Domaradzki LES Presentation

Large Eddy Simulations Goal of LES: provide flow quantities of interest with comparable accuracy as DNS but at significantly reduced computational cost (if RANS does not work)

Free turbulence Separation

Wall bounded turbulence

Heat transfer

transition

Why LES and not RANS? LES predicts transition behavior, wake mixing (Medic, Joo, Kalitzin, Sharma UTRC)

Mid-span section of Purdue transonic compressor rotor, Re = 740K, 135M cells, Tu=0.8%

Dt+ < 0.3 Dy+ < 0.1 Ds+ < 80 Dr+ < 10

Traditionally, fully turbulent RANS is used in compressor simulations

(x-xTE)/Bx=-0.041 (x-xTE)/Bx=0.0034 (x-xTE)/Bx=0.085 (x-xTE)/Bx=0.41

RANS with transition model improves predictions LES allows transition prediction and provides better wake mixing

Research projects during 2012 CTR Summer Program have contributed to the stated goal of LES by: Introducing and investigating new SGS models for

momentum, mixing, and heat transfer Developing wall models for LES for boundary layer

flows Assessing and using LES capabilities for specific flows

where RANS techniques are inadequate, e.g., flows and heat transfer for turbine blades, MAV, etc.

Exploiting particle methods as a complementary approach to LES for increasing computational efficiency for turbulence simulations

LES fundamentals

Goals:

Assess LES capabilities for simulating flows with separation, laminar, transitional, and turbulent regions (Francois Cadieux, Taraneh Sayadi, J. Andrzej Domaradzki, Sanjeeb Bose, Curtis Hamman)

Develop physics based off-wall boundary condition for LES of turbulent boundary layers (Ricardo Garcia-Mayoral, Brian Pierce, James Wallace)

Develop and evaluate new SGS models (Bing-Chen Wang, Guillaume Balarac, Mohammad Saeedi, Sanjeeb Bose, Curtis Hamman)

DNS databases: Sayadi (Nx x Ny x Nz=1536 x 300 x 128 = 60 million points; x+ =10, y+ =0.5, z + =8) Spalart and Strelets, JFM 403, 2000; mesh size about 15 million points

Benchmark problem: laminar separation bubble, Re=5x104

Goal: assess LES capabilities to reduce computational requirements for simulating separated flows significantly, to O(1%) of DNS resolution

3

4.5

6

Why LES? Because RANS for this flow are not reliable.

1. DNS: 60 million points 2. LES with dynamic model: 4% of DNS 3. No model DNS: 4% of DNS 4. No model DNS: 2% of DNS 5. No model DNS: 1% of DNS

Cp Cf

Different investigators (Florent Duchaine and Franck Nicoud) using a different code arrived at similar conclusions

Off-wall boundary condition at the top of the buffer layer at y+ = 100

Statistical properties of turbulent spots in boundary layers with bypass transition are remarkably like those in developed turbulent boundary layers. Park et al., Phys Fl. 24, 2012 (from 2010 CTR Summer Program). Motivating basis for creating an off-wall boundary condition (BC) at the top of the buffer layer for a turbulent boundary layer LES. BC to be created as a lower dimensional space-time representation of the flow at the top of a minimal flow unit taken from the transitional flow.

K-type transition Sayadi et al., 2012

PROJECT STEPS & ACHIEVEMENTS

Determine minimum flow unit size to give good statistics at y+ = 100 in transitional and developed turbulent flow regions. Obtain Fourier space-time representation of these x-z planes and explore required modes to adequately characterize the flow. Obtain the temporal modes using Dynamic Mode Decomposition (DMD) for these planes.

y+ = 100 Repeating minimal unit B. C. Turbulent channel flow

Yy+ = 250 DNS using this off-wall B.C.

u fluctuations

u fluctuations

The gradient model comes from a mathematical approximation of the filter.

Give a physical interpretation of the gradient model to improve the predicted scales transfer.

The GSSGS transfer of the gradient model is (analytical result)

Our proposal is to keep only the forward scatter term as SGS model resulting in a regularized gradient model.

Regularized SGS Gradient Model for Scalar Transport

rotation

com-

pression

stretching

Quadratic error of models are computed from filtered DNS of isotropic turbulence. From optimal estimation theory, the minimal error which is expected for a given model can be evaluated. No correction of a model could lead to smaller error than its irreducible error. This is an efficient tool to evaluate the ability of improvement of a model

Model performance is first evaluated through a priori tests (based on filtered DNS of HIT)

Minimal Error Tool for SGS Models

[Dotted lines: optimal estimators]

Quadratic errors as a function of the filter size

Model behavior in a posteriori tests: (5123-DNS of velocity and 323-LES of scalar)

LES of passive scalar in forced isotropic turbulence

Statistical scalar variance decay with time

Scalar variance spectrum (t=2)

Regularization procedure allows to correct the unphysical behavior of the classic gradient model Dynamic gradient model is less dissipative than the dynamic Smagorinsky model

Good spectrum prediction even at smallest resolved scales

Model validated in turbulent jet flow and for various grids and Schmidt numbers

Dynamic Full Linear Tensor-Diffusivity SGS Heat Flux Models (DLT) Wang et al.

k

jk

2

S

j

2

Ejx

SCx

|S|Ch

D

D

Dynamic Regularized Gradient Model Balarac et al.

Features of this scalar-flux model: Tensor diffusivity; Allows for backscatter; SGS scalar flux is not aligned with the scalar gradient; Typical to a dynamic modelling approach, it may still need clipping

in order to achieve numerical stability.

Heated Cylinder Test Case

Preliminary LES results by Sanjeeb Bose at CTR: scalar isosurface (Re=8900, 10 million CVs). SGS stress model: dynamic Vreman model (DVM), SGS scalar-flux model: DLT).

Objective: to predict mean and fluctuating Nusselt numbers at Re= 3000 and 8900, and compare with the experimental data of Nakamura & Igarashi (IJHFF, 2004).

Mesh Adaptation (Adapt Tool) and Numerical Results

Mesh adaptation at the high Reynolds number (Re=8900).

Comparison of the LES model predictions with the experimental data (data averaged over approximately 10 cylinder sheddings). Simulation performed by Sanjeeb Bose using CharLES

Necessity for mesh adaptation at high Reynolds number (demonstrated using the predicted mean Nusselt number).

A priori analysis of Dynamic Nonlinear Stress Model: Euler Angle Analysis

Se

e Se

e

Se

Perfect alignment

No rotation 0

:q Singular

Euler axis & angle characteristic of a linear constitutive relationship (Boussinesq).

Example: Smagorinsky type models

Euler axis & angle describing the attitude of eigen-frame of ij with respect to eigen-frame of sij.

)s(f ijij

Rotation matrix:

Euler angle :

)e,'ecos(e'eR jijiij

cos1)R(tr ij

Euler axis q:

)sin2/()RR(q T

Se

e

e

q Se

e

Se

ijNijWijS

*

ij CCC

Four SGS Stress Models Tested Smagorinsky type models Similarity model Dynamic two-parameter mixed model (DTPMM) Dynamic nonlinear SGS stress model (DNM) Wang et al.

Time- and spanwise-averaged wall-normal profiles of the Euler angle at Re =1750. a priori LES based on channel flow DNS data of Wu & Moin (JFM, 2012)

y+

Eu

ler

an

gle

100

101

10240

45

50

55

60

65

70

75

DNS (Wu & Moin, 2012)

DNM (Wang et al.)

DTPMM (Morinishi & Vasilyev)

Similarity (Liu & Meneveau)

Turbbulent Region, Re = 1750Line and time averaged (100 snapshots)

(deg)

A priori test in turbulent boundary layer

Accomplishments for LES Fundamentals

A benchmark case of a laminar separation bubble followed by a nonequilibrium turbulent boundary layer was proposed and adopted by several groups for testing LES models

Established that LES for the benchmark case with O(1%) of DNS resolution are feasible

Reduced-order off-wall boundary conditions for LES were explored by employing simulation databases for transitional flows

Improved SGS models were developed and tested in isotropic turbulence and heated cylinder