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NASA NTRS1987

A finite element computational method for high Reynolds number laminar flows

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.

Kim, Sang-Wook↗

NASA NTRS1988

Velocity-pressure integrated versus penalty finite element methods for high Reynolds number flows

Velocity-pressure integrated and consistent penalty finite element computations of high Reynolds number, laminar flows are presented. In both of the methods, the pressure has been interpolated using linear shape functions for a triangular element. The triangular element is contained inside the bi-quadratic isoparametric element. It has been reported previously that the pressure interpolation method, when used in the velocity-pressure integrated method, yielded accurate computational results for high Reynolds number flows. It is shown that use of the same pressure interpolation method in the consistent penalty finite element method yielded accurate velocity and pressure fields which were comparable to those obtained using the velocity-pressure integrated method. Accuracy of the two finite element methods has been demonstrated by comparing the computational results with available experimental data and/or fine-grid finite difference computational results. Advantages and disadvantages of the two methods are discussed on the basis of accuracy and convergence nature. Example problems considered include a lid-driven cavity flow for Reynolds number of 10,000, a laminar backward-facing step flow, a laminar flow through a nest of cylinders, and a channel flow with an internal blockage. A finite element computer program (NSFLOW/P) for the 2-D, incompressible Navier-Stokes equations is also presented.

Kim, Sang-Wook↗

NASA NTRS1992

An investigation of DTNS2D for use as an incompressible turbulence modelling test-bed

This paper documents an investigation of a two dimensional, incompressible Navier-Stokes solver for use as a test-bed for turbulence modelling. DTNS2D is the code under consideration for use at the Center for Modelling of Turbulence and Transition (CMOTT). This code was created by Gorski at the David Taylor Research Center and incorporates the pseudo compressibility method. Two laminar benchmark flows are used to measure the performance and implementation of the method. The classical solution of the Blasius boundary layer is used for validating the flat plate flow, while experimental data is incorporated in the validation of backward facing step flow. Velocity profiles, convergence histories, and reattachment lengths are used to quantify these calculations. The organization and adaptability of the code are also examined in light of the role as a numerical test-bed.

Steffen, Christopher J., Jr.↗

NASA NTRS1993

Control of a supersonic reattaching shear layer

A reattaching supersonic shear layer was perturbed by transverse air injection, and the effects were investigated using flow visualization. It was found that shear layer mixing was increased and that the shock system was strongly disturbed due to the heightened three dimensionality of the flow. Mixing enhancement was also achieved in an incompressible downstream-facing step flow using the same blowing procedure.

Poggie, J.↗

NASA NTRS1988

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Kim, Sang-Wook↗

NASA NTRS1989

A least-squares finite element method for incompressible Navier-Stokes problems

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method, and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Jiang, Bo-Nan↗

NASA NTRS1992

A least-squares finite element method for incompressible Navier-Stokes problems

A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.

Jiang, Bo-Nan↗

NASA NTRS1988

A fine grid finite element computation of two-dimensional high Reynolds number flows

A velocity-pressure-integrated mixed-interpolation Galerkin finite-element computation of the Navier-Stokes equations using the grids is presented. The velocity variables are interpolated using complete quadratic shape functions, and the pressure was interpolated using linear shape functions defined on a triangular element which is contained inside the quadratic element for velocity variables. Comprehensive computational results for a cavity flow at Reynolds number Re = 400-10,000 and a laminar backward-facing step flow at Re = 100-900 are presented. Many high-Re flows involve convection-dominated motion as well as diffusion-dominated motion in the flow domain. The computational results for both of the fluid motions compared favorably with high-accuracy finite-difference computational results and/or experimental data.

Kim, Sang-Wook↗

NASA NTRS2003

Step Bunching and Solution Flow

Imagine a sequence of equidistant steps parallel to one another on a crystal face growing from solution. Steps may be one or part of a lattice spacing high. With such ideal morphology, the most perfect material is expected to be produced. Sometimes this happens. Much more often, however, steps form bunches, acquire wavy shapes and interlace. With time, these spontaneous perturbations may be increased in amplitude, i.e. the stepped surface becomes morphologically unstable. Interferometric studies of Y.G. Kuznetsov, L.N. Rashkovich, P.G. Vekilov and N.A. Booth and the author demonstrated that the step bunching depends at least on direction and rate of solution flow over the interface, supersaturation and presence of impurities. In particular, if solution and step flow are parallel to one another, the steps convene into bunches. If these flows are antiparallel, the bunches disappear. As the step train propagates, the overall bunch height often increases infinitely. However, we have found recently that if the flow rate is large enough, (approximately 1 meter per second), the bunch height may be limited. All these phenomena come from interaction between steps. The interaction mechanisms are still not fully understood. I plan to overview major approaches to the still unresolved problem on how these dissipative structures on growing crystal face appear and evolve.

Chernov, A. A.↗

NASA NTRS1977

Integrated payload and mission planning, phase 3. Volume 2: Logic/Methodology for preliminary grouping of spacelab and mixed cargo payloads

The logic and methodology for a preliminary grouping of Spacelab and mixed-cargo payloads is proposed in a form that can be readily coded into a computer program by NASA. The logic developed for this preliminary cargo grouping analysis is summarized. Principal input data include the NASA Payload Model, payload descriptive data, Orbiter and Spacelab capabilities, and NASA guidelines and constraints. The first step in the process is a launch interval selection in which the time interval for payload grouping is identified. Logic flow steps are then taken to group payloads and define flight configurations based on criteria that includes dedication, volume, area, orbital parameters, pointing, g-level, mass, center of gravity, energy, power, and crew time.

Rodgers, T. E.↗

NASA NTRS2003

Step Free Surface Heteroepitaxy of 3C-SiC Layers on Patterned 4H/6H-SiC Mesas and Cantilevers

Most SiC devices are implemented in homoepitaxial films grown on 4H/6H-SiC wafers with surfaces 3 degrees to 8 degrees off-axis from the (0001) basal plane. This approach has not prevented many substrate crystal defects from propagating into SiC epilayers, and does not permit the realization of SiC heteropolytype devices. This presentation describes recent advances in SiC epitaxial growth that begun to overcome the above shortcomings for arrays of mesas patterned into on-axis 4H/6H-SiC wafers. First, we demonstrated that atomic-scale surface steps can be completely eliminated from 4H/6H-SiC mesas via on-axis homoepitaxial step-flow growth, forming (0001) basal plane surfaces (up to 0.4 mm x 0.4 mm) for larger than previously thought possible. Step-free surface areas were then extended by growth fo thin lateral cantilevers from the mesa tops. These lateral cantilevers enabled substrate defects to be reduced and relocated in homoepitaxial films in a manner not possible with off-axis SiC growth. Finally, growth of vastly improved 3C-SiC heterofilms was achieved on 4H/6H-SiC mesas using the recently develop step-free surface heteroepitaxy process. These epitaxial growth developments should enable improved homojunction and heterojunction silicon carbide prototype devices.

Neudeck, Philip G.↗

NASA NTRS1993

One-equation near-wall turbulence modeling with the aid of direct simulation data

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.

Rodi, W.↗

DOE OSTI2023

Atomistic Origins of Reversible Noncatalytic Gas–Solid Interfacial Reactions

Noncatalytic gas-solid reactions are a large group of heterogeneous reactions that are usually assumed to occur irreversibly because of the strong driving force to favor the forward direction toward the product formation. Using the example of Ni oxidation into NiO with CO 2 , herein we demonstrate the existence of the reverse element that results in the NiO reduction from the countering effect of the gaseous product of CO. Using in-situ electron microscopy observations and atomistic modeling, we show that the oxidation process occurs via preferential CO 2 adsorption along step edges that results in step-flow growth of NiO layers, and the presence of Ni atoms on the flat NiO surface promotes the nucleation of NiO layers. Simultaneously, the NiO reduction happens via preferential step-edge adsorption of CO that leads to the receding motion of atomic steps, and the presence of Ni vacancies in the NiO surface facilitates the CO adsorption induced surface pitting. Based on the in-situ TEM observations, temperature and CO 2 pressure effect maps are constructed to illustrate the spatiotemporal dynamics of the competing NiO redox reactions. We report, these results demonstrate the rich gas-solid surface reaction dynamics induced by the co-existing forward and reverse reaction elements and have practical applicability in manipulating gas-solid reactions via controlling the gas environment or atomic structure of the solid surface to steer the reaction toward the desired direction.

25 ENERGY STORAGE↗

NASA NTRS1986

Improvement of the second- and third-moment modeling of turbulence: A study of Reynolds-stress closure model

Four parts of the Reynolds-stress closure modeling are reported: (1) improvement of the k and epsilon equaitons; (2) development of the third-moment transport equation; (3) formulation of the diffusion coefficient of the momentum equation by using the algebraic-stress model of turbulence; and (4) the application of the Reynolds-stress model to a heat exchanger problem. It was demonstrated that the third-moment transport model improved the prediction of the triple-velocity products in the recirculating and reattaching flow regions in comparison with the existing algebraic models for the triple-velocity products. Optimum values for empirical coefficients are obtained for the prediction of the backward-facing step flows. A functional expression is derived for the coefficient of the momentum diffusion by employing the algebraic-stress model. The second-moment closure is applied to a heat transfer problem. The computations for the flow in a corrugated-wall channel show that the second-moment closure improves the prediction of the heat transfer rates by 30% over the k - epsilon model.

Amano, R. S.↗

NASA NTRS1984

Turbulent transport models for scramjet flowfields

Turbulence modeling approaches were examined from the standpoint of their capability to predict the complex flowfield features observed in scramjet combustions. Thus, for example, the accuracy of each turbulence model, with respect to the prediction of recirculating flows, was examined. It was observed that for large diameter ratio axisymmetric sudden expansion flows, a choice of turbulence model was not critical because of the domination of their flowfields by pressure forces. For low diameter ratio axisymmetric sudden expansions and planar backward-facing steps flows, where turbulent shear stresses are of greater significance, the algebraic Reynolds stress approach, modified to increase its sensitivity to streamline curvature, was found to provide the best results. Results of the study also showed that strongly swirling flows provide a stringent test of turbulence model assumptions. Thus, although flows with very high swirl are not of great practical interest, they are useful for turbulence model development. Finally, it was also noted that numerical flowfields solution techniques have a strong interrelation with turbulence models, particularly with the turbulent transport models which involve source-dominated transport equations.

Sindir, M. M.↗

NASA NTRS1991

An iterative implicit diagonally-dominant factorization algorithm for solving the Navier-Stokes equations

Presented here is an algorithm for solving the multidimensional unsteady Navier-Stokes equations for compressible flows. It is based on a diagonally-dominant approximate factorization procedure. The factorization error and the timewise linearization error associated with this procedure are reduced by performing Newton-type inner iterations at each time step. The inviscid fluxes are evaluated by the fourth-order central differencing scheme amended with a numerical dissipation directly proportional to the entire dissipative part of the truncation error intrinsic to the third order biased upwind scheme. The important features of the proposed solution are elucidated by the numerical results of the convection of a vortex and the backward-facing step flows.

Chen, Shu-Cheng↗

NASA NTRS1996

Multigrid, Fractional-Step Computation Of Flow

Speed of computer code solving three-dimensional Navier-Stokes equations of flow of incompressible fluid by fractional-step method increased significantly by use of multigrid procedures. In method, equations solved on general nonorthogonal curvilinear coordinate grid, using volume fluxes. At each time step, computations performed in two fractional steps. In first step, equations of conservation of momentum solved by use of gradient of pressure from previous time step via explicit approximate-factorization method, yielding approximate flow field that does not satisfy equation of conservation of mass. In second step, discrete Poisson-like equation with Neumann-type boundary conditions, formed by combining equations of conservation of momentum and mass, solved iteratively.

Kwak, Dochan↗

DOE OSTI2022

Methane liquefaction with an active magnetic regenerative refrigerator

This manuscript reports liquefaction of methane using an active magnetic regenerative refrigerator (AMRR). The AMRR used to cool from 285 K to 135 K has two identical regenerators fabricated with adjacent layers of four ferromagnetic refrigerants, each with sequentially lower Curie temperatures and lesser masses from hot to cold temperatures. The dual multilayer regenerators were assembled in opposition with a single cold region between them. For this set of experiments equal mass of helium gas was pumped through all layers of the regenerators during the two flow steps of the four-step AMR cycle. After successfully reaching 135 K, a compact condensing coil-fin tube heat exchanger (HEX) with a small storage vessel was mounted in the cold region of the dual regenerator assembly to be cooled during the hot-to-cold helium flow from alternatively demagnetized regenerators. The cold HEX was used to cool and liquefy a process stream of methane gas supplied at 295 K and different pressures in different runs. Further, by measuring time to liquefy a known volume of methane at three different pressures, cooling powers of the AMRR as a function of temperature were determined. The resultant data were compared to those predicted by the AMRR performance model. Conclusions from these experiments and suggestions for future work are presented.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗