Numerical simulation of flow past a circular base on PANS methods

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1 IOP Conference Series: Materials Science and Engineering PAPER OPEN ACCESS Numerical simulation of flow past a circular base on PANS methods To cite this article: J T Liu et al 016 IOP Conf. Ser.: Mater. Sci. Eng View the article online for updates and enhancements. Related content - Numerical simulation of flow around a simplified high-speed train model using OpenFOAM I A Ishak, M S M Ali and S A Z Shaikh Salim - Numerical Simulation of Flow and Heat Transfer Characteristics in Biomass Feeder Zhenhua Wang, Yulong Chang, Zheming Liu et al. - Numerical simulations of flow past a circular cylinder Gaurav Chopra and Sanay Mittal This content was downloaded from IP address on 0/09/018 at 17:38

2 ICPF015 IOP Conf. Series: Materials Science and Engineering 19 (016) doi: / x/19/1/01048 Numerical simulation of flow past a circular base on PANS methods J T Liu 1, Y Li 1, Y Gao 1, Q Hu 1 and Y L Wu 1 Beiing Institute of Control Engineering, Beiing , China liuintao86@hotmail.com State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beiing , China wyl-dhh@mail.tsinghua.edu.cn Abstract. A nonlinear partially averaged Navier-Stokes (PANS) method based on RNG k-ε turbulence model is evaluated by a moderately high Reynolds number turbulence flow past a circular cylinder. The ratios of unresolved-to total kinetic energy (f k) and unresolved-to-total disspation (f ε) for PANS method is sensitive to the simulation result. Simulation results based on different fk are compared with the experimental data. The quantities including mean streamline velocity, mean normal velocity, streamlines and et al. are analyzed. The computational result is reasonable when f k is less than 0.6. The PANS method can be used in the simulation of high Reynolds number turbulence flow. 1. Introduction For predictions of turbulence flow with high Reynolds number based on the Unsteady Reynolds Averaged Navier-Stokes (URANS) equations have been well discussed in the literature 1. Unfortunately, the aforementioned URANS approach couldn t capture the flow with all kinds of scales. Large Eddy Simulation (LES) could improve predictions but is not computationally economical due to the considerable high cost for engineering problems 3. As an alternative, various hybrid RANS/LES approaches have been proposed. For example, a Partially-Averaged Navier-Stokes (PANS) approach, which changes seamlessly from RANS to the direct numerical solution of the Navier-Stokes equations, was proposed by Girimai et al.. Lakshmipathy 3 analyzed the flow past a circular cylinder with high Reynolds number via PANS k-ε model. Lakshmipathy 4 proposed a new kind PANS model derived from k-ω turbulence model, which was called k-ω PANS methods. Flow around a marine propeller 5 and a twisted hydrofoil 6 in a non-uniform wake were also investigated using PANS methods. A variable-resolved PANS bridging strategy was applied to the four-equations k-ε-ξ-f turbulence model 7. Embedded large-eddy simulation using the partially averaged Navier-Stokes model was proposed via Davidson 8. Computations of flow past a circular cylinder have also been performed to evaluate the numerical as well as physical modeling aspects. Several experimental data sets are available for the flow past a circular cylinder test case in all Reynolds number regimes. Cantwell 9 studied the flow past a circular cylinder at Re d= Breuer 10 was the first to perform LES calculations of flow past a circular Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, ournal citation and DOI. Published under licence by Ltd 1

3 ICPF015 IOP Conf. Series: Materials Science and Engineering 19 (016) doi: / x/19/1/01048 cylinder at Re d= It concluded that the dynamic subgrid model gave the best results but was not decisively better than the constant Smogorinsky model for this flow. Travin 11 performed detached eddy simulations (DES) of flow past a circular cylinder at Re d= using a multiblock grid and fifth-order upwind scheme for spatial discretization. The primary obective of the present study is to validate a nonlinear RNG k-ε PANS mothod 1 in the flow past a circular cylinder at Re d= The PANS results are compared with experimental data at different f k.. Nolinear PANS model For incompressible flow, the continuity equation and Reynolds averaged Navier-Stokes equations: V, i V p U U U U t x x x x x i i i i i p U U Vi, V i x x x x x x i i i i Here, Vis the instantaneous velocity (subscript i and indicating components in different directions); U is the partially averaged velocity; t is the time; p is the pressure; denotes a constant-preserving arbitrary (implicit or explicit) filter commuting with spatial and temporal differentiation; x denotes the coordinates; is the kinematic viscosity. Here, V i is partitioned into two parts: partially averaged velocity (U) unresolved part ( ). Vi Ui ui Ui Vi (3) where U i is the resolved velocity field; u i is the unresolved field. It is used by equation 4 instead of the resolved field. In Eqs. (1) and (), the additional non-linear term τ(v i, V ) (i.e. the generalized central second moment) is defined as, V, V VV V V (4) u i The PANS models are: i i i k Uk u u u k u k Pku u t x x u x U u C P C t x x x k k u u u u * u k 1 ku u u u Considering the nolinear turbulence flow in the pump-turbine, the shear stress was solved by nolinear turbulence model which was proposed by Ehrhard [1]. U Pk U i U (7) x 1 U i U ki C P TSi C1C P T Sik Sk Skl Skli CCke T iksk kski C3C P T ik k lklki C4Cke T Skil Skli Skl C5CP T SiSkl Skl C6CP T Siklkl 3 (8) 1 1 U U k i CP min, i S 0.9S x x k S i S i i i i where C ke k, C1 0., 0.4 C, C S 3.0 exp, C4 3.0C, P C5 16.0C, P C6 16.0C,T P (1) () (5) (6)

4 ICPF015 IOP Conf. Series: Materials Science and Engineering 19 (016) doi: / x/19/1/01048 is turbulence time scale, is the turbulence velocity scale. 3. Simulation Setup Flow past a circular cylinder at R ed= was simulated using the nonlinear RNG k-ε PANS model at different resolutions. Values of the f k were 0., 0.6, 0.8 and 1. At this Reynolds number the flow is still sub-critical, i.e., the boundary layers at the cylinder separate laminarly and transition takes place in the free shear layers. In the wake strong vortex shedding is observed. The computational domain shown in Fig.1 is a square cross section of 30D 30D with the cylinder located at the center. D is the diameter of the circular cylinder at the center of the section. The spanwise lengthen of the domain is D with the circular cylinder stretching along the enter domain. The nonlinear RNG k-ε PANS model was performed via the user defined function (UDF) using a commercially available Fluent code. Enhanced wall boundary function was used at the upper and lower solid wall of the domain. No slip boundary condition was chosen for the calculations. The periodicity of the flow is assumed in the spanwise direction of the cylinder. A constant velocity inlet flow with zero turbulence intensity is imposed. Three dimensional (3D) simulations were performed with segregated and implicit solver. Second order scheme was using for the pressure discretization. SIMPLE was using for the pressure and velocity coupling. Second order upwind was using for discretizing the momentum, turbulence kinetic energy, turbulence dissipation rate. Constant velocity inlet was used at the inlet of the computational domain and outflow was using for the outlet. The time step using for the calculation was set up according to the courant number less than 1. Detailed simulation setups are shown in Table 1. Hexahedral mesh forms the computational domain. Mesh at the vicinity of the cylinder is shown in Fig.. Figure 1. Geometry of computational domain Figure. Mesh at the vicinity of the cylinder 4. Results and discussion 4.1. Influence of f k on velocity statistics The effects of varying f k values on the flow statistics are investigated. The experimental results by Cantwell and Coles are plotted alongside for comparison purposes. The mean streamwise velocity along the wake centerline (y=0) is calculated by the nonlinear PANS model and shown in Fig.3. Normalized streamwise velocity (u/u 0) of various f k values plotted alongside the experimental result. The nonlinear PANS calculation results with f k=1.0 and fk=0.8 have large tolerances compared with experimental data. With PANS calculations f k=0.6 and 0.4, the mean velocity profiles get closer to the experimental results. When f k=0.4, the calculation result is in good agreement with experimental data. In the wake region(1<x/d<5), the PANS results show monotonic improvement toward experimental data as the f k value is reduced from 1.0 to 0.4. In the far wake region(x/d>6), the PANS results are all close to the experimental data. This could be attributed to the decrease of the influence of wake flow downstream the cylinder. Results performed by Lakshmipathy 3

5 ICPF015 IOP Conf. Series: Materials Science and Engineering 19 (016) doi: / x/19/1/01048 and Girimai 10 using PANS model without nonlinear shear stress are also shown in Fig.3. It can be seen than the nonlinear PANS model is accuracy in the region (1<x/D<5). u/u o f k = f k =1.0 Laksmipathy f k = x/d Figure 3. Mean streamwise velocity along the wake centerline for various f k values Figure 4 shows the mean normal velocity on x/d=1.0 line. There has a rotational symmetry of the mean normal velocity on x/d=1.0 line. The PANS results with f k=0.6 and 0.4 predict the mean normal velocity at the x/d=1.0 line with good accuracy. The computations results with f k=1.0 and 0.8 fail to capture the trend for this velocity statistics at the wake flow. The maximum normal velocity at the x/d=1.0 line predicted with f k=0.4 is only a little large than the experimental result. For the mean velocity statistics presented above, a smaller f k values is better for the nonlinear PANS computations for turbulence flow. Exp. f k =0.4 f k =0.6 v/u o Exp f k =0.4 f k =0.6 f k =0.8 f k = y/d Laksmipathy f k =0.5 Figure 4. Mean normal velocity on x/d=1.0 line Figure 5 shows the mean streamwise velocity at x/d=1.0 line in the near wake region. The mean streamwise velocity shows a symmetry distribution by y/d=0. At x D=1.0, the PANS results with f k=0.4 are in good agreement with the experimental measurements, which show V-shaped profiles at this location. A V-shaped profile has been indicated by experiments done by Kravchenko and Moin 3, which also shows that simulation results are more accuracy when f k=0.4. As f k increases, the maximum mean streamwise velocity increases, while the minimum mean streamwise velocity decreases. When f k 0.6, the mean streamwise velocity profile on x/d=1.0 line transforms into U-shape. This could be attributed to the fact that the separation in the case of PANS computations is turbulent in nature. The peak velocity for the PANS computations with PANS of f k=0.4 showing the best agreement with experiments. Figure 6 shows the mean streamwise velocity at x/d=3.0 line in the near wake region. The mean streamwise velocity shows a symmetry distribution by y/d=0. When f k=0.4, the simulation results of mean streamwise velocity have the same shape with experimental result and it can predict the hump 4

6 ICPF015 IOP Conf. Series: Materials Science and Engineering 19 (016) doi: / x/19/1/01048 characteristic at 1.0<y/D<.0 and -.0<y/D<-1.0. At x over predict the velocity at the center. D =3.0, the PANS computations with f k u/u o Exp. f k =0.4 f k =0.6 f k =0.8 f k = y/d Figure 5. Mean streamwise velocity at x/d=1.0 line 1.0 u/u o Exp. f k =0.4 f k =0.6 f k =0.8 f k = y/d Figure 6. Mean streamwise velocity at x/d=3.0 line 4.. pressure coefficient distributions Figure 7 shows the distribution of pressure coefficient versus θ, the angle measured from the forward stagnation point along the surface of the cylinder. The nonlinear PANS results are compared with experimental data at this high Reynolds number [19]. With the reduce of f k, the minimum pressure is more and more close to the experimental result. The inflection point of the pressure coefficient line at θ=100 o is predicted accurately when f k 0.6. The pressure drop on the cylinder surface increases further as the f k value is reduced, leading to delayed separation. 5

7 ICPF015 IOP Conf. Series: Materials Science and Engineering 19 (016) doi: / x/19/1/ Exp. f k =0.4 f k =0.6 f k =0.8 f k =1.0 Cp ( o ) Figure 7. C p distribution over the cylinder surface 5. Conclusions The nonlinear PANS model modified from RNG k-ε turbulence model is performed by the commercial CFD package FLUENT using user define function. Turbulence flow past a circular cylinder at Re D= is used to evaluate the accuracy of the nonlinear PANS model. The nonlinear PANS capability of reducing the closure cut-off length-scale by decreasing the f k value is examined by performing simulations with f k values of 1.0, 0.8, 0.6, and 0.4. As can be seen from the results presented above, PANS performs very well in computing profiles and flow distributions. Based on the computed results for flow past a circular cylinder, it is reasonable to conclude that the nonlinear PANS bridging method is a theoretically sound and computationally viable variable resolution method for practical flow computations. The computational result is reasonable when f k is less than 0.6. The PANS method can be used in the simulation of high Reynolds number turbulence flow. Acknowledgments The authors would like to thank National Natural Science Foundation of China (No ) and Open research fund program of State Key Laboratory of Hydroscience and Engineering (Proect No. sklhse e-0). References [1] Wu Y L, Li S C, Liu S H, Dou H S and Qian Z D, 013 Vibration induced by hydraulic excitation in Vibration of hydraulic machinery Springer Germany [] S Girimai, R Srinivasan and E Jeong 003 PANS turbulence models for seamless transition between RANS and LES: fixed point analysis and preliminary results, ASME paper FEDSM [3] Lakshmipathy, S and Girimai, S 006 Partially-averaged Navier-Stokes method for turbulent flows: k-ω model implementation. 44th AIAA Aerospace Sciences Meeting and Exhibit ( Reno, Nevada) 119. [4] S Lakshmipathy and S Girimai 010 Journal of Fluids Engineering 13(1): [5] Ji B, Luo X W, Wu Y L, Peng X X, Xu H Y 01. International Journal of Heat and Mass Transfer 55 (3-4), [6] Ji B, Luo X W, Wu Y L, Peng X X, Duan Y L 013. International Journal of Multiphase Flow 51, [7] B Basara, S Kranović, S Girimai, and Z 011 Pavlovic. AIAA Journal 49(1): [8] L Davidson, Peng S H 013 AIAA Journal online first, doi: /1.J [9] B Contwell and D Coles 1983 J. Fluid Mech. 136(1): [10] M Breuer 000 Int. J. Heat Fluid Flow 1(5):

8 ICPF015 IOP Conf. Series: Materials Science and Engineering 19 (016) doi: / x/19/1/01048 [11] A Travin, M Shur, M Strelets, and P. Spalart 000 Turbul Combust. 63(1-4): [1] Liu J, Zuo Z, Wu Y, Zhuang B and Wang L 014 Computers & Fluids 10,