Home Search Collections Journals About Contact us My IOPscience Testing of modified curvature-rotation correction for k-ω SST model This content has been downloaded from IOPscience Please scroll down to see the full text 2016 J Phys.: Conf Ser 769 012087 (http://iopscience.iop.org/1742-6596/769/1/012087) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 80.82.77.83 This content was downloaded on 04/03/2017 at 15:38 Please note that terms and conditions apply 18th International Conference PhysicA.SPb Journal of Physics: Conference Series 769 (2016) 012087 IOP Publishing doi:10.1088/1742-6596/769/1/012087 Testing of modified curvature-rotation correction for k-ω SST model A S Stabnikov and A V Garbaruk , Peter the Great St.Petersburg Polytechnic University Russia, 195251, St.Petersburg, Polytechnicheskaya, 29 an.stabnikov@gmail.com Abstract Using eddy viscosity models (EVM) for solving Reynolds Averaged Navier-Stokes (RANS) equations is the most popular and economical way of turbulent flow computations up to date However this approach, while being very convenient, is not flawless For example, for accurate prediction of rotating flows and flows with significant streamline curvature (turbine rotors, various vortices etc.) special corrections must be used along with EVM to account for effects of these factors on turbulence Current work presents the results of testing of the recently suggested modification of the Menter-Smirnov rotation and curvature correction for SST model A range of internal and external flows is considered: flow in a plane rotating channel, flow in a channel with 180° turn, airfoil tip vortex and 3D boundary layer with the streamwise vortices produced by vortex generators It is shown that the modified correction results in better prediction than the original version for the three dimensional vortex flows and gives virtually the same results for the 2D boundary layer flows Introduction Despite of recent popularity growth of hybrid methods for computing turbulent flows, solving Reynolds Averaged Navier-Stokes (RANS) equations is still the most widely used approach in engineering computations This approach allows to predict required flow characteristics with decent accuracy using reasonable amount of computer resources For the closure of the RANS equations eddy viscosity models (EVM) are usually utilized due to their simplicity, stability and low computational cost Sadly, EVM are not universal, but some of their drawbacks are well known and can be fixed by using ad hoc corrections, like their inability to account for curvature and rotation effects on turbulence These circumstances motivate creating new and modifying existing curvature and rotation correction terms In particular, a modification [1] for the Menter-Smirnov [2] correction term for the SST k-ω two equation model turbulence model [3] was proposed based on LES of rotating homogeneous shear flow The original Menter-Smirnov correction was developed on the basis of the Spalart-Shur correction [4] for one equation SA model [5] and reads { { } } f r1, MS = max 1.25, f r1 ,0.0 , (1) where f r1 = (1 + cr1 ) 2r * ( r )) − cr1 , − cr tan −1 (cr ~ 1+ r * (2) 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, journal citation and DOI Published under licence by IOP Publishing Ltd 18th International Conference PhysicA.SPb Journal of Physics: Conference Series 769 (2016) 012087 [ IOP Publishing doi:10.1088/1742-6596/769/1/012087 ] r* = S Ω , ~ r = 2Ωik S jk (DS Dt )ij Ω D , D = max{S ,0.09ω }, tensor invariants S = Sij Sij and Ω = 2Ω ij Ω ij of the strain rate Sij and vorticity Ωij , with constants cr1 = , cr = , cr = The proposed modification [1] is based on matching evolution of turbulent kinetic energy in rotating homogeneous shear flow of LES and SST RANS for different rotation rates and is of form f r1,mod = max{f r1 , 0.0}, (3) where f r1 = (1 + cr1 ) + cr (1 − cr tan −1 (cr ~r )) − cr1 , + cr ⋅ r * −2 (4) and cr1 = 0.4 , cr = 1.0 , cr = 0.6 , cr = 0.1 In contrast to the original correction, where function (1) is used as a multiplier of the production term for both k and ω transport equations, function (3) multiplies only the production term in k equation The purpose of this paper is to test the modified correction on different flows with significant rotation and/or curvature effects Two-dimensional tasks are represented with plane rotating channel flow and a 180° U-turn duct flow with substantial streamline curvature Two other test cases are threedimensional vortical flows: wing tip vortex and co-rotating vortices in the boundary layer downstream of array of vortex generators Results of three turbulence models were compared: SST model without any correction (SST), and SST with original (SST MS CC) and modified (SST Mod CC) MenterSmirnov curvature-rotation corrections All computations were performed using the NTS code [6], the convective fluxes were approximated using a third order upwind scheme and a central difference second order scheme for viscous fluxes Two-dimensional boundary flows 2.1 Plane rotating channel Plane channel flow, rotating at rate Ω around the z axis, normal to the flow plane (fig 1) is considered at Re =Ubulk∙h/ν = 5.8·103 (Ubulk – mean flow velocity, h – channel width, and ν – kinematic viscosity) and different rotation rates corresponding to the DNS of Kristoffersen and Andersson [7] Figure Rotating channel flow scheme Velocity profiles obtained with both corrections are close to each other for different Rossby numbers Ro=Ω∙h/Ubulk (fig 2а), but results using the modified term are somewhat closer to DNS data Also, a non-physical eddy viscosity peak at the vicinity of maximum velocity is removed by correction modification (fig 2b) 18th International Conference PhysicA.SPb Journal of Physics: Conference Series 769 (2016) 012087 IOP Publishing doi:10.1088/1742-6596/769/1/012087 2.2 U-turn duct Flow in U-turn duct at Re=Vm∙H/ν=106 (Vm – mean bulk velocity, H – channel width) was studied experimentally by Monson et al [8] Computational domain (fig 3) contains a 10H length region upstream of turn, turn region, and a region with length 12H downstream of turn The computational grid has dimensions 203×111 The following boundary conditions are applied: developed turbulent velocity profile calculated by SST model at inlet, no slip condition at channel walls and constant pressure at outlet Figure а) – velocity profiles in rotating channel at Ro=0.15, 0.2, 0.5 b) – eddy viscosity profiles at Ro=0.5 Figure U-duct with 180° turn problem formulation The results were compared at three channel sections where experiment data is available: start, middle and end of the turn (fig 3) Profiles, obtained by the two corrections are almost identical (fig 4) much like in the first test case So, computations reveal no significant effect of modification for these twodimensional wall bounded flows 18th International Conference PhysicA.SPb Journal of Physics: Conference Series 769 (2016) 012087 IOP Publishing doi:10.1088/1742-6596/769/1/012087 Figure Profiles of streamwise velocity in 180° turn channel flow Three-dimensional vortex flows 3.1 NACA 0012 tip vortex Finite span wing tip vortex is considered at experimental [9] conditions: a NACA 0012 airfoil with rounded tip is put in a closed wind tunnel (fig 5) Since experiment inlet Mach number was not high (inlet mean velocity is equal to 51.8 m/s), the incompressible flow at Re=3.568·106 is considered No slip conditions were applied on the airfoil surface while slip conditions are used on the tube walls Multi-block structured chimera type mesh contains about 5.6 million cells Results show (fig 6) that use of the correction modification leads to significant improvement of 2 prediction of both streamwise and crossflow U crossflow = v + w U inlet velocity profiles downstream of the wing It is caused by more effective suppression of eddy viscosity at the vortex center (fig 7) which leads to delayed decay of the vortex Figure NACA 0012 tip vortex flow scheme 18th International Conference PhysicA.SPb Journal of Physics: Conference Series 769 (2016) 012087 IOP Publishing doi:10.1088/1742-6596/769/1/012087 Figure Streamwise and crossflow velocity profiles at the back NACA 0012 wing tip and 0.24C and 0.68C downstream (C is the airfoil chord) Figure Eddy viscosity profiles at the back NACA 0012 wing tip and 0.24C and 0.68C downstream 3.2 Streamwise vortices in the boundary layer System of uniform vortex generators (VG) in the flat plate boundary layer with supersonic free stream at M∞=1.4 is considered VG height and length are equal to h and 4h correspondingly, the angle to the incoming flow is equal to 18° (fig 8) and the distance between VG’s is 5h Flow conditions correspond to DNS [10]: the Reynolds number based on VG’s height and free-stream velocity is equal to 104 The domain is 10.5h upstream and 50h downstream of the front edge of the VG Width of the domain is equal to the distance between VGs (5h), so periodic boundary conditions are specified The inlet profiles are taken from SST RANS computation of flat plate boundary layer so that boundary layer thickness at VG front edge has thickness equal to h The mesh contains about 7.4 million cells Comparison of circulation and maximum vorticity downstream of vortex generators shows that vortex decay is much faster in RANS simulations compared to DNS (fig 9) Usage of curvature corrections 18th International Conference PhysicA.SPb Journal of Physics: Conference Series 769 (2016) 012087 IOP Publishing doi:10.1088/1742-6596/769/1/012087 somewhat improves the decay rate, using modified correction lessens the mismatch between RANS and DNS even more This improvement, much like in the case of the NACA 0012 tip vortex problem, is due to decreased eddy viscosity in the vortex center (fig 10), leading to reduced decay rate of vorticity and circulation Figure Vortex generators flow scheme Figure 9.Circulation (left) and maximum vorticity (right) downstream of vortex generators array Figure 10 Comparison of the eddy viscosity contours at the section x/h=27.6 Conclusions Testing shows that the effect of correction modification [1] depends on flow type For twodimensional wall bounded flows only little improvement is achieved while in three-dimensional vortex flows the modified correction shows significantly better results than the original Note that the results with modified correction are not inferior to the original version in any of the considered flows Therefore, the modified Menter-Smirnov correction can be recommended for usage in wide range of flows with curvature and/or rotation effects 18th International Conference PhysicA.SPb Journal of Physics: Conference Series 769 (2016) 012087 IOP Publishing doi:10.1088/1742-6596/769/1/012087 References [1] Stabnikov A and Garbaruk A 2015 Modification of curvature and rotation correction term for SST model based on LES of rotating shear layer XX School-seminar for young scientists led by academitian of Russian Academy of Science Leontiev A I “Gas dynamics and heat transfer problems in power settings”, Report Theseses, pp 71-72 (in Russian) [2] Smirnov P and Menter F 2009 Sensitization of the SST turbulence model to rotation and curvature by applying the Spalart–Shur correction term Journal of Turbomachinery, 131, 041010 [3] Menter F 1993 Zonal two equation k-ω turbulence models for aerodynamic flows AIAA Paper 93-2906 [4] Spalart P and Shur M 1997 On the sensitization of turbulence models to rotation and curvature Aerospace Science and Technology, 1(5), 297–302 [5] Spalart P and Allmaras S 1992 A one-equation turbulence model for aerodynamic flows AIAA Paper 92-0439 [6] Strelets M 2001 Detached eddy simulation of massively separated flows AIAA Paper 20010879 [7] Kristoffersen R and Andersson H 1993 Direct simulation of low-Reynolds-number turbulent flow in a rotating channel Journal of Fluid Mechanics, Vol 256, pp 163–197 [8] Monson D, Seegmiller H, Mc Connaughey P, and Chen Y 1990 Comparison of experiment with calculations using curvature-corrected zero and two equation turbulence models for a two-dimensional Uduct AIAA Paper 90-1484 [9] Chow J, Zilliac G and Bradshaw P 1997 Mean and turbulence measurements in the near field of a wingtip vortex AIAA J 35, No 10, pp 1561-1567 [10] Spalart P, Shur M, Strelets M and Travin A 2015 Direct simulation and RANS modelling of a vortex generator flow Flow, Turbulence and Combustion, Volume 95, Issue 2, pp 335-350 ... Journal of Physics: Conference Series 769 (2016) 012087 IOP Publishing doi:10.1088/1742-6596/769/1/012087 Testing of modified curvature- rotation correction for k- ω SST model A S Stabnikov and... turbulence Current work presents the results of testing of the recently suggested modification of the Menter-Smirnov rotation and curvature correction for SST model A range of internal and external... of three turbulence models were compared: SST model without any correction (SST) , and SST with original (SST MS CC) and modified (SST Mod CC) MenterSmirnov curvature- rotation corrections All computations