To address the early separation problem in the Menter Shear-Stress Transport(SST)turbulence model,a correction for the Turbulent Kinetic Energy(TKE)production term,P_(k),is introduced to account for the effect of the ...To address the early separation problem in the Menter Shear-Stress Transport(SST)turbulence model,a correction for the Turbulent Kinetic Energy(TKE)production term,P_(k),is introduced to account for the effect of the Adverse Pressure Gradient(APG).The correction is determined based on the distribution of Pkin the APG region before separation.When the friction coefficient C_(f) is decomposed,its direct dependence on Pkis clearly observed.However,with the introduction of Bradshaw’s assumption,Pkin the SST turbulence model is over-suppressed,resulting in a lower inner peak or no significant inner peak distribution at all.To address this problem,this paper proposes a Gaussian function,HGauss,which corrects the numerical values of P_(k) involved in the calculation of the Menter SST model by focusing on the inner peak region of P_(k).The modified SST model is then applied to four cases with APGs.The modification leads to an increase in the wall friction coefficient C_(f)in the APG region and causes a downstream shift in the separation location,improving the model’s consistency with high-accuracy data and experimental results.It is demonstrated that this correction can improve the early separation problem in the Menter SST turbulence model.展开更多
A terrain-following coordinate （a-coordinate） in which the computational form of pressure gradient force （PGF） is two-term （the so-called classic method） has significant PGF errors near steep terrain. Using the ...A terrain-following coordinate （a-coordinate） in which the computational form of pressure gradient force （PGF） is two-term （the so-called classic method） has significant PGF errors near steep terrain. Using the covariant equations of the a-coordinate to create a one-term PGF （the covariant method） can reduce the PGF errors. This study investigates the factors inducing the PGF errors of these two methods, through geometric analysis and idealized experiments. The geometric analysis first demonstrates that the terrain slope and the vertical pressure gradient can induce the PGF errors of the classic method, and then generalize the effect of the terrain slope to the effect of the slope of each vertical layer （φ）. More importantly, a new factor, the direction of PGF （a）, is proposed by the geometric analysis, and the effects of φ and a are quantified by tan φ.tan a. When tan φ.tan a is greater than 1/9 or smaller than -10/9, the two terms of PGF of the classic method are of the same order but opposite in sign, and then the PGF errors of the classic method are large. Finally, the effects of three factors on inducing the PGF errors of the classic method are validated by a series of idealized experiments using various terrain types and pressure fields. The experimental results also demonstrate that the PGF errors of the covariant method are affected little by the three factors.展开更多
基金supported by the National Natural Science Foundation of China(No.92252201)。
文摘To address the early separation problem in the Menter Shear-Stress Transport(SST)turbulence model,a correction for the Turbulent Kinetic Energy(TKE)production term,P_(k),is introduced to account for the effect of the Adverse Pressure Gradient(APG).The correction is determined based on the distribution of Pkin the APG region before separation.When the friction coefficient C_(f) is decomposed,its direct dependence on Pkis clearly observed.However,with the introduction of Bradshaw’s assumption,Pkin the SST turbulence model is over-suppressed,resulting in a lower inner peak or no significant inner peak distribution at all.To address this problem,this paper proposes a Gaussian function,HGauss,which corrects the numerical values of P_(k) involved in the calculation of the Menter SST model by focusing on the inner peak region of P_(k).The modified SST model is then applied to four cases with APGs.The modification leads to an increase in the wall friction coefficient C_(f)in the APG region and causes a downstream shift in the separation location,improving the model’s consistency with high-accuracy data and experimental results.It is demonstrated that this correction can improve the early separation problem in the Menter SST turbulence model.
基金jointly supported by the National Basic Research Program of China[973 Program,grant number 2015CB954102]National Natural Science Foundation of China[grant numbers41305095 and 41175064]
文摘A terrain-following coordinate （a-coordinate） in which the computational form of pressure gradient force （PGF） is two-term （the so-called classic method） has significant PGF errors near steep terrain. Using the covariant equations of the a-coordinate to create a one-term PGF （the covariant method） can reduce the PGF errors. This study investigates the factors inducing the PGF errors of these two methods, through geometric analysis and idealized experiments. The geometric analysis first demonstrates that the terrain slope and the vertical pressure gradient can induce the PGF errors of the classic method, and then generalize the effect of the terrain slope to the effect of the slope of each vertical layer （φ）. More importantly, a new factor, the direction of PGF （a）, is proposed by the geometric analysis, and the effects of φ and a are quantified by tan φ.tan a. When tan φ.tan a is greater than 1/9 or smaller than -10/9, the two terms of PGF of the classic method are of the same order but opposite in sign, and then the PGF errors of the classic method are large. Finally, the effects of three factors on inducing the PGF errors of the classic method are validated by a series of idealized experiments using various terrain types and pressure fields. The experimental results also demonstrate that the PGF errors of the covariant method are affected little by the three factors.
