Turbulent Schmidt numbers for CFD analysis with various types of flowfield

A direct numerical simulation of a turbulent channel flow with three passive scalars at different molecular Prandtl numbers is performed. Computed statistics including the turbulent Prandtl numbers are compared with existing experimental data. The computed fields are also examined to investigate the spatial structure of the scalar fields. The scalar fields are highly correlated with the streamwise velocity; the correlation coefficient between the temperature and the streamwise velocity is as high as 0.95 in the wall region. The joint probability distributions between the temperature and velocity fluctuations are also examined; they suggest that it might be possible to model the scalar fluxes in the wall region in a manner similar to the Reynolds stresses.

Transport of Passive Scalars in a Turbulent Channel Flow

As mentioned in Chapter 1 the equations governing heat transfer with small temperature differences also govern transfer of small concentrations of other passive scalar contaminants. Particle-laden flows (Chapter 7) are excluded unless the particles are so small that they move with the flow and are negligibly affected by gravity. For convenience the discussion below is phrased in terms of heat transfer but translation to pollutant-transfer problems is straightforward. We use C, c for the mean and fluctuating parts of the concentration or temperature, for generality.

Heat and mass transport

A numerical simulation of turbulent natural convection (the Rayleigh–Benard problem) has been conducted using large-eddy-simulation (LES) methods and the results compared with several experiments. The development of the LES equation is outlined and discussed. The modelling of the small-scale turbulent motion (called subgrid modelling) is also discussed. The resulting LES equations are solved and data collected over a short period of time in a similar manner to the direct simulation of the governing conservation equations. An explicit, second-order accurate, finite-difference scheme is used to solve the equations. Various average properties of the resulting flow field are calculated from the data and compared with experimental data in the literature. The use of a subgrid model allows a higher value of Ra to be simulated than was previously possible with a direct simulation. The highest Ra successfully simulated was 2.5 × 106. The problems at higher values of Ra are discussed and suggestions for improvements made.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112085002634

Numerical simulation of the turbulent Rayleigh–Bénard problem using subgrid modelling

The processes present in a turbulent boundary layer (BL) which experiences a sudden change in the surface roughness are discussed in terms of numerical models in comparison with empirical data. Consideration is limited to flow perturbations which preserve the BL approximation. Generalized continuity, momentum and turbulent energy transport equations are reviewed. The perturbed BL has two regions: one with large velocity gradients and an outer zone with smaller gradients. Expressions are defined for the velocity and temperature profiles and the roughness length after a step change in surface roughness, which causes the disturbance. A pertrurbation could also arise from a heat flux input of a pressure gradient. The effects of the shape of the perturbing step and the presence of several disturbing edges are explored. Finally, it is shown that closure forms and constants for self-preserving flows are worthy of further development because of their demonstrable abilities to describe simple perturbed flows.

A.J. Reynolds

Papers

The prediction of turbulent Prandtl and Schmidt numbers