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

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 (3 min read)

### 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.

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##### Frequently Asked Questions (2)

###### 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.