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NASA NTRS2000

Assimilation of (A) TOVS data at the NASA Goddard Data Assimilation Office

At the NASA Goddard Data Assimilation Office (DAO), a 1D variational radiance assimilation system has been developed. This system, called DAOTOVS (Tiros operational vertical sounder (TOVS)), uses (A)TOVS level 1b radiances. It has been implemented within the DAO's semi-operational system as well as within the next generation data assimilation system that uses a finite-volume dynamical core. We will show results from (A)TOVS assimilation, including stratospheric analyses and validation. We will also describe our systematic error correction scheme which is based on collocated radiosondes.

Joiner, Joanna↗
NASA NTRS2000

Remobilizing the Interfaces of Thermocapillary Driven Bubbles Retarded by the Adsorption of a Surfactant Impurity on the Bubble Surface

Thermocapillary migration is a method for moving bubbles in space in the absence of buoyancy. A temperature gradient is applied to the continuous phase in which a bubble is situated, and the applied gradient impressed on the bubble surface causes one pole of the drop to be cooler than the opposite pole. As the surface tension is a decreasing function of temperature, the cooler pole pulls at the warmer pole, creating a flow which propels the bubble in the direction of the warmer fluid. A major impediment to the practical use of thermocapillarity to direct the movement of bubbles in space is the fact that surfactant impurities which are unavoidably present in the continuous phase can significantly reduce the migration velocity. A surfactant impurity adsorbed onto the bubble interface is swept to the trailing end of the bubble. When bulk concentrations are low (which is the case with an impurity), diffusion of surfactant to the front end is slow relative to convection, and surfactant collects at the back end of the bubble. Collection at the back lowers the surface tension relative to the front end setting up a reverse tension gradient. For buoyancy driven bubble motions in the absence of a thermocapillarity, the tension gradient opposes the surface flow, and reduces the surface and terminal velocities (the interface becomes more solid-like). When thermocapillary forces are present, the reverse tension gradient set up by the surfactant accumulation reduces the temperature tension gradient, and decreases to near zero the thermocapillary velocity. The objective of our research is to develop a method for enhancing the thermocapillary migration of bubbles which have been retarded by the adsorption onto the bubble surface of a surfactant impurity, Our remobilization theory proposes to use surfactant molecules which kinetically rapidly exchange between the bulk and the surface and are at high bulk concentrations. Because the remobilizing surfactant is present at much higher concentrations than the impurity, it adsorbs to the bubble much faster than the impurity when the bubble is formed, and thereby prevents the impurity from adsorbing onto the surface. In addition the rapid kinetic exchange and high bulk concentration maintain a saturated surface with a uniform surface concentrations. This prevents retarding surface tension gradients and keeps the velocity high. In our first report last year, we detailed experimental results which verified the theory of remobilization in ground based experiments in which the steady velocity of rising bubbles was measured in a continuous phase consisting of a glycerol/water mixture containing a polyethylene glycol surfactant C12E6 (CH3(CH2)11(OCH2CH2)6OH). In our report this year, we detail our efforts to describe theoretically the remobilization observed. We construct a model in which a bubble rises steadily by buoyancy in a continuous (Newtonian) viscous fluid containing surfactant with a uniform far field bulk concentration. We account for the effects of inertia as well as viscosity in the flow in the continuous phase caused by the bubble motion (order one Reynolds number), and we assume that the bubble shape remains spherical (viscous and inertial forces are smaller than capillary forces, i e. small Weber and capillary numbers). The surfactant distribution is calculated by solving the mass transfer equations including convection and diffusion in the bulk, and finite kinetic exchange the bulk and the surface. Convective effects dominate diffusive mass transfer in the bulk of the liquid (high Peclet numbers) except in a thin boundary layer near the surface. A finite volume method is used to numerically solve the hydrodynamic and mass transfer equations on a staggered grid which accounts specifically for the thin boundary layer. We present the results of the nondimensional drag as a function of the bulk concentration of surfactant for different rates of kinetic exchange, from which we develop criteria for the concentration necessary to develop a prescribed degree of remobilization. The criteria compare favorably with the experimental results.

Palaparthi, Ravi↗
NASA NTRS2000

Using TRMM Field Campaign Data for Assessing GEOS Forecast and Assimilation Products

The wealth of in-situ measurements gathered during Tropical Rain Measuring Mission (TRMM) field campaigns over a wide range of tropical conditions constitute an important data source for evaluating the quality of global model forecasts and assimilated datasets. In this study we use selected observations of cloud microphysics and atmospheric sounding from TEFLUN-1998, SCEMEX-1998, and TRMMLBA-1999 to examine the assimilation and forecast fields produced by the operational GEOS-3 (Goddard Earth Observing System - version 3) global data assimilation system (DAS) and a new finite-volume DAS under development at the Data Assimilation Office. Additionally, TRMM field campaign measurements are used to verify the impact of assimilating rainfall and moisture data derived from TRMM Microwave Imager and Special Sensor Microwave/Imager instruments on the GEOS analysis. We will also explore issues concerning the 'error of representativeness' in using in-situ observations of quantities with large spatial and temporal variability such as precipitation for validating gridded global data products.

Hou, Arthur Y.↗
NASA NTRS2000

A Technique of Treating Negative Weights in WENO Schemes

High order accurate weighted essentially non-oscillatory (WENO) schemes have recently been developed for finite difference and finite volume methods both in structural and in unstructured meshes. A key idea in WENO scheme is a linear combination of lower order fluxes or reconstructions to obtain a high order approximation. The combination coefficients, also called linear weights, are determined by local geometry of the mesh and order of accuracy and may become negative. WENO procedures cannot be applied directly to obtain a stable scheme if negative linear weights are present. Previous strategy for handling this difficulty is by either regrouping of stencils or reducing the order of accuracy to get rid of the negative linear weights. In this paper we present a simple and effective technique for handling negative linear weights without a need to get rid of them.

Shi, Jing↗
NASA NTRS2001

Regional Climate Studies with Variable-Resolution Stretched-Grid GCMs

A variable resolution GCM using a global stretched grid with fine resolution over the area(s) of interest, is a viable new approach to regional and subregional climate studies and applications. It is an alternative to the widely used nested grid approach introduced a decade ago as a pioneering step in regional climate modeling. The first version of the SG-GCM based on the GEOS (Goddard Earth Observing System) GCM using a finite-difference approximation, has been developed and thoroughly tested during the last few years. Successful simulations have been performed with the SG-GCM for the anomalous regional climate events of the U.S. 1988 summer drought and 1993 summer flood. They have shown the practical feasibility of the SG-approach for regional climate modeling. The GEOS SG-DAS (Data Assimilation System) incorporating the SG-GCM has also been developed and tested. The assimilated regional fields and diagnostics are used for validating the SG-GCM regional simulations. Two new SG-GCMs are being developed. The first is the SG-version of the new NASANCAR FV-GCM (with the finite-volume (FV) dynamics), and the second is the SG-version of the new GCM with spectral-element dynamics. Both GCMs use the WAR CCM4 physics. Using these advanced numerics will provide increased computational efficiency for the new the SG-GCMs, and will allow us to employ more flexible stretching strategies beneficial for the efficient regional down-scaling. The major current developments are focused on: simulating the 1997-1999 (and beyond) ENSO cycle and related monsoonal circulations, with enhanced regional resolution; studying intraseasonal and interannual regional climate variability for the extended multiyear (AMIP-type) SG-GCM simulations; and studying the impact of ensemble integrations.

Fox-Rabinovitz, Michael↗
NASA NTRS2000

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗
NASA NTRS2001

Application of Aeroelastic Solvers Based on Navier Stokes Equations

The propulsion element of the NASA Advanced Subsonic Technology (AST) initiative is directed towards increasing the overall efficiency of current aircraft engines. This effort requires an increase in the efficiency of various components, such as fans, compressors, turbines etc. Improvement in engine efficiency can be accomplished through the use of lighter materials, larger diameter fans and/or higher-pressure ratio compressors. However, each of these has the potential to result in aeroelastic problems such as flutter or forced response. To address the aeroelastic problems, the Structural Dynamics Branch of NASA Glenn has been involved in the development of numerical capabilities for analyzing the aeroelastic stability characteristics and forced response of wide chord fans, multi-stage compressors and turbines. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading is available. To obtain the steady and unsteady aerodynamic forces for the complex flows around the engine components, for the flow regimes encountered by the rotor, an advanced compressible Navier-Stokes solver is required. A finite volume based Navier-Stokes solver has been developed at Mississippi State University (MSU) for solving the flow field around multistage rotors. The focus of the current research effort, under NASA Cooperative Agreement NCC3- 596 was on developing an aeroelastic analysis code (entitled TURBO-AE) based on the Navier-Stokes solver developed by MSU. The TURBO-AE code has been developed for flutter analysis of turbomachine components and delivered to NASA and its industry partners. The code has been verified. validated and is being applied by NASA Glenn and by aircraft engine manufacturers to analyze the aeroelastic stability characteristics of modem fans, compressors and turbines.

Keith, Theo G., Jr.↗
NASA NTRS1994

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

Pandya, S. A.↗
NASA NTRS2001

Linearized Unsteady Aerodynamic Analysis of the Acoustic Response to Wake/Blade-Row Interaction

The three-dimensional, linearized Euler analysis, LINFLUX, is being developed to provide a comprehensive and efficient unsteady aerodynamic scheme for predicting the aeroacoustic and aeroelastic responses of axial-flow turbomachinery blading. LINFLUX couples a near-field, implicit, wave-split, finite-volume solution to far-field acoustic eigensolutions, to predict the aerodynamic responses of a blade row to prescribed structural and aerodynamic excitations. It is applied herein to predict the acoustic responses of a fan exit guide vane (FEGV) to rotor wake excitations. The intent is to demonstrate and assess the LINFLUX analysis via application to realistic wake/blade-row interactions. Numerical results are given for the unsteady pressure responses of the FEGV, including the modal pressure responses at inlet and exit. In addition, predictions for the modal and total acoustic power levels at the FEGV exit are compared with measurements. The present results indicate that the LINFLUX analysis should be useful in the aeroacoustic design process, and for understanding the three-dimensional flow physics relevant to blade-row noise generation and propagation.

Verdon, Joseph M.↗
NASA NTRS2000

Numerical Solutions to the Third CAA Workshop Benchmark Problems

This paper presents numerical solutions to the problems of propagation of sound waves through a transonic nozzle, shock-sound interactions, and automobile noise involving feedback of the third NASA Computational Aeroacoustics (CAA) Workshop on benchmark problems. The numerical algorithm is based on a dual time scheme for temporal discretization and a third-order finite volume scheme for spatial discretization. The aims of this study are to apply a dual time stepping scheme to treat aeroacoustic problems of sound propagation and to validate our CAA solver with the benchmark problems for developing a numerical tool for noise analysis and control.

Loh, Roy H.↗
NASA NTRS2001

Heat Transfer in Adhesively Bonded Honeycomb Core Panels

The Swann and Pittman semi-empirical relationship has been used as a standard in aerospace industry to predict the effective thermal conductivity of honeycomb core panels. Recent measurements of the effective thermal conductivity of an adhesively bonded titanium honeycomb core panel using three different techniques, two steady-state and one transient radiant step heating method, at four laboratories varied significantly from each other and from the Swann and Pittman predictions. Average differences between the measurements and the predictions varied between 17 and 61% in the temperature range of 300 to 500 K. In order to determine the correct values of the effective thermal conductivity and determine which set of the measurements or predictions were most accurate, the combined radiation and conduction heat transfer in the honeycomb core panel was modeled using a finite volume numerical formulation. The transient radiant step heating measurements provided the best agreement with the numerical results. It was found that a modification of the Swann and Pittman semi-empirical relationship which incorporated the facesheets and adhesive layers in the thermal model provided satisfactory results. Finally, a parametric study was conducted to investigate the influence of adhesive thickness and thermal conductivity on the overall heat transfer through the panel.

Daryabeigi, Kamran↗
NASA NTRS2001

Thermal Analysis and Design of Multi-layer Insulation for Re-entry Aerodynamic Heating

The combined radiation/conduction heat transfer in high-temperature multi-layer insulations was modeled using a finite volume numerical model. The numerical model was validated by comparison with steady-state effective thermal conductivity measurements, and by transient thermal tests simulating re-entry aerodynamic heating conditions. A design of experiments technique was used to investigate optimum design of multi-layer insulations for re-entry aerodynamic heating. It was found that use of 2 mm foil spacing and locating the foils near the hot boundary with the top foil 2 mm away from the hot boundary resulted in the most effective insulation design. A 76.2 mm thick multi-layer insulation using 1, 4, or 16 foils resulted in 2.9, 7.2, or 22.2 percent mass per unit area savings compared to a fibrous insulation sample at the same thickness, respectively.

Daryabeigi, Kamran↗
NASA NTRS2001

Effective Thermal Conductivity of High Porosity Open Cell Nickel Foam

The effective thermal conductivity of high-porosity open cell nickel foam samples was measured over a wide range of temperatures and pressures using a standard steady-state technique. The samples, measuring 23.8 mm, 18.7 mm, and 13.6 mm in thickness, were constructed with layers of 1.7 mm thick foam with a porosity of 0.968. Tests were conducted with the specimens subjected to temperature differences of 100 to 1000 K across the thickness and at environmental pressures of 10(exp -4) to 750 mm Hg. All test were conducted in a gaseous nitrogen environment. A one-dimensional finite volume numerical model was developed to model combined radiation/conduction heat transfer in the foam. The radiation heat transfer was modeled using the two-flux approximation. Solid and gas conduction were modeled using standard techniques for high porosity media. A parameter estimation technique was used in conjunction with the measured and predicted thermal conductivities at pressures of 10(exp -4) and 750 mm Hg to determine the extinction coefficient, albedo of scattering, and weighting factors for modeling the conduction thermal conductivity. The measured and predicted conductivities over the intermediate pressure values differed by 13%.

Sullins, Alan D.↗
NASA NTRS1998

Computational Investigation and Validation of Twin-Tail Buffet Response Including Dynamics and Control

Multidisciplinary tools for prediction of single rectangular-tail buffet are extended to single swept-back-tail buffet in transonic-speed flow, and multidisciplinary tools for prediction and control of twin-tail buffet are developed and presented. The configuration model consists of a sharp-edged delta wing with single or twin tails that are oriented normal to the wing surface. The tails are treated as cantilevered beams fixed at the root and allowed to oscillate in both bending and torsion. This complex multidisciplinary problem is solved sequentially using three sets of equations on a dynamic single or multi-block grid structure. The first set is the unsteady, compressible, Reynolds-averaged Navier-Stokes equations which are used for obtaining the flow field vector and the aerodynamic loads on the tails. The Navier-Stokes equations are solved accurately in time using the implicit, upwind, flux-difference splitting, finite volume scheme. The second set is the coupled bending and torsion aeroelastic equations of cantilevered beams which are used for obtaining the bending and torsion deflections of the tails. The aeroelastic equations'are solved accurately in time using, a fifth-order-accurate Runge-Kutta scheme. The third set is the grid-displacement equations and the rigid-body dynamics equations, which are used for updating the grid coordinates due to the tail deflections and rigid-body motions. The tail-buffet phenomenon is predicted for highly-swept, single vertical tail placed at the plane of geometric symmetry, and for highly-swept, vertical twin tails placed at three different spanwise separation distances. The investigation demonstrates the effects of structural inertial coupling and uncoupling of the bending and torsion modes of vibration, spanwise positions of the twin-tail, angle of attack, and pitching and rolling dynamic motions of the configuration model on the tail buffet loading and response. The fundamental issue of twin-tail buffet alleviation is addressed using two active flow-control methods. These methods are the tangential leading-edge blowing and the flow suction from the leading-edge vortex cores along their paths. Qualitative and quantitative comparisons with the available experimental data are presented. The comparisons indicate that the present multidisciplinary aeroelastic analysis tools are robust, accurate and efficient.

Kandil, Osama A.↗
NASA NTRS2001

Distributed Relaxation for Conservative Discretizations

A multigrid method is defined as having textbook multigrid efficiency (TME) if the solutions to the governing system of equations are attained in a computational work that is a small (less than 10) multiple of the operation count in one target-grid residual evaluation. The way to achieve this efficiency is the distributed relaxation approach. TME solvers employing distributed relaxation have already been demonstrated for nonconservative formulations of high-Reynolds-number viscous incompressible and subsonic compressible flow regimes. The purpose of this paper is to provide foundations for applications of distributed relaxation to conservative discretizations. A direct correspondence between the primitive variable interpolations for calculating fluxes in conservative finite-volume discretizations and stencils of the discretized derivatives in the nonconservative formulation has been established. Based on this correspondence, one can arrive at a conservative discretization which is very efficiently solved with a nonconservative relaxation scheme and this is demonstrated for conservative discretization of the quasi one-dimensional Euler equations. Formulations for both staggered and collocated grid arrangements are considered and extensions of the general procedure to multiple dimensions are discussed.

Diskin, Boris↗
NASA NTRS2001

Computational Analyses of Propulsion Aeroacoustics for Mixed Flow Nozzle Pylon Installation at Takeoff

A CFD analyses is presented for a set of baseline and noise suppression mixed flow nozzles with and without a pylon installation. The five model configurations are as follows; a baselinecore/fan dual-stream nozzle with an external plug, a chevron mixer nozzle with a peak on the symmetry plane with external plug, both of the above nozzles with an installed bifurcatingpylon and lastly a clocked chevron mixer nozzle such that a trough is aligned with the center of the pylon. The fluid flow is simulated by solving the asymptotically steady, compressible, Reynolds-averaged Navier-Stokes equations using an implicit, up-wind, flux-difference splitting finite volume scheme and standard two equation k-epsilon turbulence model with a linear stress representation. All computations are performed using the multiblock, parallel, structuredcode PAB3D. Results indicate that the clocked chevron with pylon case achieves the most optimal levels of average and peak turbulence kinetic energy and vorticity and therefore is expected to be the quietest of the five configurations tested. Further study is required to refine expressions which are indicative of noise and mate these with rigorous noise prediction models.

Massey, Steven J.↗
NASA NTRS1994

Navier-Stokes Solutions of Rotor and Rotor-Body Flows

This paper will review the advances made recently in the Navier-Stokes CFD methods to simulate aerodynamics and aeroacoustics of helicopter rotors and rotor-body flows. Although a complete flowfield simulation of full helicopter is currently not feasible with these methods, impressive gains have been made in analyzing individual components of this complex problem in a very detailed manner. The use of the state-of-the-art numerical algorithms in solution methods, in conjunction with powerful supercomputers, like the Cray-2, have enabled noticeable progress to be made in modeling viscous-inviscid interactions, blade-vortex interactions, tip-vortex: simulation and wake effects, as well as high speed impulsive noise in hover and forward flight for isolated rotor blades. This paper will critically evaluate the presently available Euler and Navier-Stokes methods, both finite-difference and finite volume methods using structured and unstructured grids for helicopter applications for accuracy, suitability, and computational efficiency. The review will also include the recent progress made using overset grids to model rotor-body flows. All the material for this review will be drawn from the published material shown below.

Srinivasan, G. R.↗
NASA NTRS1994

The Monostatic/Bistatic Approximation

Many Radar Cross Section (RCS) prediction codes are limited to one monostatic return per run. However, such codes can calculate multiple bistatic returns per incident angle for a relatively small amount of additional computer resources. This note describes a method of using bistatic returns to generate multiple monostatic predictions for each incident angle computed. Typical results are presented and show the accuracy is initially good and then degrades as the separation angle between the incident and viewing angles becomes large. Introduction Since 1990, the monostatic/bistatic approximation has been used to reduce the number of runs required by finite-volume time-domain (FVTD) codes for making RCS versus azimuth plots. This approximation was spawned by the observation of a range test where the transmit and receive antennas were separated by a few degrees to prevent cross talk between the antennas. The measurements from this range are presented as monostatic RCS rather than bistatic: RCS. The procedure of reporting experimental bistatic RCS as the monostatic RCS at the angle bisecting the transmit and receive antennas was extended to FVTD codes and produces excellent results.

Schuh, Michael J.↗