Study of the effect of entrance length on heat transfer to fibre suspensions in annular flow heat exchangers

International Journal of Heat and Mass Transfer 78 (2014) 548–556

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Study of the effect of entrance length on heat transfer to fibre suspensions in annular flow heat exchangers S.N. Kazi a,⇑, G.G. Duffy b,1, X.D. Chen c,2 a

Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysia Department of Chemical and Materials Engineering, School of Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand c Chair of Biotechnology and Food Engineering, Department of Chemical Engineering, Faculty of Engineering, Monash University, Victoria 3800, Australia b

a r t i c l e

i n f o

Article history: Received 12 November 2013 Received in revised form 27 June 2014 Accepted 27 June 2014

Keywords: Heat transfer Natural fibre Fibre concentration Coarseness Annular flow Consistency

a b s t r a c t In internal flow the boundary layer is unable to develop without eventually being constrained. There is no satisfactory general expression for the entry length in turbulent flow and it is approximately independent of Reynolds number and remains within 10–60Dh. Present experimental investigation has highlighted the effect of entry length (23 and 38Dh) on heat transfer to fibre suspensions in annular passage. It is observed that there is no significant variation of heat transfer coefficients with change in entrance length for water flow. Fibre suspensions flow at low consistency provides data with little variation whereas at higher consistency heat transfer coefficients data provides some variations but the trend remains similar for both short and long entrance lengths in the test section. Effects of fibre concentrations and flexibility in suspensions are providing similar trends in heat transfer irrespective of entrance length in annular flow, pipe flow and a larger annular gap. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction There has been a steady but consistent increase in demand for coaxial-pipe heat exchangers in the process industries and a renewed interest has been given to annular flow [1]. However in internal laminar or turbulent flow configuration the fully developed velocity profiles are parabolic for laminar and flatter for turbulent flows due to turbulent mixing in the radial direction. In fully developed flow the velocity profile does not vary in the flow direction. In fact in this region the pressure gradient and the shear stress in the flow are in balance. The length of the pipe between the start and the point where the fully developed flow begins is called the entrance length or calming length. The entrance length is a function of the Reynolds number of the flow. The hydrodynamic entry length for laminar and turbulent pipe flow may be expressed by the Eqs. (1) and (2) respectively [2,3].

x  f ;d;h  0:05Re d lam x  fd;h 10 6 6 60 d turb

ð1Þ ð2Þ

⇑ Corresponding author. Tel.: +60 3 7967 4582; fax: +60 3 7967 5317. E-mail addresses: [email protected], [email protected] (S.N. Kazi), [email protected] (G.G. Duffy), [email protected] (X.D. Chen). 1 Tel.: +64 9 3737599x87805. 2 Tel.: +61 3 9905 9344. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.06.081 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.

In paper manufacturing process fibres are used in the suspension form at low consistency flowing to the head box of the paper machine from where it is discharged on the moving mesh under vacuum to produce paper as the final product. Thus behaviour of fibre in suspension form is playing a vital role in paper manufacturing process. It was reported earlier by the present authors about correlation of fibre and paper properties with heat transfer and friction loss characteristics of fibre suspensions [1,4] and that information could characterise fibres and aid the paper quality improvement. In the present study effect of entrance length on heat transfer and friction loss properties of suspensions in annular flow are taken into consideration. Performances of the industrial heat exchangers are evaluated in a regular basis by using standard equations. However the knowledge of entrance effect on suspensions could support the evaluation process. Heat transfer and frictional loss of fibre suspensions in pipe flow, annular flow of different dimensions were studied by Kazi et al. [1] and Kazi [5]. From the studies of fibre suspensions in pipe flow, it is observed that numerous investigators selected different calming lengths for study of fibre suspension flow. There is no specified or accepted specification for the selection of entrance length for fibre suspension in annular flow. In the study of heat transfer in annular flow, different investigators have chosen various entrance lengths depending on the hydraulic diameter of the test section. Middis [6] selected 20  Dh for study of heat transfer to fibre suspensions in annular

S.N. Kazi et al. / International Journal of Heat and Mass Transfer 78 (2014) 548–556

549

Nomenclature AR BR Dh d dm d1 d2 Hi q Re rh

without extension rod with extension rod hydraulic diameter m pipe diameter m point of maximum velocity on the velocity profile m outside diameter of the inner tube of the annulus m inside diameter of the outer tube of the annulus m Pinus radiata high coarseness heat flux W/m2 Reynolds number hydraulic radius m

flow. Study of heat transfer and subsequent fouling in evaporators with Kraft pulp black liquor was conducted by Branch [7] and Bremford [8] studied multiple effect evaporators for Kraft black liquor. Previous researchers have [7,8] used entrance lengths of 20  Dh, whereas Hasson et al. [9] selected an entrance length of 38  Dh for fouling in annular flow. An aim of this study is to investigate the effect of entrance length on heat transfer to fibre suspensions by changing the extension length of upstream at the test section. 2. Literature review The study of heat transfer and frictional pressure loss in tubes and annular spaces has been conducted to provide a basis for designing heat exchangers and cooling systems in industries. Design data are available mainly for common fluids but there are no significant published data available for fibre suspensions. Duffy et al. [10] studied heat transfer to fibre suspensions in annular flow. Water suspensions of Kraft softwood and hardwood pulps of various qualities were investigated in a simple coaxial pipe heat exchanger and heat transfer coefficient hc values were calculated. They observed systematic differences in hc values in the bulk velocity range of 0.4–2.4 m/s for different pulp suspensions at 0.4% concentration. They showed that hc values at a specified flow velocity (1.5 m/s) and fibre concentration (0.4%) correlated well with specific fibre and paper properties. These results are similar to the data obtained by same authors in pipeline flow [11]. They have proposed that hc could be used to monitor and therefore control pulp quality variations. Robertson and Mason [12] suggested that a calming length for fibre suspension flows should be about 160 pipe diameters for the flow to become established and the fibre structured suspension stabilised. Hemstrom et al. [13] stated that the pressure gradient did not reach a steady value until about 80 pipe diameters downstream and was greater than the steady-state value before this point. Their results also showed that at 20D downstream the effect of a disturbance is only slight and decreases as concentration increases. Lee and Duffy [14] used the calming lengths upstream and downstream as 110 and 10 pipe diameters respectively, while investigating flowing Kraft pine fibres with concentrations ranging from 0.21% to 1.17% for turbulent flow at bulk velocities up to 9.17 m/s. Middis [6] selected 20 hydraulic diameters Dh in his studies of heat transfer to Bleached Kraft pine fibre suspensions of concentrations 0.08% to 1.03% in annular flow. Middis [6], Branch [7] and Bremford [8] used a calming length of 20Dh but Hasson et al. [9] selected a value of 38Dh in their heat transfer fouling study in annular flow. More recent research has been focused on numerical simulation, spatial and orientation distributions of fibres in various flow

TS TTC u ULo x xfd,h

q l k

wall temperature °C temperature at thermocouple location °C Fluid velocity m/s Pinus radiata ultra low coarseness distance along x axis m hydrodynamic entry length m density kg/m3 dynamic viscosity kg/ms thermal conductivity W/m K

fields, with some experimental validation. Lin et al. [15] studied numerically the motion of fibres in an evolving mixing layer and found that Stokes number is the key parameter to determine the spatial distribution of fibres. At a small Stokes number the fibres are homogeneously distributed in the flow. They found that the effects of both the density ratio and the fibre aspect ratio on the spatial and orientation distributions are small. Lin et al. [16] simulated numerically the orientation distribution of fibres in laminar and turbulent pipe flows. The simulated results are consisted with the experimental data available in the literature. They found more fibres are aligned with the flow direction with increasing Reynolds number in laminar flow but in turbulent flow the orientation distributions become more homogeneous and the fluctuation intensity of fibre velocity in the stream wise direction is larger than those in the other two directions. Olson et al. [17] derived equations of mean and fluctuating velocities in rotation and translation motion for rigid thin inertia less fibres moving in a turbulent fluid. They have derived rotational translational dispersion coefficients from the equations of fluctuating fibre velocity and the dispersion coefficients were shown to decrease with the increase of the ratio of fibre length to Lagrangian integral length scale. Lin et al. [18] investigated theoretically and numerically the Rheological behaviour of fibre suspensions in a turbulent channel flow. The fluctuating equation for the orientation distribution function (ODF) of fibres was theoretically solved using the method of characteristics. They obtained relevant agreement with the experimental data. The shear stress of fibre suspensions increases with the decrease of first normal stress differences from the wall to the centre of the flow for varying Reynolds number. They obtained the orientation distribution of fibres in turbulent regime is much different from that in laminar regime. The randomising effect of the turbulent fluids leads to a broad orientation distribution, especially in the region near the centreline of the flow. Later Lin et al. [19] developed a new successive iteration method to calculate the mean orientation distribution of fibres and the mean and fluctuation correlated quantities of suspension in a turbulent channel flow and noticed drag reduction where Reynolds stress in the fibre suspensions were smaller than those in the Newtonian flow. They found that the amount of drag reduction augmented with the increase of the fibre mass concentration. Similar results were obtained experimentally by Kazi et al. [20]. Zhumin et al. [21] used combination of Finite element method and Brownian configuration field (BFC) method to simulate the fibre suspension flow in axisymmetric contraction and expansion passages. The results obtained for different geometry ratios are compared with the available constitutive models and experimental results. The predicted vortex length for dilute suspensions agrees well with experimental data in the literature and show the effect on vortex enhancement with the increase of the fibre volume fractions and the aspect ratios.

550

S.N. Kazi et al. / International Journal of Heat and Mass Transfer 78 (2014) 548–556

You et al. [22] studied linear instability of two dimensional channel flow of fibre suspensions based on slender-body theory and considering natural closure approximation to determine the fibre orientation. They found that the flow instability of fibre suspensions is governed by two parameters such as a ratio between the axial stretching resistance of fibres and the inertial force of the fluid and the orientation diffusivity coefficient that accounts for inter-fibre hydrodynamic interactions. They have reported that fibre additives have stabilizing effects on the flow and it is intensified for higher values of Reynolds number. Niskanen et al. [23] studied experimentally the development of fibre orientation distribution in a plane contracting channel flow and subsequently developed a model to understand the mechanisms affecting the development of fibre orientation. They noticed that a single model is enough to describe the orientation in both planes but the rotational diffusion coefficient must be adjusted for both planes separately. They said fibre orientation distribution is more isotropic, which is related to the flexibility of the fibres and in the turbulence of the flow. Some investigations have extended knowledge in the shear flow behaviour of fibre suspensions [24–26]. The aspect ratio of fibre is defined as the ratio between the fibre length and the fibre diameter whereas the coarseness of a pulp is the mass of fibres per unit length. Reduction of fibre length or strength reduces paper sheet strength and changes in fibre coarseness influence all pulp properties such as drainage, wet-web strength and the structural strength and optical properties of the dry sheets. Coarser fibres have thicker walls, fewer per unit pulp mass and have smaller specific surface area [27]. Fibre flexibility is a pulp property that plays an important role in the manufacture of paper. Fibres with low area moment of inertia would be more flexible. Wet fibre flexibility influences paper properties such as apparent sheet density and porosity [28], paper strength properties [29], surface smoothness and optical properties [28]. Heat transfer and drag loss of fibre suspensions were studied by Kazi et al. [20] and found that drag reduction enhances with the increase of fibre concentrations in the suspension. Kazi et al. [30] observed that heat transfer to fibre suspensions retards with the increase of fibre

flexibility whereas drag reduction enhances with the increase of fibre flexibility. Paul [31] studied on processing of fibre suspensions in viscous media to refine fibre properties. The objective of present work therefore, is to investigate the effect of entrance length on heat transfer to fibre suspensions and to generate data for future development of a model for heat transfer to turbulent fibre suspensions flow. 3. Experimental 3.1. Experimental set-up Schematic diagram of the annular experimental flow loop is presented in Fig. 1. The annular test rig consists of a 100 L tank, two 2.4 kW Onga pumps, an ABB Kent-Taylor Magmaster magnetic flow meter (measures with ±0.15% accuracy), a double-pipe heat exchanger for cooling the suspensions, the heated annular pipe test sections and a recycle piping system. The Perspex annular test sections (Figs. 2a and 2b) have a stainless steel heating rod with (Fig. 2a) or without (Fig. 2b) a calming extension rod mounted concentrically. A groove was made on the tip of the heater extension rod attached to the heater side to accommodate the tapered tip of the heater rod where the outer diameter of the heater rod was flushed with the outer diameter of the heater extension rod. The test section, dimensional measurements of the inlet and outlet and thermocouple locations are presented in Figs. 2a, 2b and Table 1. The inner extension rod (Fig. 2a) was 201 mm. The detailed magnitudes of the dimensions are stated in Table 1. The Perspex test section has a stainless steel heating rod with or without a calming extension rod mounted concentrically. The heat transfer measurements were conducted with the inner extension rod installed and removed. The heater rod (Fig. 2c) has four embedded E-type thermocouples (measures with ±0.35% accuracy), with three located close to the internal heater just below the rod surface for surface temperature measurement. The fourth thermocouple was used to activate a safety trip in the event of high surface temperatures. The power supply to the heated section was controlled by a 10 amp-rated Variac. Current and voltage were measured

Fig. 1. Schematic diagram of the experimental flow loop.

551

S.N. Kazi et al. / International Journal of Heat and Mass Transfer 78 (2014) 548–556 Table 1 Dimensions of the annular test section.

Fig. 2a. Schematic diagram of the coaxial pipe annular test section with stainlesssteel heater, calming length extension rod, and inlet and outlet pipes normal to the annular flow direction (all the dimensions are in mm).

Parameters

Dimensions in mm

Heat transfer test section length mm Heater length mm Heater diameter mm Annular outer diameter mm Hydraulic diameter mm Hydrodynamic entry length mm Thermal entry length mm

585.7 100.0 10.7 23.8 13.1 499.8 82.6

Fig. 2c. Schematic diagram of the heating element.

61011A relay multi-plexers. The data acquisition equipment was controlled by using a BASIC program. The program allowed the operator to choose between automatic and manual data acquisition modes according to the requirements. Details are stated elsewhere [5,10]. 3.3. Experimental procedures

Fig. 2b. Schematic diagram of the coaxial pipe annular test section with stainlesssteel heater and inlet and outlet pipes normal to the annular flow direction (all the dimensions are in mm).

and the signals were transmitted to the computer data logger through Hewlett Packard data acquisition equipment. Further details are presented elsewhere [5,10].

3.2. Data acquisition All measurements were taken at the chosen velocity and bulk temperature at the steady-state condition of the heat transfer loop. The velocity was systematically increased, the heat flux was adjusted to achieve constant DT and the calculated local heat transfer coefficients were recorded by using the manual mode of data acquisition. All temperatures, flow velocities, voltages and currents were recorded with an IBM compatible XT personal computer, a Hewlet Packard PCIB interface, a 61013A digital multi-meter and two

The heat transfer measurements were conducted for investigation of fibre suspensions at two different fibre concentrations of pine high coarseness (Hi) and one concentration of pine ultralow coarseness (ULo) to compare concentration and flexibility effects in shorter and longer extension length test sections. Before each experiment, the pulp fibres obtained in sheets were soaked for approximately 24 h and then disintegrated and finally dispersed by the pump operating in recycle mode. Recycling was maintained for approximately one hour to ensure optimum fibre dispersion and fibre wetting, and then for a further hour before any measurement was taken. Considering experimental parameters from literature review [6], practical use of annular heat exchangers at low flow rates and limitations of the test set-up, the experimental conditions are selected for the present investigation. A summary of experimental conditions is given in Table 2. Experimental corrections for the thermocouples k/x values according to Eq. (3) are presented in Table 3 for the annular test section with stainless steel heater (shorter extension length) and with heater and extension rod (longer extension length):

T w ¼ T TC  q=ðk=xÞ

ð3Þ

The fibre concentration was measured at the beginning and end of the run for each experiment. This was done by collecting 1L sample from the recycle line while the suspension was flowing through the rig. The samples were weighed, filtered, dried and then reweighed and the concentration reported as the percentage of dry fibre mass per total mass of suspension. The measured values were always in agreement with differences less than 5%. 3.4. Data reduction Data for inlet and outlet temperatures, wall temperatures, heater power input, and flow rate were logged with a Hewlett Packard data acquisition system and recorded using a digital computer. The

552

S.N. Kazi et al. / International Journal of Heat and Mass Transfer 78 (2014) 548–556

Table 2 Experimental parameters.

Re2 ¼

Variable parameters

Range

Velocity range Suspension bulk temperature Wall surface temperature Surface to bulk temperature difference Fibre concentration Heat flux

0–2.0 m/s 30 ± 0.5 °C 45 ± 0.5 °C 15 ± 0.5 °C 0.1–0.4% 5–200 kW/m2

Table 3 k/x values. Location

k/x

Values in W/k

1 2 3

k/x1 k/x2 k/x3

25,000 12,500 14,286

energy input to the heater per unit surface area was calculated as heat flux q, which is the total power input divided by the heated area A. The heater wall temperature Tw was calculated from the thermocouple reading Ttc in the test section using a calibration correction for the distance of the thermocouples below the pipe heater surface or below the heater surface of the annular test section. The temperature difference between the thermocouple embedded in the wall and the actual surface temperature is therefore given by the product of heat flux and wall resistance x/k, as presented by Eq. (3). The local heat transfer coefficient hc is determined from the calculated wall temperature Tw, the bulk temperature Tb and the heat flux q, as shown by Eq. (4):

hc ¼ q=ðT w  T b Þ

ð4Þ

The bulk temperature Tb for the annular flow is the positionweighted average value of the inlet and outlet temperatures (Ti and To respectively). Eq. (5) presents bulk temperature as a function of inlet and outlet temperatures. This was based on the assumption that the fluid temperature was increased linearly over the heated section and remained constant in the unheated sections of the rig. This is reasonable because the temperature rise between inlet and outlet thermocouples was normally less than 1 °C:

Tb ¼ Ti þ

X1 ðT o  T i Þ X2

ð5Þ

where, X1 (82.6 mm) and X2 (100 mm) are representing the heated length and distance of thermocouples tip along the flow direction respectively. The Reynolds number for pipe flow is evaluated by the Eq. (6).

Re ¼ qud=l

ð6Þ

For the annular flow the hydraulic diameter is considered in the calculation for Reynolds number and relevant parameters. Hydraulic diameter is evaluated by Eq. (7):

Hydraulic diameter;

Dh ¼ 4r h ¼ d1  d2 2

ð7Þ

2

d  dm 4r h ¼ 2 d2

ð8Þ

The point of maximum velocity dm on the velocity profile is determined from Eq. (9): 2

2

dm ¼

2

d2  d1   2 2 ln d2 =d1

ð9Þ

The Reynolds number Re2 of the outer portion of annular velocity profile is presented in Eq. (10):

4r h uq

ð10Þ

l

The physical properties of the different suspensions were taken as those of the suspending fluid in all cases. In the previous investigations and also in the present studies the thermo-physical properties of water at the specified parameters were chosen as the properties of fibre suspension. Wherever predicted values were compared with the experimental data or data reproduction were concerned a measure of the goodness-of-fit was obtained by calculating the root-mean square (rms) error. This is defined as Eq. (11):

rms error ¼

" #1 n  2 2 1X X pred  X meas n i¼1

ð11Þ

where, (Xpred  Xmeas) is the difference between the predicted and the measured data points. The rms error was chosen because it is not subject to algebraic cancellation of positive and negative differences nor is the result unduly affected by a single erroneous data point. 4. Results and discussion 4.1. Data reproducibility The rig was calibrated using water. The procedural accuracy and reproducibility of data were studied by using fibre suspensions of 0.4% for both the cases of test section with and without extension rod. The heat transfer results are presented in Figs. 3 and 4 with hc as a function of velocity for test sections with and without extension rod respectively. It is observed that the data reproduced nicely with rms errors <2% and <5% and remain within the confidence level of 95% for the test section with extension rod and without extension rod respectively. 4.2. Effect of entrance length on heat transfer Fig. 5 represents a plot of heat transfer coefficient as a function of velocity for water and two different entrance lengths (23  Dh and 38  Dh) in the test section. For water there is no significant variation in heat transfer coefficient with the increase of entrance length (longer entrance length shows 1.28% lower than shorter entrance length at a specific flow velocity of 1.5 m/s). With the lower hydrodynamic entry length 23  Dh there is a tendency to show higher heat transfer coefficient values than for the longer entrance length of 38  Dh due to induced turbulence in the boundary layer. Fig. 6 shows heat transfer coefficient as a function of velocity for water and Kraft pine high Hi and ultra-low ULo coarseness at concentrations of 0.2 and 0.4% respectively in suspension form. Data at both the short (without extension rod AR) and long (with extension rod BR) entrance length are presented. It is observed that with fibre concentration of 0.2% Hi, the heat transfer coefficient varies within 1% when the entrance length is changed, which is not a significant enough value for making any statement. Considering 0.4% ULo in suspension (Fig. 6), it is observed that with long entrance length ULo (0.4%) has an indication of lowering hc at 0.35 m/s and at the low entrance length the point of onset of lowering moves forward towards the positive side at 0.4 m/s. At a higher velocity of 1.5 m/s, hc for ULo at low entrance length is 13.9% below water and 2.3% higher than that with the longer entrance length. At an even higher velocity 2 m/s, hc at short entrance length is about 0.5% less than when the longer entrance length is used indicating that the two data sets are close to each other but remain about 13% lower than water values.

553

Heat transfer coefficient kW/m K

S.N. Kazi et al. / International Journal of Heat and Mass Transfer 78 (2014) 548–556

2

2

Heat transfer coeff. kW/m K

12 Hi (1)

10

Hi (2)

8 6 4 2 0 0

0.5

1

1.5

2

12 WATER (AR)

10

WATER (BR)

8 6 4 2 0

2.5

0

0.5

Velocity m/s

Hi 0.4(R)

8 6 4 2 0 0.5

1 1.5 Velocity m/s

2

WATER(AR)

10

Fig. 4. Heat transfer coefficient as a function of flow velocity for two runs of Kraft pine high coarseness fibre suspension. Heat transfer data were obtained at DT 15 °C, bulk temperature 30 °C and fibre concentration of 0.4% for test section without extension rod.

Heat transfer coefficient data as a function of velocity for water and Kraft pine Hi for both longer and shorter entrance lengths are presented in Fig. 7 where the fibre concentration was maintained at 0.4%. With the increase of fibre concentration the difference between data at shorter and longer entrance lengths deviates (Figs. 6 and 7) from each other at velocities both lower <0.5 m/s and higher >1 m/s. At low velocities <0.5 m/s, heat transfer coefficient values of the short entrance length are higher than those of water and when the longer entrance length is used. At a specific velocity of 0.25 m/s the heat transfer coefficient for the shorter entrance length is 69.5 and 36% higher than that for water and also for the longer entrance length respectively. At the same velocity the heat transfer coefficient for longer entrance length is 8.5% higher than that of water. The influence of short entrance length on flow and boundary layer provides higher heat transfer to the suspension, where the onset of the lowering of heat transfer coefficient below water was shifted to 0.8 m/s. On the other hand the longer entrance length provides lower onset of heat transfer coefficient below water at about 0.3 m/s. At velocities >1 m/s, the heat transfer coefficient for both the longer and shorter entrance lengths show attenuation of the heat transfer coefficient and remains below water until the end of investigation range. At a flow velocity 1.5 m/s, the heat transfer coefficient of the shorter entrance length is about 5.8% lower value than that of at longer entrance length and the difference slightly reduces to 5.2% at 2 m/s showing the tendency to become steady.

Hi0.2(AR) ULo0.4(AR)

8

WATER(BR) Hi0.2(BR)

6

ULo0.4(BR)

4 2 0 0

2.5

0.5

1 1.5 Velocity m/s

2

2.5

Fig. 6. Heat transfer coefficient as a function of velocity for water and Kraft pine high and ultra low coarseness fibre of concentration 0.2% and 0.4% respectively in suspension form. Data of both before (BR) and after (AR) removal of extended rod are presented. Heat transfer data were obtained at DT 15 °C and bulk temperature 30 °C.

2

0

Heat transfer coefficient kW/m K

10

2.5

12

2

Hi 0.4

2

Fig. 5. Heat transfer coefficient as a function of velocity for water with (BR) and without (AR) the extension rod. Heat transfer data were obtained at DT 15 °C and bulk temperature 30 °C.

Heat transfer coefficient kW/m K

12

2

Heat transfer coefficient kW/m K

Fig. 3. Heat transfer coefficient as a function of flow velocity for two runs of Kraft pine high coarseness Hi fibre suspension. Heat transfer data were obtained at DT 15 °C, bulk temperature 30 °C and fibre concentration of 0.4% for test section with extension rod.

1 1.5 Velocity m/s

12 WATER(AR)

10

WATER(BR) Hi0.4(AR)

8

Hi0.4(BR)

6 4 2 0 0

0.5

1 1.5 Velocity m/s

2

2.5

Fig. 7. Heat transfer coefficient as a function of velocity for water and Kraft pine high coarseness Hi fibre suspension of concentration 0.4%. Both before and after removal of extension rod are presented. Heat transfer data were obtained at DT 15 °C and bulk temperature 30 °C.

At 1.5 m/s the lowering of heat transfer coefficient below water is 10.9 and 4.5% respectively with shorter and longer entrance lengths and the difference reduces to 8.8 and 3.5% at flow velocity of 2.0 m/s. Thus it is essentially the same trend of hc values against velocity with longer or shorter entrance length but the magnitude varies a little due to the induced turbulence in the boundary layer at the shorter entrance length.

S.N. Kazi et al. / International Journal of Heat and Mass Transfer 78 (2014) 548–556

12

Heat transfer coefficient kW/m2 K

2

Heat transfer coefficient kW/m K

554

WATER

10 Hi 0.4

8

ULo 0.4

6 4 2 0 0

0.5

1 1.5 Velocity m/s

2

14 12 10

Water

Hi

Med

Lo

ULo

Sp

Euc

8 6 4 2 0 0

2.5

0.4

0.8

1.2

1.6

2

2.4

Velocity m/s

Fig. 8. Heat transfer coefficient as a function of velocity for water, Kraft pine high coarseness Hi and ultra-low coarseness ULo fibre suspensions having concentration of 0.4%. Heat transfer data were obtained at DT 15 °C and bulk temperature 30 °C for test section without extension rod (AR).

Fig. 9. Heat transfer coefficient as a function of velocity for water, Kraft pines, spruce and eucalyptus fibre suspensions of concentration 0.4%. Heat transfer data were obtained at DT 15 °C and bulk temperature 30 °C for test section with extension rod (BR).

It is observed that in the present case the entrance length introduces large difference in measurements at low flow velocities in comparison to high flow velocities. A fifteen fold of Dh increase in entrance length (in terms of hydraulic diameter {38Dh  23Dh}) produces a 36% difference at low velocities (<0.5 m/s) but only a 5.8% difference at higher velocities (>1 m/s). This signifies the importance of keeping constant entrance length or specifying the dimension in heat transfer investigation with suspensions.

0.73 m/s and the value remains below hc for water and ULo. Similar results were obtained for annular flow and pipe flow [20,30]. At velocities >0.73 m/s the Hi fibre suspension also shows similar behaviour to annular flow with long entrance length and in pipe flow [5]. The hc values for Hi move below water but remain above ULo all the way until the upper velocity limit of 2 m/s. The highly flexible fibres damp turbulent eddies more than the less flexible ones. At 1.5 m/s the hc of ULo fibres are the lowest and about 13.9% lower than water and 3.5% lower than Hi fibre suspension of same concentration 0.4%. At 2 m/s trend remains the same but the magnitude of deviation from water reduces. ULo and Hi shows hc value about 13% and 8.8% respectively lower than water due to the fibre interaction with the turbulent eddies. It is observed that hc decreases with the decrease of fibre coarseness (weight per unit length, see Table 4). ULo fibres are more flexible than Hi [31]. The flexibility enhances the reduction of hc as observed in annular flow [10] and by previous researchers in pipe flow as well [5,11]. Fibres damp turbulence and reduce heat transfer coefficient. With higher flexibility, the damping effect on turbulence is more and therefore the reduction of hc is more as observed previously [5]. On the other hand ULo fibres are shorter in length (1.88 mm) than Hi (2.60 mm), (see Table 4) which also contributes in the lowering of hc values as observed in previous work for both annular [10] and pipe flow [5,11]. Fig. 9 shows heat transfer coefficient as a function of velocity for different grades of Pinus radiata, short fibre Eucalyptus and Canadian spruce (flexible fibre) at a concentration of 0.4% for annular flow test section with extension rod (BR). It can also be observed that there is an increase in hc at velocities below 0.4 m/s and a lowering of hc at higher velocities similar to the case of annular flow test section without extension rod (AR). At 0.2 m/s velocity in both

4.3. Heat transfer to fibre suspensions 4.3.1. Effect of fibre flexibility Fig. 8 represents a plot of heat transfer coefficient as a function of velocity for water, Kraft pine Hi and ULo at a concentration of 0.4% for the test section with short entrance length (AR). It is observed that at a low velocity (<0.4 m/s) the heat transfer coefficient values of Hi and ULo are higher than that of water. Fibres entangle at low velocities and form flocs and an interlocking structure that causes the peripheral layer adjacent to the test piece rod to be thin. This enhances heat transfer to the suspension and hence yields higher heat transfer coefficients. At low velocities heat transfer is dominated by conduction and with high thermal energy transfer through the fibres, the hc values are higher than water. Similar observations were obtained by previous investigations in annular flow and pipe flow [5,6,20]. At 0.3 m/s, the hc for the Hi suspension at 0.4% concentration was 52% higher than for water alone. ULo exhibited 15.4% above that for water alone. At 0.4 m/s, the ULo fibre suspension data falls below the water data and remains below the water data. At a higher coarseness of fibre the hc data for the Hi is lower from

Table 4 Properties of wood fibres used in the experimental investigation [5]. Fibre type

Length L (mm)

Coarseness (mg/m)

Width W (lm)

Thickness T (lm)

WT (lm2)

Wall area (lm2)

Wall thickness t (lm)

W/T

Relative flexibility (round)

Relative flexibility (square)

Fibre density (kg/m3)

Moment of inertia, I⁄ (m4)

Relative fibre number

Hi Med Lo ULo BKP Sp Eu

2.60 2.24 2.08 1.88 2.53 2.49 0.74

0.250 0.209 0.200 0.184 0.246 0.198 0.187

30.4 30.1 30.5 30.4

10.5 9.2 9.2 9.0

318 279 281 271

202 177 174 169

3.57 3.11 3.05 2.96

3.12 3.48 3.56 3.63

1 1.139 1.154 1.189

1 1.504 1.490 1.600

1237.6 1180.8 1149.4 1088.8

9.22 6.04 5.77 5.26

25.1 12.7

8.9 6.9

223 88

130

2.57 2.48

3.04

76 100 110 125 80 123 927

2.84 1.29

I⁄: Moment of inertia (rectangular cross-section), L: length weighted average length, Hi: P. radiata high coarseness, Med: P. radiata medium coarseness, Lo: P. radiata low coarseness, ULo: P. radiata ultra low coarseness, BKP: bleached Kraft pine pulp, Sp: standard spruce, Eu: eucalyptus.

555

Hi 0.2

8

Hi 0.4

6 4 2 0 0

0.5

10

2

WATER

10

Heat transfer coefficient kW/m K

12

2

Heat transfer coefficient kW/m K

S.N. Kazi et al. / International Journal of Heat and Mass Transfer 78 (2014) 548–556

1 1.5 Velocity m/s

2

2.5

Water

8

Hi 0.1 Hi 0.2

6

Hi 0.4

4 2 0 0

0.2

0.4

0.6

0.8 1 Velocity m/s

1.2

1.4

1.6

Fig. 10. Heat transfer coefficient as a function of velocity for water and suspensions of Kraft pine Hi fibre at two different concentrations 0.2% and 0.4%. Heat transfer data were obtained at DT 15 °C and bulk temperature 30 °C for test section without extension rod (AR).

Fig. 11. Heat transfer coefficient as a function of flow velocity for different concentrations of Hi pulp fibre suspensions. Heat transfer data were obtained at DT 15 °C and bulk temperature 30 °C for test section with extension rod (BR).

the cases of shorter (Fig. 8) and longer (Fig. 9) extension lengths, water, Hi and ULo fibre suspensions at 0.4% consistency show 1.765, 3.235 and 2.706 Kw/m2 K and 1.852, 2.889 and 2.519 Kw/ m2 K respectively. These data validate the trend obtained previously for pipe and annular flow of bigger hydraulic diameter. It can be seen that there is 5%, 10% and 7% variations in water, fibre suspensions of Hi and ULo data respectively from shorter and longer entrance lengths test sections. Thus consideration of shorter and longer entrance lengths represent little variation in water data but the suspension data variations remain maximum around 10%. On the other hand the trend remains similar all the way in the investigation range.

resulting in lower hc. Similar results were obtained in previous studies with longer entrance length [5] and also by previous researchers for annular flow of different dimensions [10,6]. Data for water and the pine high coarseness are presented in Fig. 11 for three fibre concentrations (0.1%, 0.2% and 0.4%) for the test section with extension rod (BR). The experiments were conducted in the velocity range of 0.15 to 1.5 m/s. At low velocities very small amounts of fibre in suspension enhance heat transfer coefficient significantly but with the further increase of concentration in suspension heat transfer coefficient values move away from the water values. At higher velocities the data points move further below the water values as concentration increases. At 0.2 m/s water, Hi fibre of 0.2% and 0.4% concentrations show 1.85, 2.25 and 3 kW/m2 K respectively hc values indicating hc of higher concentration suspension is followed by lower concentration suspension and water. Similar results were obtained for annular flow without extension rod (AR) and previously for pipe flow and annular flow [11,32]. In the present investigation on concentration effect, the variation of hc values at long and short extension lengths for water and Hi at suspension concentrations of 0.2% and 0.4% are 4.8%, 8.9% and 5.6% respectively. Thus the variations for water and suspensions of fibres remain within maximum 5% and 10% respectively and the trend remains also same irrespective of entrance lengths in the investigated range.

4.3.2. Effect of fibre concentration Fig. 10 represents a plot of heat transfer coefficient as a function of velocity for water and Kraft pine Hi at two different concentrations (0.2% and 0.4%) for the test section without extension rod (AR). At velocities <0.5 m/s the hc for fibre at a higher (0.4%) concentration is more than at a low concentration (0.2%) and water, showing augmentation of heat transfer. At a specific velocity of 0.3 m/s, 0.4% fibre produce 52% higher hc than water and 44% higher than fibre suspension at low concentration (0.2%). However at velocity 0.3 m/s and concentration (0.2%) hc values are 5.8% higher than that of water. At 0.2 m/s water, Hi fibre of 0.2 and 0.4% concentrations show 1.765, 2.471 and 3.177 kW/m2 K hc values. Thus high concentration fibre suspension is followed by lower concentration of fibre suspension and water. Similar results were mentioned elsewhere by present author and also obtained by previous researchers in annular flow of different dimensions [5], Duffy et al. [10] and Middis [6]. The augmentation of heat transfer is due to fibre entanglement, fibre-eddy and floc eddy interactions. With the increase in flow velocity the heat transfer coefficient of fibre suspensions crosses below the water values and show a lowering of heat transfer coefficient. At 0.2% fibre suspension the onset of the lowering is at 0.35 m/s and at 0.4% it moves to 0.76 m/s. Similar effects were observed previously [5] and in the case of annular flow [10] and pipe flow [5,6]. After the onset of lowering, the hc value of the higher fibre suspension concentrations move below the lower suspension concentration and remains steady. Similarly heat transfer data at the lower concentrated fibre suspension remain below the water data but above the fibre suspension of higher concentration. The low concentration fibre suspension experiences less fibre–fibre collision and the motion of the fibre is governed by turbulent eddies. With the increase of concentration, in the boundary layer there are more fibre–fibre interactions and more eddy-floc interactions

5. Conclusions In closed conduit flow the length of the conduit from the entry to the point where the fully developed flow begins is the entrance length. Investigation of entrance length effect on heat transfer to fibre suspensions in annular flow heat exchanger reveals that there is no significant variation of heat transfer coefficient for both water and fibre suspensions of low concentration (0.2%) with change in calming length from 23 and 38Dh. At a higher fibre concentration (0.4%) there are some changes in the measured values of hc and the difference prevails throughout the range of investigation with at least two different grades of Kraft pine coarseness (Hi and ULo) whereas the trend remains same. Conflict of interest None declared. Acknowledgements The authors gratefully acknowledge High Impact Research Grant UM.C/625/1/HIR/MOHE/ENG/45 and UMRG Grant RP012D-13AET,

556

S.N. Kazi et al. / International Journal of Heat and Mass Transfer 78 (2014) 548–556

Faculty of Engineering, University of Malaya, Malaysia and The University of Auckland, New Zealand for support to conduct this research work. References [1] S.N. Kazi, G.G. Duffy, X.D. Chen, Validation of heat transfer and friction loss data for fibre suspensions in a circular and a coaxial pipe heat exchanger, Int. J. Therm. Sci. 79 (2014) 146–160. [2] W.M. Kays, M.E. Crawford, Convective Heat and Mass Transfer, third ed., McGraw-Hill, New York, 1993. [3] H.L. Langhaar, J. Appl. Mech. 64 (A-55) (1942). [4] G.G. Duffy, S.N. Kazi, X.D. Chen, Heat transfer and pressure drop characteristics of suspensions of synthetic and wood pulp fibres in annular flow, Appl. Therm. Eng. 31 (2011) 2971–2980. [5] S.N. Kazi, Heat transfer to fibre suspensions-studies in fibre characterisation and fouling mitigation (Ph.D. thesis), Chemical and Materials Engineering, The University of Auckland, Auckland, New Zealand, 2001. [6] J. Middis, Heat transfer and pressure drop for flowing wood pulp fibre suspensions (Ph.D. thesis), Chemical and Materials Engineering. The University of Auckland, Auckland, New Zealand, 1994. [7] C.A. Branch, Heat Transfer and heat transfer fouling in evaporators with kraft pulp black liquor (Ph.D. thesis), Chemical and Materials Engineering, The University of Auckland, Auckland, New Zealand, 1991. [8] J.D. Bremford, An investigation of the performance of multiple effect evaporators for kraft black liquor (Ph.D. thesis), Chemical and Materials Engineering, The University of Auckland, Auckland, New Zealand, 1996. [9] D. Hasson, M. Avriel, W. Resnick, T. Rozenman, S. Windreich, Mechanism of calcium carbonate scale deposition on heat transfer surfaces, I EC Fundam. 7 (1) (1968) 59–65. [10] G.G. Duffy, S.N. Kazi, X.D. Chen, Heat transfer to fibre suspensions in annular flow, in: Proceedings of 28th CHEMECA Conference, Perth, Australia, Paper C4.2, 2000, pp. 366–369. [11] G.G. Duffy, S.N. Kazi, X.D. Chen, Heat transfer coefficient – a new way to monitor wood pulp quality, in: Proceedings of 54th Annual Appita Conference, Melbourne, Australia, Paper 4B12 (2), 2000, pp. 605–614. [12] A.A. Robertson, S.G. Mason, The flow characteristics of dilute fibre suspensions, Tappi 40 (5) (1957) 326–333. [13] G. Hemstrom, K. Moller, B. Norman, STFI Meddelande Series B (NR288), 1974. [14] P.F.W. Lee, G.G. Duffy, Velocity profiles in the drag reducing regime of pulp suspension flow, Appita 30 (3) (1976) 219–226. [15] Jianzhong Lin, Weifeng Zhang, Zhaosheng Yu, Numerical research on the orientation distribution of fibers immersed in laminar and turbulent pipe flows, Aerosol Sci. 35 (2004) 63–82.

[16] J. Lin, X. Shi, Z. Yu, The motion of fibers in an evolving mixing layer, Int. J. Multiphase Flow 29 (8) (2003) 1355–1372. [17] J.A. Olson, R.J. Kerekes, The motion of fibers in turbulent flow, J. Fluid Mech. 377 (1998) 47–64. [18] Jianzhong Lin, Lingxin Zhang, Weifeng Zhang, Rheological behavior of fiber suspensions in a turbulent channel flow, J. Colloid Interface Sci. 296 (2006) 721–728. [19] J.Z. Lin, Z.Y. Gao, K. Zhou, T.L. Chan, Mathematical modeling of turbulent fiber suspension and successive iteration solution in the channel flow, Appl. Math. Model. 30 (2006) 1010–1020. [20] S.N. Kazi, G.G. Duffy, X.D. Chen, Heat transfer in the drag reducing regime of wood pulp fibre suspensions, Chem. Eng. J. 73 (1999) 247–253. [21] Zhumin Lu, Boo Cheong Khoo, Hua-Shu Dou, Nhan Phan-Thien, Khoon SengYeo, Numerical simulation of fibre suspension flow through an axisymmetric contraction and expansion passages by Brownian configuration field method, Chem. Eng. Sci. 61 (2006) 4998–5009. [22] You Zhenjiang, Lin Jianzhong, Yu Zhaosheng, Hydrodynamic instability of fiber suspensions in channel flows, Fluid Dyn. Res. 34 (2004) 251–271. [23] H. Niskanen, H. Eloranta, J. Tuomela, J. Hamalainen, On the orientation of probability distribution of flexible fibres in a contracting channel flow, Int. J. Multiphase Flow 37 (2011) 336–345. [24] S.M. Dinh, R.C. Armstrong, A rheological equation of state for semiconcentrated fiber suspensions, J. Rheol. 28 (1984) 207–227. [25] M. Chaouche, D.L. Koch, Rheology of non-Brownian rigid fiber suspensions with adhesive contacts, J. Rheol. 45 (2001) 369–382. [26] S.A. Ramazani, A. Ait-Kadi, M. Grmela, Rheology of fiber suspensions in viscoelastic media: experiments and model predictions, J. Rheol. 45 (2001) 945–961. [27] R.S. Seth, Fibre quality factors in papermaking-II. The importance of fibre coarseness, MRS Spring Meeting, MRS Proceedings, vol. 197, 1990. [28] L. Paavilainen, Conformability–flexibility and collapsibility-of sulphate pulp fibre, Pap. Puu 5 (9–10) (1993) 689–702. [29] O.L. Forgacs, The characterization of mechanical pulps, Pulp Pap. Mag. Can. (1963) 89–118 (Convention issue 64 C). [30] S.N. Kazi, G.G. Duffy, X.D. Chen, Heat transfer to fibre suspensions, in: IPENZ Conference, Auckland, New Zealand, 1998. [31] S.T. Paul, Fibre suspension processing in viscous media (Ph.D. thesis), Chemical and Materials Engineering, The University of Auckland, Auckland, New Zealand, 1999. [32] S.N. Kazi, G.G. Duffy, X.D. Chen, Validation of heat transfer data for fibre suspensions in coaxial pipe heat exchangers, Exp. Therm. Fluid Sci. 38 (2012) 210–222.