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NASA NTRS2015

TPSAS-NF1676L-22800-DND

This lecture will provide an overview of an advanced turbulence closure scheme used in cloud-resolving models (CRMs) and climate modeling effort with the superparameterization approach. The CRM is embedded into each atmospheric column of a climate model as a super parameterization. It replaces the traditional subgrid-scale physical parameterizations in a conventional climate model. Two sensitivity simulations with doubling of CO2 and an increase of sea surface temperature, respectively, are performed and compared to similar simulations without this advanced turbulence closure in CRM to better understand the role of low-level clouds in climate sensitivity.

Kuan-Man Xu↗

NASA NTRS1995

Classical closure theory and Lam's interpretation of epsilon-RNG

Lam's phenomenological epsilon-renormalization group (RNG) model is quite different from the other members of that group. It does not make use of the correspondence principle and the epsilon-expansion procedure. We demonstrate that Lam's epsilon-RNG model is essentially the physical space version of the classical closure theory in spectral space and consider the corresponding treatment of the eddy viscosity and energy backscatter.

Zhou, YE↗

NASA NTRS1995

Applications of direct numerical simulation of turbulence in second order closures

This paper discusses two methods of developing models for the rapid pressure-strain correlation term in the Reynolds stress transport equation using direct numerical simulation (DNS) data. One is a perturbation about isotropic turbulence, the other is a perturbation about two-component turbulence -- an extremely anisotropic turbulence. A model based on the latter method is proposed and is found to be very promising when compared with DNS data and other models.

Shih, Tsan-Hsing↗

NASA NTRS1992

The evolution equation for the flame surface density in turbulent premixed combustion

One central ingredient in flamelet models for turbulent premixed combustion is the flame surface density. This quantity conveys most of the effects of the turbulence on the rate of energy release and is obtained via a modeled transport equation, called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact, but unclosed, formulation for the turbulent Sigma-equation. In this exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the flame surface density and the turbulent flame stretch are not available from experiments and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the obvious, complementary approach to get basic information on these fundamental quantities. Three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, the effects of the Lewis number on the rate of production of flame surface area are described in great detail and meaningful comparisons with flamelet models can be performed. The analysis reveals in particular the tendency of the models to overpredict flame surface dissipation as well as their inability to reproduce variations due to thermo-diffusive phenomena. Thanks to the detailed information produced by a DNS-based analysis, this type of comparison not only underscores the shortcomings of current models but also suggests ways to improve them.

Trouve, A.↗

NASA NTRS1993

The evolution equation for the flame surface density in turbulent premixed combustion

The mean reaction rate in flamelet models for turbulent premixed combustion depends on two basic quantities: a mean chemical rate, called the flamelet speed, and the flame surface density. Our previous work had been primarily focused on the problem of the structure and topology of turbulent premixed flames, and it was then determined that the flamelet speed, when space-averaged, is only weakly sensitive to the turbulent flow field. Consequently, the flame surface density is the key quantity that conveys most of the effects of the turbulence on the rate of energy release. In flamelet models, this quantity is obtained via a modeled transport equation called the Sigma-equation. Past theoretical work has produced a rigorous approach that leads to an exact but unclosed formulation for the turbulent Sigma-equation. In the exact Sigma-equation, it appears that the dynamical properties of the flame surface density are determined by a single parameter, namely the turbulent flame stretch. Unfortunately, the turbulent flame stretch as well as the flame surface density is not available from experiments, and, in the absence of experimental data, little is known on the validity of the closure assumptions used in current flamelet models. Direct Numerical Simulation (DNS) is the alternative approach to get basic information on these fundamental quantities. In the present work, three-dimensional DNS of premixed flames in isotropic turbulent flow is used to estimate the different terms appearing in the Sigma-equation. A new methodology is proposed to provide the source and sink terms for the flame surface density, resolved both temporally and spatially throughout the turbulent flame brush. Using this methodology, our objective is to extract the turbulent flame stretch from the DNS data base and then perform extensive comparisons with flamelet models. Thanks to the detailed information produced by the DNS-based analysis, it is expected that this type of comparison will not only underscore the shortcomings of current models, but also suggest ways to improve them.

Trouve, Arnaud↗

NASA NTRS1997

Testing and Implementation of Advanced Reynolds Stress Models

A research program was proposed for the testing and implementation of advanced turbulence models for non-equilibrium turbulent flows of aerodynamic importance that are of interest to NASA. Turbulence models that are being developed in connection with the Office of Naval Research ARI in Non-equilibrium are provided for implementation and testing in aerodynamic flows at NASA Langley Research Center. Close interactions were established with researchers at Nasa Langley RC and refinements to the models were made based on the results of these tests. The models that have been considered include two-equation models with an anisotropic eddy viscosity as well as full second-order closures. Three types of non-equilibrium corrections to the models have been considered in connection with the ARI on Nonequilibrium Turbulence: conducted for ONR.

Speziale, Charles G.↗

NASA NTRS2011

Short Wavelength Electromagnetic Perturbations Excited Near the Solar Probe Plus Spacecraft in the Inner Heliosphere: 2.5D Hybrid Modeling

A 2.5D numerical plasma model of the interaction of the solar wind (SW) with the Solar Probe Plus spacecraft (SPPSC) is presented. These results should be interpreted as a basic plasma model derived from the SW-interaction with the spacecraft (SC), which could have consequences for both plasma wave and electron plasma measurements on board the SC in the inner heliosphere. Compression waves and electric field jumps with amplitudes of about 1.5 V/m and (12-18) V/m were also observed. A strong polarization electric field was also observed in the wing of the plasma wake. However, 2.5D hybrid modeling did not show excitation of whistler/Alfven waves in the upstream connected with the bidirectional current closure that was observed in short-time 3D modeling SPPSC and near a tether in the ionosphere. The observed strong electromagnetic perturbations may be a crucial point in the electromagnetic measurements planned for the future Solar Probe Plus (SPP) mission. The results of modeling electromagnetic field perturbations in the SW due to shot noise in absence of SPPSC are also discussed.

Lipatov, Alexander S.↗

NASA NTRS2000

A Strip-Yield Model for Predicting the Growth of Part-Through Cracks Under Cyclic Loading

Flaws exist in aircraft structures due to manufacturing operations and material defects. Under variable amplitude cyclic loading, these flaws grow as part-through cracks reducing the residual strength of structural components. To meet damage tolerant design requirements, accurate flaw growth predictions are needed which account for continual changes in crack shape as well as crack growth retardation and acceleration. Predicting the growth of part-through cracks under cyclic loading using an innovative and computationally efficient model is the focus of the research summarized in this report. In this research effort, a slice synthesis methodology was developed and used to construct a modified strip-yield model for the part-through semi-elliptical surface flaw, enabling prediction of plasticity-induced closure along the crack front and subsequent fatigue crack growth under constant amplitude and variable amplitude loading. While modeling the plasticity-induced closure in a part-through flaw may be performed using three dimensional elastic-plastic finite element analysis, this type of effort is impractical from an engineering perspective. A modified strip-yield model similar to that used in FASTRAN for part-through flaws is a much needed engineering design tool, particularly when computational resources are limited.

Daniewicz, S. R.↗

NASA NTRS1993

Research activities at the Center for Modeling of Turbulence and Transition

The main research activities at the Center for Modeling of Turbulence and Transition (CMOTT) are described. The research objective of CMOTT is to improve and/or develop turbulence and transition models for propulsion systems. The flows of interest in propulsion systems can be both compressible and incompressible, three dimensional, bounded by complex wall geometries, chemically reacting, and involve 'bypass' transition. The most relevant turbulence and transition models for the above flows are one- and two-equation eddy viscosity models, Reynolds stress algebraic- and transport-equation models, pdf models, and multiple-scale models. All these models are classified as one-point closure schemes since only one-point (in time and space) turbulent correlations, such as second moments (Reynolds stresses and turbulent heat fluxes) and third moments, are involved. In computational fluid dynamics, all turbulent quantities are one-point correlations. Therefore, the study of one-point turbulent closure schemes is the focus of our turbulence research. However, other research, such as the renormalization group theory, the direct interaction approximation method, and numerical simulations are also pursued to support the development of turbulence modeling.

Shih, Tsan-Hsing↗

NASA NTRS1997

Remote Marine Aerosol: A Characterization of Physical, Chemical and Optical Properties and their Relation to Radiative Transfer in the Troposphere

Our research effort is focused on improving our understanding of aerosol properties needed for optical models for remote marine regions. This includes in-situ and vertical column optical closure and involves a redundancy of approaches to measure and model optical properties that must be self consistent. The model is based upon measured in-situ aerosol properties and will be tested and constrained by the vertically measured spectral differential optical depth of the marine boundary layer, MBL. Both measured and modeled column optical properties for the boundary layer, when added to the free-troposphere and stratospheric optical depth, will be used to establish spectral optical depth over the entire atmospheric column for comparison to and validation of satellite derived radiances (AVHRR).

Clarke, Antony D.↗

NASA NTRS1981

Computing aerodynamic sound using advanced statistical turbulence theories

It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability.

Hecht, A. M.↗

NASA NTRS1985

The closure problem for turbulence in meteorology and oceanography

The dependent variables used for computer based meteorological predictions and in plans for oceanographic predictions are wave number and frequency filtered values that retain only scales resolvable by the model. Scales unresolvable by the grid in use become 'turbulence'. Whether or not properly processed data are used for initial values is important, especially for sparce data. Fickian diffusion with a constant eddy diffusion is used as a closure for many of the present models. A physically realistic closure based on more modern turbulence concepts, especially one with a reverse cascade at the right times and places, could help improve predictions.

Pierson, W. J., Jr.↗

NASA NTRS2018

kL-based Linear and Nonlinear Two-Equation Turbulence Models

The development and implementation of kL-based Reynolds Average Navier-Stokes (RANS) two-equation turbulence models are reported herein. The kL is based on Abdol-Hamid's closure and Menter's modification to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's kL equation is well suited for term-by-term modeling and displays useful features compared to other scale formulation. One of the important differences is the inclusion of higher order velocity derivatives in the source terms of the scale equation. This can enhance the ability of RANS solvers to simulate unsteady flows in URANS mode. The present report documents the formulation of two model levels of turbulence models as implemented in the computational fluid dynamics FUN3D code. The levels are the two-equation linear k-kL and the two-equation algebraic Reynolds stress model (ARSM). Free shear, separated and corner flow cases are documented and compared with experimental, and other turbulence model data. The results show generally very good comparisons with experimental data. The results from this formulation are similar or better than results using the SST two-equation turbulence model. ARSM shows great promise with similar level of computational resources as basic two-equation turbulence models.

Abdol-Hamid, K. S.↗

NASA NTRS1986

Triple-velocity products in a channel with a backward-facing step

Attention is given to the evaluation of tripple velocity products in the reattaching and developing region behind a backward facing step. The change in tripple velocity products is significant in the wake region, yielding substantial variation in the diffusion rate of the Reynolds stresses. Four models of the third-order closure are examined, and the results are compared with the experimental data for Chandrsuda and Bradshaw (1980).

Amano, R. S.↗

NASA NTRS1987

Evaluation of a theory for pressure-strain rate

A theoretical expression for the slow part (the nonlinear fluctuation part) of the pressure-strain rate is compared with simulations of anisotropic homogeneous flows. The objective is to determine the quantitative accuracy of the theory and to test its prediction that the generalized Rotta coefficient, a non-dimensionalized ratio of slow term to the Reynolds stress anisotropy, varies with direction and can be negative. Comparisons are made between theoretical and simulation values of the slow term itself and of the generalized Rotta coefficients. The implications of the comparison for two-point closure theories and for Reynolds stress modeling are pointed out.

Weinstock, J.↗

NASA NTRS1989

Discussion of turbulence modelling: Past and future

The full text of a paper presented at the Whither Turbulence Workshop (Cornell University, March 22-24, 1989) on past and future trends in turbulence modeling is provided. It is argued that Reynolds stress models are likely to remain the preferred approach for technological applications for at least the next few decades. In general agreement with the Launder position paper, it is further argued that among the variety of Reynolds stress models in use, second-order closures constitute by far the most promising approach. However, some needed improvements in the specification of the turbulent length scale are emphasized. The central points of the paper are illustrated by examples from homogeneous turbulence.

Speziale, Charles G.↗

NASA NTRS1990

Fatigue crack growth in unidirectional metal matrix composite

The weight function method was used to determine the effective stress intensity factor and the crack opening profile for a fatigue tested composite which exhibited fiber bridging. The bridging mechanism was modeled using two approaches; the crack closure approach and the shear lag approach. The numerically determined stress intensity factor values from both methods were compared and correlated with the experimentally obtained crack growth rates for SiC/Ti-15-3 (0)(sub 8) oriented composites. The near crack tip opening profile was also determined for both methods and compared with the experimentally obtained measurements.

Ghosn, Louis J.↗

NASA NTRS1991

Computational study of the aerodynamics and control by blowing of asymmetric vortical flows over delta wings

Some of the work is described which was done in a study of the flow field produced by tangential leading edge blowing on a 60 deg. delta wing. The flow is studied computationally by solving the Thin Layer Navier-Stokes equations. Steady state flow fields are calculated for various angles of attack and yaw, with and without the presence of tangential leading edge blowing. The effectiveness of blowing as a rolling moment control mechanism to extend the envelope of controllability is illustrated at pre- and post-stall angles of attack. The numerical grid is generated using algebraic grid generation and various interpolation and blending techniques. The jet emanates from a slot with linearly varying thickness and is introduced into the flow field using the concept of an actuator plane, thereby not requiring resolution of the jet slot geometry. The Baldwin-Lomax algebraic turbulence model is used to provide turbulent closure. The computational results are compared with those of experiments.

Craig, Ken↗