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At least 919 records · Page 51
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Computation and Validation of Fluid/Structure Twin Tail Buffet Response

The buffet response of the flexible twin-tail/delta wing configuration, a multidisciplinary problem, is solved using three sets of equations on a multi-block grid structure. The first set is the unsteady, compressible, full Navier-Stokes equations which are used for obtaining the flow-field vector and the aerodynamic loads on the twin tails. The second set is the coupled aeroelastic equations which are used for obtaining the bending and torsional deflections of the twin tails. The third set is the grid-displacement equations which are used for updating the grid coordinates due to the tail deflections. The computational model is similar to the one used by Washburn et. al. which consists of a delta wing of aspect ratio one and twin tails with taper ratios of 0.23. The vortex of the twin tails are located at the wing trailing edge. The configuration is pitched at 30 deg angle of attack, and the freestream Mach number and Reynolds number are 0.3 and 1.25 million, respectively. With the twin tails fixed as rigid surfaces, the problem is solved for the initial flow conditions. Next, the problem is solved for the twin tail response for uncoupled bending and torsional vibrations due to the unsteady loads produced by the vortex breakdown flow of the leading-edge vortex cores. The configuration is investigated for three spanwise positions of the twin tails; inboard, midspan and outboard locations. The computational results are validated and are in very good agreement with the experimental data of Washburn, et. al.

Massey, Steven J.↗
NASA NTRS1999

Effect of Dynamic Rolling Oscillations on Twin Tail Buffet Response

The effect of dynamic rolling oscillations of delta-wing/twin-tail configuration on twin-tail buffet response is investigated. The computational model consists of a sharp-edged delta wing of aspect ratio one and swept-back flexible twin tail with taper ratio of 0.23. The configuration model is statically pitched at 30 deg. angle of attack and then forced to oscillate in roll around the symmetry axis at a constant amplitude of 4 deg. and reduced frequency of pi and 2(pi). The freestream Mach number and Reynolds number are 0.3 and 1.25 million, respectively. This multidisciplinary problem is solved using three sets of equations on a dynamic multi-block grid structure. The first set is the unsteady, full Navier-Stokes equations, the second set is the aeroelastic equations for coupled bending and torsion vibrations of the tails, and the third set is the grid-displacement equations. The configuration is investigated for inboard position of the twin tails which corresponds to a separation distance between the twin tails of 33% wing span. The computed results are compared with the results of stationary configuration, which previously have been validated using experimental data. The results conclusively showed that the rolling oscillations of the configuration have led to higher loads, higher deflections, and higher excitation peaks than those of the stationary configuration. Moreover, increasing the reduced frequency has led to higher loads and excitation peaks and lower bending and torsion deflections and acceleration.

Sheta, Essam F.↗
NASA NTRS1978

Large eddy simulation of incompressible turbulent channel flow

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

Moin, P.↗
NASA NTRS1989

Oscillatory flow with heat transfer in a square cavity

A computational study is presented for the flow inside an oscillatory cavity. The numerical scheme employs a semi-implicit, time-splitting method to integrate the two-dimensional full Navier-Stokes equations satisfying continuity to machine accuracy. The efficient use of direct solvers for the uncoupled momentum and pressure equations is demonstrated. The oscillatory cavity flow is studied considering the effects of heat transfer, Reynolds number, and oscillatory Stokes number.

Biringen, S.↗
NASA NTRS1990

Oscillatory flow with heat transfer in a square cavity

A computational study is presented for the flow inside an oscillatory cavity. The numerical scheme employs a semiimplicit, time-splitting method to integrate the two-dimensional full Navier-Stokes equations satisfying continuity to machine accuracy. The efficient use of direct solvers for the uncoupled momentum and pressure equations is demonstrated. The oscillatory cavity flow is studied considering the effects of heat transfer, Reynolds number and oscillatory Stokes number.

Danabasoglu, G.↗
NASA NTRS1995

Experiments with explicit filtering for LES using a finite-difference method

The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture most of the energy-containing eddies, and if explicit filtering is used, the mesh must be enlarged so that these motions are passed by the filter. Given the high cost of explicit filtering, the following interesting question arises. Since the mesh must be expanded in order to perform the explicit filter, might it be better to take advantage of the increased resolution and simply perform an unfiltered simulation on the larger mesh? The cost of the two approaches is roughly the same, but the philosophy is rather different. In the filtered simulation, resolution is sacrificed in order to minimize the various forms of numerical error. In the unfiltered simulation, the errors are left intact, but they are concentrated at very small scales that could be dynamically unimportant from a LES perspective. Very little is known about this tradeoff and the objective of this work is to study this relationship in high Reynolds number channel flow simulations using a second-order finite-difference method.

Lund, T. S.↗
NASA NTRS1997

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Swanson, R. C.↗
NASA NTRS1983

Numerical study of the effect of an embedded surface-heat source on the separation bubble of supersonic flow

A numerical study of the conjugated problem of a separated supersonic flow field and a conductive solid wall with an embedded heat source is presented. Implicit finite-difference schemes were used to solve the two-dimensional time-dependent compressible Navier-Stokes equations and the time-dependent heat-conduction equation for the solid in both general coordinate systems. A detailed comparison between the thin-layer and Navier-Stokes models was made for steady and unsteady supersonic flow and showed insignificant differences. Steady-state and transient cases were computed and the results show that a temperature pulse at the solid-fluid interface can be used to detect the flow direction near the wall in the vicinity of separation without significant distortion of the flow field.

Degani, D.↗
NASA NTRS1985

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Engquist, B. E.↗
NASA NTRS1987

Applications of classical and zero-total-pressure-loss sets of Euler equations to delta wings

Classical and zero-total pressure-loss sets of Euler equations were applied to sharp- and round-edge delta wings. The origin of the total pressure was explained in the classical set. For sharp-edged delta wings, all sets of Euler equations produce the same separated flow solutions. For round-edged delta wings and for coarse grids, the solution depends on the level of dissipation, the accuracy of the surface boundary condition, and the type of Euler equations set. For round-edged delta wings and for fine grids, attached flow solutions are obtained. Also presented were three dimensional flow solutions and asymmetric flow solutions including unsteady flow for sharp-edged delta wings. Euler equations should be restricted to sharp-edged wings for real flow solutions. For roung-edged wings, Navier-Stokes equations must be used.

Kandil, Osama A.↗
NASA NTRS1987

Boundary-layer equations in generalized curvilinear coordinates

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

Panaras, Argyris G.↗
NASA NTRS1990

Aeroelastic analysis of wings using the Euler equations with a deforming mesh

Modifications to the CFL3D three dimensional unsteady Euler/Navier-Stokes code for the aeroelastic analysis of wings are described. The modifications involve including a deforming mesh capability which can move the mesh to continuously conform to the instantaneous shape of the aeroelastically deforming wing, and including the structural equations of motion for their simultaneous time-integration with the governing flow equations. Calculations were performed using the Euler equations to verify the modifications to the code and as a first step toward aeroelastic analysis using the Navier-Stokes equations. Results are presented for the NACA 0012 airfoil and a 45 deg sweptback wing to demonstrate applications of CFL3D for generalized force computations and aeroelastic analysis. Comparisons are made with published Euler results for the NACA 0012 airfoil and with experimental flutter data for the 45 deg sweptback wing to assess the accuracy of the present capability. These comparisons show good agreement and, thus, the CFL3D code may be used with confidence for aeroelastic analysis of wings.

Robinson, Brian A.↗
NASA NTRS1989

An embedded grid formulation applied to delta wings

An embedded grid algorithm for the Euler and/or Navier-Stokes equations is developed and applied to delta wings at high angles of attack in low speed flow. The Navier-Stokes code is an implicit, finite volume algorithm, using flux difference splitting for the convective and pressure terms and central differencing for the viscous and heat transfer terms. Calculations are compared with detailed experimental results over an angle of attack range up to and beyond the maximum lift coefficient, corresponding to vortex breakdown at the trailing edge, for a delta wing nominally of unit aspect ratio. The results indicate that the overall flowfield, including surface pressures, surface streamlines, and vortex trajectories, can be simulated accurately with the global grid version of the present algorithm. However, comparison of computed velocities and vorticity with experimentally measured off-body values at an angle of attack of 20.5 deg indicates the core region is substantially more diffuse in the computations than that measured with either a five-hole probe or a laser velocimeter. Embedded grids, used to improve the numerical discretization in the core region, are formulated within the framework of the implicit, upwind-biased multi-grid algorithm. Structured levels of local nested refinements are made. Three-dimensional results for both Euler and Navier-Stokes calculations are shown, with up to 3 levels of embedded refinement. The embedding procedure was effective in eliminating a crossflow secondary separation produced in the Euler solutions on coarse grids.

Thomas, James L.↗
NASA NTRS1994

A modified restricted Euler equation for turbulent flows with mean velocity gradients

The restricted Euler equation captures many important features of the behavior of the velocity gradient tensor observed in direct numerical simulations (DNS) of isotropic turbulence. However, in slightly more complex flows the agreement is not good, especially in regions of low dissipation. In this paper, it is demonstrated that the Reynolds-averaged restricted Euler equation violates the balance of mean momentum for virtually all homogeneous turbulent flows with only two major exceptions: isotropic and homogeneously-sheared turbulence. A new model equation which overcomes this shortcoming and is more widely applicable is suggested. This modele is derived from the Navier-Stokes equation with a restricted Euler type approximation made on the fluctuating velocity gradient field. Analytical solutions of the proposed modified restricted Euler equation appear to be difficult to obtain. Hence, a strategy for numerically calculating the velocity gradient tensor is developed. Preliminary calculations tend to indicate that the modified restricted Euler equation captures many important aspects of the behavior of the fluctuating velocity gradients in anisotropic homogeneous turbulence.

Girimaji, Sharath S.↗
NASA NTRS1997

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Wood, William A.↗
NASA NTRS1995

A Hybrid Parallel Preconditioning Algorithm For CFD

A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.

Barth,Timothy J.↗
NASA NTRS2006

An Accuracy Evaluation of Unstructured Node-Centred Finite Volume Methods

Node-centred edge-based finite volume approximations are very common in computational fluid dynamics since they are assumed to run on structured, unstructured and even on mixed grids. We analyse the accuracy properties of both first and second derivative approximations and conclude that these schemes can not be used on arbitrary grids as is often assumed. For the Euler equations first-order accuracy can be obtained if care is taken when constructing the grid. For the Navier-Stokes equations, the grid restrictions are so severe that these finite volume schemes have little advantage over structured finite difference schemes. Our theoretical results are verified through extensive computations.

Svard, Magnus↗