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Influence of the vertical source–cylinder spacing on the interaction of a thermal plume with a thermosiphon flow: an experimental study
Experimental Thermal and Fluid Science 28 (2004) 329–336 www.elsevier.com/locate/etfs
Influence of the vertical source–cylinder spacing on the interaction of a thermal plume with a thermosiphon flow: an experimental study Jamil Zinoubi, Rejeb Ben Maad *, Ali Belghith Facult e des Sciences de Tunis, D epartement de Physique, Laboratoire d’Energ etique et des Transferts de Chaleur et de Masse, 2092 Elmanar II, Tunis, Tunisia Received 1 March 2002; accepted 15 June 2003
Abstract The present work reports an experimental study of a turbulent natural convection flow resulting from the interaction of an axisymmetric thermal plume with a thermosiphon flow. A circular disk, heated by Joule effect at constant temperature (300 C), generates the plume. This disk is placed at the entrance of an open-ended insulated vertical cylinder of a larger diameter. Thermal radiation emitted by the hot disk heats the cylinder wall. The pressure reduction due to the acceleration of the flow at the cylinderinlet generates a thermosiphon around the thermal plume which modifies its global structure considerably. In this paper we expose results of the experimental study related to the heating source position. We study particularly the effects of the source–cylinder spacing on the flow structure. A comparative study is presented for different configurations. This study is based on experimental results concerning the average and fluctuating fields. These results are analysed and discussed in order to understand more deeply the flow development mechanisms generated by buoyancy forces. The use of thermal and dynamic factors of flatness and skewness allow a better knowledge of the flow fine structure. 2003 Elsevier Inc. All rights reserved. Keywords: Turbulent natural convection; Thermal plume; Plume–thermosiphon interaction; Rotating rolls
1. Introduction The problem of interaction of the turbulent plume with its environment generates very complex mechanisms [1,2]. The study of the flow resulting from this interaction contributes to a good general feature description. This kind of flow, encountered in fires of buildings or forests and in industrial chimney exits, has been the object of several studies. Pera and Gebhart [3] studied plume–plume and plume–enclosure interactions. Some authors tried to explain mechanisms of interaction based on the limited supply of cool air in the region situated between plumes. Mery et al. [4], while studying the behaviour of plumes penetrating in the surrounding atmosphere, measured the over-heights of plumes coming from industrial chimneys. Thereafter, Agator [5] examined the influence of the presence of a vertical wall
*
Corresponding author. E-mail addresses: [email protected] [email protected] (R. Ben Maad).
(J.
Zinoubi),
0894-1777/$ - see front matter 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0894-1777(03)00111-0
placed very close to a thermal plume generated by a hemispherical source. He also studied the influence of a second plume identical to the precedent one. He noted a flow deviation of the plume toward the enclosure and an intensification of the air entrainment between the two sources. All previous works offer an important scientific contribution to theoretical and experimental studies of the interaction between a thermal plume and its environment. However, one can note a lack of information concerning the interaction of the plume with a thermosiphon. This type of flow, found in fires of high rise buildings (stairwell or elevator shaft), has been studied recently by Mahmoud et al. [1,2]. They studied a thermal plume flow developing in a vertical cylinder for a configuration that insures a supply of cool air from below. They noted the appearance of a supplementary zone, just at the system entrance, that is added to the two classic zones mentioned in the previous works [3–5], concerning free plume. They also noted an increase of the amount of energy absorbed by the fluid and of the flow rate inside the cylinder.
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J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
Nomenclature A Ft g Gr Gr It Iv L r r1 r0 R R St T T
shape ratio of cylinder A ¼ rL1 PN 1 ðTi T Þ4 flatness factor Ft ¼ 1NPNi¼1 2 2 ðN
i¼1
ðTi T Þ Þ
gravitational acceleration m s2 gbðTs Ta Þr13 Grashof number Gr ¼ 2 m modified Grashof number ðGr AÞ ¼ pGr ffiffiffiffi02ffi T thermal turbulent intensity It ¼ Ts Ta pffiffiffiffi 02 dynamic turbulent intensity Iv ¼ uu cylinder height, m radial coordinate, m radius of cylinder, m radius of disc, m dimensionless radial coordinate R ¼ rr1 radius ratio R ¼ rr01 ! PN 1 ðT T Þ3 N i¼1 i skewness factor St ¼ PN 3=2 1 ðT T Þ2 N i¼1 i a dimensionless average temperature T ¼ TTsT Ta average temperature, C
The present study adds to the work of Mahmoud et al. [1,2] by studying the influence of the relative vertical source position at the cylinder entrance on the resulting flow (Fig. 1). Our experimental work concerns thermal and dynamic average and fluctuating fields for different vertical source positions. The thermal intermittency phenomenon is analysed and discussed using thermal flatness factor to show essential consequences of the interaction. This allows a better knowledge of the fine flow structure.
T0 Ta Ti Ts Tp Tr u u0 uref U
temperature fluctuating, C ambient temperature, C instantaneous values of temperature, C temperature of disc, C mean temperature of the cylinderwalls, C T T reference temperature Tr ¼ p 2 a vertical average component velocity, m s1 1 velocity fluctuating, ms 1=2 reference velocity uref ¼ LmGrr2 1 dimensionless vertical component velocity u U ¼ uref
Z Z1
vertical coordinate, m dimensionless coordinate Z1 ¼ Lz
Greek symbols m kinematics fluid viscosity, m2 s1 b thermal expansion coefficient, K1 q air density at average temperature, kg m3 q0 air density at ambienttemperature, kg m3 q density ratio q ¼ qq0
mation. Al–Cr thermocouples are used to measure the surface temperature of the disk. The temperature difference between the end and the centre of the disc is less than 5 C. The vertical cylinder is thermally insulated by an Armaflex cylindrical bed which has a thickness of 0.02 m (4).
2. Experimental apparatus The experimental apparatus is shown in Fig. 1. The numbers in the description presented below refer to the part numbers of Fig. 1. The thermal plume is created by a flat disk (1) having a diameter of 0.07 m. It is electrically heated by Joule effect to a surface temperature of 300 C. The disk is placed at the entrance of the open ended steel vertical cylinder (2) which has a diameter of 0.15 m and height of 0.5 m. The system is placed on a frame 80 cm above the ground to allow air supply from below (3). The uniformity of the source surface temperature is obtained by the use of wire resistors mounted behind the disk. A thermal regulation apparatus keeps the temperature of the disk as uniform as possible within a good approxi-
Fig. 1. Experimental configuration.
J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
The strong dependence of the flow on the surrounding conditions requires conducting the experiment in a quiet atmosphere. To this effect the experimental device is placed in an independent closed room. To explore the thermal and the dynamic average fields inside the cylinder, the resistant wire anemometer (5) at constant current (6) is used. This technique adopted for a long time by Doan Kim-Son et al. [6,14], in natural convection, is based on the principle of the resistance variation of a platinum wire (7.5 lm in diameter). The velocity and the temperature of the fluid are the two parameters that change the electric resistance of the wire. Doan Kim-Son et al. [14] showed that a supply current of 1.2 mA makes the probe solely sensitive to the temperature (cold wire), and a supply current of 38 mA, makes it sensitive to the temperature and the velocity (hot wire). The probe calibration allows the determination of the velocity and the temperature of the flow from the voltage across the probe [14,15]. In order to avoid the disruption of the flow, the probe is introduced vertically, through the system exit, so that its sensitive wire is perpendicular to the ascending flow. The wire thermal inertia (the wire time constant is of the order of 1 ms) does not introduce any measurement errors, especially at the low frequencies found in plumes [5,11]. Errors due to the probe calibration are lower than 1%. A computer driven displacement system (7), 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 103 m, whereas in the horizontal direction it is 2 · 105 m. A computer (8) equipped with a data acquisition card acquires instantaneous signal values at 10 ms intervals and records the digitized signals for further statistical processing.
3. Experimental results The experimental study is carried out in the particular case of Gr ¼ 1:56 107 , A ¼ 0:15 and R ¼ 0:46. In order to determine the reference parameters, the physical properties of the fluid are evaluated at a reference temperature (Tr ).
Fig. 2. Plume with thermosiphon: contraction of the plume.
Fig. 3. Plume with thermosiphon: formation of the rotation rolls.
the development of two rotating rolls symmetrical to the plume axis. In the intermediary zone ð5 cm < z 6 15 cmÞ, we observe a contraction of the plume and an ascending strong axial flow caused by buoyancy forces. In the third zone (z > 15 cm), this visualization shows the appearance of new flow behaviour where a dissipating small structures occupies all the upper part of the cylinder. The existence of these turbulent dissipating structures leads to a uniform flow in the cylinder exit. On the other hand, when the source moves away from the cylinder entrance, the flow visualization shows a progressive decrease of the rotating rolls size. Indeed, for h ¼ 6 cm, it shows a comparable structure to the free plume one (Figs. 4 and 5).
3.1. The flow visualization The flow visualization performed by illuminating the flow by a plane laser sheet reveals the evolution of the flow from the cylinder entry to its exit. It indicates the existence of three different structure zones of the flow vertical development (Figs. 2 and 3). Therefore, in the first zone in the vicinity of the hot source (z 6 5 cm), the instantaneous photos showed, above the hot disc,
331
Fig. 4. Thermal plume with thermosiphon (h ¼ 6 cm).
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J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
first zone near the hot source, a strong acceleration of the flow is observed. This is due to the relative great importance of the buoyancy forces which dominate the flow in this zone. The velocity maximum is reached when a balance of the buoyancy forces and viscous forces occurs. From this level a deceleration process of the flow starts. This process characterises the second zone of the flow. When approaching the third zone, the velocity and the temperature decrease slowly with a low longitudinal gradient. Figs. 6 and 7 also show that the shape and the amplitude profiles change when the vertical source–cylinder spacing increases. In particular a progressive increase of the axial velocity in the first zone is observed.
Fig. 5. Free plume.
3.2. Thermal and dynamic average fields 3.2.1. Axial evolution The axial evolution of the dimensionless mean temperature and velocity of the flow are plotted in Figs. 6 and 7. These figures indicate several behaviours. In the
3.2.2. Radial evolution In the following we present results concerning the first zone (Z1 ¼ 0:04) and the third zone (Z1 ¼ 0:6) of the flow only. Fig. 8 presents the radial distribution of the dimensionless average temperature of the flow for different vertical spacing h. In the first zone (Fig. 8a), the profile
1.0
0.8
Taxe
0.7
0.6 0.6 0.5
0.4
0.4
T
0.2 0.3
0.0 0.0
0.2
0.4
0.6
0.2
0.8
Z1 h = - 5 cm[1,2]
h = 2 cm
0.1
h = 6 cm
Free plume[1,2]
Fig. 6. Axial evolution of the dimensionless average temperature of the flow.
0.0 -1.0
-0.5
(a)
0.5
1.0
R h = - 5 cm[1,2]
0.5
0.0
Z1 = 0.04 h = 2 cm h = 6 cm
Free plume[1,2]
0.2
0.4
T
Uaxis
0.3 0.1
0.2
0.1
0.0 -1.0
0.0 0.0
0.2
0.4
0.6
0.8
1.0
-0.5
(b)
h = 2 cm
h = 6 cm
Free plume[1,2]
Fig. 7. Axial evolution of the dimensionless average vertical component velocity of the flow.
0.5
1.0
R
Z1 h = - 5 cm[1,2]
0.0
h = - 5 cm [1,2]
Z1 = 0.6 h = 2 cm
h = 6 cm
Free plume[1,2]
Fig. 8. Radial evolution of the dimensionless average temperature of the flow.
J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
3.3. Thermal and dynamic turbulent intensity The results concerning the thermal and dynamic fluctuating fields for different spacing h, for the first zone (Z1 ¼ 0:04) and the third zone (Z1 ¼ 0:6) of the flow are presented in Figs. 10 and 11. These profiles show clearly the effect of the vertical source–cylinder
0.25
0.20
U
0.15
0.10
0.05
0.00 -1.0
-0.5
(a)
0.0
R Z 1= 0.04 h = 2 cm
h = - 5 cm [1,2]
0.5
h = 6 cm
1.0
Free plum e[1,2]
0.3
0.2
U
has three extrema with a minimum on the axis and two symmetrical maxima centred at the plume axis. These temperature maxima are attributed to the development of two rotating rolls on the hot disk area [1,2]. In fact, at the source contact, the ambient air is rapidly heated, its density decreases strongly and its viscosity increases. We expect a strong acceleration of the flow. During its ascension, the fluid is blocked by the plume air feeding in the central region. The trapped fluid continues to turn. Then, two symmetrical rotating rolls are formed around the axis. When this air mass acquires a sufficient energy, it escapes vertically. The temperature falls on the plume axis due to the strong penetration of fresh outside air. These profiles show an important transverse gradient on each side of the maximum. This strong gradient results from the transformation of the ambient air to a hot plume in the region close to the source. On the other hand, as the source moves away from the cylinder entrance, temperature maxima come closer to the axis, to give a profile with an only one maximum for h ¼ 6 cm. For the third zone (Z1 ¼ 0:6), where the turbulence is fully developed, the temperature profiles become flat with a low transverse gradient and the structure of three extrema disappears (Fig. 8b). The radial evolution of the vertical component of the dimensionless average velocity for different spacing, h, is shown in Fig. 9. These profiles present different aspects of the global flow structure. In the first stage, close to the hot source (Z1 ¼ 0:04), Fig. 9a shows an acceleration of the flow in the side of the hot source and a deceleration in the central part. The velocity maxima result from the interaction between the plume and the thermosiphon that surrounds it. The existence of a low fluid circulation in the neighbourhood of the source axis shows that the movement is decelerated in this region. When the source–cylinder spacing grows, these profiles show a progressive increase of the velocity in the central region. Indeed, for h ¼ 6 cm, these profiles present only one maximum on the axis. This structure is comparable to free plume one, that is characterised by an important vertical velocity at the vicinity of the plume axis and relatively low at the hot source sides. In the higher part of the cylinder (Z1 ¼ 0:6) and h P 0, Fig. 9b shows the appearance of a new flow structure where the velocity profiles present an only one maximum on the axis. For h ¼ 5 cm, these profiles show the uniformity of the flow velocity in the entire cylindrical section.
333
0.1
0.0 -1.0
(b) h = - 5 cm[1,2]
-0.5
0.0
R Z 1= 0.6 h = 2 cm
0.5
h = 6 cm
1.0
Free plume[1,2]
Fig. 9. Radial evolution of the dimensionless average vertical component velocity of the flow.
spacing on the turbulent structure of the flow. In fact, at smaller heights (Z1 ¼ 0:04), Figs. 10a and 11a show the existence of the three-extrema profiles with a minimum on the axis and two symmetrical maxima around the plume axis. The relative peaks in the thermal turbulent intensity correspond to the plume region where the transversal thermal gradients are maximum. This indicates that the interaction with ambient air is more important. However, the two dynamic turbulent intensity maxima correspond to the plume region where the interaction with a source air feeding is maximal. The turbulence rate minimum is caused by the existence of the low fluid circulation in the neighbourhood of the source axis. These profiles also show that maxima of the thermal and dynamic turbulence intensity come progressively closer to the axis as the source moves away from the cylinder entrance. For a higher level (Z1 ¼ 0:6), Figs. 10b and 11b show profiles that are more flattened than those observed for the lower positions. A reduction of the thermal and dynamic turbulence rates in the central part is also observed.
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J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
12
50 10
40
Iv (%)
It (%)
8
6
30
20 4
10 2
0 -1.0
-0.5
(a)
0.0
0.5
1.0
0 -1.0
-0.5
(a)
h = - 5 cm[1,2]
0.5
1.0
R
R Z1= 0.04 h = 2 cm h = 6 cm
0.0
h = - 5 cm[1,2]
Z1= 0.04 h = 2 cm h = 6 cm
Free plume[1,2]
Free plume[1,2] 60
12 50
10 40
Iv (%)
It (%)
8
6
30
20
4 10
2 0 -1.0
0 -1.0
-0.5
(b)
0.0
0.5
1.0
h = - 5 cm[1,2]
h = - 5 cm[1,2]
h = 6 cm
Free plume[1,2]
Fig. 10. Radial evolution of the thermal turbulent intensity of the flow.
0.0
0.5
1.0
R
R Z1= 0.6 h = 2 cm
-0.5
(b)
Z1= 0.6 h = 2 cm
h = 6 cm
Free plume[1,2]
Fig. 11. Radial evolution of the dynamic turbulent intensity of the flow.
3.4. Temperature flatness and skewness 60
45
Ft
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 and the ideal gaussian probability for which the flatness and skewness factors are respectively Ft ¼ 3 and St ¼ 0. The radial evolution of the thermal flatness and skewness factors for different configurations are shown respectively in Figs. 12 and 13. For the level near the source (Z1 ¼ 0:04) and in regions where the turbulence intensity is maximum, these figures show that the distribution of the temperature fluctuations is close to a gaussian distribution. In these regions, a zero skewness indicates an equiprobability of the presence of the hot air coming from the plume and the ambient air. The negative skewness indicates the arrival in a regular way of cool air coming from outside. This air supplies the source of the plume in a region close to its axis and the flow along the hot cylinder wall. Also, high values of the thermal and dynamic flatness factor correspond to regions of the flow where the interaction between the
30
15
0 -1.0
-0.5
0.0
0.5
1.0
R h = - 5 cm[1,2]
Z1= 0.04 h = 2 cm h = 6 cm
Free plume[1,2]
Fig. 12. Radial evolution of the thermal flatness factor of the flow.
plume and the ambient air is the most important [6]. According to Compte-Bellot [7,8] and Milliat [9], these values would be associated with the intermittency phenomenon.
J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
335
This flow rate must be constant throughout the cylinder for every configuration. The heat absorbed by the fluid rising in the cylinder from the entrance to a particular elevation can be given a dimensionless form as Rr Z 1 2pCp 0 1 qurðT Ta Þ dr ¼2 q URT dR Ht ¼ pq0 Cp LmGr1=2 ðTs Ta Þ 0
12 10 8
St
6 4 2 0 -2 -1.0
-0.5
0.0
0.5
1.0
R Z1= 0.04 h = 2 cm h = 6 cm
h = - 5 cm[1,2]
Free plume[1,2]
Fig. 13. Radial evolution of the thermal skewness factor of the flow.
For different cases, the vertical evolution of the dimensionless energy absorbed by the fluid and the flow rate inside the cylinder are given in Figs. 15 and 16. For each configuration, these profiles show that the absorbed energy and the flow rate remained constant. On the other hand, when the vertical source–cylinder spacing decreases, these figures show an increase of the absorbed energy and the flow rate inside the cylinder. This improvement is due to significant thermal radiation emitted by the hot disc and absorbed by the cylinder wall, which induces a stronger thermosiphon effect.
0.8 0.20
Z1
0.6
0.15
0.4
Qv
0.2
0.0 -1.0
-0.5
0.0
0.5
0.10
0.05
1.0
R h = - 5 cm
h = 2 cm
h = 6 cm
Free plume 0.00 0.0
Fig. 14. Geometric location of the thermal flatness factor maxima.
0.2
0.4
0.6
0.8
Z1 h = - 5 cm[1.2]
The intermittency results from the interaction between the plume flow and the enveloping thermosiphon [10–13]. It provides information about more or less turbulent regions of the flow. It also indicates the degree of penetration of laminar fluid from outside. To describe these plume borders we plot the geometric location of these maxima (Fig. 14). When examining this figure we can discern the different zones of the flow.
h = 2 cm
h = 6 cm
Free plume
Fig. 15. Vertical evolution of the dimensionless flow rate.
0.8 0.7 0.6
Ht .10
3.5. Vertical evolution of the flow rate and the energy absorbed by the fluid
3
0.5 0.4 0.3
In order to get more information about the source position effect on the resulting flow, the dimensionless flow rate Qv and the energy absorbed by the fluid Ht , have been determined from the average profiles. The dimensionless volume flow rate inside the cylinder is given as Rr Z 1 2p 0 1 ruðrÞ dr ¼ 2 UR dR Qv ¼ pmLGr1=2 0
0.2 0.1 0.0 0.0
0.2
0.4
0.6
0.8
Z1 h = - 5 cm [1.2]
h = 2 cm
h = 6 cm
Free plume
Fig. 16. Vertical evolution of the dimensionless energy absorbed by the fluid.
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J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
A comparative study with the free plume results, shows that h ¼ 5 cm is an ideal position that improves flow rate and intensifies the energy absorption inside the cylinder.
[2]
[3]
4. Conclusion [4]
This study investigates the influence of the vertical source–cylinder spacing on the thermosiphon effect around a thermal plume. The analysis of the average and fluctuating fields, for different spacing, improves our understanding of the development mechanism of the resulting flow. A decrease of the source–cylinder spacing leads to • a considerable change of the plume global structure, • an improvement of the flow rate, • an increase of the absorbed energy by the fluid. However, the increase of the source–cylinder spacing causes an additional lateral intake of air, creating a similar structure to a free plume. The present study also shows, that h ¼ 5 cm, is a optimum position, that provides good homogenisation of the flow at the system exit. The integration of this system at an industrial chimney exit, with an adequate location, will improve the dispersion of air pollution reach.
[5]
[6]
[7]
[8] [9] [10]
[11] [12]
[13]
[14]
References [15] [1] A.O.M. Mahmoud, R.B. Maad, A. Belghith, Interaction d’un ecoulement de thermosiphon avec un panache thermique a
symetrie axiale: etude experimentale, Rev. Gen. Therm. 37 (1998) 385–396. A.O.M. Mahmoud, Etude de l’interaction d’un panache thermique a symetrie axiale avec un ecoulement de thermosiphon, These de Doctorat, Universite de Tunis II, Faculte des Sciences de Tunis, 1998. L. Pera, B. Gebhart, Laminar plume interactions, J. Fluid Mech. 68 (1975) 259–271. P. Mery, A. Hodin, M. Ribon, Estimation des surhauteurs du panache de cheminees industrielles, IFCE, Le tirage et la dispersion des fumees, Xeme Journees Internationales, Paris La Defense, Compte Rendu, Tome II, 1975. J.M Agator, Contribution a l’etude de la structure turbulente d’un panache thermique a symetrie axiale, Interaction du panache avec son environnement limite, These, Universite de Poitiers, 1983. Doan Kim-Son, Contribution a l’etude de la zone de transition et de la zone de turbulence etablie dans un ecoulement de convection naturelle sur une plaque plane verticale isotherme, These de Doctorat d’Etat, Universite de Poitiers, 1977. G. Compte-Bellot, The use of a contraction to improve the isotropy of grid-generated turbulence, J. Fluid Mech. 25 (part 4) (1966) 657–682. G. Compte-Bellot. These Doct. Es Sc., Grenoble, 1963. J.P. Milliat. Publ. Sc. Tech., no. 335, Paris, 1957. M. Brahimi, L. Dehmani, Doan Kim-Son, Structure turbulente de l’ecoulement d’interaction de deux panaches thermiques, Int. J. Heat Mass Transfer 32 (1989) 1551–1559. M. Brahimi, Structure turbulente des panaches thermiques-interaction, These, Universite de Poitiers, 1987. M. Brahimi, Doan Kim-Son, Experimental and numerical predictions of the mean flow of a turbulent pure plume, Arch. Mech. Warszawa 38 (1986) 519–528. M. Brahimi, M. Lamour, Doan Kim-Son, Champs moyens et fluctuants des panaches thermiques isoles ou en interaction, Rev. Gen. Therm. 315–316 (1988) 236–243. Doan-Kim-Son, M. Stage, J. Coutanceau, Transfert de chaleur entre un fil anemometrique court et un ecoulement permanent a faible vitesse, Rev. Gen. Therm. 168 (1975) 951–956. R. Ben Maad, Etude d’un ecoulement de convection naturelle dans un canal vertical chauffe, These d’Etat, Universite de Tunis, 1995.
Influence of the vertical source–cylinder spacing on the interaction of a thermal plume with a thermosiphon flow: an experimental study Jamil Zinoubi, Rejeb Ben Maad *, Ali Belghith Facult e des Sciences de Tunis, D epartement de Physique, Laboratoire d’Energ etique et des Transferts de Chaleur et de Masse, 2092 Elmanar II, Tunis, Tunisia Received 1 March 2002; accepted 15 June 2003
Abstract The present work reports an experimental study of a turbulent natural convection flow resulting from the interaction of an axisymmetric thermal plume with a thermosiphon flow. A circular disk, heated by Joule effect at constant temperature (300 C), generates the plume. This disk is placed at the entrance of an open-ended insulated vertical cylinder of a larger diameter. Thermal radiation emitted by the hot disk heats the cylinder wall. The pressure reduction due to the acceleration of the flow at the cylinderinlet generates a thermosiphon around the thermal plume which modifies its global structure considerably. In this paper we expose results of the experimental study related to the heating source position. We study particularly the effects of the source–cylinder spacing on the flow structure. A comparative study is presented for different configurations. This study is based on experimental results concerning the average and fluctuating fields. These results are analysed and discussed in order to understand more deeply the flow development mechanisms generated by buoyancy forces. The use of thermal and dynamic factors of flatness and skewness allow a better knowledge of the flow fine structure. 2003 Elsevier Inc. All rights reserved. Keywords: Turbulent natural convection; Thermal plume; Plume–thermosiphon interaction; Rotating rolls
1. Introduction The problem of interaction of the turbulent plume with its environment generates very complex mechanisms [1,2]. The study of the flow resulting from this interaction contributes to a good general feature description. This kind of flow, encountered in fires of buildings or forests and in industrial chimney exits, has been the object of several studies. Pera and Gebhart [3] studied plume–plume and plume–enclosure interactions. Some authors tried to explain mechanisms of interaction based on the limited supply of cool air in the region situated between plumes. Mery et al. [4], while studying the behaviour of plumes penetrating in the surrounding atmosphere, measured the over-heights of plumes coming from industrial chimneys. Thereafter, Agator [5] examined the influence of the presence of a vertical wall
*
Corresponding author. E-mail addresses: [email protected] [email protected] (R. Ben Maad).
(J.
Zinoubi),
0894-1777/$ - see front matter 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0894-1777(03)00111-0
placed very close to a thermal plume generated by a hemispherical source. He also studied the influence of a second plume identical to the precedent one. He noted a flow deviation of the plume toward the enclosure and an intensification of the air entrainment between the two sources. All previous works offer an important scientific contribution to theoretical and experimental studies of the interaction between a thermal plume and its environment. However, one can note a lack of information concerning the interaction of the plume with a thermosiphon. This type of flow, found in fires of high rise buildings (stairwell or elevator shaft), has been studied recently by Mahmoud et al. [1,2]. They studied a thermal plume flow developing in a vertical cylinder for a configuration that insures a supply of cool air from below. They noted the appearance of a supplementary zone, just at the system entrance, that is added to the two classic zones mentioned in the previous works [3–5], concerning free plume. They also noted an increase of the amount of energy absorbed by the fluid and of the flow rate inside the cylinder.
330
J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
Nomenclature A Ft g Gr Gr It Iv L r r1 r0 R R St T T
shape ratio of cylinder A ¼ rL1 PN 1 ðTi T Þ4 flatness factor Ft ¼ 1NPNi¼1 2 2 ðN
i¼1
ðTi T Þ Þ
gravitational acceleration m s2 gbðTs Ta Þr13 Grashof number Gr ¼ 2 m modified Grashof number ðGr AÞ ¼ pGr ffiffiffiffi02ffi T thermal turbulent intensity It ¼ Ts Ta pffiffiffiffi 02 dynamic turbulent intensity Iv ¼ uu cylinder height, m radial coordinate, m radius of cylinder, m radius of disc, m dimensionless radial coordinate R ¼ rr1 radius ratio R ¼ rr01 ! PN 1 ðT T Þ3 N i¼1 i skewness factor St ¼ PN 3=2 1 ðT T Þ2 N i¼1 i a dimensionless average temperature T ¼ TTsT Ta average temperature, C
The present study adds to the work of Mahmoud et al. [1,2] by studying the influence of the relative vertical source position at the cylinder entrance on the resulting flow (Fig. 1). Our experimental work concerns thermal and dynamic average and fluctuating fields for different vertical source positions. The thermal intermittency phenomenon is analysed and discussed using thermal flatness factor to show essential consequences of the interaction. This allows a better knowledge of the fine flow structure.
T0 Ta Ti Ts Tp Tr u u0 uref U
temperature fluctuating, C ambient temperature, C instantaneous values of temperature, C temperature of disc, C mean temperature of the cylinderwalls, C T T reference temperature Tr ¼ p 2 a vertical average component velocity, m s1 1 velocity fluctuating, ms 1=2 reference velocity uref ¼ LmGrr2 1 dimensionless vertical component velocity u U ¼ uref
Z Z1
vertical coordinate, m dimensionless coordinate Z1 ¼ Lz
Greek symbols m kinematics fluid viscosity, m2 s1 b thermal expansion coefficient, K1 q air density at average temperature, kg m3 q0 air density at ambienttemperature, kg m3 q density ratio q ¼ qq0
mation. Al–Cr thermocouples are used to measure the surface temperature of the disk. The temperature difference between the end and the centre of the disc is less than 5 C. The vertical cylinder is thermally insulated by an Armaflex cylindrical bed which has a thickness of 0.02 m (4).
2. Experimental apparatus The experimental apparatus is shown in Fig. 1. The numbers in the description presented below refer to the part numbers of Fig. 1. The thermal plume is created by a flat disk (1) having a diameter of 0.07 m. It is electrically heated by Joule effect to a surface temperature of 300 C. The disk is placed at the entrance of the open ended steel vertical cylinder (2) which has a diameter of 0.15 m and height of 0.5 m. The system is placed on a frame 80 cm above the ground to allow air supply from below (3). The uniformity of the source surface temperature is obtained by the use of wire resistors mounted behind the disk. A thermal regulation apparatus keeps the temperature of the disk as uniform as possible within a good approxi-
Fig. 1. Experimental configuration.
J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
The strong dependence of the flow on the surrounding conditions requires conducting the experiment in a quiet atmosphere. To this effect the experimental device is placed in an independent closed room. To explore the thermal and the dynamic average fields inside the cylinder, the resistant wire anemometer (5) at constant current (6) is used. This technique adopted for a long time by Doan Kim-Son et al. [6,14], in natural convection, is based on the principle of the resistance variation of a platinum wire (7.5 lm in diameter). The velocity and the temperature of the fluid are the two parameters that change the electric resistance of the wire. Doan Kim-Son et al. [14] showed that a supply current of 1.2 mA makes the probe solely sensitive to the temperature (cold wire), and a supply current of 38 mA, makes it sensitive to the temperature and the velocity (hot wire). The probe calibration allows the determination of the velocity and the temperature of the flow from the voltage across the probe [14,15]. In order to avoid the disruption of the flow, the probe is introduced vertically, through the system exit, so that its sensitive wire is perpendicular to the ascending flow. The wire thermal inertia (the wire time constant is of the order of 1 ms) does not introduce any measurement errors, especially at the low frequencies found in plumes [5,11]. Errors due to the probe calibration are lower than 1%. A computer driven displacement system (7), 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 103 m, whereas in the horizontal direction it is 2 · 105 m. A computer (8) equipped with a data acquisition card acquires instantaneous signal values at 10 ms intervals and records the digitized signals for further statistical processing.
3. Experimental results The experimental study is carried out in the particular case of Gr ¼ 1:56 107 , A ¼ 0:15 and R ¼ 0:46. In order to determine the reference parameters, the physical properties of the fluid are evaluated at a reference temperature (Tr ).
Fig. 2. Plume with thermosiphon: contraction of the plume.
Fig. 3. Plume with thermosiphon: formation of the rotation rolls.
the development of two rotating rolls symmetrical to the plume axis. In the intermediary zone ð5 cm < z 6 15 cmÞ, we observe a contraction of the plume and an ascending strong axial flow caused by buoyancy forces. In the third zone (z > 15 cm), this visualization shows the appearance of new flow behaviour where a dissipating small structures occupies all the upper part of the cylinder. The existence of these turbulent dissipating structures leads to a uniform flow in the cylinder exit. On the other hand, when the source moves away from the cylinder entrance, the flow visualization shows a progressive decrease of the rotating rolls size. Indeed, for h ¼ 6 cm, it shows a comparable structure to the free plume one (Figs. 4 and 5).
3.1. The flow visualization The flow visualization performed by illuminating the flow by a plane laser sheet reveals the evolution of the flow from the cylinder entry to its exit. It indicates the existence of three different structure zones of the flow vertical development (Figs. 2 and 3). Therefore, in the first zone in the vicinity of the hot source (z 6 5 cm), the instantaneous photos showed, above the hot disc,
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Fig. 4. Thermal plume with thermosiphon (h ¼ 6 cm).
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first zone near the hot source, a strong acceleration of the flow is observed. This is due to the relative great importance of the buoyancy forces which dominate the flow in this zone. The velocity maximum is reached when a balance of the buoyancy forces and viscous forces occurs. From this level a deceleration process of the flow starts. This process characterises the second zone of the flow. When approaching the third zone, the velocity and the temperature decrease slowly with a low longitudinal gradient. Figs. 6 and 7 also show that the shape and the amplitude profiles change when the vertical source–cylinder spacing increases. In particular a progressive increase of the axial velocity in the first zone is observed.
Fig. 5. Free plume.
3.2. Thermal and dynamic average fields 3.2.1. Axial evolution The axial evolution of the dimensionless mean temperature and velocity of the flow are plotted in Figs. 6 and 7. These figures indicate several behaviours. In the
3.2.2. Radial evolution In the following we present results concerning the first zone (Z1 ¼ 0:04) and the third zone (Z1 ¼ 0:6) of the flow only. Fig. 8 presents the radial distribution of the dimensionless average temperature of the flow for different vertical spacing h. In the first zone (Fig. 8a), the profile
1.0
0.8
Taxe
0.7
0.6 0.6 0.5
0.4
0.4
T
0.2 0.3
0.0 0.0
0.2
0.4
0.6
0.2
0.8
Z1 h = - 5 cm[1,2]
h = 2 cm
0.1
h = 6 cm
Free plume[1,2]
Fig. 6. Axial evolution of the dimensionless average temperature of the flow.
0.0 -1.0
-0.5
(a)
0.5
1.0
R h = - 5 cm[1,2]
0.5
0.0
Z1 = 0.04 h = 2 cm h = 6 cm
Free plume[1,2]
0.2
0.4
T
Uaxis
0.3 0.1
0.2
0.1
0.0 -1.0
0.0 0.0
0.2
0.4
0.6
0.8
1.0
-0.5
(b)
h = 2 cm
h = 6 cm
Free plume[1,2]
Fig. 7. Axial evolution of the dimensionless average vertical component velocity of the flow.
0.5
1.0
R
Z1 h = - 5 cm[1,2]
0.0
h = - 5 cm [1,2]
Z1 = 0.6 h = 2 cm
h = 6 cm
Free plume[1,2]
Fig. 8. Radial evolution of the dimensionless average temperature of the flow.
J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
3.3. Thermal and dynamic turbulent intensity The results concerning the thermal and dynamic fluctuating fields for different spacing h, for the first zone (Z1 ¼ 0:04) and the third zone (Z1 ¼ 0:6) of the flow are presented in Figs. 10 and 11. These profiles show clearly the effect of the vertical source–cylinder
0.25
0.20
U
0.15
0.10
0.05
0.00 -1.0
-0.5
(a)
0.0
R Z 1= 0.04 h = 2 cm
h = - 5 cm [1,2]
0.5
h = 6 cm
1.0
Free plum e[1,2]
0.3
0.2
U
has three extrema with a minimum on the axis and two symmetrical maxima centred at the plume axis. These temperature maxima are attributed to the development of two rotating rolls on the hot disk area [1,2]. In fact, at the source contact, the ambient air is rapidly heated, its density decreases strongly and its viscosity increases. We expect a strong acceleration of the flow. During its ascension, the fluid is blocked by the plume air feeding in the central region. The trapped fluid continues to turn. Then, two symmetrical rotating rolls are formed around the axis. When this air mass acquires a sufficient energy, it escapes vertically. The temperature falls on the plume axis due to the strong penetration of fresh outside air. These profiles show an important transverse gradient on each side of the maximum. This strong gradient results from the transformation of the ambient air to a hot plume in the region close to the source. On the other hand, as the source moves away from the cylinder entrance, temperature maxima come closer to the axis, to give a profile with an only one maximum for h ¼ 6 cm. For the third zone (Z1 ¼ 0:6), where the turbulence is fully developed, the temperature profiles become flat with a low transverse gradient and the structure of three extrema disappears (Fig. 8b). The radial evolution of the vertical component of the dimensionless average velocity for different spacing, h, is shown in Fig. 9. These profiles present different aspects of the global flow structure. In the first stage, close to the hot source (Z1 ¼ 0:04), Fig. 9a shows an acceleration of the flow in the side of the hot source and a deceleration in the central part. The velocity maxima result from the interaction between the plume and the thermosiphon that surrounds it. The existence of a low fluid circulation in the neighbourhood of the source axis shows that the movement is decelerated in this region. When the source–cylinder spacing grows, these profiles show a progressive increase of the velocity in the central region. Indeed, for h ¼ 6 cm, these profiles present only one maximum on the axis. This structure is comparable to free plume one, that is characterised by an important vertical velocity at the vicinity of the plume axis and relatively low at the hot source sides. In the higher part of the cylinder (Z1 ¼ 0:6) and h P 0, Fig. 9b shows the appearance of a new flow structure where the velocity profiles present an only one maximum on the axis. For h ¼ 5 cm, these profiles show the uniformity of the flow velocity in the entire cylindrical section.
333
0.1
0.0 -1.0
(b) h = - 5 cm[1,2]
-0.5
0.0
R Z 1= 0.6 h = 2 cm
0.5
h = 6 cm
1.0
Free plume[1,2]
Fig. 9. Radial evolution of the dimensionless average vertical component velocity of the flow.
spacing on the turbulent structure of the flow. In fact, at smaller heights (Z1 ¼ 0:04), Figs. 10a and 11a show the existence of the three-extrema profiles with a minimum on the axis and two symmetrical maxima around the plume axis. The relative peaks in the thermal turbulent intensity correspond to the plume region where the transversal thermal gradients are maximum. This indicates that the interaction with ambient air is more important. However, the two dynamic turbulent intensity maxima correspond to the plume region where the interaction with a source air feeding is maximal. The turbulence rate minimum is caused by the existence of the low fluid circulation in the neighbourhood of the source axis. These profiles also show that maxima of the thermal and dynamic turbulence intensity come progressively closer to the axis as the source moves away from the cylinder entrance. For a higher level (Z1 ¼ 0:6), Figs. 10b and 11b show profiles that are more flattened than those observed for the lower positions. A reduction of the thermal and dynamic turbulence rates in the central part is also observed.
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12
50 10
40
Iv (%)
It (%)
8
6
30
20 4
10 2
0 -1.0
-0.5
(a)
0.0
0.5
1.0
0 -1.0
-0.5
(a)
h = - 5 cm[1,2]
0.5
1.0
R
R Z1= 0.04 h = 2 cm h = 6 cm
0.0
h = - 5 cm[1,2]
Z1= 0.04 h = 2 cm h = 6 cm
Free plume[1,2]
Free plume[1,2] 60
12 50
10 40
Iv (%)
It (%)
8
6
30
20
4 10
2 0 -1.0
0 -1.0
-0.5
(b)
0.0
0.5
1.0
h = - 5 cm[1,2]
h = - 5 cm[1,2]
h = 6 cm
Free plume[1,2]
Fig. 10. Radial evolution of the thermal turbulent intensity of the flow.
0.0
0.5
1.0
R
R Z1= 0.6 h = 2 cm
-0.5
(b)
Z1= 0.6 h = 2 cm
h = 6 cm
Free plume[1,2]
Fig. 11. Radial evolution of the dynamic turbulent intensity of the flow.
3.4. Temperature flatness and skewness 60
45
Ft
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 and the ideal gaussian probability for which the flatness and skewness factors are respectively Ft ¼ 3 and St ¼ 0. The radial evolution of the thermal flatness and skewness factors for different configurations are shown respectively in Figs. 12 and 13. For the level near the source (Z1 ¼ 0:04) and in regions where the turbulence intensity is maximum, these figures show that the distribution of the temperature fluctuations is close to a gaussian distribution. In these regions, a zero skewness indicates an equiprobability of the presence of the hot air coming from the plume and the ambient air. The negative skewness indicates the arrival in a regular way of cool air coming from outside. This air supplies the source of the plume in a region close to its axis and the flow along the hot cylinder wall. Also, high values of the thermal and dynamic flatness factor correspond to regions of the flow where the interaction between the
30
15
0 -1.0
-0.5
0.0
0.5
1.0
R h = - 5 cm[1,2]
Z1= 0.04 h = 2 cm h = 6 cm
Free plume[1,2]
Fig. 12. Radial evolution of the thermal flatness factor of the flow.
plume and the ambient air is the most important [6]. According to Compte-Bellot [7,8] and Milliat [9], these values would be associated with the intermittency phenomenon.
J. Zinoubi et al. / Experimental Thermal and Fluid Science 28 (2004) 329–336
335
This flow rate must be constant throughout the cylinder for every configuration. The heat absorbed by the fluid rising in the cylinder from the entrance to a particular elevation can be given a dimensionless form as Rr Z 1 2pCp 0 1 qurðT Ta Þ dr ¼2 q URT dR Ht ¼ pq0 Cp LmGr1=2 ðTs Ta Þ 0
12 10 8
St
6 4 2 0 -2 -1.0
-0.5
0.0
0.5
1.0
R Z1= 0.04 h = 2 cm h = 6 cm
h = - 5 cm[1,2]
Free plume[1,2]
Fig. 13. Radial evolution of the thermal skewness factor of the flow.
For different cases, the vertical evolution of the dimensionless energy absorbed by the fluid and the flow rate inside the cylinder are given in Figs. 15 and 16. For each configuration, these profiles show that the absorbed energy and the flow rate remained constant. On the other hand, when the vertical source–cylinder spacing decreases, these figures show an increase of the absorbed energy and the flow rate inside the cylinder. This improvement is due to significant thermal radiation emitted by the hot disc and absorbed by the cylinder wall, which induces a stronger thermosiphon effect.
0.8 0.20
Z1
0.6
0.15
0.4
Qv
0.2
0.0 -1.0
-0.5
0.0
0.5
0.10
0.05
1.0
R h = - 5 cm
h = 2 cm
h = 6 cm
Free plume 0.00 0.0
Fig. 14. Geometric location of the thermal flatness factor maxima.
0.2
0.4
0.6
0.8
Z1 h = - 5 cm[1.2]
The intermittency results from the interaction between the plume flow and the enveloping thermosiphon [10–13]. It provides information about more or less turbulent regions of the flow. It also indicates the degree of penetration of laminar fluid from outside. To describe these plume borders we plot the geometric location of these maxima (Fig. 14). When examining this figure we can discern the different zones of the flow.
h = 2 cm
h = 6 cm
Free plume
Fig. 15. Vertical evolution of the dimensionless flow rate.
0.8 0.7 0.6
Ht .10
3.5. Vertical evolution of the flow rate and the energy absorbed by the fluid
3
0.5 0.4 0.3
In order to get more information about the source position effect on the resulting flow, the dimensionless flow rate Qv and the energy absorbed by the fluid Ht , have been determined from the average profiles. The dimensionless volume flow rate inside the cylinder is given as Rr Z 1 2p 0 1 ruðrÞ dr ¼ 2 UR dR Qv ¼ pmLGr1=2 0
0.2 0.1 0.0 0.0
0.2
0.4
0.6
0.8
Z1 h = - 5 cm [1.2]
h = 2 cm
h = 6 cm
Free plume
Fig. 16. Vertical evolution of the dimensionless energy absorbed by the fluid.
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A comparative study with the free plume results, shows that h ¼ 5 cm is an ideal position that improves flow rate and intensifies the energy absorption inside the cylinder.
[2]
[3]
4. Conclusion [4]
This study investigates the influence of the vertical source–cylinder spacing on the thermosiphon effect around a thermal plume. The analysis of the average and fluctuating fields, for different spacing, improves our understanding of the development mechanism of the resulting flow. A decrease of the source–cylinder spacing leads to • a considerable change of the plume global structure, • an improvement of the flow rate, • an increase of the absorbed energy by the fluid. However, the increase of the source–cylinder spacing causes an additional lateral intake of air, creating a similar structure to a free plume. The present study also shows, that h ¼ 5 cm, is a optimum position, that provides good homogenisation of the flow at the system exit. The integration of this system at an industrial chimney exit, with an adequate location, will improve the dispersion of air pollution reach.
[5]
[6]
[7]
[8] [9] [10]
[11] [12]
[13]
[14]
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