3D CFD computations of transitional flows using DES and a correlation based transition model

TL;DR: In this article, the correlation based transition model of Menter et al. in combination with the Detached Eddy Simulation (DES) methodology is applied to two cases with large degree of flow separation typically considered difficult to compute.

Abstract: The present article describes the application of the correlation based transition model of Menter et al. in combination with the Detached Eddy Simulation (DES) methodology to two cases with large degree of flow separation typically considered difficult to compute. Firstly, the flow is computed over a circular cylinder from Re = 10 to 1 × 106 reproducing the cylinder drag crisis. The computations show good quantitative and qualitative agreement with the behaviour seen in experiments. This case shows that the methodology performs smoothly from the laminar cases at low Re to the turbulent cases at high Re. Secondly, the flow is computed over a thick airfoil at high angle of attack, in this case the DU-96-W351 is considered. These computations show that a transition model is needed to obtain correct drag predictions at low angle of attack, and that the combination of transition and the DES method improve agreement in the deep stall region. Copyright © 2010 John Wiley & Sons, Ltd.

Summary

2 Introduction

• During the last years, Computational Fluid Dynamics has found wide spread use within the wind energy community, and has been shown to perform well in many cases.
• Attempting to shed some light on some of the fundamental problems connected to the deep stall physics of wind turbine blades, often equipped with thick airfoil, the present work firstly addresses the classical problem of predicting the drag crisis of a circular cylinder, secondly applying the same methodology to the flow over a thick airfoil.
• The cylinder case is mainly chosen because a large body of high quality experimental data exists, which for many other flows can be problematic to obtain for deep stall cases.
• It is well known that the movement of the separation point on the circular cylinder is highly influenced by the laminar to turbulent transition process.
• Additionally it is well know that typical RANS are not sufficiently accurate in massively separated flows, and to help alleviate this problem, the DES technique is applied.

3 Code description

• The in-house flow solver EllipSys3D is used in all computations presented in this paper.
• Both steady state and unsteady computations can be performed.
• When a convergent solution is obtained, the variables are updated, and the authors continue with the next time step.
• The problem of the LES region contaminating the RANS layer can happen when computing flows with high values of inflow turbulence typically used with the correlation based transition model.

3.1 Transition Model

• The γ− R̃eθ correlation based transition model of Menter [1], is a framework for implementing empirical correlations based transition criterions in general purpose flow solvers, that can be used together with structured, unstructured and parallelized solvers.
• The backbone of the model is two transport equations one for intermittency γ and one for the local transition onset momentum thickness Reynolds number R̃eθt .
• Based on a series of zero pressure gradient flat plate boundary layers, expressions for the two missing correlation functions relating Reθc and Flength to R̃eθt have been determined by Sørensen [15].
• (3) Comparing the present correlation for Reθc with the two correlations proposed by Toyoda et al. [16] and Pettersson et al. [17] good agreement is observed at low Reθt , see Figure 1. the expression for the Flength parameter has dimension of length, and not a dimensionless quantity as it should be.
• It is well known that the turbulence will decay from the inlet value, in the case of zero shear where there is no production in the farfield.

4.1 Computational grids

• The meshes for the computations in the present work are generated with the 2D enhanced hyperbolic grid generation program HypGrid2D [19] as a 2D slice, and the 3D grid is then generated by sweeping the grid in the span-wise direction, see Figure 2.
• The grid holds in total 8.4 million cells.
• The surface of the cylinder is modeled as a no-slip surface, and periodic conditions are used in the spanwise direction.
• The outer domain boundary is specified as inlet, except for the area downstream of the airfoil covering around +/- 45 degrees in azimuth direction, where outlet condition is used specifying fully developed flow.

4.2 Flow Over a Circular Cylinder

• The challenging case of flow over the cylinder covering the full range from laminar flow at low Reynolds numbers to transitional flow at high Reynolds numbers is investigated.
• Each machine has 2GB of memory, the interconnect is based on Gigabit Ethernet network.
• Comparing the computed drag ( FD0.5ρU2 ) as function of Reynolds Number with measured values [20], an improved agreement around the drag crisis is observed, see Figure 5, where the transitional computations predict the increase of the drag in the region of Reynolds number from 1× 104 to 2× 105 observed in the measurements.
• Observing the development of the limiting streamlines at the surface of the cylinder and the movement of the laminar to turbulent transition, insight about the actual physical process can be obtained.

4.3 Discussion of Cylinder Results

• The use of the combined DES/transitional methodology improves the prediction of the drag crisis on the cylinder compared to pure DES simulation.
• Additionally, the DES/transitional methodology predicts the correct flow phenomena, with laminar separation, turbulent reattachment followed Risø-R-1692(EN) 9 by turbulent separation along with backward shift of the separation point and the narrowing of the cylinder wake with increasing Reynolds number.

4.4 Flow over a thick airfoil

• Next, the method is applied to predicting the flow over the DU-96-W-351 airfoil, that has a thickness of 35% chord.
• Similar to the cylinder case, the separation of the flow over an airfoil is controlled by the momentum in the boundary layer flow and the skin friction distribution.
• This was identified as grid induced separation or MSD, and the application of the 10 Risø-R-1692(EN) DDES methodology seems to alleviate this problem.
• Right around the abrupt stall at 15 degrees, the computed results exhibit a large dependency on the inflow turbulence, showing a variation of nearly 20%, see Figure 12 and 13.
• Similar to the cylinder analysis, the power spectrum of the tangential force for the DU-96W-351 airfoil is analyzed to determine the Strouhal frequency of most energetic variations, performed for the case of 45 degrees angle of attack.

4.5 Discussion of Airfoil Results

• In the present work, computations of the flow over the DU-96-W-351, 35% thick airfoil in the region of stalled flow have been compared to measurements from the LM tunnel.
• In the computations the airfoil section is modeled with an extent of two chords in the spanwise direction and the use of periodic conditions.
• This is done to limit the number of cells needed to model the actual configuration, where the airfoil section is enclosed by walls.
• The problem of the wind tunnel corrections, that do not account for the interaction of the separation and the wall effects would additionally require further studies.
• The results show an improved agreement with the measured data, compared to 2D computations.

5 Conclusion

• The combination of Detached Eddy Simulations with a laminar to turbulent transition model has been demonstrated.
• The methodology has proven to be numerically very robust, and similar to the transitional computations using Reynolds Averaged Navier-Stokes approach, capable of predicting both laminar separation, turbulent reattachment, and turbulent separation.
• For the prediction of the cylinder drag crisis, a distinct improvement of the drag in the critical region is observed.
• For the airfoil the results are more inconclusive, but indicates that a very high dependency of the inflow turbulence intensity may exist for thick airfoils.

Figures

Table 1. The Strouhal number ( f ·DU ) number as function of Reynolds number.

Figure 7. Variation of Strouhal number with with Reynolds number.

Figure 12. Comparison between computed lift at various turbulence intensities and measured values from the LM tunnel.

Figure 13. Comparison between computed drag at various turbulence intensities and measured values from the LM tunnel.

Figure 1. Comparison between the four target points from the optimization and different correlation functions.

Figure 5. Comparison of computed drag force for the fully turbulent and the transitional computations with the measurements.

Figure 6. Identification of the Strouhal number for the Re=10000 case, using the power spectrum.

Figure 11. Time trace of computed normal force from a simulation at 15 degrees angle of attack for three different inflow turbulence intensities.

Figure 10. Representative snapshots of the absolute value of the vorticity behind the cylinder at four different Reynolds numbers, showing the narrowing of the wake with increasing Reynolds number.

Figure 9. Instantaneous limiting streamlines on the surface of the cylinder for four cases of the simulations for transitional flow.

Figure 3. Mesh around the DU profile.

Figure 2. Mesh around the circular cylinder.

Figure 8. Computed averaged azimuth position of the wake separation point measured from the stagnation point, compare with data from [24]

Figure 4. The time history of the drag force for the case of a Reynolds number of 5×105, showing the strong transient at the impulsive startup and the stochastic behavior in the ’periodic’ state.

Figure 16. Power spectrum of the tangential force for the DU-96-W-351 airfoil at 45 degrees angle of attack, a clear Strouhal frequncy of 0.26 Hz is visible.

Figure 14. Pressure distribution around the DU-96-W-351 airfoil, comparison between computed values and measured distribution at 10 degrees.

Figure 15. Comparison of pressure distributions around the DU-96-W-351 airfoil at 15 degrees for three different turbulence intensities. Averages at six spanwise positions are shown for each computation.

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3D CFD computations of transitional flows using DES and a correlation based
transition model
Sørensen, Niels N.
Publication date:
2009
Document Version
Publisher's PDF, also known as Version of record
Link back to DTU Orbit
Citation (APA):
Sørensen, N. N. (2009). 3D CFD computations of transitional flows using DES and a correlation based transition
model. Danmarks Tekniske Universitet, Risø Nationallaboratoriet for Bæredygtig Energi. Denmark.
Forskningscenter Risoe. Risoe-R No. 1692(EN)

Risø-R-Report
3D CFD computations of transitional flows
using DES and a correlation based transition
model
Niels N. Sørensen
Risø-R-1692(EN)
July 2009
Re = 1.e6

Author: Niels N. Srensen Risø-R-1692(EN)
Title: 3D CFD computations of transitional flows using DES and a correlation based
transition model
Department: Aeroelastic Design – Wind Energy Division
Abstract:
ISSN
The report describes the application of the correlation based tran-
sition model of of Menter et. al. [1, 2] to the cylinder drag crisis
and the stalled flow over an DU-96-W-351 airfoil using the DES
methodology. When predicting the flow over airfoils and rotors, the
laminar-turbulent transition process can be important for the aero-
dynamic performance. Today, the most widespread approach is to
use fully turbulent computations, where the transitional process is
ignored and the entire boundary layer on the wings or airfoils is
handled by the turbulence model. The correlation based transition
model has lately shown promising results, and the present paper de-
scribes the application of the model to predict the drag and shed-
ding frequency for flow around a cylinder from sub to super-critical
Reynolds numbers. Additionally, the model is applied to the flow
around the DU-96 airfoil, at high angles of attack.
ISBN 978-87-550-3749-6
Contract no.:
ENS-33033-0055
Group’s own reg. no.:
Sponsorship:
Danish Energy Agency
Cover:
Separation behind cylinder
Pages: 18
Tables: 17
References: 24
Information Service Department
Risø National Laboratory for Sustain-
able Energy
Technical University of Denmark
P.O.Box 49
DK-4000 Roskilde
Denmark
Telephone +45 4677 4004
bibl@risoe.dk
Fax +45 4677 4013
www.risoe.dk

Contents
1 Abstract 3
2 Introduction 3
3 Code description 3
3.1 Transition Model 4
4 Results 5
4.1 Computational grids 5
4.2 Flow Over a Circular Cylinder 6
4.3 Discussion of Cylinder Results 9
4.4 Flow over a thick airfoil 10
4.5 Discussion of Airfoil Results 15
5 Conclusion 15
6 Acknowledgement 15
2 Risø-R-1692(EN)

1 Abstract
The present report describes the application of the correlation based transition model of of
Menter et al. [1, 2] to the flow over a cylinder and a thick airfoils using the Detached Eddy
Simulation (DES) methodology. When predicting the flow over airfoils and rotors, the laminar-
turbulent transition process can be important for the aerodynamic performance. Today, the most
widespread approach is to use fully turbulent computations, where the transitional process is
ignored and the entire boundary layer on the wings or airfoils is handled by the turbulence
model. In the present work the possibility of combining the DES technique with a transition
model is tested for two flows featuring large separated areas.
2 Introduction
During the last years, Computational Fluid Dynamics has found wide spread use within the
wind energy community, and has been shown to perform well in many cases. Even though
much success has been achieved, important problems still exist where the standard fully tur-
bulent Reynold Averaged Navier-Stokes (RANS) approach fails to give sufficiently accurate
answers. The most obvious problem is the failure to predict the power production and load for
stall controlled turbines at high wind, corresponding to high angle of attack along the blade
span. Attempting to shed some light on some of the fundamental problems connected to the
deep stall physics of wind turbine blades, often equipped with thick airfoil, the present work
firstly addresses the classical problem of predicting the drag crisis of a circular cylinder, sec-
ondly applying the same methodology to the flow over a thick airfoil. The cylinder case is
mainly chosen because a large body of high quality experimental data exists, which for many
other flows can be problematic to obtain for deep stall cases. Additionally, cylindrical or nearly
cylindrical sections exist at the inboard part of most modern wind turbine rotors. To accomplish
the flow simulations, the new correlation based γ− Re
θ
model by Menter et al. [1] and the DES
version of the k − ω SST model by Strelets [3] is applied. It is well known that the movement
of the separation point on the circular cylinder is highly influenced by the laminar to turbulent
transition process. Additionally it is well know that typical RANS are not sufficiently accurate
in massively separated flows, and to help alleviate this problem, the DES technique is applied.
3 Code description
The in-house flow solver EllipSys3D is used in all computations presented in this paper. The
code is developed in co-operation between the Department of Mechanical Engineering at the
Technical University of Denmark and The Department of Wind Energy at Risø National Lab-
oratory, see [4, 5] and [6]. The EllipSys3D code is a multiblock finite volume discretization of
the incompressible Reynolds Averaged Navier-Stokes (RANS) equations in general curvilin-
ear coordinates. The code uses a collocated variable arrangement, and Rhie/Chow interpolation
[7] is used to avoid odd/even pressure decoupling. As the code solves the incompressible flow
equations, no equation of state exists for the pressure, and in the present work the Semi-Implicit
Method for Pressure-Linked Equations (SIMPLE) algorithm of Patankar and Spalding [8, 9] or
the Pressure Implicit with Splitting of Operators (PISO) algorithm of Issa [10, 11] is used to
enforce the pressure/velocity coupling, for steady state and transient computations respectively.
The EllipSys3D code is parallelized with the Message-Passing Interface (MPI) for executions
on distributed memory machines, using a non-overlapping domain decomposition technique.
Both steady state and unsteady computations can be performed. For the unsteady computa-
Risø-R-1692(EN) 3

Frequently asked questions

Q1. What are the contributions mentioned in the paper "3d cfd computations of transitional flows using des and a correlation based transition model" ?

The report describes the application of the correlation based transition model of of Menter et. al. [ 1, 2 ] to the cylinder drag crisis and the stalled flow over an DU-96-W-351 airfoil using the DES methodology. The correlation based transition model has lately shown promising results, and the present paper describes the application of the model to predict the drag and shedding frequency for flow around a cylinder from sub to super-critical Reynolds numbers. 

Q2. What have the authors stated for future works in "3d cfd computations of transitional flows using des and a correlation based transition model" ?

This could be the focus of further work, along with efforts to actually resolve the wind tunnel walls. The problem of the wind tunnel corrections, that do not account for the interaction of the separation and the wall effects would additionally require further studies.