Dynamic Cubic Non-linear SGS Model And The Application In Centrifugal Pumps

Rotating turbulence is a typical phenomenon in centrifugal pumps with high adverse pressure gradient,curvature and rotation effect.The strong three-dimensional fluctuating characteristics of the flow lead to the insufficiency for RANS and eddy-viscosity based LES in accurately reflecting the rotation effect and the unsteady flow in centrifugal pumps.Therefore,it is of great importance to develop the non-linear SGS models which can reflect the rotation effect and to explore the structure of the rotating turbulence in centrifugal pumps.These 2 aspects can shed light on the mechanism of the unsteady phenomenon.As the second-order non-linear SGS models are not sufficient in reflecting the rotation effect,a dynamic cubic non-linear model(DCNM)is proposed in this paper.Different from the conventional nonlinear model with the second-order term,the new model contains a cubic term of the rate-of-rotation and the rate-of-strain tensors.All the three model coefficients are determined dynamically using the extended Germano’s procedure.The modules of the non-linear models which are adaptive to any explicit non-linear models are implemented into the open source CFD code OpenFOAM.This extends the ability of OpenFOAM in solving more complex models.Based on the module,DCNM is then applied to 2 benchmark cases-turbulent rotating channel flow and Taylor-Couette flow.Comparing with the results from other SGS models and DNS,it is shown that DCNM performs better than other models and the backscatter can be reflected.In order to clarify the influence of the rotational effects on the unsteady internal flow field in centrifugal pumps,DCNM is furher applied to the centrifugal pumps.In the Pedersen pump with stalls,the new model correctly captures the locations of the stalls.In the ERCOFTAC pump with rotor-stator interaction,the better agreement with experiment is shown in the velocity distributions for the vaneless region.Based on the analysis of the Reynolds stress transport equation,the influence of the rotation term and the production term is studied.It is verified that in the impeller,the rotaion term redistributes the energy as in rotating channel flow.When the stall occurs,the production term plays the similar role in redistribution.Apart from the impeller,the rotation term is negligiable compared to the production term in the vaneless region downstream the impeller while the production term dominates.The research in this paper offers a more accurate model for rotating turbulence and improves the abitily of resolving the strong rotating flow in centrifugal pump.Additionally,the study of the turbulent field basing on the Reynolds stress transport equation also shed light on the further understanding of the complex flow field from a somewhat new perspective.