### 39

^{th}

### AIAA Fluid Dynamics Conference, San Antonio, Texas.

**A **

**A selective ** **selective review of CFD transition models** **review of CFD transition models**

### D Di Pasquale

### D Di Pasquale ^{†} A Rona A Rona ^{*} S J Garrett S J Garrett ^{‡}

### D. Di Pasquale

### D. Di Pasquale ^{†} ,, A. Rona A. Rona , , S. J. Garrett S. J. Garrett ^{‡}

†

### Marie Curie EST Fellow Engineering ddp2@le ac uk Marie Curie EST Fellow, Engineering, ddp2@le.ac.uk

*

### Lecturer, Department of Engineering, ar45@le.ac.uk,

‡

### Lecturer, Department of Mathematics, sjg50@le.ac.uk

### Transition (1)

Transition is a complex phenomenon, defined as the whole process of change from laminar to turbulent flow.

**Schematic of transition process**

### Transition (2)

### Main features

•

### Increased diffusivity in the flow.

### • Skin friction and heat transfer may increase considerably.

**Complexity:**

### • Simultaneous presence of turbulent and laminar flow, and also p ,

### interaction between the two phases.

### It involves a wide range of scales and it is very sensitive to physical

### flow features (Pressure gradient, Tu

_{∞}

### , Re, etc.).

### • It occurs through different mechanisms in different applications.

### Eight more widely used approaches have been reviewed:

**1.The stability theory approach**

### 2.The low Reynolds number turbulent closure approach

**3.The intermittency transport method with integral correlations**

### 4.The intermittency and the vorticity Reynolds number approach

### 5 The laminar fluctuation energy method

### 5.The laminar fluctuation energy method

### 6.The v

^{2}

### – f model

**7.Large Eddy Simulation (LES) for transition**

**8.Direct Numerical Simulation (DNS) for transition**

The approaches are compared to one another, highlighting their respective advantages and drawbacks.

### Stability theory approach (1)

### •Assume a laminar base flow u(x)

### •Superimpose a small disturbance u’(x y t)

### •Superimpose a small disturbance u (x,y,t)

### •Unstable if:

•

### Stable if:

### Stability theory approach (2)

**Advantage: the equations can be linearized, which makes this problem amenable **
to an analytical approach.y pp

Making use of : •Continuity equation

•Momentum equation

For 2D, incompressible, unsteady flow and neglecting quadratic terms in the The single oscillation of disturbances:

, p , y g g q

disturbance velocity components results in the Orr‐Sommerfield equation:

The problem of stability thus reduces to an eigenvalue problem.

The stability of each eigenmode is given by eigenvalues.

### Stability theory approach (3)

**Disadvantage: **

• The eigenfunctions are non‐orthogonal

Transient growth Transient growth

• The experimental critical Reynolds number exceeds its theoretical valueThe experimental critical Reynolds number exceeds its theoretical value.

• It cannot predict the transition due to non‐linear effects.

### Intermittency transport method (1)

It uses the concept of intermittency as introduced by Dhawan and Narasimha (1958) , to blend together laminar and turbulent flow regimes.

(1958) , to blend together laminar and turbulent flow regimes.

as done by : •Abu‐Ghannam (1980)

• Mayle (1991) based on empirical correlations

• Suzen & Huang (2000)

### 1

### 0

*laminar flow fully turbulent*

any value in between indicates that the flow is transitional

By letting the intermittency grow from zero to unity, the start and the evolution of transition can be imposed. Mostly, this is done by multiplying the eddy viscosity in a two‐equation turbulence model by the intermittency factor.

### Intermittency transport method (2)

**Advantages:**

• Although much more limited in capturing the real physics than DNS or LES, statistical modelling is still the only viable method to compute LES, statistical modelling is still the only viable method to compute complex flows with transition phenomena.

• Statistical RANS models can adequately capture the effects of transition

• Statistical RANS models can adequately capture the effects of transition in situations where most of the natural transition development stages are bypassed by some strong external disturbance.

• These models are relatively easy to calibrate and are often sufficiently accurate to capture the major effects of transition.

### Intermittency transport method (3)

**Disadvantages:**

### •The approach neglects the interaction between the turbulent and

### non‐turbulent regions.

### non turbulent regions.

### •The main limitation of the model is thought to be the accuracy of

### th i i l l ti i hi h th h i f t iti i

### the empirical correlations, in which the physics of transition is

### entirely contained.

### • These models have an inherently non‐local formulation, that

### precluded their implementation into general purpose CFD codes.

### Direct Numerical Simulation

A DNS computation is performed by solving the full time‐dependent NS equations

equations.

It is a suitable tool to predict transition, but in order to capture the small

l f t b l it i fi id

scales of turbulence, it requires a very fine grid.

**Disadvantages:**

• It is too costly for typical engineering application

• The proper specification of the external disturbance level and structure poses a substantial challenge

**Advantage:**

• It is an useful tool as research tool and as a substitute for controlled experiments

### Large Eddy Simulation

In LES computations, only the large scale eddies are resolved, the small scale eddies are modelled using an eddy viscosity approach such as that proposed eddies are modelled using an eddy viscosity approach such as that proposed by Smagorinsky

Th di t d t iti l ti i iti t th h i f th

The predicted transition location is very sensitive to the choice of the Smagorinsky constant that is used to calibrate the sub grid eddy viscosity

The dynamic sub‐grid model (Germano 1991) has the advantage that in the laminar BL the sub grid eddy viscosity is automatically reduced to zero

This model should be more appropriate for predicting transitional flow

### List of desirable features for CFD transition models

1. Allow the calibrated prediction of the onset and the length of transition 2. Allow the inclusion of different transition mechanisms

3. Be formulated locally (no search or line‐integration operations) 3. Be formulated locally (no search or line integration operations)

4. Avoid multiple solutions (same solution for initially laminar or turbulent boundary layer)y y )

5. Not affect the underlying turbulence model in the fully turbulent regime 6. Be formulated independent from the coordinate system

7. Applicable to three‐dimensional boundary layers

### Conclusion

• The review highlighted the difficulty in combining classical CFD to transition models

transition models

• There is clearly a need in industry for an accurate and robust transition model based on local state variables

model, based on local state variables.

• Despite its complexity, transition should not be viewed as outside the

f RANS th d i li ti t iti i t i d t

range of RANS methods: in many applications, transition is constrained to a narrow area of the flow due to geometric features, pressure gradients and/or flow separation. Even relatively simple models can capture these effects with sufficient engineering accuracy.

• The challenge to a proper engineering transition model is therefore mainly in the formulation of a model that can be implemented into a general RANS environment.