Mean flow characteristics in the wake of two prismatic bodies in tandem arrangement

Transcription

1 Indian Journal of Engineering & Materials Sciences Vol. 1, October 1994, pp ,,":. E;~T ~ts5 Mean flow characteristics in the wake of two prismatic bodies in tandem arrangement B H Lakshmana Gowda & M Mohamed Sitheeq Fluid Mechanics Laboratory, Department of Applied Mechanics, Indian Institute of Technology, Madras 00 03, India Received 25 March 1994; accepted 23 June 1994 The mean velocity profiles in the gap between two bluff bodies in tandem arrangement and in the wake of the rear body are presented. The results are discussed when the gap between the bodies is systematically varied from a low value to a large value. The reattachment point within the gap between the bodies and behind the rear body, the shear layer distortion due to the interference effects are revealed by the study. The understanding of the flow around prismatic cubical bodies (hi b = 1 and lib = 1; h is the height, I is bodies is of importance in building aerodynamics and the length and b is the width) arranged in tandem environmental aerodynamics. The wind flow gets distorted due to the presence of the structure in its position are presented. The gap (g) between the bodies is varied (glb = 1 to 7) and the velocity profiles path and the wake created may cause considerable are presented in the gap between thebedies and in the discomfort to the pedestrians and also influence the wake of the rear body at each gap ratio. wind loads on other structures around. If the structure is located near a aerodrome, the movement Experimental Procedure of the aircrafts will be affected by the turbulence The experiments are carried out using the wind generated in the wake. Further, buildings usually tunnel facility shown in Fig. 1. Air from a blower occur in various combinations with different relative passes through a set of screens and a settling chamber spacings. In all such cases the interference effects which terminates in a nozzle conforming to DIN 1952 become important in deciding both the fluid motion standards. The dimensions of the nozzle exit are and the wind loading. 130 mm x 240 mm. The velocity at exit is very There are relatively few investigations dealing with uniform, the variation both in the horizontal and the measurement of mean and turbulence quantities vertical planes (taken at the central section of the in the wake of three-dimensional bluff bodies. The nozzle exit) being less than 0.5 per cent. The characteristics of the mean flow field behind a leading turbulence level at exit is 0.4 per cent. A stand edge obstacle was investigated by Sforza and Mons.. designed and fabricated out of mild steel angles is The decay of the axial component of mean velocity used to support the surface plate on which the bodies and the longitudinal component of turbulence are placed. A smooth hylam sheet 12 mm in thickness intensity in the wake of three-dimensional bluff with a length of 1140 mm and a width of 55 mm is used bodies with different relative dimensions is as the surface plate. Pressure tappings (1 mm in investigated by Peterka and Cermak Castro and diameter) are provided all along the length of the plate Robins3 have reported some wake measurements in (on the central line) with a centre to centre distance of. their study on the flow around a surface mounted mm. There is provision for levelling the surface plate cube in uniform and turbulent streams. Ogawa and and also varying its position in the vertical direction. Oikawa4 have presented the results of a field The plate is positioned in front of the nozzle so that its investigation of the flow and diffusion around a model cube. Gowda et al. 5 have carried out the mean leading edge abuts with the lower edge of the nozzle as shown in Fig. 1. The uniform pressure distribution on flow and turbulence meeasurements in the wake of a the surface plate without the bodies confirmed the three-dimensionai bluff body. But there appears to proper alignment of the surface plate. Prismatic be hardly any information on the mean flow and the bodies with b equal to 30 mm made out of fine teak turbulence characteristics under conditions of wood and finished to have smooth surface and sharp interference between two prismatic bodies. In the edges (to avoid Reynolds number effect) are utilized. present study, the mean velocity profiles behind two There is sufficient length of the surface plate behind

2 254 INDIAN J. ENG. MAJER SCI., OCTOBER 1994,; SeWing chamb«(1000 x 1000) Thrott~ control rt ~ate Blow. 55) (All dimensions in mm) Not to scale Fig. I-Experimental set-up -r--" =: : -',,~,'rrrrrr' X x!b=o t 1.c ">; 1. O. 0 0 () 0.25 O.SO 075 1:0 U fur -. Fig. 2-Vertical profiles of mean velocity: without body the bodies for all relative po~itions (i.e. gjb ratios) All measurements are carried out at a exit velocity of investigated. A standard pi tot tube with a tip 14 mjs which gives a Reynolds number (referred to the diameter of 1 mm is made use of for the velocity width of the body) of As bodies with sharp measurements and the ambient static pressure is edges are made use of, the dependence of the results on taken to be atmospheric. At all stations, traverses the Reynolds number is only marginal and they can be were made extending up to the ground plate. But in used for analysing practical situations. The certain regions within the gap and behind the rear limitations of the present study are pointed out in the body the velocities could not be obtained with 1ast section. sufficient accuracy and confidence up to some height from the ground plane. This is because of the highly Results and Discussion recirculating nature of the flow in these regions. In all such cases, that portion of the velocity profile which Mean velocity profiles The velocity profiles at various stations without the could be measured with sufficient accuracy only is body and with a single body (i.e. without the shown. The pito.t pressure is measured using interfering body) are presented in Figs 2 and 3, micromanometer Type FC 012 (Make: Furness respectively. In these figures (and also other figures), Controls, U.K.) with an accuracy of 0.01 mm water U is the velocity at any distance y measured from the column. The measurement accuracy of the velocities ground plane and Uris the velocity in the free stream in the present study is within 3 per cent taking into approaching the bodies. This is the same in all cases consideration the fluctuations in the mean flow close (and hardly differed from the dynamic pressure at to the bodies. nozzle exit) as only the region close to nozzle exit has

3 GOWDA & SJ1HEEQ: PRlSMAllC BODIES IN TANDEM ARRANGEMENT 255 = Q,;,~"", x x/bao : fl. ~-.. >- 1. O U/Ur ---::If Fig. 3--Vertical profiles of mean velocity: single body (hjb = I) ~ ~~,-"[l,""" x' x -x'/b x/b t 1 ~-.. > :0 u/ur - Fig. 4-Vertical profiles of mean velocity: hjb = 1, gjb = I been utili sed for the measurements.. Results at Figs 2 Though the results are obtained atg/b = 1,2,3,4,5, and 3 enable one to get an idea of the comparative and 7 only those atg/b = 1,3,5 and 7 are presented as distortion of the velocity profiles with and without they are typical. Referring to fig. 4 where the results interference. From Fig. 3, it can be seen that the shear for g/b = 1 are presented, it is seen from the shape of layer separating from the front top edge of the body the velocity profiles within the gap that the thickness reattaches behind, at a distance of about twice the of the ~hear layer separating from the front body width of the body. The profiles at various x/b indicate extends up to about 0.75h above the body height. The that the growth of the outer edge of this shear layer is flow is highly disturbed even up to the height of the restricted and extends from about 0.5 h above the height of the body (atx/b = 0)toO.15hevenatlarge body. (This is the reason why the velocity profiles could be measured and presented for y/h ;:?!: 1). downstream distances. There is very little change in Cohsidering the profile at x/b = 0 (the location the profiles beyond x/b = 9 and they have very nearly, the same shape as those in Fig. 2 at these large x/b corresponds to the rear face of the downstream body), the shear layer is seen to be sufficiently thick. values. Another interesting feature is that the velocity profile

4 25 INDIAN J, ENG. MATER SCI., OcrOBER 1994 '1 [ r9r;;jjrrrrrrr.'. 3 -.'/b f'15 ~ 1. O. () ~0 u/ur - Fig. 5-Vertical profiles of mean velocity: hjb = I, gjb = 3 -.'/b./b- x/b- ~:~r:r;;;;(jr;-r'.' ~ "> () 0.25 o.~ u / Ur- Fig. -Vertical profiles of mean velocity: hlb = I, glb = 5 could be measured even up to the top edge of the body unlike at x' /b = -1 (the location corresponds to the the height up to which the velocity measurement could be carried out at these two locations. The rear rear face of the front body). This is because of the body appears to have a streamlining effect on the flow presence of the recirculating region on top of the front body at x' /b = -I, whereas, such a region appears to separating from the front body. Further, the velocity profiles behind the rear body indicate flow reattachbe non-existent on top of the rear body at x/b = O.lt ment on the ground plane to occur within a discan be conjectured that there is no shear layer tance of 1.Sb from the rear face. After reattachoriginating due to separation at the front top edge of ment, the shape of the velocity profiles change the rear body, Rather, the shear layer generated due gradually and beyond.\"/b = 9, the profiles can be to the separation at the front top edge of the upstream expected to remain unaltered. body is enveloping the downstream body. The The results atg/b = 2 indicate that there is still no reattachment of this layer occurs on the top of the rear body between x'/b = 0 and x/b = 0 which is reflected reattachment of the shear layer within the gap. But the shear layer thickness grows within the gap and the in the shape of the velocity profiles and the extent of other features are similar to those observed in Fig, 4.,

5 GOWDA & SITHEEQ: PRISMAnC BODIES IN TANDEM ARRANGEMENT L. 257 Q~'~'~~/T/" x' X -x'/b x/b- t I..c >- I. o. 0' :0 U/Ur - Fig. 7-Vertical profiles of mean velocity: h/b = 1, g/b = 7 == n-- goon.i ->'~'}"~/'x'" ~ i"-s-l g/b=1 0 R~r body Pl/b=l.l/b=1 { Front body } x'/b X g. x Single body h/b=i,l/b=l.s/b=o Single body h/b=i,l/b=i,s/b=2-0.4 Fig. 8-Interference effects on pressure distribution: g/b = 1 As the spacing between the bodies increases, the shear layer has been generated due to the flow separation at layer separating from the top edge of the front body the front top edge of the rear body itself and hence its reattaches to the ground plane within the gap thickness is sufficiently small. The velocity profiles (Figs 5-7). After reattachment there is a rapid change behind the rear body reveal the flow reattachment on in the velocity profiles as can be seen in Figs and 7. the ground plane to occur around 1.5b behind the rear Considering the results at g/b = 7 (Fig. 7) for a face. Obviously at this gap ratio (i.e. g/b = 7) the rear detailed discussion, the velocity profiles within the body does not have any streamlining effect as at gap reveal the reattachment of shear layer to occur at g/b = I (Fig. 4) and the features observed behind the about a distance of 2b behind the front body. It is rear body in Fig. 7 could be attributed to the increased interesting to compare the velocity profile at x'/b = 0 turbulence levels generated because of the front in Fig. 7 with the corresponding profile in Fig. 4. In the body, though turbulence measurements are needed later case the thickness of the shear layer is much to obtain a conclusive answer. These are planned for larger than in the former. This is because what is seen the future. at x' /b = 0 in Fig. 4 is the shear layer which is generated due to the flow separation at the top edge of Pressure measurements the front body and which is growing in thickness The pressure measurements on the ground plane along the flow. Whereas, atx'/b = Oin Fig. 7 the shear along the centre line for two cases, i.e.,gjb = 1. and 7

6 258 INDIAN J. ENG. MATER. SCI., OcrOBER 1994 ~ j:;t;,or'!)....,'..., I O. gb=7 "".-4 C O f Front body } h/b=1 I/b=1 pw R~r body' 0.Slngt.body h/b=l.t/b:i,s/b=o Sing!. body h/bzl. I/b=l.s/b=8 " Fig. 9-Interference effects on pressure distribution: g/b = 7 are presented in Figs 8 and 9. In these figures, Flow visualisation results Cpw = (p- pj/! P U~ is the pressure coefficient on the To corroborate the results of the mean velocity ground plane, p is the pressure at any point on the measurements some flow visualisation results are surface plant with the body and Pr is the pressure at the given in Fig. 10. For this purpose a aluminium surface same point on the surface plate without the body. The plate is utilized and a homogeneous mixture of lamp detailed pressure distribution for all the values of glb black and kerosene is applied uniformly on the are given in Gowda and Sitheeq. The two cases are given to highlight the correspondence between the surface plate. Runs are made at the same Reynolds number as earlier, i.e., Re = 3 x 104. mean velocity profiles and the pressure distribution. Fig. loa shows that the reattachment behind the The pressure distribution is obtained for the cases: body (without interference) occurs around hlb = 2 (i) when the single body is at the leading edge (sib = 0, which agrees well with that indicated by the velocity Fig. 8); (ii) when the single body is at some distance from the leading edge (sib = 2, Fig. 8) and (iii) under profiles shown in Fig. There is correspondence between the results presented in the previous section conditions of interference with two bodies. For the and those revealed by Figs 10b-g for various glb present purpose, considering case (iii) in Fig. 8, it is seen that the reattachment behind the rear body values. For example the reattachment within the gap is not evident forglb = 1 ~nd2(figs lob and c) which occurs around xlb = 1.5 (which is indicated by the is also the case from Fig. 4 and that for glb = In position of the peak value ofcpw). The velocity profiles Fig. lob, (glb = 3) the reattachment within the gap (in behind the rear body in Fig. 4 indicate also that the front of the rear body) can be made out which is also reattachment is occurring around the same xlb value. revealed from Fig. 5. At allg/b values (Figs lob-g) the A constant pressure in the gap between the bodies in size of the vortices behind the rear body are smaller Fig. 8 indicates a trapped recirculating flow which compared to that without interference (Fig. loa). was the reason for the difficulty in extending the This indicates a smaller reattachm~nt length behind velocity profile measurements further downwards the rear body which is borne'out by the results at than that shown in Fig. 4. The results shown in Fig. 9 for g/b = 7 indicate a reattachment of flow behind the Figs 4-7 where the velocity profiles indicate a reattachment distance of about 1.5b behind the rear rear body around xlb = 1.5. The velocity profiles for body compared to 2bbehind the front body which is thisglb value (Fig. 7) also indicate flow reattachment also revealed by the pressure measurements. Thus, around xlb = 1.5. In the gap between the bodies the there is good correspondence between the flow pressure measurements show reattachment to occur visualisation results, pressure distribution and the around x' /b = 4.75 which is in agreement with the velocity measurements. trend indicated by the velocity profiles in the gap in Limitations of the results presented Fig. 7. Thus, there is a good agreement between the Though the results presented are applicable to velocity measurements and the pressure distribution understand the flow around low rise buildings, it is on the ground plane. pointed out here that in actual practice the buildings

7 GOWDA & SmIEEQ: PRISMAl1C BODIES IN TANDEM ARRANGEMENT ",# 259 a) Single body b)g/b=1 c)g/b=2 d)g/b=3 e) g/b = 4 f)g/b=s Fig. 10 -(contd.)

8 20 INDIAN J. ENG. MATER. SCI., OCTOBER 1994 g) g/b= 7 Fig. 1 a-flow patterns are exposed to a boundary layer type of velocity Conclusions profile. As the present results are obtained with an The mean velocity profiles presented reveal the uniform approach velocity profile there is some flow to be highly distorted within the gap between two limitation on the applicability of the results to actual cubical bodies. The reattachment within the gap situation-for example there could be qljantitative occurs for g/b ;;::: The maximum outer extent of the differences in velocity distortion. Also there will be shear layer appears to be restricted to about one body some influence of the Reynolds number for buildings in height from the top surface. The reattachment length atmospheric boundary layers. But even when the behindtherearbody(~ 1.5b)forallg/bratiosisless approach velocity profile is boundary layer type, the than that without interference (~ 2b). The mean flow behind the front body would be highly disturbed and the trends in the velocity variation might not be velocity profiles behind the rear body can be expected to become similar beyond x/b = 9. very much different from the present results. Further the present study provides the necessary basic results References which can be used for obtaining the comparative 1 Sforza P M & Mons R F, AIAA. 8 (1978) influ~nce when other approach flow conditions are 2 Peterka J A & Cennak J E, 4th Int Co'!f on Wind Effects on used. Buildings and Structures. Heathrow, UK, 1975, As mentioned in the experimental procedure, a 3 Castro I P & Robins A C, J Fluid Mech, 79 (1977) pitot tube has been used to obtain the velocity 4 Ogawa Y & Oikawa S, Atmos Environ. 1 (1982) profiles. In regions close to the bodies, there will be 5 Gowda BH L, Gerhardt HJ & KramerC,J Aero Soc' Indiu. 39 some over estimate of the velocities due to the (1987) 29-3 insensitivity of the pitot probe to the inclination of the Gowda B H L & Sitheeq M M, Appl Sci Res, 47 (1990) flow