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Particle Image Velocimetry (PIV) application in the measurement of indoor air distribution by an active chilled beam
Building and Environment 45 (2010) 1932–1940
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Particle Image Velocimetry (PIV) application in the measurement of indoor air distribution by an active chilled beam Guangyu Cao a, b, *, Markku Sivukari a, Jarek Kurnitski a, Mika Ruponen c, Olli Seppa¨nen d a
Department of Energy Technology, Helsinki University of Technology, P.O. Box 4100, FIN-02015 TKK, Finland Technical Research Centre of Finland, P.O. Box 1000, FI-02044 VTT, Finland c Halton Oy, Haltonintie 1-3, 47400 Kausala, Finland d REHVA, Washington Street 40, B-1050 Brussels, Belgium b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 August 2009 Received in revised form 26 November 2009 Accepted 28 November 2009
We study the turbulent air flow behaviours of the attached plane jet discharged from an active chilled beam in a room using Particle Image Velocimetry (PIV). PIV is an innovative technology to study indoor air flow which began in the eighties of the last century for the measurement of whole air flow fields in fractions of a second. Here an experimental PIV system was built to reveal the structure of a turbulent attached plane jet in the entrainment process of the ambient air downstream from the jet slot. For the particle seeding in the PIV experiments, a few different particles were tested with the attached jet PIV application in a room. The results presented in this paper show the clear structure of the turbulent attached plane jet in the entrainment process after issuing from the chilled beam slot. The PIV visualisation results proved that the jet will attach to the ceiling and become fully turbulent a short distance downstream from the slot. The jet velocity vector fields show that the volume flow rate of the attached plane jet increases because of the large vortex mixing mechanism in the outer region of the jet. In three measurement cases, the air jet grows faster at a Reynolds number of 960 than at Reynolds numbers of 1320 and 1680. The calculated spreading angles in the cases with lower Reynolds numbers have similar values compared with the visualisation results. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Particle image velocimetry Attached plane jet Turbulent flow Reynolds number Visualisation Vector field
1. Introduction At present, the chilled beam is becoming a popular air distribution device in office environments. There are several advantages to such kinds of diffusers, including energy savings, better thermal comfort, and more silent operation [1,2]. The air flow pattern of the attached plane jet discharged from a ceilingmounted chilled beam is presented in Fig. 1 and shows the corresponding jet regions downstream from the jet slot. The earliest known work on the attached plane jet was carried out by Fo¨rthmann (1934) [3], described and quoted in [4–6]. The first theoretical investigation of the incompressible isothermal laminar attached plane jet was undertaken by Tetervin (1948) [7], presented in [8]. Tetervin predicted that the boundary layer thickness of the attached jet would grow and the local maximum velocity would decay with the downstream distance as x0.75 and
* Corresponding author. Technical Research Centre of Finland, P.O. Box 1000, FI-02044 VTT, Finland. Tel.: þ358 40 1993513; fax: þ358 20 722 7015. E-mail address: guangyu.cao@vtt.fi (G. Cao). 0360-1323/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2009.11.020
x0.5, respectively. Generally, the non-dimensional jet velocity profiles should be similar at a different distance from the jet slot in the fully developed zone of the turbulent jet. This refers to the self-similarity of the jet, which is one of the characteristics of the turbulent jet in the fully developed zone [5,6]. Glauert (1956) achieved a similarity solution for the laminar and turbulent radial and attached plane jets [9]. Bajura and Szewezyk (1970) carried out an experimental investigation of laminar wall jets and obtained good agreement with Glauert’s similarity solution in the laminar condition [10]. Under non-isothermal conditions, the different jet zones have been identified by experimental studies and found to be dependent on the initial conditions, including the slot Reynolds number and the initial Archimedes number [11]. Generally, a four-zone division into a potential core zone, transition zone, fully developed turbulent zone, and terminal zone is used to describe the free jet flow field [12,13]. As for the classification of the attached plane jet zones, two-zone divisions were used to be considered as the main zones under isothermal conditions [14]. In other studies, however, a three-zone division into a non-buoyant region, intermediate region, and buoyant region was
G. Cao et al. / Building and Environment 45 (2010) 1932–1940
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Fig. 1. Schematic view of the impingement of the attached plane jet and jet regions in a room.
described in [15]. The jet grows and becomes turbulent when the jet issues from the slot by the entrainment of the ambient air. In an air-conditioned room, the discharging jet flow from the chilled beams is designed to attach to the ceiling or the wall surface, so that the high-velocity region is restricted to the ceiling or the nearwall zone in order to free the space in the occupied zone from draught [16]. In the experimental studies of the attached jet flow, to obtain the jet velocity distribution, single-point measurements with an anemometer must be traversed to obtain measurements over the flow domain. However, scanning over the flow domain might not yield the instantaneous flow structure and could be blocked by the time consuming. The limitations of conventional anemometer measurement could not fulfil the requirement of a detailed turbulent jet behaviour study, especially at the beginning of the discharge of the jet from the potential jet core to the transition process [17,18]. In the 1990s, the PIV technique emerged from laboratories to applications in fundamental and industrial research, from aerodynamics to indoor air flow studies [19,20]. Unlike conventional anemometers, Particle Image Velocimetry (PIV) is able to measure whole flow fields in fractions of a second [21]. As for the use of PIV in attached jet studies, Shih and Gogineni measured a low turbulent attached jet flow with PIV at a Reynolds number of 1000 [22]. Gogineni and Shih carried out a series of studies on the attached jet transition process with Reynolds numbers 330–3800 [23]. Gogineni et al. studied PIV measurement with a numerical solution [24]. Kim and Giovannini carried out an experimental study of turbulent round jet flow [25], and the instantaneous two-dimensional velocity fields in the streamwisewall-normal plane were measured by using PIV in their studies. The two-dimensional attached jet flow was measured in terms of its turbulent structure in [26]. However, there have few cases of PIV application in indoor air flow studies, especially in the case of chilled beams. Here, the experiments using Particle Image Velocimetry were carried out to measure the attached jet flow in a room with an active chilled beam in the ceiling zone to obtain detailed information on the ambient air entrainment process. The objectives of this study were: to select a suitable particle seeding method in order to use PIV in a room air flow measurement; to obtain detailed information on the ambient air entrainment process, and to clarify the growth rate of an attached jet at low Reynolds numbers with an active chilled beam.
2. Experimental setup 2.1. PIV measurement system and instrumentation The PIV measurement system and PIV apparatus are shown in Fig. 2. The active chilled beam was mounted flush to the ceiling at a distance 1.6 m from the side wall. The air jet issuing from the chilled beam is parallel to the longer wall of the room. To avoid or mitigate the effect of surface reflection, the whole room to be measured was painted black. One thin laser beam trap was built perpendicular to the active chilled beam through the middle of the ceiling and the short side wall. On one long side wall, a few small openings were made in order for a CCD camera to be installed (see Fig. 3a). A laser guiding arm was used to deliver the high-power laser beams of Nd:YAG lasers controlled by the LaVision program. Before the PIV measurement, the CCD camera was calibrated by means of a calibration plate with a size 800 mm 800 mm (see
Fig. 2. Full-scale attached jet flow PIV measurement system.
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Fig. 3. PIV measurement apparatus: a) CCD camera mounted outside the side wall; b) PIV measurement calibration plate; c) installation of the hot sphere anemometers.
Fig. 3b). During the measurement, the tracer particles were induced into the jet flow through a perforated plate below the chilled beam. A double-pulse laser sheet illuminates these particles in the measured plane of the flow twice within a short time interval. The displacement of the particle images between the light pulses is used to calculate the velocity vector during the postprocessing. Five hot sphere anemometers were installed on a height-adjustable device to measure the ceiling zone jet velocity (see Fig. 3c). In the PIV measurement, a pulsed laser beam was generated by an Nd:YAG laser, which has a power of 200 mJ. The Nd:YAG laser used in this study consists of three main components: a laser material, a pump source, and an oscillator. For PIV the fundamental wavelength of 1064 nm is frequency-doubled using a non-linear crystal as a second harmonic generator (SHG), which converts the IR light to visible green light of 532 nm. The crystal axis has to be oriented at a certain angle to the laser beam (phase matching). The trigger signals for the Nd:YAG laser were produced by a LaVision Programmable Timing Unit (PTU) from a remote computer with the DaVis software package installed. By means of the software, the measured particle shift will be calculated in the post-processing to form the velocity vector field. The camera integrated into the system is based on a Charge-Coupled Device (CCD) sensor with high resolution and high sensitivity. In the measurement with the usage of the CCD camera, the power of the laser was increased in small steps to keep the camera image from being saturated; for example, the intensity is kept below the maximum grey level; here, fewer than 4095 counts should be a suitable image intensity. The laser beams were formed into sheets and overlapped in the air jet flow field with an adjustable thickness from 0.5 to 2.5 mm. The thickness of the laser light sheet was adjusted so as to be approximately 1.0 mm in the middle of the laser beam. The field of view of the CCD camera was able to resolve a region 800 mm 800 mm by illuminating a planar measuring flow field with a pulsed laser beam. The air flow that was supplied was measured using an orifice plate. A 54N50-type Low Velocity Flow Analyser was used for the measurement of the jet turbulence intensity of the supply air. To estimate the accuracy of the PIV measurement, a VelocCALC plus device and five 8475 Model anemometers were used to measure the air velocity at the jet slot and at a distance of 0.3 m from the jet slot. The accuracy of anemometer is 3.0% of reading in the range of 20.0–26.0 C.
2.2. Measurement conditions In a full-scale climate chamber, the active chilled beam was mounted flush to the ceiling; it was of the same length as the climate chamber. The air jet issuing from the active chilled beam was attached to the ceiling downstream from the supply slot. The experiments were performed under isothermal conditions and therefore, because of the absence of any heat sources, the only important dimensionless parameters in this study are the initial Reynolds number and the jet turbulence intensity. The primary air supply into the beam is provided through nozzles which induce ambient room air to flow inside the beam. The ambient air flow is induced into the beam through the perforated bottom plate. The ratio of the supply air and total air flow through the chilled beam slot is about 4.5 in this study and is similar to that reported in [27]. The mixed air flow in the beam issues from the jet slot and produces an attached plane jet with turbulence intensities ranging from 20% to 45%. Table 1 presents the PIV measurement conditions with the PIV measurement settings. The supply air temperature and room air temperature were kept at the same value, 23 0.5 C, throughout the measurement. The sampling time is 8 s, with a recording speed of 10 Hz. A total of eighty pair-image results were obtained during the measurement period. The slot Reynolds numbers were calculated on the basis of the slot height, 0.018 m, and averaged slot velocity. The measurement of the jet velocity was able to cover the initial jet flow region 0.5 m downstream from the chilled beam with three slot velocities by regulating the pressure drop in the beam. By means of PIV measurement, the recording interval time of each pair-image was determined by the Optimisation of Particle Image Shift (OPIS) method under normal room conditions. Generally, for a given flow velocity, the separation ds of the particle images on the CCD determines the selected interval time or the pulse delay, dt. For cross-correlation the separation of the particle images (in pixels) should be larger than the accuracy of the peak detection and smaller than a quarter of the selected interrogation window size (in pixels). The range of the separation distance may be expressed by the relationship:
pixel < ds <
1 d 4 IntWin
(2.1)
The recommended relation shows that the optimum separation of the particle images depends on the desired interrogation
Table 1 PIV measurement conditions.
Case 1 Case 2 Case 3
Slot average velocity (m/s)
Turbulence intensity (%)
Recording pair-image interval time (ms)
Reynolds number
Recording speed (Hz)
Pressure drop within the beam (Pa)
Measured time (s)
0.8 0.05 1.1 0.05 1.4 0.05
44 30 22
6000 5000 3000
960 1320 1680
10 10 10
100 200 300
8 8 8
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window size dIntWin (25 mm in this PIV measurement) and on the velocity fields in the PIV recording. Then the recording pair-image interval time will be in the range of:
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The flow visualisation study was carried out using a high-speed digital camera and laser sheet using an OPTIMIST smoke generator for the particle seeding. The visualisation results and the corresponding instantaneous velocity vector fields are presented in Figs. 4–6 and show the structure and the instantaneous velocity vector field of the attached plane jet issuing from the active chilled beam. The PIV visualisation results reveal the process of the entrainment of the ambient air at a distance of 28 slot heights downstream from the slot. The large-scale vortices were seen in the outer layer of the jet presented in the PIV pair-photograph. In the figures shown in the pair-photograph, the attached plane jet at a low slot Reynolds number became fully turbulent over a short
downstream distance. After that, the turbulent attached plane jet was dominated by the irregular fluctuation in both the outer free shear layer and inner layer. The figures indicate that a jet with a relatively low Reynolds number might tend to induce more ambient air into the jet after leaving the slot. The vortex formed in the outer layer of the jet contributes significantly to the increasing of the jet volume flow rate by the vortex mixing mechanism. If a jet spreading line is drawn from the jet slot at the boundary of the observed vortex, the estimated spreading angles are about 17, 15 , and 13 for the Reynolds numbers 960, 1320, and 1680, respectively, in the ambient air entrainment process. Because of the characteristics of the smoke, however, the smoke diffusion might contribute to a discrepancy in the visual result to some extent, compared to other cases. The instantaneous jet velocity vector fields in an area 500 mm 160 mm were obtained according to the particle displacement calculation shown in the PIV pair-photograph. The interval time between the two photos of the pair-photograph was 6000, 5000, and 3000 ms in the three cases with slot average velocities of 0.8, 1.1, and 1.4 m/s, respectively. The displacement distance was about 4 mm in Figs. 4–6; this may cause undistinguishable differences between the two photos. The results presented in the three instantaneous jet velocity vector fields show the clear turbulent structure of the jet flow from the inner layer to the outer layer. Even within the boundary layer near the surface of the ceiling, the laminar flow pattern could not last longer than a distance of 10 slot heights downstream from the jet slot. The instantaneous jet flow vector fields may indicate that the attached plane jet issuing from the
Fig. 4. Jet visualisation and the corresponding instantaneous vector field by PIV pairphotograph at a slot velocity of 0.8 m/s: a) laser sheet pair-image one; b) laser sheet pair-image two; c) instantaneous velocity vector field.
Fig. 5. Jet visualisation and the corresponding instantaneous vector field by PIV pairphotograph at a slot velocity of 1.1 m/s: a) laser sheet pair-image one; b) laser sheet pair-image two; c) instantaneous velocity vector field.
pixel ds 1 dIntWin < dt ¼ < Umax Umax 4 Umax
(2.2)
Here jet velocities of 1.0, 1.5, and 2.0 m/s were used to choose the interval time. After the parameters in the above relation had been substituted, the three recording interval times were obtained for the three measured velocities. 3. Measurement results 3.1. Visualisation of the jet flow
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Fig. 6. Jet visualisation and the corresponding instantaneous vector field by PIV pairphotograph at a slot velocity of 1.4 m/s: a) laser sheet pair-image one; b) laser sheet pair-image two; c) instantaneous velocity vector field.
chilled beam is dominated by the turbulent mechanism instead of the laminar one, even though the initial Reynolds number was as low as 960. The results also confirmed the finding in the earlier studies that the attached plane jet presents a very unstable characteristic as a result of the double row pairing vortex structure [22,23]. 3.2. Averaged vector field of the jet flow Fig. 7 shows the averaged velocity vector field of the plane jet calculated from ten PIV pair-photographs. In three cases, the maximum jet velocity occurs near the surface of the ceiling in the jet field downstream from the slot. However, the averaged velocity vectors still present the unstable structure in the jet boundary layer as a result of the rising vortex of the turbulent jet. Similar phenomena could be observed in the instantaneous vector field of the jet. Some earlier studies show that there would be a laminarlike jet potential core at low Reynolds numbers [22–24]. Here, no potential core with a laminar-like flow field with each Reynolds number was observed. Using the quantified velocity vectors, the averaged velocity vector field could be used to estimate the jet spreading angle on the basis of the half-height of the jet, which is defined as the place that has half the velocity of the local maximum velocity. The spreading angle of the jet was calculated after ten time slot heights downstream from the jet slot in order to avoid the effect of the initial potential core of the jet. One trend observed is that the jet grows faster at Re ¼ 960 than at Re ¼ 1680. This indicates that a jet with a relatively low Reynolds number might tend to
Fig. 7. Jet velocity vector field distributions by PIV: a) jet slot average velocity is 0.8 m/s; b) jet slot average velocity is 1.1 m/s; c) jet slot average velocity is 1.4 m/s.
induce more ambient air into the jet after leaving the slot. The calculated jet spreading angles based on the half maximum velocity were about 17, 12 , and 6 for the Reynolds numbers 960, 1320, and 1680, respectively. The spreading angles in the cases with Reynolds numbers of 960 and 1320 have similar values compared with the visualisation results. However, at a Reynolds number of 1680, the calculated angle was about half of the visualisation results. 3.3. Validation of the velocity measured with PIV The validation of the PIV results is somewhat complicated, but there is no other non-intrusive way of measuring such a large area of a flow field at once. Therefore, the PIV measurements can only be validated at certain points with another velocimetry technique or the results can be compared to computational values or analytical solutions of simplified flow phenomena [28]. The results of an earlier study suggest that the measured velocity distribution using PIV is reliable [14]. Here, the measured velocities using conventional anemometers are used to validate the velocity measured with PIV at the jet slot and 300 mm downstream from the slot at three slot velocities, 0.50, 1.00, and 2.00 m/s. All the anemometerbased measurements are made in the test room by supplying air at the same temperature as the room air temperature. During the measurement, the velocity is recorded every second and the average velocity is obtained through each 3-min period. The measured velocity at the slot is presented in Fig. 8 and shows
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4. Discussions
1.5 Anemometer measured
4.1. Particle determination for PIV measurement
PIV measured
1.2
In PIV measurement, the air must be seeded with particles that follow the air motions to record the velocity. Therefore, there is a compromise between the need for them to be small enough to follow the air motions and the need for them to be large enough to reflect sufficient light in suitable illumination [17]. In PIV measurement, a primary source of error is the influence of gravitational forces if the densities of the air flow and the tracer particles do not match. Even though it can be neglected in many practical situations, the gravitationally induced velocity Ug could be obtained from Stokes’s drag law in order to introduce the particle’s behaviour under acceleration. Therefore, assuming spherical particles in a viscous fluid at a low Reynolds number, the velocity component may be expressed as [21]:
0.9
0.6
0.3
0 0
0.3 0.6 0.9 1.2 Average supply air velocity (m/s)
Ug ¼ d2p
1.5
Fig. 8. Measured slot velocity with anemometer and PIV.
60
Anemometer measured PIV measured
50 40 30 20 10 0
Distance from the ceiling (mm)
Distance from the ceiling (mm)
a comparison of the results using an anemometer and PIV. The PIV measured average velocity obtained a good agreement with the velocity measured with the anemometer at a slot velocity of 0.8 m/s. At slot velocities of 1.1 and 1.4 m/s, the difference between the results with an anemometer and PIV is up to 14%. The measured velocity profile is presented in Fig. 9 and shows a comparison of the velocity measured with an anemometer and PIV with a 20% error bar. All the three velocity profiles measured with PIV were able to obtain a certain agreement with the profile measured with an anemometer in terms of the curve shape of the attached plane jet. The maximum velocity measured by both instruments indicates the capability of PIV being used to measure the maximum velocity of an attached plane jet at 20% inaccuracy. In the inner layer and the outer layer, the PIV results can only show an agreement with the results measured with an anemometer at the Reynolds numbers 960 and 1680, respectively, within the error bar of 20%. Therefore, it was reasonable to estimate the overall inaccuracy of the PIV measurement as approximately 20%.
0 0.3 0.6 0.9 1.2 Measured velocity (m/s)
a
60
rp r g 18m
(4.1)
where Ug is the particle gravitational velocity, dp is the diameter of the particle, rp is the density of the particle, r is the air flow, g is the acceleration caused by gravity, and m is the dynamic viscosity of the air. As shown in Eq. (4.1), the diameter of the particles should be very small in order to ensure good tracking of the fluid motion as a result of the difference in density between the fluid and the tracer particles. On the other hand, the particle diameter should not be too small, as the light-scattering properties also have to be taken into account, as will be shown in the following section. Therefore, it is clear that a compromise has to be found to obtain high-quality particle seeding. At the beginning of this study, water droplets produced by a nozzle combined with compressed air were seeded to the climate chamber. With fewer water droplets in the air flow, the water droplets tend to adhere to the inside surface of the duct. In contrast, increasing the amount of water droplets makes the whole space full of water droplets, which block the laser scattering in the measurement plane. Moreover, the particle size of the water droplets was rather small and could not provide good enough laser scattering. Two types of smoke particles were used to provide suitably sized particles. One is normal filter cigarette smoke, the other is OPTIMIST smoke. Considering the shorter-undisturbing principle of PIV particle seeding, it is difficult to inject normal
Anemometer measured PIV measured
50 40 30 20 10 0
60 Distance from the ceiling (mm)
Measured velocity (m/s)
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PIV measured
50 40 30 20 10 0 0 0.3 0.6 0.9 1.2 Measured velocity (m/s)
0 0.3 0.6 0.9 1.2 Measured velocity (m/s)
b
Anemometer measured
c
Fig. 9. Jet velocity at a distance of 300 mm downstream from the slot: a) jet slot average velocity is 0.8 m/s; b) jet slot average velocity is 1.1 m/s; c) jet slot average velocity is 1.4 m/s.
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Fig. 10. Photographs of the jet flow with seeded particles: a) unacceptable particle seeding with insufficient particles in the jet flow; b) acceptable particle seeding with suitable particles; c) unacceptable particle seeding with an excess of particles in the jet flow.
cigarette smoke particles into the attached plane jet as a result of the way in which a cigarette burns. Using OPTIMIST smoke was found to be a suitable method for the particle seeding of the indoor air flow. Generally, the higher particle seeding concentration is (the particle number in a unit volume of the seeded air, not the particle mass of a unit volume), the better spatial resolution has for a PIV measurement. But if the illumination or camera’s aperture would not be adjusted properly, the extreme high concentration of tracer particles may lead to lower spatial resolution of the measurements [29]. Photographs of the jet flow with seeded particles are presented in Fig. 10 and show a comparison between acceptable particle seeding and unacceptable particle seeding in PIV measurement. It was found that acceptable particle seeding provides a suitable particle distribution with counts in the range from 100 to 500. The counts representing the colour intensity are defined as [30]:
counts ¼ ð299*R þ 587*G þ 114*BÞ=4
(4.2)
where R is the red colour component, G is the green colour component, and B is the blue colour component. If the counts are less than 100, the PIV image may suffer from insufficient particles in the jet flow, as shown in Fig. 10a. If the counts are more than 500, the displacement of different particles may be overlapped by each other, as shown in Fig. 10c. Moreover, the excess particles may reflect the laser beam onto the ceiling and thus cause a disturbance from the ceiling under the over-seeded conditions resulting in the poor imaging performance. The ceiling regions can be recognised above the white dashed line in Fig. 10. 4.2. The PIV interrogation windows and spatial resolution The post-processing of the PIV analysis was performed with preshifted interrogation windows. The size of the interrogation windows can be reduced from 256 or 128 to 64 or 32 pixels. The size of the interrogation windows was determined by both the low phenomena and the scale of the picture and the measurement
Image correction
parameters [28]. Here, the CCD size is 2 k 2 k in the PIV system. The field of view of the CCD camera was able to resolve a region 800 mm 800 mm by illuminating a planar measuring flow field by means of a pulsed laser beam. Thus 1 pix ¼ 0.4 mm in the object plane. The spatial resolution of the velocity measurement is determined by the optical resolution, interrogation area size, and overlapping of the interrogation areas. Here, the interrogation window size is chosen to be 32 pixels 32 pixels. Thus the velocity measurement is performed over an area 12.8 mm 12.8 mm, which means the smallest resolved flow structures are about 12.8 mm 12.8 mm. Because of the different flow phenomena and the variation in the density of the droplets, it was reported that overlaps of both 50% and 25% of the interrogation windows were found to be good for the smallscale PIV measurements [28]. Here, the overlapping of the interrogation windows is set to be 75%. The velocity vectors have a spacing of 9.6 mm, which means at most one velocity vector can be obtained within a distance of 9.6 mm. For each vector position the corresponding position of the interrogation window in the raw image is calculated. When the interrogation windows are overlapped, it must be noticed that the resolution of the vector field is multiplied by the overlap and the true resolution becomes lower. In the procedure used for the post-processing, the correction of the interrogation window may be operated to improve the quality of the velocity vector calculation. There is another direct way to calculate the vectors correctly in the interrogation windows. Fig. 11 shows the corrections of the image in the procedure of the calculation of the velocity vector. It is straightforward to correct the image before the application of the standard 2D PIV post-processing. After the correction of the image, the distortion of the image was solved without any correction of the interrogation window.
4.3. Jet spreading rate The jet volume flow grows by entraining ambient air when leaving the jet slot. At the same time, the maximum core velocity
Vector correction
Fig. 11. Image corrections with interrogation windows in the calculation procedure of the velocity vector [30].
G. Cao et al. / Building and Environment 45 (2010) 1932–1940
0.4 PIV
0.35
Bradshaw and Gee (Launder and Rodi, 1981) Myers (Launder and Rodi, 1981)
dy1/2/dx
0.3 0.25
McGahan (Launder and Rodi, 1981)
0.2
Verhoff
0.15 0.1 0.05 0 0
1
2
3
4
5
6
7
8
10-3×Reslot Fig. 12. Dependence of growth rate of jet half-width on Reynolds number.
has been diminished as a result of the wall friction and free shear in the outer region. From a review of the literature, the jet growth rate for the turbulent attached plane jet was obtained as [15]:
dy1=2 ¼ 0:073 0:002 dx
(4.3)
Compared with the spread rate of jets with a higher Reynolds number shown in Eq. (4.3), the spread rate of an attached plane jet with a low Reynolds number varies in a wider range. Fig. 12 shows the spread rate of the jet under different Reynolds number jet conditions. The unsteadiness of the low wall jet may contribute to the discrepancy between different experiments. Suresh studied a rectangular nozzle with an aspect ratio of 20 for various Reynolds numbers in the range 250–6250 [31]. In this range, the characteristics of the flow development are found to be Reynolds numberdependent, in contrast to the fully developed turbulent jets, which show features that are independent of initial conditions, such as the inlet Reynolds number. For the low Reynolds number jets presented in Fig. 12, the jet spread is significantly influenced by the low frequency oscillations caused by shear layer instability. At high Reynolds numbers, the state of the turbulence becomes independent of the inlet Reynolds number and axial distance in the far field. For the transitional Reynolds number regime studied here, the overall spread rate of the jet is also heavily influenced by the Reynolds number as a result of the probable changes in the eddy formation and interaction processes. 5. Conclusions In indoor air flow studies, the PIV technology can be used to study both the simultaneous jet flow characteristics and the mean flow field behaviours. In this study, the detailed PIV experimental data of the attached plane jet velocity field were obtained in a fullscale ventilated chamber at three different air velocities corresponding to initial turbulent intensities of 44, 30, and 22%. The PIV measurement clearly shows the turbulent structure of the attached jet by the visualisation during the turbulent transition and the entrainment process after leaving the slot. At low Reynolds numbers, from 960 to 2000, the growth rate of the half-height of the jet decreases dramatically, from 0.27 down to 0.07. This confirms that the growth rates of the jet are significantly influenced by the flow oscillations caused by the instability of the outer layer. This confirms that the mutual interactions between these inner- and outer-layer vortical structures dominate the
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transition process [23]. The result also indicates that when the Reynolds number is larger than 2000, the state of the turbulence jet growth becomes independent of the initial Reynolds number and distance in the far field. This supports the finding that the Reynolds number 2000 is the critical point at which to distinguish the turbulent velocity profile and the laminar velocity profile in the attached plane jet [32]. The PIV measurement system constructed in this study was capable of measuring the average and instantaneous velocity field of the attached plane jet at a low Reynolds. The results show that the inaccuracy of the PIV measurement is about 20% in the inner and outer layers of the attached jet flow at Reynolds number of 960 and 1680, respectively. The PIV measurement provides a precise visualisation of the structure of the attached jet during the turbulent transition and entrainment process after leaving the supply slot. For the PIV experiments, it was possible to use the OPTIMIST smoke generator in the indoor air flow PIV measurement as it seeded particles with a suitable size distribution. During the PIV measurement, it was observed that the optimisation of the measurement parameters has to be performed with extreme caution. In the boundary layer of the jet, there are large velocity gradients, a high number density of particles, and deviating light intensity in the PIV frames, which lead to problems for the PIV measurement. However, these problems were solved in this study and reliable results were obtained. The information gathered is valuable for understanding the entrainment of the ambient air in an attached plane jet under room conditions. The data acquired in this study are suitable for the validation of corresponding CFD results and for the development of a jet model in jet flow analyses.
Acknowledgement The authors acknowledge the financial and experimental support of Halton Oy Finland.
References [1] Fredriksson J, Sandberg M, Moshfegh B. Experimental investigation of the velocity field and airflow pattern generated by cooling ceiling beams. Build Environ 2001;36:891–9. [2] Riffat SB, Zhao X, Doherty PS. Review of research into and application of chilled ceilings and displacement ventilation systems in Europe. Int J Energy Res 2004;28:257–86. ¨ ber [3] Fo¨rthmann E. U turbulente strahlausbreitung. Ingenieur-Arch 1934;5(1):42–54. translated as: Turbulent jet expansion. National Advisory Committee for Aeronautics, Technical Memorandum, No. 789, National Aeronautics and Space Administration, USA, 1936. [4] Schwarz WH, Cosart WP. The two-dimensional turbulent wall jet. J Fluid Mech 1961;10:481–95. [5] Rajaratnam N. Turbulent jets. Amsterdam, The Netherlands: Elsevier; 1976. p. 214–6. [6] Awbi HB. Ventilation of buildings. E& FN SPON; 1991. [7] Tetervin V. Laminar flow of a slightly viscous incompressible fluid that issues from a slit and passes over a flat plate. NACA TN, No.1644; 1948. [8] Quintana DL, Amitay M, Ortega A. Heat transfer in the forced laminar wall jet. J Heat Transfer 1997;119:451–8. [9] Glauert MB. The wall jet. J Fluid Mech 1956;1:625–43. [10] Bajura RA, Szewczyk AA. Experimental investigation of a laminar twodimensional attached plane jet. Phys Fluids 1970;13(7):1653–64. [11] Cao GY, Kurnitski J, Ruponen M, Seppa¨nen O. Modelling and experimental investigation of a buoyant attached plane jet. Appl Therm Eng 2009;29(13–14): 2790–8. [12] Hagstro¨m K, Siren K, Zhivov AM. Calculation methods for air supply design in industrial facilities. Helsinki University of Technology, HAVC Laboratory, Report B60, Finland; 1999, p. 50–8. [13] Goodfellow H, Ta¨hti E. Industrial ventilation design guidebook. USA: Academic press; 2001. [14] Cao GY, Kurnitski J, Ruponen M, Seppa¨nen O. Modelling and experimental investigation of the turbulent attached plane jet in the transition process. HVAC&R Res 2009;15(3):489–508. [15] Launder BE, Rodi W. The turbulent wall jet. Prog Aerospace Sci 1981;19: 81–128.
1940
G. Cao et al. / Building and Environment 45 (2010) 1932–1940
[16] Cao GY, Kurnitski J, Mustakallio P, Seppa¨nen O. Active chilled beam wall jet prediction by the free convection model. Int J Ventil 2008;7(2):169–78. [17] Sandberg M. Whole-field measuring methods in ventilated rooms. HVAC&R Res 2007;13(6):951–70. [18] Sun YG, Zhang YH. An overview of room air motion measurement: technology and application. HVAC&R Res 2007;13(6):929–50. [19] Diodati P, Paone N, Rossi GL, Tomasini EP. Comparison of laser-Doppler velocimetry, hotwire anemometry and particle image velocimetry for the investigation of a turbulent jet. Laser Anernornetry Advances and Applications. SPIE 1993;2052:315–22. [20] Posner JD, Buchanan CR, Dunn-Rankin D. Measurement and prediction of indoor air flow in a model room. Energy Build 2003;35:515–26. [21] Raffel M, Willert C, Wereley S, Kompehans J. Particle image velocimetry: a practical guide. 2nd ed. Springer; 2007. [22] Shih C, Gogineni S. Experimental study of perturbed laminar wall jet. AIAA J 1995;33(3):559–61. [23] Gogineni S, Shih C. Experimental investigation of the unsteady structure of a transitional plane wall jet. Exp Fluids 1997;23:121–9. [24] Gogineni S, Visbal M, Shih C. Phase-resolved PIV measurements in a transitional plane wall jet: a numerical comparison. Exp Fluids 1999;27: 126–36.
[25] Kim NS, Giovannini A. Experimental study of turbulent round jet flow impinging on a square cylinder laid on a flat plate. Int J Heat Fluid Flow 2007;28:1327–39. [26] Cao GY, Sivukari M, Kurnitski J, Ruponen M, Seppa¨nen O. Particle image velocimetry (PIV) application in the indoor air distribution measurement by an active chilled beam. Roomvent 2009 Busan, Korea, May 24–27, 2009. [27] Ruponen M, Tinker JA. A novel method to measure the air entrainment ratio of an active chilled beam. Int J Ventil 2009;7(4):299–308. [28] Hillamo HJ, Kaario O, Larmi M. Particle image velocimetry measurements of a diesel spray. SAE Technical Paper Series 2008-01-0942; 2008. [29] Bo¨hm B, Geyer D, Dreizler A, Venkatesan KK, Laurendeau NM, Renfro MW. Simultaneous PIV/PTV/OH PLIF imaging: conditional flow field statistics in partially premixed turbulent opposed jet flames. Proc Combust Inst 2007;31:709–17. [30] DaVis Software Manual for DaVis 7.0. Go¨ttingen, Germany: LaVision GmbH; 2005. [31] Suresh PR, Srinivasan K, Sundararajan T, Das Sarit K. Reynolds number dependence of plane jet development in the transitional regime. Phys Fluids 2008;20:44–105. [32] Hsiao FB, Sheu SS. Experimental studies on flow transition of a plane wall jet. Aeronaut J 1996;100(999):373–80.
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Building and Environment journal homepage: www.elsevier.com/locate/buildenv
Particle Image Velocimetry (PIV) application in the measurement of indoor air distribution by an active chilled beam Guangyu Cao a, b, *, Markku Sivukari a, Jarek Kurnitski a, Mika Ruponen c, Olli Seppa¨nen d a
Department of Energy Technology, Helsinki University of Technology, P.O. Box 4100, FIN-02015 TKK, Finland Technical Research Centre of Finland, P.O. Box 1000, FI-02044 VTT, Finland c Halton Oy, Haltonintie 1-3, 47400 Kausala, Finland d REHVA, Washington Street 40, B-1050 Brussels, Belgium b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 August 2009 Received in revised form 26 November 2009 Accepted 28 November 2009
We study the turbulent air flow behaviours of the attached plane jet discharged from an active chilled beam in a room using Particle Image Velocimetry (PIV). PIV is an innovative technology to study indoor air flow which began in the eighties of the last century for the measurement of whole air flow fields in fractions of a second. Here an experimental PIV system was built to reveal the structure of a turbulent attached plane jet in the entrainment process of the ambient air downstream from the jet slot. For the particle seeding in the PIV experiments, a few different particles were tested with the attached jet PIV application in a room. The results presented in this paper show the clear structure of the turbulent attached plane jet in the entrainment process after issuing from the chilled beam slot. The PIV visualisation results proved that the jet will attach to the ceiling and become fully turbulent a short distance downstream from the slot. The jet velocity vector fields show that the volume flow rate of the attached plane jet increases because of the large vortex mixing mechanism in the outer region of the jet. In three measurement cases, the air jet grows faster at a Reynolds number of 960 than at Reynolds numbers of 1320 and 1680. The calculated spreading angles in the cases with lower Reynolds numbers have similar values compared with the visualisation results. Ó 2009 Elsevier Ltd. All rights reserved.
Keywords: Particle image velocimetry Attached plane jet Turbulent flow Reynolds number Visualisation Vector field
1. Introduction At present, the chilled beam is becoming a popular air distribution device in office environments. There are several advantages to such kinds of diffusers, including energy savings, better thermal comfort, and more silent operation [1,2]. The air flow pattern of the attached plane jet discharged from a ceilingmounted chilled beam is presented in Fig. 1 and shows the corresponding jet regions downstream from the jet slot. The earliest known work on the attached plane jet was carried out by Fo¨rthmann (1934) [3], described and quoted in [4–6]. The first theoretical investigation of the incompressible isothermal laminar attached plane jet was undertaken by Tetervin (1948) [7], presented in [8]. Tetervin predicted that the boundary layer thickness of the attached jet would grow and the local maximum velocity would decay with the downstream distance as x0.75 and
* Corresponding author. Technical Research Centre of Finland, P.O. Box 1000, FI-02044 VTT, Finland. Tel.: þ358 40 1993513; fax: þ358 20 722 7015. E-mail address: guangyu.cao@vtt.fi (G. Cao). 0360-1323/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2009.11.020
x0.5, respectively. Generally, the non-dimensional jet velocity profiles should be similar at a different distance from the jet slot in the fully developed zone of the turbulent jet. This refers to the self-similarity of the jet, which is one of the characteristics of the turbulent jet in the fully developed zone [5,6]. Glauert (1956) achieved a similarity solution for the laminar and turbulent radial and attached plane jets [9]. Bajura and Szewezyk (1970) carried out an experimental investigation of laminar wall jets and obtained good agreement with Glauert’s similarity solution in the laminar condition [10]. Under non-isothermal conditions, the different jet zones have been identified by experimental studies and found to be dependent on the initial conditions, including the slot Reynolds number and the initial Archimedes number [11]. Generally, a four-zone division into a potential core zone, transition zone, fully developed turbulent zone, and terminal zone is used to describe the free jet flow field [12,13]. As for the classification of the attached plane jet zones, two-zone divisions were used to be considered as the main zones under isothermal conditions [14]. In other studies, however, a three-zone division into a non-buoyant region, intermediate region, and buoyant region was
G. Cao et al. / Building and Environment 45 (2010) 1932–1940
1933
Fig. 1. Schematic view of the impingement of the attached plane jet and jet regions in a room.
described in [15]. The jet grows and becomes turbulent when the jet issues from the slot by the entrainment of the ambient air. In an air-conditioned room, the discharging jet flow from the chilled beams is designed to attach to the ceiling or the wall surface, so that the high-velocity region is restricted to the ceiling or the nearwall zone in order to free the space in the occupied zone from draught [16]. In the experimental studies of the attached jet flow, to obtain the jet velocity distribution, single-point measurements with an anemometer must be traversed to obtain measurements over the flow domain. However, scanning over the flow domain might not yield the instantaneous flow structure and could be blocked by the time consuming. The limitations of conventional anemometer measurement could not fulfil the requirement of a detailed turbulent jet behaviour study, especially at the beginning of the discharge of the jet from the potential jet core to the transition process [17,18]. In the 1990s, the PIV technique emerged from laboratories to applications in fundamental and industrial research, from aerodynamics to indoor air flow studies [19,20]. Unlike conventional anemometers, Particle Image Velocimetry (PIV) is able to measure whole flow fields in fractions of a second [21]. As for the use of PIV in attached jet studies, Shih and Gogineni measured a low turbulent attached jet flow with PIV at a Reynolds number of 1000 [22]. Gogineni and Shih carried out a series of studies on the attached jet transition process with Reynolds numbers 330–3800 [23]. Gogineni et al. studied PIV measurement with a numerical solution [24]. Kim and Giovannini carried out an experimental study of turbulent round jet flow [25], and the instantaneous two-dimensional velocity fields in the streamwisewall-normal plane were measured by using PIV in their studies. The two-dimensional attached jet flow was measured in terms of its turbulent structure in [26]. However, there have few cases of PIV application in indoor air flow studies, especially in the case of chilled beams. Here, the experiments using Particle Image Velocimetry were carried out to measure the attached jet flow in a room with an active chilled beam in the ceiling zone to obtain detailed information on the ambient air entrainment process. The objectives of this study were: to select a suitable particle seeding method in order to use PIV in a room air flow measurement; to obtain detailed information on the ambient air entrainment process, and to clarify the growth rate of an attached jet at low Reynolds numbers with an active chilled beam.
2. Experimental setup 2.1. PIV measurement system and instrumentation The PIV measurement system and PIV apparatus are shown in Fig. 2. The active chilled beam was mounted flush to the ceiling at a distance 1.6 m from the side wall. The air jet issuing from the chilled beam is parallel to the longer wall of the room. To avoid or mitigate the effect of surface reflection, the whole room to be measured was painted black. One thin laser beam trap was built perpendicular to the active chilled beam through the middle of the ceiling and the short side wall. On one long side wall, a few small openings were made in order for a CCD camera to be installed (see Fig. 3a). A laser guiding arm was used to deliver the high-power laser beams of Nd:YAG lasers controlled by the LaVision program. Before the PIV measurement, the CCD camera was calibrated by means of a calibration plate with a size 800 mm 800 mm (see
Fig. 2. Full-scale attached jet flow PIV measurement system.
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Fig. 3. PIV measurement apparatus: a) CCD camera mounted outside the side wall; b) PIV measurement calibration plate; c) installation of the hot sphere anemometers.
Fig. 3b). During the measurement, the tracer particles were induced into the jet flow through a perforated plate below the chilled beam. A double-pulse laser sheet illuminates these particles in the measured plane of the flow twice within a short time interval. The displacement of the particle images between the light pulses is used to calculate the velocity vector during the postprocessing. Five hot sphere anemometers were installed on a height-adjustable device to measure the ceiling zone jet velocity (see Fig. 3c). In the PIV measurement, a pulsed laser beam was generated by an Nd:YAG laser, which has a power of 200 mJ. The Nd:YAG laser used in this study consists of three main components: a laser material, a pump source, and an oscillator. For PIV the fundamental wavelength of 1064 nm is frequency-doubled using a non-linear crystal as a second harmonic generator (SHG), which converts the IR light to visible green light of 532 nm. The crystal axis has to be oriented at a certain angle to the laser beam (phase matching). The trigger signals for the Nd:YAG laser were produced by a LaVision Programmable Timing Unit (PTU) from a remote computer with the DaVis software package installed. By means of the software, the measured particle shift will be calculated in the post-processing to form the velocity vector field. The camera integrated into the system is based on a Charge-Coupled Device (CCD) sensor with high resolution and high sensitivity. In the measurement with the usage of the CCD camera, the power of the laser was increased in small steps to keep the camera image from being saturated; for example, the intensity is kept below the maximum grey level; here, fewer than 4095 counts should be a suitable image intensity. The laser beams were formed into sheets and overlapped in the air jet flow field with an adjustable thickness from 0.5 to 2.5 mm. The thickness of the laser light sheet was adjusted so as to be approximately 1.0 mm in the middle of the laser beam. The field of view of the CCD camera was able to resolve a region 800 mm 800 mm by illuminating a planar measuring flow field with a pulsed laser beam. The air flow that was supplied was measured using an orifice plate. A 54N50-type Low Velocity Flow Analyser was used for the measurement of the jet turbulence intensity of the supply air. To estimate the accuracy of the PIV measurement, a VelocCALC plus device and five 8475 Model anemometers were used to measure the air velocity at the jet slot and at a distance of 0.3 m from the jet slot. The accuracy of anemometer is 3.0% of reading in the range of 20.0–26.0 C.
2.2. Measurement conditions In a full-scale climate chamber, the active chilled beam was mounted flush to the ceiling; it was of the same length as the climate chamber. The air jet issuing from the active chilled beam was attached to the ceiling downstream from the supply slot. The experiments were performed under isothermal conditions and therefore, because of the absence of any heat sources, the only important dimensionless parameters in this study are the initial Reynolds number and the jet turbulence intensity. The primary air supply into the beam is provided through nozzles which induce ambient room air to flow inside the beam. The ambient air flow is induced into the beam through the perforated bottom plate. The ratio of the supply air and total air flow through the chilled beam slot is about 4.5 in this study and is similar to that reported in [27]. The mixed air flow in the beam issues from the jet slot and produces an attached plane jet with turbulence intensities ranging from 20% to 45%. Table 1 presents the PIV measurement conditions with the PIV measurement settings. The supply air temperature and room air temperature were kept at the same value, 23 0.5 C, throughout the measurement. The sampling time is 8 s, with a recording speed of 10 Hz. A total of eighty pair-image results were obtained during the measurement period. The slot Reynolds numbers were calculated on the basis of the slot height, 0.018 m, and averaged slot velocity. The measurement of the jet velocity was able to cover the initial jet flow region 0.5 m downstream from the chilled beam with three slot velocities by regulating the pressure drop in the beam. By means of PIV measurement, the recording interval time of each pair-image was determined by the Optimisation of Particle Image Shift (OPIS) method under normal room conditions. Generally, for a given flow velocity, the separation ds of the particle images on the CCD determines the selected interval time or the pulse delay, dt. For cross-correlation the separation of the particle images (in pixels) should be larger than the accuracy of the peak detection and smaller than a quarter of the selected interrogation window size (in pixels). The range of the separation distance may be expressed by the relationship:
pixel < ds <
1 d 4 IntWin
(2.1)
The recommended relation shows that the optimum separation of the particle images depends on the desired interrogation
Table 1 PIV measurement conditions.
Case 1 Case 2 Case 3
Slot average velocity (m/s)
Turbulence intensity (%)
Recording pair-image interval time (ms)
Reynolds number
Recording speed (Hz)
Pressure drop within the beam (Pa)
Measured time (s)
0.8 0.05 1.1 0.05 1.4 0.05
44 30 22
6000 5000 3000
960 1320 1680
10 10 10
100 200 300
8 8 8
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window size dIntWin (25 mm in this PIV measurement) and on the velocity fields in the PIV recording. Then the recording pair-image interval time will be in the range of:
1935
The flow visualisation study was carried out using a high-speed digital camera and laser sheet using an OPTIMIST smoke generator for the particle seeding. The visualisation results and the corresponding instantaneous velocity vector fields are presented in Figs. 4–6 and show the structure and the instantaneous velocity vector field of the attached plane jet issuing from the active chilled beam. The PIV visualisation results reveal the process of the entrainment of the ambient air at a distance of 28 slot heights downstream from the slot. The large-scale vortices were seen in the outer layer of the jet presented in the PIV pair-photograph. In the figures shown in the pair-photograph, the attached plane jet at a low slot Reynolds number became fully turbulent over a short
downstream distance. After that, the turbulent attached plane jet was dominated by the irregular fluctuation in both the outer free shear layer and inner layer. The figures indicate that a jet with a relatively low Reynolds number might tend to induce more ambient air into the jet after leaving the slot. The vortex formed in the outer layer of the jet contributes significantly to the increasing of the jet volume flow rate by the vortex mixing mechanism. If a jet spreading line is drawn from the jet slot at the boundary of the observed vortex, the estimated spreading angles are about 17, 15 , and 13 for the Reynolds numbers 960, 1320, and 1680, respectively, in the ambient air entrainment process. Because of the characteristics of the smoke, however, the smoke diffusion might contribute to a discrepancy in the visual result to some extent, compared to other cases. The instantaneous jet velocity vector fields in an area 500 mm 160 mm were obtained according to the particle displacement calculation shown in the PIV pair-photograph. The interval time between the two photos of the pair-photograph was 6000, 5000, and 3000 ms in the three cases with slot average velocities of 0.8, 1.1, and 1.4 m/s, respectively. The displacement distance was about 4 mm in Figs. 4–6; this may cause undistinguishable differences between the two photos. The results presented in the three instantaneous jet velocity vector fields show the clear turbulent structure of the jet flow from the inner layer to the outer layer. Even within the boundary layer near the surface of the ceiling, the laminar flow pattern could not last longer than a distance of 10 slot heights downstream from the jet slot. The instantaneous jet flow vector fields may indicate that the attached plane jet issuing from the
Fig. 4. Jet visualisation and the corresponding instantaneous vector field by PIV pairphotograph at a slot velocity of 0.8 m/s: a) laser sheet pair-image one; b) laser sheet pair-image two; c) instantaneous velocity vector field.
Fig. 5. Jet visualisation and the corresponding instantaneous vector field by PIV pairphotograph at a slot velocity of 1.1 m/s: a) laser sheet pair-image one; b) laser sheet pair-image two; c) instantaneous velocity vector field.
pixel ds 1 dIntWin < dt ¼ < Umax Umax 4 Umax
(2.2)
Here jet velocities of 1.0, 1.5, and 2.0 m/s were used to choose the interval time. After the parameters in the above relation had been substituted, the three recording interval times were obtained for the three measured velocities. 3. Measurement results 3.1. Visualisation of the jet flow
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Fig. 6. Jet visualisation and the corresponding instantaneous vector field by PIV pairphotograph at a slot velocity of 1.4 m/s: a) laser sheet pair-image one; b) laser sheet pair-image two; c) instantaneous velocity vector field.
chilled beam is dominated by the turbulent mechanism instead of the laminar one, even though the initial Reynolds number was as low as 960. The results also confirmed the finding in the earlier studies that the attached plane jet presents a very unstable characteristic as a result of the double row pairing vortex structure [22,23]. 3.2. Averaged vector field of the jet flow Fig. 7 shows the averaged velocity vector field of the plane jet calculated from ten PIV pair-photographs. In three cases, the maximum jet velocity occurs near the surface of the ceiling in the jet field downstream from the slot. However, the averaged velocity vectors still present the unstable structure in the jet boundary layer as a result of the rising vortex of the turbulent jet. Similar phenomena could be observed in the instantaneous vector field of the jet. Some earlier studies show that there would be a laminarlike jet potential core at low Reynolds numbers [22–24]. Here, no potential core with a laminar-like flow field with each Reynolds number was observed. Using the quantified velocity vectors, the averaged velocity vector field could be used to estimate the jet spreading angle on the basis of the half-height of the jet, which is defined as the place that has half the velocity of the local maximum velocity. The spreading angle of the jet was calculated after ten time slot heights downstream from the jet slot in order to avoid the effect of the initial potential core of the jet. One trend observed is that the jet grows faster at Re ¼ 960 than at Re ¼ 1680. This indicates that a jet with a relatively low Reynolds number might tend to
Fig. 7. Jet velocity vector field distributions by PIV: a) jet slot average velocity is 0.8 m/s; b) jet slot average velocity is 1.1 m/s; c) jet slot average velocity is 1.4 m/s.
induce more ambient air into the jet after leaving the slot. The calculated jet spreading angles based on the half maximum velocity were about 17, 12 , and 6 for the Reynolds numbers 960, 1320, and 1680, respectively. The spreading angles in the cases with Reynolds numbers of 960 and 1320 have similar values compared with the visualisation results. However, at a Reynolds number of 1680, the calculated angle was about half of the visualisation results. 3.3. Validation of the velocity measured with PIV The validation of the PIV results is somewhat complicated, but there is no other non-intrusive way of measuring such a large area of a flow field at once. Therefore, the PIV measurements can only be validated at certain points with another velocimetry technique or the results can be compared to computational values or analytical solutions of simplified flow phenomena [28]. The results of an earlier study suggest that the measured velocity distribution using PIV is reliable [14]. Here, the measured velocities using conventional anemometers are used to validate the velocity measured with PIV at the jet slot and 300 mm downstream from the slot at three slot velocities, 0.50, 1.00, and 2.00 m/s. All the anemometerbased measurements are made in the test room by supplying air at the same temperature as the room air temperature. During the measurement, the velocity is recorded every second and the average velocity is obtained through each 3-min period. The measured velocity at the slot is presented in Fig. 8 and shows
G. Cao et al. / Building and Environment 45 (2010) 1932–1940
4. Discussions
1.5 Anemometer measured
4.1. Particle determination for PIV measurement
PIV measured
1.2
In PIV measurement, the air must be seeded with particles that follow the air motions to record the velocity. Therefore, there is a compromise between the need for them to be small enough to follow the air motions and the need for them to be large enough to reflect sufficient light in suitable illumination [17]. In PIV measurement, a primary source of error is the influence of gravitational forces if the densities of the air flow and the tracer particles do not match. Even though it can be neglected in many practical situations, the gravitationally induced velocity Ug could be obtained from Stokes’s drag law in order to introduce the particle’s behaviour under acceleration. Therefore, assuming spherical particles in a viscous fluid at a low Reynolds number, the velocity component may be expressed as [21]:
0.9
0.6
0.3
0 0
0.3 0.6 0.9 1.2 Average supply air velocity (m/s)
Ug ¼ d2p
1.5
Fig. 8. Measured slot velocity with anemometer and PIV.
60
Anemometer measured PIV measured
50 40 30 20 10 0
Distance from the ceiling (mm)
Distance from the ceiling (mm)
a comparison of the results using an anemometer and PIV. The PIV measured average velocity obtained a good agreement with the velocity measured with the anemometer at a slot velocity of 0.8 m/s. At slot velocities of 1.1 and 1.4 m/s, the difference between the results with an anemometer and PIV is up to 14%. The measured velocity profile is presented in Fig. 9 and shows a comparison of the velocity measured with an anemometer and PIV with a 20% error bar. All the three velocity profiles measured with PIV were able to obtain a certain agreement with the profile measured with an anemometer in terms of the curve shape of the attached plane jet. The maximum velocity measured by both instruments indicates the capability of PIV being used to measure the maximum velocity of an attached plane jet at 20% inaccuracy. In the inner layer and the outer layer, the PIV results can only show an agreement with the results measured with an anemometer at the Reynolds numbers 960 and 1680, respectively, within the error bar of 20%. Therefore, it was reasonable to estimate the overall inaccuracy of the PIV measurement as approximately 20%.
0 0.3 0.6 0.9 1.2 Measured velocity (m/s)
a
60
rp r g 18m
(4.1)
where Ug is the particle gravitational velocity, dp is the diameter of the particle, rp is the density of the particle, r is the air flow, g is the acceleration caused by gravity, and m is the dynamic viscosity of the air. As shown in Eq. (4.1), the diameter of the particles should be very small in order to ensure good tracking of the fluid motion as a result of the difference in density between the fluid and the tracer particles. On the other hand, the particle diameter should not be too small, as the light-scattering properties also have to be taken into account, as will be shown in the following section. Therefore, it is clear that a compromise has to be found to obtain high-quality particle seeding. At the beginning of this study, water droplets produced by a nozzle combined with compressed air were seeded to the climate chamber. With fewer water droplets in the air flow, the water droplets tend to adhere to the inside surface of the duct. In contrast, increasing the amount of water droplets makes the whole space full of water droplets, which block the laser scattering in the measurement plane. Moreover, the particle size of the water droplets was rather small and could not provide good enough laser scattering. Two types of smoke particles were used to provide suitably sized particles. One is normal filter cigarette smoke, the other is OPTIMIST smoke. Considering the shorter-undisturbing principle of PIV particle seeding, it is difficult to inject normal
Anemometer measured PIV measured
50 40 30 20 10 0
60 Distance from the ceiling (mm)
Measured velocity (m/s)
1937
PIV measured
50 40 30 20 10 0 0 0.3 0.6 0.9 1.2 Measured velocity (m/s)
0 0.3 0.6 0.9 1.2 Measured velocity (m/s)
b
Anemometer measured
c
Fig. 9. Jet velocity at a distance of 300 mm downstream from the slot: a) jet slot average velocity is 0.8 m/s; b) jet slot average velocity is 1.1 m/s; c) jet slot average velocity is 1.4 m/s.
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Fig. 10. Photographs of the jet flow with seeded particles: a) unacceptable particle seeding with insufficient particles in the jet flow; b) acceptable particle seeding with suitable particles; c) unacceptable particle seeding with an excess of particles in the jet flow.
cigarette smoke particles into the attached plane jet as a result of the way in which a cigarette burns. Using OPTIMIST smoke was found to be a suitable method for the particle seeding of the indoor air flow. Generally, the higher particle seeding concentration is (the particle number in a unit volume of the seeded air, not the particle mass of a unit volume), the better spatial resolution has for a PIV measurement. But if the illumination or camera’s aperture would not be adjusted properly, the extreme high concentration of tracer particles may lead to lower spatial resolution of the measurements [29]. Photographs of the jet flow with seeded particles are presented in Fig. 10 and show a comparison between acceptable particle seeding and unacceptable particle seeding in PIV measurement. It was found that acceptable particle seeding provides a suitable particle distribution with counts in the range from 100 to 500. The counts representing the colour intensity are defined as [30]:
counts ¼ ð299*R þ 587*G þ 114*BÞ=4
(4.2)
where R is the red colour component, G is the green colour component, and B is the blue colour component. If the counts are less than 100, the PIV image may suffer from insufficient particles in the jet flow, as shown in Fig. 10a. If the counts are more than 500, the displacement of different particles may be overlapped by each other, as shown in Fig. 10c. Moreover, the excess particles may reflect the laser beam onto the ceiling and thus cause a disturbance from the ceiling under the over-seeded conditions resulting in the poor imaging performance. The ceiling regions can be recognised above the white dashed line in Fig. 10. 4.2. The PIV interrogation windows and spatial resolution The post-processing of the PIV analysis was performed with preshifted interrogation windows. The size of the interrogation windows can be reduced from 256 or 128 to 64 or 32 pixels. The size of the interrogation windows was determined by both the low phenomena and the scale of the picture and the measurement
Image correction
parameters [28]. Here, the CCD size is 2 k 2 k in the PIV system. The field of view of the CCD camera was able to resolve a region 800 mm 800 mm by illuminating a planar measuring flow field by means of a pulsed laser beam. Thus 1 pix ¼ 0.4 mm in the object plane. The spatial resolution of the velocity measurement is determined by the optical resolution, interrogation area size, and overlapping of the interrogation areas. Here, the interrogation window size is chosen to be 32 pixels 32 pixels. Thus the velocity measurement is performed over an area 12.8 mm 12.8 mm, which means the smallest resolved flow structures are about 12.8 mm 12.8 mm. Because of the different flow phenomena and the variation in the density of the droplets, it was reported that overlaps of both 50% and 25% of the interrogation windows were found to be good for the smallscale PIV measurements [28]. Here, the overlapping of the interrogation windows is set to be 75%. The velocity vectors have a spacing of 9.6 mm, which means at most one velocity vector can be obtained within a distance of 9.6 mm. For each vector position the corresponding position of the interrogation window in the raw image is calculated. When the interrogation windows are overlapped, it must be noticed that the resolution of the vector field is multiplied by the overlap and the true resolution becomes lower. In the procedure used for the post-processing, the correction of the interrogation window may be operated to improve the quality of the velocity vector calculation. There is another direct way to calculate the vectors correctly in the interrogation windows. Fig. 11 shows the corrections of the image in the procedure of the calculation of the velocity vector. It is straightforward to correct the image before the application of the standard 2D PIV post-processing. After the correction of the image, the distortion of the image was solved without any correction of the interrogation window.
4.3. Jet spreading rate The jet volume flow grows by entraining ambient air when leaving the jet slot. At the same time, the maximum core velocity
Vector correction
Fig. 11. Image corrections with interrogation windows in the calculation procedure of the velocity vector [30].
G. Cao et al. / Building and Environment 45 (2010) 1932–1940
0.4 PIV
0.35
Bradshaw and Gee (Launder and Rodi, 1981) Myers (Launder and Rodi, 1981)
dy1/2/dx
0.3 0.25
McGahan (Launder and Rodi, 1981)
0.2
Verhoff
0.15 0.1 0.05 0 0
1
2
3
4
5
6
7
8
10-3×Reslot Fig. 12. Dependence of growth rate of jet half-width on Reynolds number.
has been diminished as a result of the wall friction and free shear in the outer region. From a review of the literature, the jet growth rate for the turbulent attached plane jet was obtained as [15]:
dy1=2 ¼ 0:073 0:002 dx
(4.3)
Compared with the spread rate of jets with a higher Reynolds number shown in Eq. (4.3), the spread rate of an attached plane jet with a low Reynolds number varies in a wider range. Fig. 12 shows the spread rate of the jet under different Reynolds number jet conditions. The unsteadiness of the low wall jet may contribute to the discrepancy between different experiments. Suresh studied a rectangular nozzle with an aspect ratio of 20 for various Reynolds numbers in the range 250–6250 [31]. In this range, the characteristics of the flow development are found to be Reynolds numberdependent, in contrast to the fully developed turbulent jets, which show features that are independent of initial conditions, such as the inlet Reynolds number. For the low Reynolds number jets presented in Fig. 12, the jet spread is significantly influenced by the low frequency oscillations caused by shear layer instability. At high Reynolds numbers, the state of the turbulence becomes independent of the inlet Reynolds number and axial distance in the far field. For the transitional Reynolds number regime studied here, the overall spread rate of the jet is also heavily influenced by the Reynolds number as a result of the probable changes in the eddy formation and interaction processes. 5. Conclusions In indoor air flow studies, the PIV technology can be used to study both the simultaneous jet flow characteristics and the mean flow field behaviours. In this study, the detailed PIV experimental data of the attached plane jet velocity field were obtained in a fullscale ventilated chamber at three different air velocities corresponding to initial turbulent intensities of 44, 30, and 22%. The PIV measurement clearly shows the turbulent structure of the attached jet by the visualisation during the turbulent transition and the entrainment process after leaving the slot. At low Reynolds numbers, from 960 to 2000, the growth rate of the half-height of the jet decreases dramatically, from 0.27 down to 0.07. This confirms that the growth rates of the jet are significantly influenced by the flow oscillations caused by the instability of the outer layer. This confirms that the mutual interactions between these inner- and outer-layer vortical structures dominate the
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transition process [23]. The result also indicates that when the Reynolds number is larger than 2000, the state of the turbulence jet growth becomes independent of the initial Reynolds number and distance in the far field. This supports the finding that the Reynolds number 2000 is the critical point at which to distinguish the turbulent velocity profile and the laminar velocity profile in the attached plane jet [32]. The PIV measurement system constructed in this study was capable of measuring the average and instantaneous velocity field of the attached plane jet at a low Reynolds. The results show that the inaccuracy of the PIV measurement is about 20% in the inner and outer layers of the attached jet flow at Reynolds number of 960 and 1680, respectively. The PIV measurement provides a precise visualisation of the structure of the attached jet during the turbulent transition and entrainment process after leaving the supply slot. For the PIV experiments, it was possible to use the OPTIMIST smoke generator in the indoor air flow PIV measurement as it seeded particles with a suitable size distribution. During the PIV measurement, it was observed that the optimisation of the measurement parameters has to be performed with extreme caution. In the boundary layer of the jet, there are large velocity gradients, a high number density of particles, and deviating light intensity in the PIV frames, which lead to problems for the PIV measurement. However, these problems were solved in this study and reliable results were obtained. The information gathered is valuable for understanding the entrainment of the ambient air in an attached plane jet under room conditions. The data acquired in this study are suitable for the validation of corresponding CFD results and for the development of a jet model in jet flow analyses.
Acknowledgement The authors acknowledge the financial and experimental support of Halton Oy Finland.
References [1] Fredriksson J, Sandberg M, Moshfegh B. Experimental investigation of the velocity field and airflow pattern generated by cooling ceiling beams. Build Environ 2001;36:891–9. [2] Riffat SB, Zhao X, Doherty PS. Review of research into and application of chilled ceilings and displacement ventilation systems in Europe. Int J Energy Res 2004;28:257–86. ¨ ber [3] Fo¨rthmann E. U turbulente strahlausbreitung. Ingenieur-Arch 1934;5(1):42–54. translated as: Turbulent jet expansion. National Advisory Committee for Aeronautics, Technical Memorandum, No. 789, National Aeronautics and Space Administration, USA, 1936. [4] Schwarz WH, Cosart WP. The two-dimensional turbulent wall jet. J Fluid Mech 1961;10:481–95. [5] Rajaratnam N. Turbulent jets. Amsterdam, The Netherlands: Elsevier; 1976. p. 214–6. [6] Awbi HB. Ventilation of buildings. E& FN SPON; 1991. [7] Tetervin V. Laminar flow of a slightly viscous incompressible fluid that issues from a slit and passes over a flat plate. NACA TN, No.1644; 1948. [8] Quintana DL, Amitay M, Ortega A. Heat transfer in the forced laminar wall jet. J Heat Transfer 1997;119:451–8. [9] Glauert MB. The wall jet. J Fluid Mech 1956;1:625–43. [10] Bajura RA, Szewczyk AA. Experimental investigation of a laminar twodimensional attached plane jet. Phys Fluids 1970;13(7):1653–64. [11] Cao GY, Kurnitski J, Ruponen M, Seppa¨nen O. Modelling and experimental investigation of a buoyant attached plane jet. Appl Therm Eng 2009;29(13–14): 2790–8. [12] Hagstro¨m K, Siren K, Zhivov AM. Calculation methods for air supply design in industrial facilities. Helsinki University of Technology, HAVC Laboratory, Report B60, Finland; 1999, p. 50–8. [13] Goodfellow H, Ta¨hti E. Industrial ventilation design guidebook. USA: Academic press; 2001. [14] Cao GY, Kurnitski J, Ruponen M, Seppa¨nen O. Modelling and experimental investigation of the turbulent attached plane jet in the transition process. HVAC&R Res 2009;15(3):489–508. [15] Launder BE, Rodi W. The turbulent wall jet. Prog Aerospace Sci 1981;19: 81–128.
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G. Cao et al. / Building and Environment 45 (2010) 1932–1940
[16] Cao GY, Kurnitski J, Mustakallio P, Seppa¨nen O. Active chilled beam wall jet prediction by the free convection model. Int J Ventil 2008;7(2):169–78. [17] Sandberg M. Whole-field measuring methods in ventilated rooms. HVAC&R Res 2007;13(6):951–70. [18] Sun YG, Zhang YH. An overview of room air motion measurement: technology and application. HVAC&R Res 2007;13(6):929–50. [19] Diodati P, Paone N, Rossi GL, Tomasini EP. Comparison of laser-Doppler velocimetry, hotwire anemometry and particle image velocimetry for the investigation of a turbulent jet. Laser Anernornetry Advances and Applications. SPIE 1993;2052:315–22. [20] Posner JD, Buchanan CR, Dunn-Rankin D. Measurement and prediction of indoor air flow in a model room. Energy Build 2003;35:515–26. [21] Raffel M, Willert C, Wereley S, Kompehans J. Particle image velocimetry: a practical guide. 2nd ed. Springer; 2007. [22] Shih C, Gogineni S. Experimental study of perturbed laminar wall jet. AIAA J 1995;33(3):559–61. [23] Gogineni S, Shih C. Experimental investigation of the unsteady structure of a transitional plane wall jet. Exp Fluids 1997;23:121–9. [24] Gogineni S, Visbal M, Shih C. Phase-resolved PIV measurements in a transitional plane wall jet: a numerical comparison. Exp Fluids 1999;27: 126–36.
[25] Kim NS, Giovannini A. Experimental study of turbulent round jet flow impinging on a square cylinder laid on a flat plate. Int J Heat Fluid Flow 2007;28:1327–39. [26] Cao GY, Sivukari M, Kurnitski J, Ruponen M, Seppa¨nen O. Particle image velocimetry (PIV) application in the indoor air distribution measurement by an active chilled beam. Roomvent 2009 Busan, Korea, May 24–27, 2009. [27] Ruponen M, Tinker JA. A novel method to measure the air entrainment ratio of an active chilled beam. Int J Ventil 2009;7(4):299–308. [28] Hillamo HJ, Kaario O, Larmi M. Particle image velocimetry measurements of a diesel spray. SAE Technical Paper Series 2008-01-0942; 2008. [29] Bo¨hm B, Geyer D, Dreizler A, Venkatesan KK, Laurendeau NM, Renfro MW. Simultaneous PIV/PTV/OH PLIF imaging: conditional flow field statistics in partially premixed turbulent opposed jet flames. Proc Combust Inst 2007;31:709–17. [30] DaVis Software Manual for DaVis 7.0. Go¨ttingen, Germany: LaVision GmbH; 2005. [31] Suresh PR, Srinivasan K, Sundararajan T, Das Sarit K. Reynolds number dependence of plane jet development in the transitional regime. Phys Fluids 2008;20:44–105. [32] Hsiao FB, Sheu SS. Experimental studies on flow transition of a plane wall jet. Aeronaut J 1996;100(999):373–80.