Experimental characterization of a free thermal plume and in interaction with its material environment

Applied Thermal Engineering 30 (2010) 1632e1643

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Experimental characterization of a free thermal plume and in interaction with its material environment Taoufik Naffouti a, Jamil Zinoubi b, *, Rejeb Ben Maad a a b

Faculté des Sciences de Tunis, Département de Physique, Laboratoire d’Energétique et des Transferts Thermique et Massique, El Manar 2092, Tunis, Tunisia Institut Préparatoire aux Études d’Ingénieurs El-Manar, El-Manar 2092, Tunis, Tunisia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 July 2009 Accepted 18 March 2010 Available online 25 March 2010

This investigation analyses the behaviour of a turbulent thermal plume evolving in a neutral environment and in interaction with its surrounding material. The thermal plume is created by a rectangular hot source. This source is placed at the entry of a vertical parallelepipedic canal opened at the ends. Firstly, we studied the behaviour of a free thermal plume. The flow visualization and the analysis of the thermal and dynamic fields enabled us to detect the existence of two zones during the vertical evolution of the plume. A first zone of plume development followed by a zone of established turbulence. Secondly, we described the structure of a thermal plume produced by the same source inside the vertical canal. In this case the experimental results show clearly a change of the turbulent structure of the flow in comparison with the free plume. This difference is especially characterized by the appearance of a supplementary zone just above the source that is added to the two zones described previously. In addition, the comparison of the two studied configurations showed that the structure of the plume is narrowly affected by the confinement. In order to better define the fine structure of the flow, the temperature fluctuations spectra are analyzed. This spectral analysis enables us to show the fast destruction of the big structures vortexes by the confinement effect to give a smaller structure. Ó 2010 Elsevier Ltd. All rights reserved.

Keywords: Natural convection Thermal plume Thermosiphon Flow rate Turbulence intensity Power spectral density

1. Introduction The thermal plume phenomenon that we consider is found in more practical realm which we cite for example the observed plumes of fire forest, at the chimney exit, the fires in buildings, in tower blocks and in tunnel where the plume is evolving in a free and in a confined environment [1e17]. If the plume is evolving in a confined environment it interacts narrowly with its material environment. Indeed, under the effect of thermal radiation, emitted by the plume source, the vertical walls are heated. The confinement of fluid between the hot walls causes in the lower part, an aspiration of the fresh air that supplies the boundary layers developing along the wall. This gives a flow thermosiphon that interacts with the plume. To characterize the structure of the thermal plumes, the researchers used a different form of generating source. By carrying out an experimental study of the turbulent plume induced by a disc heated uniformly at a temperature of 500
C, Nakagome and Hirata

* Corresponding author. Tel.: þ216 98 213 316. E-mail address: [email protected] (J. Zinoubi). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.03.021

[18], and George et al. [19] noticed the existence of two zones which characterize the vertical evolution of the flow. Close to the hot source, a first zone of the flow development where the buoyancy forces are dominant followed by a second zone of established turbulence where the average profiles of temperature and velocity are self-similar. After that, J.M. Agator et al. [20,21] and B. Guillou [22] studied the structure of thermal plume produced by a spherical calotte heated at a constant temperature of 500
C. Also, they showed the presence of two zones. H.Q. Yang [23] studied the transition of thermal plume between the laminar and turbulent flows. Thereafter, C. Inard [24] carried out an analysis of the average structure on a thermal plume generated by the electric convectors. In this configuration, the velocity and temperature profiles of the flow show partial similarities. L. Dehmani and Maalej [25] studied the affinity of a turbulent plume evolving in stratified environment. He shows that the affinity conditions of a thermal plume are available for a light gas plume. Then, M.V. Pham et al. [26], studied the development of a turbulent thermal plume generated by a turning hot disc. They noticed that the transition region of the flow is influenced by the vortex movement. A little later, A. Bouzinaoui et al. [27] exposed the thermal and dynamical fields of two thermal plumes generated by a hot disc and by a hot vertical cylinder. He

T. Naffouti et al. / Applied Thermal Engineering 30 (2010) 1632e1643

noticed that the structure of the thermal plume is axisymmetric for the two configurations. In order to simulate a fire which evolving in a free and unlimited environment, A.O.M. Mahmoud et al. [13] studied the effects of a thermal plume entrainment mode on the flow structure. The plume in confined environment is not independent of the flow at the vertical wall surrounding it. The two flows are obviously coupled in most cases. This coupling introduces a considerable complexity in the analysis of these kinds of flows. This interaction phenomenon was the subject of several researches. J.M. Agator [20] studied a thermal plume initially in the presence of a second identical plume. Then, he was interested at the plume interaction with a vertical plane wall placed in the vicinity. He noted a strong interaction between two plumes and plume-wall. By studying the interaction of two turbulent plumes of the same power generated by two flat discs, M. Brahimi et al. [28] noticed also the subdivision of the resulting flow in two distinct zones. He also noted that the evolution of the thermal and dynamic fields of high altitudes is similar to that one observed in the established zone of the free plume. A.O.M. Mahmoud et al. [29,30] are the first who were interested in the evolution of a thermal plume in confined surrounding. They studied the evolution of a thermal plume produced by a flat disc heated at 300
C inside an open-ended vertical cylinder. They noted that the plume interacts narrowly with the thermosiphon flow which develops along the internal wall of the cylinder. Contrary to previous work [20e22,28,29], they noticed the appearance of a supplementary zone in addition to the two classic zones which characterize the vertical evolution of the free plume. Just above of the source, the instability zone is characterized by the formation of rotating rolls and by the existence of three extrêma of temperature and velocity profiles. Higher, a second zone of turbulence pre-established followed by a last zone where the turbulence is fully established. A little later, J. Zinoubi et al. [31,32] continued this experimental work by studying the form factors effect of the plume evolution inside a vertical cylinder. Using the visualization and analysis of the thermal and dynamic profiles of the flow, he showed the existence of three zones described previously. Also, he noticed that a reduction of the source-cylinder spacing causes a fast homogenisation of the flow, an intensification of the energy absorbed by the fluid and an increase of the average flow rate. By examining flatness and dissymmetry factors of the thermal and dynamic fields, he showed that the law governing the temperature and velocity fluctuations approaches the ideal law of Gauss in the region where the turbulent intensity is maximal. Thereafter, by studying the influence of the cylinder height, J. Zinoubi et al. [33] noted a blocking of the ascending flow in the third zone due to the lateral expansion of the plume. In addition, he showed that a choice of the cylinder height not exceeding the second zone of the flow let us avoid this blocking. J. Bouslimi et al. [34] studied a turbulent plume guided by a cylinder whose the supply in fresh air is only by the sides. Contrary to the former works [29e32], he noticed that the flow structure is divided into two different zones. After that, J. Zinoubi et al. [35] studied the evolution of a thermal plume generated by a flat disc inside a rectangular canal. He noted the existence of the three zones observed in the cylindrical geometry. Also, he noticed the contraction of the rotating rolls size located in the first zone of the flow. The previous work shows a lack of information on the thermal plume evolving in confined environment with plane walls. This kind of the flow is encountered in the fires which are declared in the tunnels or buildings. Inside these confined environments, the fire generated by the accident of oil trucks or cars interacts with the plane walls surrounding the plume. To better understand the different mechanisms involved in these kinds of flows, we

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simulated this problem in laboratory by studying the evolution of a thermal plume generated by a rectangular source heated at constant temperature. We thought to use a rectangular source which adapts better with the plane walls. This source is placed at the entrance of a vertical canal, with plane walls, open at both ends on a quiet temperature uniform. Under the effect of thermal radiation, emitted by the hot source, the canal walls are heated. It produces a thermosiphon flow coming envelope and interacts with the plume. Thus, it is necessary to develop a new study on the evolution of a thermal plume produced by a rectangular source. In a first stage we studied the structure of a plume evolving in a free and unlimited environment. In a second stage, we are interested in the confinement effect on the plume development. 2. Experimental device and visualization and measurements techniques 2.1. Experimental device The experimental apparatus is shown in Fig. 1. The numbers in the description presented below refer to the part numbers of Fig. 1a. The thermal plume is created by a rectangular source (1) having a length L1 ¼ 40 cm and a width b1 ¼ 6 cm. It is electrically heated by the Joule effect at a temperature uniform and constant of 300
C. The uniformity of the source surface temperature is obtained by the use of wire resistors mounted behind the surface. A thermal regulation apparatus keeps the temperature of the source as uniform as possible within a good approximation. AleCr thermocouples are used to measure the surface temperature of the source. The temperature difference between the end and the centre of the disc is less than 1%. In order to reduce the heat losses from below and minimise the temperature variation of the ambient air, this source is insulated at this side. The interaction between thermal plume and its materiel environment is simulated by a generating source placed at the entrance of the open-ended steel vertical canal (2) (Fig. 1b). The canal consists of two Duralumin (AU4G) square parallel flat plates of low emissivity and two other rectangular Plexiglas plates to close the canal. The canal has a 2b2 ¼ 15 cm of width and an L2 ¼ 42 cm of height. In a similar way, the canal walls are thermally insulated at the back to minimise heat losses. The system is placed on a frame at 0.80 m above the ground to allow air supply from below (3). The strong dependence of the flow on the surrounding conditions requires conducting the experiment in a quiet atmosphere. To this effect, the experimental apparatus is placed in an independent closed room. In order to check the thermal stability of ambient air, several thermocouples are fixed at different heights in the room. 2.2. Visualization and measurements techniques The visualization system used during this study is presented in Fig. 2. It is constituted of a HeeNe Laser with a power of 35 mW (1), an electric vibrant plate (2), a digital camera (5) and a smoke distributor (4). On the vibrant plate is glued a plane mirror of good quality, that receives a horizontal laser beam and it reflects according to the canal vertical axis. The displacement of the plate makes revolve the mirror around a horizontal axis creating a plane laser sheet (3) on the entire transverse section of the canal. By natural aspiration, the distributor allows smoke to impregnate all the flow without any disruption. Preliminary studies of visualization and measurements by the hot wire anemometry made it possible to notice that the smoke introduced at the entry of the system does not disturb the flow. To record video sequences from visualization a numerical camera (5) is used.

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Fig. 1. Experimental apparatus e (a): free thermal plume e (b): plume in confinement.

To explore thermal and dynamic average and fluctuating fields inside the canal, we used the technique of hot wire anemometry at constant current (CCA) (4). It is based on the principle of the resistance variation of a platinum wire. The sensitive platinum wire of the probe has a diameter of Df ¼ 7.5 mm and a length of Lf ¼ 3 mm. The principle of this method is based on the resistance variation of the sensitive wire according to the temperature and velocity when it is supplied by a constant current [19,36]. The measurements of the thermal field are carried out by cold wire anemometer supplied by a current of 1.2 mA instead of using thermocouples. Indeed, the time-constant of the sensitive wire is 1 ms and that of thermocouple of 25 mm in diameter is 50 ms. In addition, the thermal inertia of the probe does not introduce any measurement errors especially at the low frequencies found in thermal plume [31,37]. The hot wire anemometer is used to measure the local velocity of the flow. In this case the probe is supplied by a current of

50 mA which makes it sensitive simultaneously to the temperature and the velocity [35,38]. In order to avoid the disturbance of the flow, the probe is introduced vertically through the system exit, so that its sensitive wire is perpendicular to the ascending average flow. Errors due to the probe calibration are lower than 1%. A computer driven displacement system (6), allowing the traversing of the probe in two directions, is used to explore the thermal and dynamic average fields at every level of the flow. The minimal displacement in the vertical direction is 1 mm, whereas in the horizontal direction it is 2 mm. On the other hand, a computer (7) equipped with a data acquisition card acquires instantaneous signal values at 10 ms intervals and records the digitized signals for further statistical processing. In application of the Shannon theorem, the period of sampling of 15 ms was chosen. 3. Results and discussions The results which we present here are carried out with air. The Grashof number of the flow is Gr ¼ 0.31  107 and the shape ratio is A ¼ 0.18. Given the similarity of profiles in each zone, we present a section in each zone (Fig. 3). 3.1. Free thermal plume flow

Fig. 2. Flow visualization system.

3.1.1. Flow visualization Before measuring the temperature and velocity fields we visualized the flow. The flow visualization performed by illuminating the flow by a plane laser sheet reveals the evolution of the flow from the hot source until the expiry of the plume. Also reveals the evolution of the flow from the canal entry to its exit. Fig. 4a and b presents two instantaneous photo drawings from the video recording. This figure shows two different behaviours of the plume flow during its vertical rise. Near the source, the plume is supplied in fresh air by the low and by the sides. In this region, the photos show the entrainment of fresh air by the upward flow. The fluid directed towards the source central region is consisted by big sizes vortexes evolving mainly in a vertical direction. Higher of the source, the behaviour of the flow is changed and the vortexes are small. On the other hand, the figure shows the plume expansion towards outside in the second region.

T. Naffouti et al. / Applied Thermal Engineering 30 (2010) 1632e1643

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Z*

Z* Z * = 0.92

Vertical canal L2

Z * = 0.20 Z * = 0.05 X*

X* b1

Source heated

a

b1

b

b2

Fig. 3. Study sections e (a): free thermal plume e (b): plume in confinement.

By taking account of this qualitative description, we were brought to suppose the existence of two zones characterizing the global structure of the thermal plume generated by a rectangular hot source. 3.1.2. Average characteristics of the flow To visualize the flow thermal field, we traced the isothermal measured in a transverse plane of the source (xOz). Fig. 5 presents the isotherms and the transverse distribution of the dimensionless average temperature of the flow for two different levels Z*. This isotherm shows a global view of a thermal field of the plume flow. Also, it highlights the existence of two distinct zones. Just above the source a first development region of the flow is characterized by high thermal gradients. Downstream, a second zone of transverse expansion of the plume where the thermal gradients are relatively weak. In addition for the level close to the source (Z* ¼ 0.05) the temperature profile presents a maximum on the median plane. Also it shows strong gradients on both sides of median plane of the source (yOz). This is due to a brutal transformation of the ambient air into hot plume. While moving away from the generating source (Z* ¼ 0.92), the profile is flattened and the thermal gradients become weak, thus indicating the establishment of a new flow mode.

Fig. 4. Thermal plume visualization.

The transverse repartition of the vertical component dimensionless average velocity is plotted in Fig. 6. The profiles confirm the existence of two different flow evolutions. For the level Z* ¼ 0.05, the flow is accelerated only in the central region above the hot source. In addition for level Z* ¼ 0.92, the profile is widened translating the transverse expansion of the thermal plume. Fig. 7 presents the vertical evolution of the dimensionless flow rate and the energy absorbed by the fluid. The calculation of these parameters was carried out by the average thermal and dynamic fields. These profiles show that the energy remains constant and the flow rate increases as we move away from the hot source. This increase of the flow rate is due to the entrainment phenomenon of the ambient air by the plume. These results were noted in a previous work by M. Brahimi et al. [28] and B. Guillou [22] on the study of a thermal plumes created respectively by a circular disc and a spherical calotte. 3.1.3. Fluctuating characteristics of the flow In order to better characterize the flow structure of the plume, the study of the thermal and dynamic fluctuating fields is necessary. Fig. 8 shows the iso-values and the profiles of the standard deviation of the thermal fluctuations reported to the temperature difference between the hot source and the ambient air. This figure allowed us to rediscover the two flow zones announced previously. In the first zone, near the hot source (Z* ¼ 0.05), the profile highlights the existence of one maximum of turbulence rate on the median plane (yOz). This maximum corresponds to a strong interaction between the ambient air and the plume. The same observation is noted by Brahimi et al. [28] and A.O.M. Mahmoud et al. [29] in the study of a thermal plume generated by a flat disc. Higher of the source (Z* ¼ 0.92), the turbulence rate is relatively weak thus indicating the establishment of turbulence in the second zone. The evolution of the flow dynamic turbulence intensity for two different sections is presented in Fig. 9. Just above the hot source, the profile shows three extrêma of turbulence. The minimum on the median plane (yOz) is due to the predominance of the more laminar aspect of the flow. The two maximum on both sides of the source characterize the interaction between the plume and the ambient environment in particular the ambient air penetrates at the borders of the flow. In addition, as altitude Z* increases these maximum move away from the median plane (yOz) with a slight rise of the turbulence rate due to the plume expansion.

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0,3 Z * =0, 92 0.9

0,2

0.8

0,1

0.7 0.6

T*

0,0

0.5

0,3 Z * =0, 05

0.4

0,2

0.3 0.2

0,1

0.1

0,0 -1,0

0

-0,5

0,0

0,5

1,0

X* Fig. 5. Dimensionless thermal average field.

Fig. 10 presents the vertical evolution of the extrêma of the thermal turbulence rate. This figure makes it possible to consolidate the preceding observations. For levels near the hot source (Z* < 0.30), this rate does not exceed 9% in the entire plume. For superior levels (Z*  0.30), the turbulence decreases and the difference between the maximum and the minimum intensity is almost constant. This indicates the establishment of turbulence in this region. However, the general form of these profiles is similar to that one found by J.M. Agator [20] in the study of a thermal plume induced by a spherical calotte. The study of the flatness and skewness factors allows the characterization of the difference between the probability density law governing the fluctuations distribution of the flow temperature

0,6

and the ideal Gaussian probability for which the flatness and skewness factors are respectively F ¼ 3 and S ¼ 0. The repartition of these factors is plotted in Fig. 11. In the central region of the first zone (Z* ¼ 0.05), the flatness factors values are superior to 3. The maxima of thermal flatness Ft translate the existence of the intermittency phenomenon between the plume and the ambient air. Also, they correspond to the predominance of the more laminar aspect of the flow in this region. In addition, this figure shows negative values of skewness factor on the median plane (yOz). These values translate an existence of a puff fresh air coming from outside to supply the plume. A positive skewness shows the predominance of the hot plume. On both sides of the source, zero skewness indicates an equiprobability of the presence of the hot air coming from the plume and the ambient air. Higher (Z*  0.30), the flatness factors are close to value 3 and practically zero skewness. This indicates that the distribution of the temperature fluctuations is close to a Gaussian distribution in these regions.

Z* =0, 92

0,4

0,03

0,6 Free plume

0,2 0,4

0,02

0,2

0,01

0,3 Z* =0, 05

H*

Qv *

U*

0,0

0,2 0,1 0,0 0,0

0,0 -1,0

-0,5

0,0 X*

0,5

Fig. 6. Dimensionless dynamic average field.

1,0

0,00 0,2

0,4

Z* Qv*

0,6

0,8

1,0

H*

Fig. 7. Vertical evolution of the dimensionless flow rate and the energy absorptive by the fluid.

T. Naffouti et al. / Applied Thermal Engineering 30 (2010) 1632e1643

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5,0 8.5

4,5

Z* = 0 , 9 2

7.5

4,0 6.5

3,5

I t (% )

5.5

4.5

3,0 9 Z* = 0 , 0 5

8

3.5

7 2.5

6 5

1.5

4 0.5

3 -1,0

-0,5

0,0

0,5

1,0

X* Fig. 8. Thermal turbulent intensity.

3.2. Thermal plume flow in interaction with its material environment 3.2.1. Flow visualization Fig. 12 shows that the plume and the canal walls supply themselves regularly in fresh air by the low. The fresh air arriving from outside, by every side of the hot source, divides into three fluid

50 Z * = 0 , 9 2

40

30

threads. The first thread and its symmetrical in relation to the median plane, pursues its path directly towards the central part of the flow to form an impenetrable envelope at the sides above the hot source. The second thread pursued its path directly towards the flow central region while forming a vortex which exhausts vertically. In fact, when the vortex exhausts, the thread is repelled towards the wall to continue its way along this one. Simultaneously, the symmetrical thread undergoes the important attractive effect of the plume during the formation of the vortexes. The second thread, relatively near to the canal wall, undergoes at the start a strong attraction by the plume before coming back to supply the flow along the canal walls. Elsewhere, we remarked that the ascending flow undergoes a transversal contraction above the hot source, and then it enlarges to reach the walls. From this level, this visualization shows the appearance of new flow behaviour where a small structure occupies all the upper part of the canal. The

9

Free plume

8

10 50

7 Z * = 0 , 0 5

40

It (%)

I d (%)

20

30

6 5 4 3

20

2 10 -1,0

-0,5

0,0 X*

0,5

Fig. 9. Dynamic turbulent intensity.

1,0

0,0

0,2

0,4

0,6

0,8

Z* I max

Itmin

Fig. 10. Vertical evolution of thermal turbulence rate extrêma.

1,0

T. Naffouti et al. / Applied Thermal Engineering 30 (2010) 1632e1643

Fd

1638

12 10 8 6 4 2 0 8

Ft

6

Z*=0,05

Z*=0,92

4 2 0

1,8 1,2 0,6 0,0 -0,6

Sd

Fig. 12. Thermal plume inside canal visualization.

St

1,8 1,2 0,6 0,0 -0,6 -1,0

-0,5

0,0 X*

0,5

1,0

Fig. 11. Evolution of thermal and dynamic flatness and skewness factors.

existence of these turbulent dissipating structures leads to a uniform flow in the canal exit. In this region, the visualization shows the absence of the ascending flow blocking noticed by Jamil Zinoubi et al. [31] in the cylindrical geometry study. This qualitative description enables us to suppose the existence of three zones which characterize the vertical evolution of the flow inside the canal (Fig. 7). In the first zone, we attend the development of a flow strongly influenced by the hot source. This behaviour changes completely in the second zone where a plume contraction takes place, whereas the flow becomes homogeneous in the upper part of the canal. 3.2.2. Average characteristics of the flow The isotherms of the dimensionless average temperature measured in transverse plane (xOz) inside the canal are plotted in Fig. 13. Contrary to the free plume, these isotherms show the existence of three different evolutions. Near the hot source, this figure confirms the existence of the impenetrable envelope signalled during the visualization and shows a low temperature on both sides of the source. These low temperatures reflect the arrival of fresh air from outside to supply the system only by the low. In the central region of the flow the temperatures are strong due to the predominance of the hot plume. However, we note the absence of rotating rollers noticed by A.O.M. Mahmoud et al. [29] and J. Zinoubi et al. [31] on the study of the thermal plume evolution inside a vertical cylinder. One moved away of the source, these isotherms show a contraction of the flow followed a lateral expansion. Additionally, this figure shows the persistence of the fluid threads even in this zone. Higher, a third zone where the thermal field is everywhere homogeneous in the upper part of the canal. In same Fig. 13, the average profiles of the temperature are presented for three sections each one in a zone. These profiles show three different evolutions. In the first zone and for the section Z* ¼ 0.05, the fresh air warms up quickly and reaches important

temperatures above the source. On both sides of the median plane (yOz), the profile shows strong thermal gradients translating a brutal transformation of the fresh air into hot plume. In intermediate space between the source and the vertical walls of the canal, the fresh air dominates the flow except close to the walls where we record a light rise of temperature due to the heating of these last by thermal radiation of the hot source. In the second zone and for level Z* ¼ 0.20, the profile shows an attenuation of the temperature in the canal central region accompanied by a flow contraction. For a higher level (Z* ¼ 0.92), a noticeable uniformity of the flow temperature is registered. This thermal homogenisation of the flow is due to the establishment of a new mode in upper part of the canal. Fig. 14 shows the transverse distribution dimensionless average velocity of the flow inside the canal. Therefore, we can distinguish three different zones of the flow announced previously. In the first zone close to source (Z* ¼ 0.05), the profile shows very strong velocity gradients on both sides of the hot source. This translates the existence of the supply puff which envelope the plume. The minimum of velocity observed in the vicinity of the median plane of the source indicates the existence of a weak circulation region of the fluid. In the second zone of the flow and for a level Z* ¼ 0.20, this profile shows a clear acceleration of the flow in the central region. This acceleration is related to the flow contraction in this zone. In the third zone and for the upper level Z* ¼ 0.92, the velocity profile becomes more flattened and the dynamic gradients are weak. The vertical evolution of the flow rate and the energy absorbed by the fluid are plotted in Fig. 15. The profiles show the conservation of these parameters from the entry to exit of the canal. Compared to the free plume, we note an increase of the flow rate and the amount energy absorbed by the fluid in the canal. For that configuration, the thermosiphon intervenes to activate the mixture of the fluid and to push it towards the upper side. However, A.O.M. Mahmoud et al. [29] and J. Zinoubi et al. [21,32], showed an increase of the flow rate by studying the evolution of a thermal plume generated by a hot disc placed at the entry of a vertical cylinder. 3.2.3. Fluctuating characteristics of the flow In Fig. 16 is presented the thermal turbulent intensity iso-values measured in a transversal plane (xOz). This figure confirms the existence of three different zones. Near the hot source, the turbulence rates are very weak on both sides of the source due to the existence of the supply puff. On the other hand, in the central region, the turbulence increase is related to the predominance of the buoyancy forces. Downstream, the turbulence rates increase thus translate the pre-establishment of turbulence in a second zone

T. Naffouti et al. / Applied Thermal Engineering 30 (2010) 1632e1643

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0,3

Z*=0,92 0.9

0,2

0.8

0,1

0.7

0,0 0,3

Z*=0,20

0.6

T*

0,2

0.5

0,1

0.4

0,0 0,3

Z*=0,05

0.3

0,2 0.2

0,1 0.1

0,0 -1,0

0

-0,5

0,0

0,5

1,0

X* Fig. 13. Dimensionless average thermal iso-values.

of the resulting flow. In the upper zone of the canal, the turbulent rate variation is relatively weak thus indicating the establishment of turbulence. The profiles relating to the transverse distribution of the thermal turbulent intensity for three sections, each one in a zone is plotted in same Fig. 16. In first zone and for level Z* ¼ 0.05, the profile of turbulence rate shows the existence of three extrêma. The minimum on the median plane of the canal is due to a weak

1,00

Z*=0,92 0,75 0,50 0,25 0,00 1,00 0,75

Z*=0,20

circulation region of the flow inside the impenetrable envelope announced previously. The two peaks correspond to the flow regions where the transverse thermal gradients are maxima. In the vicinity of the canal walls, the turbulence rates are relatively low due to the predominance of the laminar mode in this region. In the intermediate zone and for level Z* ¼ 0.20, the turbulence rate increases in the central region above the hot source. The maxima of turbulence are related to the cycle formation and exhaust of the vortexes at the top of the envelope. In addition, for the level Z* ¼ 0.92, the fluctuating profile is flattened in all upper part of the canal. This indicates the turbulence establishment in third zone of the flow. The transverse distribution of the dynamic turbulent intensity is presented in Fig. 17. Therefore, we can distinguish three different evolutions of the flow. Indeed, in first zone of flow and for level Z* ¼ 0.05, the profile shows the existence of two maximum of dynamic turbulence rates near the median plane (yOz). These maximum corresponds to a strong interaction between the plume

0,09

1,8

0,50

H

0,25

1,2

0,00 1,00

0,06

Z*=0,05

H*

0,75

*

* QV

U*

*

QV

0,6

0,03

0,50 0,25 0,00 -1,0

0,0

-0,5

0,0

0,5

X* Fig. 14. Transversal repartition of dimensionless average velocity.

1,0

0,00 0,0

0,2

0,4

0,6

0,8

1,0

Z* Fig. 15. Vertical evolution of the dimensionless flow rate and the energy absorptive by the fluid.

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5,0 8.5

Z*=0,92

4,5 4,0

7.5

3,5 6.5

3,0 7

Z*=0,20

5.5

I t (%)

6

4.5

5 4

3.5

3 9

Z*=0,05

8

2.5

7 6

1.5

5 4

0.5

3 -1,0

-0,5

0,0

0,5

1,0

X* Fig. 16. Thermal turbulent intensity iso-values.

and the supply puff coming from the ambient environment. The minimum of dynamic turbulence on the median plane is due to a weak circulation of the resulting flow inside the envelope described previously. On both sides of the source, the turbulence rates are very weak about 2%. This indicates the existence of a flow laminar mode. The profile relating to the intermediate zone Z* ¼ 0.20 shows a reduction of the dynamic turbulent rate about 30% in the central region of the flow. In addition, the dynamic turbulent intensity increases relatively near to the canal walls. This

60

Z*=0,92 40 20

increase of turbulence shows a strong interaction between the supply puff, that continues to persist in this zone, and the vortexes exhaust. In third zone and for level Z* ¼ 0.92, the fluctuating dynamic profile becomes more flattened thus translating the turbulence establishment in the upper part of the canal. Fig. 18 shows the extrêma vertical evolution of thermal turbulence rate. These profiles confirm the existence of three zones of the resulting flow. In first zone near to the hot source (Z* < 0.16) the turbulence rates do not exceed 6%. In second zone (0.16  Z*  0.52) the turbulence intensity increases due to the appearance of a new mode of turbulence pre-establishment. In third zone (0.52 < Z*) the turbulence remains uniform about 4%. Otherwise, the difference between the intensity of the peak and that of the minimum is maintained at constant value. This indicates the turbulence establishment in the upper part of the canal. However, the general form of these profiles is similar to that one found by J. Zinoubi et al. [35] in the study of development of an axisymmetric thermal plume between vertical plates.

0 60

7 Plume in interaction

40

6 20

It ( % )

Id (% )

Z*=0,20

0 60

5

Z*=0,05 40

4

20 0 -1,0

3 0,0 -0,5

0,0

0,5

X* Fig. 17. Dynamic turbulent intensity.

1,0

0,2

0,4

0,6

0,8

Z*

It max

It min

Fig. 18. Vertical evolution of thermal turbulence rate extrêma.

1,0

0,35

1641

-b-

Z*=0,92

5,9

-d-

4,1 4,1

0,21

9,6

0,14 7,88

0,07

2,7

0,00 0,12

Z*=0,05

-a-

Z*=0,05

-c-

0,09

Z*=0,05 Z*=0,20 Z*=0,92

0,06

1,3

0,03

1,9

0,00 0,1

1

10

0,1 n(Hz)

Free plume

1,8 1,2 0,6 0,0 -0,6

1

10

Plume in interaction

Fig. 20. Power spectral density of the temperature fluctuations.

St

-1,0

Z*=0,92

0,28

nE(n)

12 10 8 6 4 2 0 6 5 4 3 2 1 0 4 3 2 1 0 -1

-0,5

0,0

0,5

1,0

X* Fig. 19. Evolution of thermal and dynamic flatness and skewness factors.

The vertical evolution of the thermal and dynamic flatness and skewness factors is plotted in Fig. 19. The skewness and flatness factors of the temperature fluctuations show that the latter have a nearly Gaussian distribution in the third zone where the turbulence is fully developed, but that deviates gradually in the other region. For a level Z* ¼ 0.05, the negative skewness indicates the arrival in a regular way of cool air coming from outside. This air supplies the source of the plume and the flow along the hot canal walls. For a level Z* ¼ 0.20, the values of thermal and dynamic flatness factors are strong on both sides of the median plane (yOz). These values translate the existence of the intermittency phenomenon between the plume flow and the supply fresh air. On both sides of median plane, the positive values of the thermal skewness factors characterize the hot air puffs transported by the plume towards a region where the temperature is lower. The high values of the dynamic skewness factors show the predominance of a positive fluctuation induced by a flow of strong velocity which interacts with the plume at the source border. For a level Z* ¼ 0.92, the skewness factors are practically zero close to canal walls. This shows an equiprobability of the existence of the plume and the supply puffs air that continue their way even in the upper part of the canal. Indeed, at the moment of the transverse expansion of the plume in this region, we notice the entrainment of hot air by this supply puffs during its ascension. This shows the absence of the flow blocking noticed by J. Zinoubi et al. [33] in the study of a thermal plume evolving in a vertical cylinder. 3.3. Spectral analysis of the thermal fluctuations

coordinate permits the setting in evidence of the spectral strips containing a considerable energy, while taking in consideration the delimited areas by the spectra [21,32,42]. For the free plume, and near the hot source (Z* ¼ 0.05), most of the energy is concentrated in a rather broad frequency band centred around 1.3 Hz. This indicates that the proportion of the big vortexes increases in front of that of the small structures. Higher of the source (Z* ¼ 0.92), Fig. 20b shows the appearance of a new secondary peaks and a displacement of the spectra towards high frequencies around 6 Hz. This shows that the flow reached a turbulent mode in this region where the dissipative vortexes structures are dominant [21]. For the flow plume in interaction with the thermosiphon, the general displacement of the thermal spectra towards the highest frequencies is observed (about 9 Hz). This translates the increase of the proportion of the small dissipative vortexes due to the confinement effect which comes to accelerate the homogeneity of the resulting flow. The vertical evolution of the spectral density of thermal energy is plotted in Fig. 21. For the free plume, the profile confirms the existence of two zones of the flow structure. A first zone near the

1,0 0,9 0,8 0,7 0,6 E(n)

Sd

Ft

Fd

T. Naffouti et al. / Applied Thermal Engineering 30 (2010) 1632e1643

0,5 1,0 0,9 0,8 0,7

In order to better contribute in the comprehension of the fine structure of turbulent flow, it is interesting to analyze the spectra of thermal fluctuations. This spectral analysis gives more information on the size and frequency of vortex structures as they are related [39e41]. Fig. 20 presents the thermal spectra for two different levels (Z* ¼ 0.05 and Z* ¼ 0.92). This representation in a semi-logarithmic

0,6 0,5 0,0

0,2 Free plume

0,4

Z*

0,6

0,8

1,0

Plume in interaction

Fig. 21. Vertical evolution of power spectral density of the temperature fluctuations.

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T. Naffouti et al. / Applied Thermal Engineering 30 (2010) 1632e1643

hot source is characterized by a very strong production of energy which indicates the predominance of the big vortexes structures (Z* < 0.30). A second zone characterized by the energy transfer towards the small vortexes (Z*  0.30). When the plume interacts with the thermosiphon, the profile consolidates the three different evolutions noticed previously. Close to hot source and for low levels Z* < 0.16, the spectral energy is maximum translating a strong production of energy by the large vortexes which develop at the entrance of the system. For intermediary levels 0.16 < Z* < 0.50 the energy decreases as we move away from the hot source due to energy transfer towards the averages vortexes. Further from source (Z*  0.50), the energy becomes weak and stabilized thus indicating the preponderance of the dissipative vortexes structures in this region. This shows that the confinement effect undergoes the successive destruction of the large vortexes to give rise to increasingly small vortexes inside the canal.

4. Conclusion The results mentioned in this article are a first contribution to knowledge the structure of a thermal plume generated by a rectangular source heated by Joule effect at a uniform temperature. In this work, we exposed the results of the thermal plume evolving in an unlimited and in a semi-confined environment. For a thermal plume which develops in a free and unlimited environment, the visualization as well as the average and fluctuating fields shows that the global structure of the flow is divided into two zones. Near the hot source, a first zone of plume development. In this region, the source is supplied in fresh air by the low and by the sides. Higher of the source, a second zone of transversal expansion of the plume is noted. In addition, we noticed that the energy absorbed by the fluid remains constant and the flow rate increases as we move away from the generating source. However, the spectral analysis of the temperature fluctuations showed that the proportion of the big vortexes structures is dominant compared to that of small structures. In order to identify the confinement effect on a thermal plume, we studied its development inside a canal to walls flat. The experimental results have shown a change of the structure of the flow in comparison to the case of the free plume. This confinement affects considerably the flow structure in particular at the entry of the system and limits the expansion of the plume in the upper part of the canal. Indeed, these results have shown the appearance of a supplementary zone that is added to the two zones of the free plume. In the first zone where an impenetrable envelope in the sides is formed, the flow development is strongly influenced by the hot source. This behaviour changes completely in the second zone where the flow is contracted. In the third zone the flow is homogenised in the upper part of the canal. In addition, visualization and isotherms and skewness factors show that the supply puffs air continue their way even in the upper part of the canal. This indicates the absence of the flow blocking observed in the cylindrical geometry. In order to better quantify and fully interpret such influence, results from a free plume case were compared with those obtained under confined plume; we noticed that the confinement effect causes an increase of the flow rate and an intensification of thermal energy. However, the spectral analysis showed an increase of the proportion of the smaller sizes vortexes by the confinement effect which comes to accelerate the homogeneity of the ascending flow. Indeed, the thermosiphon which interacts with the plume undergoes the successive destruction of the large vortexes structures carrying energy to give rise a dissipative smaller structures at the exit of the canal.

This experimental work brings many interesting information on the development mechanisms of the thermal plumes. Thus, this study can enable us to control the free fires and the fires in interaction with their material environment. Nomenclature A b1 b2 Cp Df E (n) Fat Fad Fdt Fdd g Gr Gr* H H* It Id L2 L1 L2 Lf n Qv Q*v T T0 Ta Ts T* U U0 U* Uref (x,y,z) X* Z*

b v

r r0 r*

shape ratio (A ¼ b2/L2) source width, m canal half-width, m specific heat, J kg1 K1 sensitive wire diameter, m energy spectral density pffiffiffiffiffiffiffi 4 thermal flatness factors ðFt ¼ T 04 =ð p T 02 Þ Þ ffiffiffiffiffiffiffi 02 Þ4 Þ dynamic flatness factors ðFd ¼ U 04 =ð pUffiffiffiffiffiffi ffi 3 03 thermal skewness factors ðSt ¼ T =ð p T 02 Þ Þ ffiffiffiffiffiffiffi dynamic skewness factors ðSd ¼ U 03 =ð U 02 Þ3 Þ gravitational acceleration, m s2 Grashof number ðGr ¼ g bðTs  Ta Þb42 =L2 n2 Þ modified Grashof number (Gr* ¼ AGr) energy absorbed by the fluid Rb ðH ¼ L2 Cp b2 2 ruðT  Ta ÞdxÞ, W dimensionless energy absorbed by the fluid R1 * T * dX * Þ ðH * ¼ H=r0 Cp Uref ðTs  Ta Þb2 L2 ¼ 1 r* Up ffiffiffiffiffiffiffi 02 =T  T Þ thermal turbulent intensity of flow ðIt ¼ p Tffiffiffiffiffiffiffi s a dynamic turbulent intensity of flow ðId ¼ U 02 =UÞ height of the canal, m length of the source, m length of the canal, m length of the sensitive wire, m frequency, Hz Rb flow rate of the flow ðQv ¼ L2 b2 2 uðxÞdxÞ, m2 s2 dimensionless flow rate of the flow R1 Qv* ¼ Qv =U ref b2 L2 ¼ 1 U * dX * average temperature, K fluctuation of the temperature, K temperature of the ambient air, K temperature of the hot source, K dimensionless temperature ðT * ¼ T  Ta =Ts  Ta Þ average velocity of the flow, m s1 velocity fluctuating, m s1 dimensionless average velocity of the flow ðU * ¼ U=Uref Þ reference velocity ðUref ¼ L2 nðGr* Þ1=2 =b22 Þ, m s1 Cartesian coordinates dimensionless coordinate ðX * ¼ x=b2 Þ dimensionless height ðZ * ¼ z=L2 Þ thermal expansion coefficient, K1 kinematic fluid viscosity, m2 s1 air density at average temperature, kg m3 air density at ambient temperature, kg m3 air density ratio ðr* ¼ r=r0 Þ

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