Data-Driven Closure Models (DDCMs)
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Comparison of the Jones-Launder, Ng-Spalding, Saffman-Wilcox, and Wilcox-Traci two-equation turbulence models has been conducted. It was shown that the Saffman-Wilcox and Wilcox-Traci dissipation-rate formulations admit straightforward integration through the viscous sublayer, whereas integration through the viscous sublayer is a more difficult issue with the Jones-Launder dissipation-function and the Ng-Spalding length-scale formulations. Numerical computations were conducted in which the models were applied to four equilibrium boundary layer flows including adverse, zero, and favorable pressure gradients. Computations of zero pressure gradient flow over a convex wall composed the final part of the comparison.
Computations based on several second-order turbulence models, including full Reynolds stress and two-equation models, are compared with a number of boundary-layer experiments. In general, the models represent the data reasonably well, with skin friction tending to be somewhat overpredicted in the far downstream region of the adverse pressure gradient experiments. A discussion of the behavior of the ARAP full Reynolds stress model in predicting the components of the Reynolds stress tensor is given. It is concluded that compatibility at the wall may necessitate the use of more than one length scale.
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Recent applications of the turbulent transport model originally developed by Donaldson to some problems of practical importance in micrometeorology are discussed. Four particular examples considered are the local boundary layer gust front emanating from a thunderstorm; the low-level wind and turbulent distributions of a tornado; the transport of momentum, heat and species within a surface layer canopy, and longitudinal roll vortices in the unstable planetary boundary layer. Results for the last example are discussed in some detail. Comparisons are made between a one-dimensional and a two-dimensional computation of this phenomenon.
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A study is made for the development and computations of the separating and reattaching shear flows. The highlight of the study is an attempt to predict the third-moments of turbulent velocity which is responsible for the diffusion transport of the Reynolds stresses. The present computations show that the third-moments obtained by employing the law-Reynolds number model of transport equations improve the prediction of the third-moments. The modelling for scalar variables is also performed for the heat transfer computations. Since the transport equations for (u sub j theta)* and (u sub i u sub j theta) have been given in the last NASA CR, the study has been extended further to the modeling of (theta sup 2), (u sub i theta sup 2) and epsilon sub theta (dissipation rate of (theta sup 2)). The formulations are shown in this report.
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An extended kappa-epsilon turbulence model is proposed and tested with successful results. An improved transport equation for the rate of dissipation of the turbulent kinetic energy, epsilon, is proposed. The proposed model gives more effective response to the energy production rate than does the standard kappa-epsilon turbulence model. An extra time scale of the production range is included in the dissipation rate equation. This enables the present model to perform equally well for several turbulent flows with different characteristics, e.g., plane and axisymmetric jets, turbulent boundary layer flow, turbulent flow over a backward-facing step, and a confined turbulent swirling flow. A second-order accurate finite difference boundary layer code and a nearly second-order accurate finite difference elliptic flow solver are used for the present numerical computations.
To predict the diffusion process of the Reynolds stresses in reattaching shear flows, the transport model for the triple-velocity products has been developed and tested for the computation of the flow in a channel with a backward-facing step. Upon comparison of the results of uuv, uvv, and vvv with those obtained by using existing algebraic correlations, it was shown that the present model improved the prediction of the triple-velocity products.
A study is made for the development and computations of the separating and reattaching shear flows. The highlight of the study is an attempt to predict the third-moments of turbulent velocity which is responsible for the diffusion transport of the Reynolds stresses. The present computations show that the third-moments obtained by employing the low-Reynolds number model of transport equations improve the prediction of the third-moments.
A multigrid method is presented for calculating turbulent jets in crossflow. Fairly rapid convergence is obtained with the k-epsilon turbulence model, but computations with a full Reynolds stress turbulence model (RSM) are not yet very efficient. Grid dependency tests show that there are slight differences between results obtained on the two finest grid levels. Computations using the RSM are significantly different from those with k-epsilon model and compare better to experimental data. Some work is still required to improve the efficiency of the computations with the RSM.
A hybrid Reynolds averaged/assumed pdf approach has been developed and applied to the study of turbulent combustion in a supersonic mixing layer. This approach is used to address the 'laminar-like' treatment of the thermochemical terms that appear in the conservation equations. Calculations were carried out for two experiments involving H2-air supersonic turbulent mixing. Two different forms of the pdf were implemented. In general, the results show modest improvement from previous calculations. Moreover, the results appear to be somewhat independent of the form of the assumed pdf.
A full Reynolds stress turbulence model is applied to calculate the flow in various channels with complex cross-section. The model is shown to be more robust and to produce more consistent results than algebraic stress models. The relationship between various versions of the latter is provided. It is shown that differential or algebraic stress models derived from a direct application of a popular linear approximation for the pressure-strain terms in the Reynolds stress equations will always underpredict the secondary motion, and hence the accompanying distortion of other flow properties. A simple approximation which leads to better predictions is presented and related to previous practice.
The topics are presented in viewgraph form and include: (1) an alternative relaxed strain energy (RSE) model; (2) shear layers/spread rate comparisons; (3) general comments on RSE models; and (4) the law of the wall.
A new computer code to solve the time averaged Navier-Stokes equations is developed. Many of the state-of-the-art numerical techniques and algorithms have been tested and implemented in the program in order to achieve a better numerical accuracy and code efficiency. Various turbulence models are tested for a wide range of flows. The initial focus has been on two-equation eddy-viscosity models, which are the most advanced available in current compressible flow codes. The long term goal will be to test Reynolds-Stress models and to explore their performance in the high Mach number range. Although testing and improvement of turbulence models for supersonic and hypersonic flows is the primary objective of this research, part of the effort has been devoted to analyzing the vortex breakdown phenomena using new computer programs. Some preliminary results on the breakdown of a vortex flow in a tube are reported. Present calculations are restricted to two dimensional flow geometry.
The flow over two different multi-element airfoil configurations is computed using linear eddy viscosity turbulence models and a nonlinear explicit algebraic stress model. A subset of recently-measured transition locations using hot film on a McDonnell Douglas configuration is presented, and the effect of transition location on the computed solutions is explored. Deficiencies in wake profile computations are found to be attributable in large part to poor boundary layer prediction on the generating element, and not necessarily inadequate turbulence modeling in the wake. Using measured transition locations for the main element improves the prediction of its boundary layer thickness, skin friction, and wake profile shape. However, using measured transition locations on the slat still yields poor slat wake predictions. The computation of the slat flow field represents a key roadblock to successful predictions of multi-element flows. In general, the nonlinear explicit algebraic stress turbulence model gives very similar results to the linear eddy viscosity models.