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NASA NTRS1986

Direct simulation of a turbulent boundary layer up to R(sub)(theta)= 1410

The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub theta = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectra method with up to about 10 to the 7th power grid points. Periodic spanwise and stream-wise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is examined and compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.

Spalart, Philippe R.↗

NASA NTRS1988

Direct simulation of a turbulent boundary layer up to R sub theta = 1410

The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub theta = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectral method with up to about 10 to the 7th grid points. Periodic spanwise and streamwise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.

Spalart, Philippe R.↗

NASA NTRS1991

Streamwise Algorithm For Simulation Of Flow

Algorithm for numerical solution of Euler and Navier-Stokes equations of unsteady flow incorporates upwind differencing based on streamwise direction. Generalized to calculate unsteady transonic flows over wings; suitable for analyses of flutter of wings affected by such flows.

Goorjian, Peter M.↗

NASA NTRS1990

Fluid dynamics and low gravity effects of chemical vapor deposition

Based on the comparison between experimental data and numerical results for the growth of GaAs from TMGa, it was shown that 3D simulations are necessary to simulate rectangular CVD reactors even when operated under subcritical (Ra) conditions. The important points found are summarized in the three attached reprints. The experimental studies of mixed convection in horizontal channels have shown three regimes of high Ra (22,220) number flows. At Re = 18.5, the rolls develop very quickly, significantly modulating the axial velocity even before it reaches the beginning of the hot plate. A few centimeters downstream, the velocities become asymmetric about the vertical centerplane and at x = 12 cm, become unsteady. These asymmetries were predicted theoretically, but experimental evidence has not been published prior to this work. At Re = 36, the axial velocity is only slightly modified at x = 0. Although the flow remains steady and symmetric about the vertical centerplane, there is a small spatial oscillation in the velocities over the length of the channel. The period of this oscillation was around 5 cm. At Re = 54, the longitudinal rolls developed smoothly over a length of 30 cm, with no asymmetries, unsteadiness, or spatial oscillations. Comparison of numerical simulations of these flows to experiments has revealed the importance and difficulty of setting proper thermal boundary conditions on the sidewalls. Calculated flows and experimentally measured flows showed very similar profiles, but at different axial locations, with the rolls developing more rapidly in the experiments. This is directly attributable to partially conducting sidewalls of the apparatus being hotter in the entrance section than the adiabatic walls of the simulations. A thorough comparison of the experimental data and numerical results for a variety of sidewall boundary conditions is in preparation.

Nyce, Thomas A.↗

NASA NTRS1985

Simulation of Multistage Turbine Flows

The numerical simulation of turbine flows serves to enhance the understanding of the flow phenomena within multistage turbomachinery components. The direct benefit of this activity is improved modeling capability, which can be used to improve component efficiency and durability. A hierarchy of equations was formulated to assess the difficulty in analyzing the flow field within multistage turbomachinery components. The Navier-Stokes equations provides the most complete description. The simplest description is given by a set of equations that govern the quasi-one-dimensional flow. The number of unknowns to be solved for increases monotonically above the number of equations. The development of the additional set of equations needed to mathematically close the system of equations forms the closure problem associated with that level of description. For the Navier-Stokes equation there is no closure problem. For the quasi-one-dimensional equation set random flow fluctuations, unsteady fluctuations, nonaxisymmetric flow variations, and hub-to-shroud variations on the quasi-one-dimensional flow must be accounted for.

Celestina, M. L.↗

NASA NTRS1989

Computation of rarefied hypersonic flows

Numerical techniques for the simulation of hypersonic flows of rarefied gases are examined in an analytical review. The direct-simulation Monte Carlo (DSMC) method developed to interpret measurement data obtained by the Space Shuttle in the SUMS project is described; the fundamental limitations of the DMSC approach are discussed; and modifications to improve the physical plausibility of DSMC predictions are proposed. Particular attention is given to the use of a double-peaked molecular distribution function for the internal flow in the SUMS probe, a downstream vacuum-reservoir condition as a simplifying assumption, and an explicit forward-time centered-space differencing scheme for the discretization of the SUMS problem. Typical simulation results are presented in extensive graphs and briefly characterized.

Cheng, Sin-I↗

NASA NTRS1993

Near wake structure for a generic ASTV configuration

Results of a numerical study are presented for hypersonic low-density flow about a 70-deg blunt cone using the direct simulation Monte Carlo method. Particular emphasis is given to the near wake flow and its sensitivity to rarefaction and other parametric variations. The flow conditions simulated are attainable in existing low-density hypersonic wind tunnels; that is, Mach 20 nitrogen flow encompassing freestream Knudsen numbers of 0.03 to 0.001. A stable vortex forms in the near wake at and below a freestream Knudsen number of 0.01 and the size of the vortex increases with decreasing freestream Knudsen number. The base region of the flow remains in thermal nonequilibrium for all cases. There is no formation of a lip separation shock or a distinct wake shock at these rarefied conditions.

Dogra, Virendra K.↗

NASA NTRS1999

Bubble Dynamics on a Heated Surface

In this work, we study steady and oscillatory thermocapillary and natural convective flows generated by a bubble on a heated solid surface. The interaction between gas and vapor bubbles with the surrounding fluid is of interest for both space and ground-based processing. A combined numerical-experimental approach is adopted here. The temperature field is visualized using Mach-Zehnder and/or Wollaston Prism Interferometry and the flow field is observed by a laser sheet flow visualization technique. A finite element numerical model is developed which solves the transient two-dimensional continuity, momentum, and energy equations and includes the effects of temperature-dependent surface tension and bubble surface deformation. Below the critical Marangoni number, the steady state low-g and 1-g temperature and velocity fields predicted by the finite element model are in excellent agreement with both the visualization experiments in our laboratory and recently published experimental results in the literature. Above the critical Marangoni number, the model predicts an oscillatory flow which is also closely confirmed by experiments. It is shown that the dynamics of the oscillatory flow are directly controlled by the thermal and hydrodynamic interactions brought about by combined natural and thermocapillary convection. Therefore, as numerical simulations show, there are considerable differences between the 1-g and low-g temperature and flow fields at both low and high Marangoni numbers. This has serious implications for both materials processing and fluid management in space.

Kassemi, M.↗

NASA NTRS1994

Regional-scale flows in mountainous terrain. Part 1: A numerical and observational comparison

This study uses observed data and a numerical simulation to examine the generation of thermally driven flows across the Colorado mountain barrier on meso-beta to meso-alpha scales. The observations were collected from remote surface observing systems at exposed mountaintop locations throughout the state of Colorado, over the summers of 1984-88, as part of the Rocky Mountain Peaks Experiment (ROMPEX). The data show the development of a recurrent circulation system across the Colorado mountain barrier, operating on a diurnal timescale. From the observations, the basic structure of the flow system appears as a daytime inflow toward the highest terrain, and a nocturnal outflow away from it. However, when examined in detail, the flow system exhibits more unusual behavior, especially west of the barrier crest. Here, winds in the early evening are occasionally observed to onset abruptly from an easterly direction, generally counter to the upper-level winds. Observations from ROMPEX for 26 August 1985 are used to provide comparison data for a numerical simulation with the Regional Atmospheric Modeling System (RAMS). This three-dimensional case study experiment is initialized with data from the National Meteorological Center and incorporates two-way interactive grid nesting. From the observed data and case study simulation, four distinct phases of the regional-scale circulation system have been identified. In the development phase, a deep mountain-plains solenoid is generated through terrain heating along the Front Range. This circulation system transforms in the late afternoon transition phase into a westward-propagating density current (WPDC). The third phase, called the 'density-current propagation phase,' occurs as the WPDC moves westward across the mountains, leaving in its wake strong southeasterly flow at the mountaintop level. This current appears to be the cause of the peculiar easterly component winds found in the ROMPEX mountaintop observations along the western slope. In the final late-night adjustment phase, the WPDC dissipates near the western edge of the Colorado mountains and steady southerly flow evolves over the high mountain terrain. This southerly flow is the steady response to the differential heating that develops between the low-lying plains and the intermountain region.

Bossert, James E.↗

NASA NTRS1982

Scattering and collapse of Langmuir waves driven by a weak electron beam

Wave-wave interactions are examined, particularly for significance in relation to Langmuir turbulence associated with type III solar radio emissions. The Zakharov equations are considered as two coupled nonlinear partial differential equations for the low-frequency density and the Langmuir envelope, and the electron and ion temperatures are regarded as equal. The Zhakharov equations are solved in one dimension, and display no collapse of a driven broadband pump, indicating that scattering instabilities are important in the saturation of a beam-plasma instability. A two-dimensional numerical simulation is developed to interpret the role of parametric instabilities, and it is concluded that the distortion of a wave packet is due to scattering instability, and not a change in the physics of direct collapse due to an artificial numerical damping. Further discussions are presented for comparisons of models of Langmuir turbulence in type III bursts.

Hafizi, B.↗

NASA NTRS1998

3-D Modeling of Directional Solidification of a Non-Dilute Alloy with Temperature and Concentration Fields Coupling via Materials Properties Dependence and via Double Diffusive Convection

Numerical simulation of the HgCdTe growth by the vertical Bridgman method was performed using FIDAP finite element code. Double-diffusive melt convection is analyzed, as the primary factor at controls inhomogeneity of the solidified material. Temperature and concentration fields in the model are also coupled via material properties, such as thermal and solutal expansion coefficients with the dependence on both temperature and concentration, and melting temperature evaluation from pseudobinary CdTe-HgTe phase diagram. Experimental measurements were used to obtain temperature boundary conditions. Parametric study of the melt convection dependence on the gravity conditions was undertaken. It was found, that the maximum convection velocity in the melt can be reduced under certain conditions. Optimal conditions to obtain a near flat solidified interface are discussed. The predicted interface shape is in agreement with one obtained experimentally by quenching. The results of 3-D calculations are compared with previous 2- D findings. A video film featuring 3-D melt convection will be presented.

Bune, Andris V.↗

NASA NTRS1989

Numerical investigation of the control of the secondary instability process in boundary layers

A numerical model has been developed for investigating boundary layer transition control for a flat plate boundary layer. Active control of a periodically forced boundary layer in an incompressible fluid is studied using surface heating techniques. The spatially evolving boundary layer is simulated. The Navier-Stokes and energy equations are integrated using a fully implicit finite difference/spectral method. Temperature perturbations are introduced locally along finite heater strips to directly attenuate the instability waves in the flow. A feedback control loop is employed in which a downstream sensor is used to monitor wall shear stress fluctuations. Active control of small amplitude two-dimensional and three-dimensional disturbances is numerically simulated. With proper phase control, in-phase reinforcement and out-of-phase attenuation are demonstrated. A receptivity study of the localized temperature perturbations is made. It is shown that narrow heater strips are more receptive in that they maximize the amplitude level of the disturbances in the flow. Active control of the early stages of the fundamental breakdown process is also numerically simulated. Control is achieved with either two-dimensional or three-dimensional control inputs.

Kral, L. D.↗

NASA NTRS1985

Evolution of a vortical structure associated with the bursting event in a channel flow

The temporal evolution of a horseshoe vortex structure in a channel is investigated by a numerical simulation. A spectral numerical method is employed to integrate the time-dependent, three-dimensional Navier-Stokes equations. The initial vortical structure is obtained by applying a conditional sampling technique to a data base generated from a direct simulation of a turbulent channel flow. The evolution of this vortical structure under the influence of the self-induced motion and the mean shear is presented. It is shown that the initial sheet-like vortical structure rolls up into a vortex tube as it is convected downstream. Turbulence structures associated with the vortex stretching are investigated. Production of vorticity stretching is high inside the vortex legs, although it is also substantial in the tip region and above the legs. High Reynolds shear stress is produced near the tip of the vortex.

Kim, J.↗

NASA NTRS2002

Annual Research Briefs, 2002: Center for Turbulence Research

Turbulent combustion remains the largest component of the CTR's core program. This program and several related activities at CTR are supported by NASA's Ultra Efficient Engine Technology Program. It is also intimately connected with the Department of Energy's ASCI program at Stanford which develops the technology for numerical simulation of realistic aircraft engines using state of the art massively parallel computers. In combustion modeling the attention has been directed to the modeling of higher levels of complexity such as spray dynamics, radiation and soot formation. Major aircraft engine manufacturers have shown considerable interest in this program; in particular, a significant active collaboration exists between CTR and the Pratt & Whitney Corporation. CTR's combustion program is essentially based on the large-eddy simulation technique, LES, which is actively being pursued at CTR for this and many other applications. Important accomplishments in LES included simulations with three-dimensional filters which result in grid independent calculations (that is why we call it "true" LES), and the development of the methodology for integration of LES and Reynolds Averaged computations. Optimization techniques are being studied and used for the important problem of wall boundary conditions for LES as well as for optimal shape design for aeroacoustic and aerodynamic performance gains.

ULTRA EFFICIENT ENGINE TECHNOLOGY↗

NASA NTRS1990

Numerical simulation of spatially-evolving instability control in plane channel flow

The applicability of active control by periodic suction-blowing in spatially evolving plane Poiseuille flow is investigated by the direct simulations of the two-dimensional, incompressible Navier-Stokes equations. All the computations were performed for Reynolds number (Re = 7500) which is linearly unstable for this flow. The result reveal that significant reductions in perturbation amplitudes can be obtained by a proper choice of the control wave amplitude and phase even for large disturbance amplitudes. The upstream influence of the control wave is also investigated.

Danabasoglu, G.↗

NASA NTRS1993

Numerical simulation using vorticity-vector potential formulation

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Tokunaga, Hiroshi↗

NASA NTRS2018

Numerical Studies of Hall Thruster Acceleration Region Electron Transport

Azimuthal direction 1-D and azimuthal and axial direction 2-D Particle in Cell (PIC) simulations of the Hall thruster acceleration and near-plume regions are presented. The axial extent of the 2-D computational domain is based on the ExB drift parameter, 𝑫𝑬𝒙𝑩, the number of times around the channel an electron ExB drifts before being scattered. With only high energy main beam ions, the simulations produced a broad potential profile in the acceleration region. The addition of a small amount of ionization in the acceleration domain at a rate consistent with Hall thruster parameters causes the potential profile to develop two distinct regions. In the upstream portion of the computational domain, the potential profile is very steep, typical of Hall thruster acceleration regions. In the downstream portion, the potential profile is almost flat, like potentials in Hall thruster near plume regions. This bifurcation happens naturally; there is no other change in code parameters between the two results. Without the addition of a small amount of ionization in the acceleration region, the axial electron transport is very low. With ionization, the calculated ratio of electron current to ion current is the same order of those measured in Hall thrusters. This suggests that in regions with lower energy electrons and ions, plasma waves are effective in allowing crossfield transport, and axial electric fields are small. In the acceleration region, the plasma waves are less effective at scattering the energetic electrons, and high axial electric fields are needed to produce the observed cross-field electron transport.

Ortega, Alejandro Lopez↗

NASA NTRS1983

Repeated-Measures Analysis of Image Data

It is suggested that using a modified analysis of variance procedure on data sampled systematically from a rectangular array of image data can provide a measure of homogeneity of means over that array in single directions and how variation in perpendicular directions interact. The modification of analysis of variance required to account for spatial correlation is described theoretically and numerically on simulated data.

Newton, H. J.↗