Stress-Blended Eddy Simulation (SBES) - A new Paradigm in hybrid RANS-LES Modeling

Transcription

1 Stre-Blended Eddy Simulation (SBES) - A new Paradigm in hybrid RANS-LES Modeling Menter F.R. ANSYS Germany GmbH Introduction It i oberved in many CFD imulation that RANS model how inherent technology limitation for certain type of flow (for example, flow with large/maive eparation, flow with trong mixing zone, flow with trong interaction of different flow feature). For thi reaon, there i an ongoing drive in the turbulence community to augment RANS capabilitie by Scale-Reolving Simulation (SRS) method. Motivated by the high cot of conventional Large Eddy Simulation (LES) and Wall Modelled LES (WMLES) for wall boundary layer imulation, hybrid RANS-LES model have been developed over the pat two decade. The mot prominent model are from the family of Detached Eddy Simulation (DES) variant propoed by Spalart [1]. The tarting point for DES wa the deire of utilizing LES in large eparation zone and for free hear flow without being forced into the exceive grid- and time-tep reolution requirement of LES for attached and mildly eparated boundary layer. DES wa therefore originally deigned to cover all attached boundary layer in RANS mode and to only witch to LES mode in detached region. In further tep DES wa extended to alo operate in Wall-Modelled LES (WMLES) format, where the RANS portion of the model i only active in the innermot part of the boundary layer and LES i applied over the ret of the domain. The aving in thi mode are much maller, a RANS only reduce the otherwie exceive near wall grid requirement of wall-reolved LES. The mot prominent verion capable of WMLES i IDDES [2] developed pecifically for that purpoe. For indutrial imulation, DES and variant (DDES, IDDES) have hown weaknee in the following apect: Shielding of boundary layer intended to be olved in RANS mode. A known, DES can lead to Grid-Induced Separation (GIS) when the meh i refined in the boundary layer a the RANS model can be affected by the grid limiter without proper balancing between RANS and LES turbulence content.

2 Slow tranition from RANS to LES in Separating Shear Layer (SSL). Conventional DES/DDES provide overly large value of eddy-vicoity in SSL and therefore prevent their fat break-up into reolved turbulence. Thi i caued by the pecific way the LES portion of DES i formulated. In recent year more modern verion of DES have been developed, which addre ome of thee deficiencie, mot noticeably the model verion [3]. However, in indutrial CFD imulation, additional requirement arie. Over the year, many CFD uer have voiced a deire for a more modular approach, whereby they could ue a pre-elected RANS and another preelected LES model intead of the mix of both formulation within one et of equation. In many intance, indutrial group have ued certain LES model (e.g. dynamic LES model in the combution ector) and want to extend their imulation to include part of the domain which can only be covered by RANS model (piping, blade, ). During that change, they don t want to witch their validated and truted LES model. In addition, a frequently voiced uer-requet wa to be able to clearly ditinguih region where the model run in RANS and region where the model run in LES mode. Finally, uer prefer model formulation which can be run afely in DES-mode with trong hielding but alo in WMLES mode in region of ufficient numerical reolution (and an uptream trigger into LES-mode). Stre-Blended Eddy Simulation (SBES) i an approach to cover all the above requirement. A thi paper repreent an invited lecture to the conference on indutrial apect of turbulence modelling, only the baic principle of SBES can be provided. The detail of the blending formulation are proprietary. Stre-Blended Eddy Simulation SBES i a fairly imple concept where exiting RANS and LES model are blended by a hielding (or blending) function. In the current approach, thi i performed on the tre-level: RANS LES f 1 f (1) In cae both model are eddy-vicoity model (a i typically the cae) the formulation implifie: RANS LES t t f t 1 f (2) In other word, SBES i not a new hybrid RANS-LES model, but a way to blend exiting model to achieve optimal performance.

3 While the formulation i eemingly imple, it complexity i concentrated in the hielding function f, which ha to atify the following requirement. 1. Provide high degree (aymptotic) hielding of RANS boundary layer under meh refinement. 2. Switch reliably and wiftly from RANS to LES in SSL. 3. Allow operation in WMLES mode. 4. Allow combination of all RANS and all (algebraic) LES model. 5. Remain robut even on non-perfect indutrial mehe. Previou author have formulated model baed on witching the eddyvicoity [e.g. 4]. However, the reulting model have typically not been able to atify the above requirement. Epecially requirement 1. i very hard to achieve, particularly in combination with point 4. Shielding of RANS Boundary Layer Shielding mean that RANS boundary layer are protected againt the LES (grid dependent) formulation to avoid compromiing that portion of the olution. GIS i a very evere problem in general indutrial flow imulation, a grid quality and reolution cannot be controlled to the level required by the deign of DES/DDES. Figure 1: Eddy-vicoity profile for DES(left) and DDES(middle) and SBES (right)under grid-refinement. (Note that range for SBES goe from r= ). Figure 1 how eddy-vicoity profile of DES and DDES and SBES under grid refinement. The parameter r i the ratio of the maximum edge length of the grid (a ued in DES) relative to the boundary layer thickne. It can be een that DES tart to deteriorate relative to the olid line (SST) once r<1. DDES provide improved hielding, but then alo break down for r~0.2. It i intereting to note that while DDES i uperior, it doe break down much more rapidly due to the interaction of the

4 impaired turbulence with the hielding function of that model (it hould alo be noted that IDDES provide only limited hielding imilar to DES). SBES provide perfect hielding even down to value of r~10-4 (note that the value for the grid pacing have been pecified within the turbulence model by hand independent from the underlying meh to avoid exceive CPU requirement). The ability of SBES to hield the RANS boundary layer far beyond what DES/DDES can achieve i an eential improvement in hybrid RANS-LES reliability. In addition, the trong hielding i a pre-requiite for blending the model at the tre level. Without uch trong hielding, SBES could not maintain the RANS mode for boundary layer on almot any realitic meh. Rapid RANS-LES Tranition The ability to hift from RANS to LES in a SSL i teted with the help of a tet cae where a flat plate boundary layer goe pat a 90 corner into a free mixing layer (Figure 2). The ingle-tream mixing layer flow wa experimentally invetigated in [5]. The experimental ection conit of a flat plate which uddenly terminate with a tep (Figure 36), which induce the formation of the mixing layer from the eparation point. The experiment i carried out at a Reynold number of Re θ=4650 baed on the momentum thickne θ of the incoming boundary layer and on the freetream velocity U 0. Figure 2: The domain and grid for the ingle tream mixing layer flow Figure 3 how io-urface of the Q-criterion to viualize reolved turbulence tructure. It can clearly be een that SBES provide rapid tranition between the RANS and the LES olution while DDES prevent the formation of 3D tructure due to overly high eddy-vicoity level. Figure 4 how the correponding velocity and treamwie velocity fluctuation RMS value, again demontrating the uperior performance of SBES. (The SDES curve will be explained in the final paper).

5 Summary The concept behind the SBES model formulation ha been explained. Specific characteritic of the model, like it aymptotic hieling propertie and rapid RANS-LES tranition have been demontrated. The fully paper will alo contain example demontrating the WMLES capability of the formulation. Figure 3: Io-urface of the Q-criterion coloured with the velocity magnitude. Left SBES, right DDES Figure 4: Profile of the mean (left) and u -RMS velocity (right) at different ection (x/θ=19.3, 29.6, 40.6, and 54.2) for mixing layer tet cae. Reference [1] Spalart, P. R. Detached Eddy Simulation, Annu. Rev. Fluid Mech., vol. 41, pp , [2] Shur, M.L., Spalart, P.R., Strelet, M.K. and Travin, A.K., (2008), A hybrid RANS-LES Approach with Delayed-DES and Wall-modeled LES Capabilitie, International Journal of Heat and Fluid Flow 29, pp [3] Spalart, P., Deck, S., Shur, M., Squire, K., Strelet, M., Travin, A. (2006), A New Verion of Detached Eddy Simulation, Reitant to Ambiguou Grid Denitie, Journal of Theoretical and Computational Fluid Dynamic 20, pp [4] Batten, P., Goldberg, U., Chakravarthy, S., LNS An Approach toward Embedded LES. AIAA Paper [5] S. C. Morri and J. F. Fo, Turbulent boundary layer to ingle-tream hear layer: the tranition region, Journal of Fluid Mechanic Fluid Mech., vol. 494, pp , 2003.