Turbulence Chapter 4: Laminar-turbulent Transition Modeling

This chapter addresses the physical mechanisms governing laminar–turbulent transition and the challenges of modeling transition within the RANS framework. Different transition routes are introduced from a physical perspective, followed by a discussion of why traditional turbulence models fail to capture transition. Modern RANS-compatible transition models are then described, focusing on intermittency-based and laminar kinetic energy approaches used in industrial CFD.

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Why Transition Matters in Engineering CFD

Most engineering flows operate at Reynolds numbers where:

• Boundary layers are neither fully laminar nor fully turbulent

• Large portions of surfaces may remain laminar

Transition strongly affects:

• Wall shear stress (drag)

• Heat transfer rates

• Separation and reattachment

• Losses in turbomachinery

• Aerodynamic efficiency of airfoils and blades

Assuming “fully turbulent everywhere” often:

• Overpredicts drag and heat transfer

• Suppresses laminar separation bubbles

• Produces incorrect pressure distributions

What Is Laminar–Turbulent Transition

Transition is the progressive breakdown of an initially laminar flow into turbulence.

Key characteristics:

• It is not instantaneous

• It occurs over a finite spatial region

• Flow alternates between laminar and turbulent states locally

The flow in this region is called transitional, and its properties differ significantly from both laminar and turbulent limits.

Routes to Transition

Three main physical routes to transition are identified.

4.1 Natural Transition

Occurs when:

• Free-stream turbulence is very low

• Flow instabilities grow from small disturbances

Mechanism:

• Small-amplitude waves (Tollmien–Schlichting waves) amplify downstream

• Flow becomes three-dimensional

• Turbulent spots form and merge

Key features:

• Strongly Reynolds-number dependent

• Sensitive to surface quality and pressure gradients

• Long transition length

Natural transition is typical of:

• External aerodynamics

• Wind turbine blades

• Aircraft wings in clean environments

4.2 By-Pass Transition

Occurs when:

• Free-stream turbulence is moderate to high

• External disturbances penetrate the laminar boundary layer

Mechanism:

• Free-stream fluctuations generate streaks via lift-up mechanism

• Instabilities bypass classical linear instability stages

• Transition occurs much earlier

Characteristics:

• Shorter transition region

• Weaker Reynolds-number dependence

• Strong sensitivity to turbulence intensity and length scales

Typical in:

• Turbomachinery

• Internal flows

• Flows with upstream wakes

4.3 Separation-Induced Transition

Occurs when:

• Laminar boundary layer separates under adverse pressure gradient

Mechanism:

• Laminar separation creates a free shear layer

• Shear-layer instabilities rapidly grow

• Turbulence forms during or shortly after reattachment

Features:

• Very rapid transition

• Strong coupling with separation dynamics

• Large impact on pressure losses

Common in:

• Low-pressure turbine blades

• Wind turbine suction sides

• Compressor cascades

Why Standard RANS Models Cannot Predict Transition

Conventional RANS models assume:

• Fully developed turbulence

• Continuous turbulence production

• No laminar regime

As a result:

• Turbulence is artificially generated at the leading edge

• Laminar regions cannot exist

• Transition location is not predicted, only imposed

This motivates special transition models, not just modified turbulence closures.

Modeling Transition Within RANS

Transition modeling must satisfy:

• Local formulation (no boundary-layer integration)

• Compatibility with unstructured meshes

• Ability to handle different transition routes

• Robustness in complex geometries

This excludes:

• eⁿ stability methods

• Non-local correlation-based approaches

• Boundary-layer marching techniques

Intermittency Concept

A key idea in transition modeling is intermittency.

Intermittency represents:

• The fraction of time a flow behaves turbulently at a given location

Interpretation:

• Intermittency = 0 → fully laminar

• Intermittency = 1 → fully turbulent

• 0 < intermittency < 1 → transitional flow

Engineering quantities are obtained by blending laminar and turbulent behavior based on intermittency.

Transport-Based Intermittency Models

Modern transition models solve:

• A transport equation for intermittency

• One or more auxiliary equations to trigger transition onset

This approach:

• Avoids non-local operations

• Works on unstructured grids

• Is compatible with parallel solvers

The intermittency variable locally suppresses or activates turbulence production in the RANS equations.

Transition SST Model

9.1 Core Idea

The Transition SST model combines:

• SST k–ω turbulence model

• Intermittency transport equation

• Transition onset criterion based on empirical correlations

Transition onset depends on:

• Free-stream turbulence intensity

• Pressure gradient

• Boundary layer history

9.2 Local Formulation via Vorticity Reynolds Number

Instead of boundary-layer thickness:

• A vorticity-based Reynolds number is computed everywhere

• Its maximum inside the boundary layer correlates with transition onset

This allows:

• Fully local evaluation

• Use in complex 3D geometries

9.3 Separation-Induced Transition Treatment

Special corrections allow:

• Rapid turbulence growth after laminar separation

• Correct prediction of laminar separation bubbles

Without this correction:

• Reattachment is often predicted too far downstream 

Intermittency Transition Model

This model:

• Uses a single intermittency equation

• Relies entirely on empirical correlations

• Avoids transport of transition Reynolds number

Advantages:

• Simpler formulation

• Can predict crossflow transition

Limitations:

• Strong dependence on calibration database

• Less physically transparent than SST-based approach 

Laminar Kinetic Energy (k–kₗ–ω) Model

This approach introduces:

• A transport equation for laminar kinetic energy

• Represents pre-transitional fluctuations

Physical idea:

• Free-stream turbulence induces velocity fluctuations in laminar boundary layers

• These fluctuations grow until turbulence develops

Advantages:

• More physics-based

• Good for bypass transition

Limitations:

• Less robust

• More sensitive to inlet turbulence specification 

Practical Mesh and Modeling Requirements

Transition models require:

• Near-wall resolution (typically y⁺ < 1)

• Smooth wall-normal mesh expansion

• Accurate inlet turbulence specification

Poor mesh quality:

• Can shift transition location dramatically

• Can suppress laminar separation bubbles

Transition modeling is more sensitive to mesh and BCs than turbulence modeling.

Engineering Intuition

• Transition controls where turbulence starts

• Turbulence models control how turbulence behaves

• Separation-induced transition is often the dominant mechanism in practice

• Fully turbulent simulations can miss key physics

A useful rule:

If separation or heat transfer matters, transition modeling matters.

Study Priorities

If short on time, focus on:

1. Physical routes to transition

2. Intermittency concept

3. Why RANS cannot predict transition by itself

4. Differences between Transition SST and k–kₗ–ω

5. Sensitivity to mesh and inlet turbulence

Key Takeaways

• Transition is a finite, spatial process.

• Three main routes: natural, bypass, separation-induced.

• Standard RANS assumes fully turbulent flow.

• Intermittency enables RANS-based transition modeling.

• Transition SST is the industrial workhorse.

• Mesh quality and inlet turbulence are critical.