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NASA NTRS2005

Matching Multistage Schemes to Viscous Flow

Multistage, explicit time stepping can be tailored to accelerate convergence for scalar advection-diffusion problems by using optimized multistage coefficients that vary with the local cell Reynolds number. And, when combined with local preconditioning, variable-coefficient multistage schemes for computational fluid dynamics codes can also provide an order of magnitude faster convergence, relative to standard, fixed-coefficient schemes, for the Navier-Stokes system of equations.

Kleb, William L.↗

NASA NTRS1975

Theoretical face pressure and drag characteristics of forward-facing steps in supersonic turbulent boundary layers

A theoretical investigation of the pressure distributions and drag characteristics was made for forward facing steps in turbulent flow at supersonic speeds. An approximate solution technique proposed by Uebelhack has been modified and extended to obtain a more consistent numerical procedure. A comparison of theoretical calculations with experimental data generally indicated good agreement over the experimentally available range of ratios of step height to boundary layer thickness from 7 to 0.05.

Patel, D. K.↗

NASA NTRS1984

Turbulent heat transfer in a channel with two right-angled bends

A numerical study is reported on the flow and heat transfer in a channel with two right-angled bends. The k-epsilon turbulence model with a refined near-wall model is adopted for the computation of the flow field for step ratios ranging H/W = 1-4 and for Reynolds numbers Re = 3,000-10,000. The solution method of the governing transport equations is based on the modified hybrid scheme which produces very small truncation error. As a result of extensive computations, the complex flow patterns in the channel with two bends are clarified and the mechanisms of heat transfer are explained relating to the flow behaviors of separation, deflection, recirculation, and reattachment.

Amano, R. S.↗

NASA NTRS1986

ISCCP reduced resolution satellite radiance data

The International Satellite Cloud Climatology Project (ISCCP) is the first active project of the World Climate Research Program. It is a multinational data collection project focused on collecting a data set that will improve the ability to predict and/or simulate the radiative effects of clouds on climate. For specified cloud parameters, the goals are to archieve values for 3-hour periods over the whole globe for 5 years at 30 km resolution. The task of collecting and processing radiance data from both geosynchronous and polar orbiting satellites began in July 1983. A diagram was shown illustrating the flow of data from the transmitting satellites to the various receiving institutions that handle it. The various stages of processing were then explained in detail, emphasizing Level B3-normalized, reformatted, reduced raw satellite data. The reduction of data by sampling is an essential step in the flow. By the time the ISCCP data reaches the Global Processing Center at Goddard Institute for Space Studies (GISS), the volume has been reduced by a factor of 1000. The Pilot Climate Data System (PLDS) will provide access to the ISCCP data set. It should prove to be one of the cleanest satellite data sets because it will have been through three filters--that of the operational agency, the Global Processing Center, and the PCDS. The ISCCP data set also includes other correlative data sets delivered in compatible format.

Rossow, W.↗

NASA NTRS2013

Time-Accurate Local Time Stepping and High-Order Time CESE Methods for Multi-Dimensional Flows Using Unstructured Meshes

With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.

Chang, Chau-Lyan↗

NASA NTRS1992

MHD flow past an obstacle - Large-scale flow in the magnetosheath

As a step to the study of the large-scale flow in the magnetosheath, the MHD flow past an obstacle is investigated. A time asymptotic method is used to obtain 3D steady-state solutions. The results indicate the formation of a depletion layer near the obstacle due to the increase of the magnetic field. Along the earth-sun line the plasma density increases first and then decreases from the post bow shock to the magnetopause. The local density maximum in front of the magnetopause may correspond to what was recently observed. When the interplanetary magnetic field direction is tilted from the solar wind flow, the IMF influences the shape of the bow shock as well as the location of the stagnation point at the magnetopause in a way consistent with observation. In addition, the results show the existence of a magnetosheath current in the post parallel-shock region.

Wu, C. C.↗

NASA NTRS1991

Instabilities and large structures in reattaching boundary layers

The underlying premise in this work is that large structures in turbulent shear flows are not universal and similar large structures in different flows owe their origins to basically similar instabilities. The turbulent boundary-layer flow over a backward-facing step and also the reattaching transitional boundary layer behind a large spanwise rod have been studied experimentally in parallel primarily to understand the origin of the curious large structures observed in the far downstream region (after 39 step heights) of the former flowfield. Simultaneous flow visualization and hot-wire anemometry and also plain-flow visualization have been carried out. In the backward-facing step, the three-dimensional mixing layer developing after detachment persists even after reattachment. The flow does not recover fully back to a regular turbulent boundary layer even far downstream of reattachment. The turbulence-producing instability of a turbulent boundary layer continues to compete with the wall-bounded mixing layer instability, giving rise to the curious schismatic arrays of large structures.

Bandyopadhyay, Promode R.↗

NASA NTRS1994

Developments and applications of dynamic models for large eddy simulation of complex flows

The dynamic modeling procedure for large eddy simulation of turbulent flows is reviewed and recent developments in the theoretical aspects and applications are described. Methods for inclusion of backscatter of energy from small to large scale motions are presented. New formulations of the dynamic procedure are proposed which are optimized based on the subgrid scale flux vector or the energy dissipation rate instead of the subgrid scale stress tensor. Recent results from application of the model to forced isotropic turbulence with an inertial subrange, flow over a backward facing step at Reynolds number of 28000, and flow over a concave curved surface are presented.

Moin, P.↗

NASA NTRS1989

Unsteady Navier-Stokes computations past oscillating delta wing at high incidence

The unsteady, thin-layer, compressible Navier-Stokes equations, written in the moving frame of reference for the flow relative motion, is solved for the steady and unsteady supersonic flow around a round-edged delta wing. For supersonic flow, local conical flow solution has been obtained from the three-dimensional equations. Pseudotime stepping is used for the steady flow, while time-accurate stepping is used for the unsteady flow. The computational scheme is an implicit approximately-factored finite volume scheme which uses explicit and implicit dissipation terms. The scheme is verified for the steady flow solution. The scheme is then applied to a delta wing undergoing rolling oscillation at a reduced frequency of 1.137 with 15- deg maximum amplitude about a mean angle of attack of 10 deg for a Mach number of 2 and a Reynolds number of 500,000.

Kandil, Osama A.↗

NASA NTRS1994

Scientific Visualization of Large Scale Unsteady Fluid Flow

In a numerical flow simulation. it is common to generate several thousand time steps of unsteady (time-dependent) flow data. Each time step may require tens to hundreds of megabytes for disk storage, and the total disk requirement for storing the unsteady flow data may be hundreds of gigabytes. Interactive visualization of unsteady flow data of this magnitude is presently impossible with the current hardware technology. This chapter describes the current approaches for unsteady flow visualization. An effective particle tracing technique for unsteady flow is also described. First, the life cycle of a typical numerical flow simulation is outlined. Several unsteady flow data sets from real-world problems are then given. The current approaches for visualizing unsteady flow are then described. There are many existing systems for flow visualization, and some of them are discussed. Streaklines depict time-varying phenomena that are sometimes difficult or impossible to see with other visualization techniques. The algorithms for computing streaklines are described. Several unsteady flow data sets have been visualized using streaklines, and the results are presented. Finally, some current issues in unsteady flow visualization are discussed.

Lane, David A.↗

NASA NTRS1993

Towards a generalized computational fluid dynamics technique for all Mach numbers

Currently there exists no single unified approach for efficiently and accurately solving computational fluid dynamics (CFD) problems across the Mach number regime, from truly low speed incompressible flows to hypersonic speeds. There are several CFD codes that have evolved into sophisticated prediction tools with a wide variety of features including multiblock capabilities, generalized chemistry and thermodynamics models among other features. However, as these codes evolve, the demand placed on the end user also increases simply because of the myriad of features that are incorporated into these codes. In order for a user to be able to solve a wide range of problems, several codes may be needed requiring the user to be familiar with the intricacies of each code and their rather complicated input files. Moreover, the cost of training users and maintaining several codes becomes prohibitive. The objective of the current work is to extend the compressible, characteristic-based, thermochemical nonequilibrium Navier-Stokes code GASP to very low speed flows and simultaneously improve convergence at all speeds. Before this work began, the practical speed range of GASP was Mach numbers on the order of 0.1 and higher. In addition, a number of new techniques have been developed for more accurate physical and numerical modeling. The primary focus has been on the development of optimal preconditioning techniques for the Euler and the Navier-Stokes equations with general finite-rate chemistry models and both equilibrium and nonequilibrium thermodynamics models. We began with the work of Van Leer, Lee, and Roe for inviscid, one-dimensional perfect gases and extended their approach to include three-dimensional reacting flows. The basic steps required to accomplish this task were a transformation to stream-aligned coordinates, the formulation of the preconditioning matrix, incorporation into both explicit and implicit temporal integration schemes, and modification of the numerical flux formulae. In addition, we improved the convergence rate of the implicit time integration schemes in GASP through the use of inner iteration strategies and the use of the GMRES (General Minimized Resisual) which belongs to the class of algorithms referred to as Krylov subspace iteration. Finally, we significantly improved the practical utility of GASP through the addition of mesh sequencing, a technique in which computations begin on a coarse grid and get interpolated onto successively finer grids. The fluid dynamic problems of interest to the propulsion community involve complex flow physics spanning different velocity regimes and possibly involving chemical reactions. This class of problems results in widely disparate time scales causing numerical stiffness. Even in the absence of chemical reactions, eigenvalue stiffness manifests itself at transonic and very low speed flows which can be quantified by the large condition number of the system and evidenced by slow convergence rates. This results in the need for thorough numerical analysis and subsequent implementation of sophisticated numerical techniques for these difficult yet practical problems. As a result of this work, we have been able to extend the range of applicability of compressible codes to very low speed inviscid flows (M = .001) and reacting flows.

Walters, R. W.↗

NASA NTRS2000

Phase Shift Interferometer and Growth Set Up to Step Pattern Formation During Growth From Solutions. Influence of the Oscillatory solution Flow on Stability

We have assembled an experimental setup based on Michelson interferometry with the growing crystal surface as one of the reflective surfaces. The crystallization part of the device allows optical monitoring of a face of a crystal growing at temperature stable within 0.05 C in a flow of solution of controlled direction and speed. The reference arm of the interferometer contains a liquid crystal element that allows controlled shifts of the phase of the interferograms. We employ an image-processing algorithm, which combines five images with a pi/2 phase difference between each pair of images. The images are transferred to a computer by a camera capable of capturing 60 frames per second. The device allows data collection on surface morphology and kinetics during the face layers growth over a relatively large area (approximately 4 sq. mm) in situ and in real time during growth. The estimated depth resolution of the phase shifting interferometry is approximately 50 Angstroms. The data will be analyzed in order to reveal and monitor step bunching during the growth process. The crystal chosen as a model for study in this work is KH2PO4 (KDP). This optically non-linear material is widely used in frequency doubling applications. There have been a number of studies of the kinetics of KDP crystallization that can serve as a benchmark for our investigations. However, so far, systematic quantitative characteristics of step interaction and bunching are missing. We intend to present our first quantitative results on the onset, initial stages and development of instabilities in moving step trains on vicinal crystal surfaces at varying supersaturation, flow rate, and flow direction. Behavior of a vicinal face growing from solution flowing normal to the steps and periodically changing its direction in time was considered theoretically. It was found that this oscillating flow reduces both stabilization and destabilization effects resulted from the unidirectional solution flow directed up the step stream and down the step stream. This reduction of stabilization and destabilization comes from effective mixing which entangles the phase shifts between the spatially periodic interface perturbation and the concentration wave induced by this perturbation. Numerical results and simplified mixing criterion will be discussed.

Chernov, Alex A.↗

NASA NTRS2014

Dissertation Defense: Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional validation by test only mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions.Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations. This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System spacecraft system.Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

Fluid Dynamics↗

NASA NTRS2014

Dissertation Defense Computational Fluid Dynamics Uncertainty Analysis for Payload Fairing Spacecraft Environmental Control Systems

Spacecraft thermal protection systems are at risk of being damaged due to airflow produced from Environmental Control Systems. There are inherent uncertainties and errors associated with using Computational Fluid Dynamics to predict the airflow field around a spacecraft from the Environmental Control System. This paper describes an approach to quantify the uncertainty in using Computational Fluid Dynamics to predict airflow speeds around an encapsulated spacecraft without the use of test data. Quantifying the uncertainty in analytical predictions is imperative to the success of any simulation-based product. The method could provide an alternative to traditional "validation by test only" mentality. This method could be extended to other disciplines and has potential to provide uncertainty for any numerical simulation, thus lowering the cost of performing these verifications while increasing the confidence in those predictions. Spacecraft requirements can include a maximum airflow speed to protect delicate instruments during ground processing. Computational Fluid Dynamics can be used to verify these requirements; however, the model must be validated by test data. This research includes the following three objectives and methods. Objective one is develop, model, and perform a Computational Fluid Dynamics analysis of three (3) generic, non-proprietary, environmental control systems and spacecraft configurations. Several commercially available and open source solvers have the capability to model the turbulent, highly three-dimensional, incompressible flow regime. The proposed method uses FLUENT, STARCCM+, and OPENFOAM. Objective two is to perform an uncertainty analysis of the Computational Fluid Dynamics model using the methodology found in "Comprehensive Approach to Verification and Validation of Computational Fluid Dynamics Simulations". This method requires three separate grids and solutions, which quantify the error bars around Computational Fluid Dynamics predictions. The method accounts for all uncertainty terms from both numerical and input variables. Objective three is to compile a table of uncertainty parameters that could be used to estimate the error in a Computational Fluid Dynamics model of the Environmental Control System /spacecraft system. Previous studies have looked at the uncertainty in a Computational Fluid Dynamics model for a single output variable at a single point, for example the re-attachment length of a backward facing step. For the flow regime being analyzed (turbulent, three-dimensional, incompressible), the error at a single point can propagate into the solution both via flow physics and numerical methods. Calculating the uncertainty in using Computational Fluid Dynamics to accurately predict airflow speeds around encapsulated spacecraft in is imperative to the success of future missions.

CFD↗

NASA NTRS1950

Hydrodynamic Properties of Planing Surfaces and Flying Boats

The study of the hydrodynamic properties of planing bottom of flying boats and seaplane floats is at the present time based exclusively on the curves of towing tests conducted in tanks. In order to provide a rational basis for the test procedure in tanks and practical design data, a theoretical study must be made of the flow at the step and relations derived that show not only qualitatively but quantitatively the inter-relations of the various factors involved. The general solution of the problem of the development of hydrodynamic forces during the motion of the seaplane float or flying boat is very difficult for it is necessary to give a three-dimensional solution, which does not always permit reducing the analysis to the form of workable computation formulas. On the other had, the problem is complicated by the fact that the object of the analysis is concerned with two fluid mediums, namely, air and water, which have a surface of density discontinuity between them. The theoretical and experimental investigations on the hydrodynamics of a ship cannot be completely carried over to the design of floats and flying-boat hulls, because of the difference in the shape of the contour lines of the bodies, and, because of the entirely different flow conditions from the hydrodynamic viewpoint.

Sokolov, N. A.↗

NASA NTRS1991

Computation of three-dimensional flows using two stream functions

An approach to compute 3-D flows using two stream functions is presented. The method generates a boundary fitted grid as part of its solution. Commonly used two steps for computing the flow fields are combined into a single step in the present approach: (1) boundary fitted grid generation; and (2) solution of Navier-Stokes equations on the generated grid. The presented method can be used to directly compute 3-D viscous flows, or the potential flow approximation of this method can be used to generate grids for other algorithms to compute 3-D viscous flows. The independent variables used are chi, a spatial coordinate, and xi and eta, values of stream functions along two sets of suitably chosen intersecting stream surfaces. The dependent variables used are the streamwise velocity, and two functions that describe the stream surfaces. Since for a 3-D flow there is no unique way to define two sets of intersecting stream surfaces to cover the given flow, different types of two sets of intersecting stream surfaces are considered. First, the metric of the (chi, xi, eta) curvilinear coordinate system associated with each type is presented. Next, equations for the steady state transport of mass, momentum, and energy are presented in terms of the metric of the (chi, xi, eta) coordinate system. Also included are the inviscid and the parabolized approximations to the general transport equations.

Greywall, Mahesh S.↗

NASA NTRS1961

Static Longitudinal Stability of a Rocket Vehicle Having a Rear-Facing Step Ahead of the Stabilizing Fins

Tests were conducted at Mach numbers of 3.96 and 4.65 in the Langley Unitary Plan wind tunnel to determine the static longitudinal stability characteristics of a fin-stabilized rocket-vehicle configuration which had a rearward facing step located upstream of the fins. Two fin sizes and planforms, a delta and a clipped delta, were tested. The angle of attack was varied from 6 deg to -6 deg and the Reynolds number based on model 6 length was about 10 x 10. The configuration with the larger fins (clipped delta) had a center of pressure slightly rearward of and an initial normal-force-curve slope slightly higher than that of the configuration with the smaller fins (delta) as would be expected. Calculations of the stability parameters gave a slightly lower initial slope of the normal-force curve than measured data, probably because of boundary-layer separation ahead of the step. The calculated center of pressure agreed well with the measured data. Measured and calculated increments in the initial slope of the normal-force curve and in the center of pressure, due to changing fins, were in excellent agreement indicating that separated flow downstream of the step did not influence flow over the fins. This result was consistent with data from schlieren photographs.

Keynton, Robert J.↗

NASA NTRSDate not supplied

A Preliminary Assessment of Step Effects on the BOLT Geometry in Mach 6 Flow

An infrared thermography measurement technique has been installed in the Langley Aerothermodynamic Laboratory. The system is calibrated for use with commercially available thermoplastics and ceramic materials, and to the surface temperature ranges when exposed to the facility hypersonic flow. Herein an uncertainty quantification is performed, revealing 5% surface temperature and 20% heat transfer uncertainty bands to two-sigma confidence. As a first application of the test measurement technique, an investigation was conducted to explore the correlation between the height of forward facing (FF) and rearward facing (RF) two-dimensional steps, free stream Reynolds number, and the onset of boundary layer transition from laminar to turbulent in Mach 6 flow on a 50% scale Boundary Layer Transition (BOLT) flight test vehicle geometry. Computational predictions were generated to identify potential x/L locations of transition onset for various flow conditions with a smooth outer mold line geometry and are compared to experimental results. The BOLT Step Test was conducted in the NASA Langley Aerothermodynamic Laboratory 20-inch Mach 6 wind tunnel at Reynolds numbers between 1.4 and 11.3 million conditions for various step heights. Data were collected using a developmental infrared thermography test technique and reduced to heat transfer for comparison with CFD solutions. This is a preliminary assessment of the developmental infrared thermography test technique used to acquire and reduce the experimental data. insight into the ongoing comparative analysis of the effects of FF and RF steps on boundary layer transition for the BOLT geometry in Mach 6 flow.

BOLT↗