Non-linear theory of unstable plane Poiseuille flow.
Limit-cycle oscillations of unstable plane Poiseuille flow analyzed by nonlinear Navier- Stokes equations
Dowell, E. H.↗
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A numerical study of the flow in the vortex angular-rate sensor
Vortex angular rate sensor flow characteristics, solving Navier-Stokes equations by numerical technique
Richards, C. G.↗
Shock-wave-induced turbulent boundary-layer separation at hypersonic speeds
An experiment is described that tests and guides computations of the interaction of a shock wave with a turbulent boundary layer. Numerical solutions of the time-averaged Navier-Stokes equations for the entire flow field employing algebraic eddy viscosity and turbulent Prandtl number models for shear stress and heat flux are presented and used to illustrate the dependence of the computations on the particulars of the turbulence models. To guide modifications in the models, the mean flow profiles and surface measurements of pressure, shear, and heat flux are analyzed critically. The results show that the models of eddy viscosity require substantial modifications in the interaction region. Improved solutions employing the experimentally modified models are presented.
Horstman, C. C.↗
A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations
An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.
Cooke, C. H.↗
Future requirements and roles of computers in aerodynamics
While faster computers will be needed to make solution of the Navier-Stokes equations practical and useful, most all of the other aerodynamic solution techniques can benefit from faster computers. There is a wide variety of computational and measurement techniques, the prospect of more powerful computers permits extension and an enhancement across all aerodynamic methods, including wind-tunnel measurement. It is expected that, as in the past, a blend of methods will be used to predict aircraft aerodynamics in the future. These will include methods based on solution of the Navier-Stokes equations and the potential flow equations as well as those based on empirical and measured results. The primary flows of interest in aircraft aerodynamics are identified, the predictive methods currently in use and/or under development are reviewed and two of these methods are analyzed in terms of the computational resources needed to improve their usefulness and practicality.
Gregory, T. J.↗
A study of a multiple Cray-1 for fluid mechanics simulation
A study of the performance of the CRAY-1 and its architectural extensions was performed on 2-D and 3-D codes for the solution of the Navier-Stokes equations describing aerodynamic fluid flow. A standard 2-D code was benchmarked on the CRAY-1 and a preliminary version of a simulator of the CRAY-1 was programmed.
Calahan, D. A.↗
A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations
An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The continuous cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.
Cooke, C. H.↗
Numerical solution of a three-dimensional shock wave and turbulent boundary-layer interaction
A rapid numerical scheme is used to solve the complete mass-averaged Navier-Stokes equations for supersonic turbulent flow over a three-dimensional compression corner. A simple eddy viscosity model is developed, and the interaction of a swept shock wave and a three-dimensional turbulent boundary layer is studied. Good agreement is obtained between the present results and experimental measurements for the case of a wedge with an angle of 6 deg on a flat-plate sidewall. For the case of a 12-deg wedge angle, the computed results do not show the existence of a peak pressure found experimentally. However, the range of interaction, the plateau pressure, and the peak heat transfer are closely predicted for all cases. The high heat transfer near the axial corner is due to the thinning of the boundary layer and inflow of fresh high-momentum fluid. The heat transfer is relieved through pressure reduction and boundary-layer thickening.
Hung, C. M.↗
Computation of turbulent near wake for asymmetric airfoils
A numerical procedure for studying the turbulent near wake of two dimensional airfoil sections is presented. The Reynolds Navier-Stokes equations were written for flow about bodies of arbitrary geometry and solved on an arbitrary nonuniform curvilinear computational mesh. Eddy viscosity and Reynolds stress turbulence transport models are considered. Specific examples are shown for airfoil section by using an algebraic viscosity model with streamwise relaxation and the interactive Reynolds stress model.
Deiwert, G. S.↗
A split finite element algorithm for the compressible Navier-Stokes equations
An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.
Baker, A. J.↗
Basic lubrication equations
Lubricants, usually Newtonian fluids, are assumed to experience laminar flow. The basic equations used to describe the flow are the Navier-Stokes equation of motion. The study of hydrodynamic lubrication is, from a mathematical standpoint, the application of a reduced form of these Navier-Stokes equations in association with the continuity equation. The Reynolds equation can also be derived from first principles, provided of course that the same basic assumptions are adopted in each case. Both methods are used in deriving the Reynolds equation, and the assumptions inherent in reducing the Navier-Stokes equations are specified. Because the Reynolds equation contains viscosity and density terms and these properties depend on temperature and pressure, it is often necessary to couple the Reynolds with energy equation. The lubricant properties and the energy equation are presented. Film thickness, a parameter of the Reynolds equation, is a function of the elastic behavior of the bearing surface. The governing elasticity equation is therefore presented.
Hamrock, B. J.↗
Bluff-body flameholder wakes - A simple numerical solution
Numerical finite difference predictions are made of recirculation zones behind bluff-body flame stabilizers, showing quantitatively the effects of forebody geometry, blockage ratio, lateral position of the blockage and inlet swirl on the central recirculation zone. A simple transient Navier-Stokes solution algorithm and laminar flow simulation are used with 'free slip' and 'no slip' wall boundary conditions, thus illustrating how a basic approach may be used to solve a sophisticated fluid dynamic problem.
Vatistas, G. H.↗
Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic
A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.
Baker, A. J.↗
User's guide to the NOZL3D and NOZLIC computer programs
Complete FORTRAN listings and running instructions are given for a set of computer programs that perform an implicit numerical solution to the unsteady Navier-Stokes equations to predict the flow characteristics and performance of nonaxisymmetric nozzles. The set includes the NOZL3D program, which performs the flow computations; the NOZLIC program, which sets up the flow field initial conditions for general nozzle configurations, and also generates the computational grid for simple two dimensional and axisymmetric configurations; and the RGRIDD program, which generates the computational grid for complicated three dimensional configurations. The programs are designed specifically for the NASA-Langley CYBER 175 computer, and employ auxiliary disk files for primary data storage. Input instructions and computed results are given for four test cases that include two dimensional, three dimensional, and axisymmetric configurations.
Thomas, P. D.↗
Aspects of a penalty finite element algorithm for the turbulent three-dimensional parabolic Navier-Stokes equations
The formal derivation of the three-dimensional parabolic Navier-Stokes equations for subsonic turbulent flow is reviewed. A penalty finite element algorithm is established for numerical solution of the sixteen dependent variable system. Key numerical results are summarized documenting applications in various problem definitions.
Baker, A. J.↗
Prediction of transonic separated flows
Johnson et al. (1982) have provided a detailed comparison between a thoroughly documented transonic flow with shock-induced separations and solutions of the flow using the Navier-Stokes equations. According to this comparison, there were several deficiencies in the computations. The present investigation takes into account new experimental data which have been obtained in a larger wind tunnel with the same test model for a wider range of freestream Mach numbers. The results of new Navier-Stokes computations using more compatible boundary conditions are shown, and the effects of the turbulence model choice on predicting Mach number trends are assessed.
Horstman, C. C.↗
Computation of flow around a circular cylinder in a supercritical regime
Compressible flows around a circular cylinder in a supercritical regime at Mach number 0.3 have been calculated by using the Beam-Warming-Steger scheme based on the full Navier-Stokes equations with improved accuracy. The flow patterns are visualized extensively to observe the characteristics in this regime. The computations show that the flow at certain Reynolds numbers in a supercritical regime becomes rather steady and irregular with small drag coefficients. This may correspond to the experimental observations that the Strouhal number can not be measured clearly at a certain Reynolds number range in the supercritical regime.
Ishii, K.↗
Reversed flow above a plate with suction
A minor extension is developed for Kovasznay's (1948) solution, and an exact solution is presented for Navier-Stokes equations that may represent the reversed flow about a flat plate with suction. This exact solution is the result of a search for a solution that may serve as an exact basic flow for a model stability analysis of nonparallel flows involving flow reversal.
Lin, S. P.↗