Nasa Proposal

Developing a test bed for the validation of

wall-modeled LES and RANS LES hybrid methods for

complex high Reynolds number flows

Francois Cadieux

Department of Aerospace & Mechanical Engineering

University of Southern California

Scott Murman

Fundamental Modeling & Simulation Branch

NASA Advanced Supercomputing Division

February 2, 2015

Abstract

Large eddy simulation (LES) has proven to be an accurate and relatively robust tool forpredicting transitional, separated and unsteady flows. Flows over complex geometries at highReynolds numbers such as full aircrafts at cruise speeds are out of reach for wall-resolved largeeddy simulation (LES) due to the stringent requirements to resolve thin turbulent boundarylayers (TBL). Wall-modeled LES (WMLES) and hybrid RANS LES (HRL) methods try tobridge this gap by removing the need to resolve the flow near surfaces. A number of contendershave made significant progress, but the wall models and HRL models developed have not beenscrutinized and validated to the same extent as LES models, which casts doubts over theirpredictive power and accuracy. The first part of the proposed research project is to implementthe two most promising approaches dynamic slip wall model (LES-DSWM), dynamic hybridRANS LES (DHRL). The second goal is to validate and compare their performance on a numberof canonical and complex geometries for which either experimental or DNS data is readilyavailable. The use of a high order discontinuous Galerkin (DG) compressible Navier-Stokes solverwill allow the unambiguous assessment of the impact of these models without the influence ofunquantified numerical dissipation. The final goal is then to compare their accuracy and relativecomputational cost to using a single of large layer of high order elements extending from thesurface to the beginning of the log-layer, making full use of the flexibility of a discontinuousGalerkin CFD solver.

1 Introduction

1.1 Context

Large eddy simulation (LES) has proven to be an accurate and relatively robust tool for predictingtransitional, separated and unsteady flows despite its shortcomings. LES converges to DNS resultsas the resolution is increased instead of grid-converged LES results because the filter width isgenerally tied to the grid size instead of a physical quantity [15]. Its performance is also stronglycorrelated with the level of numerical dissipation and thus the order of accuracy of the solver used

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February 2, 2015 F. Cadieux, S. Murman

since subgrid scale (SGS) dissipation provided by LES models is often of the same order or smallerthan numerical dissipation [11, 5]. Flows over complex geometries at high Reynolds numberssuch as full aircrafts at cruise speeds remain out of reach for wall-resolved large eddy simulation(LES) due to the stringent requirements to resolve thin turbulent boundary layers (TBL) [16].Reynolds averaged Navier-Stokes (RANS) turbulence modeling approaches are more tractable butprovide limited insight into these types of flows because they preclude some important transientand unsteady dynamics. Unsteady Reynolds averaged Navier-Stokes (URANS) is an improvement,but it only provides partial unsteady information due to the large eddy viscosity damping thegrowth of most instabilities. Wall-modeled LES (WMLES) and hybrid RANS LES (HRL) methodstry to bridge this gap by removing the need to resolve the flow near surfaces while providingsufficient insight into the flow dynamics and unsteadiness. Much emphasis has been placed on thedevelopment of WMLES and HRL methods in the last 20 years to enable more accurate treatmentof unsteady high Reynolds number flows over complex geometries.

Although successful in many ways, Spalarts detached eddy simulation (DES) approach has endemicissues that may be fundamental to the method: log-layer mismatch caused by modeled stressdepletion (MSD), and non-monotonic grid dependence which can cause grid induced separation[21, 22]. Attempts to address these issues without heavily modifying the original formulation likedelayed detached eddy simulation (DDES) [21], and zonal methods [7, 6] have had some successbut also discovered other issues in their application such as sensitivity to grid skewness [2].

Partially averaged Navier-Stokes (PANS) [10, 1] and other variable resolution approaches such asthe scale-adaptive simulation (SAS) [13, 9] and turbulence-resolving RANS (TRANS) [20] avoidthese issues by tying the eddy viscosity to physical quantities like energy grid density or an integrallength scale. Their turbulence modeling approaches and results are often closer to URANS thanLES and are thus limited in their ability to capture transient and unsteady effects accurately [13].Their accuracy in pure LES mode has also not been thoroughly validated [17].

The dynamic hybrid RANS LES (DHRL) framework trades the simplicity of DES and PANS fora more mathematically and physically grounded approach. The velocity is decomposed into threecomponents: the Reynolds averaged (u), resolved fluctuating (u), and unresolved fluctuating (u)velocity.

ui = ui + u

i+ u

i= ui + u

i(1)

u is the ongoing time average of u. The modeled Reynolds and sub grid scale stresses are computedand balanced using local turbulent quantities produced by each model [2]. The formulation is thusmodel independent any RANS and SGS model pair may be used and shows some significantimprovements over other HRL methods whilst avoiding some of their pitfalls [24]. The simulationmay start in pure LES mode until enough time averaging is obtained to have the RANS modelactive, allowing better predictions of transition at the cost of a coarse LES. This difficulty may beavoided in cases where transition is not present by starting the simulation from a RANS or URANSsolution.

Most LES wall models make one of two assumptions which are too strict to allow their widespreaduse: they either assume an equilibrium boundary layer like in RANS, or they assume a specificform of the mean velocity profile [14]. The recent dynamic slip velocity wall model makes no suchassumption and derives an off-wall boundary condition for LES based on a specific differential filterform and a dynamic procedure [3]. The method is able to resolve a recirculating region at the end ofa NACA 4412 airfoil where most RANS and URANS models fail [3]. To achieve similar agreement

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for the same case with a 3D URANS type wall model on an embedded grid, the turbulence modelcoefficients have to be adjusted using a local and time averaged dynamic procedure [14].

1.2 Motivation

It is clear that a number of contenders to bridge the gap between wall-resolved LES and RANShave made significant progress, but the LES wall models and HRL models developed have notbeen scrutinized and validated to the same extent as LES models, which casts doubts over theirpredictive power and accuracy [17]. HRL methods often require new turbulence models or modifiedSGS models which have often not been thoroughly validated in pure LES mode, or even in pureRANS mode. Yet, some important weaknesses have already been identified in a number of thesemethods. New methods like the DHRL which claim to avoid these pitfalls deserve more scrutiny[2, 24]. Similarly, a number of recent LES wall models aim to properly predict non-equilibrium flowswith pressure gradients and recirculation regions. Some extending RANS ideas, whereas others likethe dynamic slip velocity model take a different approach. The accuracy and computational costof these models remains to be explored and compared to HRL methods.

2 Proposed project

The proposed project is to validate the most promising hybrid RANS LES method, DHRL, andLES wall-model, dynamic slip velocity (LES-DSWM), on a number of canonical and complex highReynolds number flows for which experimental and/or DNS data are available. In addition, a novelmethod unique to the discontinuous Galerkin formulation is to be developed and tested. Eachmethods performance will be compared on a number of relevant metrics: skin friction, pressurecoefficient, mean velocity profiles, RMS velocities, as well as computational cost.

2.1 Technical approach

The first step will be to implement the dynamic hybrid RANS LES method [2] and dynamic slipvelocity wall model [3] in an unstructured discontinuous Galerkin Navier-Stokes solver. This willallow the unambiguous evaluation of each method without any effects from unquantified numericaldissipation. To make sure of this, the numerical dissipation of the solver can be computed usingthe method developed by Schranner et al [18] and compared to that of the models employed inthese methods. Each method should then be tested and validated on a simple canonical flow suchas turbulent channel flow at a Reynolds number for which both experimental and DNS data areavailable, e.g. 590, to ensure it is performing as the authors of the method reported. The twomethods will then be applied to more complex flows to test the accuracy of their predictions, andtheir convergence characteristics when the grid is refined as well as when the order of the polynomialbases in the discontinuous Galerkin elements is increased. For example, the Ahmed body at aReynolds number of 7.68105 with a sub-critical slant angle of = 25 remains an important casewhere experimental data is available. Previous HRL methods like DES and wall-modeled LES haveimproved upon RANS results for this case but failed to capture the reattachment observed near themiddle of the slant in experiments and high order LES [19]. Given the importance of the turbulentboundary layers in this case, particular care should be devoted to verifying that the DHRL methoddoes not suffer from modeled-stress depletion (MSD) or the log-layer mismatch observed in DES.

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Another interesting case would be to simulate an airfoil near stall at a moderately high Reynoldsnumber of 2 106 such as to investigate the capability of the DHRL and LES-DSWM approachesto capture the successively occurring separation bubble, reattachment, and turbulent separation onthe suction side of the airfoil [12]. Grid refinement studies would need to be performed to ensure themethods converge to a solution monotonically and that they do not exhibit particular sensitivity togrid-induced separation. This test will also serve as a good indication of the performance to expectfrom these methods in massively separated flows.

Discontinuous Galerkin (DG) methods allow another unique solution avenue to reduce computa-tional requirements near the wall: a single layer of large higher order (N=32 to N=64 in the vertical)elements could be used instead of a wall model or RANS hybrid model. Such large elements nearthe wall can mitigate time step restrictions. Significant savings can also be achieved by usinghigher order polynomials: a laminar separation bubble flow was resolved accurately in an LES withonly 32 Chebyshev points in the vertical for a domain twice as large as the maximum turbulentboundary layer thickness at the outflow [4]. The computational cost of a single layer of large highorder elements spanning y+ = 0 to y+ = 80 may be comparable to HRL method, but will benefitfrom remaining closer to a pure LES. Coupled with the truncated Navier-Stokes (TNS) approach[8, 23], the proposed method could even side-step assumptions made in LES, i.e. that the filteredNavier-Stokes equations are the appropriate equations when the smallest eddies are not resolved.By using DG with TNS, the pure Navier-Stokes dynamics are preserved, and filtering is applied toremove energy accumulated in the small scales only when it reaches unphysical levels. This thirdapproach requires few modifications, and should provide an interesting benchmark to compare theDHRL and LES-DSWM approaches to. Although it is specific to discontinuous and finite elementformulations, this method may allow wall-resolved LES to reach higher Reynolds numbers thatwould otherwise be prohibitively expensive to compute.

2.2 Expected Outcomes

Two novel approaches to simulate high Reynolds number flows over arbitrary geometry will beimplemented in a discontinuous Galerkin solver: the dynamic hybrid RANS LES method, and theLES with dynamic slip wall modeling. Each will be validated on a canonical flow, and then furtherscrutinized through simulations of complex high Reynolds number flows for which experimentaldata is available. Their grid convergence properties, sensitivity to grid-induced separation, andtheir ability to capture turbulent and massively separated flows will be investigated. Comparisonsto pure LES with large high order elements near the surfaces will help better understand theeffects of the wall-models on the flow. Knowledge gained from this endeavor will help better ourunderstanding of these methods and how to best apply them. Ultimately, this effort is to helpsimulations at even higher Reynolds numbers succeed where other HRL methods have only hadmitigated success.

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IntroductionContextMotivation

Proposed projectTechnical approachExpected Outcomes

Documents

Nasa Proposal