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All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Design, construction and testing of annular diffusers for high speed civil transportation combustor applications

A theoretical and an experimental design study of subsonic flow through curved-wall annular diffusers is being carried out in order to establish the most pertinent design parameters for such devices and the implications of their application in the design of engine components in the aerospace industries. This investigation consists of solving numerically the full Navier Stokes and Continuity equations for the time-mean flow. Various models of turbulence are being evaluated for adoption throughout the study and comparisons would be made with experimental data where they exist. Assessment of diffuser performance based on the dissipated mechanical energy would also be made. The experimental work involves the application of Computer Aided Design software tool to the development of a suitable annular diffuser geometry and the subsequent downloading of such data to a CNC machine at Central State University. The results of the investigations are expected to indicate that more cost effective component design of such devices as effective component design of such devices as diffusers which normally contain complex flows can still be achieved. In this regard a review paper was accepted and presented at the First International Conference on High Speed Civil Transportation Research held at North Carolina A&T in December of 1994.

Okhio, Cyril B.↗
NASA NTRS1993

The 3-D numerical study of airflow in the compressor/combustor prediffuser and dump diffuser of an industrial gas turbine

This paper describes the 3D computations of a flow field in the compressor/combustor diffusers of an industrial gas turbine. The geometry considered includes components such as the combustor support strut, the transition piece and the impingement sleeve with discrete cooling air holes on its surface. Because the geometry was complex and 3D, the airflow path was divided into two computational domains sharing an interface region. The body-fitted grid was generated independently in each of the two domains. The governing equations for incompressible Navier-Stokes equations were solved using the finite volume approach. The results show that the flow in the prediffuser is strongly coupled with the flow in the dump diffuser and vice versa. The computations also revealed that the flow in the dump diffuser is highly nonuniform.

Agrawal, Ajay K.↗
NASA NTRS1995

Two-stream modeling of plasmaspheric refilling

Plasmaspheric refilling on an L = 4 flux tube was studied by using a time-dependent, hydrodynamic plasmaspheric flow model in which the ion streams from the two hemispheres are treated as distinct fluids. In the model the continuity, momentum, and energy equations of a two-ion (O(+) and H(+)), quasi-neutral, currentless plasma are solved along a closed geomagnetic field line; diffusive equilibrium is not assumed. collisions between all stream pairs and with neutral species are included. The model includes a corotating, tilted dipole magnetic field and neutral winds. Ionospheric sources and sinks are accounted for in a self-consistent manner. Electrons are assumed to be heated by photoelectrons. The model flux tube extends from a 200-km altitude in one hemisphere to a 200-km altitude in the other hemisphere. Initially, the upwelling streams pass through each other practically unimpeded. When the streams approach the boundary in the conjugate ionosphere, a shock develops there, which moves upward and dissipates slowly; at about the same time a reverse shock develops in the hemisphere of origin, which moves upward. After about 1 hour, large shocks develop in each stream near the equator; these shocks move toward the equator and downward after crossing the equator. However, these shocks are probably artificial, because counterstreaming flows occur in each H(+) fluid, which the model can only handle by creating shocks.

Guiter, S. M.↗
NASA NTRS1991

The role of particle diffusion in the lower transition region: Revised interpretation of emission measures

Our energy-balance models of the lower transit ion region were presented in a previous paper (New Models of the Chromosphere and Transition Region). Here we show the influence of particle diffusion on the calculated hydrogen and helium number densities for a given temperature-density model (model C in the preceding paper). We have also solved the statistical equilibrium and radiative transfer equations for a 13-level He I atom (22 radiative transitions) and a 6-level He II ion (15 radiative transitions) together with He III. The resulting He I and He II level-1 number densities and He III density are shown as functions of temperature. Diffusion substantially increases eta(sub HeI) for T greater than 35,000 K and decreases eta(sub HeI) (while increasing eta(sub(HeII)) between 9,000 and 25,000 K. Including the effects of diffusion also increases eta(sub HeIII) for T less than 60,000 K.

Avrett, Eugene H.↗
NASA NTRS1997

Wave Driven Exothermic Heating in the Mesopause Region

A full-wave propagation model was developed that describes the propagation of gravity waves from the Earth's surface to the upper boundary, which can be placed anywhere between 150 and 500 km altitude. The model includes a realistic background atmosphere, and includes the effects of mean horizontal winds and their vertical shears, mean vertical temperature gradients, the eddy and molecular diffusion of heat and momentum, and the effects of ion-drag. This model solves five coupled second-order differential equations (continuity, momentum, and energy) in the vertical coordinate to derive the perturbation variables u', v', w' (horizontal and vertical velocity components), T' (temperature) and p' (pressure). The upper boundary can be automatically selected based on tests using the radiation condition at the upper boundary, wherein the height is increased until the wave is experiencing severe dissipation at the upper boundary, ensuring that substantial absorption occurs for any waves reflected from the upper boundary. The determination of wave amplitude is a key requirement of wave energetics. Therefore, the fullwave model has been applied to airglow observations in order to determine wave amplitudes as a function of altitude. This was accomplished by using the full-wave model output to drive a chemistry perturbation module that describes minor species perturbations and the resulting airglow perturbations. The full-wave output was multiplied by an altitude-independent factor such that the modeled and observed relative airglow intensity perturbations were equal. The effects of mean winds were included in these studies, and found to be the most important model input affecting the calculations (being more important than the choice of eddy diffusion profiles and chemical kinetic coefficients). In one study (Hickey et al., 1997a) these winds could not be well estimated from the measurements, whereas in the second study (Hickey et al.,1997b) the mean were well defined with a sodium wind-temperature lidar.

Hickey, Michael P.↗
NASA NTRS1979

High-altitude gas releases - Transition from collisionless flow to diffusive flow in a nonuniform atmosphere

The paper is motivated by a need for describing high-altitude gas releases from rockets or the Space Shuttle. In the tenuous upper atmosphere, the injected gases expand from a collisionless to a collision-dominated state. The analysis presented extends the efforts of Baum (1973-1974) to include the effects of a nonuniform background atmosphere and a velocity-dependent collision frequency. The unsteady expansion of gas releases is analyzed using gas kinetic theory. The Boltzmann equation with the Krook collision integral is solved numerically. At late times (after many collisions with the background atmosphere) the solution is identical to the one given by diffusion in a nonuniform atmosphere (Bernhardt, 1979). The theoretical model predicts elongation and heating of the vapor trails due to collisions.

Bernhardt, P. A.↗
NASA NTRS1992

Diffusive shock acceleration - Acceleration rate, magnetic-field direction and the diffusion limit

This paper reviews the concept of diffusive shock acceleration, showing that the acceleration of charged particles at a collisionless shock is a straightforward consequence of the standard cosmic-ray transport equation, provided that one treats the discontinuity at the shock correctly. This is true for arbitrary direction of the upstream magnetic field. Within this framework, it is shown that acceleration at perpendicular or quasi-perpendicular shocks is generally much faster than for parallel shocks. Paradoxically, it follows also that, for a simple scattering law, the acceleration is faster for less scattering or larger mean free path. Obviously, the mean free path can not become too large or the diffusion limit becomes inapplicable. Gradient and curvature drifts caused by the magnetic-field change at the shock play a major role in the acceleration process in most cases. Recent observations of the charge state of the anomalous component are shown to require the faster acceleration at the quasi-perpendicular solar-wind termination shock.

Jokipii, J. R.↗
NASA NTRS1984

Climate sensitivity with a seasonal cycle energy balance model

The sensitivity of climate which may have a local maximum as the ice cap passes through a midlatitude region where the atmosphere's transport efficiency varies strongly with latitude is examined. This behavior, found in a two level primitive equations climate model forced with annual mean insolation, was reproduced in an energy balance model (EBM) by making the diffusion coefficient a function of latitude. The two level seasonally varying EBM was applied and the global mean surface temperature vs. solar constant for this model are shown and two regions of enhanced sensitivity appear. The snowcover distributions around the year for three cases are shown.

Suarez, M. J.↗
NASA NTRS1987

Current-driven magnetohydrodynamic thermal instabilities in sheared fields

Approximate analytic solutions are sought for the dispersion relation for the MHD stability of magnetized medium in current-driven filamentation modes such as those observed in the solar atmosphere. The magnetic field is assumed to have a self-consistent sheared equilibrium structure. The analysis is carried out in the small wavenumber regime, where shear length is similar to the mode wavelength. Instability is found to depend on the ratio between the thermal and magnetic diffusivities, i.e., the Prandtl number, which identifies the unstable transverse wavenumbers. The instability conditions are expressed in an algebraic equation amenable to numerical solution. Results are provided from use of the model to determine the maximum growth rate and typical scale lengths of instabilities in a precoronal atmosphere and the lower transition region.

Bodo, G.↗
NASA NTRS1988

Analysis of homogeneous turbulent reacting flows

Full turbulence simulations at low Reynolds numbers were made for the single-step, irreversible, bimolecular reaction between non-premixed reactants in isochoric, decaying homogeneous turbulence. Various initial conditions for the scalar field were used in the simulations to control the initial scalar dissipation length scale, and simulations were also made for temperature-dependent reaction rates and for non-stoichiometric and unequal diffusivity conditions. Joint probability density functions (pdf's), conditional pdf's, and various statistical quantities appearing in the moment equations were computed. Preliminary analysis of the results indicates that compressive strain-rate correlates better than other dynamical quantities with local reaction rate, and the locations of peak reaction rates seem to be insensitive to the scalar field initial conditions.

Leonard, A. D.↗
NASA NTRS1992

Adaptive multigrid domain decomposition solutions for viscous interacting flows

Several viscous incompressible flows with strong pressure interaction and/or axial flow reversal are considered with an adaptive multigrid domain decomposition procedure. Specific examples include the triple deck structure surrounding the trailing edge of a flat plate, the flow recirculation in a trough geometry, and the flow in a rearward facing step channel. For the latter case, there are multiple recirculation zones, of different character, for laminar and turbulent flow conditions. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable, non-staggered grid computation.

Rubin, Stanley G.↗
NASA NTRS1992

The reversal of the solar polar magnetic fields. IV - The polar fields near sunspot maximum

The evolution of solar polar magnetic fields between Carrington rotations 1815 and 1834 is described using magnetic data from the Mount Wilson Observatory and the National Solar Observatory. The observations are compared with simulations using the flux transport equation. It is shown that the evolution of the polar field cannot be reproduced accurately by simulations of the diffusion and poleward drift of the emerging active regions at sunspot latitudes. Histograms of the distribution of the field intensities derived from daily magnetograms are presented which indicate that flux emerges at high latitudes and contributes to the evolution of the magnetic patterns.

Murray, N.↗
NASA NTRS1993

A three-dimensional pressure flux-split RNS application to sub/supersonic flow in inlets and ducts

The reduced Navier-Stokes (RNS) formulation is combined with a pressure based flux split procedure for the computational analysis of three dimensional flow. Only lowest order diffusion, that is required to satisfy the no-slip boundary condition is retained in this approximation. The governing equations are appropriately differenced such that the physical boundary conditions are closely coupled and combined to form a closed discrete system. No numerical or characteristic type boundary conditions are required. A global pressure relaxation procedure, i.e. multi-sweep PNS, is considered. A sparse matrix direct solver is applied to the crossplane solution. At the outflow boundary only the pressure or pressure gradient is prescribed. The resulting formulation has been applied to the solution of three-dimensional subsonic/supersonic internal flows in inlets and ducts.

Khosla, P. K.↗
NASA NTRS1993

Analysis of direct numerical simulation data of a Mach 4.5 transitional boundary-layer flow

This paper describes the creation, by temporal direct numerical simulation and the analysis based on the Reynolds stress transport equations, of a high-quality data set that represents the laminar-turbulent transition of a high-speed boundary-layer flow. Following Pruett and Zang (1992), and with the help of algorithmic refinements, the evolution of an axial, Mach 4.5 boundary-layer flow along a hollow cylinder is simulated numerically. Favre-averaged Reynolds stress transport equations are derived in generalized curvilinear coordinates and are then specialized to the cylindrical geometry at hand. Reynolds stresses and various turbulence quantities, such as turbulent kinetic energy and turbulent Mach number, are calculated from the numerical data at various stages of the transition process. The kinetic energy 'budgets' are constructed from the transport equations. Various contributing terms for the evolution of kinetic energy, like the rates of production and dissipation, transport, and diffusion, are presented. The compressible dissipation rate is small in comparison with the solenoidal dissipation rate for all times. The pressure-dilatation term is of the same order of magnitude as the compressible dissipation rate.

Dinavahi, Surya P. G.↗
NASA NTRS1997

Reduced Navier Stokes Relaxation Procedures for Internal Flows

In spite of significant advancement in the field of high speed computing, flow calculations involving complex geometries and/or flow behavior still require large amounts of CPU time and memory. In order to predict such flows without sacrificing grid convergence and accuracy, adaptive gridding techniques that provide optimal resolution are highly desirable. The present work combines multigrid techniques and domain decomposition concepts to provide local, solution adaptive, grid refinement. Several viscous compressible and incompressible, two and three-dimensional, flows with strong inviscid interaction and/or axial flow reversal, are considered with a segmented multigrid domain decomposition (SMGDD) procedure for which uniform meshes result in each domain. A pressure-based form of flux-vector splitting is applied to the Navier-Stokes equations, which are represented by an implicit lowest-order reduced Navier-Stokes (RNS) system and a purely diffusive, higher-order, deferred-corrector. A trapezoidal or box-like form of discretization insures that all mass conservation properties are satisfied at interfacial and outflow boundaries, even for this primitive-variable non-staggered grid computation. The SMGDD technique presented herein has previously been applied for incompressible two dimensional flows. The present work offers improvement in the gridding strategy, by allowing for disjoint subdomains that provide optimal resolution of disparate flow features. It also extends the SMGDD technique to three dimensional compressible flows. Laminar and turbulent flow in a backward facing step channel is considered; although the procedure is applicable to more severe geometries. The standard K-epsilon model is applied for turbulence closure. For Re greater than 400, differences between two-dimensional theory and experiment are resolved through a three dimensional simulation, which confirms the experimentally observed three dimensionality of the recirculation patterns on the upper and lower surfaces.

Rubin, Stanley G.↗
NASA NTRS2019

Adjoint-Based Mesh Adaptation and Shape Optimization for Simulations with Propulsion

We demonstrate a well-posed formulation of permeable boundary conditions and mass- flow-rate functionals for adjoint-based mesh refinement and shape optimization governed by the steady Euler equations. The boundary conditions are used to model propulsion- system effects of inlets and nozzles. A two-shock diffuser with an analytic solution is used to verify the implementation. Numerical examples show that the adjoint solution is smooth at the boundary, indicating that the discretization is adjoint consistent when exit pressure is specified at subsonic outflow, and stagnation temperature and pressure at subsonic inflow. The results focus on improving simulation techniques for low-boom aircraft analysis and design. By including mass-flow-rate outputs, we obtain reliable estimates of engine flow rates concurrently with nearfield pressure signatures without increasing simulation cost. We also demonstrate the importance of mass-flow-rate constraints in shape optimization by examining trade-offs between maximizing performance of a shrouded supersonic nozzle and minimizing shocks in its nearfield.

Nemec, Marian↗
NASA NTRS2011

Comparison of Four Mixed Layer Mesoscale Parameterizations and the Equation for an Arbitrary Tracer

In this paper we discuss two issues, the inter-comparison of four mixed layer mesoscale parameterizations and the search for the eddy induced velocity for an arbitrary tracer. It must be stressed that our analysis is limited to mixed layer mesoscales since we do not treat sub-mesoscales and small turbulent mixing. As for the first item, since three of the four parameterizations are expressed in terms of a stream function and a residual flux of the RMT formalism (residual mean theory), while the fourth is expressed in terms of vertical and horizontal fluxes, we needed a formalism to connect the two formulations. The standard RMT representation developed for the deep ocean cannot be extended to the mixed layer since its stream function does not vanish at the ocean's surface. We develop a new RMT representation that satisfies the surface boundary condition. As for the general form of the eddy induced velocity for an arbitrary tracer, thus far, it has been assumed that there is only the one that originates from the curl of the stream function. This is because it was assumed that the tracer residual flux is purely diffusive. On the other hand, we show that in the case of an arbitrary tracer, the residual flux has also a skew component that gives rise to an additional bolus velocity. Therefore, instead of only one bolus velocity, there are now two, one coming from the curl of the stream function and other from the skew part of the residual flux. In the buoyancy case, only one bolus velocity contributes to the mean buoyancy equation since the residual flux is indeed only diffusive.

Canuto, V. M.↗
NASA NTRS1974

Analysis of sound propagation in ducts using the wave envelope concept

A finite difference formulation is presented for sound propagation in a rectangular two-dimensional duct without steady flow for plane wave input. Before the difference equations are formulated, the governing Helmholtz equation is first transformed to a form whose solution does not oscillate along the length of the duct. This transformation reduces the required number of grid points by an order of magnitude, and the number of grid points becomes independent of the sound frequency. Physically, the transformed pressure represents the amplitude of the conventional sound wave. Example solutions are presented for sound propagation in a one-dimensional straight hard-wall duct and in a two-dimensional straight soft-wall duct without steady flow. The numerical solutions show evidence of the existence along the duct wall of a developing acoustic pressure diffusion boundary layer which is similar in nature to the conventional viscous flow boundary layer. In order to better illustrate this concept, the wave equation and boundary conditions are written such that the frequency no longer appears explicitly in them. The frequency effects in duct propagation can be visualized solely as an expansion and stretching of the suppressor duct.

Baumeister, K. J.↗