Laminar flow past a sphere at high Mach number.
Laminar hypersonic flow past sphere based on constant-density approximation, solving Navier- Stokes equations and comparing with values of shock Reynolds number
LAMINAR FLOW↗
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Computation of supersonic viscous flows over ogive-cylinders at angle of attack
The parabolic Navier-Stokes (PNS) marching finite-difference method is applied to 3-D viscous flow over pointed ogive-cylinders, and to turbulent flow over a cone. Ogive computations were performed using the new technique recently reported by Vigneron, Rakich, and Tannehill. Comparison is made with experiment and inviscid computations. The present results show that this method, which neglects part of the pressure gradient in the x-momentum equation, is nevertheless valid for flows with a strong favorable pressure gradient. In addition, turbulent separated flow over a cone has been computed using the older PNS code due to Lubard and Helliwell. It is found that one must freeze the turbulent eddy-viscosity model upstream of 3-D separation to get agreement with experiment.
Rakich, J. V.↗
Navier Stokes solution of the flowfield over ice accretion shapes
The numerical simulation of flow about ice accretion shapes has been accomplished by solving the Navier-Stokes equations using MacCormack's explicit finite difference scheme. The computations were performed on a CRAY-XMP computer. The influence of turbulence is taken into account by means of an algebraic eddy-viscosity model. In order to optimize the grid spacing and to achieve near orthogonality at the surface of the complex ice shapes, a hyperbolic grid generation scheme is utilized. Particular attention is given to the heat transfer process for which good agreement between the numerical and experimental results is achieved. In addition, liquid water droplet trajectories are coupled within the flowfield along with the resulting collection efficiencies using a parabolized Navier-Stokes formulation.
Scott, J. N.↗
Further Refinement of the LEWICE SLD Model
A research project is underway at NASA Glenn Research Center to produce computer software that can accurately predict ice growth for any meteorological conditions for any aircraft surface. This report will present results from version 3.2 of this software, which is called LEWICE. This version differs from previous releases in that it incorporates additional thermal analysis capabilities, a pneumatic boot model, interfaces to external computational fluid dynamics (CFD) flow solvers and has an empirical model for the supercooled large droplet (SLD) regime. An extensive comparison against the database of ice shapes and collection efficiencies that have been generated in the NASA Glenn Icing Research Tunnel (IRT) has also been performed. The complete set of data used for this comparison will eventually be available in a contractor report. This paper will show the differences in collection efficiency and ice shape between LEWICE 3.2 and experimental data. This report will first describe the LEWICE 3.2 SLD model. A semi-empirical approach was used to incorporate first order physical effects of large droplet phenomena into icing software. Comparisons are then made to every two-dimensional case in the water collection database and the ice shape database. Each collection efficiency condition was run using the following four assumptions: 1) potential flow, no splashing; 2) potential flow, with splashing; 3) Navior-Stokes, no splashing; 4) Navi r-Stokes, with splashing. All cases were run with 21 bin drop size distributions and a lift correction (angle of attack adjustment). Quantitative comparisons are shown for impingement limit, maximum water catch, and total collection efficiency. Due to the large number of ice shape cases, comprehensive comparisons were limited to potential flow cases with and without splashing. Quantitative comparisons are shown for horn height, horn angle, icing limit, area, and leading edge thickness. The results show that the predicted results for both ice shape and water collection are within the accuracy limits of the experimental data for the majority of cases.
Wright, William B.↗
Evaluation of Navier-Stokes and Euler solutions for leading-edge separation vortices
Extensive study on the numerical simulation of the vortical flow over a double delta wing is carried out using the thin layer Navier-Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium, and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The C sub L - alpha characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with the experiment on the C sub L - alpha characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading edge separation vortex, are not consistent with the experiment. Even for the fine grid Navier-Stokes computations, further grid resolution is required to obtain good quantitative agreement with the experiment.
Fujii, K.↗
Evaluation of Navier-Stokes and Euler solutions for leading-edge separation vortices
Extensive study on the numerical simulation of the vortical flow over a double delta wing is carried out using the thin layer Navier-Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium, and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The C sub L - alpha characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with the experiment on the C sub L - alpha characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading edge separation vortex, are not consistent with the experiment. Even for the fine grid Navier-Stokes computations, further grid resolution is required to obtain good quantitative agreement with the experiment.
Fujii, K.↗
Progress in computing nozzle/plume flow fields
The long-term goal is to develop the capability to predict chemically-reacting, multi-stream nozzle and plume flow fields. Two basic Navier-Stokes solvers, including the widely used F-3D code, are upgraded to include several upwind difference schemes and portable chemistry packages. Current computational capabilities for solving equilibrium single-stream and multi-stream, frozen gas, and finite rate chemistry problems are described. A variety of complex nozzle and plume flows were computed. Solutions presented include axisymmetric plume flow for ideal and equilibrium air, 3-D NASP nozzle/afterbody flow, and an internal nozzle calculation comparing various finite-rate chemistry packages.
Ruffin, Stephen M.↗
Drag reduction at a plane wall
The objective is to determine by analytical means how drag on a plane wall may be modified favorably using a minimal amount of flow information - preferably only information at the wall. What quantities should be measured? How should that information be assimilated in order to arrive at effective control? As a prototypical problem, incompressible, viscous flow, governed by the Navier-Stokes equations, past a plane wall at which the no-slip condition was modified was considered. The streamwise and spanwise velocity components are required to be zero, but the normal component is to be specified according to some control law. The challenge is to choose the wall-normal velocity component based on flow conditions at the wall so that the mean drag is as small as possible. There can be no net mass flux through the wall, and the total available control energy is constrained. A turbulent flow is highly unsteady and has detailed spatial structure. The mean drag on the wall is the integral over the wall of the local shear forces exerted by the fluid, which is then averaged in time; it is a 'macroscopic' property of the flow. It is not obvious how unsteady boundary control is to be applied in order to modify the mean flow most effectively, especially in view of the non- self-adjoint nature of the governing equations. An approximate analytical solution to the suboptimal scheme is pursued.
Hill, D. C.↗
Numerical and Experimental Studies of the Natural Convection Flow Within a Horizontal Cylinder Subjected to a Uniformly Cold Wall Boundary Condition
Numberical solutions are obtained for the quasi-compressible Navier-Stokes equations governing the time dependent natural convection flow within a horizontal cylinder. The early time flow development and wall heat transfer is obtained after imposing a uniformly cold wall boundary condition on the cylinder. Solutions are also obtained for the case of a time varying cold wall boundary condition. Windware explicit differ-encing is used for the numerical solutions. The viscous truncation error associated with this scheme is controlled so that first order accuracy is maintained in time and space. The results encompass a range of Grashof numbers from 8.34 times 10,000 to 7 times 10 to the 7th power which is within the laminar flow regime for gravitationally driven fluid flows. Experiments within a small scale instrumented horizontal cylinder revealed the time development of the temperature distribution across the boundary layer and also the decay of wall heat transfer with time.
Stewart, R. B.↗
Natural Rolling Responses of a Delta Wing in Transonic and Subsonic Flows
The unsteady, three-dimensional, full Navier-Stokes (NS) equations and the Euler equations of rigid-body dynamics are sequentially solved to simulate the natural rolling response of slender delta wings of zero thickness at moderate to high angles of attack, to transonic and subsonic flows. The governing equations of fluid flow and dynamics of the present multi-disciplinary problem are solved using the time-accurate solution of the NS equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. The main focus is to analyze the effect of Mach number and angle of attack on the leading edge vortices and their breakdown, the resultant rolling motion, and overall aerodynamic response of the wing. Three cases demonstrate the natural response of a 65 deg swept, cropped delta wing in a transonic flow with breakdown of the leading edge vortices and an 80 deg swept delta wing in a subsonic flow undergoing either damped or self-excited limit-cycle rolling oscillations as a function of angle of attack. Comparisons with an experimental investigation completes this study, validating the analysis and illustrating the complex details afforded by computational investigations.
Menzies, Margaret A.↗
Flow computations for the Space Shuttle in ascent mode using thin-layer Navier-Stokes equations
The application of CFD techniques to the Space Shuttle ascent environment was aggressively undertaken in the wake of the Challenger accident in order to secure a major new source of aerodynamic information for both the nominal and mission-abort conditions, using Cray 2 and Cray YMP supercomputers. Due to the integrated vehicle's complexity, the 'chimera' composite grid approach, in which an overset body-conforming grid is used to represent each geometric component as well as special flow regions, was employed for the discretization process. Calculation results exhibit general agreement in both flow structure and surface pressure with the available wind tunnel and flight-test results.
Martin, F. W., Jr.↗
The non-Newtonian heat and mass transport of He 2 in porous media used for vapor-liquid phase separation
This investigation of vapor-liquid phase separation (VLPS) of He 2 is related to long-term storage of cryogenic liquid. The VLPS system utilizes porous plugs in order to generate thermomechanical (thermo-osmotic) force which in turn prevents liquid from flowing out of the cryo-vessel (e.g., Infrared Astronomical Satellite). An apparatus was built and VLPS data were collected for a 2 and a 10 micrometer sintered stainless steel plug and a 5 to 15 micrometer sintered bronze plug. The VLPS data obtained at high temperature were in the nonlinear turbulent regime. At low temperature, the Stokes regime was approached. A turbulent flow model was developed, which provides a phenomenological description of the VLPS data. According to the model, most of the phase separation data are in the turbulent regime. The model is based on concepts of the Gorter-Mellink transport involving the mutual friction known from the zero net mass flow (ZNMF) studies. The latter had to be modified to obtain agreement with the present experimental VLPS evidence. In contrast to the well-known ZNMF mode, the VLPS results require a geometry dependent constant (Gorter-Mellink constant). A theoretical interpretation of the phenomenological equation for the VLPS data obtained, is based on modelling of the dynamics of quantized vortices proposed by Vinen. In extending Vinen's model to the VLPS transport of He 2 in porous media, a correlation between the K*(GM) and K(p) was obtained which permits an interpretation of the present findings. As K(p) is crucial, various methods were introduced to measure the permeability of the porous media at low temperatures. Good agreement was found between the room temperature and the low temperature K(p)-value of the plugs.
Yuan, S. W. K.↗
Theoretical analysis of aircraft afterbody flow
Computational methods solving the thin shear layer formulation of the compressible, Reynolds-averaged Navier-Stokes equations are presently used to investigate the strongly interactive flow field about aircraft afterbodies. Solutions for a variety of axisymmetric afterbody and nozzle geometries are solved by means of a time-dependent implicit numerical algorithm for both subsonic and supersonic external flows, and the results obtained are compared with experimental data. A novel adaptive-grid technique is used to resolve flow regimes having large gradients, as well as to improve the accuracy and efficiency of the computational scheme.
Deiwert, George S.↗
Numerical Simulation of Flow Through an Artificial Heart
A solution procedure was developed that solves the unsteady, incompressible Navier-Stokes equations, and was used to numerically simulate viscous incompressible flow through a model of the Pennsylvania State artificial heart. The solution algorithm is based on the artificial compressibility method, and uses flux-difference splitting to upwind the convective terms; a line-relaxation scheme is used to solve the equations. The time-accuracy of the method is obtained by iteratively solving the equations at each physical time step. The artificial heart geometry involves a piston-type action with a moving solid wall. A single H-grid is fit inside the heart chamber. The grid is continuously compressed and expanded with a constant number of grid points to accommodate the moving piston. The computational domain ends at the valve openings where nonreflective boundary conditions based on the method of characteristics are applied. Although a number of simplifing assumptions were made regarding the geometry, the computational results agreed reasonably well with an experimental picture. The computer time requirements for this flow simulation, however, are quite extensive. Computational study of this type of geometry would benefit greatly from improvements in computer hardware speed and algorithm efficiency enhancements.
Rogers, Stuart E.↗
The 3-D Navier-Stokes analysis of crossing, glancing shocks/turbulent boundary layer interactions
Three dimensional viscous flow analysis is performed for a configuration where two crossing and glancing shocks interact with a turbulent boundary layer. A time marching 3-D full Navier-Stokes code, called PARC3D, is used to compute the flow field, and the solution is compared to the experimental data obtained at the NASA Lewis Research Center's 1 x 1 ft supersonic wind tunnel facility. The study is carried out as part of the continuing code assessment program in support of the generic hypersonic research at NASA Lewis. Detailed comparisons of static pressure fields and oil flow patterns are made with the corresponding solution on the wall containing the shock/boundary layer interaction in an effort to validate the code for hypersonic inlet applications.
Reddy, D. R.↗
3-D Navier-Stokes analysis of crossing, glancing shocks/turbulent boundary layer interactions
Three dimensional viscous flow analysis is performed for a configuration where two crossing and glancing shocks interact with a turbulent boundary layer. A time marching 3-D full Navier-Stokes code, called PARC3D, is used to compute the flow field, and the solution is compared to the experimental data obtained at the NASA Lewis Research Center's 1 x 1 ft supersonic wind tunnel facility. The study is carried out as part of the continuing code assessment program in support of the generic hypersonic research at NASA Lewis. Detailed comparisons of static pressure fields and oil flow patterns are made with the corresponding solution on the wall containing the shock/boundary layer interaction in an effort to validate the code for hypersonic inlet applications.
Reddy, D. R.↗
Vortex breakdown in an axisymmetric flow
The breakdown for both an isolated vortex and a vortex flow in a tube is studied by means of a numerical solution of the axisymmetric Navier-Stokes equations for an unsteady, incompressible, and laminar flow. Results are compared to those of other authors and to experiments. Various numerical solution methods and various physical boundary conditions are used in order to explain the existence of different solutions. The computational results reveal that the existence of different solutions is due to slightly different inflow conditions. The numerical problem for the isolated vortex becomes ill-posed at a certain time for the inflow condition of zero axial gradient of the radial velocity component. Different inflow conditions yield breakdown flowfields containing different features of the experimentally observed breakdown structure.
Menne, Stefan↗
Active control of asymmetric vortical flows around cones using injection and heating
The effectiveness of certain active-control methods for asymmetric flows around circular cones is investigated by using computational solution of the unsteady, compressible full Navier-Stokes equations. Two main methods of active control which include flow injection and surface heating are used. For the flow-injection-control method, flow injection is used either in the normal direction to the surface or in the tangential direction to the surface. For the surface-heating-control method, the temperature of the cone surface is increased. The effectiveness of a hybrid method of flow control which combines normal injection with surface heating has also been studied. The Navier-Stokes equations, subjected to various surface boundary conditions, are solved by using an implicit, upwind, flux-difference splitting, finite-volume scheme for locally-conical flow solutions.
Kandil, Osama A.↗