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NASA NTRS1985

On the penetration of a hot diapir through a strongly temperature-dependent viscosity medium

The ascent of a hot spherical body through a fluid with a strongly temperature-dependent viscosity has been studied using an axisymmetric finite element method. Numerical solutions range over Peclet numbers of 0.1 - 1000 from constant viscosity up to viscosity variations of 100,000. Both rigid and stress-free boundary conditions were applied at the surface of the sphere. The dependence of drag on viscosity variation was shown to have no dependence on the stress boundary condition except for a Stokes flow scaling factor. A Nusselt number parameterization based on the stress-free constant viscosity functional dependence on the Peclet number scaled by a parameter depending on the viscosity structure fits both stress-free and rigid boundary condition data above viscosity variations of 100. The temperature scale height was determined as a function of sphere radius. For the simple physical model studied in this paper pre-heating is required to reduce the ambient viscosity of the country rock to less than 10 to the 22nd sq cm/s in order for a 10 km diapir to penetrate a distance of several radii.

Daly, S. F.↗

NASA NTRS1987

A comparison of numerical flux formulas for the Euler and Navier-Stokes equations

Numerical flux formulas for the convection terms in the Euler or Navier-Stokes equations are analyzed with regard to their accuracy in representing steady nonlinear and linear waves (shocks and entropy/shear waves, respectively). Numerical results are obtained for a one-dimensional conical Navier-Stokes flow including both a shock and a boundary layer. Analysis and experiments indicate that for an accurate representation of both layers the flux formula must include information about all different waves by which neighboring cells interact, as in Roe's flux-difference splitting. In comparison, Van Leer's flux-vector splitting, which ignores the linear waves, badly diffuses the boundary layer. The results of MacCormack's scheme, if properly tuned, are significantly better. The use of a sufficiently detailed flux formula appears to reduce the number of cells required to resolve a boundary layer by a factor 1/2 to 1/4 and thus pays off.

Van Leer, Bram↗

NASA NTRS1986

Space Station gas-grain simulation facility - Application to exobiology

The technical issues involved in performing experiments on the behavior and properties of aerosols in a microgravity environment provided by the Space Station are reviewed. The displacement of a particle resulting from g-jitter for ballistic, Knudsen, and Stokes flow regimes is examined in detail, and the radiation, acoustic, electrostatic, and electromagnetic mechanisms for the control of this motion are described. The simulation of organic haze production on Titan has been selected as an example experiment for detailed study. The purpose of this experiment was to simulate the photolysis of methane and the subsequent formation of the organic haze particles in the Titan upper atmosphere.

Mckay, C. P.↗

NASA NTRS1989

The lubrication force between two viscous drops

The present determination of the hydrodynamic force resisting the relative motion of two unequal drops moving in Stokes flow conditions along their line of centers assumes that the drops are in near-contact, and possess sufficiently high interfacial tension to remain spherical. Depending on the ratio of drop viscosity to that of the continuous phase, as well as on the ratio of the distance between drops to their reduced radius, three possible flow situations arise: these correspond to nearly-rigid drops, drops with partially mobile interfaces, and drops with fully mobile interfaces.

Davis, Robert H.↗

NASA NTRS1988

The Galerkin/least-squares method for advective-diffusive equations

Galerkin/least-squares finite-element methods are presented for advective-diffusive equations. Galerkin/least-squares represents a conceptual simplification of streamline-upwind Petrov-Galerkin methods, and is in fact applicable to a wide variety of other problem types. A convergence analysis and error estimates are presented. Some numerical results for compressible Navier-Stokes flows are presented.

Hughes, T. J. R.↗

NASA NTRS1990

Navier-Stokes computations on swept-tapered wings, including flexibility

A procedure to couple the Navier-Stokes solutions with modal structural equations of motion is presented for computing aeroelastic responses of flexible fighter wings. The Navier-Stokes flow equations are solved by a finite-difference scheme with dynamic grids. The coupled aeroelastic equations of motion are solved using the linear-acceleration method. The configuration-adaptive dynamic grids are time-accurately generated using the aeroelastically deformed shape of the wing. The coupled calculations are compared with experiments when available. Effects of flexibility and pitch rate are demonstrated for flows with vortices. Turbulent flow computations are also compared with laminar flow computations.

Guruswamy, Guru P.↗

NASA NTRS1992

Two-dimensional unstructured triangular grid generation

The capability of generating 2-D unstructured triangular meshes about arbitrary geometries is demonstrated. This work uses a distribution of boundary points and triangulates the computational domain using a Delaunay triangulation algorithm. Typically, initial cells are added based on cell aspect ratios or cell areas. A resulting mesh can then be used along with the connectivity of the cells to solve either a Euler or Navier-Stokes flow problem.

Jorgenson, Philip C. E.↗

NASA NTRS1992

CFD analysis of pump consortium impeller

Cheng, Gary C.↗

NASA NTRS1992

Relaxation in two dimensions and the 'sinh-Poisson' equation

Long-time states of a turbulent, decaying, two-dimensional, Navier-Stokes flow are shown numerically to relax toward maximum-entropy configurations, as defined by the "sinh-Poisson" equation. The large-scale Reynolds number is about 14,000, the spatial resolution is (512)-squared, the boundary conditions are spatially periodic, and the evolution takes place over nearly 400 large-scale eddy-turnover times.

Montgomery, D.↗

NASA NTRS1990

Reduction of vortex-induced vibration in vane geometries

Computations using a time-accurate, compressible Navier-Stokes flow model were conducted to analyze both unsteady laminar and turbulent flows over two curved configurations of vanes which were shaped to treat a 4.0 kHz vibration problem which has occurred in several SSMEs. This problem involves vortex shedding from vanes which causes excessive vane vibration and cracking. The original vane configuration exhibited strong flow-induced vibrations at a Strouhal number near 0.19 for a the first bending mode excitation. Scalloping of the leading edge raised the frequency of the vane's first torsional mode, which in turn increased the onset flow velocity at lock-in. Beveling the vane's trailing edge eliminated vortex shedding at the trailing edge, which decoupled the flow oscillation from the vibrating wave. A modified vane configuration with a beveled trailing edge at a 30 deg angle was also studied.

Liu, B. L.↗

NASA NTRS1993

Computation of wake/exhaust mixing downstream of advanced transport aircraft

The mixing of engine exhaust with the vortical wake of high speed aircraft operating in the stratosphere can play an important role in the formation of chemical products that deplete atmospheric ozone. An accurate analysis of this type of interaction is therefore necessary as a part of the assessment of the impact of proposed High Speed Civil Transport (HSCT) designs on atmospheric chemistry. This paper describes modifications to the parabolic Navier-Stokes flow field analysis in the UNIWAKE unified aircraft wake model to accommodate the computation of wake/exhaust mixing and the simulation of reacting flow. The present implementation uses a passive chemistry model in which the reacting species are convected and diffused by the fluid dynamic solution but in which the evolution of the species does not affect the flow field. The resulting analysis, UNIWAKE/PCHEM (Passive CHEMistry) has been applied to the analysis of wake/exhaust flows downstream of representative HSCT configurations. The major elements of the flow field model are described, as are the results of sample calculations illustrating the behavior of the thermal exhaust plume and the production of species important to the modeling of condensation in the wake. Appropriate steps for further development of the UNIWAKE/PCHEM model are also outlined.

Quackenbush, Todd R.↗

NASA NTRS1993

Numerical study of 3-D inducer and impeller for pump model development

Current design of high-performance turbopumps for rocket engines requires effective and robust analytical tools to provide design information in a productive manner. The main goal of this study is to develop a robust and effective CFD pump model for general turbopump design and analysis applications. A finite difference Navier-Stokes flow solver, FDNS, which includes an extended k-epsilon turbulence model and appropriate moving zonal interface boundary conditions, was developed to analyze turbulent flows in turbomachinery devices. In the present study, two key components of the turbopump, the inducer and impeller, were investigated by the proposed pump model, and the numerical results were benchmarked by the experimental data provided by Rocketdyne.

Cheng, G. C.↗

NASA NTRS1993

A hydrodynamic model of the oscillating screen viscometer

The viscometer consists of an oscillating screen immersed in a fluid and free to rotate about an axis in its plane. The viscosity can be determined from the measured ratio of the periodic driving force to the screen motion when an adequate hydrodynamical model of the immersed oscillator is available. The screen is formed by a square mesh of thin wire whose dimensions invite comparison with asymptotic results for narrow hollow bodies translating in Stokes flow. These indicate that the closed hole structure of the grid plays an important role in determining its motion. It is shown that this role diminishes as the frequency increases. The computed results, obtained from a system of linear equations, are consistent with experimental values over the appropriate range of frequency.

Davis, A. M. J.↗

NASA NTRS1994

Inducer analysis/pump model development

Current design of high performance turbopumps for rocket engines requires effective and robust analytical tools to provide design information in a productive manner. The main goal of this study was to develop a robust and effective computational fluid dynamics (CFD) pump model for general turbopump design and analysis applications. A finite difference Navier-Stokes flow solver, FDNS, which includes an extended k-epsilon turbulence model and appropriate moving zonal interface boundary conditions, was developed to analyze turbulent flows in turbomachinery devices. In the present study, three key components of the turbopump, the inducer, impeller, and diffuser, were investigated by the proposed pump model, and the numerical results were benchmarked by the experimental data provided by Rocketdyne. For the numerical calculation of inducer flows with tip clearance, the turbulence model and grid spacing are very important. Meanwhile, the development of the cross-stream secondary flow, generated by curved blade passage and the flow through tip leakage, has a strong effect on the inducer flow. Hence, the prediction of the inducer performance critically depends on whether the numerical scheme of the pump model can simulate the secondary flow pattern accurately or not. The impeller and diffuser, however, are dominated by pressure-driven flows such that the effects of turbulence model and grid spacing (except near leading and trailing edges of blades) are less sensitive. The present CFD pump model has been proved to be an efficient and robust analytical tool for pump design due to its very compact numerical structure (requiring small memory), fast turnaround computing time, and versatility for different geometries.

Cheng, Gary C.↗

NASA NTRS1994

Numerical design of advanced multi-element airfoils

The current study extends the application of computational fluid dynamics to three-dimensional high-lift systems. Structured, overset grids are used in conjunction with an incompressible Navier-Stokes flow solver to investigate flow over a two-element high-lift configuration. The computations were run in a fully turbulent mode using the one-equation Baldwin-Barth turbulence model. The geometry consisted of an unswept wing which spanned a wind tunnel test section. Flows over full and half-span Fowler flap configurations were computed. Grid resolution issues were investigated in two dimensional studies of the flapped airfoil. Results of the full-span flap wing agreed well with experimental data and verified the method. Flow over the wing with the half-span was computed to investigate the details of the flow at the free edge of the flap. The results illustrated changes in flow streamlines, separation locations, and surface pressures due to the vortex shed from the flap edge.

Mathias, Donovan L.↗

NASA NTRS1994

Applications of automatic differentiation in computational fluid dynamics

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

Green, Lawrence L.↗

NASA NTRS1993

CFD Parametric Study of Consortium Impeller

Current design of high performance turbopumps for rocket engines requires effective and robust analytical tools to provide design impact in a productive manner. The main goal of this study is to develop a robust and effective computational fluid dynamics (CFD) pump model for general turbopump design and analysis applications. A Finite Difference Navier-Stokes flow solver, FDNS, which includes the extended k-epsilon turbulence model and appropriate moving interface boundary conditions, was developed to analyze turbulent flows in turbomachinery devices. A second-order central difference scheme plus adaptive dissipation terms was employed in the FDNS code, along with a predictor plus multi-corrector pressure-based solution procedure. The multi-zone, multi-block capability allows the FDNS code to efficiently solve flow fields with complicated geometry. The FDNS code has been benchmarked by analyzing the pump consortium inducer, and it provided satisfactory results. In the present study, a CFD parametric study of the pump consortium impeller was conducted using the FDNS code. The pump consortium impeller, with partial blades, is a new design concept of the advanced rocket engines. The parametric study was to analyze the baseline design of the consortium impeller and its modification which utilizes TANDEM blades. In the present study, the TANDEM blade configuration of the consortium impeller considers cut full blades for about one quarter chord length from the leading edge and clocks the leading edge portion with an angle of 7.5 or 22.5 degrees. The purpose of the present study is to investigate the effect and trend of the TANDEM blade modification and provide the result as a design guideline. A 3-D flow analysis, with a 103 x 23 x 30 mesh grid system and with the inlet flow conditions measured by Rocketdyne, was performed for the baseline consortium impeller. The numerical result shows that the mass flow rate splits through various blade passages are relatively uniform. Due to the complexity of blade geometries, the TANDEM blade configurations were analyzed with the multi-zone grid structure. Both the 7.5 deg- and the 22.5 deg-clocking TANDEM blade cases utilized a 80K mesh system. The numerical result of two TANDEM blade modifications indicates the efficiency and the head are worse than those of the baseline case due to larger flow distortion. The gap between the TANDEM blade and the full blade allows the flow passes through and heavily loads the pressure side of the partial blade such that flow reversal occurs near the suction side of the splitter. The flow split at the exit of impeller blades is very non-uniform for TANDEM blade cases, and this will greatly induce the side load on the diffuser. Therefore, the TANDEM blade modification in the present CFD analysis does not improve the performance of the consortium impeller.

Cheng, Gary C.↗

NASA NTRS1995

Development of numerical methods for overset grids with applications for the integrated Space Shuttle vehicle

Algorithms and computer code developments were performed for the overset grid approach to solving computational fluid dynamics problems. The techniques developed are applicable to compressible Navier-Stokes flow for any general complex configurations. The computer codes developed were tested on different complex configurations with the Space Shuttle launch vehicle configuration as the primary test bed. General, efficient and user-friendly codes were produced for grid generation, flow solution and force and moment computation.

Chan, William M.↗