Buoyant jet in a ventilated room: Velocity field, temperature field and airflow patterns analysed with three different whole-field methods

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Building and Environment 44 (2009) 137–145 www.elsevier.com/locate/buildenv

Buoyant jet in a ventilated room: Velocity field, temperature field and airflow patterns analysed with three different whole-field methods Per-A˚ke Elvse´n, Mats Sandberg Division of Indoor Environment, Centre for Built Environment, KTH Research School, University of Ga¨vle, 801 76 Ga¨vle, Sweden Received 4 April 2007; received in revised form 25 January 2008; accepted 16 February 2008

Abstract The instantaneous velocity field and temperature field were measured and the airflow patterns visualised close to a diffuser for displacement ventilation. Since the low-velocity diffuser was located above the floor and the inlet air temperature was below the room temperature, the flow was governed by both momentum and buoyancy forces. The data were recorded with whole-field measuring techniques, particle streak velocimetry (PSV), particle image velocimetry (PIV) and infrared thermography (IR), in conjunction with a low thermal mass screen. The environment is very complex, supply of buoyant air with a commercial supply terminal with 20 nozzles pointing in different directions, which makes it difficult to use point-measuring techniques or computational fluid dynamics (CFD). The aim was twofold: (a) to explore what kind of information can be derived from whole-field measurement techniques in this context and (b) to investigate the trajectory of the flow discharged into the room and the entrainment of the flow. r 2008 Elsevier Ltd. All rights reserved. Keywords: Whole-field method; Particle streak velocimetry; Particle image velocimetry; Infrared thermography

1. Introduction Displacement ventilation is a ventilation principle based on the properties of stratified flow. Air with a lower temperature than the room air temperature is supplied directly into the occupied zone. Because the air is supplied directly into the occupied zone, it is efficient ventilation. The problem is the risk of draught. To minimise the risk, the air is supplied at a low velocity. If the supply air terminal is located above the floor the flow generated is an inclined buoyant jet. When the buoyant jet hits the floor, it spreads on the floor as the gravity current. Due to the risk of draught it is important to monitor the air temperature and the velocity within the buoyant jet. Within the region of the air stream where the comfort criteria are not met, people cannot stay for a longer time. Therefore, the air penetration into the room must be monitored, which calls for determining the trajectory. Corresponding author. Tel.: +46 26 648124; fax: +46 26 648181.

E-mail address: [email protected] (P.-A˚. Elvse´n). URL: http://www.hig.se/tb/iv/forskn_lvk/ (P.-A˚. Elvse´n). 0360-1323/$ - see front matter r 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2008.02.009

Fig. 1 displays the supply air terminal used in our study. It is a typical low-velocity terminal. The terminal has 20 nozzles of diameter 8 cm located within an area of 44  38 cm2. The orientation of the nozzles can be individually regulated. A perforated covering plate of dimensions 54  45 cm2 and porosity 37% covers the nozzles. The design of the terminal makes the flow from the supply terminal very complex. The air is always in transition between different states. The limited size of the room will limit the length of the trajectory. Therefore, it is not certain that the flow will reach an asymptotic state known as the zone of flow establishment (ZOF). The complex geometry of the terminal with nozzles oriented in different directions and the presence of buoyancy make computational fluid dynamics (CFD) predictions very difficult. A fine grid is required and the flow inside the terminal must be simulated, as was done by Cehlin [1]. To record the velocity within a large volume with a pointmeasuring technique, e.g., hot-wire anemometry, is an enormous task and in a field trial almost impossible. However, a whole-field method for measuring velocities

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Nomenclature A(0) Ar(0) B(0) E g H h lT L LTraj m q

initial area of jet (m2) Archimedes number at the inlet, defined in Eq. (12) specific buoyancy flux (m4/s3), defined in Eq. (2) entrainment in the jet (m2/s) acceleration due to gravity (m/s2) distance between floor and the centre of the supply device (m) height of supply diffuser (m) thermal length (m), defined in Eqs. (8) and (9) characteristic length of supply air terminal (m) length of trajectory, according to Eq. (14) (m) specific momentum flux (m4/s2) volumetric flow rate (m3/s)

and/or temperatures gives us the possibility to explore the whole buoyant jet within the room.

2. Properties of buoyant jets The literature on buoyant jets is vast. Many studies concern problems with wastewater disposal. A recent review article on turbulent buoyant jets is by [2]. Some properties of jets and plumes are more easily derived by using the Lagrangian approach, and particle streak velocimetry (PSV) is basically a Lagrangian method. A book on jets and plumes using the Lagrangian approach is [3].

Re s t T Tin DT U Uin UF UH UN x y n

Reynolds number, defined in Eq. (13) distance along trajectory (m) time (s) temperature in the room (K) supply temperature (K) temperature difference between T and Tin (K) velocity (m/s) supply velocity (m/s) supply velocity, face plate (convex hull of holes) (m/s) supply velocity, face-plate hole (m/s) supply velocity, nozzle (m/s) horizontal distance from diffuser (m) vertical distance from the centre of the diffuser (m). kinematic viscosity (m2/s)

Fig. 2 shows a sketch of the main parameters. In order to be able to get an expression we can make a simplification with respect to our real test conditions by assuming that there is no ambient cross flow and no vertical temperature gradient. The boundary conditions are the following: The specific momentum flux is mð0Þ ¼ qð0ÞUð0Þ

(1)

and the specific buoyancy flux is Bð0Þ ¼ qð0Þg

DTð0Þ T

Fig. 1. Supply air terminal without covering plate.

(2)

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The thermal length for a round buoyancy jet is equal to g

h

Uð0ÞAð0Þ1=4 l T ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gDT=T and for the plane buoyant jet is equal to !1=3 Uð0Þ4 h . lT ¼  2 gDT=T

x s

y

Fig. 2. The main parameters of a buoyant jet discharged horizontally.

The horizontal component mx of the specific momentum flux is conserved, mx ¼ mð0Þ

(3)

The vertical component is changed at a rate equal to the specific buoyancy flux B, dmy ¼ Bð0Þ dt

(5)

(6)

Beyond ZOF the entrainment rate is proportional to the centreline velocity (Taylor’s hypothesis). The effect of the density (temperature) difference is usually taken into account by introducing the local densimetric Froude number, see e.g., [2]. The differential equation for the trajectory can be written as [4, p. 374]: d2 y 1 qðsÞ ¼ Constant 2 2 dx l T qð0Þ

(10)

For a plane jet the flow rate beyond ZOF is proportional to the square root of the x and the drop in y is yx5=2

(11)

When the flow approaches the floor it is decelerated. The effect of the floor is felt at some distance above the floor. This zone is called the impinging zone. This zone has been investigated by several authors, e.g. [5–7]. 3. Methodology

The volumetric flow rate q increases by entrainment of ambient air dq ¼E ds

yx3

(4)

In case the density (temperature) is uniform, the specific buoyancy flux is constant and we obtain after integration of Eq. (4) the vertical component of the momentum flux after time t, my ¼ Bð0Þt.

(9)

If we have had no entrainment (q(s)=q(0)), one obtains the usual ballistic trajectory, yx2. This is a limiting case in the sense that it is the trajectory with the least drop (smallest exponent). When the curvature of the trajectory is small (cos(y)E1), one may set q(s)=q(x) and the differential equation for the trajectory can be solved analytically. For a round jet with a trajectory of small curvature, the volumetric flow rate beyond the ZOF grows linearly with x, see e.g. [4], and one obtains

θ H

(8)

(7)

where lT is the thermal length for the buoyancy jet. In this study it is preferred to use the concept of thermal length, see Eqs. (8) and (9), to characterise a buoyant jet instead of the Archimedes number. Since the thermal length is measured in metres, the effect of buoyancy can be compared to the dimensions of the room and diffuser.

3.1. Test room The experiment took place in a climate chamber with a size of (L  W  H) 3.14  4.18  2.75 m3 and a displacement ventilation system. A flat diffuser, with a height of 0.45 m and a length of 0.54 m, was located at the centre of one of the walls. The diffuser had a face area, convex hull of face-plate holes, A=0.1995 m2. For the characteristic length of the supply device, L=OA, which is equal to 0.45 m, is used. 3.2. Test conditions In the room the mean air temperature was 21 1C. The air was supplied at a flow rate between 0.013 and 0.035 m3/s, and a temperature of 17 1C. The tests were conducted at stationary conditions. We checked the temperature difference between supply and room air and waited until we got a stable temperature difference. A parameter study was performed where the effects of the changes in thermal length were studied. This was done with the diffuser located at the height of H=1.56 m. The temperature difference between the supply air and the room air was kept constant, whereas the supply flow rate was varied. The vertical temperature gradient was for a ventilation flow rate of 0.035 m3/s, 0.7 1C/m and at 0.013 m3/s, 0.6 1C/m. The test conditions are summarised in Table 1.

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The Archimedes number was calculated according to pffiffiffiffiffiffiffiffiffiffi DT Að0Þ Arð0Þ ¼ g (12) TU 2in and the Reynolds number was calculated as UL (13) n The thermal length was less than the characteristic length of the air-supply diffuser. This is an indication that the airflow from the beginning was very much governed by the buoyancy forces. Re ¼

3.3. PSV measurements To measure the velocity of the airflow, PSV was used. PSV is a whole-field method to measure two- and threedimensional velocity fields in enclosures and is used in

Table 1 Test conditions q (m3/s) H (m) UF (m/s) UN (m/s) UH (m/s) Renozzle Rehole T (K) DT (K) B(0) (m4/s3) lT (m) lT/H lT/OA Ar(0)

0.013 1.56 0.06 0.26 0.13 890 60 294.7 4.4 0.0019 0.11 0.07 0.26 15.5

0.021 1.56 0.10 0.42 0.20 1440 93 294.4 4.5 0.0031 0.18 0.12 0.41 6.1

0.030 1.56 0.15 0.60 0.29 2060 135 294.4 4.4 0.0044 0.26 0.17 0.59 2.9

0.035 1.56 0.18 0.70 0.34 2400 158 294.3 4.5 0.0053 0.30 0.19 0.68 2.2

many technical applications to measure the velocity of tracer particles following the flow of interest. The technique used can be classified as being based on direct tracking of individual particles and measurement of the displacement vector Dx, Dy in a small time interval Dt. To visualise the flow, small seeding particles are used, in this case helium-filled soap bubbles. They have an average lifetime of about 2 min. The bubbles were injected into the supply duct. The maximum flow rate of bubbles amounted to about 3% of the minimum ventilation flow rate. The bubbles are lit up by a halogen lamp, so that the camera will have sufficient light to capture the streaks on the CCD element. PSV only needs one particle in the light sheet for every velocity vector. During the relatively long camera exposure time, two streak sequences will be generated by the computercontrolled shutter system. A digital image processing program searching for streak combinations in the digital picture that have the characteristics of a sequence, and then analyses the digital image. Transforming to room coordinates and knowing the pulse time gives the velocity vectors that are sought. The type of system used was a PSV system developed in house. For detailed information about this measurement method, see [8]. 3.4. PIV measurements Particle image velocimetry (PIV) is a non-intrusive optical whole-field technique using a laser-light sheet and a CCD camera to investigate two-dimensional flow velocity structures. In brief the technique can be described as positioning the CCD cameras optical axis at right angle to the laser sheet and taking two exposures of the seeded airflow. The displacement vectors can then be calculated by performing a cross-correlation on the images. When the

Fig. 3. (a) IR image, q ¼ 0.013 m3/s, lT ¼ 0.11 m. (b) IR image, q ¼ 0.035 m3/s, lT ¼ 0.30 m.

ARTICLE IN PRESS P.-A˚. Elvse´n, M. Sandberg / Building and Environment 44 (2009) 137–145 Table 2 Regression functions that accurately follow the jets q (m3/s)

LTraj/L

LTraj/H

Function

I2

0.013 0.021 0.030 0.035

4.1 4.4 5.1 5.6

1.03 1.10 1.27 1.39

y ¼ 0.27  2.1 y ¼ 0.07  1.9 y ¼ 0.02  2.0 y ¼ 0.01  2.1

0.959 0.999 0.979 0.998

50

100

0 0

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to infrared radiation in the range 7.5–13 mm. The absolute accuracy of the S60 is about 72 1C and the relative accuracy is about 70.1 1C. The measuring screen, with the size of 2.2  1.4 m2, is made of two sheets glued together. The front sheet is made of thin coarse paper while the rear sheet is made of aluminium foil to decrease the radiation from the background. The screen was located perpendicular to the diffuser’s centre and parallel with the airflow direction during the experiment. In this plane the temperatures were mapped with the infrared camera perpendicular to the measuring screen. Two thermocouples were installed in the test room for measuring the room temperature, T, and the inlet temperature, Tin. 3.6. Measurements on the images

y [pixel]

-50

To find the trajectory of the jet, one IR image from each test was evaluated in an image-analysing programme. The centre of the trajectory was obtained by an eyeball analysis. For several points, marked along the curve of the jet, the image coordinates were measured. Since the lens introduces errors in the transformation between the room coordinates and the image coordinates, a correction of those errors must be made. The most common lens error is barrel distortion, which occurs in many wide-angle lenses. Straight lines are bent

-100

-150

21

20.5

-200 x [pixel] 0.013 0.030

0.021 0.035

20 [m3/s]

19.5

displacement vectors, the time between the exposures, and the magnification factor are known, it is straightforward to calculate the velocity vector field. The type of system used was a PIV system from Dantec Dynamics, including their FlowManager software, HiSense MkII camera with a resolution of 1344  1024 pixels, and a NewWave Solo Nd:YAG laser.

T [°C]

Fig. 4. Regression functions following the trajectory of the jets.

19

18.5

18

3.5. IR measurements In the whole-field temperature measuring method the air temperature is measured indirectly by using infrared thermography (IR) with a digital infrared camera and a measuring screen. For detailed information about this measurement method, see [9]. The type of camera used was a ThermaCAM S60 (FLIR Systems) with a resolution of 320  240 pixels and sensitive

17.5

17 diffuser 0.035

y-position 0.030

floor 0.021

Fig. 5. Temperature of the jet centre line.

0.013

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away from the centre of the image: a rectangle looks like a barrel. Shifting each pixel radially performs correction of these distortions. The displacement is calculated using a polynomial function, whose coefficients are specific to the particular lens. The error-compensating programme employs a high-quality sampling algorithm with negligible image degradation, to prevent new errors from occurring during the process. The correcting function is a third-order polynomial. It relates the distance of a pixel from the centre of the source image (rsrc) to the corresponding distance in the corrected image (rdest): rsrc ¼ ða n r3dest þ b n r2dest þ c n rdest þ dÞ n rdest To implement a function for the trajectory of the jet, corrected image coordinates marked along the curve were used in conjunction with regression. The regression function is a power function of the form y ¼ a n xb that fits the data by performing a least-squares fit using the transformed model function ln ðyÞ ¼ ln ðaÞ þ b n ln ðxÞ:

Fig. 6. Spatial location of PIV measurements.

4. Results and discussion 4.1. IR measurements The results from the IR measuring method were images with different colours representing different temperatures of the air close to the diffuser. The IR images in Figs. 3a and b show the changes of the jet for two different thermal lengths, highest and lowest supply flow rate. The trajectory of the jet on the corrected image coordinates was found to track the following power functions well, see Table 2 and Fig. 4. The length of the trajectory when it reaches the floor is obtained from Z xðy¼HÞ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 dy 1 þ dx dx (14) LTraj ¼ 0

The non-dimensional lengths LTraj/L and LTraj/H are displayed in Table 2. The ratio between the length of the trajectory and the characteristic length of the supply device is less than 6. For an isothermal jet with a high Reynolds number a distance of about six times the characteristic dimension of the supply device is required to achieve an established flow with respect to the mean velocity field. At a lower Reynolds number a longer distance is required. This is an indication that the flow in our case did not reach a state of flow establishment.

Fig. 7. (a) Upper and lower flow map of PIV measurements, 0.013 m3/s. (b) Upper and lower flow map of PIV measurements, 0.035 m3/s.

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The exponent in the equations for the trajectories is approximately two in every case and does not follow the asymptotic expressions in Eq. (10) or (11) that are valid for an established flow. This supports the conclusion that the flow is far from established. Another complication is the presence of the vertical temperature gradient of 0.6–0.7 1C/m.

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The IR images show that there must be an entrainment, since the jet’s temperature rises approximately 2–3 1C on its path down towards the floor, see Fig. 5. In the IR study, the case with the lowest thermal length showed a steeper curve than expected and a worse curve adaptation. The flow seems to follow the wall, as can be seen in Figs. 3a and 8a. This phenomenon is probably

Fig. 8. (a) PSV measurement showing image of unprocessed streaks and associated velocity vector field, 0.013 m3/s. (b) PSV measurement showing image of unprocessed streaks and associated velocity vector field, 0.035 m3/s.

ARTICLE IN PRESS Flow rate: 0.013 [m3/s] diffuser

caused by the Coanda˘ effect (the tendency of a moving fluid to follow a nearby curved or inclined surface). Fig. 5 shows that the temperature increase of the jet with the smallest supply flow rate (smallest thermal length) is more rapid than the other jets. This is caused by heat transfer from the wall, which is approximately 1 1C warmer than the air in the jet. One problem that can take place when using a screen in whole-field IR is the difficulty of placing the measuring screen without disturbing the airflow. Experiments with smoke can show a rather diverse flow with and without a screen. These errors could be caused by the Coanda˘ effect and the fact that the screen will prevent entrainment. In this experiment the problem was eliminated by placing the screen in the symmetry plane.

uavg = 0.58

uavg = 0.71 y-position

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4.2. PIV measurements

floor

uavg = 0.56

low

high

velocity Flow rate: 0.035 [m3/s]

diffuser

The entrainment into the buoyant jet close to the supply has been studied with PIV measurement, see Fig. 6. The results from the average flow maps show a small entrainment in the jet at the upper part of the upper flow map that appears to be of the same magnitude independently of the flow rate. The entrainment in the underside of the jet shows a different behaviour. Here the entrainment is more extensive and increases with the flow rate, see Fig. 7a and b. On the upper side, buoyancy forces create a stabilising stratification that tends to inhibit entrainment. On the lower side, the buoyancy forces produce a convectively unstable situation and mixing between the buoyant jet and the ambient is enhanced. In the upper flow map, the left image of the image pairs, airflow towards the ceiling can be seen in both of the flow maps. This is probably due to how the nozzles inside the diffuser are directed, see Fig. 1.

uavg = 0.80

uavg = 0.71

4.3. PSV measurements

y-position

uavg = 1.0

uavg = 0.92

uavg = 0.96 floor

Unlike the PIV measurement, the PSV measurement covers most of the buoyant jet as can be seen in Fig. 8a and b. Also see Fig. 6 for a relative comparison. The soap bubbles are supplied through the diffuser, resulting in almost all of the visible streaks being located in the buoyancy jet. The velocity of the air stream as a function of the y-position can then be measured, see Fig. 9a and b. In Fig. 9a and b the magnitude of the velocity of all the streaks has been plotted against the y-position as well as the average magnitude in four different height regions. As a reference for the average velocities, the highest average velocity in the two different flow rate cases was used. The result shows that the average speed increases in the buoyancy jet on its way down to the floor, except close to the floor. This increasing velocity is due to the action of buoyancy (gravity) according to Eq. (4). Close to the floor there is a widening of the buoyant jet, which causes a reduction in velocity.

low

velocity

high

Fig. 9. (a) Velocity magnitude as a function of y-position, 0.013 m3/s. (b) Velocity magnitude as a function of y-position, 0.035 m3/s.

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5. Conclusion In this study the trajectory of profile and the entrainment of air in a non-isothermal jet were studied with three different whole-field measuring methods. The first one, the IR method, shows that the trajectory was found to follow an x2-curve much better than the expected x3-curve. The main explanation for this deviation is that the flow is not fully established. An indication of this is that the ratio, LTraj/L, between the length of the trajectory and the characteristic dimension of the supply device was between four and six. For a non-established flow, Eq. (7) is not valid. Another complication is the presence of a vertical temperature gradient of approximately 0.6 1C/m. The IR images show that there must be an entrainment since the jet’s temperature rises approximately 2–3 1C along the trajectory’s downward curvature. The second method, the PIV measuring method, shows a small, approximately constant entrainment at the upper side of the jet. The entrainment on the underside of the jet shows a different behaviour. Here the entrainment is more extensive and increases with the flow rate. The third method, the PSV method, shows that the average velocity increases in the buoyancy jet on its way down to the floor, except in the floor region, where a widening of the buoyant jet takes place and causes a reduction in velocity. This increase in velocity definitely proceeds from the buoyancy force acting on the nonisothermal jet. The results from these three whole-field methods together provide information about this complex airflow,

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that would have been impossible to determine with conventional point measurements. Acknowledgements The help from Dr. Mirko Radic at the University of Ga¨vle, Tomohiro Kobayashi at the University of Osaka and Dr. Jens Fransson at KTH is gratefully acknowledged. References [1] Cehlin M. Paper IV: Numerical modelling of a complex diffuser in a room with displacement ventilation. Doctoral thesis. KTH, Stockholm 2006. ISBN 91-7178-342-3. [2] Jirka GH. Integral model for turbulent buoyant jets in unbounded stratified flows. Part 1: single round jet. Environmental Fluid Mechanics 2004;4:1–56. [3] Lee JHW, Chu VH. Turbulent Jets and Plumes—A Lagrangian Approach. Dordrecht: Kluwer Academic; 2003 ISBN I-4020-7520-0. [4] Etheridge D, Sandberg M. Building Ventilation—Theory and Measurement. Chichester, UK: Wiley; 1996. [5] Beltaos S, Rajaratnam N. Plane turbulent impinging jet jets. Journal of Hydraulic Research 1973;1:29–60. [6] Karimipanah T, Sandberg M. Decay of momentum and velocity in an axisymmetric jet. In: Proceedings Roomvent ‘94,Vol. 1, Cracow, Poland, 15–17 June 1994. [7] Maurel S, Solliec C. A turbulent plane jet impinging nearby and far from a flat plate. Experiments in Fluids 2001;31:687–96. [8] Elvse´n PA˚, Sandberg M. Particle streak velocimetry for room air flow—some improvements. Roomvent, Coimbra in Portugal, 5–8 September 2004. [9] Cehlin M, Moshfegh B, Sandberg M. Visualisation and measuring of air temperatures based on infrared thermography. In: Proceedings of the seventh international conference on air distribution in rooms, vol. 1; 2000. p. 339–47.