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At least 1,117 records · Page 62

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NASA NTRS1989

Numerical simulation of vortex unsteadiness on slender bodies of revolution at large incidence

Time-accurate, fine-grid Navier-Stokes solutions were obtained for flow over a slender ogive-cylinder body of revolution at angles of attack ranging from 10 deg to 40 deg. The results indicate the progressive growth of crossflow separation and the development of the leeward side vortex pattern with increasing incidence. The computed flows show good agreement with experimental measurements. As the angle of attack was increased, the flows become less damped, and at 40 deg a nonsteady flow exhibiting self-sustained fluctuations was observed. The nonsteadiness was linked to the presence of small-scale three-dimensional vortices moving along the primary surfaces of crossflow separation. The behavior of the fluctuations with incidence parallels the trend observed in experiments.

Schiff, Lewis B.↗

NASA NTRS1989

An analysis of finite-difference and finite-volume formulations of conservation laws

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Vinokur, Marcel↗

NASA NTRS1989

Comparison of two- and three-dimensional Navier-Stokes solutions with NASA experimental data for CAST-10 airfoil

The two-dimensional (2-D) and three-dimensional Navier-Stokes equations are solved for flow over a NAE CAST-10 airfoil model. Recently developed finite-volume codes that apply a multistage time stepping scheme in conjunction with steady state acceleration techniques are used to solve the equations. Two-dimensional results are shown for flow conditions uncorrected and corrected for wind tunnel wall interference effects. Predicted surface pressures from 3-D simulations are compared with those from 2-D calculations. The focus of the 3-D computations is the influence of the sidewall boundary layers. Topological features of the 3-D flow fields are indicated. Lift and drag results are compared with experimental measurements.

Swanson, R. Charles↗

NASA NTRS1989

Time-dependent viscous incompressible Navier-Stokes equations - The finite difference Galerkin formulation and streamfunction algorithms

Numerical techniques are developed to solve the Navier-Stokes equations for unsteady incompressible flow. The extension of the finite-difference Galerkin (FDG) method of Stephens et al. (1984) to the continuous-time case in two or three space dimensions is explained, and the numerical implementation of the method is discussed with particular attention to the staggered-MAC-grid primitive-variable discretization, the application of discrete mass balance to avoid problems inherent in FDG schemes, the direct interpretation of the FDG expansion variables as a discrete streamfunction, and a mass-balance approach to two-dimensional problems with throughflow or obstacles. Numerical results are presented graphically for the evolution of asymptotic steady flow in a driven cavity at Reynolds number 400, 1000, or 3200; good agreement with published experimental data is demonstrated, with accurate predictions of secondary-vortex formation from wall bubble recirculations at Reynolds number 1000.

Goodrich, John W.↗

NASA NTRS1989

Coupled fluid-thermal-structural analysis for aerodynamically heated structures

A finite element approach for integrated fluid-thermal-structural analysis of aerodynamically heated structures is described. The approach is used to solve: (1) the Navier-Stokes equations for the aerodynamic flow, (2) the energy equation of the structure for the temperature response, and (3) the quasi-static equilibrium equations of the structure for the structural response. Coupling between the three disciplines is demonstrated using two applications: Mach 7 flow over a panel and Mach 8 shock-shock interference on a cylinder.

Dechaumphai, Pramote↗

NASA NTRS1990

Temporal-adaptive Euler/Navier-Stokes algorithm for unsteady aerodynamic analysis of airfoils using unstructured dynamic meshes

A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.

Kleb, William L.↗

NASA NTRS1989

Multitasking a three-dimensional Navier-Stokes algorithm on the Cray-2

A three-dimensional computational aerodynamics algorithm has been multitasked for efficient parallel execution on the Cray-2. It provides a means for examining the multitasking performance of a complete CFD application code. An embedded zonal multigrid scheme is used to solve the Reynolds-averaged Navier-Stokes equations for an internal flow model problem. The explicit nature of each component of the method allows a spatial partitioning of the computational domain to achieve a well-balanced task load for MIMD computers with vector-processing capability. Experiments have been conducted with both two- and three-dimensional multitasked cases. The best speedup attained by an individual task group was 3.54 on four processors of the Cray-2, while the entire solver yielded a speedup of 2.67 on four processors for the three-dimensional case. The multiprocessing efficiency of various types of computational tasks is examined, performance on two Cray-2s with different memory access speeds is compared, and extrapolation to larger problems is discussed.

Swisshelm, Julie M.↗

NASA NTRS1991

A General-Coordinate Formulation For Boundary-Layer Flow

Formulation for solution of equations of boundary-layer flow in general body-fitted curvilinear coordinates retains velocities in Cartesian coordinates. Increases stability of numerical simulations by avoiding coordinate source terms. In formulation, curvilinear coordinates do not have to be orthogonal, and much of software developed previously for use in numerical simulations of flow based on Navier-Stokes equations used.

Steger, Joseph L.↗

NASA NTRS1990

Temporal-adaptive Euler/Navier-Stokes algorithm for unsteady aerodynamic analysis of airfoils using unstructured dynamic meshes

Kleb, William L.↗

NASA NTRS1991

A numerical investigation of turbulent baseflow

The turbulent base flow of a cone with a sting in hypersonic flow is investigated using a time-dependent Navier-Stokes code called UWIN. A PNS solver provides the upstream flow conditions which drive the development of the base flow. The computational method is described along with its application to the base flow problem. The grid generation and boundary conditions are described. The results and the summary conclude this note.

Chaussee, Denny S.↗

NASA NTRS1991

Navier-Stokes solutions for an oscillating double-delta wing

An upwind-biased implicit scheme is used to investigate steady-state and unsteady Navier-Stokes solutions of the vortical flow over a double-delta wing configuration. The governing equations are solved numerically with a fully upwind, implicit, iterative, and factorized numerical scheme. Steady-state solutions for fixed angles of attack and unsteady solutions for a sinusoidal oscillatory motion are obtained. The steady-state solutions on the baseline grid are in agreement with the experiment, and grid refinements show some improvements of the predictions. The higher-order accuracy of the present scheme yields equivalent solutions on smaller grid densities compared to solutions obtained with a second-order accurate method on larger grids. As the angle of attack increases, the grid resolution requirements for adequate resolution of the leeward-side vortical flowfield become very severe. The unsteady solutions are in general agreement with the measurements and show a qualitative correlation with the experiment.

Ekaterinaris, John A.↗

NASA NTRS1992

Experimental results and numerical modeling of solidification during aircraft high-g arcs

The question of how the Coriolis and gravity gradient forces during high-gravity maneuvers compare to that for common centrifuges is addressed. Microstructural examination of samples solidified during high-gravity arcs reveals no evidence of convection dampening. As a first approximation, the high-gravity arc is modeled as a centrifuge with a radius of 20,480 ft and angular speed of 0.318 rpm. Scaling analysis indicates that the Coriolis and gravity gradient expected on the aircraft high gravity arc are less than that for the centrifuges by a factor of 100. Detailed Navier-Stokes analysis of the fluid flow and thermal fields during solidification of aluminum and Cd-Te during KC-135 high gravity show that convective flows of about 1 mm/s are induced. The thermal field is only slightly modified by the convection. Coriolis and gravity gradient during solidification in KC-135 high-gravity arcs, even at accelerations that have been shown to produce significant convective flow dampening in the centrifuge systems, are found to have no significant influence on the melt thermal and flowfields.

Curreri, P. A.↗

NASA NTRS1987

CFD validation needs for advanced concepts at Northrop Corporation

Information is given in viewgraph form on the Computational Fluid Dynamics (CFD) Workshop held July 14 - 16, 1987. Topics covered include the philosophy of CFD validation, current validation efforts, the wing-body-tail Euler code, F-20 Euler simulated oil flow, and Euler Navier-Stokes code validation for 2D and 3D nozzle afterbody applications.

George, Michael W.↗

NASA NTRS1992

Increased heat transfer to elliptical leading edges due to spanwise variations in the freestream momentum: Numerical and experimental results

A study of the effect of spanwise variation in momentum on leading edge heat transfer is discussed. Numerical and experimental results are presented for both a circular leading edge and a 3:1 elliptical leading edge. Reynolds numbers in the range of 10,000 to 240,000 based on leading edge diameter are investigated. The surface of the body is held at a constant uniform temperature. Numerical and experimental results with and without spanwise variations are presented. Direct comparison of the two-dimensional results, that is, with no spanwise variations, to the analytical results of Frossling is very good. The numerical calculation, which uses the PARC3D code, solves the three-dimensional Navier-Stokes equations, assuming steady laminar flow on the leading edge region. Experimentally, increases in the spanwise-averaged heat transfer coefficient as high as 50 percent above the two-dimensional value were observed. Numerically, the heat transfer coefficient was seen to increase by as much as 25 percent. In general, under the same flow conditions, the circular leading edge produced a higher heat transfer rate than the elliptical leading edge. As a percentage of the respective two-dimensional values, the circular and elliptical leading edges showed similar sensitivity to span wise variations in momentum. By equating the root mean square of the amplitude of the spanwise variation in momentum to the turbulence intensity, a qualitative comparison between the present work and turbulent results was possible. It is shown that increases in leading edge heat transfer due to spanwise variations in freestream momentum are comparable to those due to freestream turbulence.

Rigby, D. L.↗

NASA NTRS1992

Prediction of airfoil stall using Navier-Stokes equations in streamline coordinates

A Navier-Stokes procedure to calculate the flow about an airfoil at incidence was developed. The parabolized equations are solved in the streamline coordinates generated for an arbitrary airfoil shape using conformal mapping. A modified k-epsilon turbulence model is applied in the entire domain, but the eddy viscosity in the laminar region is suppressed artificially to simulate the region correctly. The procedure was applied to airfoils at various angles of attack, and the results are quite satisfactory for both laminar and turbulent flows. It is shown that the present choice of the coordinate system reduces the error due to numerical diffusion, and that the lift is accurately predicted for a wide range of incidence.

Choi, D. H.↗

NASA NTRS1992

Boundary conditions for direct computation of aerodynamic sound generation

A numerical scheme suitable for the computation of both the near field acoustic sources and the far field sound produced by turbulent free shear flows utilizing the Navier-Stokes equations is presented. To produce stable numerical schemes in the presence of shear, damping terms must be added to the boundary conditions. The numerical technique and boundary conditions are found to give stable results for computations of spatially evolving mixing layers.

Colonius, Tim↗

NASA NTRS1992

Numerical simulation of shock-induced combustion/detonation

A numerical study is conducted to simulate the shock-induced combustion in premixed H2-air mixtures. Two types of bodies, blunt (spherical projectile) and sharp (wedge), are considered in the study. A nine-species, 18-step finite-rate H2-air chemical reaction mechanism coupled with the Navier-Stokes equations is solved. The flow field over the blunt body is found to be unsteady, when the projectile velocity is same as the Chapman-Jouget velocity of the mixture. The unsteadiness is caused by the periodic instabilities originating in the stagnation zone. Numerical results show good qualitative agreement with the ballistic range shadowgraph. In addition, the frequency of oscillations, determined by using the Fourier power spectrum, is found to be in good agreement with the experiment. The flow field over the wedge is found to be stable for the conditions considered in this study. The oblique detonation wave structure is investigated and the important flow features are discussed.

Singh, D. J.↗

NASA NTRS1994

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Gunzburger, Max D.↗