Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Stokes flow”

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.

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

At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Quantitative Approach for the Accurate CFD Simulation of Hover in Turbulent Flow

Time-dependent Navier-Stokes simulations have been carried out for a V22 rotor in hover using an improved, low-diffusion, HLLE++ upwind algorithm in the OVERFLOW code. Emphasis is placed on lessons learned over the past decade regarding the effects of high-order spatial accuracy, grid resolution, and the use of detached eddy simulation in predicting the rotor performance, i.e., figure-of-merit (FM). A quick-start procedure is described together with a statistical measure of FM convergence that reduces hover computations by 5 times, similar in computational work for forward flight. Furthermore, Cartesian adaptive mesh refinement in the rotor wake revealed a complex turbulent flow with worm-like structures of various scales. These turbulent worms, found computationally more than a decade ago, have recently been observed in a separate German Aerospace Center (DLR) experiment. Moreover, adaptive mesh refinement has been used to resolve the tip-vortex to its correct physical size.

Neal M. Chaderjian↗
NASA NTRS1991

An upwind-biased space marching algorithm for supersonic viscous flow

The modifications are documented which were made to the Langley Aerothermodynamic Upwind Relaxation Algorithm which allow it to compute solutions in a space marching manner. The space marching flux is formulated to be either first- or second-order accurate, using Roe's upwind differencing or Symmetric Total Variation Diminishing differencing, respectively. The algorithm solves the thin layer Navier-Stokes equations, and is subject to the same flow restrictions as a parabolized Navier-Stokes solver. Each cross flow plane is locally iterated in time until converged, then marched in space to the next station. The algorithm is tested on a sphere-cone geometry and a geometry which models the windward side of the Space Shuttle Orbiter. Computational results for surface heating are compared to ground based experimental data. In addition, space marching predictions for surface pressure are compared against values from the original algorithm.

Greene, Francis A.↗
NASA NTRS1993

Numerical simulation of upstream disturbance on flows around a slender body

Numerical solutions of the thin-layer approximation of the compressible Navier-Stokes equations have been obtained for flows around an ogive-cylinder body with and without a small fixed disturbance placed upstream of the body tip. Locating the disturbance at positions in the flow field upstream of the tip provokes the same range of behavior of the asymmetric flow that was numerically produced earlier by use of a geometrical disturbance on the body tip. Results remain consistent with the presence of a convective instability mechanism, and demonstrate the potential for a precise mapping of the body's receptivity to fixed disturbances in the flow field. Numerical solutions were also obtained for the flow-field responses to impulsive upstream disturbances to determine whether there is a growing response to an asymmetric impulsive disturbance that is consistent with presence of a convective instability mechanism. Results for surface pressure are interpreted with the aid of a mathematical model. The model suggests that the observed growth of surface pressure gradient with time and distance along a ray in response to an asymmetnc impulsive disturbance is in accord with the solution of a Ginzberg-Landau equation, with distinguishing features of the solution being consistent with the convective instability mode of behavior.

Degani, David↗
NASA NTRS1993

Unsteady aerodynamic flow phenomena in a transonic compressor stage

A three-dimensional unsteady, viscous aerodynamic analysis has been developed for the flow inside a transonic, high-through-flow, single stage compressor. The compressor stage is comprised of a low-aspect-ratio rotor and a closely coupled stator. The analysis is based on a numerical method for solving the three-dimensional Navier-Stokes equation for unsteady viscous flow through multiple turbomachinery blade rows. The method solves the fully three-dimensional Navier-Stokes equation with an implicit scheme. A two-equation turbulence model with a low-Reynolds-number modification is applied for the turbulence closure. A third-order accurate upwinding scheme is used to approximate convection terms while a second-order accurate central difference scheme is used for the discretization of the viscous terms. A second-order accurate scheme is employed for the temporal discretization. The numerical method is applied to study the unsteady flow field inside a transonic, high-through-flow, axial compressor stage. The numerical results are compared with available experimental data.

Hah, C.↗
NASA NTRS1993

Three-dimensional unsteady flow calculations in an advanced gas generator turbine

This paper deals with the application of a three-dimensional, unsteady Navier-Stokes code for predicting the unsteady flow in a single stage of an advanced gas generator turbine. The numerical method solves the three-dimensional thin-layer Navier-Stokes equations, using a system of overlaid grids, which allow for relative motion between the rotor and stator airfoils. Results in the form of time averaged pressures and pressure amplitudes on the airfoil surfaces will be shown. In addition, instantaneous contours of pressure, Mach number, etc. will be presented in order to provide a greater understanding of the inviscid as well as the viscous aspects of the flowfield. Also, relevant secondary flow features such as cross-plane velocity vectors and total pressure contours will be presented. Prior work in two-dimensions has indicated that for the advanced designs, the unsteady interactions can play a significant role in turbine performance. These interactions affect not only the stage efficiency but can substantially alter the time-averaged features of the flow. This work is a natural extension of the work done in two-dimensions and hopes to address some of the issues raised by the two-dimensional calculations. These calculations are being performed as an integral part of an actual design process and demonstrate the value of unsteady rotor-stator interaction calculations in the design of turbomachines.

Rangwalla, Akil A.↗
NASA NTRS1990

Global pressure relaxation for laminar two-dimensional internal flow

This study extends the reduced Navier-Stokes (RNS) global pressure relaxation procedure developed by Rubin and co-workers for external flow to internal flow applications. The streamwise pressure gradient is split into a backward-differenced or initial value component, as in boundary layer marching, and a forward-differenced or boundary value component that represents the elliptic downstream effects. The streamwise convection terms are upwind-differenced and all other streamwise derivatives are backward-differenced. A standard boundary layer marching technique imbedded in a conventional line relaxation technique is obtained. For compressible flow the pressure iteration determines the interior flow interaction as well as the inlet mass flux that is consistent with the outflow pressure boundary condition. Results have been computed for incompressible flow in both rectangular and curved channels, and for subsonic compressible flow in the simulation of an aerofoil in a wind tunnel. Converged solutions were obtained over a range of Reynolds numbers generating small to moderately large separation bubbles.

Rosenbaum, D.↗
NASA NTRS1986

A computational/experimental study of the flow around a body of revolution at angle of attack

The incompressible Navier-Stokes equations are numerically solved for steady flow around an ogive-cylinder (fineness ration 4.5) at angle of attack. The three-dimensional vortical flow is investigated with emphasis on the tip and the near wake region. The implicit, finite-difference computation is performed on the CRAY X-MP computer using the method of pseudo-compressibility. Comparisons of computational results with results of a companion towing tank experiment are presented for two symmetric leeside flow cases of moderate angles of attack. The topology of the flow is discussed and conclusions are drawn concerning the growth and stability of the primary vortices.

Zilliac, Gregory G.↗
NASA NTRS2002

Unsteady Simulation of a Landing-Gear Flow Field

This paper presents results of an unsteady Reynolds-averaged Navier-Stokes simulation of a landing-gear flow field. The geometry of the four-wheel landing gear assembly consists of several of the fine details including the oleo-strut, two diagonal struts, a door, yokes/pin and a flat-plate simulating the wing surface. The computational results, obtained by using 13.3 million grid points, are presented with an emphasis on the characteristics of the unsteadiness ensuing from different parts of the landing-gear assembly, including vortex shedding patterns and frequencies of dominant oscillations. The results show that the presence of the diagonal struts and the door significantly influence the flow field. Owing to the induced asymmetry, vortices are shed only from one of the rear wheels and not the other. Present computations also capture streamwise vortices originating from the upstream corners of the door.

Li, Fei↗
NASA NTRS2008

Flow Solver for Incompressible 2-D Drive Cavity

This software solves the Navier-Stokes equations for the incompressible driven cavity flow problem. The code uses second-order finite differencing on a staggered grid using the Chorin projection method. The resulting intermediate Poisson equation is efficiently solved using the fast Fourier transform. Time stepping is done using fourth-order Runge-Kutta for stability at high Reynolds numbers. Features include check-pointing, periodic field snapshots, ongoing reporting of kinetic energy and changes between time steps, time histories at selected points, and optional streakline generation.

Kalb, Virginia L.↗
NASA NTRS1986

Symmetry and stability in Taylor-Couette flow

The flow of a fluid between concentric rotating cylinders (the Taylor problem) is studied by exploiting the symmetries of the system. The Navier-Stokes equations, linearized about Couette flow, possess two zero and four purely imaginary eigenvalues at a suitable value of the speed of rotation of the outer cylinder. There is thus a reduced bifurcation equation on a six-dimensonal space which can be shown to commute with an action of the symmetry group 0(2) x S0(2). The group structure is used to analyze this bifurcation equation in the simplest (nondegenerate) case, and to compute the stabilities of solutions. In particular, when the outer cylinder is counterrotated, transitions which seem to agree with recent experiments of Andereck, Liu, and Swinney (1984) are obtained. It is also possible to obtain the 'main sequence' in this model. This sequence is normally observed in experiments when the outer cylinder is held fixed.

Golubitsky, M.↗
NASA NTRS1989

Numerical simulation of flow through the Langley parametric scramjet engine

The numerical simulation of a three-dimensional turbulent, reacting flow through the entire Langley parametric scramjet engine has been obtained using a piecewise elliptic approach. The last section in the combustor has been analyzed using a parabolized Navier-Stokes code. The facility nozzle flow was analyzed as a first step. The outflow conditions from the nozzle were chosen as the inflow conditions of the scramjet inlet. The nozzle and the inlet simulation were accomplished by solving the three-dimensional Navier-Stokes equations with a perfect gas assumption. The inlet solution downstream of the scramjet throat was used to provide inflow conditions for the combustor region. The first two regions of the combustor were analyzed using the MacCormack's explicit scheme. However, the source terms in the species equations were solved implicitly. The finite rate chemistry was modeled using the two-step reaction model of Rogers and Chinitz. A complete reaction model was used in the PNS code to solve the last combustor region. The numerical solutions provide an insight of the flow details in a complete hydrogen-fueled scramjet engine module.

Srinivasan, Shivakumar↗
NASA NTRS1986

Investigation of chemically reacting and radiating supersonic internal flows

The two-dimensional spatially elliptic Navier-Stokes equations are used to investigate the chemically reacting and radiating supersonic flow of the hydrogen-air system between two parallel plates and in a channel with a ten degree compression-expansion ramp at the lower boundary. The explicit unsplit finite-difference technique of MacCormack is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The tangent slab approximation is employed in the radiative flux formation. Both pseudo-gray and nongray models are used to represent the absorption characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the flow field.

Mani, M.↗
NASA NTRS1987

Numerical solutions of chemically reacting and radiating flows

The two-dimensional spatially elliptic Navier-Stokes equations are used to investigate the chemically reacting and radiating supersonic flow of the hydrogen-air system between two parallel plates and in a channel with a ten-degree compression-expansion ramp at the lower boundary. The explicit unsplit finite-difference technique of MacCormack is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The tangent slab approximation is employed in the radiative flux formulation. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the flow field.

Mani, M.↗
NASA NTRS1988

Patched-grid computations of high-speed inlet flows

Two implicit algorithms for the compressible Navier-Stokes equations are applied to the computation of high-speed inlet flows typical of those which are encountered on propulsion systems of advanced hypersonic vehicles. A patched grid formulation is used to treat accurately the blunt cowl interaction with the forebody compression field and efficiently treat variations in inlet geometry downstream of the inlet entrance. Results from the two algorithms, each based on an upwind-biased spatial differencing approach for the convective and pressure terms within a flux-difference-splitting framework, are compared with experimental results for both inlets, and reasonable agreement is found.

Thomas, J. L.↗
NASA NTRS1990

Numerical simulation of steady and unsteady asymmetric vortical flow

The unsteady, compressible, thin-layer, Navier-Stokes equations are solved to simulate steady and unsteady, asymmetric, vortical laminar flow around cones at high incidences and supersonic Mach numbers. The equations are solved by using an implicit, upwind, flux-difference splitting, finite-volume scheme. Locally conical flows are assumed and the solutions are obtained by forcing the conserved components of the flowfield vector to be equal at two axial stations located at 0.95 and 1.0. Computational examples cover steady and unsteady asymmetric flows around a circular cone and its control using side strakes. Unsteady asymmetric flows are also presented for elliptic- and diamond-section cones, which model asymmetric vortex shedding around round and sharp-edged delta wing flows.

Kandil, O. A.↗
NASA NTRS1993

Accuracy considerations in the computational analysis of jet noise

The application of computational fluid dynamics methods to the analysis of problems in aerodynamic noise has resulted in the extension and adaptation of conventional CFD to the discipline now referred to as computational aeroacoustics (CAA). In the analysis of jet noise accurate resolution of a wide range of spatial and temporal scales in the flow field is essential if the acoustic far field is to be predicted. The numerical simulation of unsteady jet flow has been successfully demonstrated and many flow features have been computed with reasonable accuracy. Grid refinement and increased solution time are discussed as means of improving accuracy of Navier-Stokes solutions of unsteady jet flow. In addition various properties of different numerical procedures which influence accuracy are examined with particular emphasis on dispersion and dissipation characteristics. These properties are investigated by using selected schemes to solve model problems for the propagation of a shock wave and a sinusoidal disturbance. The results are compared for the different schemes.

Scott, James N.↗
NASA NTRS1992

Navier-Stokes analysis of blunt trailing edge airfoils

The flow around blunt trailing edge airfoils was studied by solving the Reynolds-averaged Navier-Stokes equations. The solution procedure combines a grid around the airfoil with a second grid for the wake so that the time advancement over the domain is fully implicit. This is not only very efficient for the algorithm but also allows implicit solutions of a one equation turbulence model appropriate for both boundary layers and wakes. An algebraic and two one-equation turbulence models are tested for a blunt RAE 2822 airfoil section and detailed comparisons with experimental data are presented in the trailing edge region.

Stanaway, Sharon↗