Diurnal Change of Wall Flows and Energy Balance on the South Facing Wall When Background Wind is Absent

Transcription

1 Diurnal Change of Wall Flows and Energy Balance on the South Facing Wall When Background Wind is Asent Yifan Fan 1,*, Yuguo Li 1, Jian Hang 2 and Kai Wang 1 1 Department of Mechanical Engineering, the University of Hong Kong, Hong Kong 2 Department of Atmospheric Sciences, School of Environmental Science and Engineering, Sun Yat-Sen University, Guangzhou, China *corresponding author: u3219@hku.hk Astract The in-situ measurement of wall flows during clear days on a 16 story uilding in Guangzhou, China is introduced and analyzed in this paper. The surface temperature was measured y infrared camera and thermal couples. The amient temperature, relative humidity, wind velocity and solar radiation were recorded y weather stations. The 14 Rayleigh numer of wall flows reached as high as We found that the different kind of heat flu reach its maimum value in a day cycle at different time. The transmittance of the atmosphere keeps decreasing from the sunrise to the sunset in Guangzhou typical clear days. The wall surface temperature and flow were visualized y nfrared videos. The diurnal change of energy alance on the south facing wall was calculated ased on the solar radiation, long wave radiation and heat transfer caused y natural convection adjacent to the wall. Keywords: Wall flows, Energy alance 1. ntroduction The wall flow is important in ventilating a city and uilding energy alance when there is no synoptic wind [1] [2] [3] [4] [5] [6] [7] [8]. Even the ackground wind eists, it would e locked y the dense high-rise uildings in the uran area [9] [1] [11] [12].The energy alance in the uilding walls can influence oth indoor and outdoor environment in thermal comfort, energy saving and uran ventilation. Natural convective heat transfer is a connection etween the flow in the uran canopy layer and the energy alance in uilding walls. To study the energy alance in the uran canopy layer, the mechanism of the wall flows caused y natural convection must e also well understood. Natural convection along a vertical heated plate (wall flows) has een studied for a long time [13] [14] [15] [16] [17], while the flow and heat transfer along a real high-rise uilding wall caused y natural convection was never measured due to the difficulty in finding a high-rise uilding with a flat wall, getting the permission of taking measurement and installing the measurement devices adjacent to the wall. Wells & Worster[18] modeled the wall flows with a two-layer oundary layer structure when the Rayleigh numer can reach as large as 1 2. The eperiment results of Fan et al.[19] [2] support the Wells & Worster s theory. Measurement sites and methods (including modelling of solar radiative heat flu, long wave radiative heat flu and natural convective heat flu) are introduced in chapter 2. Results on amient conditions, diurnal change of atmosphere transmittance and different type of heat flues are gave in chapter 3. Finally, conclusions are summarized in chapter Measurement and methods The energy alance on the south facing wall surface was calculated ased on the energy conservation, which is shown in the Figure 1. Paper D:19 1

2 Fig. 1 Heat flu through the wall surface. Heat conduction = Solar radiation - Natural convection - Long wave radiation The surface temperature were measured y oth infrared camera and thermal couples. The uniformity of the wall surface temperature can e shown in Figure 2 Fig. 2 nfrared picture of the south facing wall. t was taken at 12:, 15 th Octoer. The position of thermal couples are marked on the picture. Only two levels can e oserved due to the limitation of the R camera scope. The two levels shown in the figure is from 1 th to 14 th floor 2.1. Solar radiation The position of the sun relative to the horizontal surface can e descried y the solar zenith angle z, solar elevation angle and solar azimuth angle, which are illustrated in the Figure 3. Paper D:19 2

3 Fig 3. llustration of solar zenith angle, solar elevation angle and solar azimuth angle z Solar radiation is the sum of direct solar radiation dir and diffuse irradiance dif. The calculation of dir and dif are shown in the Equations (1)-(2) given y Bouguer s law: dir E P sin cos (1) dif. 5F s sin 1 P sin 11. 4ln P (2) where is solar constant with a value of 1367 W m -2, which is recommended y Fröhlich & Brusa [21]; E 1. 33cos 2d 365 is defined y Duffie & Beckman [22] as eccentricity correction factor of the n earth s orit and d is the day numer of the year from 1 st January; P is the atmosphere transmittance of solar n radiation; is solar elevation angle (also called solar altitude); is solar incidence angle. etween the calculated surface and sky. The definition of solar incidence angle is given in Equation (3): F s is shape factor cos cos cos sin sin cos z z (3) where is the slope of the calculated surface ( = when the surface is horizontal and = 9 when the surface is vertical); z is solar zenith angle; is solar azimuth angle; is the azimuth angle of the calculated surface ( = when the surface is facing south, = 9 when the surface is facing east and = -9 when the surface is facing west). The solar zenith angle z, solar altitude and solar azimuth ( = when the sun is in south, = 9 when the sun is in east and = -9 when the surface is in west) are otained in Equations (4)-(6): cos z cos cos cosh sin sin 9 z (4) (5) Paper D:19 3

4 cos sin sin sin cos cos (6) where sin36 d n North Hemisphere is positive and the South Hemisphere is negative); 12 is solar declination; is the geographic latitude in degrees (the h 15 h r is hour angle ( h r is the local time value, e.g. h r =12 at noon and h r =18 at 6 o clock afternoon). All the variales to calculate the solar radiation are known ecept for P, the atmosphere transmittance of solar radiation. Fortunately, the solar radiation on the horizontal surface was measured y weather stations, so the transmittance can e calculated y the following Equation (7): measure dir dif E P sin sin 1 P cos. 5Fs sin (7) 11. 4ln P The latitude of the measurement point is N The eperiment was carried out in 14 th Octoer to 16 th Octoer, 214. The weather station was set on the roof of the 16 story uilding and the surrounding area is relatively open, so the shape factor F can e assumed to e 1 for the weather station location. s After the transmittance is solved, the short wave radiation on the south facing vertical wall sv can e calculated y Equation (8): sv a 1 (8) dirv difv where a is aledo. dirv respectively Long wave radiation and difv are direct radiation and diffuse radiation on the south facing vertical wall The long wave radiation can e divided into two parts: (1) etween the vertical wall and sky; (2) etween the vertical wall and other ground surfaces. To calculate the long wave radiation etween the vertical wall and sky, the sky temperature need to e modeled. Berdahl & Martin (1984) s sky temperature model has een widely used, which is shown in the Equation (9): T sky T a 2 1 / T. 73T. 13cos 15t 4 dp dp (9) where T sky (K) is sky temperature; T a (K) is amient dry ul temperature; T dp ( ) is dew point temperature; t is hour from midnight. The long wave radiation lw of the vertical wall can e calculated ased on Stefan-Boltzmann law y the Equations (1)-(12): lw ls lg (1) Paper D:19 4

5 ls lg F s g F T g 4 sky T T 4 g 4 T 4 (11) (12) 8 where W m -2 K -4 is Stefan-Boltzmann constant. and g are emissivity for the test uilding wall surface and surrounding ground respectively. The emissivity of the surrounding surfaces are assumed to e uniform. ls is long wave radiation heat flu etween the vertical wall and sky. lg is long wave radiation etween the vertical wall and other surfaces, which is calculated ased on simplified equation for non-enclosed envelope. The tested uilding is much higher than its surroundings and locate in an open area, so the shape factors F (shape factor etween the uilding vertical wall and sky) and F (shape factor etween the uilding vertical wall and the g ground) are assumed to e.5. T and Tg are surface temperature of the vertical wall and the surface temperature of surround surfaces respectively Natural convective heat transfer The local convective heat transfer rate can e represented y the non-dimensional Nusselt numer Nu, which is defined in the Equation (13): s Nu h (13) where h is local convective heat transfer coefficient; is characteristic length scale, which is vertical coordinate along the wall in this eperiment; is thermal conductivity. The local Rayleigh numer Ra is defined as Equation (14): Ra gt 3 (14) where is length scale. g is acceleration of gravity. is thermal epansion coefficient. T is difference etween the fluid temperature and amient temperature. is kinematic viscosity. is thermal diffusivity. The correlation etween Nu and Ra for convection is shown in Equation (15): Nu cra (15) where c and are constants. The ackground wind speed was small when the eperiment was carried out. The weather was clear and there was no clouds. The convective heat transfer was dominated y natural convection, which is also confirmed in Fan et al. [19] and Fan et al. [2]. Therefore, the natural convection correlation etween Nu and Ra can e adopted. Wells & Worster [18] and Fan et al. [19] suggested that the flow was in region, where the uoyancy instaility dominate and the heat flu is constant, under this eperiment condition. Tsuji & Paper D:19 5

6 Nagano [16] and Wells & Worster [18] supported the correlation of natural convection along a heated vertical wall in region, which is shown as Equation (16): 3 Nu. 12 (16) Ra Based on Equations (13)-(16), the heat flu q caused y natural convective heat transfer can e otained as Equation (17): q h T g T 4 / 3 (17) As we can see in the Equation (17), the local heat flu is independent of vertical coordinate, which means that the heat flu is constant over the wall. Negative in the Equation (17) means the heat flu is from the wall to the amient air Turulent flow visualization method y infrared videos The thermal image method has een adopted y many researchers, such as, Hetsroni, Rozenlit & Yarin [23], Hetsroni & Rozenlit [24], Kowalewski et al. [25], Hetsroni et al. [26]. Reference[27] gave a detailed description on how to get velocity of the turulent flow from thermal videos and called the method as thermal image velocimetry (TV). The general procedure for TV is shown in Figure 4. Fig. 4 General procedure of Thermal mage Velocimetry (TV) The application of TV method can e affected y the following factors: (1) the characteristics of tested surfaces (surfaces that have small thermal storage and thermal conductivity are preferred); (2) the temperature difference etween the surface and amient fluid (the temperature difference should e large enough); (3) the resolution of infrared camera; (4) the distance etween the camera and the surface (the small distance is preferred. f the distance is large, the infrared ray emitted y the surface can e partially asored y the atmosphere etween the surface and thermal camera, which will cover the fluctuation of the surface temperature). Due to the limitations of eperiment conditions, such as large thermal storage of the wall, the long distance etween the wall and the camera, only qualitative visualization was done. 3. Results The solar radiation on the uilding roof is measured y the weather station. The measured solar radiation, calculated diffuse radiation, direct radiation and transmittance are shown in Figure 5. Paper D:19 6

7 Fig. 5 Solar radiation on the horizontal surface. The transmittance in the figure is atmospheric transmittance of solar radiation According to dso [28], the atmospheric transmittance is mainly influenced y three factors: the asorption and scattering y water vapor; the asorption and scattering y dust in the air; scattering y dry dust-free air. The transmittance calculated ased on the measured solar radiation keeps decreasing from the sunrise to the sunset. The diffuse solar radiative heat flu is larger than that of the direct radiation after 16: in each day, when the solar elevation angle and transmittance are very small. The direct radiation, diffuse radiation and transmittance have a ig fluctuation around 12:, 16 th Octoer (circled y dashed elliptical in Figure 5). The fluctuation is caused y the clouds cover over the sky at that time. The cover of the clouds also show the influence on the ratio of the diffuse radiation to the direct radiation during that period. The flow along the wall caused y natural convection is shown in Figure 6. Fig. 6 Visualization of the wall flow caused y natural convection. The average data is otained from 5 minute image sequence. The temperature shown in the figure is fluctuation after the average is removed. The frequency of videos are 3 Hz. The time interval etween (a) () and (c) is 1.33 second Paper D:19 7

8 The coherent structure circulated y the yellow dashed elliptical in Figure 6 can e oserved oviously moving upwardly. The short wave radiation received y the south facing vertical wall, the heat flu given off y the wall and the conductive heat flu are summarized in Figure 7. Fig. 7 Energy alance on the wall surface during clear days. The short wave radiation is the received solar radiative heat flu (include direct radiation and diffuse radiation) of the south facing wall. The long wave radiation is the long wave radiative heat flu (include the radiation etween the wall and the ground and the radiation etween the wall and the sky). The conductive heat flu is the heat conducted into the wall (positive heat flu) and the heat conducted out of the wall (negative heat flu) As oserved in the Figure 7, the phase for different kind of heat flues are different under clear day condition. The conductive heat flu into the wall first reach its maimum at around 11:, and then the short wave radiation appear the peak at around 12:. The following is the convective heat flu caused y natural convection, when the surface temperature is largest at around 14:. The long wave radiation heat flu appear its peak in the last at around 15:. During night time, the heat in the wall is mainly transferred out y long wave radiation. The conductive heat flu out of the wall equal to the long wave radiation heat flu at night. Therefore, if the uilding density in uran area is too large, it could reduce the long wave radiation and trap the heat in the uran canopy layer. The heat flu caused y natural convection and long wave radiation are in the same order during daytime. The slope of conductive heat flu is large in the morning due to the small slope of convective heat flu and long wave radiation heat flu. The large thermal inertia prevent the wall surface temperature increasing rapidly, leading to the small slope of convective heat flu and long wave radiative heat flu in the morning. 4. Conclusions The wall flows, surface temperature and radiation along a high-rise uilding are measured and calculated. The flow along the wall caused y natural convection is visualized y the fluctuation of the surface temperature otained from the infrared image. The flows along the wall are dominated y natural convection during the calm clear days, so the natural convective heat transfer is used in the energy alance analysis. Solar radiative heat flu Paper D:19 8

9 and long wave radiative heat flu are also calculated to complete energy alance model on the wall surface. The atmosphere transmittance is not a constant and keeps decreasing from sunrise to sunset during clear days. The reason is complicated since it can e influenced y the pollutants and water vapor in the atmosphere. The different kind of heat flu reach its maimum value in a day cycle at different time. The conductive heat flu first reach the peak. Afterwards, the solar radiative heat flu get the maimum point and then followed y the natural convective heat flu and long wave radiative heat flu. Natural convective heat flu has the same order with long wave radiative heat flu during day time. Since the heat conduction outside of the wall is dominated y the long wave radiation, the dense high rise uildings will trap the heat in the uran canopy layer. References: [1] Barlow JF, Harman N, Belcher SE (24) Scalar flues from uran street canyons. Part : Laoratory simulation. Bound-lay Meteorol, vol. 113, pp [2] Rotach M, Gryning S-E, Batchvarova E, Christen A, Vogt R (24) Pollutant dispersion close to an uran surface the BUBBLE tracer eperiment. Meteorol Atmos Phys, vol. 87, pp [3] Hang J, Sanderg M, Li Y (29) Age of air and air echange efficiency in idealized city models. Build Environ, vol. 44, pp [4] Yang L, Li Y (29) City ventilation of Hong Kong at no-wind conditions. Atmos Environ, vol. 43, pp [5] Hang J, Li Y (212) Macroscopic simulations of turulent flows through high-rise uilding arrays using a porous turulence model. Build Environ, vol. 49, pp [6] Hernandez M, Medina M, Schruen D (23) Verification of an energy alance approach to estimate indoor wall heat flues using transfer functions and simplified solar heat gain calculations. Math Comput Model, vol. 37, pp [7] Ghiaus C (213) Causality issue in the heat alance method for calculating the design heating and cooling load. Energy, vol. 5, pp [8] Naveros, Bacher P, Ruiz D, Jiménez M, Madsen H (214) Setting up and validating a comple model for a simple homogeneous wall. Energ Buildings, vol. 7, pp [9] Macdonald RW (2) Modelling the mean velocity profile in the uran canopy layer. vol., pp. [1] Belcher SE, Jerram N, Hunt JCR (23) Adjustment of a turulent oundary layer to a canopy of roughness elements. J Fluid Mech, vol. 488, pp [11] Coceal O, Belcher SE (24) A canopy model of mean winds through uran areas. Q J Roy Meteor Soc, vol. 13, pp [12] Di Saatino S, Solazzo E, Paradisi P, Britter R (27) A Simple Model for Spatially-averaged Wind Profiles Within and Aove an Uran Canopy. Bound-lay Meteorol, vol. 127, pp [13] Eckert E, Jackson TW. Analysis of turulent free-convection oundary layer on flat plate. 227: Lewis Flight Propulsion Laoratory Cleveland, Ohio; 195. [14] Ostrach S. An analysis of laminar free-convection flow and heat transfer aout a flat plate parallel to the direction of the generating ody force: National Advisory Committee for Aeronautics; [15] Cheesewright R (1968) Turulent natural convection from a vertical plane surface. Journal of Heat Transfer, vol. 9, pp 1-6. [16] Tsuji T, Nagano Y (1988) Turulence measurements in a natural convection oundary layer along a vertical flat plate. nt J Heat Mass Tran, vol. 31, pp [17] Au-Mulaweh H, Chen T, Armaly B (2) Effects of free-stream velocity on turulent natural-convection flow along a vertical plate. Ep Heat Transfer, vol. 13, pp [18] Wells AJ, Worster M (28) A geophysical-scale model of vertical natural convection oundary layers. J Fluid Mech, vol. 69, pp [19] Fan Y, Li Y, Hang J, Wang K (215) Wall flows along a high-rise uilding. Unpulished Manuscript, vol., pp. Paper D:19 9

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