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At least 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Spectral element methods for the incompressible Navier-Stokes equations

Spectral element methods are high-order weighted-residual techniques for partial differential equations that combine the geometric flexibility of finite element techniques with the rapid convergence rate of spectral schemes. The theoretical foundations and numerical implementation of spectral element methods for the incompressible Navier-Stokes equations are presented, considering the construction and analysis of optimal-order spectral element discretizations for elliptic and saddle (Stokes) problems, as well as the efficient solution of the resulting discrete equations by rapidly convergent tensor-product-based iterative procedures. Several examples of spectral element simulation of moderate Reynolds number unsteady flow in complex geometry are presented.

Maday, Yvon↗
NASA NTRS1991

Navier-Stokes Computations On Zonal Grids

Report describes numerical simulations of transonic flow of air about isolated wing and about wing and fuselage (not tail assembly) of F-16A aircraft. Fast, diagonalized Beam-Warming numerical-integration algorithm for solution of Euler and Navier-Stokes equations applied via Transonic Navier-Stokes computer program, using computational grids divided into zones of coarse and finer meshes.

Flores, Jolen↗
NASA NTRS1990

Indicial response approach derived from Navier-Stokes equations. Part 1: Time-invariant equilibrium state

The indicial response approach is recast in a form appropriate to the study of vortex induced oscillations phenomena. An appropriate form is demonstrated for the indicial response of the velocity field which may be derived directly from the Navier-Stokes equations. On the basis of the Navier-Stokes equations, it is demonstrated how a form of the velocity response to an arbitrary motion may be determined. To establish its connection with the previous work, the new approach is applied first to the simple situation wherein the indicial response has a time invariant equilibrium state. Results for the aerodynamic response to an arbitrary motion are shown to confirm to the form obtained previously.

Truong, K. V.↗
NASA NTRS1990

Flowfield of a lifting hovering rotor: A Navier-Stokes simulation

The viscous, three-dimensional flowfield of a lifting helicopter rotor in hover is calculated by using an upwind, implicit, finite-difference numerical method for solving the thin layer Navier-Stokes equations. The induced effects of the wake, including the interaction of tip vortices with successive blades, are calculated as a part of the overall flowfield solution without using any ad hoc wake models. Comparison of the numerical results for the subsonic and transonic conditions show good agreement with the experimental data and with the previously published Navier-Stokes calculations using a simple wake model. Some comparisons with Euler calculations are also presented, along with some discussions of the grid refinement studies.

Srinivasan, G. R.↗
NASA NTRS1991

A multiple-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations

A multiple block multigrid method for the solution of the three dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell vertex method which employs central difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques and variable coefficient numerical dissipation results in an efficient and robust scheme is discussed. The multiblock strategy places the block loop within the Runge-Kutta Loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one and two block calculations in which the two block grid is generated by splitting the one block grid. Results are presented for both Euler and Navier-Stokes computations of wing/fuselage combinations.

Atkins, Harold↗
NASA NTRS1991

A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems

An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction.

Thompson, C. P.↗
NASA NTRS1990

Application of a new Navier-Stokes inverse method to the design of advanced airfoils

A new inverse airfoil design method has been developed. This method couples a two-dimensional Navier-Stokes code to a residual-correction design algorithm to produce an efficient design code. Since this method can be used to design airfoils near the limits of performance capabilities, a technique to investigate the limits of lift has been developed to guide the design of new airfoils. Examples of the use of the inverse Navier-Stokes code and the maximum lift technology in the design of new airfoils are presented.

Narramore, J. C.↗
NASA NTRS1991

A multi-block multigrid method for the solution of the Euler and Navier-Stokes equations for three-dimensional flows

A multi-block multigrid method for the solution of the three-dimensional Euler and Navier-Stokes equations is presented. The basic flow solver is a cell-vertex method which employs central-difference spatial approximations and Runge-Kutta time stepping. The use of local time stepping, implicit residual smoothing, multigrid techniques, and variable-coefficient numerical smoothing results in an efficient and robust scheme. The multi-block strategy places the block loop within the Runge-Kutta loop such that accuracy and convergence are not affected by block boundaries. This has been verified by comparing the results of one- and two-block calculations in which the two-block grid is generated by splitting the one-block grid. Results are presented for both Euler and Navier-Stokes computations of wings and wing-fuselage combinations.

Atkins, H. L.↗
NASA NTRS1991

Thin-layer and full Navier-Stokes, locally-conical and three-dimensional asymmetric solutions

The unsteady, compressible thin-layer and full Navier-Stokes equations are used to numerically simulate steady and unsteady asymmetric, supersonic, locally-conical flows around a 5-deg-semiapex angle circular cone. The main computational scheme used for the present computations is the implicit, upwind, flux-difference splitting, finite-volume scheme. Comparisons of the solutions using the two sets of equations are presented for the flow asymmetry and its control. Computational studies are also presented to investigate the effects of the freestream Reynolds number and the locally-scaled Reynolds number on the flow asymmetry. These studies are carried out using the full Navier-Stokes equations. Three-dimensional, asymmetric flow solutions are also presented for a 5-deg-semiapex angle cone of unit length and a cone-cylinder configuration. The three-dimensional solutions are obtained by using the thin-layer equations and short-duration transient side-slip disturbances along with a very fine grid.

Kandil, O. A.↗
NASA NTRS1990

Computation and control of asymmetric vortex flow around circular cones using Navier-Stokes equations

The unsteady, compressible, thin-layer and full Navier-Stokes equations are used to numerically simulate steady and unsteady asymmetric, supersonic, locally conical flows around a 5-deg semiapex angle circular cone. The main computational scheme is the implicit, upwind, flux-difference splitting, finite-volume scheme. Comparison of asymmetric flow solutions using the thin-layer and full Navier-Stokes equations is presented and discussed. The implicit, upwind, flux-vector splitting, finite-volume scheme has also been used to solve for the unsteady asymmetric flow with vortex shedding. The unsteady-flow solution using the flux-vector splitting scheme perfectly agrees with the previously obtained solution using the flux-difference splitting scheme. Passive control of asymmetric flows has been demonstrated and studied using sharp- and round-edged, thick and thin strakes.

Kandil, Osama A.↗
NASA NTRS1991

High-order ENO methods for the unsteady compressible Navier-Stokes equations

The adaptive stencil concepts of ENO (Essentially Non-Oscillatory) methods are applied to the laminar Navier-Stokes equations to yield a high-order, time-accurate algorithm with a shock-capturing capability. The method targets problems in the areas of nonlinear acoustics, compressible transition, and turbulence which, due to the presence of shocks or complex geometries, are not easily solved by spectral methods. The present approach has been implemented and tested for the full three-dimensional Navier-Stokes equations in a transformed curvilinear coordinate system. Validation results are presented for a variety of problems which verify the method's accuracy properties and shock capturing capabilities, as well as demonstrate its use as a direct simulation tool.

Atkins, H. L.↗
NASA NTRS1991

Navier-Stokes analysis of a liquid rocket engine disk cavity

This paper presents a Navier-Stokes analysis of hydrodynamic phenomena occurring in the aft disk cavity of a liquid rocket engine turbine. The cavity analyzed in the Space Shuttle Main Engine Alternate Turbopump currently being developed by NASA and Pratt and Whitney. Comparison of results obtained from the Navier-Stokes code for two rotating disk datasets available in the literature are presented as benchmark validations. The benchmark results obtained using the code show good agreement relative to experimental data, and the turbine disk cavity was analyzed with comparable grid resolution, dissipation levels, and turbulence models. Predicted temperatures in the cavity show that little mixing of hot and cold fluid occurs in the cavity and the flow is dominated by swirl and pumping up the rotating disk.

Benjamin, Theodore G.↗
NASA NTRS1991

A Fourier-Chebyshev pseudospectral method for solving steady 3-D Navier-Stokes and heat equations in cylindrical cavities

A Fourier-Chebyshev pseudospectral method for solving steady 3D Navier-Stokes equations in cylindrical cavities is presented and discussed. The general method is pseudo-unsteady and uses a semi-implicit finite difference scheme for the time discretization. The generalized ADI (Alternating Direction Implicit) procedure is then applied to reduce the problem to a successive solution of one-dimensional problems. The spatial approximation uses a Fourier-Galerkin approximation in the periodic direction and a Chebyshev-collocation approximation in the other directions. Difficulties related to the pressure are surmounted by using the artifical compressibility method. A suitable variable change was chosen to avoid the problem of singularity at the axis generated by cylindrical coordinates. The method is first tested on an advection-diffusion equation and then on the Navier-Stokes equations. Finally, the method is illustrated by a convection problem of a differentially heated fluid.

Pulicani, J. P.↗
NASA NTRS1991

Transonic Navier-Stokes flow computations over wing-fuselage geometries

The steady-state transonic viscous flows over two wing-fuselage configurations are solved numerically. The 3D compressible thin-layer Navier-Stokes equations are solved by means of multistage timestepping similar to the Runge-Kutta method. The timestepping technique is applied with a multigrid scheme to make the transonic Navier-Stokes computations using the Baldwin-Lomax turbulence for closure and converging the solution on a grid of 1.52 million grid points with a C-O topology. Both generic and fighter wing-fuselage geometries are solved, and the results are compared to experimental studies. Solution convergence is found to be fast, and the fine grid generates accurate results for both configurations by means of the Baldwin-Lomax turbulence model. Results from the Johnson-King model calculations produce results that are more consistent with experimental results for the fighter configuration.

Agrawal, S.↗
NASA NTRS1991

Navier-Stokes solutions about the F/A-18 wing-LEX-fuselage configuration with multi-block structured grids

Three-dimensional thin-layer Navier-Stokes computations are presented for the F/A-18 configuration. The modeled configuration includes an accurate surface representation of the fuselage, leading-edge-extension, as well as the wing with and without leading-edge-flap deflection. A multi-block structured volume grid with various topologies is generated using transfinite interpolation technique. The flowfield domain is divided into twenty blocks, each representing a particular geometrical complexity of the configuration. The results are obtained from an algorithm for solving the compressible Navier-Stokes equations that incorporates an upwind-biased, flux-difference-splitting approach. In addition, a newly developed capability that allows for generalized surface patching among blocks is employed. Turbulent results are presented for flow conditions that correspond to recent NASA F/A-18 High Alpha Research Vehicle flight experiments. Good correlations between the computations and the flight test results are disclosed for both surface flow patterns as well as surface pressure distributions.

Ghaffari, Farhad↗
NASA NTRS1992

Developing A Navier-Stokes Algorithm For Supercomputers

Report discusses development of algorithm for solution of Navier-Stokes equations of flow on parallel-processing supercomputers. Involves combination of prior techniques to form algorithm to compute flows in complicated three-dimensional configurations. Includes explicit finite-difference numerical-integration scheme applicable to flows represented by hierarchy of mathematical models ranging from Euler to full Navier-Stokes. Of interest to researchers looking for ways to structure problems for greater computational efficiency.

Swisshelm, Julie M.↗
NASA NTRS1992

An iterative implicit DDADI algorithm for solving the Navier-Stokes equation

An algorithm utilizing a first order upwind split flux technique and the diagonally dominant treatment is proposed to be the temporal operator for solving the Navier-Stokes equations. Given the limit of a five point stencil, the right hand side flux derivatives are formulated by several commonly used central and upwind schemes. Their performances are studied through a test case of free vortex convection in a uniform stream. From these results, a superior treatment for evaluating the flux term is proposed and compared with the rest. The application of the proposed algorithm to the full Navier-Stokes equations is demonstrated through a calculation of flow over a backward facing step. Results are compared against the calculation done by using the fourth order central differencing scheme with artificial damping.

Chen, S. C.↗
NASA NTRS1992

The Proteus Navier-Stokes code

An effort is currently underway at NASA Lewis to develop two and three dimensional Navier-Stokes codes, called Proteus, for aerospace propulsion applications. Proteus solves the Reynolds-averaged, unsteady, compressible Navier-Stokes equations in strong conservation law form. Turbulence is modeled using a Baldwin-Lomax based algebraic eddy viscosity model. In addition, options are available to solve thin layer or Euler equations, and to eliminate the energy equation by assuming constant stagnation enthalpy. An extensive series of validation cases have been run, primarily using the two dimensional planar/axisymmetric version of the code. Several flows were computed that have exact solution such as: fully developed channel and pipe flow; Couette flow with and without pressure gradients; unsteady Couette flow formation; flow near a suddenly accelerated flat plate; flow between concentric rotating cylinders; and flow near a rotating disk. The two dimensional version of the Proteus code has been released, and the three dimensional code is scheduled for release in late 1991.

Towne, Charles E.↗