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

The prediction of turbulent Prandtl and Schmidt numbers

A theory is developed for the stagnation point boundary layer with injection under the hypothesis that turbulence is produced at the wall by injection. From the existing experimental heat transfer rate data obtained in wind tunnels, the wall mixing length is deduced to be a product of a time constant and an injection velocity. The theory reproduces the observed increase in heat transfer rates at high injection rates. For graphite and carbon-carbon composite, the time constant is determined to be 0.0002 sec from the existing ablation data taken in an arc-jet tunnel and a balistic range.

Injection-induced turbulence in stagnation-point boundary layers

With the advances in large scale computers, reliable numerical methods and efficient post-processing environment, direct numerical simulation (DNS) has become a valuable and indispensable resource for fundamental turbulence research, although DNS is possible only when the turbulent Reynolds (or Peclet) number remains small to moderate. This paper reviews the contribution that various DNSS have made to understanding and modelling turbulent transport phenomena. After general remarks are made on the grid requirements and numerical methods of DNS, its novelties as a numerical experiment are summarized and some of them are demonstrated by introducing typical DNS results at the University of Tokyo. Emphasis is laid upon new findings on the turbulence statistics, their budgets and quasi-coherent eddy structures revealed by the simulations of the fully developed channel flow with heat transport at different Prandtl numbers, and also a recent modelling attempt to take into account the new knowledge extracted from these DNSS, i. e. a remarkable change of the destruction mechanism of turbulent scalar flux with the Prandtl number and a low Reynolds number effect on the redistribution process of the Reynolds stress.

Contribution of direct numerical simulation to understanding and modelling turbulent transport

Line and band models for infrared spectral absorption are discussed. Radiative transmittance and integrated absorptance of Lorentz, Doppler, and voigt line profiles were compared for a range of parameters. It was found that, for the intermediate path lengths, the combined Lorentz-Doppler (Voigt) profile is essential in calculating the atmospheric transmittance. Narrow band model relations for absorptance were used to develop exact formulations for total absorption by four wide band models. Several continuous correlations for the absorption of a wide band model were compared with the numerical solutions of the wide band models. By employing the line-by-line and quasi-random band model formulations, computational procedures were developed for evaluating transmittance and upwelling atmospheric radiance. Homogeneous path transmittances were calculated for selected bands of CO, CO2, and N2O and compared with experimental measurements. The upwelling radiance and signal change in the wave number interval of the CO fundamental band were also calculated.

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A.T. Wassel

Papers

Calculation of turbulent boundary layers over flat plates with different phenomenological theories of turbulence and variable turbulent prandtl number

Molecular gas radiation and laminar or turbulent heat diffusion in a cylinder with internal heat generation

Diffusion from a line source in a neutral or stably stratified atmospheric surface layer