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RNG in turbulence and modeling of bypass transition

Two projects are considered: the Renormalization Group (RNG) analysis of turbulence modeling, and the calculation of bypass transition through turbulence modeling. RNG is a process which eliminates small scales on the uneliminated large scales as the change in the transport properties. It is because of this property of RNG that it was previously suggested that RNG could be used as a model builder in turbulence modeling. The possibility is studied of constructing RNG based turbulence models, and to try to proceed to do the modeling through RNG in parallel with the classical approach. The numerical predictions made by RNG models and by classical models is compared against data from Direct Numerical Simulation. While in an environment with freestream turbulence, the transition initiated by the instability of the laminar boundary layer to Tollmien-Schlichting waves is found to be a bypass one in which turbulent spots are formed without T-S wave amplification. The formation is a random process, and flow within a turbulent spot is almost fully turbulent. This suggests the possibility of using turbulence modeling to describe and predict the bypass transition.

Yang, Zhigang↗

The Dissipation Rate Transport Equation and Subgrid-Scale Models in Rotating Turbulence

The dissipation rate transport equation remains the most uncertain part of turbulence modeling. The difficulties arc increased when external agencies like rotation prevent straightforward dimensional analysis from determining the correct form of the modelled equation. In this work, the dissipation rate transport equation and subgrid scale models for rotating turbulence are derived from an analytical statistical theory of rotating turbulence. In the strong rotation limit, the theory predicts a turbulent steady state in which the inertial range energy spectrum scales as k(sup -2) and the turbulent time scale is the inverse rotation rate. This scaling has been derived previously by heuristic arguments.

Rubinstein, Robert↗

Modeling of convective cells, turbulence, and transport induced by a radio-frequency antenna in the tokamak boundary plasma

The edge turbulence model Hermes (Dudson et al 2017 Plasma Phys. Control. Fusion 59 05401) is set up for plasma boundary simulations with an radiofrequency (RF) antenna, using parameters characteristic of a tokamak edge. Cartesian slab geometry is used with thin plate limiters representing the ion cyclotron range of frequency (ICRF) antenna side-wall limiters. Ad-hoc DC electric biasing of the limiters, motivated by calculations with VSim (Nieter et al 2004 J. Comput. Phys. 196 448), represents an induced RF sheath rectified potential in the plasma turbulence model. Flux-driven turbulence simulations demonstrate a realistic distribution of plasma profiles and fluctuations. There is a clear effect of the antenna sheath voltage leading to formation of convective cells; bias-induced convective transport flattens the scrape-off layer density profile and fluctuations penetrate into the shadow region of the limiters as the bias voltage increases. Turbulent transport for impurity ions is inferred by following ion trajectories in the simulated plasma turbulence fields, showing Bohm-like effective diffusion rates. All in all, the model elucidates the key physical phenomena governing the effects of ICRF-induced antenna biasing on the tokamak boundary plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A near-wall two-equation model for compressible turbulent flows

A near-wall two-equation turbulence model of the K - epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K - omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper.

Zhang, H. S.↗

A near-wall two-equation model for compressible turbulent flows

A near-wall two-equation turbulence model of the k-epsilon type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic flat plate boundary layer - with an adiabatic wall and with wall cooling - for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K-omega model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers, provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number - a deficiency that will be addressed in a future paper.

Zhang, H. S.↗

Limitations and empirical extensions of the k-epsilon model as applied to turbulent confined swirling flows

Shortcomings and recommended corrections to the standard two-equation k-epsilon turbulence model suggested by previous investigators are presented. They are assessed regarding their applicability to turbulent swirling recirculating flow. Recent experimental data on swirling confined flows, obtained with a five-hole pitot probe and a six-orientation hot-wire probe, are used to obtain optimum values of the turbulence parameters C-mu, C2, and sigma-epsilon for swirling flows. General predictions of moderately and strongly swirling flows with these values are more accurate than predictions with the standard or previous simple extensions of the k-epsilon turbulence model.

Lilley, D. G.↗

Drift reduced Landau fluid model for magnetized plasma turbulence simulations in BOUT++ framework

Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture $n$ = 0 axisymmetric mode evolution in realistic tokamak configurations. As we report here, these improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transient (e.g., ELM, disruption) and transport time-scale simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Laminar flamelet modeling of turbulent diffusion flames

In modeling turbulent combustion, decoupling the chemistry from the turbulence is of great practical significance. In cases in which the equilibrium chemistry model breaks down, laminar flamelet modeling (LFM) is a promising approach to decoupling. Here, the validity of this approach is investigated using direct numerical simulation of a simple chemical reaction in two-dimensional turbulence.

Mell, W. E.↗

An Improved Model for the Turbulent PBL

Second order turbulence models of the Mellor and Yamada type have been widely used to simulate the PBL. It is however known that these models have several deficiencies. For example, they all predict a critical Richardson number which is about four times smaller than the Large Eddy Simulation (LES) data, they are unable to match the surface data, and they predict a boundary layer height lower than expected. In the present model, we show that these difficulties are all overcome by a single new physical input: the use of the most complete expression for both the pressure-velocity and the pressure-temperature correlations presently available. Each of the new terms represents a physical process that, was not accounted for by previous models. The new model is presented in three different levels according to Mellor and Yamada's terminology, with new, ready-to-use expressions for the turbulent, moments. We show that the new model reproduces several experimental and LES data better than previous models. As far as the PBL is concerned, we show that the model reproduces both the Kansas data as analyzed by Businger et al. in the context of Monin-Obukhov similarity theory for smaller Richardson numbers, as well as the LES and laboratory data up to Richardson numbers of order unity. We also show that the model yields a higher PBL height than the previous models.

Cheng, Y.↗

One-Equation Algebraic Model Of Turbulence

One-equation model of turbulence based on standard equations of k-epsilon model of turbulence, where k is turbulent energy and e is rate of dissipation of k. Derivation of one-equation model motivated partly by inaccuracies of flows computed by some Navier-Stokes-equations-solving algorithms incorporating algebraic models of turbulence. Satisfies need to avoid having to determine algebraic length scales.

Baldwin, B. S.↗

Boundary layer integral matrix procedure: Verification of models

The three turbulent models currently available in the JANNAF version of the Aerotherm Boundary Layer Integral Matrix Procedure (BLIMP-J) code were studied. The BLIMP-J program is the standard prediction method for boundary layer effects in liquid rocket engine thrust chambers. Experimental data from flow fields with large edge-to-wall temperature ratios are compared to the predictions of the three turbulence models contained in BLIMP-J. In addition, test conditions necessary to generate additional data on a flat plate or in a nozzle are given. It is concluded that the Cebeci-Smith turbulence model be the recommended model for the prediction of boundary layer effects in liquid rocket engines. In addition, the effects of homogeneous chemical reaction kinetics were examined for a hydrogen/oxygen system. Results show that for most flows, kinetics are probably only significant for stoichiometric mixture ratios.

Bonnett, W. S.↗

Computation of turbulent flows using an extended k-epsilon turbulence closure model

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.

Chen, Y.-S.↗

Thin-layer approximation and algebraic model for separated turbulent flows

An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.

Baldwin, B.↗

Confined Turbulent Swirling Recirculating Flow Predictions

Turbulent swirling flow, the STARPIC computer code, turbulence modeling of turbulent flows, the k-xi turbulence model and extensions, turbulence parameters deduction from swirling confined flow measurements, extension of the k-xi to confined swirling recirculating flows, and general predictions for confined turbulent swirling flow are discussed.

Abujelala, M. T.↗

Group-kinetic scaling as a basis for modeling large scale turbulence

It was found that new concepts and methods were needed to develop a statistical theory of turbulence. The group kinetic method was devised for the transformation of the dynamical system into a kinetic system as the basis for a statistical treatment of turbulence. Spectral structure is used as a basis for turbulence modeling.

Tchen, C. M.↗

Modeling of Turbulent Free Shear Flows

The modeling of turbulent free shear flows is crucial to the simulation of many aerospace applications, yet often receives less attention than the modeling of wall boundary layers. Thus, while turbulence model development in general has proceeded very slowly in the past twenty years, progress for free shear flows has been even more so. This paper highlights some of the fundamental issues in modeling free shear flows for propulsion applications, presents a review of past modeling efforts, and identifies areas where further research is needed. Among the topics discussed are differences between planar and axisymmetric flows, development versus self-similar regions, the effect of compressibility and the evolution of compressibility corrections, the effect of temperature on jets, and the significance of turbulent Prandtl and Schmidt numbers for reacting shear flows. Large eddy simulation greatly reduces the amount of empiricism in the physical modeling, but is sensitive to a number of numerical issues. This paper includes an overview of the importance of numerical scheme, mesh resolution, boundary treatment, sub-grid modeling, and filtering in conducting a successful simulation.

Yoder, Dennis A.↗

Turbulent transport modeling of shear flows around an aerodynamic wing. Development of turbulent near-wall model and its application to recirculating flows

Progress in implementing and refining two near-wall turbulence models in which the near-wall region is divided into either two or three zones is outlined. These models were successfully applied to the computation of recirculating flows. The research was further extended to obtaining experimental results of two different recirculating flow conditions in order to check the validity of the present models. Two different experimental apparatuses were set up: axisymmetric turbulent impinging jets on a flat plate, and turbulent flows in a circular pipe with a abrupt pipe expansion. It is shown that generally better results are obtained by using the present near-wall models, and among the models the three-zone model is superior to the two-zone model.

Amano, R. S.↗