Prediction of transition in wall-modeled LES

Parviz Moin Center for Turbulence Research

Stanford FA9550-11-1-0111

Physics-based modeling of compressible turbulence and its interaction with shock waves

2014 Parviz Moin --- FA9550-11-1-0111 --- Stanford University

Wall-Modeling in Large Eddy Simulations (LES) State-of-the-art is insufficient to predict complex flows at realistic Reynolds numbers present in hypersonic propulsion systems

Large eddy simulations of complex multi-physics flows at realistic Reynolds numbers

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Integrate sub-grid scale, wall and combustion models for high-fidelity simulations of scramjets Analysis of turbulence length scales yields criteria to couple the wall-model to the LES, removing the “log-layer mismatch” and leading to an accurate prediction of skin friction Flamelet-based combustion models account for complex chemistry (e.g., hydrocarbon fuels) at a feasible simulation cost

Wall-Modeled LES of Non-Equilibrium High-Speed Flows Validated simulations of hypersonic propulsion systems incorporating complex non-equilibrium physics

Supersonic Jet Noise from a realistic, faceted military-style nozzle Expensive ground testing provides partial information Difficult to control pressure ratio and temperature ratio simultaneously due to uncertainties of internal boundary layers

High fidelity LES of crackling hot, supersonic jet Unstructured LES code CharLES coupled with mesh adaptation tools (Adapt) focuses resolution where needed. Simulation scaled on 1 million processors on IBM Blue Gene Q (LLNL) N-shaped waves emerge directly from from jet turbulence Conditional averaging and convection velocities support connection to large scales Intrinsic temperature effect (contrary to Ffowcs Williams’ 1975 hypothesis)

Above: Conditionally-averaged pressure field computed by reverting simulation to a precise instant prior to crackle event. (JEGTP, 2013)

At right: Snapshot of flow field from LES showing contours of pressure (blue)

and jet temperature (orange-red-yellow) on a vertical slice.

(AIAA, 2013)

New Understanding of Source Mechanisms of Jet Crackle High-fidelity simulation of a spatially developing, round jet enables observation of crackle waves forming in connection with large scale flow features

Experimental military nozzle

Wall pressure inside the isolator and combustor of the HIFiRE-2 scramjet engine in cold and hot conditions at the spanwise centerline for wall-modeled LES (lines) and ground test experiment (symbols) (Bermejo-Moreno et al. 2013)

Instantaneous flow features from wall-modeled LES of HIFiRE-2 scramjet engine inside the combustor.

Transition in high-speed flows

LES Prediction of Transitional and Turbulent Boundary Layers

SGS Models unable to capture wall effects (do not carry enough subgrid stress)

Dynamic models predict transition location well on coarse

grid, but underpredict the skin-friction overshoot (no wall model here)

Constant coefficient models get it completely wrong

Note: grids have 10-20 pts per δ – as in wall-modeled LES

Needs wall modeling

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DNS of different types of transition scenarios

DNS of different transition scenarios

• Conducted direct numerical simulations of controlled transition to developed turbulence in BL

• K- type transition: TS wave plus oblique wave @ same frequency (~2%)

• H-type transition: TS wave plus oblique wave @ sub-harmonic frequency (~1%)

• By-pass transition: periodic and continuous free-stream forcing.

DNS, computational setup

Laminar inflow Transitional region Turbulent section

Sponge and reshaping

section

Sponge in the wall normal direction

Disturbance strip,

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Exit s

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Rex = 105

Inflow, Ma = 0.2

• Each DNS calculation 1.1 billion grid points • Maximum of 32K processors were utilized • Each flow through time (FTT) 2 million CPU hours

H and K type Transitions

(K-) Klebanoff type transition (H-) Herbert type transition

DNS K-type Transition prediction: 1.2B, 32k Cores

Sweep Through Instantaneous Snapshot

V1, V6

V2

,V

5

2 4 6 8 10

0.001

0.002

0.003

0.004

0.005

0.006

Laminar

H-type

K-type

Bypass

Transition prediction: DNS results

Comparison of skin friction profiles vs.

Comparison of skin friction profiles vs.

V1

V2

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4

200 400 600 800 1000 1200 1400

0.001

0.002

0.003

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H-type

K-type

Bypass

Transition prediction: DNS results

500 1000 15000

0.005

0.01

0.015

0.02

0.025

H-type transition

K-type transition

FST

FST continuous

Laminar

500 1000 15001

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

H-type transition

K-type transition

FST

FST continuous

Laminar

Integral parameters • The results are compared to the freestream turbulence (FST)

bypass transitions of Wu & Moin 20101 and 20122

1. X. Wu and P. Moin. Transitional and turbulent boundary layer with heat transfer. Physics of Fluids, 22:85–105, 2010. 2. X. Wu and P. Moin. Visualization of flat-plate boundary layer with continuous freestream turbulence, 2012 (submitted)

Shape factor, Displacement thickness

① All boundary layers go through different transition scenarios ② The resulting turbulent integral parameters are irrelevant of the transitional regime

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H-type transition

K-type transition

FST

FST continuous

Mean streamwise velocity at Re = 1250 θ

Velocity power spectra (K-type) near skin-friction maximum

Evidence for feasibility of reduced order modeling of near wall

turbulence

Similar Flow Structure in Spots Park, Wallace, Wu and Moin (2012)

Reynolds shear stress contribution from Dynamic Mode Decomposition1

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Fig: Iso-surfaces of Q colored by the streamwise velocity

Fig: Reynolds Shear stress gradient

1. Sayadi, Schmid, Nichols and Moin. J. Fluid Mech., 748:278–301, 2015.

Summary DNS

• Different transition scenarios lead to the same developed turbulence statistics for Re>800

• The basic structure of the developed turbulence is similar to the structure in the late transition zone

• The visualized flow organization is different depending on the downstream distance and initialization

• But, the fact that flow statistics are the same is significant and implies that hairpin packet solution of NS (late transition) is a plausible reduced order model

• Minimal flow unit (Jimenez & Moin) as an example of reduced order model

Wall-modeled LES of transitional and turbulent boundary layers

Cf

Recall…

Wall Modeling- A pacing item for LES A turbulent boundary layer and the required LES grid resolution:

Wall Model Implementation

Wall-modeling approaches for LES

• RANS-Based models:

- Equilibrium wall models

- Non-equilibrium wall models (full 3D

unsteady RANS near wall equations) Unclear for transition applications: more rigorous formulations for transition are needed.

• Slip wall model: not RANS-based and no adjustable coefficients.

Need transition sensors

Non-equilibrium wall-modeled LES

Wall-modeled LES

Application to NACA 4412 airfoil

Non-equilibrium with sensors

Slip wall

Wall-modeled LES for SCRAMJETS

(In)stability of supersonic combustion

• Instantaneous unsteady flow in a supersonic combustor

• Near-wall region colored by progress variable (~T) shows long-time global instability related to corner flow separations.

Sidewall this side

symmetry this side

Corner flow

Summary WMLES

• RANS-based wall models require transition sensors. Sensitivities to these sensors have to be determined.

• Is DNS required for the transition region to capture the growth of disturbances?

• Slip Wall is a new and very attractive approach for wall modeling. Further study needed for transition region.