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On the estimation of wind speed in urban canyons for ventilation purposes—Part 2: Using of data driven techniques to calculate the more probable wind speed in urban canyons for low ambient wind speeds
ARTICLE IN PRESS
Building and Environment 43 (2008) 1411–1418 www.elsevier.com/locate/buildenv
On the estimation of wind speed in urban canyons for ventilation purposes—Part 2: Using of data driven techniques to calculate the more probable wind speed in urban canyons for low ambient wind speeds M. Santamouris, C. Georgakis, A. Niachou Group of Building Environmental Physics, University of Athens, Building Physics 5, University Campus, 157 84 Athens, Greece
Abstract For low ambient wind speeds, airflow in deep urban canyons is characterized by a high scatter and important fluctuation as no coupling is established between the undisturbed wind flow and the flow inside the canyon. Thus, thermal and mechanical forces determine the wind speed characteristics. Existing studies based on experimental comparison have shown that under the above boundary conditions, deterministic models may predict with sufficient accuracy the mean wind speed but not the fluctuation caused by the thermal phenomena. In the present paper, data have been collected through an extensive experimental campaign in seven canyons. Then, data driven techniques, to predict the more probable wind speed in deep urban canyons as a function of the prevailing thermal and inertia phenomena, have been developed. The proposed methodologies are strictly valid inside the limits of the experimental data, i.e. aspect ratios between 1.7 and 3.25, and can be used to estimate the more probable wind speed close to the facades of urban canyons. r 2007 Elsevier Ltd. All rights reserved.
1. Introduction Urban heat island is the more documented phenomenon of climate change. High urban temperatures affect the cooling load of buildings as well as the potential of natural ventilation techniques when applied to urban buildings [1–3]. Knowledge of the wind speed in urban canyons is a necessary input to estimate the natural ventilation potential of urban buildings as well as thermal comfort in open areas [4]. The wind flow inside canyons is driven and determined by the interaction of the flow field above buildings and the uniqueness of local effects as topography, building geometry and dimensions, streets, traffic and other local features. The wind speed in low aspect ratio canyons can be easily predicted using computerized flow dynamic techniques.
Corresponding author. Tel.:+30 210 7276847; fax:+30 210 7295282.
E-mail address: [email protected] (M. Santamouris). 0360-1323/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2007.01.042
Knowledge of the wind speed in deep and high aspect ratio urban canyons is resulting either from numerical studies or from field experiments within real urban canyons or within scaled physical models in wind tunnels. Various mathematical algorithms have been proposed for calculating the wind speed inside such canyons [5–8]. Computerised fluid dynamic techniques may be applied especially when the ambient wind speed above the canyons is quite high and there is a coupling between the flow inside the canyon and the undisturbed wind speed [9]. For high wind speeds the airflow in the canyon can be seen as a secondary circulation feature driven by the above roof imposed flow [5]. If the wind speed out of the canyon is below some threshold value the coupling between the upper and secondary flow is lost [5], and the relation between wind speeds above the roof and within the canyon is characterized by a considerable scatter. In this case, thermal and mechanical phenomena may play a very important role, and determine the final wind speed. Under these conditions and given the thermal regime in a canyon, wind speed may present a very important variability and
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fluctuation. Thus, the above-mentioned deterministic models that do not consider thermal effects may not be appropriate to estimate the wind speed in a canyon especially when thermal phenomena are important [10–12]. According to De Paul and Shieh [13], the threshold value to establish the coupling is between 1.5 and 2 m=s. Similar values are reported by Nakamura and Oke [5], who worked with a canyon having an aspect ratio close to unity (1.06). Also, Mc Cormick [14] reports a threshold wind speed close to 2 m=s. However, as shown by Santamouris et al. [15], for canyons with a higher aspect ratio, coupling is established for much higher ambient wind speeds ranging between 4 and 5 m=s. The present paper in combination with Georgakis and Santamouris [16] aims to present the results of a recent research carried out in the frame of the Reshyvent and UrbVent research projects. The programs have developed and tested computational methods to calculate the wind speed in urban canyons to be used for hybrid and natural ventilation studies. The research involved detailed experiments in seven canyons, development and testing of computational methods against the experimental data. Two types of algorithms have been developed. In Georgakis and Santamouris [16], the proposed algorithms to calculate the wind speed in canyon, when there is a coupling between the undisturbed wind flow and the flow inside the canyon, are presented. Such a situation occurs for quite high wind speeds. The actual paper proposes a new calculation methodology when such a coupling is not achieved. In particular, data driven techniques have been developed to estimate the wind speed near the canyon facades when the wind speed out of the canyon is below the threshold value over which the coupling is achieved. The proposed data driven techniques have been developed using the collected experimental data and thus are valid inside the boundaries of the specific experiments.
influenced by thermal and mechanical phenomena. Important temperature differences between the canyon walls and the air is the source of upward or downward flows that may be much more important than the flow induced by the wind above the canyon. Thus, even for a constant value of the ambient wind speed, the flow in the canyon may present a very high fluctuation. This is clear in Fig. 1 where the fluctuation of the measured wind speed for various points inside a representative canyon is given. The specific graph refers to a flow oblique to the canyon axis and for ambient wind speeds varying between 1 and 2 m=s. A similar variability and fluctuation have been found for almost all angles of incidence and in all canyons. The application of deterministic techniques [10–12], for low ambient wind speeds, has shown that the wind speed inside canyons is characterized by: (A) highly uncertain boundary conditions, (B) a combination of complex phenomena that in certain cases are not of a deterministic nature. To support the above statements, the previously mentioned deterministic techniques have been applied for all the set of the experimental data, low wind speeds, and have been compared against the measured values. Fig. 1 shows the range of the predicted against the measured values for a representative canyon. As shown, there is a quite good agreement as it concerns the prediction of the mean value of the wind speed, however, the used models cannot follow the experimental values when important thermal phenomena occurs. Given the random characteristic of the phenomena and the important fluctuation of the wind speed it is considered that a statistical representation of the phenomena is more appropriate to describe the phenomena.
2. Experimental procedure In the frame of the European Projects Urbvent, and Reshyvent field experiments were performed during the summers of 2001 and 2002 in seven pedestrian deep street canyons, in Athens. The aspect ratio of the studied canyons varied around 1.7–3.3. Experiments took place for three days and for 12 or 24 h per day. The experimental campaigns, which took place in each of the seven canyons, involved measurements of the wind speed and ambient temperature outside and in selected places inside the canyon as well as well measurements of the surface temperature. Details on the followed experimental campaigns as well as on the characteristics of the canyons can be found in [17–20]. 3. Airflow characteristics in canyons under low ambient wind speeds As already mentioned, the wind speeds in deep urban canyons under low ambient wind speeds is highly
Fig. 1. Fluctuation of the measured wind speed at various positions inside an urban canyon for ambient wind speeds varying between 1 and 2 m/s. The red bars refer to the estimated wind speeds in the specific points. 1. Vout, 2. Winward NE fac- ade, wind from NE direction, 3. Leeward SW facade, wind from NE direction, 4. Winward NE fac- ade, wind from SE direction, 5. Leeward SE fac- ade, wind from SE direction, 6. Leeward NE fac- ade, wind from the SW direction, 7. Winward SW fac- ade, wind from SW direction, 8. Leeward NE fac- ade, wind from NW direction, 9. Winward SW fac- ade, wind from NW fac- ade, 10. wind at 3.5 m height, 11. wind at 7.5 m height, 12. wind at 11.5 m height, 13. wind at 15.5 m height.
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representative distribution of the obtained data. As shown, there are clusters characterized by:
4. Statistical description of the phenomena Both Buoyancy mechanical and inertia phenomena are responsible for the airflow in canyons. Buoyancy phenomena caused by the temperature differences between the canyon surfaces and the ambient air are of very high importance and may be the main source of the airflow in canyons [15]. Buoyancy phenomena may be described by the local Grashof number, defined as: Gr ¼ gbðT surf T air ÞH 3 n2 , (1) where b ¼ 1=T, T surf ¼surface temperature at (x), T air is the ambient temperature at same height as x, H is the height of point x inside the canyon where the wind speed has to be calculated and n is the viscosity. Inertia forces may be considered by using the Reynolds number, Re ¼ Vh=n,
(2)
where V is the undisturbed wind speed measured at height h outside the canyon, and n is the viscosity. Airflow characteristics in canyons are classified according to the direction of the ambient wind speed as:
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parallel to the canyon axis; perpendicular to the canyon axis; and oblique to the canyon axis. Data from all canyons have been processed and a very important data set has been created. The data set is restricted to the cases where the undisturbed wind speed is lower than 5 m/s. For each of the above cases four data groups may be defined (i.e. for the perpendicular flow): (a) wind angle 90 15 (windward fac- ade), (b) wind angle 180 15 (windward fac- ade), (c) wind angle 90 15 (leeward fac- ade), and (d) wind angle 180 15 (leeward fac- ade).
For each data point of the above groups the local Gr as well as the Re number may be calculated for a specific position (x; H), inside the canyon. Then for each group a plot Gr 4Re may be obtained. Fig. 2 shows a
Low Reynold and negative Grashof numbers. Low Reynold and negligible Grashof numbers. High Grashof and low Reynold numbers. High Reynold numbers.
Each of the above clusters represents a different flow regime driven either by the inertia or the gravitational forces or from both of them. By applying fussy clustering techniques to each case n clusters may be defined. Clustering is a mathematical method to classify numerical data based on the identification of sub-groups on a data set, called ‘clusters’, where all objects are described by similar characteristics. Every cluster involves a number of objects, members of the cluster, represented by given position in the space as well as a centre of the cluster defined as the point in the cluster space where the sum of the specific distances of every member object belonging in the cluster is minimized. Various mathematical methods have been proposed for clustering of a data set. Fuzzy clustering is a quite modern, ‘intelligent’ technique considering that each individual member in the data set belongs to a cluster to some degree that is defined by a membership function [21,22]. When clusters of different flow regimes are defined, the probability density function of the air speed at the position (x; h), corresponding to each cluster, may be calculated. A representative distribution for the whole set of data is given in Fig. 3. It is pointed out that only data corresponding to ambient wind speeds lower than 5 m/s have been considered. Thus for each cluster the more probable wind speed inside and outside the canyon is calculated. In parallel, the corresponding temperature difference between the air and the canyon surfaces at the point where the wind speed is estimated have been found. Thus, a reduced data space including the three above parameters (more probable wind
Fig. 2. Distribution of the data as a function of their Reynold and Grashof numbers.
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speed inside and outside the canyon and the corresponding temperature difference) has been created. 5. Development and description of a 3D interpolation data driven model Using the reduced data space a 3D interpolation data driven model has been created to calculate the wind speed at a point x inside the canyon. In the following details of the method is given. For the perpendicular and oblique flows, specific models have been developed for the windward and leeward parts of the canyon. For the case where the flow is parallel to the canyon axis, a single method has been developed. Thus five specific models have been proposed. It is evident that the
Fig. 3. Probability density function of the wind speed inside and outside the canyon for a representative cluster.
developed methods may be applied inside the input values for which they have been developed. The developed models are described in the following. 5.1. Perpendicular flow Using as input the developed reduced space inputs to a 3D spline interpolation technique [23], a graphical representation of the 3D space V ðHÞ, H=w and DT, has been obtained, where V ðH; xÞ is the wind speed at height H, w is the width of the canyon and DT is the temperature difference between the ambient air and the canyon surface at the specific point (x; H). The developed graphical methods for the windward and the leeward facades are given in Figs. 4 and 5, respectively. The method allows to estimate using the developed graph, the more probable wind speed inside the canyon at a height H, as a function of the temperature difference DT between the surface canyon temperature and the ambient one at H, and the geometric factor H=w. As shown, prediction of the wind speed inside the canyon can be achieved only as a function of three parameters: the temperature difference, the relative position of the point where the wind has to be calculated and the width of the canyon. No correlation has been found between the wind speed inside the canyon and the undisturbed wind above the street. For the windward facades, it has been found that three zones of the more probable wind speed occur. For the lower parts of the canyon, H=w ratios below 1.5, the more probable wind speed is low and around 0.5 m/s. For medium heights, 1:5oH=wo2, the corresponding mean value is around 1 m/s, while for the higher parts of the canyon, the wind speed increases considerably and may reach values close to 2.5 m/s.
Fig. 4. Developed graphical data driven model to predict the more probable wind speed close to the windward canyon facades when the flow is perpendicular to the canyon axis.
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For the leeward facades, as expected, much lower wind speeds have been found. For temperatures differences up to 5 C, the average more probable wind speed close to the leeward facades is around 0.5 m/s. For higher temperature differences, the corresponding value may increase up to 1 m/s. 5.2. Parallel flow For the case where the flow inside the canyon is parallel to the canyon axis, it is found that the more probable wind speed may be predicted as a function of the undisturbed wind speed above the canyon and of the ratio between the height where the wind speed has to be estimated, H to the height of the canyon, Hcanyon, Fig. 6. As shown, for the lower parts of the canyon the average more probable wind speed is close to 0.5 m/s and it is not influenced by the undisturbed wind speed. For H/Hcanyon between 0.4 and 0.5 the corresponding value increases up to 1 m/s and there is a slight relation to the ambient wind speeds. For the higher parts of the canyon, a clear relation to the undisturbed wind speed is found. In this case the average more probable wind speed may increase up to 2 m/s for ambient wind speeds between 2 and 3 m/s.
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is found. In this case the speed inside the canyon may reach values close to 3 m/s. For the leeward facades of the canyons, it is found that the more probable wind speed may be predicted as a function of the temperature difference and of the ratio H=w (Fig. 8), where H is the height in the canyon where the wind speed has to be calculated and w is the width of the canyon. In this case, for H=w ratios lower than 0.3, the average more probable wind speed is not influenced by the temperature difference. For H=w higher than 1.6 and for temperature differences higher than 15 C, the average more probable wind speed increases considerably and may reach values close to 2 m/s. 6. Development of simplified data driven models In order to evaluate the possibility to develop more simplified data driven models to predict the more probable
5.3. Oblique flow For the windward facades of the canyon, it is found that the more probable wind speed may be predicted as a function of the undisturbed wind speed and of the ratio between the height H where the wind speed has to be estimated to the canyon width, w, Fig. 7. As shown, for the lower parts of the canyon, the more probable wind speed is not influenced by the wind speed above the canyon. In this case an average value of the more probable wind speed is close to 0.5 m/s. For the higher parts of the canyon and for wind speeds higher than 2 m/s, a clear relation between the more probable canyon wind speed and the undisturbed one
Fig. 5. Developed graphical data driven model to predict the more probable wind speed close to the leeward canyon facades when the flow is perpendicular to the canyon axis.
Fig. 6. Developed graphical data driven model to predict the more probable wind speed close to the canyon facades when the flow is parallel to the canyon axis.
Fig. 7. Developed graphical data driven model to predict the more probable wind speed close to the windward canyon facades when the flow is oblique to the canyon axis.
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wind speed in canyons, the developed reduced data space has been used and two simplified data driven models have been created to calculate the more probable wind speed at a point x inside the canyon. In particular: (a) a simple linear correlation method and (b) a decision tree method, have been developed. The results described in the following refer to the case of windward perpendicular to the canyon axis ambient wind flow. Results of similar type have been obtained for all other cases of ambient wind flow. 6.1. Linear correlation method A simple correlation model of the form V ðH; xÞ ¼ 0:537 þ 0:957H=w 0:012 DT þ 0:0039 V out
ð3Þ
has been obtained. V ðH; xÞ is the more probable wind speed inside the canyon at height H, w is the width of the canyon, DT is the temperature difference between the ambient air and the canyon surface temperatures at height H. Finally, V out is the undisturbed wind speed. 6.2. A decision tree method Using decision tree methodologies [24], a flow chart algorithm has been developed to calculate the more probable wind speed inside the canyon at height H. The calculated decision flow chart is given in Fig. 9. In the figure, 2, 3 and 4 are the ratio H=w, the temperature difference DT and the undisturbed wind speed V out . 7. Comparison against the experimental data The three methodologies have been compared against the experimental data included in the reduced space data set. The results of the comparison for the case of windward perpendicular to the canyon axis ambient wind flow are given in Fig. 10. The R2 correlation coefficients are: 0.96 for the 3D graphical interpolation model, 0.84 for the tree decision method and 0.74 for the linear correlation method. As shown, the 3D graphical interpolation model predicts the more probable wind speed inside the canyon with sufficient accuracy, while the tree decision method, although it is of sufficient accuracy for low speeds, fails to predict high wind speeds inside the canyon. Finally, the linear correlation method, as expected, presents a limited accuracy. Similar results have been obtained for all the other cases of airflow. 8. Conclusions
Fig. 8. Developed graphical data driven model to predict the more probable wind speed close to the leeward canyon facades when the flow is oblique to the canyon axis.
AirFlow in deep urban canyons may be characterized by a high scatter and important fluctuation especially when the ambient wind speed is low and no coupling is established
Fig. 9. Decision flow chart algorithm.
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3
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Tree Decision Method 2
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Linear Correlation
3D Graphical Interpolation
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0.5
0 1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
Fig. 10. Comparison of the predicted against the experimental values of the more probable wind speed inside the canyon at a height H.
between the undisturbed wind flow and the flow inside the canyon. Under such conditions thermal and mechanical forces determine the wind speed characteristics. Comparison with extensive experimental data has shown that under these boundary conditions, existing deterministic models can predict with sufficient accuracy the mean wind speed but not the fluctuation caused by the thermal phenomena. Using data collected in an extensive experimental campaign in seven canyons, data driven techniques have been developed that allow to predict the more probable wind speed in deep urban canyons as a function of the prevailing thermal and inertia phenomena. The developed methodologies are strictly valid inside the limits of the experimental data, i.e. aspect ratios between 1.7 and 3.25, and can be used to estimate the more probable wind speed close to the facades of urban canyons. Acknowledgement The present study was partly financed by the European Commission, Directorate General for Science, Research and Technology under the contract ‘‘UrbVent’’: Natural ventilation in urban areas—Potential assessment and optimal facade design, ENK6-CT-2000-00316. The contribution of the Commission is gratefully acknowledged. References [1] Santamouris M, editor. Energy and climate in the urban environment. James and James Science Publishers; 2001. [2] Santamouris M. Heat island research in Europe The state of the art. Advances Building Energy Research; (ABER) 2006:1.
[3] Geros V, Santamouris M, Tsangrassoulis A, Guarracino G. Experimental evaluation of night ventilation phenomena. Energy and Buildings 1999;29:141–54. [4] Santamouris M. Energy in the urban built environment—the role of natural ventilation in natural ventilation in the urban environment. In: Allard F, Ghiaus C, editors. James and James Science Publishers; 2005. [5] Nakamura Y, Oke TR. Wind temperature and stability conditions in an E-W oriented urban canyon. Atmospheric Environment 1988;22(12):2691–700. [6] Nicholson S. A pollution model for street-level air. Atmospheric Environment 1975;9:19–31. [7] Hotchkiss RS, Harlow FH. Air pollution and transport in street canyons. Office of Research and Monitoring U.S., Washington DC, 1973. [8] Yamartino RJ, Wiegand G. Development and evaluation of simple models for the flow, turbulence and pollution concentration fields within an urban street canyon. Atmospheric Environment 1986; 20:2137–56. [9] Vardoulakis S, Fisher B, Pericleous K, Gonzalez-Flesca N. Modeling air quality in street canyons: a review. Atmospheric Environment 2003;37:155–82. [10] Ghiaus C, Allard F, Santamouris M, Georgakis C, Nicol F. Urban environment influence on natural ventilation potential. Building and Environment 2006;41(4):395–406. [11] Assimakopoulos V, Georgakis C, Santamouris M. Experimental validation of computational fluid dynamic codes to predict the wind speed in street canyons for passive cooling purposes. Solar Energy 2006;80:423–34. [12] Pospisil J, Jicha M, Niachou K, Santamouris M. Computational modelling of airflow in urban street canyon and comparison with measurements. International Journal of Environmental and Pollution, 2005;25(1–4):191-200. [13] DePaul FT, Sheih CM. Measurements of wind velocities in a street canyon. Atmospheric Environment 1986;20:445–59. [14] McCormick RA. Air pollution in the locality of buildings. Philosophical Transactions of the Royal Society of London Series A 1971;269:515–26.
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[15] Santamouris M, Papanikolaou N, Koronakis I, Livada I, Assimakopoulos DN. Thermal and air flow characteristics in a deep pedestrian canyon and hot weather conditions. Atmospheric Environment 1999;33(27):4503–21. [16] Georgakis C, Santamouris M. On the estimation of wind speed in urban canyons for ventilation purposes. Part one: Coupling between the undisturbed wind speed and the canyon wind. Building and Environment 2007, in press, doi: 10.1016/j.buildenv.2007.01.041. [17] Georgakis C, Santamouris M. On the airflow in urban canyons for ventilation purposes. International Journal of Ventilation 2004;3(1):53–65. [18] Georgakis C, Santamouris M. Experimental investigation of airflow and temperature distribution in deep urban canyons for natural ventilation purposes. Energy and Buildings 2006;38(4):367–76. [19] Niachou K, Livada I, Santamouris M. Experimental study of temperature and airflow distribution inside an urban street canyon during hot summer weather conditions. Part 1. Air and Surface
[20]
[21] [22] [23]
[24]
Temperatures. Building and Environment 2007, in press, doi: 10.1016/j.buildenv.2007.01.039. Niachou K, Livada I, Santamouris M. Experimental study of temperature and airflow distribution inside an urban street canyon during hot summer weather conditions. Part 2. Air Flow analysis. Building and Environment 2007, in press, doi: 10.1016/j.buildenv. 2007.01.040. Bezdek JC. Pattern recognition with fuzzy objective function algorithms. New York: Plenum Press; 1981. Chiu S. Fuzzy model identification based on cluster estimation. Journal of Intelligent and Fuzzy Systems 1994;2(3). Sandwell DT. Biharmonic spline interpolation of GEOS-3 and SEASAT altimeter data. Geophysical Research Letters. 1987;2: 139–42. Breiman L, Friedman J, Olshen R, Stone C. Classification and regression trees. London: Chapman & Hall; 1993.
Building and Environment 43 (2008) 1411–1418 www.elsevier.com/locate/buildenv
On the estimation of wind speed in urban canyons for ventilation purposes—Part 2: Using of data driven techniques to calculate the more probable wind speed in urban canyons for low ambient wind speeds M. Santamouris, C. Georgakis, A. Niachou Group of Building Environmental Physics, University of Athens, Building Physics 5, University Campus, 157 84 Athens, Greece
Abstract For low ambient wind speeds, airflow in deep urban canyons is characterized by a high scatter and important fluctuation as no coupling is established between the undisturbed wind flow and the flow inside the canyon. Thus, thermal and mechanical forces determine the wind speed characteristics. Existing studies based on experimental comparison have shown that under the above boundary conditions, deterministic models may predict with sufficient accuracy the mean wind speed but not the fluctuation caused by the thermal phenomena. In the present paper, data have been collected through an extensive experimental campaign in seven canyons. Then, data driven techniques, to predict the more probable wind speed in deep urban canyons as a function of the prevailing thermal and inertia phenomena, have been developed. The proposed methodologies are strictly valid inside the limits of the experimental data, i.e. aspect ratios between 1.7 and 3.25, and can be used to estimate the more probable wind speed close to the facades of urban canyons. r 2007 Elsevier Ltd. All rights reserved.
1. Introduction Urban heat island is the more documented phenomenon of climate change. High urban temperatures affect the cooling load of buildings as well as the potential of natural ventilation techniques when applied to urban buildings [1–3]. Knowledge of the wind speed in urban canyons is a necessary input to estimate the natural ventilation potential of urban buildings as well as thermal comfort in open areas [4]. The wind flow inside canyons is driven and determined by the interaction of the flow field above buildings and the uniqueness of local effects as topography, building geometry and dimensions, streets, traffic and other local features. The wind speed in low aspect ratio canyons can be easily predicted using computerized flow dynamic techniques.
Corresponding author. Tel.:+30 210 7276847; fax:+30 210 7295282.
E-mail address: [email protected] (M. Santamouris). 0360-1323/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2007.01.042
Knowledge of the wind speed in deep and high aspect ratio urban canyons is resulting either from numerical studies or from field experiments within real urban canyons or within scaled physical models in wind tunnels. Various mathematical algorithms have been proposed for calculating the wind speed inside such canyons [5–8]. Computerised fluid dynamic techniques may be applied especially when the ambient wind speed above the canyons is quite high and there is a coupling between the flow inside the canyon and the undisturbed wind speed [9]. For high wind speeds the airflow in the canyon can be seen as a secondary circulation feature driven by the above roof imposed flow [5]. If the wind speed out of the canyon is below some threshold value the coupling between the upper and secondary flow is lost [5], and the relation between wind speeds above the roof and within the canyon is characterized by a considerable scatter. In this case, thermal and mechanical phenomena may play a very important role, and determine the final wind speed. Under these conditions and given the thermal regime in a canyon, wind speed may present a very important variability and
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fluctuation. Thus, the above-mentioned deterministic models that do not consider thermal effects may not be appropriate to estimate the wind speed in a canyon especially when thermal phenomena are important [10–12]. According to De Paul and Shieh [13], the threshold value to establish the coupling is between 1.5 and 2 m=s. Similar values are reported by Nakamura and Oke [5], who worked with a canyon having an aspect ratio close to unity (1.06). Also, Mc Cormick [14] reports a threshold wind speed close to 2 m=s. However, as shown by Santamouris et al. [15], for canyons with a higher aspect ratio, coupling is established for much higher ambient wind speeds ranging between 4 and 5 m=s. The present paper in combination with Georgakis and Santamouris [16] aims to present the results of a recent research carried out in the frame of the Reshyvent and UrbVent research projects. The programs have developed and tested computational methods to calculate the wind speed in urban canyons to be used for hybrid and natural ventilation studies. The research involved detailed experiments in seven canyons, development and testing of computational methods against the experimental data. Two types of algorithms have been developed. In Georgakis and Santamouris [16], the proposed algorithms to calculate the wind speed in canyon, when there is a coupling between the undisturbed wind flow and the flow inside the canyon, are presented. Such a situation occurs for quite high wind speeds. The actual paper proposes a new calculation methodology when such a coupling is not achieved. In particular, data driven techniques have been developed to estimate the wind speed near the canyon facades when the wind speed out of the canyon is below the threshold value over which the coupling is achieved. The proposed data driven techniques have been developed using the collected experimental data and thus are valid inside the boundaries of the specific experiments.
influenced by thermal and mechanical phenomena. Important temperature differences between the canyon walls and the air is the source of upward or downward flows that may be much more important than the flow induced by the wind above the canyon. Thus, even for a constant value of the ambient wind speed, the flow in the canyon may present a very high fluctuation. This is clear in Fig. 1 where the fluctuation of the measured wind speed for various points inside a representative canyon is given. The specific graph refers to a flow oblique to the canyon axis and for ambient wind speeds varying between 1 and 2 m=s. A similar variability and fluctuation have been found for almost all angles of incidence and in all canyons. The application of deterministic techniques [10–12], for low ambient wind speeds, has shown that the wind speed inside canyons is characterized by: (A) highly uncertain boundary conditions, (B) a combination of complex phenomena that in certain cases are not of a deterministic nature. To support the above statements, the previously mentioned deterministic techniques have been applied for all the set of the experimental data, low wind speeds, and have been compared against the measured values. Fig. 1 shows the range of the predicted against the measured values for a representative canyon. As shown, there is a quite good agreement as it concerns the prediction of the mean value of the wind speed, however, the used models cannot follow the experimental values when important thermal phenomena occurs. Given the random characteristic of the phenomena and the important fluctuation of the wind speed it is considered that a statistical representation of the phenomena is more appropriate to describe the phenomena.
2. Experimental procedure In the frame of the European Projects Urbvent, and Reshyvent field experiments were performed during the summers of 2001 and 2002 in seven pedestrian deep street canyons, in Athens. The aspect ratio of the studied canyons varied around 1.7–3.3. Experiments took place for three days and for 12 or 24 h per day. The experimental campaigns, which took place in each of the seven canyons, involved measurements of the wind speed and ambient temperature outside and in selected places inside the canyon as well as well measurements of the surface temperature. Details on the followed experimental campaigns as well as on the characteristics of the canyons can be found in [17–20]. 3. Airflow characteristics in canyons under low ambient wind speeds As already mentioned, the wind speeds in deep urban canyons under low ambient wind speeds is highly
Fig. 1. Fluctuation of the measured wind speed at various positions inside an urban canyon for ambient wind speeds varying between 1 and 2 m/s. The red bars refer to the estimated wind speeds in the specific points. 1. Vout, 2. Winward NE fac- ade, wind from NE direction, 3. Leeward SW facade, wind from NE direction, 4. Winward NE fac- ade, wind from SE direction, 5. Leeward SE fac- ade, wind from SE direction, 6. Leeward NE fac- ade, wind from the SW direction, 7. Winward SW fac- ade, wind from SW direction, 8. Leeward NE fac- ade, wind from NW direction, 9. Winward SW fac- ade, wind from NW fac- ade, 10. wind at 3.5 m height, 11. wind at 7.5 m height, 12. wind at 11.5 m height, 13. wind at 15.5 m height.
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representative distribution of the obtained data. As shown, there are clusters characterized by:
4. Statistical description of the phenomena Both Buoyancy mechanical and inertia phenomena are responsible for the airflow in canyons. Buoyancy phenomena caused by the temperature differences between the canyon surfaces and the ambient air are of very high importance and may be the main source of the airflow in canyons [15]. Buoyancy phenomena may be described by the local Grashof number, defined as: Gr ¼ gbðT surf T air ÞH 3 n2 , (1) where b ¼ 1=T, T surf ¼surface temperature at (x), T air is the ambient temperature at same height as x, H is the height of point x inside the canyon where the wind speed has to be calculated and n is the viscosity. Inertia forces may be considered by using the Reynolds number, Re ¼ Vh=n,
(2)
where V is the undisturbed wind speed measured at height h outside the canyon, and n is the viscosity. Airflow characteristics in canyons are classified according to the direction of the ambient wind speed as:
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parallel to the canyon axis; perpendicular to the canyon axis; and oblique to the canyon axis. Data from all canyons have been processed and a very important data set has been created. The data set is restricted to the cases where the undisturbed wind speed is lower than 5 m/s. For each of the above cases four data groups may be defined (i.e. for the perpendicular flow): (a) wind angle 90 15 (windward fac- ade), (b) wind angle 180 15 (windward fac- ade), (c) wind angle 90 15 (leeward fac- ade), and (d) wind angle 180 15 (leeward fac- ade).
For each data point of the above groups the local Gr as well as the Re number may be calculated for a specific position (x; H), inside the canyon. Then for each group a plot Gr 4Re may be obtained. Fig. 2 shows a
Low Reynold and negative Grashof numbers. Low Reynold and negligible Grashof numbers. High Grashof and low Reynold numbers. High Reynold numbers.
Each of the above clusters represents a different flow regime driven either by the inertia or the gravitational forces or from both of them. By applying fussy clustering techniques to each case n clusters may be defined. Clustering is a mathematical method to classify numerical data based on the identification of sub-groups on a data set, called ‘clusters’, where all objects are described by similar characteristics. Every cluster involves a number of objects, members of the cluster, represented by given position in the space as well as a centre of the cluster defined as the point in the cluster space where the sum of the specific distances of every member object belonging in the cluster is minimized. Various mathematical methods have been proposed for clustering of a data set. Fuzzy clustering is a quite modern, ‘intelligent’ technique considering that each individual member in the data set belongs to a cluster to some degree that is defined by a membership function [21,22]. When clusters of different flow regimes are defined, the probability density function of the air speed at the position (x; h), corresponding to each cluster, may be calculated. A representative distribution for the whole set of data is given in Fig. 3. It is pointed out that only data corresponding to ambient wind speeds lower than 5 m/s have been considered. Thus for each cluster the more probable wind speed inside and outside the canyon is calculated. In parallel, the corresponding temperature difference between the air and the canyon surfaces at the point where the wind speed is estimated have been found. Thus, a reduced data space including the three above parameters (more probable wind
Fig. 2. Distribution of the data as a function of their Reynold and Grashof numbers.
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speed inside and outside the canyon and the corresponding temperature difference) has been created. 5. Development and description of a 3D interpolation data driven model Using the reduced data space a 3D interpolation data driven model has been created to calculate the wind speed at a point x inside the canyon. In the following details of the method is given. For the perpendicular and oblique flows, specific models have been developed for the windward and leeward parts of the canyon. For the case where the flow is parallel to the canyon axis, a single method has been developed. Thus five specific models have been proposed. It is evident that the
Fig. 3. Probability density function of the wind speed inside and outside the canyon for a representative cluster.
developed methods may be applied inside the input values for which they have been developed. The developed models are described in the following. 5.1. Perpendicular flow Using as input the developed reduced space inputs to a 3D spline interpolation technique [23], a graphical representation of the 3D space V ðHÞ, H=w and DT, has been obtained, where V ðH; xÞ is the wind speed at height H, w is the width of the canyon and DT is the temperature difference between the ambient air and the canyon surface at the specific point (x; H). The developed graphical methods for the windward and the leeward facades are given in Figs. 4 and 5, respectively. The method allows to estimate using the developed graph, the more probable wind speed inside the canyon at a height H, as a function of the temperature difference DT between the surface canyon temperature and the ambient one at H, and the geometric factor H=w. As shown, prediction of the wind speed inside the canyon can be achieved only as a function of three parameters: the temperature difference, the relative position of the point where the wind has to be calculated and the width of the canyon. No correlation has been found between the wind speed inside the canyon and the undisturbed wind above the street. For the windward facades, it has been found that three zones of the more probable wind speed occur. For the lower parts of the canyon, H=w ratios below 1.5, the more probable wind speed is low and around 0.5 m/s. For medium heights, 1:5oH=wo2, the corresponding mean value is around 1 m/s, while for the higher parts of the canyon, the wind speed increases considerably and may reach values close to 2.5 m/s.
Fig. 4. Developed graphical data driven model to predict the more probable wind speed close to the windward canyon facades when the flow is perpendicular to the canyon axis.
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For the leeward facades, as expected, much lower wind speeds have been found. For temperatures differences up to 5 C, the average more probable wind speed close to the leeward facades is around 0.5 m/s. For higher temperature differences, the corresponding value may increase up to 1 m/s. 5.2. Parallel flow For the case where the flow inside the canyon is parallel to the canyon axis, it is found that the more probable wind speed may be predicted as a function of the undisturbed wind speed above the canyon and of the ratio between the height where the wind speed has to be estimated, H to the height of the canyon, Hcanyon, Fig. 6. As shown, for the lower parts of the canyon the average more probable wind speed is close to 0.5 m/s and it is not influenced by the undisturbed wind speed. For H/Hcanyon between 0.4 and 0.5 the corresponding value increases up to 1 m/s and there is a slight relation to the ambient wind speeds. For the higher parts of the canyon, a clear relation to the undisturbed wind speed is found. In this case the average more probable wind speed may increase up to 2 m/s for ambient wind speeds between 2 and 3 m/s.
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is found. In this case the speed inside the canyon may reach values close to 3 m/s. For the leeward facades of the canyons, it is found that the more probable wind speed may be predicted as a function of the temperature difference and of the ratio H=w (Fig. 8), where H is the height in the canyon where the wind speed has to be calculated and w is the width of the canyon. In this case, for H=w ratios lower than 0.3, the average more probable wind speed is not influenced by the temperature difference. For H=w higher than 1.6 and for temperature differences higher than 15 C, the average more probable wind speed increases considerably and may reach values close to 2 m/s. 6. Development of simplified data driven models In order to evaluate the possibility to develop more simplified data driven models to predict the more probable
5.3. Oblique flow For the windward facades of the canyon, it is found that the more probable wind speed may be predicted as a function of the undisturbed wind speed and of the ratio between the height H where the wind speed has to be estimated to the canyon width, w, Fig. 7. As shown, for the lower parts of the canyon, the more probable wind speed is not influenced by the wind speed above the canyon. In this case an average value of the more probable wind speed is close to 0.5 m/s. For the higher parts of the canyon and for wind speeds higher than 2 m/s, a clear relation between the more probable canyon wind speed and the undisturbed one
Fig. 5. Developed graphical data driven model to predict the more probable wind speed close to the leeward canyon facades when the flow is perpendicular to the canyon axis.
Fig. 6. Developed graphical data driven model to predict the more probable wind speed close to the canyon facades when the flow is parallel to the canyon axis.
Fig. 7. Developed graphical data driven model to predict the more probable wind speed close to the windward canyon facades when the flow is oblique to the canyon axis.
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wind speed in canyons, the developed reduced data space has been used and two simplified data driven models have been created to calculate the more probable wind speed at a point x inside the canyon. In particular: (a) a simple linear correlation method and (b) a decision tree method, have been developed. The results described in the following refer to the case of windward perpendicular to the canyon axis ambient wind flow. Results of similar type have been obtained for all other cases of ambient wind flow. 6.1. Linear correlation method A simple correlation model of the form V ðH; xÞ ¼ 0:537 þ 0:957H=w 0:012 DT þ 0:0039 V out
ð3Þ
has been obtained. V ðH; xÞ is the more probable wind speed inside the canyon at height H, w is the width of the canyon, DT is the temperature difference between the ambient air and the canyon surface temperatures at height H. Finally, V out is the undisturbed wind speed. 6.2. A decision tree method Using decision tree methodologies [24], a flow chart algorithm has been developed to calculate the more probable wind speed inside the canyon at height H. The calculated decision flow chart is given in Fig. 9. In the figure, 2, 3 and 4 are the ratio H=w, the temperature difference DT and the undisturbed wind speed V out . 7. Comparison against the experimental data The three methodologies have been compared against the experimental data included in the reduced space data set. The results of the comparison for the case of windward perpendicular to the canyon axis ambient wind flow are given in Fig. 10. The R2 correlation coefficients are: 0.96 for the 3D graphical interpolation model, 0.84 for the tree decision method and 0.74 for the linear correlation method. As shown, the 3D graphical interpolation model predicts the more probable wind speed inside the canyon with sufficient accuracy, while the tree decision method, although it is of sufficient accuracy for low speeds, fails to predict high wind speeds inside the canyon. Finally, the linear correlation method, as expected, presents a limited accuracy. Similar results have been obtained for all the other cases of airflow. 8. Conclusions
Fig. 8. Developed graphical data driven model to predict the more probable wind speed close to the leeward canyon facades when the flow is oblique to the canyon axis.
AirFlow in deep urban canyons may be characterized by a high scatter and important fluctuation especially when the ambient wind speed is low and no coupling is established
Fig. 9. Decision flow chart algorithm.
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Fig. 10. Comparison of the predicted against the experimental values of the more probable wind speed inside the canyon at a height H.
between the undisturbed wind flow and the flow inside the canyon. Under such conditions thermal and mechanical forces determine the wind speed characteristics. Comparison with extensive experimental data has shown that under these boundary conditions, existing deterministic models can predict with sufficient accuracy the mean wind speed but not the fluctuation caused by the thermal phenomena. Using data collected in an extensive experimental campaign in seven canyons, data driven techniques have been developed that allow to predict the more probable wind speed in deep urban canyons as a function of the prevailing thermal and inertia phenomena. The developed methodologies are strictly valid inside the limits of the experimental data, i.e. aspect ratios between 1.7 and 3.25, and can be used to estimate the more probable wind speed close to the facades of urban canyons. Acknowledgement The present study was partly financed by the European Commission, Directorate General for Science, Research and Technology under the contract ‘‘UrbVent’’: Natural ventilation in urban areas—Potential assessment and optimal facade design, ENK6-CT-2000-00316. The contribution of the Commission is gratefully acknowledged. References [1] Santamouris M, editor. Energy and climate in the urban environment. James and James Science Publishers; 2001. [2] Santamouris M. Heat island research in Europe The state of the art. Advances Building Energy Research; (ABER) 2006:1.
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