Flow Behavior in the Transition Flow Regime

Key Takeaways

• The transition flow regime defines flows with a moderate Reynolds number.

• The conditions that lead to transition flow are system-specific.

• Transitional flow can be seen as a mixture of laminar and turbulent flow occurring simultaneously.

Several factors can combine to produce transitional flow along an open system, and the resulting turbulent flow behavior can be visualized in CFD simulations.

When systems are engineered to direct or take advantage of fluid flow, the system is designed such that flow occurs in two possible regimes: turbulent and laminar. There is also a transition regime; the flow behavior is said to evolve from laminar to turbulent flow as the Reynolds number increases. Although it is correct that laminar and turbulent flow lie at the extreme ends of the Reynolds number spectrum, the transitional regime does not involve a sudden evolution of flow into turbulence. Instead, transition flow regime behavior can be thought of as a combination of laminar and turbulent flow simultaneously. The best way to spot the deviation from laminar flow is from measurements of turbulence or through the use of CFD simulations. The limits on laminar and turbulent flow should be determined in engineered systems to ensure a design can operate as intended.

Characteristics of the Transition Flow Regime

In any system involving fluid flow, the geometric complexity in a system will create regions of varying flow velocity, which can be determined in a CFD simulation. The accuracy of such results can vary at a granular level, but the variation in broader flow rates throughout the system can be clearly seen. The same idea applies to a simple system, such as in the flow through a pipe, where the flow rate will be some function of the cross-sectional diameter and the flow rate in the boundary layer may have different characteristics than in the bulk fluid.

In different regions of the system, the internal and external forces governing flow characteristics will also vary. It is this variation in inertial forces in a system that can drive a boundary layer to undergo a transition from laminar to turbulent flow. With this in mind, transitional flow occurs due to interactions between two different flows in two regions of any system:

• Flow in the boundary layer, which initially begins as fully laminar at moderate Reynolds numbers but eventually develops progressively greater turbulent kinetic energy along the direction of the free stream flow.

• Turbulent flow in the freestream, where random perturbations in the free stream flow exert inertial forces on fluid in the boundary between, causing random perturbations to build up to turbulence.

In the Boundary Layer

In some flows involving moderate Reynolds numbers, the boundary layer may initially begin as laminar but eventually exhibit a transition from laminar to turbulence along the direction of the flow path. This will only occur if fluid flow in the bulk is already turbulent, which should underscore why transitional flow is often described as simultaneously laminar and turbulent.

The image below shows an example where fluid flow in the boundary layer (along the bottom wall surface) is initially laminar, but eventually the boundary layer flow transitions to turbulent flow.

Transitional flow development along a closed channel. Development of turbulent flow is clearly seen downstream.

In short, the transition is driven by inertial forces increasing beyond the ability of viscosity and friction to maintain steady laminar flow. Roughness along the surface is known to be one factor encouraging this transition. When inertial forces become large, fluid shedding occurs and turbulence will develop in the boundary layer. Note that, in the above flow field image, the velocity field at the inlet already exhibited some turbulence, while the flow along the wall was initially laminar. This development of turbulence due to fluid shedding is known to cause turbulence or vortical flow in other systems, such as flow separation along the backside of an airfoil at high attack angle.

In the Free Stream

When the turbulent kinetic energy in the bulk fluid is non-negligible, meaning the inertial forces it exerts on other fluid layers are larger than the viscous force, the free stream will eventually drive a laminar boundary layer to become turbulent. The underlying mechanism that drives free-stream perturbations is still unknown, but it can be modeled as a linear instability problem, where the growth/decay rate is based on an imbalance between viscosity and inertial forces.

Regardless of the underlying cause, many systems desire to operate as close to the edge of laminar flow as possible, but without experiencing transitional flow. Therefore, identifying the conditions under which transitional flow becomes fully turbulent in the boundary layer is very important for systems designers.

Simulating the Transition Flow Regime

Because the transition flow regime involves turbulence, it cannot be quantified analytically. Instead, numerical simulations are needed to determine the appropriate limits of flow parameters at which transitional flow begins to develop into turbulence. Certain systems, such as turbomachinery, rely on laminar flow and will see less efficient performance when transitional flow begins.

Some of the major CFD simulation methods used to determine the onset of turbulence include:

• Vorticity Reynolds number: This is the ratio of circulation around a turbulent vortex to the fluid viscosity; this is one way to estimate the decay rate for transitional flow.
• Large eddy simulation (LES): This numerical simulation technique requires applying spatial averaging to the Navier-Stokes equations to reduce the computational burden required to calculate turbulent flow.
• Reynolds-averaged Navier-Stokes (RANS): In contrast to LES, this method requires applying temporal averaging to the Navier-Stokes equations in order to simulate fluctuations about the average flow rate, i.e., turbulent kinetic energy.
• Detached eddy simulation (DES): This method mixes RANS and LES by applying spatial and temporal averaging to provide high resolution near wall boundaries, which is where the greatest resolution and accuracy are required in a transitional flow simulation.
• Direct numerical simulation (DNS): This turbulence simulation starts from the Navier-Stokes equations with specific initial conditions. This simulation method requires the most computational power but has the potential to provide results with the greatest accuracy.

When you need to evaluate system behavior in the transition flow regime and identify the onset of turbulence, you can investigate and simulate flow behavior with the meshing tools in Pointwise and the complete set of fluid dynamics analysis and simulation tools in Omnis 3D Solver from Cadence. These two applications give systems designers everything they need to build and run CFD simulations with modern numerical approaches.

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