comparison of heat transfer characteristics in a sudden pipe expansion ... · zohir a. e. and abdel...

Journal of Engineering Sciences, Assiut University, Vol. 34, No. 4, pp. 1239-1253, July 2006

COMPARISON OF HEAT TRANSFER CHARACTERISTICS IN A SUDDEN PIPE EXPANSION WITH UPSTREAM AND

DOWNSTREAM PULSATING SYSTEM _____________________________________________________________________

Zohir A. E. Mechanical Engineering Department, Tabbin Institute for Metallurgical Studies, Cairo, Egypt

Abdel Aziz A. A.

Mechanical Engineering Department, Shoubra Faculty of Engineering, Benha University, Cairo, Egypt

(Received May 6, 2006. Accepted May 31, 2006)

ABSTRACT– The present work aimed to study experimentally the heat transfer characteristics of pulsating turbulent flow in abrupt pipe expansion with constant wall heat flux. The combined effect of sudden pipe expansion and pulsation frequency on the heat transfer was carried out for both locations of pulsating system (upstream and downstream) when the upstream flow was unheated and fully developed. The experiments were made for upstream small diameter (d) to downstream large diameter (D) ratios of 0.32, 0.49, and 0.61 and Reynolds number range of 7760 to 40084 (based on test section diameter D) and frequency range of 1.4 to 13 Hz. In absence of pulsation, the relative mean Nusselt number of sudden pipe expansion increases as the diameter ratio (d/D) decreases. The pulsation frequency has a small significant effect on the relative mean Nusselt number for any d/D values. The enhancement obtained by d/D = 0.32 is greater than that obtained by the other higher values of d/D. The downstream pulsator gives more enhancement in heat transfer than that of upstream pulsator for all values of studied pulsation frequencies with d/D = 0.61 and Re = 14005. For d/D = 0.32 and 0.49, the enhancement due to the upstream pulsator is higher than that obtained by the downstream pulsator. Flow visualization technique was used to view the flow separation, recirculation, and reattachment to support the thermal results. The experimental correlations of the relative mean Nusselt number (Nupm/Nuom) with different diameter ratios are developed in terms of the dimensionless frequency and the Reynolds number.

KEYWORDS: Pulsating Flow – Sudden Expansion – Heat Transfer Characteristics.

1. INTRODUCTION

A well-known method to improve the heat transfer from a smooth pipe is to apply an axisymmetric sudden expansion. A number of experimental investigations

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Zohir A. E. and Abdel Aziz A. A. ________________________________________________________________________________________________________________________________ 1240

NOMENCLATURE

Symbols Units Cpm Specific heat of fluid at mean temperature J/kg oC d Test section upstream diameter m. D Test section downstream diameter m. F Pulsation frequency Hz fb Turbulence bursting frequency Hz H Step height, H = 0.5(D-d) m km Thermal conductivity of the fluid W/m.K L Test section pipe length m.

.

m Mass flow rate kg/s

N Revolution per minute of the rotating valve spindle rpm Num Mean Nusselt number for sudden expansion without

pulsation Dimensionless

Nuom Mean Nusselt number for smooth pipe without pulsation Dimensionless Nuox Local Nusselt number for smooth pipe without pulsation Dimensionless Nupm Pulsated mean Nusselt number with sudden pipe

expansion Dimensionless

Nupx Local pulsated Nusselt number with sudden pipe expansion

Dimensionless

Nupx/Nuox Relative local pulsated Nusselt number with sudden expansion

Dimensionless

Nupx/Nux Local pulsated Nusselt number ratio Dimensionless Nurm Relative mean Nusselt number, Nurm = Nupm/Nuom Dimensionless Nur Mean Nusselt number ratio, Nur = Nupm/Num Dimensionless Nux Local Nusselt number for sudden expansion without

pulsation Dimensionless

Nufd The fully developed Nusselt number at constant mass flow rate

Dimensionless

Nus* The fully developed Nusselt number at constant pumping power

Dimensionless

qo Net heat flux = Qnet/πdoL W/m2 Q Input heat rate W

Heat loss through the insulation W Qnet Net of heat transferred to the test section W Tbi Fluid bulk inlet temperature oC Tbo Fluid bulk outlet temperature oC

Tbulk Fluid bulk temperature oC

Tbx Bulk temperature of the fluid at section x oC

U* Friction velocity, U* = 0.199um/ Re0.125 m/s

Greek Symbols

Ω Angular frequency of pulsation, ω = 2πf rad/s ω* Dimensionless frequency, ω* = ωD/U* Dimensionless ωb Angular bursting frequency rad/s ωbm Mean angular bursting frequency rad/s

COMPARISON OF HEAT TRANSFER CHARACTERISTICS IN…. ________________________________________________________________________________________________________________________________

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have been published on the heat transfer characteristics in downstream axisymmetric sudden expansion pipes[1-3]. Also, some numerical investigations [4,5] have been applied to solve the problem. For example, in some engineering applications (heat exchanger (corrugated tubes), combustion chambers, and chemical mixing equipment), flow separation occurs and heat transfer characteristics are often significantly altered by the nature of the flow separation and subsequent flow redevelopment.

In 2003, Manica and Bortoli [6] analyzed incompressible Newtonian and non-Newtonian fluids flow through channels with sudden expansion. Effect of pulsation on heat transfer remains a problem of interest to researchers due to its wide existence in industry. The operation of modern power-producing facilities and industrial equipment used in metallurgy, aviation, chemical and food technology, and other technologies are governed to a large extent by pulsation flows. Cavitations in hydraulic pipelines, pressure surges and flow parameters affect the performance of many thermal engineering applications. Most of the previous investigators considered a small number of the operating variables (such as Reynolds number, amplitude, and pulsation frequency) in their studies.

The flow characteristics in the turbulent pulsating flow were studied by many investigators [7,8] to clarify the influence of pulsation on the flow velocity and the pressure distribution. Some investigators [9], found that there is a bursting phenomenon that occurs in the steady turbulent flow in form of periodic turbulent bursts. These turbulent bursts are significantly affected with the imposed pulsation; as a result the heat transfer is affected also. The effect of pulsation on the turbulent flow has been discussed by in [7]. However, very little is known about the heat transfer characteristics of the pulsating flows. From the previous work, it can be observed that, due to the variety of heat transfer control parameters, conflicting results for the effect of pulsation on heat transfer are obtained. Some investigators reported increase in heat transfer from pulsated flow [10] whereas, reduction in heat transfer was reported by Genin et al and Laio & Wang, [7, 9]. In some cases, both increase and reduction were reported in a single experiment [11]. Thus, in order to have a complete understanding of introducing pulsation into a flow with heat transfer, it is necessary to consider various parameters and cover a wide range of the controlling parameters.

In 2000, Zephyr [12] investigated experimentally the effect of pulsation on heat transfer characteristics through smooth pipe in absence of sudden expansion under different conditions of Reynolds number varied from 750 to 50000, pulsation frequency (f) ranging from 1 to 30 Hz, pulsator location (upstream and downstream), and tube diameter. The results showed that the relative mean Nusselt number is strongly affected by both pulsation frequency, pulsator location, and Reynolds number. The maximum increase in mean Nusselt number was about 50% which was achieved at f = 10 Hz for Re of 8462 and also at pulsation frequency of 22.8 Hz for Reynolds number of 14581.

El-Shazly et. al., [13] investigated experimentally the influence of pulsation frequency in addition to sudden pipe expansion on the local and average Nusselt number. Pulsator system was located downstream of an axisymmetric abrupt expansion pipe. With low Reynolds number (Re=7760), the mean Nusselt number increased up to 138% at f=10 Hz and d/D=0.61. A numerical investigation aimed at understanding the flow and heat transfer characteristics for the pulsating turbulent flow in abrupt pipe


expansion is carried out in 2003 by Said et. al., [14]. For all pulsation frequency, as the diameter ratio increases the mean time averaged Nu ratio increases and reaches a peak at a diameter ratio of 0.5 and then decreases for further increase in the diameter ratio.

The present investigation is concerned with the heat transfer enhancement characteristics of turbulent pulsation flow through a sudden pipe expansion. Experiments were carried out to determine both the entrance and fully developed local Nusselt number distributions. The pulsated flow was produced by locating the pulsator upstream of test section. The pulsating frequency ranged from 1.4 to 13 Hz and Reynolds number (7760 to 40084) with three selected values of the d/D (0.61, 0.49, and 0.32). Flow visualization (using smoke tunnel) technique was used to indicate clearly the qualitative characteristics of flow (separation, reattachment point, and recirculation zone) through sudden expansion pipe with different diameter ratios.

2. TEST RIG AND INSTRUMENTATION

Study of the heat transfer characteristics of pulsating airflow through the sudden pipe expansion was carried out by a specially designed test rig. The flow system consists of an air supply unit (air blower of 7 hp and air flow control unit), an orifice meter, settling chamber, upstream, calming tube, test section, downstream calming tube and pulsating mechanism (Figure 1). The test section, as shown in Figure 2a, consists of a main pipe, heaters, and insulating materials. In general, the test section tube was covered by a layer of Teflon sheet of 0.2 mm thickness and employed to insulate the tube electrically. The wire of the heaters was electrically insulated by very ductile Teflon pipes of 0.1 mm thickness and 2 mm diameter and then wound uniformly along the tube with about 1 mm pitch to achieve a uniform heat flux. Heating elements were made of nickel chromium wire type, which has a resistance of 4.35 Ω/m and 0.6 mm diameter. Sheets of aluminum of 0.2 mm thickness were wound below and above the heater wires to distribute the heat uniformly. Then a layer of glass wool insulation of 50 mm thickness was employed to cover the pipe. The total heat loss from the heaters was calculated and found to be less than 6% of the total heat input. The main tube of the test section was made of stainless steel of 82 mm inner diameter, 2000 mm length and 3.5 mm thickness.

The surface temperatures have been measured by 49 thermocouples of K-type (having about 0.3 mm wire diameter). The thermocouples were located at different axial positions along the tube as shown in Figure 2b. The non-uniform axial thermocouple spacing ranged from 5 mm near the abrupt expansion corner to 200 mm near the exit of the large diameter. Most of the axially distributed thermocouples were at the top mid-plane of the tube. However, five additional thermocouples, placed at other angular locations, were used to check the symmetry of the heat transfer to the flow. The pulsating mechanism shown in Figure 3 was constructed of three main parts, an AC electric motor of 3/4 hp and 1000 rpm, a variable speed transmission (three stepped pulleys), and a rotating ball valve of 50 mm inner diameter. The valve spindle was connected to the motor through three-stepped pulleys and two V-belts as a transmission. The frequency of pulsation (f) is defined as f = (2*N/60) in Hz. The dimensionless frequency for the turbulent pulsating flow is calculated from

** /UDωω = as defined by Gibson and Diakoumakos [8].


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1. Air blower 6. Orifice meter 10. Transmission mechanism 2. By-pass valve 7. Downstream tube of orifice (D= 100mm) 11. AC electric motor 3. Flow control valve 8. Settling chamber (D = 500 mm) 12. Upstream calming tube (d=82, 50, 37.5, 25 mm) 4. Flexible connection 9. Pulsator valve 13. Test section (D = 82 mm). 5. Upstream tube (Diameter = 100 mm)

Figure 1: The layout of the turbulent flow test rig.

Figure 2a: The test section details.

Figure 2b: Thermocouple distributions on the downstream smooth pipe.

70 mm

24 Tc* 5 mm 4 Tc * 25 mm 3 Tc * 50 mm 3 Tc * 75 mm 3 Tc * 100 mm 3 Tc * 150 mm

2 Tc * 200 mm

265 mm

X

100 mm

135 mm 175 mm 150 mm 225 mm

Flow

1 2 3

4 5 6

7 8 9

10

12

13

11

2 3 4

1. Stainless steel of 82 mm inner diameter 2. Electric Heaters 3. Insulation 4. Flange 5. Tephlon Piston

Dimensions in mm

82

89

194

2000

1

5


1. Downstream calming tube. 2. The pulsator. 3. Stepped pulley.

4. Stepped pulley. 5. V-belts. 6. AC electric motor.

Figure 3: The layout of the pulsation mechanism.

The net heat transferred by convection to the flowing fluid can be calculated from equation (1). The local mean bulk temperatures of the fluid flowing into the test

section are calculated from equation (2) where oq.

is the net average heat flux. The

local heat transfer coefficient and Nusselt numbers are calculated from equations (3) and (4). The mean Nusselt number can be calculated from equation (5).

)()(.

bibopmlossnet TTCmQQQ −=−= (1)

Tbx=Tbi +qoπDLs/mCpm (2)

)/(.

bxsxox TTqh −= (3)

)( bxsxm

ox TTk

DqNu

−= (4)

∫=L

xm

mean dxhLk

DNu

0

(5)

4. RESULTS AND DISCUSSION

Before initiating experiments with upstream pulsating flow, the local Nusselt numbers were measured for a sudden expansion pipe with different diameter ratios and compared with the downstream pulsated turbulent air flow that was investigated by El-Shazly et. al., [13]. The results are presented in the form of relative local Nusselt number (Nupx/Nuox) where Nupx is the local Nusselt number of the pulsated flow through the sudden pipe expansion and Nuox is the corresponding value of the steady


1245

unpulsated flow through the smooth pipe without sudden expansion. Figure 4 shows the variation of the relative local Nusselt number (Nux/Nuox) without pulsation for sudden expansion ratio d/D = 0.61. Stream-wise distance is normalized by the step height H (H = 0.5(D-d)). At the leading edge of the test section, the (Nux/Nuox) approaches the unity and downstream the sudden expansion it increases to a peak value as moving away from the sudden expansion where the flow is reattached to the pipe surface. The (Nux/Nuox) increases beyond unity in the region upstream the reattachment because of the recirculation zones which appear near the sudden expansion. At recirculation zones, the boundary layers are destroyed by the formation of back flow in these zones so the heat transfer is increased. The (Nux/Nuox) then decreases as the axial distance (x/H) is increased and approaches to be nearly constant at the beginning of the fully developed region. The maximum enhancement reaches about 115 % for Re = 7760 and about 74 % for Re = 40084 and occurs at x/H = 7.2. Figure 5 illustrates the variation of (Nux/Nuox) versus axial distance for various expansion ratios. It is observed that as the expansion ratio (d/D) increases decreases, the relative local Nusselt number ratio increases and the reattachment length increases (distance from sudden abrupt to the flow impingement point). Because of the growth up of the thermal boundary layer, the (Nux/Nuox) ratio decreases gradually downstream the impingement point.

At constant Re Figures 6, 7, and 8 show the variations of (Nupx/Nuox) versus axial distance for different values of pulsation frequency (upstream pulsator system) at d/D = 0.61, 0.49, and 0.32, respectively. Upstream the reattachment point the maximum enhancement of the (Nupx/Nuox) takes place at f =10, 10, and 4.1 Hz for d/D = 0.61, 0.49, and 0.32, respectively, while through the downstream region, the maximum corresponding enhancement was found at f = 1.4, 10, and 4.1, respectively. The local (Nupx/Nuox) ratios have the same fashion for different values of pulsation frequency. The local (Nupx/Nuox) ratio increases sharply to a peak value at about x/H = 6.5 , 7.0, and 7.5 for d/D=0.61, 0.49, and 0.32, respectively.

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

2.1

2.3

0 10 20 30 40 50 60 70 80x/H

Nu x

/Nu o

x

Re_7760 Re_14005 Re_19255 Re_30469 Re_40084

0.3

0.8

1.3

1.8

2.3

2.8

3.3

3.8

0 10 20 30 40 50 60 70 80

x/H

Nu x

/Nu o

x

d/D = 0.32 d/D = 0.49 d/D = 0.61

Figure 4: Variation of relative local Nusselt number versus the axial distance for different values of (Re) in absence of pulsation (d/D = 0.61, f = 0 Hz).

Figure 5: Variation of relative local Nusselt number versus the axial distance for different values of d/D in absence of pulsation (Re = 7760, f = 0 Hz).


0

0.5

1

1.5

2

2.5

3

0 10 20 30 40 50 60

x/H

Nu p

x/N

u ox

f=0 f=1.4 f=4.1 f=6 f=10 f=13

0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30 35 40 45

x/H

Nu p

x/N

u ox

f=0 f=1.4 f=4.1 f=6 f=10 f=13

Figure 6: Variation of relative local Nusselt number versus the axial distance for different pulsation frequencies, (d/D = 0.61, Re = 7760).


0

0.5

1

1.5

2

2.5

3

3.5

4

0 5 10 15 20 25 30 35

x/H

Nu p

x/N

u ox

f=0 f=1.4 f=4.1 f=6 f=10 f=13


Combined effects of pulsation frequency and sudden pipe expansion on heat transfer were discussed in terms of relative mean Nusselt number of pulsated flow (Nurm = Nupm/Nuom), while the effects of pulsation frequency only on heat transfer were discussed in terms of mean Nusselt number ratio (Nur = Nupm/Num). Figure 9 shows the effect of d/D on the (Nupm/Nuom) in absence of pulsation (f=0). For same value of d/D it is found that as the Reynolds number increases, the (Nupm/Nuom) decreases and when d/D ratio decreases the (Nupm/Nuom) increases for all values of the studied Reynolds number. For different values of Reynolds number Figure 10 shows the variation of the (Nupm/Nuom) against the pulsation frequency at d/D = 0.32. It can be


1247

seen that an enhancement in heat transfer is obtained for different values of both Reynolds number and pulsation frequency. The maximum enhancement of (Nupm/Nuom) is obtained at f = 4.1 Hz when Re = 7760 and 14005, while the minimum enhancement is obtained at f = 1.4 Hz and Re = 19255. The enhancement that was obtained by d/D = 0.32 is greater than that obtained by the other higher values of d/D. Figure 11 illustrates the variations of the (Nupm/Nuom) against the pulsating frequency for different values of diameter ratio (d/D) and at Re = 7760. A relatively small effect of pulsating frequency is observed on the (Nupm/Nuom) while it increases as the d/D ratio decreases. Figure 12 shows the variation of the mean Nusselt number ratio (Nupm/Num) against pulsation frequency for different values of Reynolds numbers with d/D = 0.32. An enhancement was obtained with all values of pulsation frequencies except for f = 1.4 Hz and a maximum enhancement of about 20% was obtained at Re = 14005. There is no significant effect of Reynolds number on the (Nupm/Num) specially at f ≤ 1.4 Hz and at f=10 Hz. For the present study the Reynolds number range lies between 7760 and 40084, the turbulent bursting frequency lies in the range of 4.5 to 21 Hz, while the imposed pulsation frequency lies in the range of 1 to 13 Hz; where the

turbulent bursting frequency (fb) is calculated as fb ≈ um/5D, [4]. It can be concluded from the present results that when the Reynolds number increases, the turbulent bursting frequency increases. Therefore, the turbulent bursting damping by forced fluctuations of imposed pulsation frequency increases too.

Some reasons are provided to interpret why the enhancement in the mean Nusselt number ratio was obtained. First reason may be attributed to the increase in level of turbulence due to pulsation. At higher frequencies, larger or more frequent disturbances can be obtained, depending on Reynolds number, hence improved turbulence and higher heat transfer rates can be obtained. Second reason may be attributed to the forced circulation, which is introduced in the boundary layer due to pulsation. This forced circulation may increase the heat transfer rate by promoting eddies formation, thus introducing convection mode in the boundary layer. Third important reason is due to the interaction between the turbulent bursting frequency and the imposed pulsation frequency. In pulsation turbulent flow, if the flow pulse frequency is close to the frequency with which the viscous sub-layer is renewed, bursting frequency, a certain resonance “interaction” may occur. This interaction affects the heat transfer characteristics and leads to an increase or decrease in the heat transfer rate. Figures 13 and 14 illustrate -as a sample- the variation of mean Nusselt number ratio with the Reynolds number for different values of d/D. Figures 15 to 20 show the effect of pulsator locations on the relative mean Nusselt number when located upstream or downstream the sudden pipe expansion. As shown in Figure 15 for all values of studied pulsation frequencies (d/D=0.61 and Re=14005), the downstream pulsator gives more enhancement in heat transfer than that of upstream pulsator. For d/D = 0.61, Re = 40084, and f≥6 and for d/D = 0.49, Re = 7760, and f ≤ 4.1, the enhancement in heat transfer for upstream pulsator becomes more closer to that obtained with downstream pulsator, as shown in Figures 16 and 17, respectively. However, for d/D = 0.49 and Re = 30469, the enhancement due to upstream pulsator is higher than that due to downstream pulsator as shown in Figure 18. At low values of Re and at d/D=0.32, the enhancement due to the upstream pulsator is higher than that obtained by the downstream pulsator as shown in Figures 19 and 20.


0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35 40 45

Re x 10-3

Nu p

m/N

u om

d/D=0.61 d/D=0.49 d/D=0.32

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14f (Hz)

Nu p

m/N

u om

Re=7760 Re=14005 Re=19255

Fig. 9: Relative mean Nusselt number variation versus Reynolds number for different values of d/D, (f =0Hz).

Fig. 10: Relative mean Nusselt number variation versus frequency for different values of Reynolds numbers (d/D = 0.32).

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14

f (Hz)

Nu p

m/N

u om

d/D=0.61 d/D=0.49 d/D=0.32

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 2 4 6 8 10 12 14f (Hz)

Nu

pm

/Nu

m

Re=7760 Re=14005 Re=19255

Fig. 11: Relative mean Nusselt number variation versus frequency for different values of d/D (Re = 7760).

Fig. 12: Mean Nusselt number ratio variation versus frequency for different values of Reynolds numbers (d/D = 0.32).

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 5 10 15 20 25 30 35 40 45

Re x 10-3

Nu p

m/N

u m

d/D=0.61 d/D=0.49 d/D=0.32

0.6

0.7

0.8

0.9

1

1.1

1.2

0 5 10 15 20 25 30 35 40 45

Re x 10-3

Nu p

m/N

u m

d/D=0.61 d/D=0.49 d/D=0.32

Fig. 13: mean Nusselt number ratio variation versus with Reynolds number for different values of d/D, (f = 1.4 Hz).

Fig. 14: mean Nusselt number ratio variation versus Reynolds number for different values of d/D, (f = 13 Hz).


1249

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 2 4 6 8 10 12 14

f (Hz)

Nu p

m/N

u om

Downstream Upstream

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

0 2 4 6 8 10 12 14f (Hz)

Nu p

m/N

u om

Downstream Upstream

Fig. 15: The influence of pulsator location on relative mean Nusselt number for different pulsation frequencies (Re = 14005, d/D = 0.61).


0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12 14f (Hz)

Nu p

m/N

u om

Downstream Upstream

0.6

0.8

1

1.2

1.4

1.6

1.8

0 2 4 6 8 10 12 14f (Hz)

Nu p

m/N

u om

Downstream Upstream



1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

0 2 4 6 8 10 12 14f (Hz)

Nu p

m/N

u om

Downstream Upstream

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 2 4 6 8 10 12 14f (Hz)

Nu p

m/N

u om

Downstream Upstream

Fig. 19: The influence of pulsator location on relative mean Nusselt number for different pulsation frequencies (Re = 7760, d/D = 0.32) .



For practical applications, to provide a comparison between the heat transfer performance of sudden pipe expansion, an equal pumping power constrain must be taken into account. For equal pumping constraint, the pressure drop across the test section due to pulsation process is important regarding the heat transfer enhancement. To keep the pumping power constant, the flow velocity for smooth pipe with no pulsation must be increased. The pumping power required to feed the fluid flow through the sudden pipe expansion is proportional to Reynolds number. The combined effects of pulsation frequency and Reynolds number on (Nupm/Nus

*) at constant pumping power and (Nupm/Nufd) at constant mass flow rate are shown in Figure 21 for turbulent pulsated flow through a sudden pipe expansion with d/D = 0.61. It is observed that, at equal pumping power constraint, the ratio (Nupm/Nus

*) have a lower value than that of equal mass flow rate constraint (Nupm/Nufd). Also, it is found that the high values of Reynolds number have a more significant decreasing effect on the heat transfer enhancement than lower values. It can be seen that the dependence of (Nupm/Nus

*) on the pulsation frequency (f) is more significant while the dependence of (Nupm/Nufd) on (f) is not significant for the present mentioned range of Reynolds number.

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Re X 10-4

Nu p

m/N

u s*

0.00

0.50

1.00

1.50

2.00

2.50

Nu p

m/N

u fd

f = 1.4 f = 4.1 f = 6 f = 10 f = 13f = 1.4 f = 4.1 f = 6 f = 10 f = 13

Fig. 21: Effect of Reynolds number on the average Nusselt number ratio for different values of pulsation frequency under the two constraints for d/D=0.61.

The experimental data are correlated by a general dimensionless equation (6).

dcbaNu *2*3*rm +ω+ω+ω= ; )560(),40084Re7760( * ≤≤≤≤ ω (6)

The constants a, b, c, and d are functions of Reynolds number and are obtained by curve fitting and Table 1 gives the conclusion of all constants for the correlations

for 0=f to 13 Hz )560( * −=ω .


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Table 1: Correlations constants of equation (1).

Figure 22 shows the recirculating flow with corner vortices downstream the sudden expansion for different diameter ratios. It is observed that as the diameter ratio (d/D) decreases the formed wake region is extended and the flow is reattached to the smooth surface. These results show that the flow appears more likely to reattach to smooth tube surface and this yields good enhancement for heat transfer.

d/D = 0.61 d/D = 0.49 d/D = 0.32

Fig. 22: Flow visualization through sudden expansion with different diameter ratios (Re = 7760), (Front view).

5. CONCLUSIONS

Observation of the local Nusselt number behavior of turbulent flow through sudden pipe expansion revealed that the improvement in heat transfer coefficient occurred at the recirculation zones. The following points represent the final conclusions.

D/D=0.32 d/D=0.49 d/D=0.61 Re 7760-19255 19255-30469 7760 – 14005 19255 - 40084 7760 - 14005

-3.87×10-9.Re + 2.4×10-5

1.98×10-9.Re - 6.89×10-5

-3.71×10-9.Re + 1.68×10-5

-3.62×10-8.Re + 8.29×10-4

-2.94×10-9.Re - 5.19×10-5 a.

1.74×10-7.Re - 9.39×10-4

-1.13×10-9.Re + 1.15×10-3

1.62×10-7.Re - 3.6×10-4

1.16×10-6.Re - 2.97×10-2

-2.99×10-7.Re + 4.52×10-3 b.

-2.22×10-6.Re + 1.4×10-2

-1.02×10-6.Re + 1.38×10-2

-1.38×10-6.Re - 1.98×10-3

-1.26×10-5.Re + 0.36

5.64×10-6.Re - 7.37×10-2 c.

-1.2×10-5.Re + 2.24

-8.98×10-6.Re + 1.82

-2.49×10-5.Re + 2.07

2.97×10-5.Re + 0.36

-3.25×10-5.Re + 2.02 d.

16 % 8 % 8 % 11 % 8 % Max. error (%)


1. For all values of expansion ratio and frequency, an increase in the Reynolds number results in a decrease in the peak value of relative local Nusselt number.

2. As the expansion ratio increases (i.e., decreasing d/D) the distance to the position of maximum heat transfer increases; a behavior consistent with the variation in the reattachment point is observed in the plane. The relative mean Nusselt number with sudden pipe expansion increases as the d/D ratio decreases.

3. The maximum enhancement of relative mean Nusselt number, that reaches about 77%, was obtained with f = 10 Hz, d/D = 0.61, and Re = 14005 for downstream pulsator while the maximum enhancement, that was obtained with the same f, d/D, and Re reaches about 62% for upstream pulsator.

4. The maximum enhancement for the upstream pulsator, which is about 74%, was obtained for d/D = 0.49 with f = 6 Hz and Re = 30469, while the enhancement that was obtained for downstream pulsator at the same d/D, f, and Re, is about 52%. The maximum enhancement, that was obtained with d/D = 0.32 and Re = 7760, is about 142% at f = 4.1 Hz for upstream pulsator while at the same values, the enhancement for the downstream pulsator is about 122%.

5. Flow visualization is reliable in understanding the flow regime downstream the sudden expansion.

ACKNOWLEDMENT

I wish to express my deep special thanks to Prof. M. R. El-Tahlawi, Prof. of Geology Engineering, Assiut University, for his assistance and guidance to complete the publication of this paper.

REFERENCES [1] Vogel, J. C., Eaton, J. K. (1985), “Combined heat and fluid dynamic

measurements downstream of a backward facing step”, Journal of Heat Transfer, Vol. 107, pp.992-9.

[2] Dallen back, P. A., Metzger, D. E., Neitzel, G. P., (1987), “Heat transfer to turbulent swirling flow through a sudden axisymmetric expansion”, Journal of Heat Transfer, Vol. 109, pp.613-20.

[3] Baughn, J. W., Hoffman, M. A., Launder, B. E., Daehee, L., Yap, C. (1989), “Heat Transfer, temperature and velocity measurements downstream of an Abrupt expansion in a circular tube at a uniform temperature”, Journal of Heat Transfer, Vol. 111, pp.870-6.

[4] Amano, R. S., Jenson, M. K., Geol, P. (1983), “A numerical and experimental investigation of turbulent transport downstream from an abrupt pipe expansion”, Journal of Heat Transfer, Vol. 105, pp. 862-9.

[5] Valencia, A., Fiebig, M., Mitra, N. K., (1996), “Heat transfer enhancement by longitudinal vortices in a fin-tube heat exchanger with flat tubes”, Journal of Heat Transfer, Vol. 118 No. 1, pp.209-11.

[6] Manica, R., and Bortoli, A. L., (2003), “Simulation of Incompressible Non-Newtonian Flows Through Channels with Sudden Expansion Using the Power-Law Model”, TEMA Tend. Mat. Appl. Comput., Vol. 4, No. 3, pp. 333-340.


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[7] Genin, L. G., Koval, A. P., Manchkha, S. P., and Sciridow, V. G., (1992), “Hydrodynamics and Heat Transfer with Pulsating Fluid Flow in Tubes”, Thermal Engineering, Vol. 39, No. 5, pp. 30-34.

[8] Gibson, M. M., and Diakoumakos, E., (1993),“Oscillating Turbulent Boundary Layer on a Heated Wall”. 9th Symposium “Turbulent Shear Flows”. Kyoto, Japan.

[9] Laio M. S., and Wang, C. C., (1988), “An Investigation of Heat Transfer in Pulsating Turbulent Pipe Flow”, ASME, Fundamentals of Forced and Mixed Convection HTD, Vol. 42, pp. 53-60.

[10] Said, S. A. M., Al-Farayedhi, A., Habib, M., Gbadebo, S. A., Asghar, A., and Al-Dini, S., (1998), “Experimental Investigation of Heat Transfer in Pulsating Turbulent Pipe Flow”. 2nd International Conference on Turbulent Heat Transfer.

[11] Mamayyev, V. V., Nosov, S., Syromyatnikov, I., (1976), “Investigation of heat transfer in pulsed flow of air in pipes”, Heat transfer Soviet research 8 (3), 111-116.

[12] Zohir, A. E., (2000),“An Experimental Investigation of Heat Transfer to Laminar and Turbulent Pulsating Pipe Flows”, PhD. thesis., Cairo University.

[13] El-Shazly, K. M., Zohir, A. E., Abdel Aziz, A. A., and Abdel Mohimen, M. (2005), “Heat transfer characteristics of pulsated flow downstream of abrupt expansion through pipes”, 2nd International Conference on Advances in Engineering Science&Technologies.

[14] Said, S. A. M., Habib, M .A., and Igbal, M. O., (2003), “Heat transfer to pulsating turbulent flow in an abrupt pipe expansion”, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 13, No. 3, pp. 286-308.

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