Abstract. 1 Introduction

Transcription

1 Parametization of aerodynamic roughness parameters in relation with air pollutant removal efficiency of streets M. Bottema Laboratoire de Mecanique des Fluides, URA CNRS1217 et SUB-MESO Groupement de Recherches CNRS 1102, Ecole Centrale de Nantes, 1 Rue de la Noe, F Nantes Cedex 03, France Abstract A new approach for judging the air pollutant removal efficiency of streets is proposed, based on the relation between (1) the average roof level pollutant flux w' c' and (2) u* and the roughness parameters ZQ and za of the logarithmic wind profile. An analytical model for evaluation of ZQ and z<j is presented. Building density and streamwise relative building length turn out to be the key parameters. Predicted ZQ compares well with published experimental data, but fine tuning is not yet possible because of experimental uncertainties. 1 Introduction Pedestrian level pollutant concentrations are not only determined by the strength of local pollutant sources, but also by aerodynamic properties of streets. A street design with optimized aerodynamical properties will yield considerable improvement in local environmental quality. A street aerodynamics 'database' as a predictive tool for town planners would be of great value. Unfortunately, generating such a 'database' is not easy because of the great number of parameters entering the problem. A first simplification would be to neglect for the time being the pollutant source related parameters, and to consider parameters related to street aerodynamics only. In a qualitative sense, this leads to a flow regime classification as presented by Oke [1]. A quantitative approach for uniform terrain is proposed in this paper. The following issues will be discussed: relation between street level and surface layer pollutant fluxes, analytical modeling of the roughness parameters ZQ and Zd, a sensitivity study with the analytical model, and model validation. 2 Surface fluxes; basic assumptions Conventional surface layer theory suggests a strong relation between kinematic momentum flux - u' w' = u*% and flux of a passive pollutant - w' c' = u*c*, with c* a concentration scale. The scale c* is supposed to depend mostly on source properties (e.g. position) which are not considered explicitly in this paper.

2 236 Air Pollution Engineering and Management - 1> Figure 1: Definition sketch for the street ventilation efficiency parameter Q _ At roof level, there also seems to be a strong similarity between u' w' and w' c'. Let us consider the concept of street ventilation efficiency, and define a ventilation parameter Ey (see figure 1) as: " o-'-- where Q is the source strength per unit area (kg/m^s), c the pollutant concentration (kg/irp), h the building height, and U(zref) a reference wind speed (zref taken sufficiently high to avoid spatial inhomogeneities; preferably in logarithmic layer). Finally, We is an entrainment or mixing velocity which follows from dimensional considerations. Thcrfact that We represents mixing does suggest that it is related to the local u' w'. Data of Raupach et al [2] indicate that in the roughness sublayer (between the obstacle tops and the logarithmic surface layer) - u' w' remains almost constant and equal to u*%, so that Wg would also be closely related to u*. Although no definitive proof is found that aerodynamics of streets and source properties can be fully separated by splitting -w' c' into u* and c*, it seems - for the present application - to be a reasonable first approximation to assume that c* is a 'constant'. Then, we can use u* as principal estimator of - w' c' in different geometries. For comparison of different street designs it is convenient to consider not u* but the aerodynamic roughness parameters ZQ and z^, as the latter are not directly dependent on wind speed. If desired, we can estimate Ey by replacing the We in eq. Ibyau* evaluated from the logarithmic wind profile. 3 Modeling of roughness parameters Equation 2 gives a general expression for ZQ which can be derived from the logarithmic law, using the fact that T = pu*2 (% _ in N/m^ - is the drag force per unit area and p is the air density in kg/rn^), and assuming that the surface drag is caused by pressure drag on the roughness elements only: ( -- K ^ Y0.5^C/z^,...y where ZQ is the roughness length, Zj the displacement height, Zref a reference height (where the log-profile is valid), Cd = 2Ap/(pUref^wh) the drag coefficient of the roughness elements, and K = 0.40 the Von Karman constant; Ap is pressure difference over each roughness element in N/nA

3 Air Pollution Engineering and Management 237 Figure 2: Notation definition for regular building groups. Wind direction is 0 when perpendicular to the longest building face (with width w). The frontal area density Af is defined as: i _ w h _ N-w-h /W ~^~^^~~" ~~~~~~~~'~~ (3) ' d-d. S where w is the building width, h the building height, dx the streamwise building spacing, dy the lateral building spacing, N the total number of obstacles in a group, and S the total surface (of the group, town district etc.). Figure 2 gives a definition sketch to clarify the notation. In practice, we have no 'universal' expression for Cj in building groups, so some assumptions have to be made to account for mutual sheltering. A commonly used approach [3] (and starting point) is to choose z^f= h, C<j = Q(zref=h) = Cdh» and to use z^ to account for mutual sheltering. Now the main problem is shifted to estimation of a proper z<j. Raupach [3], for his random arrangement model which gives a solution up to Af ~ 0.25, evaluates Zj by assuming that it is related to the vertical dimension of the shear layer bounding the obstacles' wake. He also multiplies Zg/h in eq. (2) with a small roughness sublayer correction term exp(y) (note: Raupach's [3] value of Y can not be copied as his equations 29 and 31 contain a sign error). The above estimate of z<j seems doubtful in regular building arrangements with large lateral spacings (say Sy/w > 1). Therefore, the present model discriminates between an in-plane (sheltering) displacement height Zd,pi, and an overall (profile) displacement height z^. Essentially, this is an argument based on the displaced flow volume. For consistency, z<j,pi is also evaluated using the volumes of buildings and their recirculation zones. Comparison with data should indicate which approach is the best. Anyway, the present model has the advantages that it is also valid for high densities (Af > 0.25), and that the effect of a greater number of geometrical parameters can be investigated. In the present model, the volumes of the frontal and lee recirculation zones are estimated [4] to be about (whlp)/3 and (whl^)/3 where Lp and LR are the lengths of the frontal and leeward recirculation zones. Then, the following expressions for z^pi can be derived for the case of a normal pattern:

4 238 Air Pollution Engineering and Management where the righthand expression is for high densities (s% < LR + Lp); Sx is the clear streamwise spacing. The profile displacement height Zd = (w/dy)zd,pi. The expression for ZQ for a normal pattern is: h h Note that the roughness sublayer correction term Y has been neglected. In the staggered case we have the following expression if there is no sheltering by the row immediately upstream, i.e. if Sy/w > 1 : 1 +(2- ***** )(s,+dj p d,pi^,p h 2d, h 2d, where the right hand expression again is for high densities (s% + dx < LR + Lp and Sy/w > 1). In both cases, Zd = 2(w/dy)zd,pi; ZQ is evaluated with eq. (5). For dense staggered arrays, with Sy/w < 1 we use: (7) - " w """ " W """ " The roughness length ZQ can be evaluated by eq. (5), but only after Xf has been replaced by (Sy/w)Xf. Finally, the model parameters LR, Lp and Cdh should be estimated. In a previous study [5], LR and to a lesser extent Lp were found to be proportional to an influence scale Lg: w-h,, with Lp ~ Lg and 2Lg < LR < 5Lg (depending on roughness). For the present application, Lp + LR = 4Lg seems to be a good approximation. Cdh values representative of small densities (h/zo ~ 5000) have been used. Numerical estimates have been used to ensure that data were not contaminated by upstream roughness change ('smooth turntable') effects [6]. A preliminary interpolation formula is: Ca, «1.2 max(l (1, / h),0.82) - min( (w / h),1.0) (9) 4 Sensitivity study Figure 3 shows the dependence of Zg/h on A,f and on other - secondary - parameters. The basic case consists of cubes in regular arrangement. Relative building length lx/h and the pattern type are highly significant. The effect of increasing Cdh by 25% is most pronounced at low A,f, but it is only moderate (zo/h +25%) for A,f « The effect of increasing w/h or Sx/Sy by 100% is moderate for all Af. The sensitivity of Zo/h to LR+LF is small (10% for a 25% 'forcing'), which justifies the rather crude approximations of recirculation zone volume in the present model. Figure 3 suggests a maximum ZQ - and maximum street ventilation - for If ~ 0.2. However, it should be noted that both peak Zo/h and peak location (Xf) are sensitive to lx/h: for lx/h = O(l) both are proportional to (lx/h)p with -0.6 < p < -1.

5 Air Pollution Engineering and Management 239 0,001 0,01 0,1 (wh)/(dxdy) Figure 3: Sensitivity of Zo/h (as a function of Kf) to the main model parameters. Solid line: basic case of cubes in normal pattern. Dashed line: lx/h = 2. Dashdotted line: Cdh is increased by 25%. Dotted line: cubes in staggered pattern Orientation and wind direction are also important parameters. Test calculations with the present model showed that a factor 2 change in Sx/Sy or w/h can already yield a difference of a factor 2 in Zo/h for 0 and 90. Further calculations, and measurements [7], showed that Zo/h may even vary some orders of magnitude if w& becomes sufficiently large (e.g. > 8). It is interesting here to consider the concentrations of fig. 8 (street level source) in Hoydysh and Dabberdt [8]. The present model predicts Zo/h =_Op28 for 0, and Zo/h = for 90 ; no experimental estimate of ZQ or w' c' is available. Nevertheless it is interesting to note that for 90 - when ZQ is low -, measured concentrations decrease much more with height than in the 0 case, indicating decreased mixing for the 90 case. The experiments do also show minimum concentrations for oblique flow. Such effects should be predicted by future model versions. 5 Model validation An extensive literature review [4] revealed that very few reliable experimental ZQ- and za data are available. The main reasons for the unreliability of data were: Part of the wind profile was taken outside the logarithmic height range (which is roughly 2h < z < [4], see also [2,9]; S=boundary layer height). Conditions for the existence of a proper logarithmic height range were not satisfied. For groups of finite size, fetch was often too short, resulting in too small an internal boundary layer height hibl- Its effect is comparable to that of too small a 5. Typically, hml (or 8) was less than loh, whereas the first requirement demands S/h or hiei/h > 8 as an absolute minimum. Corrections will require detailed data, or schemes to account for 8/h, hibl/h, and dp/dx. Examples of both above given cases are data of Counihan [10] Hussain [11] and Visser [12]. Another common error source is underestimation or neglect of Zd (e.g. in [13,14]), the latter may well cause a factor 2 error in ZQ.

6 240 Air Pollution Engineering and Management (wh)/(dxdy) Figure 4: Ratio of predicted and measured ZQ*. Zo(pred.)/Zo(exp.) as a function of frontal area density If. Open symbols: original exp. value; Black symbols: (partly) corrected: see text for details. Figure 4 gives the ratio of predicted and measured Zo/h as a function of frontal area density Xf. It contains about 100 data points, on which the following corrections have been applied: Counihan [10]: 9 points (A), case specific finite fetch correction by his fig. 2. Hussain [11]: 33 points (?), original profiles were taken between the roughness elements; ZQ from reported Cj and U(z/h=1.5); zd,pi from Jackson's [15] hypothesis on the relation between zj and the pressure distribution on the roughnesses. Note: no correction could be made for the fact that hibl/h -1.5 Visser [12]: 16 points (») (only the data without 'trees'), ZQ evaluated in the same way, Zd,pi is evaluated by the present model as no pressure distributions were available. No correction could be made for the fact that hrbl/h ~ * Iqbal et al [14]: 11 points (««); screens, reported Zd = 0 even for A,f > 0.2. ZQ is corrected using Zd from present model and their reported profile height range. Some other 20 points could not be corrected, some other 5 points (cylinders, from [16]) should be reliable. Reference [4] gives further details, also on a few other included revised data points ( ). The present model seems to agree quite well with experimental data, although the predictions seem to be somewhat on the high side for If > 0.1, and on the low side for Xf < 0.1. However, experimental errors due to e.g. too small a 8/h may also be dependent on Xf.The predicted position of peaks - in terms of Kf - is generally about 50% higher than in the experiments, corresponding to 25% smaller spacings. The sensitivity of (peak/maximum) Zo/h to lx/h and to pattern type as shown in figure 3 is confirmed by Hussain's [11] data. An overall linear fit yielded: Zo/h(mod.) = zo/h(exp.); the correlation coefficient r = The agreement seems acceptable, given the great sensitivity of ZQ to experimental errors, and the experimental 'problems' discussed above. The latter is the reason why the author is reluctant to make any definitive conclusion. In case of Raupacrf s [3] model, the main problem is the estimation of his wake length or shear stress deficit area parameter 'c' (defined in [3]). No experimental guidance was found. Assuming that the downstream extent of the shear stress deficit area «1.5LR yields, for h/zo = O(100) and w/h» 1, c «1. However, comparison with experiments shows on average a factor 3

7 Air Pollution Engineering and Management 241 underestimation of Zo/h if c = 1, whereas c ~ 0.6 would yield largely correct results. Hence, it is of great importance that better estimates of 'c' become available. For configurations with trees (wind tunnel data in [12]; see [4] for full scale data), ZQ is generally not predicted well; tree may even dominate roughness for Af < This feature obviously needs to be considered. 6 Conclusions and future work Optimization of street design with respect to air ventilation or pollutant removal is difficult because a great number of parameters enters the problem. This paper proposes a simplified approach based on the assumption that the pollutant concentration flux -w'c' (= u*c* in the surface layer) can be split in an aerodynamic component (u*) and another component (c*) that is related to pollutant source properties. Surface layer theory and roughness sublayer data seem to support this idea, but a hard proof will be difficult to obtain. Once we accept that u* and u' w' are good estimators for w' c', we can relate the aerodynamic roughness length ZQ and the displacement height z<j to w' c'. The optimum air pollutant removal will then correspond to a maximum ZQ. This paper proposes a simple analytical model to compute Zg and z<j as a function of building height h, and of other geometrical parameters of a homogeneous building group. The key parameter is the frontal density A,f = (wh)/(dxdy). Important secondary parameters - both in model results and in experiments [11] - are the building pattern and the relative building depth 1%/h. The Zo/h peak - with optimum street ventilation - is found at A,f = O(0.2), but both peak magnitude and peak position are sensitive to lx/h. Finally, both dispersion [8] and roughness parameters are sensitive to wind direction. Comparison of the present roughness model with experimental data suggests fairly good model performance. However, fine tuning is not possible because of experimental uncertainties, caused by: (a) inclusion of data outside logarithmic height range, (b) too small a 8/h or hjbl/h to allow for the existance of a proper logarithmic range and (c) neglect or underestimation of z<j. Some tests have been carried with Raupachf s model [3]. Better guidance for the choice of the wake length parameter 'c' is urgently needed. However, even with the proper V, RaupacrTs model gives no solution for high densities (say Xf > 0.25). Moreover, it does not predict any sensitivity to lx/h. With regard to future work, the following is recommended (see also [4]): First of all, some experimental or numerical work would be desirable to test the hypothesis that the concentration scale c* is only weakly dependent on street aerodynamical properties (proposed test: choose a building pattern and a source type; keep street geometry constant, i.e., do vary lx only). Furthermore, better experimental estimates of ZQ and z^ are required. A practical problem is the fact that a sufficiently large logarithmic height range, requires a 8/h or hrbl/h > 16, which corresponds to a fetch x = O(250h). Also, better guidance should be available to estimate the model constants. This applies especially to Raupach's shear stress deficit area parameter 'c', but also to the drag coefficient Qh. For practical application, it is important that a roughness model of general validity is constructed, i.e. a roughness model that can cope with irregular patterns, with trees, and with oblique flow (see data of [8]). Urban internal boundary layers should also become a key topic, as in many practical cases, surface fluxes over inhomogeneous terrain need to be known.

8 242 Air Pollution Engineering and Management 7 Acknowledgement Many thanks to Prof. B.E. Lee who provided me of copies of ref. [11], to Ing. G.Th. Visser for his copy of [12] and to many others (e.g. colleagues at CSTB-Nantes) who helped me gathering the literature and data required. This work was supported by CNRS, France and by the European commision under Human Capital and Mobility grant no. ERBCHBGCT (DISPURB). References 1. Oke, T.R. Street design and urban canopy layer climate, Energy and Buildings, 1988, 11, Raupach, M.R., Antonia, R.A. & Rajagopalan, P.G. Rough wall turbulent boundary layers, Appl. Mech. Revs. 1988, 44, Raupach, M.R. Drag and drag partition on rough surfaces, Boundary- Layer Meteorol., 1992, 60, Bottema, M. Aerodynamic roughness parameters for homogeneous building groups, Document SUB-MESO, Report, Ecole Centrale de Nantes, France, 1995 (in preparation) 5. Bottema, M. Wind climate and urban geometry, PhD Thesis, Eindhoven University of Technology, The Netherlands, Bottema, M. & Wisse, J.A. Effects of turntable roughness on low rise building pressures, pp , Proc. 9th Int. Conf. on Wind Engineering Jan. 1995, New Delhi, India, Jackson, B.S. & Carroll, JJ. Aerodynamic roughness as a function of wind direction over assymetric surface elements, Boundary-Layer MeteoroL, 1978, 14, Hoydysh, W.G. & Dabberdt, W.F. Kinematics and dispersion characteristics of flows in assymetric street canyons, Atmospheric EfzWmrzmfrzf, 1988, 22, Tennekes, H. The logarithmic wind profile., J. Atm. Sci., 1973, 30, Counihan, J. Wind tunnel determination of the roughness length as a function of the fetch and the roughness density of three-dimensional roughness elements, Atmospheric Environment, 1971, 5, Hussain, M. A study of the wind forces on low rise building arrays and their application to natural ventilation design methods, PhD thesis, University of Sheffield, UK, Visser, G.Th. Model development for the evaluation of ventilation losses in districts consisting of identical building groups (in Dutch), Report , TNO-IMET-ST, Apeldoorn, NL, O'Loughlin, E.M. & MacDonald, E.G. Some roughness-concentration effects on boundary resistance, 1964, La houille blanche, 7, Iqbal, M., Khatry, A.K. & Seguin, B. A study of the roughness effects of multiple windbreaks, 1977, Boundary-Layer MeteoroL, 11, Jackson, P.S. On the displacement height in the logarithmic wind profile, 1981, J. Fluid Mech.,111, Raupach, M.R.,Thorn, A.S. & Edwards, I. A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces, 1980, Boundary- Layer MeteoroL, 18,