Prof. A.V.Primak at that time was the first among professionals in the USSR who would understand and participate in the early stages development of the turbulent transport VAT for the Urban Air Pollution Modeling. Dr. S.M.Komkov participated in fields of the VAT Urban Air Pollution Modeling and Chemical Engineering.

**Air Pollution Modeling (1978-1989)**

An understanding of the ways the two- and three-phase URL phenomena of transport have to be modeled with the VAT scaled approach, supported the original developments of VAT for the urban air pollution modeling and was the opening point in development of turbulent transport scaled modeling in porous media and URL. As such the development and application of heterogeneous nonlinear and turbulent phenomena scaled description (VAT) began with these advancements in air pollution modeling in 1982-86.

Urban rough atmospheric boundary layer - is the layer which main distinguished feature is the actual existence of a two-phase medium in which turbulent transport meteoelements and pollutants occur. Of ever-growing importance are urban pollutants transport processes resulting from of interaction of the atmospheric boundary layer with the ground roughness elements. It is natural that the problems of atmospheric diffusion and heat pollution in large urban settlements are to be formulated with an allowance for the interaction of the atmospheric turbulent boundary layer (ABL) with an underlying surface consisting of urban roughness layer (URL) obstacles. In order to determine and choose a model for turbulent transfer in a URL medium and over it in an ABL, it was necessary to distinguish specific types of models. Depending upon time and space scale descriptions and the quantization of a modeling object, which concern the fields of meteorological elements and pollutants, pollution sources together with the morphologically determined region of their spreading, deterministic or stochastic models may be appropriate. In a city, the main features of an analysis are the non-homogeneity of the distribution of pollution sources in space and the problem of description or parameterization of the underlying surface roughness - buildings, trees, architecture elements, etc.

A technique for obtaining a mathematical description of a surface with a randomly non-homogeneous roughness layer has been elaborated in 1980-82. The technique is different from the few known methods and is based upon the analysis of morphometric characteristics obtained in the so-called elementary statistical volumes (ESV), into which the urban roughness layer is divided. Afterward the experimental morphometric data can be used in the URL volume averaging theory models.

The urban roughness layer turbulent transport VAT models offered not general, but for the specific city strictly experimental allowance for the morphological characteristics of the randomly non-homogeneous roughness layer of specific urban housing systems and phytocenosis and made it possible to assess their effect on the characteristics of the turbulent boundary layer and diffusion of harmful impurities in the urban roughness layer. Proceeding from the simulations results for the real urban morphology characteristics in one of local area in the city of Kiev arrived at the conclusion that the arrays of experimental data of the harmful pollutant concentrations obtained in the lower part of the URL are significantly affected by the morphometric characteristics of the URL properties. It was apparent that available models did not predict the increased levels of concentration of pollutants in the URL nor the atmospheric weather elements.

In the 1986-1989th these results were used for an assessment of ABL pollution problem for the very large oil deposit exploration project "Tengiz", which is now under continuous development by international partners (including USA partners) in Kazakhstan.

The Morrin-Martinelli-Gier Memorial Heat Transfer Laboratory of the UCLA was the place of developments in VAT using funds obtained from different US government agencies and private sources. The Department of Energy (DOE) Office of Basic Energy Sciences supported the VAT development research: "Basic Studies of Transport Processes in Porous Media" for more than 11 years. Also the funds from DOD ARPA and later DOD DARPA grants were instrumental for VAT basic research. The fields of Fluid Mechanics and Thermal Physics were primary fields in focus of students involvement at this lab. Among students the few were special as H.Dichtl and Ph.D. student K.Hu. Amid results could be mentioned the following:

VAT methods involving the strict analytical or statistical description of the morphological aspects of heterogeneous two- and three-phase media were employed in the theory. Essentially the influence of structural morphology was determined by utilizing various analytical (statistical), numerical methods for closure and solution. Models were developed, beginning at the pore-scale level. Boundary and interphase conditions were incorporated at various scales leading to descriptions of transport in porous media.

**Single-Phase Flow in Porous Media**

Transport models for forced, single phase fluid nonlinear and turbulent convection were extended for non-uniformly and randomly structured highly porous media. Special attention was given to the evaluation of two-temperature energy and two-concentration solute transport models while emphasizing local solid phase morphology. The random characteristics of the porous medium were simulated by the use of regular and unspecified statistical, pre-assigned solid phase morphologies. The following issues were studied: the influence of medium morphology upon transport process characteristics, methods for the closure of the mathematical equations, the incorporation of specifics of turbulent mass, momentum and heat transfer process descriptions into the models, the expression of physically accurate boundary conditions, and coupled transport modes in highly porous media.

Have solved the problem for the stochastic distribution straight pore porous medium laminar and turbulent flow and heat transfer on the two (2) scales exactly for the first time. This problem is given in each textbook on porous medium transport, but never was solved correctly even for laminar flow.

**Development of Second-Kind Turbulent Transport Models in Highly Porous Media: Heat Transfer Studies**

Special models that correctly account for the medium morphology characteristics were developed to describe turbulent flow and diffusion of admixtures and energy processes in a highly porous medium. Equation sets for turbulent filtration and two-temperature or two-concentration diffusion were obtained for non-isotropic porous media with interface exchange and microroughness based on second order turbulence models. The equations developed with an advanced averaging technique and a hierarchical modeling methodology involving fully turbulent models capable of accommodating Reynolds stresses and fluxes in the space of every pore. The equations for both developed flow and diffusive processes in a random, highly porous medium were obtained. Additionally, the statistical and numerical methodology was developed both to close the equation set and to treat the fluctuation terms for various assigned random porous morphologies.

Nonlinear models for two-temperature heat and momentum turbulent transport require the evaluation of additional terms and transport coefficient models. This approach required that the coefficients in the equations, as well as the form of the equations themselves, be consistent to accurately model the processes and morphology of the porous medium. A first approximation for the coefficients e.g. drag resistance or heat transfer was obtained from experimentally determined coefficient correlations. Existing models for variable morphology functions such as porosity and specific surface were used to obtain comparisons with other works in a relatively high Reynolds number range.

All the coefficient models used and discussed in the study were strictly connected to assumed (or admitted) porous medium morphology models, meaning that the coefficient values are determined in a manner consistent with the selected geometry. Comparison of modeling results occasionally posed difficulty not only because other models utilized different mathematical treatments, but also because results for such specific treatments of the medium morphology were rarely obtained by other authors.

The two-temperature models were compared with a one-temperature model using thermal diffusivity coefficients and effective coefficients from various authors. The calculated pressure drop showed very good agreement with experiment for a porous structure of spherical beads. The transport equations were sensitive to the types of morphology assumed and the descriptive ability of the transport coefficients used. It was shown for the case of the overall drag coefficient that morphology assumptions implicit in the coefficient models make themselves known by the regimes in which the models predict. A multiple contribution formulation for the overall drag coefficient resolved order of magnitude discrepancies among globular and capillary tube morphology models by modifying the morphology assumption to that of a bi-porous medium. The form of the local thermal equilibrium statement used, however, proved somewhat insensitive to the effective conductivity model used and displayed excellent agreement with a weighted temperature from a two-temperature energy statement at high porosity, mediocre agreement at moderate void fraction. The effective thermal conductivity model presented shows minor sensitivity to fluid phase contributions while emphasizing those of the solid structure for the high conductivity solid phase (steel). Turbulent eddy conduction is observed to have increased impact within the two-temperature energy model at high void-fractions.

Numerical evaluations of the models show distinct differences in the overall drag coefficient among the straight capillary and globular models for both the regular and simple cubic morphologies. Unsurprisingly, the Nikuradze formulae (capillary models) were shown to predict overall drag coefficients approximately two orders of magnitude below the globular model values for identical local void fraction and specific surface in the considered cases.

We have solved few turbulent heat and momentum transport problems in heterogeneous media exactly (developed scaled closure and simulation).

was a key figure participating in the Thermal Physics and Fluid Mechanics HSP-VAT fields. His Laboratory's participating within the studies on convective transport in heterostructures and porous media since 1994. We have developed a number of ideas and methodologies in the area of interaction of continuous and scaled two-phase heat transport experiments and modeling.

Our collaboration brought up the understanding of some issues on how to make experimental set-ups for heterogeneous hierarchical media convective heat transport. Specifically much of study was done on pressure loss and heat exchange effective coefficients. Pressure loss and heat transfer experiment analysis procedure was developed using the VAT as the tool for model formulation for heat exchangers experimental data reduction.

In an effort to relate the scaled volume average theory (VAT) description and simulation of heat transfer devices (heat sinks) to experimental measurements, there were developed a process of coupling for the two scale Detailed Micro Modeling - Direct Numerical Modeling (DMM-DNM) of local and non-local characteristics (temperature,velocities, pressure and so on) and their corresponding experimental results for few designs of semiconductor heat sinks.

Developed by VT (V.S.Travkin) basic issues in fundamentals of two-scale heterogeneous experimental technique for parameters measurement and design for the volumetric convective heat exchanging devices were used in a series of exact mathematical simulations. The exact relationships and improvements to the widely used in industry parameters of heat exchange performance were developed and shown how to connect experiments on lower scales with the direct lower and upper scale simulations.

Copyright © 2001...Sunday, 24-Sep-2017 19:14:40 GMT V.S.Travkin, Hierarchical Scaled Physics and Technologies™