Article

New transition/turbulence model for the flow transition in supersonic boundary layer

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Abstract

A new κ-ω-γ transition/turbulence model is established to consider the instability modes associated with the compressibility. The particular features of the new model are: (1) the fluctuating kinetic energy κ includes the non-turbulent, as well as turbulent components modelled with the stability analysis; (2) a function for the source term in γ equation is developed to trigger the transition onset; (3) it is strictly based on local variables by introducing a new length scale normal to wall and compatible with the modern CFD methods. The present model was numerically proved to be applied into the analyses of natural transition and bypass transition with a wide range of Mach number.

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... The so-called correlationbased models232425 have become helpful tools for industry owing to their use of integral (or global) boundary layer parameters. Recently, transport equation models26272829 which rely on (local ) information to circumvent some complicated procedures in the early methods, have been introduced. These transport equation models solve several ''transport'' partial differential equations written for various transition quantities in addition to the baseline turbulence models. ...
... Some of these models are the intermittency transport equation models of Suzen and Huang [24,25] and the correlation-based k–ω SST transition model of Menter et al. [26] . More recently truly single point RANS approaches such as the k–k L –ω transition model of Walters and Leylek [28] which essentially eliminate the need for the intermittency , and a variant of the SST model called the k–ω–γ model of Fu and Wang [29] have been introduced. Such models are suitable for straightforward implementation within RANS methods as they solve additional transport equations for predicting transition phenomena that rely on local information only, in contrast with the global information, as used in the early methods. ...
... Transition correlations are user dependent data retrieved from benchmark experiments obtained at different laboratories. A number of investigators have tried to develop their own correlations of the model parameters against different experimental cases [29,30] as the original parameter set remains proprietary [26]. The k–k L –ω model [28] is considered as a three-equation eddyviscosity type, which includes transport equations for turbulent kinetic energy (k), laminar kinetic energy (k L ), and specific dissipation rate (ω). ...
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Transition-sensitive, single point eddy viscosity models are fairly new and performance assessment of these models is required. In this study, the performance of transition and turbulence models is first evaluated for predicting low Re number flows having laminar separation bubbles that are traditionally quite difficult to predict for RANS-based CFD methods. Second, suppression of the laminar separation bubbles using blowing and/or suction is investigated for a single aerofoil. A prior experimental study using hot-wire anemometry for a clean (no jet) NACA 2415 aerofoil at α=8° at a Reynolds number of 2×105 shows the presence of a laminar separation bubble. For this flow, the recently developed k–kL–ω transition model is first shown to accurately predict the location and extent of the experimentally measured separation bubble. Following this, the same transition model was used to predict the flow over the NACA 2415 aerofoil using single or simultaneous blowing or suction. In the single blowing or suction cases, the separation bubble is not completely eliminated, but either abated or moved downstream. Smaller blowing velocity ratios cause more effective suppression of the separation bubble than larger blowing ratios, independent of the blowing locations. In contrast, larger suction velocity ratios are better than smaller suction ratios for the suppression. Moreover, the lift/drag ratios increase as the jet location moves from the leading edge to a downstream direction in both cases. In the simultaneous blowing and suction cases, the k–kL–ω transition model is shown to suppress the separation bubble by using a mix of jet parameters which result in increased lift/drag ratios.
... Walters & Leylek [29] adopted Mayle & Schulz's [28] idea and developed a locally formulated transport equation for the laminar kinetic energy that describes the development of the non-turbulent streamwise fluctuations in the pre-transitional boundary layer region, but Walters & Leylek' transition model has too many model constants. In order to model of the high-speed flow transition, Wang & Fu [30] developed a k−ω −γ three-equation approach that is capable of accommodating the effect of the second instability mode, while non-local parameter is required in Wang & Fu's transition model such as the local mean velocity at the generalized inflection point. ...
... Fig. 12 represents the computation results of non-turbulent viscosity, we can observe that the non-turbulent viscosity is near zero in the laminar region and fully turbulent region as the streaky fluctuations will break down and will not exist in the fully turbulent region, so we can deduce that the transport equation of nonturbulent viscosity can predict the correct distribution and is responsible for the bypass transition process. Due to the dissipation term of the non-turbulent viscosity transport equation, the value of the non-turbulent viscosity will be zero in the post-transitional region what is physical and different to Warren & Hassan [29] and Fu & Wang [30] models. But we can also observe that the non-turbulent viscosity does not decay quickly outside the boundary layer in the fully turbulent region in Fig. 12, and the dissipation term of the non-turbulent viscosity transport equation should be improved in the future. ...
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It is very important to predict the bypass transition in the simulation of flows through turbomachinery. This paper presents a four-equation eddy-viscosity turbulence transition model for prediction of bypass transition. It is based on the SST turbulencemodel and the laminar kinetic energy concept. A transport equation for the non-turbulent viscosity is proposed to predict the development of the laminar kinetic energy in the pre-transitional boundary layer flow which has been observed in experiments. The turbulence breakdown process is then captured with an intermittency transport equation in the transitional region. The performance of this new transition model is validated through the experimental cases of T3AM, T3A and T3B. Results in this paper show that the new transition model can reach good agreement in predicting bypass transition, and is compatible with modern CFD software by using local variables.
... Researchers in China have also carried out related studies and obtained several promising achievements. In 2009, a new k-ω-γ model was introduced by Wang and Fu [9] , succeeding in predicting boundary transitions in subsonic, supersonic, and hypersonic fields. In the present work, an R t -γ transition prediction model [10] is adopted, which is a brand new model embedding transport equations of intermittency factor with the one-equation R t model [11] . ...
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A new transition prediction model is introduced, which couples the intermittency effect into the turbulence transport equations and takes the characteristics of fluid transition into consideration to mimic the exact process of transition. Test cases include a two-dimensional incompressible plate and a two-dimensional NACA0012 airfoil. Performance of this transition model for incompressible flows is studied, with numerical results consistent to experimental data. The requirement of grid resolution for this transition model is also studied.
... The current chapter is largely based on Langtry and Menter [25]. More recent articles on model validation and development can be found in262728. ...
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