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All sourcesNASA NTRSDOE OSTI
NASA NTRS2009

Hypersonic Viscous Flow Over Large Roughness Elements

Viscous flow over discrete or distributed surface roughness has great implications for hypersonic flight due to aerothermodynamic considerations related to laminar-turbulent transition. Current prediction capability is greatly hampered by the limited knowledge base for such flows. To help fill that gap, numerical computations are used to investigate the intricate flow physics involved. An unstructured mesh, compressible Navier-Stokes code based on the space-time conservation element, solution element (CESE) method is used to perform time-accurate Navier-Stokes calculations for two roughness shapes investigated in wind tunnel experiments at NASA Langley Research Center. It was found through 2D parametric study that at subcritical Reynolds numbers of the boundary layers, absolute instability resulting in vortex shedding downstream, is likely to weaken at supersonic free-stream conditions. On the other hand, convective instability may be the dominant mechanism for supersonic boundary layers. Three-dimensional calculations for a rectangular or cylindrical roughness element at post-shock Mach numbers of 4.1 and 6.5 also confirm that no self-sustained vortex generation is present.

Chang, Chau-Lyan↗
NASA NTRS2009

Hypersonic Viscous Flow Over Large Roughness Elements

Viscous flow over discrete or distributed surface roughness has great implications for hypersonic flight due to aerothermodynamic considerations related to laminar-turbulent transition. Current prediction capability is greatly hampered by the limited knowledge base for such flows. To help fill that gap, numerical computations are used to investigate the intricate flow physics involved. An unstructured mesh, compressible Navier-Stokes code based on the space-time conservation element, solution element (CESE) method is used to perform time-accurate Navier-Stokes calculations for two roughness shapes investigated in wind tunnel experiments at NASA Langley Research Center. It was found through 2D parametric study that at subcritical Reynolds numbers, spontaneous absolute instability accompanying by sustained vortex shedding downstream of the roughness is likely to take place at subsonic free-stream conditions. On the other hand, convective instability may be the dominant mechanism for supersonic boundary layers. Three-dimensional calculations for both a rectangular and a cylindrical roughness element at post-shock Mach numbers of 4.1 and 6.5 also confirm that no self-sustained vortex generation from the top face of the roughness is observed, despite the presence of flow unsteadiness for the smaller post-shock Mach number case.

Chang, Chau-Lyan↗
NASA NTRS1982

A new numerical approach for compressible viscous flows

A numerical approach for computing unsteady compressible viscous flows was developed. This approach offers the capability of confining the region of computation to the viscous region of the flow. The viscous region is defined as the region where the vorticity is nonnegligible and the difference in dilatation between the potential flow and the real flow around the same geometry is also nonnegligible. The method was developed and tested. Also, an application of the procedure to the solution of the steady Navier-Stokes equations for incompressible internal flows is presented.

Wu, J. C.↗
NASA NTRS1991

Computations Of Impulsively Started Viscous Flow

Report discusses computation of impulsively started flow of viscous fluid about circular cylinder. Validation of methods for computation of these phenomena important step in development of ability to simulate flows in more complicated geometries; such as design of airfoils. Cylinder model has practical implications for such engineering problems as interactions of winds and currents with cylindrical structural members.

Davis, Sanford S.↗
NASA NTRS1979

A calculation procedure for viscous flow in turbomachines, volume 1

A method for analyzing the nonadiabatic viscous flow through turbomachine rotors is presented. The field analysis is based upon the numerical integration of the full incompressible stream function vorticity form of the Navier-Stokes equations, together with the energy equation, over the rotor blade-to-blade stream channels. The numerical code used to solve the governing equations employs a nonorthogonal boundary fitted coordinate system that suits the most complicated blade geometries. A numerical scheme is used to carry out the necessary integration of the elliptic governing equations. The flow characteristics within the rotor of a radial inflow turbine are investigated over a wide range of operating conditions. The calculated results are compared to existing experimental data. The flow in a radial compressor is analyzed in order to study the behavior of viscous flow in diffusing cascades. The results are compared qualitatively to known experimental trends. The solution obtained provides insight into the flow phenomena in this type of turbomachine. It is concluded that the method of analysis is quite general and gives a good representation of the actual flow behavior within turbomachine passages.

Khalil, I.↗
NASA NTRS1997

Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes

An adaptive refinement strategy based on hierarchical element subdivision is formulated and implemented for meshes containing arbitrary mixtures of tetrahendra, hexahendra, prisms and pyramids. Special attention is given to keeping memory overheads as low as possible. This procedure is coupled with an algebraic multigrid flow solver which operates on mixed-element meshes. Inviscid flows as well as viscous flows are computed an adaptively refined tetrahedral, hexahedral, and hybrid meshes. The efficiency of the method is demonstrated by generating an adapted hexahedral mesh containing 3 million vertices on a relatively inexpensive workstation.

Mavriplis, D. J.↗
NASA NTRS1991

Time-derivative preconditioning for viscous flows

A time-derivative preconditioning algorithm that is effective over a wide range of flow conditions from inviscid to very diffusive flows and from low speed to supersonic flows was developed. This algorithm uses a viscous set of primary dependent variables to introduce well-conditioned eigenvalues and to avoid having a nonphysical time reversal for viscous flow. The resulting algorithm also provides a mechanism for controlling the inviscid and viscous time step parameters to be of order one for very diffusive flows, thereby ensuring rapid convergence at very viscous flows as well as for inviscid flows. Convergence capabilities are demonstrated through computation of a wide variety of problems.

Choi, Yunho↗
NASA NTRS1991

Time-derivative preconditioning for viscous flows

A time-derivative preconditioning algorithm that is effective over a wide range of flow conditions from inviscid to very diffusive flows and from low speed to supersonic flows was developed. This algorithm uses a viscous set of primary dependent variables to introduce well-conditioned eigenvalues and to avoid having a nonphysical time reversal for viscous flow. The resulting algorithm also provides a mechanism for controlling the inviscid and viscous time step parameters to be of order one for very diffusive flows, thereby ensuring rapid convergence at very viscous flows as well as for inviscid flows. Convergence capabilities are demonstrated through computation of a wide variety of problems.

Choi, Yunho↗
NASA NTRS2015

Use of a Viscous Flow Simulation Code for Static Aeroelastic Analysis of a Wing at High-Lift Conditions

In this paper, we present a static aeroelastic analysis of a wind tunnel test model of a wing in high-lift configuration using a viscous flow simulation code. The model wing was tailored to deform during the tests by amounts similar to a composite airliner wing in highlift conditions. This required use of a viscous flow analysis to predict the lift coefficient of the deformed wing accurately. We thus utilized an existing static aeroelastic analysis framework that involves an inviscid flow code (Cart3d) to predict the deformed shape of the wing, then utilized a viscous flow code (Overflow) to compute the aerodynamic loads on the deformed wing. This way, we reduced the cost of flow simulations needed for this analysis while still being able to predict the aerodynamic forces with reasonable accuracy. Our results suggest that the lift of the deformed wing may be higher or lower than that of the non-deformed wing, and the washout deformation of the wing is the key factor that changes the lift of the deformed wing in two distinct ways: while it decreases the lift at low to moderate angles of attack simply by lowering local angles of attack along the span, it increases the lift at high angles of attack by alleviating separation.

Aeroelastic↗
NASA NTRS1980

Computation of three-dimensional viscous flows with the Navier-Stokes equations

The paper presents computations of three-dimensional viscous flows generated with the General Interpolation Method/STAR code based on the time-averaged Navier-Stokes equations. Calculations are presented for three viscous flow problems, and a two dimensional nozzle-exhaust shear flow case is solved and compared to an inviscid slip-line code. This nozzle-exhaust flow case is then extended to three dimensions and the steady solution displayed at pressure contours in the cross planes. The third problem consists of a simulated two-dimensional aircraft inlet flow which includes calculation of the 'spillage' flow and a shock wave/boundary layer interaction in the nozzle.

Spradley, L. W.↗
NASA NTRS1974

Integral representation of field variables for the finite element solution of viscous flow problems

The kinematics aspects of compressible and incompressible viscous flow problems are recasted into an integral representation for the velocity vector. For the incompressible flow problem, the kinetics aspect is similarly recasted into an integral representation. The result is a system of integral equations ideally suited for the finite element method. The integral representations are shown to permit the confinement of the computation field to the region of nonnegligible vorticity and dilatation which, for the incompressible flow, is identified with the viscous region. This drastic reduction in computation field results in a superior solution speed which is further improved by the use of a flowfield segmentation technique. The new approach is further shown to remove the difficulties associated with previous methods in specifying the far field and extraneous boundary conditions.

Wu, J. C.↗
NASA NTRS1986

A boundary element method for unsteady viscous flows

A potential vorticity method for the analysis of unsteady viscous incompressible flow past arbitrarily shaped objects is discussed which is based on the Helmholtz decomposition. It is found that the correct boundary condition to be imposed is on the normal component of the velocity for the cases of both inviscid and viscous flows. The no-slip condition is shown to be automatically satisfied for viscous flows. Numerical solutions for two-dimensional flow problems are given for attached flows in addition to those involving separation. The vorticity is confined, at least for the case of symmetric flows, to a small region in the immediate vicinity of the body, making possible the minimization of the number of node points in the field, and hence the computational time, without loss of accuracy.

Bharadvaj, B. K.↗
NASA NTRS1983

On numerical simulation of viscous flows

Numerical simulation methods for viscous incompressible laminar flows are reviewed, with a focus on finite-difference schemes. The approaches to high/moderate-Reynolds-number flows (strong-viscous-interaction model or single sets of equations) and the factors affecting the versatility, reliability, and accuracy of the analysis algorithms are considered; approximate-factorization implicit solution techniques for low-Reynolds-number flows are discussed; and the procedures used in a number of specific problems are indicated.

Ghia, K. N.↗
NASA NTRS1978

Viscous flow analysis in mixed flow rotors

A method for analyzing the viscous flow through turbomachine rotors is presented. The field analysis is based upon the solution of the full Navier-Stokes equations over the rotor blade-to-blade stream channels. An Alternating-Direction-Implicit method is employed to carry out the necessary numerical integration of the elliptic governing equations. The flow analysis may be applied to various types of turbomachine rotors. Preliminarily, only the case of laminar flows are considered in this paper. The flow characteristics within the rotors of a mixed flow turbine and a radial bladed compressor are investigated over a wide range of operating conditions. Excellent results are obtained when compared with existing experimental data. The method of this analysis is quite general and can deal with a wide range of applications. Possible modification of the present study to deal with turbulent flow cases are also identified.

Khalil, I.↗
NASA NTRS1983

Two-dimensional internal compressible viscous flows using semi-elliptic analysis

Subsonic viscous flows through planar cascades are examined by means of a semielliptic form of the Navier-Stokes equations, which is obtained by neglecting the streamwise diffusion of momentum and energy in their respective equations and providing upstream interaction through the pressure field. The influence of downstream conditions is propagated upstream in the subsonic flow, via a streamwise implicit determination of the pressure field, in order to permit departure-free solutions for the overall flow problem. The continuity equation is thereby satisfied directly. Governing equations are written in strong conservation law form, in terms of general, nonorthogonal transformed coordinates and Cartesian velocity components.

Ghia, K. N.↗
NASA NTRS1978

Viscous flow simulation requirements

Although significant advances have been made in the simulation of two-dimensional compressible laminar viscous flows by numerically solving the compressible Navier-Stokes (N.S.) equations, problem areas still remain to be solved before viscous flows requiring solution of the compressible N.S. equations can be efficiently and accurately simulated for flows of aerodynamic interest. These problem areas include turbulence (three-dimensional character), complex geometry, flow unsteadiness, placement of artificial boundaries relative to solid boundaries, specification of boundary conditions, and large flow gradients near surfaces and in the vicinity of shock waves for supersonic flows.

Harris, J. E.↗
NASA NTRS1993

A dual reciprocal boundary element formulation for viscous flows

The advantages inherent in the boundary element method (BEM) for potential flows are exploited to solve viscous flow problems. The trick is the introduction of a so-called dual reciprocal technique in which the convective terms are represented by a global function whose unknown coefficients are determined by collocation. The approach, which is necessarily iterative, converts the governing partial differential equations into integral equations via the distribution of fictitious sources or dipoles of unknown strength on the boundary. These integral equations consist of two parts. The first is a boundary integral term, whose kernel is the unknown strength of the fictitious sources and the fundamental solution of a convection-free flow problem. The second part is a domain integral term whose kernel is the convective portion of the governing PDEs. The domain integration can be transformed to the boundary by using the dual reciprocal (DR) concept. The resulting formulation is a pure boundary integral computational process.

Lafe, Olu↗