MODELLING OF THE HEAT ISLAND GENERATED BY AN URBAN UNIT F. Pignolet-Tardan *, P. Depecker**, F. Garde*, L. Adelard*, J.C. Gatina*. * Laboratoire de Génie Industriel, Université de la Réunion, 15 avenue René Cassin, 97715 St DENIS Cédex 9, La Réunion, France. • Tel : 02 62 93 82 21 • Email : [email protected] **Centre de Thermique de l'Insa de Lyon (CETHIL), Bat 307, Insa De Lyon, 20 avenue A. Einstein, 69621 Villeurbanne , France. • Tel : 03 72 43 84 61 • Email : [email protected] ABSTRACT Outdoor Meso-climate This paper presents the theoretical modelling work of an elementary urban units (street), thermal Solar radiation Humidity behaviour. The calculation code Codyflow was set up as a way to model the thermal response (structure Radiation surface temperature and ambient air temperature) of Diffusion an urban system to the solicitations of the outside climate. The determination of the air temperature in Conduction an urban unit allows the calculation of the ∆T u-r Convection factor representing the difference between the air temperature in the urban system (u) and the air Advection temperature recorded at the closest meteorological station (r), generally situated in the country side. This factor, introduced by OKE, enables the analysis Air temperature Wind of the heat island generated by an urban system. The Fig 1. Overall external solicitations and internal heat simulation results obtained from the Codyflow code, ∆ flows considered in the evaluation of the urban enable the study of the intensity of the Tu-r factor canyon thermal answer. in relation to various parameters : physical and geometrical configurations, presence of air flow solicitations... System and Descriptive Cl imatic environment data base data base INTRODUCTION description The presence of an urban site creates perturbations in Radiative and ENSOL F LUENT temperature, humidity and velocity fields of the airflow meso-climatic environment. The urban system can solicitations be assimilated to a climate transformer as it calculation Radiative flux Air speed generates, from these meso-climatic characters, a specific micro-climate. This micro-climate T hermal BATIMENT SOL corresponds to the thermal airflow response of the answer urban system to the meso-climatic environmental calculation solicitations. It results in internal thermal transfers facade surface ground surface from conductive and convective origins and in temperature temperature advection and diffusion exchanges in the urban air AIR (fig. 1) The calculation code, Codyflow [1] was set up as a means to model the micro-climate generated by an Air temperature elementary urban unit (street, green space, building Fig 2. General layout of the Codyflow calculation group). This code is composed of a certain number of code. modules, each one characterising the thermal comportment of one part of the physical system (fig. The objective, in the work presented, is the 2). simulation of the air temperature in an urban canyon, as a way to make evident the heat island phenomena. The air temperature constitutes the major factor, in the study of a heat island, generated by a building group. The urban topology and the construction The calculation of the air temperature in an urban material used, lead to an ambiant air temperature unit requires the consideration of two cases : with or greater than that representative of the meso-climate without wind. The wind or airflow solicitation have, environment, due to the heat flows emitted and in fact, an effect on the thermodynamic behaviour of absorbed by the surfaces. This differnce between the ambient air. The presence, or absence of airflow urban and rural temperatures, represented by the ∆Tu- solicitation, induces different physical phenomena r factor, enables the quantification of the intensity of (fig. 3). the heat island generated. The common hypothesis used regarding its formation is listed in table 1. Thermal behavior of ambiant air Altered energy balance terms Features of urbanization underlying leading to positivethermal anomaly energy balance changes Solicitation With wind without wind Increased absorption of short-wave Canyon geometry - increased surface area and multiple reflection Phenomenon radiation interesting the Advection Diffusion Increased long-wave radiation from Air pollution - greater absorption ambiant air and re-emission the sky Phenomenom Canyon geometry- reduction of interesting the Forced Natural Decreased long-wave radiation sky vie w factor convection convection loss surperficial exchanges Anthropogenic heat source Building and traffic heat losses Fig. 3 Physical phenomena resulting from the type of airflow solicitation Construction materials - Increased sensible heat increased thermal admittance storage The no wind case Decreased evapotranspiration Construction materials - increased "water-proofing" Close to the walls and the ground, the air heats up Decreased total turbulent heat Canyon geometry - reduction and creates a turbulence from a convective origin. of wind speed transport This accumulated heat, is transferred by turbulent Table 1 : Commonly hypothesised causes of the diffusion to the ambient air volume. The evolution canopy layer urban heat islan d (OKE, 1982) of the air temperature is governed by a system of equations, covering the diffusion of the heat in the The study will initially describe the equations and air and the boundary conditions on the upper and physical models used for the determination of the air lateral faces of the system (eq.1): temperature in an urban unit. Secondly, the results ∂Tai ∂ ∂Tai ∂ ∂Tai of the simulation, obtained from Codyflow, which = kx + ky enable the study of the intensity of the heat island ∂t ∂x ∂x ∂y ∂y generated, are presented and analysed. ∂ ∂Tai + kz EQUATIONS AND MODELS ∂z ∂z Description of the study configuration The configuration studied was that of an urban canyon and its meso-climatic environment. The Boundary condition for the air nodes near physical system is defined as a variable the surfaces configuration regarding its geometry (building ∂ height, road width, roof overhang) and its physical Tai ρ C Vi = Si hci Tsi - Tai characteristics (wall composition, ground surface ∂t layer, surface state of the facades). The total of all the information concerning the Boundary condition for the upper layer air node description of the urban system is held in a descriptive data base, ahead of the mathematical ∂Tai models. ρ C Vi = Si kz Tai - Tmétéo The meso-climatic data (air temperature Tamétéo, air ∂t humidity Ha, wind intensity V and direction γ) is held in a meteorological data base. Boundary condition for the lateral layer air node 2 ∂ T ai = 0 ∂x2 Calculation of the air tempe rature in an The turbulent phenomena is covered in the heat urban unit equation, through the empirical turbulent coefficients 2 of perceptible sensible heat kx, ky and kz, defined in ∂ T x, t ∂ T x, t function of the atmospheric stability f by [2]: = a kz = A . f . z ∂t ∂ x2 k = 1 k x 2 z en x = 0 k = 1 k T 0, t = Tsi y 2 z en x = e A is an empirical constant equal to 0.05. ∂ Tsint ρ C = hg Tint - Tsint In a no wind situation, the thermal exchanges main ∂t direction is vertical. The values taken by k illustrate well the increase in heat exchanges at the moment when the atmospheric instability is at a maximum Indoor Outdoor (12 PM.) ◊ The superficial temperatures T si are Tint T T T Tsint i+1 i mi calculated from a thermal balance at the surface. This • •••• • Tsi balance covers the whole of the flow, soliciting the surface or exchanged by it (eq. 2): ∂Tsi λ ρ C = hc Tai - Tsi + Tmi - Tsi ∂t e n σ 4 4 φ φ + ∑ Fij Tsj - Tsi + Clo + Atmos e 0 j =1 Fig. 4 : The thermokinetic model - F ε σ T 4 iciel i si n where • ∑ σ T 4 - T 4 represents the heat •hc Tai - Tsi represents the heat transfers by Fij sj si convection between the surface and the adjacent air j =1 layer. The convective exchange coefficient hc, is a exchange by long wave radiations between a surface i function of the established state of convection. In a and the surrounding surfaces j. no wind situation, the superficial exchanges are • Φ represents the short wave radiant flow, governed by a natural convection flow rate. In this Clo case the convective exchange coefficient hc is received by the surface element. calculated according to the difference between the φClo = ξ I cos h . sin β . cos ( a - γ) surface temperatures and the air. Following to this β the correlation established by ASHRAE[3] was + sin h cos + dH FCiel retained. n + ∑ Fij ρj GH λ j = 1 • e Tmi - Tsi represents the conductive transfer (eq. 4) in the wall or the ground. The conduction is considered unidirectional. The temperature Tmi is It is made up of the direct solar radiation, of diffused defined as the temperature in the wall at a distance ∆x flows from the sky and reflected flows, composed by of the surface; ∆x having been set up by the the overall diffuse reflected radiation by the operator. The determination of Tmi is obtained by surrounding surfaces. the resolution of a thermokinetic model, composed The short wavelength flows bring an effect, on the ξ of the heat equation and the adequate necessary one side, the shade factor ,enabling the boundary condition , enabling the consideration of consideration of the partial or non partial occultation the thermal conditions inside the ground and the of the surface element (ξ ∈ 0 , 1] ) and on the buildings (fig. 4). other, the form factors between the surfaces and between a surface and the sky. These shape factors were determined with the use of the Gouffe method[4]. • Φatmos represents the diffuse atmospheric flows. solicitations), hc is calculated in function of the air It takes into consideration the long wave flows speed close to the wall, using the correlation emitted by the atmosphere and received by a surface established by Sturrock[5].