Full-potential integral solution for transonic flows with and without embedded Euler domains
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Kandil, Osama A.↗
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Towards a rational theory for CFD global stability
The fundamental notion of the consistent stability of semidiscrete analogues of evolution PDEs is explored. Lyapunov's direct method is used to develop CFD semidiscrete algorithms which yield the TVD constraint as a special case. A general formula for supplying dissipation parameters for arbitrary multidimensional conservation law systems is proposed. The reliability of the method is demonstrated by the results of two numerical tests for representative Euler shocked flows.
Baker, A. J.↗
Numerical solutions of the linearized Euler equations for unsteady vortical flows around lifting airfoils
A linearized unsteady aerodynamic analysis is presented for unsteady, subsonic vortical flows around lifting airfoils. The analysis fully accounts for the distortion effects of the nonuniform mean flow on the imposed vortical disturbances. A frequency domain numerical scheme which implements this linearized approach is described, and numerical results are presented for a large variety of flow configurations. The results demonstrate the effects of airfoil thickness, angle of attack, camber, and Mach number on the unsteady lift and moment of airfoils subjected to periodic vortical gusts. The results show that mean flow distortion can have a very strong effect on the airfoil unsteady response, and that the effect depends strongly upon the reduced frequency, Mach number, and gust wave numbers.
Scott, James R.↗
Numerical solutions of the linearized Euler equations for unsteady vortical flows around lifting airfoils
A linearized unsteady aerodynamic analysis is presented for unsteady, subsonic vortical flows around lifting airfoils. The analysis fully accounts for the distortion effects of the nonuniform mean flow on the imposed vortical disturbances. A frequency domain numerical scheme which implements this linearized approach is described, and numerical results are presented for a large variety of flow configurations. The results demonstrate the effects of airfoil thickness, angle of attack, camber, and Mach number on the unsteady lift and moment of airfoils subjected to periodic vortical gusts. The results show that mean flow distortion can have a very strong effect on the airfoil unsteady response, and that the effect depends strongly upon the reduced frequency, Mach number, and gust wave numbers.
Scott, James R.↗
Numerical solutions of the linearized Euler equations for unsteady vortical flows around lifting airfoils
A linearized unsteady aerodynamic analysis is presented for unsteady, subsonic vortical flows around lifting airfoils. The analysis fully accounts for the distortion effects of the nonuniform mean flow on the imposed vortical disturbances. A frequency domain numerical scheme which implements this linearized approach is described, and numerical results are presented for a large variety of flow configurations. The results demonstrate the effects of airfoil thickness, angle of attack, camber, and Mach number on the unsteady lift and moment of airfoils subjected to periodic vortical gusts. The results show that mean flow distortion can have a very strong effect on the airfoil unsteady response, and that the effect depends strongly upon the reduced frequency, Mach number, and gust wave numbers.
Scott, James R.↗
An installed nacelle design code using a multiblock Euler solver. Volume 2: User guide
This is a user manual for the general multiblock Euler design (GMBEDS) code. The code is for the design of a nacelle installed on a geometrically complex configuration such as a complete airplane with wing/body/nacelle/pylon. It consists of two major building blocks: a design module developed by LaRC using directive iterative surface curvature (DISC); and a general multiblock Euler (GMBE) flow solver. The flow field surrounding a complex configuration is divided into a number of topologically simple blocks to facilitate surface-fitted grid generation and improve flow solution efficiency. This user guide provides input data formats along with examples of input files and a Unix script for program execution in the UNICOS environment.
Chen, H. C.↗
Computational fluid dynamics application to hypersonic flow over a Martian entry vehicle (MEV) - A correlation with experiment
A class of vehicles for a mission to Mars are analyzed for aerodynamic characteristics using advanced Computational Fluid Dynamics (CFD). The general configuration is a modified cone-conical-frustum geometry where the nose radius has a large influence on the flowfield. Inviscid-compressible flow using the Euler equations and viscous-compressible flow using the thin-layer Navier-Stokes equations is applied to the configuration. The surface modeling, grid generation and application of state-of-the-art CFD software are described. The effects of nose radius, angle of attack, and hypersonic velocity on the flight characteristics of the vehicle are discussed. The numerical simulations demonstrate the merits of the inviscid and viscous software. Results are compared with wind tunnel experiments.
Stewart, John E.↗
Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP
The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time, load balancing, and scalability will be provided.
Vadyak, Joseph↗
Computation of steady and unsteady vortex dominated flows
The unsteady Euler equations have been written in the conservation form for the relative motion in a rotating frame of reference. The resulting equations are solved by using a central-difference finite-volume scheme with four-stage Runge-Kutta time stepping. For steady flow problems, local time stepping is used and for unsteady flow problems, the minimum global time stepping is used. A three-dimensional fully vectorized computer program has been developed and applied to steady and unsteady maneuvering delta wing. The capability of the three-dimensional program has been demonstrated for a rigid sharp-edged delta wing undergoing uniform rolling in a conical flow and rolling oscillations in a locally conical flow.
Kandil, Osama A.↗
Euler solutions for high-speed flow about complex three-dimensional configurations
A numerical algorithm based on a finite-volume explicit scheme with Runge-Kutta time integration of the Euler equations is presented for calculating high-speed three-dimensional flow about complex aerospace configurations. The use of enhancing factors such as artificial dissipative terms, enthalpy damping and local time-stepping are described. An algebraic method for generating quasi-three-dimensional computational grids for realistic aerospace configurations is presented. Computed results for various three-dimensional bodies at different Mach numbers and angles of attack have been obtained using the methods for grid-generation and flow simulation. Comparison of computed and experimental data for an advanced tactical aircraft-like configuration is presented, and a reasonable agreement of the data is noticed.
Moitra, A.↗
Finite element methods for integrated aerodynamic heating analysis
Over the past few years finite element based procedures for the solution of high speed viscous compressible flows were developed. The objective of this research is to build upon the finite element concepts which have already been demonstrated and to develop these ideas to produce a method which is applicable to the solution of large scale practical problems. The problems of interest range from three dimensional full vehicle Euler simulations to local analysis of three-dimensional viscous laminar flow. Transient Euler flow simulations involving moving bodies are also to be included. An important feature of the research is to be the coupling of the flow solution methods with thermal/structural modeling techniques to provide an integrated fluid/thermal/structural modeling capability. The progress made towards achieving these goals during the first twelve month period of the research is presented.
Peraire, J.↗
Flutter analysis of supersonic axial flow cascades using a high resolution Euler solver. Part 1: Formulation and validation
This report presents, in two parts, a dynamic aeroelastic stability (flutter) analysis of a cascade of blades in supersonic axial flow. Each blade of the cascade is modeled as a typical section having pitching and plunging degrees of freedom. Aerodynamic forces are obtained from a time accurate, unsteady, two-dimensional cascade solver based on the Euler equations. The solver uses a time marching flux-difference splitting (FDS) scheme. Flutter stability is analyzed in the frequency domain. The unsteady force coefficients required in the analysis are obtained by harmonically oscillating (HO) the blades for a given flow condition, oscillation frequency, and interblade phase angle. The calculated time history of the forces is then Fourier decomposed to give the required unsteady force coefficients. An influence coefficient (IC) method and a pulse response (PR) method are also implemented to reduce the computational time for the calculation of the unsteady force coefficients for any phase angle and oscillation frequency. Part 1, this report, presents these analysis methods and their validation by comparison with results obtained from linear theory for a selected flat plate cascade geometry. A typical calculation for a rotor airfoil is also included to show the applicability of the present solver for airfoil configurations. The predicted unsteady aerodynamic forces for a selected flat plate cascade geometry and flow conditions correlated well with those obtained from linear theory for different interblade phase angles and oscillation frequencies. All the three methods of predicting unsteady force coefficients, namely, HO, IC, and PR, showed good correlations with each other. It was established that only a single calculation with four blade passages is required to calculate the aerodynamic forces for any phase angle for a cascade consisting of any number of blades, for any value of the oscillation frequency. Flutter results, including mistuning effects, for a cascade of stator airfoils are presented in Part 2 of the report.
Reddy, T. S. R.↗
Transonic and supersonic Euler computations of vortex-dominated flow fields about a generic fighter
Flow fields about a generic flighter model were computed using FL057, a 3-D, finite volume Euler code. Computed pressure coefficients, forces, and moments at several Mach numbers (0.6, 0.8, 1.2, 1.4, and 1.6) are compared with wind tunnel data over a wide range of angles of attack in order to determine the applicability of the code for the analysis of fighter configurations. Two configurations were studied, a wing-body and a wing-body-chine. FL057 predicted pressure distributions, forces, and moments well at low angles of attack, at which the flow was fully attached. The FL057 predictions were also accurate for some test conditions once the leading edge vortex became well established. At the subsonic speeds, FL057 predicted vortex breakdown earlier than that seen in the experimental results. Placing the chine on the forebody delayed the onset of bursting and improved the correlation between numerical and experimental data at the subsonic conditions.
Goodsell, Aga M.↗
Researched applied to transonic compressors in numerical fluid mechanics of inviscid flow and viscous flow
A streamline Euler solver which combines high accuracy and good convergence rates with capabilities for inverse or direct mode solution modes and an analysis technique for finite difference models of hyperbolic partial difference equations were developed.
Thompkins, W. T., Jr.↗
Comparison of Euler and full potential marching techniques for flows over complex configurations
Two recently developed aerodynamic prediction techniques based on the steady full potential equation and the unsteady Euler equations have been applied to a variety of three-dimensional supersonic flow problems exhibiting embedded subsonic regions. Both techniques utilize planar Gauss-Seidel relaxation in the marching direction and approximate factorization in the cross-flow plane. A conservative switching scheme and flux bias technique are employed in the full potential method to transition from the supersonic marching procedure to a subsonic relaxation algorithm and vice versa. A new unified approach with finite volume, high accuracy (up to third order) Total Variation Diminishing formulation (based on Roe's scheme) is used in the Euler solver. In the supersonic regions of the flow an 'infinitely large' time step is employed, and a finite time step is applied in the subsonic regions of the flow to reach the steady-state as a time-asymptote. Numerical solutions are obtained for a number of complex configurations, including: (1) an elliptic waverider, (2) a realistic fighter configuration, (3) the Space Shuttle, and (4) a Shuttle-like configuration. Both the Full Potential and Euler numerical results are in good agreement with available experimental data.
Szema, K. Y.↗
Euler solver for three-dimensional supersonic flows with subsonic pockets
A new finite-difference scheme has been developed to solve efficiently the unsteady Euler equations for three-dimensional inviscid supersonic flows with subsonic pockets. The technique utilizes planar Gauss-Seidel relaxation in the marching direction and approximate factorization n the crossflow plane. An 'infinitely large' time step is used in parts of the flowfield where the component of velocity in the marching direction is supersonic - here the Gauss-Seidel sweeps are restricted to the forward direction only, and the procedure reduces to simple space-marching; a finite time step is used in parts of the flowfield where the marching component of velocity is subsonic - here, backward and forward Gauss-Seidel sweeps are employed to allow for upstream and downstream propagation of signals, and a time-asymptotic steady state is obtained. The discretization formulas are based on finite-volume implementation of high accuracy (up to third-order) total variation diminishing formulations. Numerical solutions are obtained for an analytically defined forebody, a realistic fighter configuration, and the Space Shuttle. The results are in very good agreement with available experimental data and numerical solutions of the full-potential equation.
Chakravarthy, Sukumar R.↗
Euler analysis of the three-dimensional flow field of a high-speed propeller - Boundary condition effects
The results of an investigation of the effects of far field boundary conditions on the solution of the three dimensional Euler equations governing the flow field of a high speed single rotation propeller are presented. The results show that the solutions obtained with the nonreflecting boundary conditions are in good agreement with experimental data. The specification of nonreflecting boundary conditions is effective in reducing the dependence of the solution on the location of the far field boundary. Details of the flow field within the blade passage and the tip vortex are presented. The dependence of the computed power coefficient on the blade passage and the tip vortex are presented. The dependence of the computed power coefficient on the blade setting angle is examined.
Nallasamy, M.↗
A streamwise upwind algorithm for the Euler and Navier-Stokes equations applied to transonic flows
A new algorithm was developed for the Euler and Navier-Stokes equations that uses upwind differencing based on the streawise direction. This algorithm is time accurate and can be used in codes for calculating unsteady transonic flows over wings. Such codes can be used for the flutter analysis of wings. In this algorithm, the coordinate system is locally rotated to align with the streamwise direction. For differencing the convective terms in the streamwise direction, a new form of flux splitting is employed, in which the biasing depends on the local Mach number. In the plane perpendicular to the stream direction, the new flux splitting uses the condition of no flow in that local plane. By using a locally rotated coordinate system, the convective flux vector biasing depends on the total Mach number. Hence, the switching of the flux vector biasing occurs across shock waves and the proper domain of dependence is used in supersonic regions. For comparison, many other upwind methods switch differencing based on Mach number of shock waves in multidimensional flows. The formulas for the convective flux vector differencing do not contain any user specified parameters. So, the amount of numerical dissipation is automatically determined.
Goorjian, Peter M.↗