficiency and pollutant emission characteristics of practical combustion devices often depend critically on interactions between turbulent flow, finite-rate combustion chemistry, and thermal radiation from combustion products and soot. Due to the complex nonlinear coupling of these phenomena, modeling and/or simulation of practical combustors or even laboratory flames undergoing significant extinction and reignition or strong soot formation remain elusive. Methods based on the determination of the probability density function (PDF) of the joint thermochemical scalar variables are one of the most promising approaches for handling turbulence-chemistry-radiation interactions in flames. PDF methods have gained wide acceptance in the context of Reynolds-Averaged Navier-Stokes (RANS) approaches to predicting mean flowfields as evidenced by their availability in commercial CFD codes such as FLUENT™. Over the past 6 years, the development and application of the filtered mass density function (FMDF) approach in the context of large eddy simulations (LES) of turbulent flames has gained considerable ground. Some of the key issues remaining to be explored regarding the FMDF approach in LES are related to mixing model and chemical mechanism sensitivities of predicted flame statistics, especially for flames undergoing significant extinction and reignition, and application of the approach to more realistic flames, for example, those involving soot formation and luminous thermal radiation. In this study, we explore the issue of mixing model sensitivity, as well as the role of the presumed constant (independent of chemistry and species) mixing frequency, for several laboratory and idealized piloted turbulent diffusion flames at different Reynolds numbers and hence, different levels of local flame extinction/reignition. The laboratory flames are modeled after the Sandia Turbulent Nonpremixed Flames D, E, and F and are predicted using a RANS/PDF transport model in FLUENT. The idealized flames are simulated using an in-house LES/FMDF code modified to allow different mixing models. In addition, we extend the in-house LES/FMDF code to include luminous thermal radiation from a flamelet soot model, and conduct simulations of idealized strongly radiating turbulent flames. A new parallel radiation solver, employing the discrete ordinates method (DOM), is developed and tested as part of this effort. Our findings from both studies confirm that the level of local extinction/reignition predicted in the flame is sensitive to the choice of mixing model and the mixing frequency and suggest the use of a variable mixing frequency could improve the models. Also, our idealized strongly radiating flame studies demonstrate the utility of the LES/FMDF approach for such flames, highlight the importance of turbulence-radiation interactions, and pave the way for the inclusion of finite-rate soot transport and kinetics models and quantitative prediction of laboratory scale sooting flames in the future

Numerical Simulations of Mhd Fluid Flow and Heat Transfer in a Lid-Driven Cavity at High Hartmann Numbers

Numerical calculations of the 2D steady incompressible magnetohydrodynamic (MHD) driven cavity flow and heat transfer are presented. The Navier−Stokes equations in the stream function and vorticity formulation, and the energy equation are solved numerically using a uniform mesh of size 601 × 601. The effect of magnetic field in terms of the Hartmann number (Ha ≤ 1000) are studied for steady incompressible driven cavity flow for various Prandtl numbers (0.001 \u3c Pr \u3c 10). Contours of stream function, vorticity, and temperature, and profiles of centerline velocities and Nusselt number (Nu) at the hot boundary are presented to assess the MHD effects. While the magnetic field makes all flows one-dimensional with stretching observed in the direction of the magnetic field, its effect on heat transfer is more pronounced only with increased Pr

Accurate and Efficient Numerical Simulations of Magnetohydrodynamic (MHD) Mixed Convection at High Hartmann Numbers

Massively parallel numerical calculations of 2-D steady incompressible magnetohydrodynamic (MHD) mixed convection heat transfer at high-Hartmann numbers (Ha) are conducted in a square cavity using a scalable computational implementation developed here. The mixed convection phenomena is a result of the forced convection from an adiabatic and moving top wall, and natural convection from buoyant effects in a domain that has hot and cold walls on each side. The Navier-Stokes equations in the form of a vorticity-streamfunction formulation, and the energy equation, are solved numerically using a uniform mesh of size 1200 × 1200, and simulations are conducted on up to 256 parallel computing cores. The effects of magnetic field in terms of Ha ≤ 1000 are studied for flows at various Richardson numbers (0.1 ≤ Ri ≤ 100). Contours of streamfunction, vorticity and temperature, and profiles of centerline velocities are presented to assess the MHD effects. While the magnetic field makest all flows one-dimensional, with stretching observed in the direction of the magnetic field, its effect on heat transfer is more pronounced only with increased Ri

Towards FFT-based direct numerical simulations of turbulent flows on a GPU

The accurate simulation of turbulence and the implementation of corresponding turbulence models are both critical to the understanding of the complex physics behind turbulent flows in a variety of science and engineering applications. Despite the tremendous increase in the computing power of central processing units (CPUs), direct numerical simulation of highly turbulent flows is still not feasible due to the need for resolving the smallest length scale, and today\u27s CPUs cannot keep pace with demand. The recent development of graphics processing units (GPU) has led to the general improvement in the performance of various algorithms. This study investigates the applicability of GPU technology in the context of fast-Fourier transform (FFT)-based pseudo-spectral methods for DNS of turbulent flows for the Taylor–Green vortex problem. They are implemented on a single GPU and a speedup of unto 31x is obtained in comparison to a single CPU

Leray-α LES of Magnetohydrodynamic Turbulence at Low Magnetic Reynolds Number

A series of large eddy simulations is performed for decaying homogeneous magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number (Rem \u3c\u3c1) with different strengths of magnetic field. The initial isotropic turbulence problem has the Taylor scale Reynolds number (Re λ) of 120. The regularization-based Leray-α model is used for sub-grid scale (SGS) closure for the first time and comparisons are made with our own direct numerical simulation (DNS) calculations conducted as part of this study. Analyses of turbulent kinetic energy decay rates, energy spectra, and vorticity fields are made between the varying magnetic field cases. The SGS model assessments are also made between the Leray-α model and the classic non-dynamic Smagorinsky with several model coefficients. Overall, the Leray-α model was unable to capture the anisotropy associated with MHD flows as well as the non-dynamic Smagorinsky model in this study or even the dynamic Smagorinsky model in previous studies