NATO ASI Conference, Kyiv MODELING AND SIMULATION OF TURBULENT PENETRATIVE CONVECTION AND POLLUTANT DISPERSION ABOVE THE URBAN HEAT ISLAND IN STABLY STRATIFIED ENVIRONMENT A.F. Kurbatskiy Institute of Theoretical and Applied Mechanics SB RAS Novosibirsk State University Novosibirsk, Russia L.I. Kurbatskaya Institute of Computational Math. and Math. Geophysics SB RAS Novosibirsk, Russia

NATO ASI Conference, Kyiv-2004 O u t l i n e  Introduction  Objectives  Turbulent Transport Models for Environmental Stratified Flows  Modeling and Simulation of Urban Heat Island Phenomenon and Pollutant Dispersion  Numerical Results  Conclusion

NATO ASI Conference, Kyiv Introduction  For stratified atmospheric flows the LES models and third-order closure models should be considered as fundamental research tools because of their large computer demands.  A growing need for detailed simulations of turbulent structures of stably stratified flows motivates the development and verification of computationally less expensive closure models for applied research in order to reduce computational demands to a minimum.

NATO ASI Conference, Kyiv Objectives  The algebraic modeling techniques can be used in order to obtain for buoyant flows the fully explicit algebraic models for turbulent fluxes of the momentum, heat and mass.  The principal object of this work is the development of three-four-parametric turbulence model minimizes difficulties in simulating of turbulent transport in stably stratified environment and reduces efforts needed for the numerical implementation of model.

NATO ASI Conference, Kyiv Governing Equations Governing equations describing the turbulent stratified environmental flows are being written down in the hydrostatic approximation at absence of the Coriolis force and radiation with use a Boussinesq approximation.

NATO ASI Conference, Kyiv Governing Equations in RANS-approach

NATO ASI Conference, Kyiv Transport Equations for heat and mass fluxes

NATO ASI Conference, Kyiv Explicit Algebraic Expressions for Turbulent Fluxes  The explicit algebraic models for the turbulent heat flux vector and turbulent mass vector were derived by truncation of the closed transport equations for turbulent fluxes of heat and concentration by assuming weak equilibrium, but retaining all major flux production terms.  For turbulent stresses we applied eddy viscosity expression.

NATO ASI Conference, Kyiv CLOSURE: full explicit turbulent fluxes models for active (heat) and passive (mass) scalars

NATO ASI Conference, Kyiv CLOSURE: three-equation model for act ive (heat) scalar field

NATO ASI Conference, Kyiv CLOSURE : four-equation model for passive scalar field

NATO ASI Conference, Kyiv Modeling of Urban Heat Island The ability of the proposed full explicit algebraic models for turbulent fluxes of heat and mass to reproduce correctly the environmental flows with a strong thermal stratification was tested on a large-scale circulation flow above an urban heat island

NATO ASI Conference, Kyiv Modeling of Urban Heat Island In the phenomenon of the unsteady turbulent penetration convection above an urban heat island the two remarkable features are shown. The first, due to heating from bellow the interactions between stable and unstable regions occur, because the mixed turbulent ground layer to grow into a stable region.

NATO ASI Conference, Kyiv Modeling of Urban Heat Island The second, there is the entrainment of overlaying non- turbulent fluid into mixed layer causing very step gradients at the interface. These features explain why the phenomenon of urban heat island represents a very challenging test case for turbulent models.

NATO ASI Conference, Kyiv Objectives  Thus, t he principal aim of this investigation is the modeling and simulation of large-scale turbulent circulation flow above the urban heat island and pollutant dispersion in the stably stratified environment.

NATO ASI Conference, Kyiv Limitations of Laboratory Measurements for Full-scale Simulation There are important limitations utilized in the laboratory experiment and simulation of the real urban heat-island in the nighttime atmosphere:  Very large heat fluxes from the heater surfaces  Very strong temperature gradients that required to obtain the low aspect ratios (z i /D) and small Froude numbers.

NATO ASI Conference, Kyiv Structure of heat-island circulation  The penetrative turbulent convection is induced by the constant heat flux H 0 from the surface of a plate with diameter D. It simulates a prototype of an urban heat island with the low-aspect-ratio plume (z i / D « 1) under near calm conditions and stably stratified atmosphere.

NATO ASI Conference, Kyiv NUMERICAL MODELING OF HEAT ISLAND CIRCULATION The problem of development of circulation above a heat island is assumed to be axisymmetric. The domain of integration is a cylinder of a given height.

NATO ASI Conference, Kyiv Numerical Method F r, F z – turbulent fluxes of momentum, heat and mass Semi-implicit alternating direction scheme

NATO ASI Conference, Kyiv Mesh  The numerical method uses a staggered mesh.  The difference equations are solved by the three-diagonal- matrix algorithm. Staggered mesh –    z r zz 0  r/2 rr  z/2 UrUr UzUz  E, , T,, C,

NATO ASI Conference, Kyiv Main Results of Simulation  The results of simulation correspond to a quasi-steady state of circulation over an area heat source in stable stratified environment.  Figure (c): shadowgraph picture at t = 240 sec when the full circulation is established.

NATO ASI Conference, Kyiv

NATO ASI Conference, Kyiv Calculation of Normal Turbulent Stresses In this problem a simple gradient transport model preserves certain anisotropy of the normal turbulent stresses is turbulent viscosity.

NATO ASI Conference, Kyiv

NATO ASI Conference, Kyiv

NATO ASI Conference, Kyiv

NATO ASI Conference, Kyiv RESULTS: Temperature profiles  Calculated temperature profiles inside the plume have characteristic “swelling”: the temperature inside the plume is lower than the temperature outside at the same height creating an area of negative buoyancy due to the overshooting of the plume at the center.  This behavior indicates that the plume has a dome-shaped upper part in the form of a “hat”.

NATO ASI Conference, Kyiv

29 CONCLUSION  The three-equation model of turbulent transport of heat reproduces structural features of the penetrative turbulent convection over the heat island in a stably stratified environment.  This model minimizes difficulties in describing the non-homogeneous turbulence in a stably stratified environment and reduces computational resources required for the numerical simulation.