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A Reynolds-stress expression based on DNS data in non-linear eddy-viscosity turbulence model for complex flows
Abstract
A Reynolds-stress expression used in a non-linear eddyviscosity turbulence model is developed based on the Direct Numerical Simulation (DNS) data of fully developed turbulent channel flow of Kim et al. (1987) for both Re T = 180 and 395. The data are initially used to analyze the accuracy of various Reynolds-stress expressions used in the non-linear turbulence models in order to find the expression that gives the closest Reynolds-stress values to the DNS data. The use of the DNS data directly in the expression is to ensure that the errors in the solutions are not from the modeled transport equations of the turbulent kinetic energy and its dissipation rate. It is found that both Reynolds shear stress and normal Reynolds stresses from the Reynolds-stress expression of Craft et al. (1996) are closer to the DNS data than the other expressions for both Reynolds numbers. The present work aims to further improve the accuracy of the expression of Craft et al. in predicting the Reynolds stresses and consequently the mean velocity profiles. The main objective of the current work is to find the f μ expression based on the non-linear Reynolds-stress expression of Craft et al. that gives the closest agreement to the values of f μ extracted from the DNS data. It is found that the Reynolds-stress expression of Craft et al. with the f μ of Gibson and Dafa'Alla (1994) gives the closer agreement to the DNS data for all Reynolds stresses and mean velocity profile in the case of fully-developed turbulent channel flow. The expression is then evaluated for more complex three-dimensional flow through a straight square duct where there are secondary flows. The DNS data of Gavrilakis (1992) are used for comparison. The present expression shows the improvement in the prediction of the mean spanwise velocity profile at the position near the edge of the duct. The damping function of Gibson and Dafa'Alla is hence the more suitable damping function to be used with the non-linear Reynolds-stress expression of Craft et al.
... The possible errors are the Reynolds-stress expression, the linear base model and the near-wall modeling. The different nonlinear Reynolds-stress expressions were compared by Juntasaro et al. [3] using a priori method. The Reynoldsstress expression of Craft et al. [4] was the most accurate expression in predicting the secondary flows in a straight square duct. ...
... Additionally, Juntasaro et al. [3] has found by using a priori method that the damping function of Gibson and Dafa'Alla [8] can predict the mean spanwise velocity profile closer to the DNS data than the original damping function of Craft et al. [4] especially in the near wall region. The damping function of Gibson and Dafa'Alla [8] can be written as ...
The characteristics of flow field in the internal passage of turbine blade cooling are affected by the combined effects of the secondary flows and the rotation of the blade. These secondary flows occur in the near wall regions and have the great effect on the characteristics of the primary flow and the cooling rate. Accurate modeling of the flow in the near wall regions is therefore necessary. This paper aims to analyze the performance of the various near-wall models in predicting the flow field in a rotating square duct when they are implemented in the nonlinear turbulence model. The nonlinear turbulence model used in this work is developed from the most suitable Reynolds-stress expression and the linear base model from the previous works. It is found that the non-equilibrium wall function should be used in the case of the flow through the straight square duct without the rotation effect. The damping function of Craft et al. (1996) is more suitable for the case of the rotating square duct as the near-wall modeling for the nonlinear turbulence model.
The realistic simulation of cavitation on a marine propeller is important for the efficient design of the propeller. However, the flow characteristic that occurred on the marine propeller is complicated and difficult to predict due to the combined effects of turbulence, cavitation, and multiphase phenomena. There is still currently no turbulence model that can predict these combined effects satisfactory. The nonlinear turbulence model is therefore modified and applied to predict the cavitation on a marine propeller for the first time in this work. It is found that the nonlinear turbulence model can predict the cavitation and hence the thrust and torque coefficients much more accurately than the existing Reynolds-averaged Navier-Stokes turbulence models including the Reynolds-stress model. [DOI: 10.1115/1.4003564]
The flow over a stepped spillway is free surface, multiphase and turbulent. Moreover, a recirculation region occurs at each step of the spillway. The flow characteristic is hence complicated and difficult to predict. In previous work on stepped spillways (Chen et al. Journal of Hydraulic Engineering, ASCE, 128 (7), 683–688 and Xiangju et al. Science in China Series E: Technological Sciences, 49 (3), 674–684), only the linear turbulence model was applied which gave low accuracy. Furthermore, there are still no optimised model constants for this kind of flow. The present work therefore aims to apply the large eddy simulation (LES), the non-linear and the modified non-linear turbulence models to simulate the flow over the spillways with various slopes and step heights. It is found that the modified model is able to predict the flow close to the LES but requires less computational time by a factor of up to 4. Moreover, the modified model gives higher accuracy than the LES for the cases of the spillways with higher slopes and step heights.
The existing anisotropic k-epsilon models are briefly reviewed, and a new anisotropic k-epsilon model is proposed. The validity of the model proposed here is examined by applying it to simple two-dimensional turbulent shear flows. It is shown that the model is capable of reproducing the distributions of anisotropic Reynolds stresses right up to the wall, providing a correct description of the wall-limiting behavior.