SEARCH · Search NASA

Results for “Stokes”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13

All sources NASA NTRS DOE OSTI

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.↗

NASA NTRS1992

Navier-Stokes computations of a viscous optimized waverider

The performance of a Mach 6 viscous optimized waverider was calculated using the 3-D Navier-Stokes equations. The Mach 6 viscous optimized waverider was generated using MAXWARP, a code developed at the University of Maryland. The computations were performed using CFL3D, an implicit upwind-biased finite-volume algorithm developed at NASA Langley. Results show that good agreement was found between the calculated performance by MAXWARP and results from the Mach 6 Navier-Stokes computation. Furthermore, off-design performance of the Mach 6 optimized waverider was computed at Mach 4 and 8. The performance at these Mach numbers compared well with the performance of the viscous optimized waveriders specifically designed for these Mach numbers. Finally, contours of different flow parameters in the cross-flow plane were examined for the three calculations. The results indicate that the flow gradients are relatively small within the captured flow, and the variation itself is well behaved; thus, making the waverider configuration a promising choice for an engine/airframe design, especially for cruise-type applications.

Takashima, Naruhisa↗

NASA NTRS1991

Analysis of regularized Navier-Stokes equations. I, II

A regularized form of the conventional Navier-Stokes equations is analyzed. The global existence and uniqueness are established for two classes of generalized solutions. It is shown that the solution of this regularized system converges to the solution of the conventional Navier-Stokes equations for low Reynolds numbers. Particular attention is given to the structure of attractors characterizing the solutions. Both local and global invariant manifolds are found, and the regularity properties of these manifolds are analyzed.

Ou, Yuh-Roung↗

NASA NTRS1990

An error analysis of least-squares finite element method of velocity-pressure-vorticity formulation for Stokes problem

A theoretical proof of the optimal rate of convergence for the least-squares method is developed for the Stokes problem based on the velocity-pressure-vorticity formula. The 2D Stokes problem is analyzed to define the product space and its inner product, and the a priori estimates are derived to give the finite-element approximation. The least-squares method is found to converge at the optimal rate for equal-order interpolation.

Chang, Ching L.↗

NASA NTRS1992

Navier-Stokes analyses of flows over slender airframes

An account is given of the current development status of Navier-Stokes algorithms for the analysis of 3D viscous flows over slender airframes, emphasizing the design and analysis of practical configurations. The pacing items of the numerical algorithms used encompass grid generation, spatial and temporal differencing, and transition and turbulence modeling. Attention is given to the high angle-of-attack prediction capability of the various methods whose results are compared with experimental data; it is in that regime that Navier-Stokes methods surpass the prediction capabilities of flow solvers based on simpler mathematical models.

Thomas, James L.↗

NASA NTRS1992

Transonic airfoil and wing design using Navier-Stokes codes

An iterative design method has been implemented into 2D and 3D Navier-Stokes codes for the design of airfoils or wings with given target pressure distributions. The method begins with the analysis of an initial geometry, and obtains the analysis pressure distributions of that geometry. The differences between analysis pressures and target pressures are used to drive geometry changes through the use of a streamline curvature method. This paper describes the procedure that makes the iterative design method work for Navier-Stokes codes. Examples of 2D airfoil design, and 3D wing design are included. It is demonstrated that the method is highly effective for airfoil or wing design at flow conditions where no substantial separation occurs. Problems encountered in the airfoil design with shock induced flow separations are discussed.

Yu, N. J.↗

NASA NTRS1992

Navier-Stokes solutions with surface catalysis for Martian atmospheric entry

In this study numerical solutions have been obtained for two-dimensional axisymmetric hypersonic nonequilibrium CO2 flow over a high angle blunt cone with appropriate surface boundary conditions to account for energy and mass conservation at the body surface. The flowfield is described by the Navier-Stokes equations and multicomponent conservation laws which account for both translational and internal vibrational nonequilibrium effects. Complete forebody solutions have been obtained for the peak heating point of the Mars entry trajectory specified in the proposed NASA MESUR (Mars Environmental Survey) project. In these solutions, radiative equilibrium wall temperature and surface heating distributions are determined over the MESUR aeroshell forebody for entry velocity equal to 7 km/sec with varying degrees of surface catalysis. The effects of gas kinetics, surface catalysis, transport properties, and vibrational relaxation times on the surface heating are examined. The results identify some important issues in the prediction of surface heating for flows in thermochemical nonequilibrium and show that the Navier-Stokes code used herein is effective for thermal protection system design and materials selection.

Chen, Y.-K.↗

NASA NTRS1992

Calibration of Stokes and scattering matrix format polarimetric SAR data

An equivalence is noted between the backscatter and the polarimetric radar system assumptions for the approaches given by Klein (1992) and van Zyl (1990). It is shown that, to first order in the radar system crosstalk, an exact solution to the Stokes matrix format data calibration problem exists, and that van Zyl's approach can give this first-order solution for appropriately symmetrized polarimetric radar data. If the data are suitably symmetrized, the van Zyl approach can be used to calibrate both scattering matrix and Stokes matrix format data.

Freeman, Anthony↗

NASA NTRS1992

Navier-Stokes turbine heat transfer predictions using two-equation turbulence closures

Navier-Stokes calculations were carried out in order to predict the heat-transfer rates on turbine blades. The calculations were performed using TRAF2D which is a k-epsilon, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using Coakley's q-omega and Chien's k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a nonperiodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the SSME high-pressure fuel turbine. The comparison serves to highlight the weaknesses of the turbulence models for use in turbomachinery heat-transfer calculations.

Ameri, Ali A.↗