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NASA NTRS2001

Modeling of Convective-Stratiform Precipitation Processes: Sensitivity to Partitioning Methods and Numerical Advection Schemes

Six different convective-stratiform separation techniques, including a new technique that utilizes the ratio of vertical and terminal velocities, are compared and evaluated using two-dimensional numerical simulations of a tropical [Tropical Ocean Global Atmosphere Coupled Ocean-Atmosphere Response Experiment (TOGA COARE)] and midlatitude continental [Preliminary Regional Experiment for STORM-Central (PRESTORM)] squall line. The simulations are made using two different numerical advection schemes: 4th order and positive definite advection. Comparisons are made in terms of rainfall, cloud coverage, mass fluxes, apparent heating and moistening, mean hydrometeor profiles, CFADs (Contoured Frequency with Altitude Diagrams), microphysics, and latent heating retrieval. Overall, it was found that the different separation techniques produced results that qualitatively agreed. However, the quantitative differences were significant. Observational comparisons were unable to conclusively evaluate the performance of the techniques. Latent heating retrieval was shown to be sensitive to the use of separation technique mainly due to the stratiform region for methods that found very little stratiform rain. The midlatitude PRESTORM simulation was found to be nearly invariant with respect to advection type for most quantities while for TOGA COARE fourth order advection produced numerous shallow convective cores and positive definite advection fewer cells that were both broader and deeper penetrating above the freezing level.

Lang, Steve↗

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 NTRS2002

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

A stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

N.D. Sandham↗

NASA NTRS1995

A Numerical Investigation of the Burnett Equations Based on the Second Law

The Burnett equations have been shown to potentially violate the second law of thermodynamics. The objective of this investigation is to correlate the numerical problems experienced by the Burnett equations to the negative production of entropy. The equations have had a long history of numerical instability to small wavelength disturbances. Recently, Zhong corrected the instability problem and made solutions attainable for one dimensional shock waves and hypersonic blunt bodies. Difficulties still exist when attempting to solve hypersonic flat plate boundary layers and blunt body wake flows, however. Numerical experiments will include one-dimensional shock waves, quasi-one dimensional nozzles, and expanding Prandlt-Meyer flows and specifically examine the entropy production for these cases.

Comeaux, Keith A.↗

NASA NTRS2001

On the Numerical Study of Heavy Rainfall in Taiwan

Heavy rainfall events are frequently observed over the western side of the CMR (central mountain range), which runs through Taiwan in a north-south orientation, in a southwesterly flow regime and over the northeastern side of the CMR in a northeasterly flow regime. Previous studies have revealed the mechanisms by which the heavy rainfall events are formed. Some of them have examined characteristics of the heavy rainfall via numerical simulations. In this paper, some of the previous numerical studies on heavy rainfall events around Taiwan during the Mei-Yu season (May and June), summer (non-typhoon cases) and autumn will be reviewed. Associated mechanisms proposed from observational studies will be reviewed first, and then characteristics of numerically simulated heavy rainfall events will be presented. The formation mechanisms of heavy rainfall from simulated results and from observational analysis are then compared and discussed. Based on these previous modeling studies, we will also discuss what are the major observations and modeling processes which will be needed for understanding the heavy precipitation in the future.

Tao, Wei-Kuo↗

NASA NTRS2002

Numerical Simulation of Screech Tones from Supersonic Jets: Physics and Prediction

The objectives of this project are to: (1) perform a numerical simulation of the jet screech phenomenon; and (2) use the data of the simulations to obtain a better understanding of the physics of jet screech. The original grant period was for three years. This was extended at no cost for an extra year to allow the principal investigator time to publish the results. We would like to report that our research work and results (supported by this grant) have fulfilled both objectives of the grant. The following is a summary of the important accomplishments: (1) We have now demonstrated that it is possible to perform accurate numerical simulations of the jet screech phenomenon. Both the axisymmetric case and the fully three-dimensional case were carried out successfully. It is worthwhile to note that this is the first time the screech tone phenomenon has been successfully simulated numerically; (2) All four screech modes were reproduced in the simulation. The computed screech frequencies and intensities were in good agreement with the NASA Langley Research Center data; (3) The staging phenomenon was reproduced in the simulation; (4) The effects of nozzle lip thickness and jet temperature were studied. Simulated tone frequencies at various nozzle lip thickness and jet temperature were found to agree well with experiments; (5) The simulated data were used to explain, for the first time, why there are two axisymmetric screech modes and two helical/flapping screech modes; (6) The simulated data were used to show that when two tones are observed, they co-exist rather than switching from one mode to the other, back and forth, as some previous investigators have suggested; and (7) Some resources of the grant were used to support the development of new computational aeroacoustics (CAA) methodology. (Our screech tone simulations have benefited because of the availability of these improved methods.)

Tam, Christopher K. W.↗

NASA NTRS2001

Experimental and Numerical Investigation of Buoyancy Driven Convection During PDAMNA Thin Film Growth

This paper presents results from numerical simulations as well as laboratory experiments of buoyancy driven convection in an ampoule under varying heating and gravitational acceleration loadings. The modeling effort in this work resolves the large scale natural convective motion that occurs in the fluid during photodeposition of polydiacetelene films which is due to energy absorbed by the growth solution from a UV source. Consequently, the growth kinetics of the film are ignored in the model discussed here, and also a much simplified ampoule geometry is considered. The objective of this work is to validate the numerical prediction on the strength and structure of buoyancy driven convection that could occur under terrestrial conditions during nonlinear optical film growth. The validation is used to enable a reliable predictive capability on the nature and strength of the convective motion under low gravity conditions. The ampoule geometry is in the form of a parallelepiped with rectangular faces. The numerical results obtained from the solution to the Boussinesq equations show that natural convection will occur regardless of the orientation of the UV source with respect to the gravity vector. The least strong convective motion occurred with the UV beam directed at the top face of the parallelepiped. The strength of the convective motion was found to be almost linearly proportional to the total power of the UV source. Also, it was found that the strength of the convective motion decreased linearly with the gravity due to acceleration. The pattern of the convective flow on the other hand, depended on the source location.

Antar, Basil N.↗

NASA NTRS2002

Numerical Viscous Flow Analysis of an Advanced Semispan Diamond-Wing Model at High-Life Conditions

Turbulent Navier-Stokes computational results are presented for an advanced diamond wing semispan model at low speed, high-lift conditions. The numerical results are obtained in support of a wind-tunnel test that was conducted in the National Transonic Facility (NTF) at the NASA Langley Research Center. The model incorporated a generic fuselage and was mounted on the tunnel sidewall using a constant width standoff. The analyses include: (1) the numerical simulation of the NTF empty, tunnel flow characteristics; (2) semispan high-lift model with the standoff in the tunnel environment; (3) semispan high-lift model with the standoff and viscous sidewall in free air; and (4) semispan high-lift model without the standoff in free air. The computations were performed at conditions that correspond to a nominal approach and landing configuration. The wing surface pressure distributions computed for the model in both the tunnel and in free air agreed well with the corresponding experimental data and they both indicated small increments due to the wall interference effects. However, the wall interference effects were found to be more pronounced in the total measured and the computed lift, drag and pitching moment due to standard induced up-flow effects. Although the magnitudes of the computed forces and moment were slightly off compared to the measured data, the increments due the wall interference effects were predicted well. The numerical predictions are also presented on the combined effects of the tunnel sidewall boundary layer and the standoff geometry on the fuselage fore-body pressure distributions and the resulting impact on the overall configuration longitudinal aerodynamic characteristics.

Ghaffari, F.↗

NASA NTRS1994

Dynamics of Numerics and CFD

This lecture attempts to illustrate the basic ideas of how the recent advances in nonlinear dynamical systems theory (dynamics) can provide new insights into the understanding of numerical algorithms used in solving nonlinear differential equations (DEs). Examples will be given of the use of dynamics to explain unusual phenomena that occur in numerics. The inadequacy of the use of linearized analysis for the understanding of long time behavior of nonlinear problems will be illustrated, and the role of dynamics in studying the nonlinear stability, accuracy, convergence property and efficiency of using time- dependent approaches to obtaining steady-state numerical solutions in computational fluid dynamics (CFD) will briefly be explained.

Yee, H. C.↗

NASA NTRS2001

Adaptive Numerical Dissipation Controls for High Order Methods

A numerical scheme for direct numerical simulation of shock-turbulence interactions of high speed compressible flows would ideally not be significantly more expensive than the standard fourth or sixth-order compact or non-compact central differencing scheme. It should be possible to resolve all scales down to scales of order of the Kolmogorov scales of turbulence accurately and efficiently, while at the same time being able to capture steep gradients occurring at much smaller scales efficiently. The goal of this lecture is to review the progress and new development of the low dissipative high order shock-capturing schemes proposed by Yee et al. Comparison on the efficiency and accuracy of this class of schemes with spectral and the fifth-order WENO (weighted essentially nonoscillatory) scheme will be presented. A new approach to dynamically sense the appropriate amount of numerical dissipation to be added at each grid point using non-orthogonal wavelets will be discussed.

Yee, Helen C.↗

NASA NTRS2002

Two- and Three-Dimensional Numerical Experiments Representing Two Limiting Cases of an In-Line Pair of Finger Seal Components

The work presented here concerns the numerical development and simulation of the flow, pressure patterns and motion of a pair of fingers arranged behind each other and axially aligned in-line. The fingers represent the basic elemental component of a Finger Seal (FS) and form a tight seal around the rotor. Yet their flexibility allows compliance with rotor motion and in a passive-adaptive mode complies also with the hydrodynamic forces induced by the flowing fluid. While the paper does not treat the actual staggered configuration of a finger seal, the inline arrangement represents a first step towards that final goal. The numerical 2-D (axial-radial) and 3-D results presented herein were obtained using a commercial package (CFD-ACE+). Both models use an integrated numerical approach, which couples the hydrodynamic fluid model (Navier-Stokes based) to the solid mechanics code that models the compliance of the fingers.

Braun, M. J.↗

NASA NTRS2002

Numerical Modeling of Cavitating Venturi: A Flow Control Element of Propulsion System

In a propulsion system, the propellant flow and mixture ratio could be controlled either by variable area flow control valves or by passive flow control elements such as cavitating venturies. Cavitating venturies maintain constant propellant flowrate for fixed inlet conditions (pressure and temperature) and wide range of outlet pressures, thereby maintain constant, engine thrust and mixture ratio. The flowrate through the venturi reaches a constant value and becomes independent of outlet pressure when the pressure at throat becomes equal to vapor pressure. In order to develop a numerical model of propulsion system, it is necessary to model cavitating venturies in propellant feed systems. This paper presents a finite volume model of flow network of a cavitating venturi. The venturi was discretized into a number of control volumes and mass, momentum and energy conservation equations in each control volume are simultaneously solved to calculate one-dimensional pressure, density, and flowrate and temperature distribution. The numerical model predicts cavitations at the throat when outlet pressure was gradually reduced. Once cavitation starts, with further reduction of downstream pressure, no change in flowrate is found. The numerical predictions have been compared with test data and empirical equation based on Bernoulli's equation.

Majumdar, Alok↗

NASA NTRS2002

Simultaneous Laser Raman-rayleigh-lif Measurements and Numerical Modeling Results of a Lifted Turbulent H2/N2 Jet Flame in a Vitiated Coflow

An experiment and numerical investigation is presented of a lifted turbulent H2/N2 jet flame in a coflow of hot, vitiated gases. The vitiated coflow burner emulates the coupling of turbulent mixing and chemical kinetics exemplary of the reacting flow in the recirculation region of advanced combustors. It also simplifies numerical investigation of this coupled problem by removing the complexity of recirculating flow. Scalar measurements are reported for a lifted turbulent jet flame of H2/N2 (Re = 23,600, H/d = 10) in a coflow of hot combustion products from a lean H2/Air flame ((empty set) = 0.25, T = 1,045 K). The combination of Rayleigh scattering, Raman scattering, and laser-induced fluorescence is used to obtain simultaneous measurements of temperature and concentrations of the major species, OH, and NO. The data attest to the success of the experimental design in providing a uniform vitiated coflow throughout the entire test region. Two combustion models (PDF: joint scalar Probability Density Function and EDC: Eddy Dissipation Concept) are used in conjunction with various turbulence models to predict the lift-off height (H(sub PDF)/d = 7,H(sub EDC)/d = 8.5). Kalghatgi's classic phenomenological theory, which is based on scaling arguments, yields a reasonably accurate prediction (H(sub K)/d = 11.4) of the lift-off height for the present flame. The vitiated coflow admits the possibility of auto-ignition of mixed fluid, and the success of the present parabolic implementation of the PDF model in predicting a stable lifted flame is attributable to such ignition. The measurements indicate a thickened turbulent reaction zone at the flame base. Experimental results and numerical investigations support the plausibility of turbulent premixed flame propagation by small scale (on the order of the flame thickness) recirculation and mixing of hot products into reactants and subsequent rapid ignition of the mixture.

Cabra, R.↗

NASA NTRS2003

Development of Numerical Codes for Modeling Electromagnetic Behavior at High Frequencies Near Large Objects

A study into the problem of determining electromagnetic solutions at high frequencies for problems involving complex geometries, large sizes and multiple sources (e.g. antennas) has been initiated. Typical applications include the behavior of antennas (and radiators) installed on complex conducting structures (e.g. ships, aircrafts, etc..) with strong interactions between antennas, the radiation patterns, and electromagnetic signals is of great interest for electromagnetic compatibility control. This includes the overall performance evaluation and control of all on-board radiating systems, electromagnetic interference, and personnel radiation hazards. Electromagnetic computational capability exists at NASA LaRC, and many of the codes developed are based on the Moment Method (MM). However, the MM is computationally intensive, and this places a limit on the size of objects and structures that can be modeled. Here, two approaches are proposed: (i) a current-based hybrid scheme that combines the MM with Physical optics, and (ii) an Alternating Direction Implicit-Finite Difference Time Domain (ADI-FDTD) method. The essence of a hybrid technique is to split the overall scattering surface(s) into two regions: (a) a MM zone (MMZ) which can be used over any part of the given geometry, but is most essential over irregular and "non-smooth" geometries, and (b) a PO sub-region (POSR). Currents induced on the scattering and reflecting surfaces can then be computed in two ways depending on whether the region belonged to the MMZ or was part of the POSR. For the MMZ, the current calculations proceed in terms of basis functions with undetermined coefficients (as in the usual MM method), and the answer obtained by solving a system of linear equations. Over the POSR, conduction is obtained as a superposition of two contributions: (i) currents due to the incident magnetic field, and (ii) currents produced by the mutual induction from conduction within the MMZ. This effectively leads to a reduction in the size of linear equations from N to N - Npo with N being the total number of segments for the entire surface and Npo the number of segments over the POSR. The scheme would be appropriate for relatively large, flat surfaces, and at high frequencies. The ADI-FDTD scheme provides for both transient and steady state analyses. The restrictive Courant-Friedrich-Levy (CFL) condition on the time-step is removed, and so large time steps can be chosen even though the spatial grids are small. This report includes the problem definition, a detailed discussion of both the numerical techniques, and numerical implementations for simple surface geometries. Numerical solutions have been derived for a few simple situations.

Joshi, R. P.↗

NASA NTRS2004

Experimental and Numerical Correlation of Gravity Sag in Solar Sail Quality Membranes

Solar sails are among the most studied members of the ultra-lightweight and inflatable (Gossamer) space structures family due to their potential to provide propellentless propulsion. They are comprised of ultra-thin membrane panels that, to date, have proven very difficult to experimentally characterize and numerically model due to their reflectivity and flexibility, and the effects of gravity sag and air damping. Numerical models must be correlated with experimental measurements of sub-scale solar sails to verify that the models can be scaled up to represent full-sized solar sails. In this paper, the surface shapes of five horizontally supported 25 micron thick aluminized Kapton membranes were measured to a 1.0 mm resolution using photogrammetry. Several simple numerical models closely match the experimental data, proving the ability of finite element simulations to predict actual behavior of solar sails.

Black, Jonathan T.↗

NASA NTRS2004

Sensitivity of Simulated Warm Rain Formation to Collision and Coalescence Efficiencies, Breakup, and Turbulence: Comparison of Two Bin-Resolved Numerical Models

Numerical models that resolve cloud particles into discrete mass size distributions on an Eulerian grid provide a uniquely powerful means of studying the closely coupled interaction of aerosols, cloud microphysics, and transport that determine cloud properties and evolution. However, such models require many experimentally derived paramaterizations in order to properly represent the complex interactions of droplets within turbulent flow. Many of these parameterizations remain poorly quantified, and the numerical methods of solving the equations for temporal evolution of the mass size distribution can also vary considerably in terms of efficiency and accuracy. In this work, we compare results from two size-resolved microphysics models that employ various widely-used parameterizations and numerical solution methods for several aspects of stochastic collection.

Fridlind, Ann↗

NASA NTRS2005

3 Lectures: "Lagrangian Models", "Numerical Transport Schemes", and "Chemical and Transport Models"

The topics for the three lectures for the Canadian Summer School are Lagrangian Models, numerical transport schemes, and chemical and transport models. In the first lecture I will explain the basic components of the Lagrangian model (a trajectory code and a photochemical code), the difficulties in using such a model (initialization) and show some applications in interpretation of aircraft and satellite data. If time permits I will show some results concerning inverse modeling which is being used to evaluate sources of tropospheric pollutants. In the second lecture I will discuss one of the core components of any grid point model, the numerical transport scheme. I will explain the basics of shock capturing schemes, and performance criteria. I will include an example of the importance of horizontal resolution to polar processes. We have learned from NASA's global modeling initiative that horizontal resolution matters for predictions of the future evolution of the ozone hole. The numerical scheme will be evaluated using performance metrics based on satellite observations of long-lived tracers. The final lecture will discuss the evolution of chemical transport models over the last decade. Some of the problems with assimilated winds will be demonstrated, using satellite data to evaluate the simulations.

Anne Douglass↗

NASA NTRS1999

Common Analysis Tool Being Developed for Aeropropulsion: The National Cycle Program Within the Numerical Propulsion System Simulation Environment

The NASA Lewis Research Center is developing an environment for analyzing and designing aircraft engines-the Numerical Propulsion System Simulation (NPSS). NPSS will integrate multiple disciplines, such as aerodynamics, structure, and heat transfer, and will make use of numerical "zooming" on component codes. Zooming is the coupling of analyses at various levels of detail. NPSS uses the latest computing and communication technologies to capture complex physical processes in a timely, cost-effective manner. The vision of NPSS is to create a "numerical test cell" enabling full engine simulations overnight on cost-effective computing platforms. Through the NASA/Industry Cooperative Effort agreement, NASA Lewis and industry partners are developing a new engine simulation called the National Cycle Program (NCP). NCP, which is the first step toward NPSS and is its initial framework, supports the aerothermodynamic system simulation process for the full life cycle of an engine. U.S. aircraft and airframe companies recognize NCP as the future industry standard common analysis tool for aeropropulsion system modeling. The estimated potential payoff for NCP is a $50 million/yr savings to industry through improved engineering productivity.

Follen, Gregory J.↗