BPS5234A Chap.2 Turbulence Models and Near-Wall Treatment
Turbulence Models and Near-Wall Treatment
Why a model is needed at all
Turbulent airflow in a room or a street contains eddies from the size of the space down to millimetres. Resolving all of them directly is far beyond any practical computer for building-scale problems, so the flow is split into a mean and a fluctuating part and the equations are averaged.
Averaging leaves one new set of unknowns, the Reynolds stresses, and every turbulence model is a way of supplying them.
The families and what they cost
Eddy viscosity models assume turbulent stress behaves like viscous stress with a much larger, flow-dependent viscosity.
The k–&epsilon family computes that viscosity from turbulent kinetic energy and its dissipation and is the workhorse for design and compliance. The shear stress transport model blends a near-wall formulation with k–&epsilon in the free stream and copes better with separating flow and with heat transfer at walls.
Reynolds stress models drop the eddy viscosity idea and solve for each stress, which helps in swirling or strongly curved flow.
Large eddy simulation resolves the large eddies in time and models only the small ones, at a cost one to three orders of magnitude higher.
The evidence the course offers
Benchmark comparisons show where the cheap model fails: a ceiling jet predicted too thick, stagnation-point heat transfer over-predicted in an impinging jet, and vortex shedding averaged away.
They also show that for many mean-flow design questions the cheaper model is adequate.
The wall region
Near a surface the velocity changes steeply. Wall functions bridge that layer if the first cell sits in the right zone, and outdoor studies must also make the ground roughness consistent with the incoming wind profile.
What this chapter covers
- 01
Reynolds decomposition and the closure problem
- 02
Eddy viscosity and the k-epsilon variants
- 03
SST, Reynolds stress models and large eddy simulation
- 04
Benchmark evidence on jets and stratified rooms
- 05
Wall functions and the y-plus zones
- 06
Sand-grain and aerodynamic roughness in wind studies
Worked example · free
How large is the turbulent viscosity?
- 1Write the eddy viscosity relation of the k-epsilon model.
- 2Substitute and evaluate the turbulent viscosity.
- 2Form the ratio to molecular viscosity and interpret it.
Key terms
- Reynolds Decomposition
- Splitting an instantaneous flow variable into a mean value and a fluctuation about it before averaging the equations.
- Eddy Viscosity
- A flow-dependent viscosity used to model turbulent stress in proportion to the mean rate of strain.
- Turbulent Kinetic Energy
- The kinetic energy per unit mass contained in velocity fluctuations, written k.
- SST Model
- A two-equation closure that uses a k-omega form near walls and a k-epsilon form away from them.
- Large Eddy Simulation
- A transient approach that resolves the large turbulent structures and models only the sub-grid scales.
- Aerodynamic Roughness Length
- The height parameter describing terrain roughness in a logarithmic wind profile.
- Log-Law Region
- The part of the near-wall layer where velocity varies with the logarithm of wall distance, where standard wall functions apply.
Turbulence Models and Near-Wall Treatment FAQ
Which turbulence model should a building study use by default?
For mean-flow design and compliance work, a realizable or RNG k-epsilon model is the usual starting point and is what most of the course labs use. Move to SST when separating and reattaching flow or wall heat transfer decide the answer, and reserve Reynolds stress models and LES for anisotropic flows, transient phenomena or research.
Why does k-epsilon over-predict heat transfer at the stagnation point of an impinging jet?
Heat transfer there is governed by a thin viscous sub-layer, and the standard model assumes fully turbulent flow, so it produces too much turbulence near the wall. The lecture shows the effect against measured Nusselt numbers for a circular jet.
What does y-plus tell you about a mesh?
It is the non-dimensional distance of the first cell centre from the wall. Values between about 40 and 130 place the cell in the log-law region where standard wall functions work; enhanced wall treatment and low-Reynolds models need much smaller values.
Why can an inflow wind profile change before it reaches the buildings?
If the wall function on the ground uses a sand-grain roughness that does not correspond to the aerodynamic roughness implied by the inlet profile, the flow adjusts as it travels across the empty upstream region, so the buildings receive a different profile from the one specified.
Is LES always more accurate than RANS for a building?
It resolves unsteady structures and peaks that RANS averages away, and benchmarks rate it highly for shedding and stratified flow, but it costs far more and needs finer meshes and time steps. For comparing design options on mean quantities, a well-verified RANS study is often the better use of time.
Assessment move
Build a one-page table of your own with four rows, one per model family, and three columns: what it solves, a flow it handles well, and a flow it gets wrong with the reason. Fill the reasons from the benchmark examples rather than from memory, then test yourself on the reasons only.
