ARTICLE IN PRESS Journal of Wind Engineering and Industrial Aerodynamics 96 (2008) 2383– 2402
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Scale, boundary and inlet condition effects on impinging jets Zhuyun Xu , Horia Hangan The Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario, London, Ontario, Canada N6A5B9
a r t i c l e in f o
a b s t r a c t
Article history: Received 30 October 2006 Received in revised form 20 March 2008 Accepted 1 April 2008 Available online 19 May 2008
The sensitivity of the orthonormal impinging jets with respect to scale (Reynolds number), boundary conditions (geometry and surface roughness) as well as inlet conditions is investigated. Due to the unsteady separation in the near-wall region the flow field is Reynolds number dependent. The depth of the boundary layer formed on the impinging surface decreases, while the maximum radial velocity increases with Reynolds number below a critical, Recr, value. Above one order of Recr the flow becomes asymptotically independent of Reynolds number. When Reynolds number reaches a fully roughness region the depth of the surface layer increases with roughness height only. The flow is found to be only weakly dependent on the distance between the jet and the surface for distances larger than the ring-vortex formation length. Radial confinements of diameters less than approximately 10 jet diameters and axial confinements placed at less than 1 jet diameter above the surface affect the pressure distribution on the impinging plate. The inlet turbulence affects mostly the freejet flow region. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Impinging jet Downburst simulations Reynolds number Boundary conditions Inlet conditions Hot-wire measurements Surface pressure measurements
1. Introduction Impinging jets have extensive practical applications ranging from industrial processing such as mixing, heating/cooling or drying, to environmental flows related to ventilation or pollutiondispersion. The importance of impinging jets in wind engineering relates to the fact that this flow is the simplest generic flow to produce laboratory (or numerical) simulations of downburst
Corresponding author. Tel.: +1 519 661 3338; fax: +1 519 661 3339.
E-mail addresses:
[email protected] (Z. Xu),
[email protected] (H. Hangan). 0167-6105/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jweia.2008.04.002
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Notations b D H Hc Hv L Lw M Rc Re Rel
r, y, z
radial, azimuthal and axial coordinates, see Fig. 1. St Strouhal number corresponding to the formation of ring vortices u, w mean radial and axial velocities, m/s umax maximum radial mean velocity for a specified r, m/s u0 , w0 fluctuating radial and axial velocities, m/s /u0 w0 S Reynolds shear stress of the flow, m2/s2 Wjet axial jet velocity at the center of the pipe outlet, m/s z(umax) distance from plate corresponding to maximum radial mean velocity, m t, t time, s D roughness height of the sand paper grain, m d thickness of the jet pipe wall, m
mesh width of the grid at the pipe outlet, m diameter of the jet pipe (R is radius), m axial distance between jet and impinging surface, m height of confinement cylinder, m ring-vortex formation distance, m axial distance between the grid and the pipe outlet, m axial integral length scale of the jet flow, m distance between grid bars, m radius of confinement cylinder, m Reynolds number of the flow based on D and Wjet local Reynolds number of the flow based on r and umax
high-intensity winds. Recent wind engineering studies (Fujita, 1990; Holmes, 2002) revealed that downbursts are the most destructive winds in inland North America. These winds are jets of cold and moist air originating from thunderstorm clouds, impinging on the ground surface and producing tempo-spatial localized high-intensity winds very close to the surface. Due to its practical generic importance the impinging jet was widely investigated both experimentally and numerically. The macro-flow dynamics was progressively revealed through flow visualizations (e.g. Popiel and Trass, 1991), overall velocity field PIV measurements (e.g. Landreth and Adrian, 1990; Fairweather and Hargrave, 2002), detailed hot-wire measurements for both unforced and forced jets (e.g. Cooper et al., 1993; Didden and Ho, 1985), surface pressure measurements
Bell-mouth
Impinging Plate r
Settling Chamber
D(1.5”)
L
H
Pressure Measuring System Pressure Taps
z
Jet Pipe Hotwire Probe
Blower (5 hp)
3-D Traverser Dantec System
Fig. 1. Schematic arrangement of the experimental setup (not to scale).
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(e.g. Kataoka et al., 1982; Hall and Ewing, 2006), and experimental measurement and numerical simulation (Sengupta and Sarkar, 2008). Due to its orthonormal boundary conditions the same flow posed new challenges to numerical simulations and it was therefore thoroughly investigated through RANS, LES and DNS numerical simulations (e.g. Craft et al., 1993; Dianat et al., 1996; Tsubokura et al., 2003). From the wind engineering perspective, experimental and numerical studies have focused on some aspects of impinging jets of relevance to the simulation of downburst winds such as translation, pressure distribution on ground obstacles (Letchford and Illidge, 1999; Letchford et al., 2002) as well as some insight into the role played by various boundary and starting conditions (Choi, 2004; Mason et al., 2005). The present experimental study undertakes a rather exhaustive quest on the role played by scale, boundary and inlet conditions on the impinging jet flow. The role of these conditions is crucial when (i) Reynolds number and laboratory confinement effects are considered in designing reliable laboratory simulations of downburst winds and (ii) the relation to the full-scale phenomenon is investigated with regard to the thunderstorm base-cloud height and turbulence conditions. The impinging jet can be regarded as a superposition of three flow regions: (i) a free jet region characterized by an initial Kelvin–Helmholtz instability that generates the primary vortex ring structures; (ii) an impinging flow region where the normal (axial) velocity component is attenuated by the presence of the surface via a pressure–strain mechanism; and (iii) a wall jet flow within which self-similarity is attained. While some studies have investigated the role of Reynolds number and nozzle-to-plate distance (e.g. Martin, 1977) on the heat and mass transfer, fluid mechanics and wind engineering oriented studies focused on a relative narrow range of Reynolds numbers corresponding to typical laboratory scales (e.g. Cooper et al., 1993; Fairweather and Hargrave, 2002). The exploration of a larger range of Reynolds numbers is important for scaling purposes. Also, the influence of geometric conditions such as the jet-to-surface distance, radial and axial confinements and the surface roughness are of vital importance when generic laboratory results are to be extended to full-scale conditions. Moreover, the relation or sensitivity to the inlet conditions needs further exploration (Tsubokura et al., 2003).
2. Experimental setup 2.1. Impinging jet rigs Hot-wire and surface pressure measurements were performed in two impinging jet rigs. A small impinging jet (SIJ) was used for preliminary tests for Reynolds numbers (based on jet diameter and exit velocity) varying between 15,000 and 23,000. A second, larger impinging jet (LIJ) rig was later constructed to extend the range of Reynolds numbers from 27,000 to 190,000 and allow for more detailed measurements in the near-surface region of the flow. The jet flows were generated by fully developed horizontal pipe flows impinging on vertical aluminum plates. The flows were conditioned by using filters mounted in settling chambers with machined bell-mouths at the exits towards the pipes. A schematic of the impinging jet facilities is presented in Fig. 1. The pipes were long enough (approximately 60D) to produce a fully developed flow at the exit towards the impinging plates. The main reason of producing a fully developed flow was to ensure comparison of present experiments with existing results and to produce reliable benchmarking data for computational fluid dynamics (CFD) simulations. Mean and r.m.s. axial velocity profiles measured with an X-hotwire for the two symmetry axes at the pipe exit (LIJ) are plotted in Fig. 2. The mean velocity profiles are also well compared to a fully developed turbulent flow profile (solid dot in Fig. 2). The pipe wall thickness d for LIJ was 7 mm or d/D ¼ 0.0324. The rectangular test plate dimensions were H W ¼ 0.92 m 0.92 m (SIJ) and 3.0 m 3.0 m (LIJ) corresponding to 13D 13D. For the SIJ the entire plate was made out of aluminum while for the LIJ the center part (H W ¼ 2.5 m 2.5 m), instrumented with pressure taps, was surrounded by
ARTICLE IN PRESS Z. Xu, H. Hangan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 2383–2402
0.1
w/Wjet
1 0.9
0.09
0.8
0.08
0.7
0.07
0.6
0.06
0.5
0.05
0.4
0.04 Fully developed w/Wjet w'/Wjet
0.3 0.2 0.1 0 -0.5
w'/Wjet
2386
0.03 0.02 0.01
-0.3
-0.1
0.1
0.3
0 0.5
x/D
0.1
0.9
0.09
0.8
0.08
0.7
0.07
0.6
0.06
0.5
0.05
0.4
0.04
Fully developed w/Wjet w'/Wjet
0.3 0.2
0.03 0.02
0.1 0 -0.5
w'/Wjet
w/Wjet
1
0.01 0 -0.3
-0.1
0.1
0.3
0.5
y/D Fig. 2. Axial jet outlet velocity profiles (mean and r.m.s., error bar in 71 standard deviation): (a) along the x-axis and (b) along the y-axis.
plywood. For the SIJ the distance between the jet exit and the plate was fixed for H/D ¼ 2, while for the LIJ this distance was varied such as: H/D ¼ 1, 2, 3, 4. Further on, using the large test facility (LIJ) the surface of the impinging plate was covered with various fine grain sand papers between grain ]20 and ]400 (roughness height from 0.85 to 0.03 mm). Hot-wire profile measurements were repeated for r/D ¼ 0.8–3.0 and for all rough surfaces in order to
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assess the effect of roughness on the velocity field and implicitly on the depth of the surface layer for Reynolds numbers between 27,000 and 190,000. Moreover, a grid was installed inside the pipe near the outlet at various axial positions (for the LIJ) producing a range of inflow turbulence conditions. The grid was used to investigate the effect of inflow turbulence intensity and length scales on the flow field. 2.2. Hot-wire measurements Velocity profiles orthonormal to the impinging plate were measured for radial positions ranging from r/D ¼ 0.8 to 3 and for various H/D ratios, surface roughness and inlet conditions. A traversing mechanism was used to mount two types of probes: one cross hot-wire probe (AUSPEC A55P61) and a boundary layer probe (Dantec 55P15) both connected to a Dantec 90C10 anemometer system. The cross hot-wire probe allowed for two component velocity measurements for axial distances from the surface zX3 mm (z/D ¼ 0.014); the boundary layer probe could reach closer to the plate up to z ¼ 1 mm (z/D ¼ 0.0046). The probes were calibrated using a Dantec 90H10 calibration systems. Nine angles (from 201 to +201, in 51 increments) were used for the direction calibration. The velocity calibration errors associated with experimental uncertainties were less than 1% for radial velocity (u) and less than 10% for the axial velocity (w). Sampling times of 5–10 s for a sampling frequency range of 2000–6000 Hz were employed.
2.3. Surface pressure measurements The fluctuating pressures on the impinging plate were simultaneously measured. For the SIJ 137 pressure taps were distributed over six concentric rings for r/D ¼ 0.25, 0.5, 1.0, 1.5, 2.0 and 2.5 plus one tap located at the plate center. These rings contained 8, 16, 16, 32, 32 and 32 equally spaced flush-mounted taps with an inner diameter of 1.2 mm. For the larger facility (LIJ) 331 taps were distributed over six concentric rings for r/D ¼ 0.25, 0.5, 1.0, 1.5, 2.0 and 2.5 plus one tap located at the plate center. These rings contained 8, 16, 16, 32, 32 and 32 equally spaced flush-mounted taps. All taps had an inner diameter of 1.2 mm and were connected via Tygon tubing to a series of ESP model 16TL pressure transducers that were multiplexed using a special design A/D system at the Boundary Layer Wind Tunnel Laboratory. Pressure signals were sampled at 800 Hz (the limit of the A/D system) for a specially designed long tubing system. The dynamic responses of the tubes and the systems were calibrated by applying a fluctuating pressure signal before testing. The resulting tubing system transfer function was then used to correct the instantaneous pressure measurements, and the corrected response was found to be flat for frequencies between 10 and 400 Hz. Also, spectral analysis showed quite good agreement between fluctuating pressure measurements with this simultaneous pressure transducer system and previous microphone measurements performed with the SIJ, see Hall and Ewing (2006).
3. Results 3.1. The effect of Reynolds number and nozzle-to-plate distance These measurements are similar and complementary to the measurements reported by Didden and Ho (1985) and by Cooper et al. (1993). The main parameters explored by these three sets of measurements are summarized in Table 1. Essentially, the present experiments extend the range of Reynolds numbers (23,000–190,000), refine the nozzle-to-plate ratios for H/D between 1 and 4 and also refine the radial (r/D) coverage. The aim is to better characterize the Reynolds number dependency in order to ensure proper scaling and to refine the spatial discretion in order to better capture the axial transition between the jet mixing (outer layer) and the wall shear layer as well as the radial transition between the impinging and the wall jet regions.
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Table 1 Comparison of the parameters for the three sets of experiments Parameters
Present tests (SIJ)
Present tests (LIJ)
Didden and Ho
Cooper et al.
Diameter (m) r/D H/D Re
0.0381 1–1.9 2 23,000
0.216 0.8–3.0 1, 2, 3, 4 27,000–190,000
0.0381 0.8–1.6 4 19,000
0.026, 0.102 0.5–3.0 2, 4, 6, 10 23,000, 71,000
0.25 0.2
Re = 4.3E05 Re = 1.1E05
0.15 0.1 0.05
0.15
Re = 1.9E05
0.1 0.05
0
0 0
0.2
0.4 0.6 u/Wjet
0.25
0.8
1
0
0.2
0.4 0.6 u/Wjet
0.25
Re = 2.7E04 Re = 4.3E05 Re = 1.1E05 Re = 1.9E05
0.2 0.15 0.1 0.05
0.8
1
Re = 2.7E04 Re = 4.3E05 Re = 1.1E05 Re = 1.9E05
0.2 z/D
z/D
Re = 2.7E04
0.2 z/D
z/D
0.25
Re = 2.7E04 Re = 4.3E04 Re = 1.1E05 Re = 1.9E05
0.15 0.1 0.05
0 0
0.2
0.4 0.6 u/Wjet
0.8
1
0 0
0.2
0.6 0.4 u/Wjet
0.8
1
Fig. 3. Radial mean velocity profiles, Reynolds number dependency, r/D ¼ 1: (a) H/D ¼ 1; (b) H/D ¼ 2; (c) H/D ¼ 2; and (d) H/ D ¼ 4.
3.1.1. The mean velocity field The hot-wire velocity measurements showed that for the entire range of Reynolds number interrogated herein (Re ¼ 23,000–190,000), the maximum radial velocities are reached at a radial position of approximately r/D ¼ 1.1 and very close to the impinging surface (approximately 0.03D). In order to observe the Reynolds number dependency the profiles at r/D ¼ 1 are plotted in physical coordinates (as opposed to self-similar coordinates) and for various fixed H/D ratios in Figs. 3a–d. Reynolds number dependency is observed only for the surface layer where the relative maximum velocity increases and the position of this maximum approaches the surface with increasing Reynolds number. Note that this dependency is less evident with increasing Reynolds number, an encouraging fact for the physical and laboratory simulation of downbursts. In order to show the effect of the nozzle-to-plate distance ratio (H/D), a generic representation of the ratio between the base-cloud altitude and the downburst diameter, the profiles for r/D ¼ 1 are replotted for fixed Reynolds numbers in Figs. 4a–d. The profiles show a monotonic shift with H/D ratio:
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0.35
H/D = 4 H/D = 3 H/D = 2 Cooper's, H/D = 2, Re = 2.3E04 H/D = 1
0.3
0.2
H/D = 4 H/D = 3 H/D = 2 H/D = 1
0.2 0.15 z/D
z/D
0.25
0.25
2389
0.15
0.1
0.1 0.05
0.05 0 0
0.2
0.4 0.6 u/Wjet
0.25
0
1
0
0.2
0.4 0.6 u/Wjet
0.25
H/D = 4 H/D = 3 H/D = 2 H/D = 1
0.2
0.1
0.8
1
H/D = 4 H/D = 3 H/D = 2 H/D = 1
0.2
0.15 z/D
z/D
0.8
0.15 0.1
0.05
0.05
0
0 0
0.2
0.4 0.6 u/Wjet
0.8
1
0
0.2
0.4 0.6 u/Wjet
0.8
1
Fig. 4. Radial mean velocity profiles, H/D dependency, r/D ¼ 1: (a) Re ¼ 27,000; (b) Re ¼ 43,000; (c) Re ¼ 110,000; and (d) Re ¼ 190,000.
as the nozzle-to-plate distance decreases the position of the maximum and the lower half of the profile departs from the surface, a result of the increasing suppression of the axial component. Meanwhile the outer half of the profile has the tendency to approach the surface as H/D decreases. The variation of the maximum radial velocity umax, which is one of the scaling parameters in Figs. 3 and 4, is presented in Fig. 5. For fixed H/D ratios (here we show H/D ¼ 2 only) the radial variation of the relative maximum radial velocity (umax/Wjet) is independent of Reynolds number, Fig. 5a, while for constant Reynolds number (here we show Re ¼ 190,000 only), the same ratio varies with H/D (Fig. 5b). This variation is more pronounced in the impinging region (r/Do1.4) where the umax decreases with increasing nozzle-to-plate distance, a result of the free jet dissipating with increasing axial distance. Axial velocity profiles for H/D ¼ 2 are shown in Figs. 6a–d for various Reynolds numbers. Naturally in the impingement region (r/Do1.4), the axial component is directed towards the surface, while for r/D41.4 it is directed away from it. The absolute maximum values at impingement tend to increase with Reynolds number. The maximum upward velocity is encountered at approximately r/D ¼ 1.8 and it decreases with increasing Reynolds number. 3.1.2. The fluctuating velocity field The r.m.s. radial velocity profiles are presented in Figs. 7a–d for H/D ¼ 2 only and for several Reynolds numbers. Again, the physical scaling, using the jet velocity and diameter for normalization, 10u0 /Wjet vs. z/D, is chosen for clarity and in accordance with Cooper et al. (1993). The present results for Re ¼ 27,000 compare well with results by Cooper et al. (1993) for Re ¼ 23,000. Overall the radial
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1.2 1
umax/Wjet
0.8 0.6
SIJ, Rej = 23000 Rej = 27000
0.4 Rej = 43000
0.2
Rej = 110000 Rej = 190000
0 0
0.5
1
1.5
2
2.5
3
3.5
r/D
1.2 1
umax/Wjet
0.8 0.6 H/D = 1
0.4
H/D = 2
0.2
H/D = 3 H/D = 4
0 0
1
2 r/D
3
4
Fig. 5. Maximum mean radial velocity vs. radius: (a) H/D ¼ 2, various Re and (b) Re ¼ 190,000, various H/D.
normal stress (proportional to u0 ) profiles present two maxima: one in the inner layer, very close to the impinging surface corresponds to the wall shear, and the second, in the outer layer, corresponds to the mixing layer between the free jet and the developing boundary layer. The first peak is not entirely captured herein due to inherent measurement difficulties in that region. The second peak is located at z/D ¼ 0.15 near impingement and approaches the surface attaining z/D ¼ 0.08 for r/D ¼ 2. As the wall shear increases the magnitude of the r.m.s. increases radially, reaches a maximum around r/D ¼ 1.8 and gradually decays as the shear weakens afterwards. The overall magnitude shows a slight increase with Reynolds number. However, the two peaks (corresponding to the wall and the mixing layers) are relatively better defined and are qualitatively different for the lowest Reynolds number (Re ¼ 27,000, Fig. 9a). For all nozzle-to-plate distances H/D41 these trends are similar (not shown here) with a slight increase in magnitude with increasing jet-to-surface distance. For H/D ¼ 1 the maxima in the inner layer is better captured and shows larger values relative to the outer layer maxima. R.m.s. axial velocity profiles are presented in Figs. 8a–d for H/D ¼ 2 only and for several Reynolds numbers. While differences between the present results (LIJ, Re ¼ 27,000) and Cooper’s results (Re ¼ 23,000) for the radial fluctuations (Fig. 7a), were minimal, the differences are more evident for
ARTICLE IN PRESS Z. Xu, H. Hangan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 2383–2402
r/D = 0.8 r/D = 1 r/D = 1.1 r/D = 1.2 r/D = 1.4 r/D = 1.6 r/D = 1.8 r/D = 2.0 r/D = 2.5 r/D = 3.0
z/D
0.2 0.15 0.1
0.25
0.15
0.05 0.1 -w/Wjet
0.15 0.1
0 -0.1 -0.05
0.2
r/D = 0.8 r/D = 1 r/D = 1.1 r/D = 1.2 r/D = 1.4 r/D = 1.6 r/D = 1.8 r/D = 2.0 r/D = 2.5 r/D = 3.0
0.2 z/D
0.15
0
0.05 0.1 -w/Wjet
0.25
0.15
0.2
r/D = 0.8 r/D = 1 r/D = 1.1 r/D = 1.2 r/D = 1.4 r/D = 1.6 r/D = 1.8 r/D = 2.0 r/D = 2.5 r/D = 3.0
0.2 z/D
0
0.25
0.15 0.1 0.05
0.05 0 -0.1 -0.05
0.1 0.05
0.05 0 -0.1 -0.05
r/D = 0.8 r/D = 1 r/D = 1.1 r/D = 1.2 r/D = 1.4 r/D = 1.6 r/D = 1.8 r/D = 2.0 r/D = 2.5 r/D = 3.0
0.2 z/D
0.25
2391
0
0.05 0.1 -w/Wjet
0.15
0.2
0 -0.1 -0.05
0
0.05 0.1 -w/Wjet
0.15
0.2
Fig. 6. Axial mean velocity profiles, H/D ¼ 2: (a) Re ¼ 27,000; (b) Re ¼ 43,000; (c) Re ¼ 110,000; and (d) Re ¼ 190,000.
the axial fluctuations (Fig. 8a). Overall, the axial normal stresses are damped near the surface, increasing further away and reaching peak values in the outer layer. There are no pronounced variations in profiles in the impinging region, r/Do1.4. However, for r/D41.4 the magnitude of the axial fluctuations increases monotonically with radial distance. The position of the maximum approaches the surface at approximately r/D ¼ 1.4–1.5. This corresponds to the position where the secondary vortex, formed by the separation–reattachment of the surface layer (Kim and Hangan, 2006), is lifted and wrapped around the primary, ring vortex (Didden and Ho, 1985). The position of the maximum then departures from the surface as the radial distance increases towards the outflow region. Note that for some Reynolds numbers (e.g. Re ¼ 43,000) the axial r.m.s. values are larger compared to the radial ones (see also Cooper et al., 1993). The general increase in magnitude with Reynolds number is more pronounced compared to the radial stresses. Reynolds number dependency is associated with the dynamics of the unsteady separation and therefore it is better reflected by the axial stress variation. Similar behavior was observed for H/D ¼ 2, 3 and 4. For H/D ¼ 1, however, the magnitude of the axial r.m.s. increases by roughly a factor of 2, a result of the more direct impingement in this case. For Re ¼ 190,000, this nozzle-to plate distance (H/D ¼ 1) approximately corresponds to the ring-vortex formation distance, Hvffi0.68/St, where the Strouhal number (St) is based on the surface pressure measurements. Reynolds shear stress /u0 w0 S profiles are presented in Figs. 9a–d for H/D ¼ 2 only. The present results for Re ¼ 27,000 are again compared with results by Cooper et al. (1993) for Re ¼ 23,000. There are pronounced variations of the maxima position with radial distance while the maximum stresses increase monotonically. When compared to the normal stresses the shear stresses are smaller (not shown herein), indicating that the turbulence energy is mainly generated by normal straining rather than shear. As expected the shear stress levels increase with increasing Reynolds number.
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0.3
0.3
0.25
0.25
0.2
0.2
0.15
z/D
z/D
2392
r/D = 1 r/D = 1.4 r/D = 2 r/D = 2.5 Cooper's, r/D = 1 Cooper's, r/D = 1.5 Cooper's, r/D = 2 Cooper's, r/D = 2.5
0.1 0.05 0 0
0.5
1 10u'/Wjet
0.15 0.1 0.05 0
1.5
0.3
0
2
0.15
1 10u'/Wjet
1.5
2
r/D = 0.8 r/D = 1 r/D = 1.4 r/D = 2 r/D = 2.5 r/D = 3
0.25 0.2 z/D
0.2
0.5
0.3
r/D = 0.8 r/D = 1 r/D = 1.4 r/D = 2 r/D = 2.5 r/D = 3
0.25
z/D
r/D = 0.8 r/D = 1 r/D = 1.4 r/D = 2 r/D = 2.5 r/D = 3
0.15
0.1
0.1
0.05
0.05 0
0 0
0.5
1 10u'/Wjet
1.5
2
0
0.5
1 10u'/Wjet
1.5
2
Fig. 7. r.m.s. radial velocity profiles (single wire measurements), H/D ¼ 2: (a) Re ¼ 27,000 (Cooper’s test, Re ¼ 23,000); (b) Re ¼ 47,000; (c) Re ¼ 110,000; and (d) Re ¼ 190,000.
3.2. Surface roughness effects In order to investigate the roughness effects the surface of the impinging plate of the LIJ facility was covered with various grades of sand paper varying between D/D ¼ 0.00014 and 0.004. Velocity profiles were measured at fixed radial positions using the boundary layer probe. As the flow evolves radially from the stagnation point a boundary layer develops on the surface. The distance from the surface corresponding to maximum radial velocity, z(umax), correlates to the position of the mixing layer between the free jet and the surface regions and it is strongly affected by the surface roughness. Fig. 10 shows the evolution of this interface, with Reynolds number and surface roughness for r/D ¼ 1 and for H/D ¼ 1, 2 and 4. Experimental results are presented for smooth and rough surfaces based on the LIJ measurements as well as for smooth surface measurements in the SIJ facility. For smooth surfaces and low Reynolds numbers the newly developed boundary layer is laminar and therefore its depth (here related to z(umax)) decreases with increasing Reynolds number. This smooth surface laminar boundary layer can be approximated by a Blassius type solution for a flat plate. Further, by comparing the solution of a plane stagnation point flow, (Hiemenz, 1911), with that of an axial symmetric stagnation flow, (Homann, 1936, one can observe that the depth of the boundary layer developed in the plane flow case is 1.2 times of the one for the axial symmetric flow. Therefore the boundary layer solution in an impinging jet over smooth surface and low Reynolds number can be approximated as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffi rW jet zðumax Þ 3:2 ¼ pffiffiffiffiffiffiffi for Re1 o2:5 104 (1) D Rel Dumax
ARTICLE IN PRESS Z. Xu, H. Hangan / J. Wind Eng. Ind. Aerodyn. 96 (2008) 2383–2402
r/D = 0.8 r/D = 1 Cooper's, r/D = 1 r/D = 1.4 r/D = 2 Cooper's, r/D = 2 r/D = 2.5 r/D = 3
0.25
z/D
0.2 0.15
0.3
0.2 0.15
0.1
0.1
0.05
0.05
0
0 0
0.05
0.1 w'/umax
0.2
0.15
0.3
0
0.1 w'/umax
0.15
0.2
0.1 w'/umax
0.15
0.2
0.25 0.2 z/D
0.2
0.05
0.3
r/D = 0.8 r/D = 1 r/D = 1.4 r/D = 2 r/D = 2.5 r/D = 3
0.25
z/D
r/D=0.8 r/D=1 r/D=1.4 r/D=2 r/D=2.5 r/D=3
0.25
z/D
0.3
2393
0.15
0.15
0.1
0.1
0.05
0.05
0
r/D = 0.8 r/D = 1 r/D = 1.4 r/D = 2 r/D = 2.5 r/D = 3
0 0
0.05
0.1 w'/umax
0.15
0.2
0
0.05
Fig. 8. r.m.s. axial velocities, H/D ¼ 2: (a) Re ¼ 27,000 (Cooper’s test, Re ¼ 23,000); (b) Re ¼ 43,000; (c) Re ¼ 110,000; and (d) Re ¼ 190,000.
where Rel is local Reynolds number, Rel ¼ rumax/n; r is the radius from the stagnation point, m; umax is the maximum radial mean velocity for a specified r, m/s; n is the kinematical viscosity, m2/s. For local Reynolds numbers above one order of the critical value the resulting boundary layer flow becomes turbulent and, based on the present experimental results, an empirical expression (see Xu et al., 2008) of a similar form to the Moody diagrams for rough wall pipe flows applies (here we rewrite the equation according to the normalized parameter D): " # rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r D 139 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ ¼ 1:95 ln (2) for Re1 42:5 105 zðumax Þ 0:08D Rel 2zðumax Þ=D When Rel becomes very large, the term including roughness dominates, the above equation simplifies to r D 2 ; for fully turbulent regions (3) ¼ 3:8 ln zðumax Þ 0:08D When D ¼ 0 (for smooth surfaces), the term including roughness disappears, Eq. (2) simplifies to " # rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r 139 p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 1:95 ln for turbulent regions and smooth surfaces (4) zðumax Þ Rel 2zðumax Þ=D The resulting curves for both the laminar and the turbulent boundary layer expressions (1), (2) and (4) are presented in Figs. 10a and compare well with the experimental results. Figs. 10b and c show
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0.300
r/D = 1 Cooper's, r/D = 1 r/D = 1.2 r/D =1.4 r/D = 1.6 r/D = 1.8 Cooper's, r/D = 2
0.250 z/D
0.200 0.150
0.250 0.200
0.100
0.050
0.050 0.000 -0.004 0
0.004 0.008 0.012 0.016 0.02
/umax2
0.300
0.300
r/D = 0.75 r/D = 1 r/D = 1.2 r/D = 1.4 r/D = 1.6 r/D = 1.8
0.250
0.250 0.200 z/D
0.200 0.150
0.100
0.050
0.050 0.004 0.008 0.012 0.016 0.02 /umax2
0.004 0.008 0.012 0.016 0.02 /umax2
r/D = 0.75 r/D = 1 r/D = 1.2 r/D = 1.4 r/D = 1.6 r/D = 1.8
0.150
0.100
0.000 -0.004 0
r/D = 0.75 r/D = 1 r/D = 1.2 r/D = 1.4 r/D = 1.6 r/D = 1.8
0.150
0.100
0.000 -0.004 0
z/D
0.300
z/D
2394
0.000 -0.004 0
0.004 0.008 0.012 0.016 0.02 /umax2
Fig. 9. Reynolds stress, H/D ¼ 2: (a) Re ¼ 27,000 (Cooper’s test, Re ¼ 23,000); (b) Re ¼ 43,000; (c) Re ¼ 110,000; and (d) Re ¼ 190,000.
similar trends for H/D ¼ 2 and 4, respectively, with z(umax) increasing monotonically with roughness height for the fully turbulent regions. These diagrams have practical importance as they allow for the extrapolation of laboratory results to various scales and surface roughness. Fig. 11 shows the radial variation of the maximum velocity, umax, for various roughness at H/D ¼ 1 and for Reynolds number 190,000. As expected, with increasing roughness the intersection between the newly developed surface boundary layer and the free jet region moves away from the impinging surface resulting in lower umax values. This tendency was found to be consistent over the range of Reynolds numbers. Figs. 12a and b show radial turbulence intensity profiles for various roughness heights at r/D ¼ 1 for Reynolds numbers 27,000 and 190,000, respectively. Turbulence levels generally increase with Reynolds number. For the mixing and outer layers the turbulence intensity tends to decrease with increasing roughness. The wall region, however, behaves differently: at the lowest Reynolds number the suppression of the near wall region peak for the highest roughness may indicate a fully rough regime, see Ligrani and Moffat (1986). However, the depth of the surface layer increases with Reynolds number, see Fig. 10, and therefore, for the same surface, the flow becomes transitional, see the surface peaks in Fig. 12b for the roughest surfaces.
3.3. Confinement effects Confinement tests were conducted to investigate the effect of surrounding boundaries on the impinging jet flow. Particularly an axial and a radial confinement were investigated. The two confinements are considered representative to boundary conditions imposed by the presence of
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0.07
Test, Smooth Test, ∆/D = 0.00014 Test, ∆/D = 0.0003 Test, ∆/D = 0.0010 Test, ∆/D = 0.0019 Test,∆/D = 0.004 Smooth, SIJ Model, Laminar
0.06
z (umax)/D
0.05 0.04
2395
Model, Smooth Model, ∆/D = 0.00014 Model, ∆/D = 0.0003 Model, ∆/D = 0.0010 Model, ∆/D = 0.0019 Model, ∆/D = 0.004 Landreth et al.
0.03 0.02 0.01 0 1.00E+03
1.00E+04
1.00E+05
1.00E+06
1.00E+05
1.00E+06
Re
0.07 Smooth
0.06
∆/D = 0.00014 ∆/D = 0.00030
z (umax)/D
0.05 0.04
∆/D = 0.0010 ∆/D = 0.0019 ∆/D = 0.004
0.03 0.02 0.01 0 1.00E+03
1.00E+04 Re
0.07 0.06
z (umax)/D
0.05 0.04
Smooth ∆/D = 0.00014 ∆/D = 0.00030 ∆/D = 0.0010 ∆/D = 0.0019 ∆/D = 0.004
0.03 0.02 0.01 0 1.00E+03
1.00E+04
1.00E+05
1.00E+06
Re Fig. 10. Evolution of z(umax) at r/D ¼ 1 with Reynolds number and surface roughness: (a) H/D ¼ 1; (b) H/D ¼ 2; and (c) H/ D ¼ 4.
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1 0.9 0.8 umax/Wjet
0.7 0.6 0.5 smooth
0.4
∆/D = 0.00014
0.3
∆/D = 0.0003
0.2
∆/D = 0.001
0.1
∆/D = 0.0019 ∆/D = 0.004
0 0
0.5
1
1.5
2
2.5
3
3.5
r/D Fig. 11. umax/Wjet variation with roughness, H/D ¼ 1, Re ¼ 190,000.
walls or ceiling encountered in laboratory spaces. Moreover, the axial confinement may be considered representative for the presence of the cloud base in full-scale situations. Given the fact that the unsteady separation/reattachment of the boundary layer happens in the very close vicinity of the wall, the surface pressure measurements were considered to provide a good indicator of the effects of various boundary conditions on the flow. A plate parallel to the impingement plate and of the same dimensions was used to simulate the axial confinement. The distance between the confinement plate and the impinging plate is designated as Hc, and therefore Hc/H ¼ 1 means the confinement plate being flush with the pipe outlet. The tests were conducted for H/D ¼ 1, 0.5 and 0.25. This axial confinement tests showed virtually no effects on the mean and fluctuating pressure distribution for H/D40.5. Figs. 13a and b illustrate this fact presenting the mean and the r.m.s. pressure variation under axial confinement for H/D ¼ 1. Circular plexyglass cylinders of various radii were used to represent radial confinements. The heights of the confinement cylinders were chosen to be Hc/D ¼ 4 and 8 and were of various radii, Rc, with Rc/D between 2 and 5. While the mean pressure field is rather insensitive to various radial confinements, see Fig. 14a, the fluctuating (r.m.s.) pressures show that confinements of radius 64Rc/ D42 tend to modify the flow dynamics (Fig. 14b). Essentially with a stronger radial confinement (smaller Rc values), the maximum of the pressure fluctuations diminishes.
3.4. The effect of inflow conditions In order to examine the effects of the inflow turbulence on the impinging jet flow, a square lattice mesh of circular shape was fixed inside the pipe near the outlet at various axial positions. The results of Baines and Peterson (1949) and Vickery (1968) were used in selecting the mesh characteristics, see Table 2. The ratio between the mesh position axially from the pipe outlet, L, and the thickness of the mesh bar, b, was varied between L/b ¼ 8 and 128 by placing the mesh inside the pipe at various axial positions from the outlet. Five sets of turbulence characteristics, corresponding to different mesh positions, were examined and the turbulent intensities and length scales at the pipe outlet center were determined. The axial integral length scales (Vickery, 1968) were calculated as Z 1 0 hw ðtÞw0 ðt þ tÞi Lw ¼ w dt (5) hw0 2 i 0
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0.3 0.25
z/D
0.2 smooth ∆/D = 0.00014 ∆/D = 0.0003 ∆/D = 0.001 ∆/D = 0.0019 ∆/D = 0.004
0.15 0.1 0.05 0 0
0.2
0.4
0.6 0.8 10u'/wjet
1
1.2
1.4
0.3 0.25 smooth ∆/D = 0.00014 ∆/D = 0.0003 ∆/D = 0.001 ∆/D = 0.0019 ∆/D = 0.004
z/D
0.2 0.15 0.1 0.05 0 0
0.4
0.8 10u'/Wjet
1.2
1.6
Fig. 12. Radial turbulence intensity profiles at r/D ¼ 1 and for (a) Re ¼ 27,000 and (b) Re ¼ 190,000.
Turbulence intensity levels are insensitive to the outlet velocity but depend on the mesh axial position. The turbulence intensities measured at the center of the pipe outlet are listed in Table 3. Figs. 15a and b present the resulting variation with L/b of the turbulent intensities and length scales, respectively, for three mean jet exit flow velocities: Wjet ¼ 2.8, 6.8 and 11 m/s. The results compare well with Baines and Peterson (1949). Hot-wire velocity profiles were measured at the radial position r/D ¼ 1 and for various Reynolds numbers for the five inflow turbulence cases. The effect of the turbulence characteristics on the radial mean and fluctuating velocities is presented in Figs. 16a and b, respectively. As expected, the width of the mean radial velocity profiles increases monotonically as the inflow integral length scales increase (and turbulence intensity decreases) (Fig. 16a). The influence of the inflow turbulence is less clear in terms of the radial turbulence intensity profiles (Fig. 16b). In the free jet region, far from the surface, the radial turbulence intensity tends to decrease with increasing inflow axial turbulence (or decreasing length scales). Near the surface, in the impingement region, the response to the outlet turbulence is damped by the wall effects.
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0.4 0.2 0
cpmean
0
0.5
1
1.5
2
-0.2
2.5
3 no con Hc/H = 7 Hc/H = 5
-0.4
Hc/H = 3 Hc/H = 2
-0.6
Hc/H = 1
-0.8 -1
r/D
0.1 no con
0.09 Hc/H = 7
0.08
cprms
Hc/H = 5
0.07
Hc/H = 3
0.06
Hc/H = 2
0.05
Hc/H = 1
0.04 0.03 0.02 0.01 0 0
0.5
1
1.5 r/D
2
2.5
3
Fig. 13. Axial confinement for H/D ¼ 1: (a) mean pressures and (b) fluctuating pressures.
4. Concluding remarks The sensitivity of the axial orthonormal impinging jet flow to scale (Reynolds number), boundary conditions (jet-to-surface distance, surface roughness and radial and axial confinements) and inflow conditions is experimentally investigated. These conditions are generic representations of cloud-base height and flow characteristics or terrain roughness encountered in downburst winds as well as scale and boundary conditions encountered in downburst simulations.
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0.4 0.2 0 cpmean
0
0.5
1
1.5
2
-0.2 -0.4 -0.6
3 2.5 no con Rc/D = 5 Rc/D = 4.5 Rc/D = 4 Rc/D = 3.5 Rc/D = 3 Rc/D = 2.5 Rc/D = 2
-0.8 -1
r/D
0.09
no con Rc/D= 5 Rc/D = 4.5 Rc/D = 4 Rc/D = 3.5 Rc/D = 3 Rc/D = 2.5 Rc/D = 2
0.08 0.07
cprms
0.06 0.05 0.04 0.03 0.02 0.01 0 0
0.5
1
1.5 r/D
2
2.5
3
Fig. 14. Radial confinement for H/D ¼ 1: (a) mean pressures and (b) fluctuating pressures.
Table 2 Mesh parameters Thickness of the bar, b Distance between the bars, M Mesh positions from the pipe outlet, L
b ¼ 3.2 mm; b/DE1/70 10 mm 8b, 16b, 32b, 64b, 128b
It is found that, due to the unsteady separation of the surface flow, the surface velocity field (both mean and fluctuating) is Reynolds number dependent. While the outer layer is rather insensitive to Reynolds number, the depth of the surface layer, z(umax), decreases with increasing Reynolds number
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Table 3 Turbulent intensities at the center of pipe outlet for different mesh positions Wjet (m/s)
2.67 6.82 11.0
wr.m.s./Wjet L/b ¼ 8
L/b ¼ 16
L/b ¼ 32
L/b ¼ 64
L/b ¼ 128
0.223 0.217 0.208
0.124 0.120 0.117
0.064 0.066 0.067
0.038 0.042 0.043
0.025 0.027 0.028
1 Wjet = 2.8 m/s Wjet = 6.8 m/s Wjet = 11.0 m/s
w'/w
Baines', b/M = 1:4
0.1
0.01 1
10
100
1000
L/b
Lw/b
10
Wjet=2.8 m/s Wjet = 6.8 m/s Wjet = 11.0 m/s Baines', min Baines', max
1
0.1 1
10
100
1000
L/b Fig. 15. Flow turbulence behind a uniform grid: (a) axial turbulence intensities and (b) axial integral length scales.
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0.3 0.25
z/D
0.2 0.15 no grid w'/Wjet = 0.028 w'/Wjet = 0.043 w/Wjet = 0.067 w'/Wjet = 0.117 w'/Wjet = 0.208
0.1 0.05 0 0
0.2
0.4
0.6 u/Wjet
1
0.8
1.2
0.3 0.25
z/D
0.2 0.15 no grid w'/Wjet = 0.028 w'/Wjet = 0.043 w'/Wjet = 0.067 w'/Wjet = 0.117 w'/Wjet = 0.208
0.1 0.05 0 0
0.05
0.1 u'/Wjet
0.15
0.2
Fig. 16. Inflow effects on: (a) radial mean velocities and (b) r.m.s. radial velocities (H/D ¼ 1, r/D ¼ 1, Wjet ¼ 11.0 m/s).
until an asymptotic behavior is reached. The Reynolds number effects are more pronounced towards the lower range (Reo27,000) where the flow structure is also expected to be different. The effects of the nozzle-to-plate (H) distance on the mean and turbulent velocity fields and on the maximum radial velocity umax are investigated. When H is larger compared to the ring-vortex formation length the results are qualitatively similar. For smaller distances (e.g. H/Do1 for Re ¼ 190,000) a stronger pressure–strain mechanism results in increased maximum radial velocities and normal stresses. Above one order of a critical Reynolds number the flow depends only on the surface roughness, with the surface layer increasing with increasing roughness. It was therefore possible to construct a ‘‘Moody-type’’ diagram for impinging jets which allows the extension of laboratory results to fullscale applications. Radial confinements of diameter less than 10 of the jet diameter influence the surface pressure distribution on the impinging plate. When positioned closed to the impinging surface (less than 1 jet diameters) axial confinements also affect the pressure distributions.
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The inflow turbulence conditions influence mainly the outer layer region of the flow while in the surface region these effects tend to be damped out.
Acknowledgments This work was made possible through funding provided by Natural Science and Environmental Research of Canada (NSERC) Grant no. 166732 and funding from Manitoba Hydro. References Baines, W.D., Peterson, E.G., An investigation of the flow through screens. Report to the Office of Naval Research by Iowa Institute of Hydraulics, July 1949. Choi, C.C.E., 2004. Field measurement and experimental study of wind speed profile during thunderstorms. J. Wind Eng. Ind. Aerodyn. 92, 275–290. Craft, T.J., Graham, L.J.W., Launder, B.E., 1993. Impinging jet studies for turbulence model assessment—II: An examination of the performance of four turbulence models. Int. J. Heat Mass Transfer 36 (10), 2685–2697. Cooper, D.C., Jackson, D.C., Launder, B.E., Liao, G.X., 1993. Impinging jet studies for turbulence model assessment–I: Flow-field experiments. Int. J. Heat Mass Transfer 36 (10), 2675–2684. Dianat, M., Fairweather, M., Jones, W.P., 1996. Reynolds stress closure applied to axisymmetric, impinging turbulent jets. Theor. Comput. Fluid Dyn. 295, 305–335. Didden, N., Ho, C.M., 1985. Unsteady separation in a boundary layer produced by an impinging jet. J. Fluid Mech. 160, 235–256. Fairweather, M., Hargrave, G.K., 2002. Experimental investigation of an axisymmetric, impinging turbulent jet. 1. Velocity field. Exp. Fluids 33, 464–471. Fujita, T.T., 1990. Downbursts: meteorological features and wind field characteristics. J. Wind Eng. Ind. Aerodyn. 36, 75–86. Hall, J.W., Ewing, D., 2006. On the dynamics of the large-scale structures in round impinging jets. J. Fluid Mech. 555, 439–458. Hiemenz, K., 1911. Die Grenzschicht an einem in den gleichfo¨rmigen Flu¨ssigkeitsstrom eingetauchten geraden Kreiszylinder. Dinglers Polytech. J. 326, 321. Holmes, J.D., 2002. A re-analysis of record extreme wind speeds in region A. Aust. J. Struct. Eng. 4 (1). Homann, F., 1936. Der Einfluss grosser Za¨higkeit bei der Stro¨mmung um den Zylinder und umdie Kugel. Z. Angew. Math. Mech. 16, 153–164. Kataoka, K., Kamiyama, Y., Hashimoto, S., Komai, T., 1982. Mass transfer between a plane surface and an impinging turbulent jet: the influence of surface-pressure fluctuation. J. Fluid Mech. 119, 91–105. Kim, J., Hangan, H., 2006. Numerical simulations of impinging jets with application to downbursts. J. Wind Eng. Ind. Aerodyn. 95 (4), 279–298. Landreth, C.C., Adrian, R.J., 1990. Impingement of a low Reynolds number turbulent circular jet. Exp. Fluids 9, 74–84. Letchford, C.W., Illidge, G., 1999. Turbulence and topographic effects in simulated thunderstorm downbursts by wind tunnel jet. In: Larsen, A., et al. (Eds.), Wind Engineering into the 21st Century. Balkema, Rotterdam. Letchford, C.W., Mans, C., Chay, M.T., 2002. Thunderstorms—their importance in wind engineering (a case for next generation wind tunnel). J. Wind Eng. Ind. Aerodyn. 90, 1415–1433. Ligrani, P.M., Moffat, R.J., 1986. Structure of transitionally and fully rough turbulent boundary layers. J. Fluid Mech. 162, 69–98. Martin, H., 1977. Heat and mass transfer between impinging gas jets and solid surfaces. Adv. Heat Transfer 13, 1–60. Mason, M., Letchford, C.W., James, D., 2005. Pulsed jet simulation of a stationary thunderstorm downburst, Part A: Physical structure and flow field characterization. J. Wind Eng. Ind. Aerodyn. 93, 557–580. Popiel, C.O., Trass, O., 1991. Visualization of a free and impinging round jet. Exp. Therm. Fluid Sci. 4, 253–264. Sengupta, A., Sarkar, P.P., 2008. Experimental measurement and numerical simulation of an impinging jet with application to thunderstorm microburst winds. J. Wind Eng. Ind. Aerodyn. 96 (3), 345–365. Tsubokura, T., Kobayashi, T., Taniguchi, N., Jones, W.P., 2003. A numerical study on the eddy structures of impinging jets excited at the inlet. Int. J. Heat Fluid Flow 24, 500–511. Vickery, B.J, 1968. Wind loads on buildings. Ph.D. Thesis, University of Sydney. Xu, Z., Hangen, H., Yu, P., 2008. Analysis solutions for a family of Gaussian impinging jets. J. Appl. Mech. 75 (2), 021019.