Efficient numerical solution of two dimensional compressible fluid flow fields using a cell centered finite volume technique

A vertex based finite volume method for the solution of the three dimensional Reynolds averaged Navier-Stokes equations has been developed. The computations can be carried out blockwise after dividing the computational domain into smaller blocks to reduce the memory requirement for a single processor computer and also to facilitate parallel computing. A five stage Runge-Kutta scheme has been used to advance the solution in time. Enthalpy damping, implicit residual smoothing, local time stepping, and grid sequencing are used for convergence acceleration. In order to get smooth convergence for transonic, viscous flows, the artificial dissipation has been modified by using the time step for advective and diffusive equations. An algebraic turbulence model has been used to determine the turbulent eddy viscosity. The method has been used to compute transonic flow over a cropped delta wing and the ONERA M-6 wing, and subsonic flow over a launch vehicle configuration. The results obtained show good agreement with available experimental data.

As the complexity of spacecraft and space systems increases, there is an ever increasing need for more accurate and robust estimators to track the system. While the demand placed on an individual spacecraft is increasing, the spacecraft itself is being pushed towards smaller, independent pieces of hardware which may have limited power and/or computational abilities. One such initiative is often refereed to as Operational Responsive Space (ORS). The primary goal of ORS systems is acceleration of the mission conception-to-launch timeline of spacecraft by means of utilizing off-the-shelf type modular components for construction of the spacecraft. With such modular systems, customized interfacing and software necessary to direct all data to a central processor may not be possible given the accelerated timeline, the unfortunate result of which would be degradation of the estimates due to missing data. Graduate Student, Department of Mechanical & Aerospace Engineering. E-mail: ckn@buffalo.edu. Student Member AIAA. Professor, Department of Mechanical & Aerospace Engineering. E-mail: johnc@buffalo.edu. Associate Fellow AIAA. Senior Professional Staff I, SEG, Space Department. Email: adam.fosbury@jhuapl.edu. Member AIAA. Assistant Professor, Department of Aerospace Engineering. Email: cheng@ae.msstate.edu, Senior Member AIAA.

Tether dynamics investigations for the Canadian OEDIPUS sounding rocket program

An experimental study of the breakdown of leading-edge vortices on diamond, cropped, delta, and double delta wings during dynamic pitching

Beech 1900D flight test to characterize propeller noise on the fuselage exterior

The finite volume method is used to model radiative heat transfer in three-dimensional irregular geometries. Transparent and participating media are examined. These test cases indicate that the finite volume method is a viable radiation heat transfer solution procedures for three-dimensional enclosures. NOMENCLATURE a coefficient in the discretization equation b source term in the discretization equation Dc direction cosine integrated over An I actual intensity L total number of control angles n outward unit normal of control volume face ./V, Number of control volumes in / direction Ng, Nj Number of control angles in 6 and directions ex, ey, ez unit vectors in x, y and z directions q heat flux q* nondimensional incident intensities, q/0Tg s distance traveled by a beam S source function Sm modified source function T temperature x, y, z coordinate directions /3 extinction coefficient, K+ a f3m modified extinction coefficient M area of control volume faces Av volume of the control volume AH control angle 9 polar angle measured from e2 K absorption coefficient a scattering coefficient or Stefan-Boltzmann constant O scattering phase function azimuthal angle measured from ex f, 77, Y curvilinear coordinates Copyright 1996 by J. C. Chai. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. *Assistant Professor, Department of Mechanical Engineering, P. O. Box 5014, Cookeville, TN 38505, Member AIAA +Aerospace Engineer, Internal Fluid Mechanics Division & Ph.D. Candidate, Department of Mechanical Engineering: Presently: Research Engineer, Honeywell Technology Center, MN. Subscripts b blackbody E, W, N, S, east, west, north, south, rear and front R, F neighbors of P e, w, n, s, east, west, north, south, rear and front control r,f volume faces g gas P control volume P x, y, z coordinate directions £, 77, Y curvilinear coordinates Superscripts I, I' angular directions

Reacting flow calculations are stiff for time-stepping. Recently, Zhong derived three sets of semi-implicit Runge-Kutta(SIRK) methods for split ordinary differential equations in the form of u' = /(«) 4g(u), where the nonstiff term / is treated explicitly while the stiff term g is simultaneously treated implicitly. The purpose of this work is twofold: first, to simulate multidimensional detonation waves using the high-order Rosenbrock semi-implicit Runge-Kutta time-stepping scheme(SIRK-3C); secondly to quantitatively compare the performance of SIRK with the second-order timesplitting schemes in dealing with the hyperbolic conservation laws with stiff relaxation terms. In the simulation of two-dimensional detonations, a full set of elementary hydrogen-oxygen kinetics with nine species are linear-implicitly treated while the explicit discretization of the basic advection equations are achieved by the third-order ENO schemes. Several model problems of hyperbolic systems with stiff relaxation are considered in the comparison of the Time-Splitting and the SIRK-3C scheme. A set of low-storage SIRK(LSSIRK) schemes is derived and tested to be high-order accurate and strongly A-stable. The results show that high-order SIRK time-stepping methods are suitable for stiff reactive flow simulations like the multi-dimensional detonations. INTRODUCTION In the reactive flow field solutions and the combustion related problems, the existence of several nonequilibrium states impose additional difficulties in the solutions of the reactive Euler equations with stiff relaxation terms. Since the smallest time scale is introduced from the chemical reaction kinetics, the second-order time-splitting method of Strang^ allows an independent calculation of the stiff ODE for the source term via implicit methods in one step, and an explicit highorder convective calculation in the following time steps. By the main source of stiffness from the basic hyperbolic conservation laws, it can accomplish a •Graduate Student, Member AIAA 'Assistant Professor, Mechanical and Aerospace Engineering Department, Member AIAA Copyright ©1997 by American Institute of Aeronautics and Astronautics, Inc. AH rights reserved. robust and easy-to-implement computation of reactive flow of current interests. Despite the second-order in time accuracy and the robustness of these methods, there are two main difficulties with the stiffness which have been minimally handled. The spurious solutions are one of the often observed phenomena, which are stable and free of oscillations, and yet may be completely incorrect.'-' Some type of resolution technique is needed to treat this known difficulties.^'!] The degrading of the second-order time accuracy to the first-order is another and quite recent observation when there exist solutions with many small-scaled structures of high-degree of complication. Jin® has modified the Strang splitting into the secondorder time-splitting methods which preserve its highorder accuracy when the considered solutions are complicated. New third-order semi-implicit Rosenbrock type Runge-Kutta scheme, based on the original version of Zhong'---', is computationally efficient with the linearized source term integration, thus requiring no iterations during the implicit treatment of the stiff source term. Third-order ENO schemes discretize the convective fluxes such that both implicit and explicit terms are treated at each of the three Runge-Kutta stages. This high-order Runge-Kutta scheme(SIRK-3C) still possesses the typical under-resolved characteristics of unphysical spurious numerical results of the TimeSplitting method. However the reduction to lower order if the small relaxation time is not temporally wellresolved, is successfully removed. Multi-dimensional Detonations Detonation waves are multi-dimensional and unstable phenomenon in nature as demonstrated by the early experiments of Urtiew and Oppenheinv-'. Existence of the triple points'^, consisting of an incident shock, a reflecting shock and a Mach stem, is the main characteristic of the reacting region behind the propagating shock front, and these detaching triple points from the leading front further contributes to the rolling up of vortices of opposite strength. One distinctive feature of the instability process observed in experiments is the formation of regular cell structures as triple points collide as they come together in the incident shock and move away from each other in the newly formed Mach stem. Figure[13] depicts this process of triple point col-

The supersonic combustion flow field of two hydrocarbon fuels, ethylene and propane, is studied numerically. Both configurations have the feature of the existence of a generic rearward-facing step in the upper longitudinal wall. Sonic pilot ethylene and propane are injected at the step base parallel to the incoming supersonic air. The main ethylene and propane are injected from the upper wall normal to the incoming air with sonic speeds. The wedge, located downstream of the rearward-facing step in the ethylene case study, showed a good potential towards enhancing the fuel-air mixing in addition to helping initiating and stabilizing the main flame. Sweeping the step from both end sides, in the propane case study, enhances the fuel-air mixing in the far field domain. The 3-D version of Fluent CFD code is used in the present study. The results show typical features of such flow field. The current work is a step towards an ongoing research work aiming at examining the combustion characteristics of a variety of hydrocarbon fuels. The motivation for this is to study the feasibility of using both pure hydrocarbon fuels and mixtures of hydrogen and hydrocarbons in engines for Graduate Research Assistant, Department of Mechanical Engineering, Student Member AIAA. Eminent Professor/Scholar, Department of Mechanical Engineering, Associate Fellow AIAA. Associate Professor, Mechanical Engineering Technology Dept., Member ASME. the mid-speed range of the hypersonic flight.

Stabilization of a Mach 5.92 Boundary Layer by Two-Dimensional Finite-Height Roughness

The interaction between the shedding of vortices and square-wave oscillations applied to a circular cylinder is investigated in this paper. Furthermore, the effect on vortex shedding of a sudden transverse movement of a circular cylinder is investigated. The simulations are carried out using a 2D discrete vortex method including viscous diffusion. Three kinds of square waves are studied: square-wave oscillations of the cylinder position, square-wave oscillations of the cylinder-cross velocity and square-wave oscillations of the cylinder-cross acceleration. The near wake structure and force coefficient are presented for different values of amplitude and frequencies of these disturbances. Large amplitudes of rapid movement of a circular cylinder are simulated in order to investigate how the original vortex wake reestablishes itself after a sudden movement has occurred. The work presented here is part of a series of numerical investigations in which the main objective is to study in closer detail the effect of general, and externally applied disturbances on vortex shedding. 'Doctor Assistant Professor, Department of Mechanical Engineering, Member AIAA. PhD Student, Member AIAA. Professor of Experimental Aerodynamics, Department of Aeronautics, Member AIAA. Copyright © 1997 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

The two-dimensional Euler equations have been solved by a finite volume method (FVM). The computational domain is divided into either quadrilateral or triangular cells. Spatial discretization of the Euler equations on each cell yields a system of ordinary differential equations (ODEs) in time. A rational Runge-Kutta (RRK) scheme is used to integrate the system of ODEs. The implicit residual averaging (IRA) and local time step have been employed to accelerate the convergence to a steady state. Numerical solutions are presented for flows past a circular cylinder at Mach 0.38, the NACA 0012 airfoil at Mach 0.8 and an angle of attack of 1.25°, and a channel flow at Mach 0.675. The effects of the shape of control volume and convegence acceleration techniques are investigated by comparing the results with those of the conventional finite difference discretization method (FDM). It is concluded that accuracy and efficiency of the FVM are comparable to those of the FDM.

1 Ph.D. Student, AIAA Student Member, Email: haohe@me1.eng.wayne.edu 2 Senior Research Associate, AIAA Member, zczhang@me1.eng.wayne.edu Associate Professor, AIAA Member, Email: styu@eng.wayne.edu ; http://141.217.13.61/ 4 Senior Scientist, AIAA Member, Email: Sin-Chung.Chang@grc.nasa.gov ABSTRACT In this paper, we report the experience of calculating three-dimensional detonations by the Space-Time Conservation Element and Solution Element (CE/SE) Method using a cost-effective Beowulf cluster. The Time-Surfer, a 16-processor PC cluster, was built and tested as part of this effort. The total cost was about twenty thousand 1999-dollars. The efficiency and accuracy of the CE/SE method on the Beowulf cluster are assessed to determine feasibility of applying the CE/SE method to CFD calculations of using five million mesh nodes and above on this low-cost platform. The numerical solutions of threedimensional detonations propagating in a square tube are calculated. The diagonal instability pattern of three-dimensional detonations is reported.

Using the SIMONA Research Simulator for Human-machine Interaction Research

Hot-wire velocity measurements were made on the lee-side of a 6:1 prolate spheroid, ReL = 4.2xl0, at 10° and 20° angles of attack, and at x/L = 0.600 and 0.772. The dominant feature of each of these flowfields is the presence of a shed vortex due to cross-flow separation. This is a source of considerable noise and vibration. At a = 10° the most turbulent fluid is confined to the near wall region. At a = 20° the most turbulent fluid appears away from the wall at locations where the flow is separating. Velocity spectra for regions with weaker 3-D effects exhibit features that are observed for equilibrium flows. Spectra in strong vortical flow regions show unusual and apparently non-equilibrium behavior. This behavior has some qualitative similarities with surface pressure fluctuation spectra. Nomenclature______________ L Model length, 1.37 m. p Pressure fluctuation at the model surface qe Dynamic pressure at boundary layer edge Graduate Assistant, Student Member AIAA f Jack E. Cowling Professor, Fellow AIAA * Former Graduate Assistant 5 Member AIAA, now at David Taylor Model Basin CD/NSWC, Bethesda, MD 1 Associate Professor, Senior Member AIAA Copyright © 1998 By M. Goody, R. Simpson, M. Engel, C. Chesnakas, and W. Devenport. Published by the American Institute of Aeronautics and Astronautics with permission. ReL TKE Distance from model surface along a line perpendicular to the model axis Reynolds number, U_L / v Turbulent kinetic energy, denned as, TKE = V2p(u+ V*+ w) Friction velocity, (%/p) u, v, w Fluctuating velocity components in the directions of U, V, and W, respectively Velocity component in a plane parallel to the surface, in the axial direction Total velocity at edge of shear layer Wind tunnel free-stream velocity Mean velocity component normal to the local model surface Mean velocity component in a plane parallel to the local model surface and perpendicular to the axial direction (positive in -$ direction) Axial distance from the nose of the model ru/v Angle of attack of model relative to incoming flow Boundary layer thickness Boundary layer streamwise displacement thickness, defined as U

We present a h t e dfference method for solving the equations of combustion in the limit of zero Mach number. In this limit, acoustic waves are weak and do not contribute significantly to the fluid dynamics or energetics. For the equations describing thls limit, we construct an efficient, hlgh-resolution numerical method that allows for large temperature and density variations and correctly accounts for expansion due to heat release. The method, a projection method, is a second order fractional step scheme. In the first step, we compute the solution to advection-reaction-diffusion equations for the velocity, temperature, and species. In the second step, we impose the constraint on the divergence of the velocity field that represents the effect of bulk compression and expansion of the fluid due to heat release. We demonstrate our method on the problem of combustion in an enclosed container. Nomenclature specific heat spatial indces reaction rate time index perturbational pressure heat release coefficient time velocity central difference divergence operator *Graduate student, Dept. of Mechanical Engineering, student member AIAA **Group Leader, Applied Mathematics Group, member AIAA ***Professor, Dept. of Mechanical Engineering, member AIAA Copyright c 1993 by Mindy Lai. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. Go central dfference gradient operator I identity operator L~ dscrete viscous operator M Mach number P pressure Po bulk thermodynamic pressure P projection operator Pr Prandtl number R ideal gas constant Re Reynolds number Sc S c h d t number T temperature Uij = (uij,vij) discrete velocity Z mass fraction a coefficient of species diffusion K coefficient of thermal &ffusion P density Y ratio of specific heats P absolute viscosity 0 spatial domain 0 CFL number Ah standard five point Laplacian Li five pt variable coefficient operator Ax mesh spacing in the x drection A Y mesh spacing m the y direction Introduction In th~s paper we present a numerical method for solving a system of equations describing combustion in the zero Mach n~unber limit. This limiting system was first developed for inviscid flow by Baum and Rehrn[8] and later extended to viscous flow by Majda and Sethian[7]. In this limit, the acoustic waves are fast and weak, and they do not contribute significantly to the fluid dynamics. The starting point for the derivation of the limiting set of equations is the following scaling behavior for -9C