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At least 109 records · Page 6

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NASA NTRS1983

Numerical analysis of a scramjet inlet flow field using the three-dimensional Navier-Stokes equations

A computer program has been developed to analyze supersonic combustion ramjet (scramjet) inlet flow fields. The program solves the three-dimensional Euler or Navier-Stokes equations in full conservation form by a well-known explicit, predictor-corrector technique. Turbulence is modeled by an algebraic eddy-viscosity model. Detailed laminar and turbulent flow results are presented for a symmetric wedge corner and a comparison is made with the available experimental results to allow assessment of the program. Results are then presented for an actual scramjet inlet configuration.

Kumar, A.↗

NASA NTRS1983

A new consistent spatial differencing scheme for the transonic full-potential equation

A new spatial differencing scheme for the transonic full-potential equation in conservative form has been developed. This scheme guarantees zero truncation error on any curvilinear mesh for freestream flows in either two- or three-space dimensions. Solutions obtained with this new differencing scheme, away from freestream regions, exhibit greatly improved accuracy, especially for nonsmooth or singular meshes.

Flores, J.↗

NASA NTRS1983

Transonic flow simulation of prop-fan configurations

This paper presents the results of a study that used a three-dimensional transonic analysis method to analyze flow around a wing-mounted prop-fan configuration. The transonic analysis method employs a cell-oriented finite volume approach to solve the full potential equation in conservative form over a numerically generated surface-fitted grid. The propeller slipstream effects are simulated using a linearized transpiration boundary condition. The results of analyses of flow over clean wing/body, wing/body/nacelle, and wing/body nacelle with slipstream are compared to test data.

Samant, S. S.↗

NASA NTRS1983

Viscous shock-layer flowfield analysis by an explicit-implicit method

The present work extends the recently reported implicit analogue of MacCormack's earlier widely-used explicit method to external axisymmetric laminar flows with strong entropy gradients. The details of the 'numerics' of the implicit part are provided in a body-oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analogue may appeal to researchers for using it in the analysis of three-dimensional flow problems.

Gupta, R. N.↗

NASA NTRS1983

Three-dimensional transonic nacelle/inlet flowfield computations using an efficient approximate factorization algorithm

A highly efficient computer analysis has been developed for predicting transonic nacelle/inlet flowfields. This algorithm can compute the three-dimensional transonic flowfield about axisymmetric or asymmetric nacelle/inlet configurations at zero or nonzero incidence. The flowfield is determined by solving the full-potential equation in conservative form on a body-fitted curvilinear computational mesh. The difference equations are solved using the AF2 approximate factorization scheme. The effects of boundary layer viscous entrainment are approximated in the inviscid algorithm by applying a surface transpiration velocity which is determined from the calculated boundary layer growth. Computed results and correlations with existing methods and experiment are presented to illustrate application of the analysis.

Vadyak, J.↗

NASA NTRS1982

Assessing the quality of curvilinear coordinate meshes by decomposing the Jacobian matrix

An algebraic decomposition of the Jacobian matrix which relates physical and computational variables is presented. This invertible decomposition parameterizes the mesh by the physically intuitive qualities of cell orientation, cell orthogonality, cell volume, and cell aspect ratio. The decomposition can be used to analyze numerically generated curvilinear coordinate meshes and to assess the contribution of the mesh to the truncation error for any specific differential operator and algorithm. This is worked out in detail for Laplace's equation in nonconservative and conservative forms. The analysis is applied to the solution of the full potential code TAIR, showing grid plots, carpet plots, and truncation error for a NACA 0012 airfoil.

Kerlick, G. D.↗

NASA NTRS1983

Design of shock-free compressor cascades including viscous boundary layer effects

A computer code that generates shock-free transonic compressor cascade shapes while taking into account viscosity effects is developed. The mathematical model for the inviscid flow field is the full potential equation. The Kutta-Joukowski condition is satisfied by varying the free stream angle at downstream infinity. A boundary fitted computational grid of C-type is generated using a sequence of conformal mapping and nonorthogonal coordinate stretching and shearing transformations. The inviscid calculation is performed sequentially on up to four consecutively refined grids thereby accelerating the convergence of the solution process. The full potential equation is solved using a finite area technique and rotated, type-dependent finite differencing. Artificial viscosity of the first order is added in a fully conservative form. Shock-free cascade airfoil shapes are obtained using the fictitious gas concept of Sobieczky and the method of characteristics in the rheograph plane. Viscosity effects are incorporated via a boundary layer displacement thickness. The integral boundary layer code is based on Rotta's turbulence model and assumes transition region of zero length.

Dulikravich, G. S.↗

NASA NTRS1983

A Computer Program for the Calculation of Three-Dimensional Transonic Nacelle/Inlet Flowfields

A highly efficient computer analysis was developed for predicting transonic nacelle/inlet flowfields. This algorithm can compute the three dimensional transonic flowfield about axisymmetric (or asymmetric) nacelle/inlet configurations at zero or nonzero incidence. The flowfield is determined by solving the full-potential equation in conservative form on a body-fitted curvilinear computational mesh. The difference equations are solved using the AF2 approximate factorization scheme. This report presents a discussion of the computational methods used to both generate the body-fitted curvilinear mesh and to obtain the inviscid flow solution. Computed results and correlations with existing methods and experiment are presented. Also presented are discussions on the organization of the grid generation (NGRIDA) computer program and the flow solution (NACELLE) computer program, descriptions of the respective subroutines, definitions of the required input parameters for both algorithms, a brief discussion on interpretation of the output, and sample cases to illustrate application of the analysis.

Vadyak, J.↗

NASA NTRS1981

BGRID: A block-structured grid generation code for wing sections

The operation of the BGRID computer program is described for generating block-structured grids. Examples are provided to illustrate the code input and output. The application of a fully implicit AF (approximation factorization)-based computer code, called TWINGB (Transonic WING), for solving the 3D transonic full potential equation in conservation form on block-structured grids is also discussed.

Chen, H. C.↗

NASA NTRS1983

A direct method for the solution of unsteady two-dimensional incompressible Navier-Stokes equations

The unsteady incompressible Navier-Stokes equations are formulated in terms of vorticity and stream function in generalized curvilinear orthogonal coordinates to facilitiate analysis of flow configurations with general geometries. The numerical method developed solves the conservative form of the transport equation using the alternating-direction implicit method, whereas the stream-function equation is solved by direct block Gaussian elimination. The method is applied to a model problem of flow over a back-step in a doubly infinite channel, using clustered conformal coordinates. One-dimensional stretching functions, dependent on the Reynolds number and the asymptotic behavior of the flow, are used to provide suitable grid distribution in the separation and reattachment regions, as well as in the inflow and outflow regions. The optimum grid distribution selected attempts to honor the multiple length scales of the separated-flow model problem. The asymptotic behavior of the finite-differenced transport equation near infinity is examined and the numerical method is carefully developed so as to lead to spatially second-order accurate wiggle-free solutions, i.e., with minimum dispersive error. Results have been obtained in the entire laminar range for the backstep channel and are in good agreement with the available experimental data for this flow problem.

Ghia, K. N.↗

NASA NTRS1983

A modified Dodge algorithm for the parabolized Navier-Stokes equations and compressible duct flows

A revised version of Dodge's split-velocity method for numerical calculation of compressible duct flow was developed. The revision incorporates balancing of mass flow rates on each marching step in order to maintain front-to-back continuity during the calculation. The (checkerboard) zebra algorithm is applied to solution of the three dimensional continuity equation in conservative form. A second-order A-stable linear multistep method is employed in effecting a marching solution of the parabolized momentum equations. A checkerboard iteration is used to solve the resulting implicit nonlinear systems of finite-difference equations which govern stepwise transition. Qualitative agreement with analytical predictions and experimental results was obtained for some flows with well-known solutions. Previously announced in STAR as N82-16363

Cooke, C. H.↗

NASA NTRS1984

A strongly implicit procedure for the compressible Navier-Stokes equations

The strongly implicit procedure of Stone is used to obtain numerical solutions of the compressible Navier-Stokes equations in conservative form. In contrast to the spatially split Douglas-Gunn type methods, the method is shown to be numerically stable for the three-dimensional wave equation. The method is applied to a variety of external and internal two-dimensional flow problems involving shock wave boundary-layer interaction for both laminar and turbulent flows. The results are in good agreement with other methods and/or experiments. The storage penalty associated with the method is discussed and a simple, yet effective, means of minimizing the problem is presented.

Walters, R. W.↗

NASA NTRS1984

Improved finite difference schemes for transonic potential calculations

Engquist and Osher (1980) have introduced a finite difference scheme for solving the transonic small disturbance equation, taking into account cases in which only compression shocks are admitted. Osher et al. (1983) studied a class of schemes for the full potential equation. It is proved that these schemes satisfy a new discrete 'entropy inequality' which rules out expansion shocks. However, the conducted analysis is restricted to steady two-dimensional flows. The present investigation is concerned with the adoption of a heuristic approach. The full potential equation in conservation form is solved with the aid of a modified artificial density method, based on flux biasing. It is shown that, with the current scheme, expansion shocks are not possible.

Hafez, M.↗

NASA NTRS1984

Numerical solution of a coupled pair of elliptic equations from solid state electronics

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem. Previously announced in STAR as N83-30109

Phillips, T. N.↗

NASA NTRS1984

A combined direct/inverse three-dimensional transonic wing design method for vector computers

A three-dimensional transonic-wing design algorithm for vector computers is developed, and the results of sample computations are presented graphically. The method incorporates the direct/inverse scheme of Carlson (1975), a Cartesian grid system with boundary conditions applied at a mean plane, and a potential-flow solver based on the conservative form of the full potential equation and using the ZEBRA II vectorizable solution algorithm of South et al. (1980). The accuracy and consistency of the method with regard to direct and inverse analysis and trailing-edge closure are verified in the test computations.

Weed, R. A.↗

NASA NTRS1986

Analysis of Scramjet Inlets

NASCRIN analyzes two-dimensional flow fields in supersonic combustion ramjet (scramjet) inlets. Solves two-dimensional Euler or Navier-Strokes equations in conservative form by unsplit, explicit, two-step finitedifference method. More recent explicit/implicit, two-step scheme also incorporated for viscous flow analysis. Algebraic, two-layer eddy-viscosity model used for turbulent flow calculations.

Kumar, A.↗

NASA NTRS1984

Metric-discontinuous zonal grid calculations using the Osher scheme

Computations on zonal grids - in particular, grids with metric discontinuities resulting from the interspersion of highly clustered regions with coarse regions - are possible using a fully conservative form of the Osher upwind scheme. These zonal grids can result from an abrupt clustering of points near solution discontinuities or near other flow features that require improved resolution. The zonal approach is shown to capture shocks with almost 'shock-fitting' quality but with minimal effort. Results for inviscid flow, including quasi-one-dimensional nozzle flow, supersonic flow over a cylinder, and blast-wave diffraction by a ramp, are presented. These calculations demonstrate the powerful capabilities of the Osher scheme used in conjunction with zonal grids in simulating flow fields with complex shock patterns.

Rai, M. M.↗

NASA NTRS1985

Numerical simulation of flow through scramjet inlets using a three-dimensional Navier-Stokes code

A three-dimensional Reynolds-averaged Navier-Stokes code has been used to numerically analyze flow through a two-strut, supersonic combustion ramjet (scramjet) inlet configuration. It solves the governing equations in full conservation form using either the fully explicit or explicit-implicit method due to MacCormack. An algebraic two-layer eddy viscosity model is used for turbulent flow calculations. The analysis allows inclusion of end effects which are caused by the aft placement of the cowl on the underside of the inlet. A special grid has been developed to accommodate the struts embedded in the inlet flow field. Detailed numerical results are presented here for the two-strut configuration, and a comparison is made with the available experimental results.

Kumar, A.↗