An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows
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1,159 citations
Cites background from "An explicit algebraic Reynolds stre..."
...More advanced nonlinear eddy viscosity models have also been proposed (Pope 1975; Craft et al. 1996; Wallin & Johansson 2000) which rely on higher-order products of the mean strain rate and rotation rate tensors....
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References
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"An explicit algebraic Reynolds stre..." refers background in this paper
...For a more thorough comparison between K–ε and K–ω models the reader may wish to consult Menter (1994)....
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Additional excerpts
...Other possibilities than y+ are Rey ≡ √ Ky/ν or the turbulent Reynolds number Ret ≡ K2/νε (see e.g. Wilcox 1993)....
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3,855 citations
"An explicit algebraic Reynolds stre..." refers background or methods or result in this paper
...4 by Launder et al. (1975), but more recent studies have suggested a higher value close to 5 9 , see e.g. Lumley (1978) and Shabbir & Shih (1992). This means that the last term in equation (1.13) is of quite small influence, also noticed by Taulbee (1992). Setting c2 = 5 9 one obtains the simplified but still implicit equation ( c1 − 1 + P ε ) a = − 8 15 S + 4 9 (aΩ−Ωa) ....
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...Moreover, the Launder et al. (1975) model gives quite poor predictions of this case when used in a differential form. The very good predictions of the present EARSM can thus be regarded as a bit fortuitous. Nevertheless, the self-consistent approach gives a model with the correct asymptotic behaviour, which is a pre-requisite for reasonable predictions in the limit of high shear. It is important to make clear that the proposed model is not intended for these extreme high shear rates and the normal stress components are not as well predicted as the turbulent kinetic energy. It is, however, an important step towards a more general engineering model that the model is able to give reasonable results in extreme flow cases also. In flows with an adverse pressure gradient, the production to dissipation ratio is greater than 1 and eddy-viscosity models with constant Cμ overestimate the turbulent viscosity or the a12 anisotropy. Bradshaw’s assumption, which is adopted by Menter (1993) in the shear stress transport (SST) model, forces the a12 anisotropy to be constant for P/ε ratios greater than unity, which gives β1 ∼ 1/σ....
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...The value of c2 in the rapid pressure–strain model was originally suggested to be 0.4 by Launder et al. (1975), but more recent studies have suggested a higher value close to 5 9 , see e.g. Lumley (1978) and Shabbir & Shih (1992)....
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...The Taulbee (1992) model could, however, be directly compared to the implicit ARSM since the basic approach is the Launder et al. (1975) model with similar choices of the model coefficients....
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...Solution of the general quasi-linear ARSM equation So far, the explicit solution of the ARSM resulting from the special case of the Launder et al. (1975) model with c2 = 5 9 has been analysed....
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2,783 citations
"An explicit algebraic Reynolds stre..." refers methods in this paper
...For that choice, the standard Wilcox (1988) K–ω, also without damping functions, must be used as the platform....
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...This case is computed using the standard Wilcox (1988) K–ω model and the EARSM based on that....
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...Figure 21 shows the computational results for the two-dimensional RAE2822 aerofoil profile using the proposed EARSM compared to the Wilcox (1994) K–ω model. The flow in this case is compressible and the formulation is modified in a manner described in § 4. The EARSM approach clearly improves the position of the shock and the results are very much in line with differential Reynolds stress computations by Hellström, Davidson & Rizzi (1994) for exactly the same conditions and geometry. The damping function in the EARSM is formulated in terms of y as well as y∗ and the figure shows no major differences between these approaches except in the separated region where the y formulation gives a somewhat larger negative skin friction. In the figure a computation using the proposed EARSM without any damping functions whatsoever is also shown. For that choice, the standard Wilcox (1988) K–ω, also without damping functions, must be used as the platform....
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...Figure 21 shows the computational results for the two-dimensional RAE2822 aerofoil profile using the proposed EARSM compared to the Wilcox (1994) K–ω model....
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...Figure 21 shows the computational results for the two-dimensional RAE2822 aerofoil profile using the proposed EARSM compared to the Wilcox (1994) K–ω model. The flow in this case is compressible and the formulation is modified in a manner described in § 4. The EARSM approach clearly improves the position of the shock and the results are very much in line with differential Reynolds stress computations by Hellström, Davidson & Rizzi (1994) for exactly the same conditions and geometry....
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2,470 citations
"An explicit algebraic Reynolds stre..." refers background or methods in this paper
...This behaviour is not a natural part of eddy-viscosity based models, but was incorporated in a somewhat ad hoc manner by Menter (1993)....
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...For a more thorough comparison between K–ε and K–ω models the reader may wish to consult Menter (1994). It is also interesting to note the clear improvement in the K-profiles with the proposed EARSM both for the K–ε and K–ω models in figure 14....
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...Bradshaw’s assumption, which is adopted by Menter (1993) in the shear stress transport (SST) model, forces the a12 anisotropy to be constant for P/ε ratios greater than unity, which gives β1 ∼ 1/σ....
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...The current model ( ) compared to the eddy-viscosity model ( ) and the Menter (1993) SST model ( )....
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...The current model without ( ) and with ( ) diffusion model compared to an eddy-viscosity model ( ) and the Menter (1993) SST model ( )....
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