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NASA NTRS1988

Turbulent viscosity

A model for fully developed turbulence is proposed whose predictions compare favorably with those of the direct interaction approximation (DIA) model and whose main equations are easy to handle. Four different expressions for the turbulent viscosity are derived which contain no free parameters. Two of the expressions are given in terms of properties of the turbulent fluid itself; the other two are given in terms of the instability that generated the turbulence and of the properties of the mean flow. The numerical coefficients entering these relations are evaluated and found to be in good agreement with previous theoretical estimates based on Kraichnan's DIA, the renormalization group method, and turbulence modeling. In the case of shear in the mean flow, the Shakura-Sunyaev alpha parameter is shown to be less than 0.01. The four expressions can be generalized to include the effect of rotation and/or magnetic fields.

Canuto, V. M.↗
NASA NTRS1988

Anharmonic and screening corrections to the melting of a two-dimensional charged colloidal crystal

The Kosterlitz-Thouless-Halperin-Nelson-Young theory of melting is applied to a two-dimensional charged colloidal crystal. The renormalization of elastic constants due to anharmonic and dislocation pair-screening effects is calculated. For colloidal spheres ('polyballs') suspended in a thin film of water confined between two glass plates whose surfaces are highly charged, as in recent experimental configurations, the corrections to the harmonic results simply require an altered effective polyball charge to reproduce virtually the identical melting curve of the harmonic approximation (which agrees well with experiment). The effect on the melting curve of added salt is also calculated; the corresponding experiments have yet to be performed. For a film between uncharged surfaces the anharmonic correction again softens the lattice significantly. Dislocation pair screening causes an additional but minor reduction of the elastic constants. Neither correction eliminates a nonmelting behavior characteristic of the two-dimensional screened Coulomb system in this configuration.

Chang, Enson↗
NASA NTRS1989

Quantization effects in Viterbi decoding rate 1/n convolutional codes

A Viterbi decoder's performance loss due to quantizing data from the additive white Gaussian noise (AWGN) channel is studied. An optimal quantization scheme and branch metric calculation method are presented. The uniformly quantized channel capacity C(sub u)(q) is used to determine the smallest number of quantization bits q that does not cause a significant loss. The quantizer stepsize which maximizes C(sub u)(q) almost minimizes the decoder bit error rate (BER). However, a slightly larger stepsize is better, like the value that minimizes the Bhattacharyya bound. The range and renormalization of state metrics is analyzed, in particular for K = 15 decoders such as the Big Viterbi Decoder (BVD) for the Galileo mission. These results are required to design reduced hardware complexity Viterbi decoders with a negligible quantization loss.

Onyszchuk, I. M.↗
NASA NTRS1990

Classical theory of radiating strings

The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.

Copeland, Edmund J.↗
NASA NTRS1990

Charge transfer polarisation wave and carrier pairing in the high T(sub c) copper oxides

The High T(sub c) oxides are highly polarizable materials and are charge transfer insulators. The charge transfer polarization wave formalism is developed in these oxides. The dispersion relationships due to long range dipole-dipole interaction of a charge transfer dipole lattice are obtained in 3-D and 2-D. These are high frequency bosons and their coupling with carriers is weak and antiadiabatic in nature. As a result, the mass renormalization of the carriers is negligible in complete contrast to conventional electron-phonon interaction, that give polarons and bipolarons. Both bound and superconducting pairing is discussed for a model Hamiltonian valid in the antiadiabatic regime, both in 3-D and 2-D. The stability of the charge transfer dipole lattice has interesting consequences that are discussed.

Chakraverty, B. K.↗
NASA NTRS1990

Cascade model for fluvial geomorphology

Erosional landscapes are generally scale invariant and fractal. Spectral studies provide quantitative confirmation of this statement. Linear theories of erosion will not generate scale-invariant topography. In order to explain the fractal behavior of landscapes a modified Fourier series has been introduced that is the basis for a renormalization approach. A nonlinear dynamical model has been introduced for the decay of the modified Fourier series coefficients that yield a fractal spectra. It is argued that a physical basis for this approach is that a fractal (or nearly fractal) distribution of storms (floods) continually renews erosional features on all scales.

Newman, W. I.↗
NASA NTRS1990

Absence of first-order unbinding transitions of fluid and polymerized membranes

Unbinding transitions of fluid and polymerized membranes are studied by renormalization-group (RG) methods. Two different RG schemes are used and found to give rather consistent results. The fixed-point structure of both RG's exhibits a complex behavior as a function of the decay exponent tau for the fluctuation-induced interaction of the membranes. For tau greater than tau(S2) interacting membranes can undergo first-order transitions even in the strong-fluctuation regime. These estimates for tau(S2) imply, however, that both fluid and polymerized membranes unbind in a continuous way in the absence of lateral tension.

Grotehans, Stefan↗
NASA NTRS1990

Deformation effects of droplet fluctuations on dynamics in an Ising ferromagnetic state

Deformation effects of droplet fluctuations on the dynamics in an Ising ferromagnetic state in two dimensions are studied in the case of an order-parameter-nonconserving system by investigating an equation of motion for a domain boundary. Analytic and numerical studies show that the deformation effects on the survival probability of the droplets simply result in changing the time scale or renormalizing a kinetic coefficient.

Nakanishi, Hiizu↗
NASA NTRS1990

Charged polymers in high dimensions

A Monte Carlo study of charged polymers with either homogeneously distributed frozen charges or with mobile charges has been performed in four and five space dimensions. The results are consistent with the renormalization-group predictions and contradict the predictions of Flory-type theory. Introduction of charge mobility does not modify the behavior of the polymers.

Kantor, Yacov↗
NASA NTRS1991

An analysis of RNG based turbulence models for homogeneous shear flow

In a recent paper, the authors compared the performance of a variety of turbulence models including the k-epsilon model and the second-order closure model based on Renormalization Group (RNG) Methods. The performance of these RNG models in homogeneous turbulent shear flow was found to be quite poor, apparently due to the value of the constant C(sub epsilon1) in the modeled dissipation rate equation which was substantially lower than its traditional value. However, recently a correction has been made in the RNG based calculation of C(sub epsilon1). It is shown that with the new value of C(sub epsilon1), the performance of the RNG k-epsilon model is substantially improved. On the other hand, while the predictions of the revised RNG second-order closure model are better, some lingering problems still remain which can be easily remedied by the addition of higher order terms.

Speziale, Charles G.↗
NASA NTRS1991

Development of turbulence models for shear flows by a double expansion technique

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Yakhot, V.↗
NASA NTRS1991

An algebraic RNG-based turbulence model for three-dimensional turbomachinery flows

An algebraic eddy viscosity turbulence model based on Renormalization Group (RNG) theory for complex three-dimensional turbomachinery flows is presented. Modifications are made to the baseline RNG model for wakes and separated flows. The model has several advantages over popular algebraic models most notably its lack of empirically determined coefficients. The model is used to compute the mean flow in a low speed axial compressor rotor. The agreement with blade boundary layer and radial flow experimental data is very good and shows improvement over the Baldwin-Lomax model. The development of the tip leakage vortex is also well predicted. The computed wake decay also compares favorably with recent experimental data.

Kirtley, K. R.↗
NASA NTRS1991

Nonlinear Reynolds stress model for turbulent shear flows

A nonlinear algebraic Reynolds stress model, derived using the renormalization group, is applied to equilibrium homogeneous shear flow and fully developed flow in a square duct. The model, which is quadratically nonlinear in the velocity gradients, successfully captures the large-scale inhomogeneity and anisotropy of the flows studied. The ratios of normal stresses, as well as the actual magnitudes of the stresses are correctly predicted for equilibrium homogeneous shear flow. Reynolds normal stress anisotropy and attendant turbulence driven secondary flow are predicted for a square duct. Profiles of mean velocity and normal stresses are in good agreement with measurements. Very close to walls, agreement with measurements diminishes. The model has the benefit of containing no arbitrary constants; all values are determined directly from the theory. It seems that near wall behavior is influenced by more than the large scale anisotropy accommodated in the current model. More accurate near wall calculations may well require a model for anisotropic dissipation.

Barton, J. Michael↗
NASA NTRS1991

An analysis of RNG-based turbulence models for homogeneous shear flow

In a recent paper, the authors compared the performance of a variety of turbulence models including the k-epsilon model and the second-order closure model based on Renormalization Group (RNG) Methods. The performance of these RNG models in homogeneous turbulent shear flow was found to be quite poor, apparently due to the value of the constant C(sub epsilon 1) in the modeled dissipation rate equation which was substantially lower than its traditional value. However, recently a correction has been made in the RNG-based calculation of C(sub epsilon 1). It is shown that with the new value of C(sub epsilon 1), the performance of the RNG k-epsilon model is substantially improved. On the other hand, while the predictions of the revised RNG second-order closure model are better, some lingering problems still remain which can be easily remedied by the addition of higher order terms.

Speziale, Charles G.↗
NASA NTRS1992

Analysis of an RNG based turbulence model for separated flows

A two-equation turbulence model of the K-epsilon type was recently derived by using Renormalization Group (RNG) methods. It was later reported that this RNG based model yields substantially better predictions than the standard K-epsilon model for turbulent flow over a backward facing step - a standard test case used to benchmark the performance of turbulence models in separated flows. The improvements obtained from the RNG K-epsilon model were attributed to the better treatment of near wall turbulence effects. In contrast to these earlier claims, it is shown in this paper that the original version of the RNG K-epsilon model substantially underpredicts the reattachment point in the backstep problem. This is a deficiency that is traced to the modeling of the production of dissipation term. However, with the most recent improvements in the RNG K-epsilon model, excellent results for the backstep problem are now obtained.

Speziale, C. G.↗
NASA NTRS1991

Center for Modeling of Turbulence and Transition (CMOTT). Research briefs: 1990

Brief progress reports of the Center for Modeling of Turbulence and Transition (CMOTT) research staff from May 1990 to May 1991 are given. The objectives of the CMOTT are to develop, validate, and implement the models for turbulence and boundary layer transition in the practical engineering flows. The flows of interest are three dimensional, incompressible, and compressible flows with chemistry. The schemes being studied include the two-equation and algebraic Reynolds stress models, the full Reynolds stress (or second moment closure) models, the probability density function models, the Renormalization Group Theory (RNG) and Interaction Approximation (DIA), the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Povinelli, Louis A.↗
NASA NTRS1991

Turbulence modeling

The performance of existing two-equation eddy viscosity models was examined. An effort was made to develop better models for near-wall turbulence using direct numerical simulations of plane channel and boundary layer flows. The asymptotic near-wall behavior of turbulence was used to examine the problems of current second order closure models and develop new models with the correct near-wall behavior. Rapid Distortion Theory was used to analytically study the effects of mean deformation on turbulence, obtain analytical solutions for the spectrum tensor, Reynolds stress tensor, anisotropy tensor and its invariants, which can be used in the turbulence model development. The potential of the renormalization group theory in turbulence modeling was studied, as well as compressible turbulent flows, and modeling of bypass transition.

Shih, Tsan-Hsing↗