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Validation of heat transfer data for fibre suspensions in coaxial pipe heat exchangers
Experimental Thermal and Fluid Science 38 (2012) 210–222
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Validation of heat transfer data for fibre suspensions in coaxial pipe 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, Monash University, Victoria 3800, Australia b
a r t i c l e
i n f o
Article history: Received 9 September 2011 Received in revised form 12 December 2011 Accepted 17 December 2011 Available online 26 December 2011 Keywords: Pressure drop Heat transfer Synthetic fibre Natural fibre Fibre concentration Coarseness Population Annular flow
a b s t r a c t Heat transfer data obtained previously in a small coaxial pipe heat exchanger were validated using a new, larger annular-area test unit with longer calming section and axial entry flow. Water and two suspensions of long-fibre softwood Kraft pulps with fibres having different coarseness (mass/unit fibre length) values were used. Data in both systems were obtained over a range of flow rates with the fibre concentration at 0.4% and compared. Heat transfer coefficient hc was found to decrease with increasing annular gap size for both water and fibre suspension flow at equal velocities. Various fibre dimensions and fibre characteristics are also shown to vary systematically with hc at the same experimental conditions. The effect of hydrodynamic annular entry length on heat transfer and pressure loss using water and fibre suspensions (concentrations 0.2% and 0.4%) are also described. It was found that that extending the central calming extension rod made no significant difference to hc values at the low fibre concentration of 0.2%, and only small differences at the higher concentration of 0.4%. The successful validation of data from the smaller-annulus coaxial pipe heat exchanger show that the relationships among heat and momentum transfer and fibre characteristics and specific properties of paper are also valid for both heat exchangers. Ó 2011 Elsevier Inc. 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. An investigation of heat transfer and pressure drop in annular flow with and internal coaxial heater was reported previously by the present authors but there was some concern with the results as spiralling flow was observed in some instances caused by the inlet flow being perpendicular to the tube axis. The calming length was regarded as insufficient to settle the flow in the test section and the flow pattern changed with velocity. The problem was exacerbated with fibre suspensions as the small annular gap meant that there was a stronger possibility for fibre–fibre bundling at the lower flow rates. Hence it was decided to rebuild the apparatus with axial flow entry, a longer calming length, and a larger annular gap. The modified test section offered an opportunity to investigate the effects of calming length and hydraulic diameter on drag reduction and heat transfer in annular flow, that have not been reported in the literature previously. This and the validation of pre-
⇑ 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. 0894-1777/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2011.12.009
vious research into the flow of fibre suspensions in annular flow is the subject of this present work.
2. Literature review The study of heat transfer and frictional pressure loss in tubes and annular spaces has been used to provide a basis for designing heat exchangers and cooling systems in industry. Design data are available mainly for common fluids but there are no significant published data for fibre suspension systems. Duffy et al. [1] studied heat transfer to fibre suspensions in annular flow. Various Kraft softwood and hardwood pulp water suspensions were investigated using 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 [2]. They have proposed that hc could be used to monitor and therefore control pulp quality variations. It has long been known that pipe friction loss for fibre suspensions is diameter dependent [3] and decreases with increasing diameter. This is caused by the plug-like character at low flow rates [4]. The diameter effect is weaker in turbulent flow which is the
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Nomenclature hydraulic diameter (m) pipe diameter (m) fanning friction factor heat flux (W/m2) Reynolds number hydraulic radius (m) wall temperature (°C)
drag reducing regime for fibre suspensions [5,6]. Sharma [7] also found lower drag reduction in bigger diameter pipes. Patterson et al. [8] also showed that the diameter effect on drag reduction is extremely weak when comparisons are made at constant velocity instead of constant Reynolds number. Hence a study of the variation in annular gap is significant as nothing has been reported in the literature. Robertson and Mason [3] 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. [9] 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 [10] 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 [11] selected 20 hydraulic diameters Dh in his studies of heat transfer to fibre suspensions in annular flow. Previous researchers Middis [11], Branch [12], and Bremford [13] used a calming length of 20 Dh whereas Hasson et al. [14] selected a value of 38Dh in their heat transfer fouling study in annular flow. More recent research [15–17,18–22], has been focussed on numerical simulation, spatial and orientation distributions of fibres in various flow fields, with some experimental validation. Some investigations have extended knowledge in the shear flow behaviour of fibre suspensions [23–25]. The aim of present work, therefore, is to generate more experimental data for future development of a model for turbulent fibre suspensions flow.
3. Experimental 3.1. Experimental set-up The measurement of heat transfer and pressure loss were performed in a new annular test section with dimensional details shown schematically in Fig. 1b, and the common flow loop in Fig. 1a. Details of the previously used test section are presented in Fig. 2. The magnitudes of the dimensional differences are stated in Table 1. The pressure drop across the test section was measured with a differential pressure transducer at the tapping points designated in Fig. 1b. The Perspex test section has a stainless steel heating rod with a calming extension rod mounted concentrically. The heater rod has four embedded E-type thermocouples, with three located close to the internal heater just below the rod surface for surface temperature measurement. The fourth thermocouple is used to activate a safety trip in the event of high surface temperatures. The power supply to the heated section is controlled by the 10 amp-rated Variac. Current and voltage are measured and the signals are transmitted to the computer data logger through a
temperature at thermocouple location (°C) fluid velocity (m/s) distance along x axis (m) density (kg/m3) shear stress (N/m2) dynamic viscosity (kg/ms) thermal conductivity (W/mK)
TTC u x
q s l k
Hewlett Packard data acquisition equipment. Further details are presented elsewhere [1,26].
Annular cooler Heater Tout
Dp cell
Dh d f q Re rh TS
Flow meter Magnetic Flow meter
Bypass
Tin
Test section
Tank
Pump
Cooling pump
Cooling water tank
Fig. 1a. Schematic diagram of the experimental flow loop.
Heater
57
20 Flow out Pressure 3 tapping 10.7 Heater element Stainles steel
370 96
820 26
3 Pressure tapping
1117
20 Extension rod Perspex outer tube Flow in 20
6
150
35
44 96
Fig. 1b. Schematic diagram of the coaxial-pipe, annular Test Section B with the larger hydraulic diameter and extended calming rod.
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20
Heater
60
Flow out Pressure taping
384.5
Heater element
T S ¼ T TC q=ðk=xÞ
585.7 15 9.8
Extension rod
ð1Þ
Fibre concentration was measured at the beginning and end of each run and the measured values were always in agreement with differences less than 5%.
19.8
2
20
Different types of synthetic filaments were also investigated and details are given elsewhere [27]. Before each experiment, the pulp fibres obtained in sheets were soaked for approximately 24 h and then dispersed by the pump operating in recycle mode. Recycling was maintained for approximately 1 h to ensure optimum fibre dispersion and fibre wetting, and then for a further hour before any measurements were taken. A summary of experimental conditions is given in Table 1. Experimental corrections for the thermocouples k/x values in both the cases before and after the annular test section modifications are presented in Table 2 according to the following equation:
3.4. Data reduction
Flow in
Reynolds number:
3
Re ¼ qud=l
10.7 Fig. 2. Schematic diagram of the coaxial pipe annular Test Section A (small gap) with stainless-steel heater, short calming length extension rod, and inlet pipe normal to the annular flow direction.
Hydraulic diameter:
Dh ¼ 4r h ¼ d1 d2 2
Parameters
Test Section A (smaller pipe diameter)
Test Section B (larger pipe diameter)
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
1135.0
100.0 10.7 23.8
100.0 10.7 44.0
13.1
33.3
499.8
1021.6
82.6
82.6
3.2. Data acquisition
2
2
dm ¼
ð3Þ
d2 dm d2
4r h ¼ Table 1 Dimensions of the annular test section before and after modifications with differences highlighted.
ð2Þ
ð4Þ
2
d2 d1 2
ð5Þ
2
lnðd2 =d1 Þ
The Reynolds number Re2 of the outer portion of annular velocity profile is presented in the following equation:
Re2 ¼
4r h uq
ð6Þ
l
The friction factor f2 on the outer wall of annulus bears the same relationship to the Reynolds Number, Re2 as is given in Eq. (7) for circular tubes:
ð2:1 103 < Re < 105 Þ
f ¼ 0:079Re0:25
ð7Þ
The shear stress s2 on the outer wall of the annulus is stated in the following equation:
s2 ¼ f2 qu2 =2
ð8Þ
The shear stress s1 on the inner wall is expressed by: All temperatures, flow velocities, differential pressures, voltages and currents were recorded with an IBM compatible XT personal computer, a Hewlet Packard PCIB interface, a 61013A digital multi-meter and two 61011A relay multi-plexers. The data acquisition equipment is controlled using a BASIC program. The program allows the operator to choose between automatic and manual data acquisition modes according to the requirements. Details are stated elsewhere [1,26].
3.3. Experimental procedures Fibres used in these experiments were prepared by the Kraft chemical process. These included four pine pulps (pinus radiata), one bleached spruce Sp, a bleached eucalyptus Eu, and a market Kraft bleached pine pulp. The four pine pulps were produced from different aged trees and the fibres varied in length and coarseness (mass/unit length). They are designated in terms of coarseness: High Hi, Medium Med, Low Lo and Ultra low ULo coarseness pulps.
s1 ¼ s2 ðd2 =d1 Þ
2
2
2
2
dm d1
! ð9Þ
d2 dm
4. Results and discussion 4.1. Data reproducibility The rig with the new Test Section B (see Table 1) was calibrated using water. The procedural accuracy and reproducibility of data
Table 2 k/x values before and after modifications. Location
k/x
Values (before modification)
Values (after modification)
1 2 3
k/x1 k/x2 k/x3
25,000 12,500 14,286
20,000 14,286 20,000
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Bleached Kraft pine (BK) fibre of mean length 2.53 mm and coarseness 0.246 mg/m was used in the test runs to study the effect of fibres and fibre concentration on heat transfer. The data are present as hc versus flow velocity in Fig. 5 for four different fibre concentrations (0.1–0.4%) with water as the reference. At velocities greater than about 0.5 m/s there is a spread of hc data below the water values similar to that obtained previously for pipe flow [27], as well as the data from the smaller Test Section A (see Fig. 6). At lower velocities (<0.5 m/s) there is a noticeable increase of hc above water values due to fibre–fibre interactions and some network fragment structures being formed. The thermal conductivity of fibre is less than that of water but fibres provide a solid path for heat conduction through the fibres themselves at low velocity which contributes to higher overall heat transfer coefficient values [11,27]. The data trends validate the results obtained from previous investigations. 4.3. Effect of fibre flexibility Fig. 7 shows heat transfer coefficient hc as a function of velocity for different grades of pine, spruce and eucalyptus fibres at a concentration of 0.4%. For the pine fibre suspensions, hc decreases as both fibre length and fibre coarseness (mass/unit length) decrease, in agreement with data obtained in the smaller annular Test Section A (Fig. 8). The largest relative spacing for the data is at 1.5 m/s in both annular flow systems. 4.4. Hydraulic diameter/heat transfer to water and fibre suspensions Data are presented in Fig. 9 for heat transfer coefficient as a function of flow velocity for water and two different pine fibre suspensions (Hi and ULo) in annular flow for the two different annular channel gaps or hydraulic diameters (0.0131 and 0.0333 m) [Annular Test Sections A and B]. Heat transfer coefficient values of the Hi and ULo pine fibre suspensions at 0.4% concentration are of the
Heat transfer coeff. kW/m2 K
12 Water (1) Water (2)
9
Pressure drop ( Δ P/L) Pa/m
Water (1)
250
Water (2)
200 150 100 50 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 4. Pressure drop as a function of flow velocity for two water runs. DP/L data were obtained at DT 15 °C and a bulk temperature of 30 °C.
Heat transfer coefficient kW/m2 K
4.2. Fibre concentration effect
300
12 Water
10 BK0.1 BK0.2
8
BK0.3
6
BK0.4
4 2 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 5. Heat transfer coefficient as a function of flow velocity for water and different concentrations of bleached Kraft pulp fibre suspensions (Annular Test Section B). The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
Heat transfer coefficient kW/m2 K
were studied, and the data obtained compared with results with those from Test Section A used previously. The heat transfer results are presented in Fig. 3 with hc as a function of velocity, and the pressure drop data are presented in Fig. 4. Data reproducibility in both cases was very good with an rms error <3% within the confidence level of 95% for heat transfer, an average rms error <5% within the confidence level of 95% for the pressure drop data for the two water runs.
10 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
1.2
1.4
1.6
Velocity m/s 6
Fig. 6. Heat transfer coefficient as a function of flow velocity for different concentrations of pulp Hi fibre suspensions (Annular Test Section A with the smaller annular gap.) Heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
3
0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 3. Heat transfer coefficient as a function of flow velocity for two water runs. The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
same relative order in both Test Sections A and B with respect to water. Fig. 10 depicts hc as a function of Re (based on hydraulic diameter) for water and the Hi and ULo fibre suspensions at 0.4% fibre concentration. The Reynolds number corresponding to 1.5 m/s in the smaller annular Test Section A is 24,643 whereas
Heat transfer coefficient kW/m2 K
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12 10 8
Water
Hi
Med
Lo
ULo
Sp
Eu
6 4 2 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 7. Heat transfer coefficient as a function of flow velocity for water and different grades (Hi, Med, Lo and ULo) of Kraft pine fibre suspensions of concentration 0.4% (Test Section B with larger annular area). The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
higher than all hc values in the larger annular Test Section B indicating that there are higher turbulence-augmented hc values in the smaller annular area test section. For a more accurate comparison of hc values corresponding to each velocity [28], the shear stress at the wall of the inner heating rod has been calculated for both water and suspension flows. The hc values are presented as a function of shear stress in the two cases [smaller (S) and larger (L) hydraulic diameter] in Fig. 11. It is observed that hc increases with increasing wall shear stress in all cases. As mentioned above, the hc values for water and fibre suspensions are always larger in the smaller annular Test Section A. Percentage differences are similar to the values of hc obtained as a function of velocity (Fig. 9). Thus either shear stress or velocity can be chosen as a variable parameter for comparison of hc. From these investigations it is obvious that the hc increases with decreasing annular gap (hydraulic diameter of the annulus space) for water and fibre suspension flow but the trends are still systematic and of the same order of magnitude.
12 10
Water
Hi
Med
Lo
ULo
Sp
Euc
8 6 4 2 0 0
0.4
0.8
1.2
1.6
2
2.4
Velocity m/s
Heat transfer coefficient kW/m2 K
Fig. 8. Heat transfer coefficient as a function of velocity for water, Kraft pine, spruce and eucalyptus fibre suspensions of concentration 0.4% (Test Section A with the smaller annular area). Heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
12 10 8
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
4 2 0 0.4
0.8
4.6. Hydraulic diameter and pressure drop of water and fibre suspensions Frictional pressure drop as a function of velocity for water and two different fibre suspensions (Hi and ULo) are presented in Fig. 13. The magnitude of pressure drop for water and ULo and
6
0
Fig. 12 shows heat transfer coefficient hc as a function of velocity for water and Kraft pine Hi and ULo coarseness at two concentrations 0.2% and 0.4% respectively for both annular test sections. The centrally located heating rod has a removable extension rod of the same diameter to aid in providing adequate calming. Data are presented in Fig. 12 without extension rod AR., and with extension rod BR. The typical increase in hc at low velocities is seen at both concentrations, with or without the calming extension rod. It can be observed that the data sets are in close agreement over the whole range of velocities for both fibre concentrations (about 13% lower than water values). This is significant as it shows that the upstream calming rod has little effect on the values obtained. A 65% increase in calming length in terms of hydraulic diameter (38 Dh and 23 Dh) only produces a 5.8% maximum difference at higher velocities (>1 m/s).
1.2
1.6
2
2.4
Velocity m/s Fig. 9. Heat transfer coefficient as a function of flow velocity for water and Hi and ULo pine fibre suspensions in annular flow for two different hydraulic diameters Dh [0.0131(S) and 0.0333(L) m]. The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
Heat transfer coefficient kW/m2 K
Heat transfer coefficient kW/m2 K
4.5. Effect of calming length on heat transfer 14
12 10 8 6 4 2
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
0 0
15
30
45
60
75
90
3
Reynolds number x10 the corresponding value at the same velocity in the larger Test Section B is 82,934. A comparison can be made on the basis of similar Re. At the Re of 24,643, the value of hc in the smaller annular Test Section A is
Fig. 10. Heat transfer coefficient as a function of Reynolds number for water and Hi and ULo pine fibre suspensions in annular flow for two different hydraulic diameters Dh [0.0131(S) and 0.0333(L) m]. The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
215
Heat transfer coefficient kW/m2 K
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
12 10 8
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
6 4 2 0 0
3
6
9
12
15
18
Shear stress N/m2
Heat transfer coefficient kW/m2 K
Fig. 11. Heat transfer coefficient as a function of wall shear stress for water and Hi and ULo fibre suspensions in annular flow for two different hydraulic diameters Dh (0.0131 and 0.0333 m). The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
12 WATER(AR)
10
Hi0.2(AR) ULo0.4(AR)
8
WATER(BR) Hi0.2(BR)
6
ULo0.4(BR)
4 2 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 12. Heat transfer coefficient as a function of velocity for water and pine Hi and ULo fibre suspensions at concentrations of 0.2 and 0.4, without the calming extension rod (AR), and with the extension rod (BR). Heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
Hi fibre suspensions of 0.4% concentration are of the same order in both the cases. DP/L for smaller hydraulic diameter is higher than those of larger hydraulic diameter at all velocities as expected. Frictional pressure drop is presented as a function of Re (based
on hydraulic diameter Dh) in Fig. 14. The Reynolds number corresponding to 1.5 m/s in the smaller annular gap is 24,643, whereas in larger annulus, it is 82,934. It is observed that the order of magnitude of DP/L for water, ULo and Hi, is similar in both the cases of the smaller and larger annular gaps. At a particular Reynolds number (24,643 corresponding to 1.5 m/s in smaller annulus), the magnitude of DP/L for water, ULo, and Hi in smaller Dh annular flow are respectively 99.7%, 99.2% and 98.8% higher than those of in the larger Dh. Further analysis of unit frictional pressure drop DP/L in the annulus test section was extended by plotting the data as a function of wall shear stress on the outer surface of the inner rod. Fig. 15 represents frictional pressure drop as a function of shear stress in the smaller and larger annular gaps for water, Hi and ULo fibre suspensions at 0.4% concentration. DP/L clearly increases with the increase of shear stress in all the cases over the entire range of investigation. It can be seen that when the shear stress level on the heater rod outer surface is equal in the two annular set-ups, DP/L levels in the smaller annular flow unit are higher than all those in the larger annular space unit (for water, ULo and Hi suspension). At a specified shear stress (9.6 N/m2) corresponding to a velocity 1.5 m/s, DP/L values are 96.8%, 96.1% and 95.3% higher in the smaller annular unit than in the larger annulus (for water, ULo and Hi suspensions respectively). These values are similar to the values obtained in the case of DP/L versus velocity (Fig. 13). It can be concluded that in the heat transfer study the observed values of hc in the smaller annulus are almost same percentages higher than those of larger annulus, irrespective of whether hc is presented as a function of velocity or shear stress. 4.7. Study of pressure drop in the test section with long and short calming lengths Fig. 16 depicts pressure drop as a function of velocity for water flow in the annular test section with both the extended BR and with virtually no calming lengths AR (after removal). The pressure drop was measured across the whole test section. At a specific velocity of 1.5 m/s, the pressure drop is about 23.5% lower than with longer calming length. The difference increases with increasing velocity. Removing the extended inlet-calming length rod from central heater reduces the constriction and calming of the inlet flow, causing fluid impact on the leading face of the heater rod that affects the magnitude of the pressure loss.
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
Pressure drop (ΔP/L) kPa/m
Pressure drop ( ΔP/L) kPa/m
10 10 8 6 4 2
8
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
6 4 2 0
0 0
0.4
0.8
1.2
1.6
2
2.4
Velocity m/s Fig. 13. Pressure drop (DP/L) as a function of velocity for water, Hi and ULo fibre suspensions in annular flow for two different hydraulic diameters Dh (0.0131 and 0.0333 m). DP/L was measured at DT 15 °C, bulk temperature 30 °C and fibre concentration of 0.4%.
0
15
30
45
60
75
90
3
Reynolds number x10
Fig. 14. Pressure drop (DP/L) as a function of Reynolds number for water and Hi and ULo fibre suspensions in annular flow for two different hydraulic diameters Dh (0.0131 and 0.0333 m). DP/L was measured at DT 15 °C, bulk temperature 30 °C and fibre concentration of 0.4%.
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Pressure drop ( ΔP/L) kPa/m
10
8
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
6
4
2
0 0
3
6
9
12
15
18
Shear stress N/m2 Fig. 15. Pressure drop (DP/L) as a function of shear stress for water, Hi and ULo fibre suspensions in annular flow for two different hydraulic diameters (0.0131 and 0.0333 m). DP/L was measured at DT 15 °C, bulk temperature 30 °C and fibre concentration of 0.4%.
5. Conclusions
9
Pressure drop ( Δ P/L) kPa/m
was selected which was similar to values chosen for pipeline studies. The measuring techniques and procedures used with the smaller Test Section A had been of concern initially because of observed spiral entry flow, and the potential ongoing effect of the smallerthan-normal calming entry length. The research reported here with the improved set-up of coaxial pipe heat exchanger (Test Section B), resulted in a large amount of data that compared favourably with the previous experimental data obtained from the coaxial pipe heat exchanger of different dimensions. Clearly the concerns were allayed, and the results confirm that heat transfer coefficient and pressure drop measurements are promising ways of monitoring fibre variations and hence pulp quality. Some of the extensive correlations relating both fibre characteristics and the properties of paper made from the same fibres, are presented in the Appendix A. The results of this study using a larger annular space [Test Section B] further support the validation of that the comparable data obtained with the original heat exchanger [1].
8
Water(AR)
7 Water(BR)
6 5 4 3 2 1 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 16. Frictional pressure drop across the test section for water as a function of velocity, before (BR) and after (AR) removing the central calming extension rod. Friction loss data were obtained at DT 15 °C and a bulk temperature 30 °C.
4.8. Summary of comparisons The trends in the data reported here obtained from the larger, annular-gap coaxial pipe heat exchanger (Test Section B) validate the results obtained from the previously-used, smaller annulargap Test Section A [1]. The larger annular gap unit with the improved entry and extended calming rod length indeed gave more accurate and in some cases slightly better correlations, but overall these extensive tests validated the previous work [1] and showed that those results could also be used with confidence.
4.9. Fibre characterisation and validation of the two heat exchangers Extensive research programmes had been carried out previously to determine how various fibre properties would modify turbulence and hence provide a means of measuring and monitoring fibre characteristics and pulp quality. It had been found in pipe flow [2] that specific fibre characteristics and some fibre properties could be assessed by both heat transfer measurements and friction loss determination. Following those studies there was a need to evaluate smaller quantities of fibre in a smaller flow loop, and hence a small coaxial pipe heat changer was used [1]. Again heat and momentum transfer measurements were used and both hc and DP/L values obtained over a range of flow conditions. A comparative condition of 1.5 m/s and 0.4% fibre concentration
The results from this present study confirm that the data obtained in a smaller, annular-space coaxial heat exchanger are valid even though the results were not as accurate as those obtained in the larger annular test unit. Heat transfer to fibre suspensions is observed to increase with decreasing hydraulic diameter for water and fibre suspensions, either at equal velocities or equal shear stress levels. Hence, either shear stress or velocity can be used to compare hc values calculated from data obtained in an annular space because experimentally, the similar Dhc were obtained in two different annular test sections with different hydraulic diameters. Heat transfer to water or to fibre suspensions of low concentrations (0.2%) does not change significantly with change of calming length but at higher fibre concentration (0.4%) the difference is detectable but still very small.
Appendix A Graphical comparison of fibre and paper properties as a function of hc and DP/L of fibre suspensions flowing through the smaller Annular Test Section A and Larger Annular Test Section B for direct comparison. (L0 = mean fibre length, D = mean fibre diameter, P = fibre perimeter, t = fibre thickness).
A.1. Smaller annular space A.1.1. Test Section A Fibre properties versus hc (see Figs. A1–A6). Paper properties versus hc (see Figs. A7–A10). Fibre properties versus DP/L (see Figs. A11–A16). Paper properties versus DP/L (see Figs. A17–A20).
Appendix B B.1. Larger annular space B.1.1. Test Section B Fibre properties versus hc (see Figs. B1–B6). Paper properties versus hc (see Figs. B7–B10). Fibre properties versus DP/L (see Figs. B11–B16). Paper properties versus DP/L (see Figs. B17–B20).
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225 Hi
2
2.5
Fibre wall area μm
2 1.5 1
Hi
Med
Lo
ULo
Sp
Euc
0.5
Med
150 125
7.2
7.4
7.6
7.8
8
7.2
7.4
7.6
7.8
8 2
Heat transfer coefficient kW/m K Fig. A5. Fibre wall area versus hc.
Fig. A1. Length L0 versus hc.
35
130
Relative fibre number
Dimentional ratio L'/ P
Sp
175
Heat transfer coefficient kW/m2 K
30 25 20 15
Hi
Med
Lo
ULo
Sp
Euc
120
Hi
Med
ULo
Sp
Lo
110 100 90 80
10
70 7.2
7.4
7.6
7.8
8
7.2
7.4
Heat transfer coefficient kW/m2 K
7.6
7.8
8
Heat transfer coefficient kW/m2 K
Fig. A2. L0 /P versus hc.
Fig. A6. Relative fibre number versus hc.
35 ULo
Lo
Med
Hi
Sp
Euc
Tensile index mN.m 2/g
120
30
Ratio P /t
ULo
100 7
25 20 15
17 14.5
100
10
12 80
9.5 7
60
Hi
Med
Lo
Ulo
Hi
Med
Lo
Ulo
4.5
40 7.2
7.4
7.6
7.8
8
2 7.5
Heat transfer coefficient kW/m2 K
7.6
7.7
7.8
7.9
8
Heat transfer coefficient kW/m2 K
Fig. A3. P/t versus hc.
Fig. A7. Paper tensile and tear indices versus hc.
0.3
9
0.26
Hi
Med
Lo
Ulo
8
0.22
Burst index
Coarseness
Lo
200
Tear index mN.m2/g
Fibre length L' mm
3
0.18 Hi
Med
Lo
ULo
Sp
Euc
0.14 0.1
7 6 5
0.06 0.02
4 7
7.2
7.4
7.6
7.8
Heat transfer coefficient kW/m2 K Fig. A4. Coarseness versus hc.
8
8.2
7.5
7.6
7.7
7.8
7.9
Heat transfer coefficient kW/m2 K Fig. A8. Burst index versus hc.
8
218
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
35 Hi
Med
Lo
ULo
30
25
Ratio P /t
Lt. Scatt. Coeff. m2 /kg
30
20
Lo
Med
Hi
Sp
Euc
25 20
15 15 10
10 7.5
7.6
7.7
7.8
7.9
8
4.9
5
5.1
2
5.2
5.3
5.4
5.5
Pressure drop kP/m
Heat transfer coefficient kW/m K
Fig. A13. P/t versus DP/L.
Fig. A9. Light scattering coefficient versus hc.
0.3
4.6 Hi
Med
Lo
ULo
Sp
0.26
4.2
Coarseness
Formation Index
ULo
3.8 3.4
Hi
Med
Lo
ULo
Sp
Euc
0.22 0.18 0.14 0.1
3 0.06 2.6 7.2
7.4
7.6
7.8
0.02
8
4.5
4.7
4.9
Heat transfer coefficient kW/m2 K Fig. A10. Formation index versus hc.
5.5
225
2.5
Hi
Med
Lo
ULo
Sp
Euc
Hi
Fibre wall area μm2
Fibre length L' mm
5.3
Fig. A14. Coarseness versus DP/L.
3
2 1.5 1 0.5
Med
Lo
ULo
Sp
200 175 150 125 100
4.5
4.7
4.9
5.1
5.3
5.5
4.7
4.9
Pressure drop kP/m
5.3
5.5
Fig. A15. Fibre wall area versus DP/L.
150
Relative fibre number
35
30
25
20
15 4.7
5.1
Pressure drop kP/m
Fig. A11. L0 versus DP/L.
Dimentional ratio L'/P
5.1
Pressure drop kP/m
4.9
Hi
Med
Lo
ULo
Sp
Euc
5.1
Pressure drop kP/m Fig. A12. L0 /P versus DP/L.
5.3
5.5
130
Hi
Med
ULo
Sp
Lo
110
90
70 4.7
4.9
5.1
5.3
Pressure drop kP/m Fig. A16. Relative fibre number versus DP/L.
5.5
219
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
3
14.5 100 12 80
9.5 7
60
Hi
Med
Hi
40 4.9
Med
Lo
ULo
Lo
4.5
ULo
Fibre length L' mm
17
Tear index mN.m 2/g
Tensile index mN.m2/g
120
2.5 2 1.5 1
Hi
Med
Lo
ULo
Sp
Eu
2 5
5.1
5.2
5.3
5.4
5.5
0.5 6.75
Pressure drop kP/m
6.85
6.95
7.05
7.15
7.25
7.35
2
Heat transfer coefficient kW/m K
Fig. A17. Tensile and tear indices versus DP/L.
Fig. B1. Length L0 versus hc.
9 Hi
Med
Lo
40
Ulo
Dimentional ratio L'/P
Burst index
8 7 6 5 4 4.9
5
5.1
5.2
5.3
5.4
5.5
Hi
Lo
ULo
Sp
Eu
30
25
20 6.75
Pressure drop kP/m
Med
35
6.85
6.95
7.05
7.15
7.25
7.35
2
Heat transfer coefficient kW/m K
Fig. A18. Burst index versus DP/L.
Fig. B2. L0 /P versus hc.
35 Hi
Med
Lo
ULo
25
30
Ratio P /t
Lt. Scatt. Coeff. m2 /kg
30
20
15
Hi
Med
Lo
ULo
Sp
Eu
25 20 15
10 4.9
5
5.1
5.2
5.3
5.4
10 6.75
5.5
Pressure drop kP/m
6.85
6.95
7.05
7.15
7.25
7.35
Heat transfer coefficient kW/m2 K
Fig. A19. Light scattering coefficient versus DP/L. Fig. B3. P/t versus hc.
0.3
4.6 4.2
Coarseness
Formation Index
0.26
3.8 3.4 3
Hi
Med
Lo
Ulo
Sp
5
5.1
5.2
5.3
Pressure drop kP/m Fig. A20. Formation index versus DP/L.
5.4
Med
Lo
ULo
Sp
Eu
0.22 0.18 0.14 0.1 0.06
2.6 4.9
Hi
5.5
0.02 6.75
6.85
6.95
7.05
7.15
7.25 2
Heat transfer coefficient kW/m K Fig. B4. Coarseness versus hc.
7.35
220
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
30 Hi
Med
Lo
ULo
Sp
Lt. Scatt. Coeff. m2/kg
Fibre wall area μm2
250 225 200 175 150 125 100 6.75
6.85
6.95
7.05
7.15
7.25
Hi
6.85
130
7.15
7.25
7.35
4.6
120
Hi
Med
ULo
Sp
Lo
Hi
Formation Index
Relative fibre number
7.05
Fig. B9. Light scattering coefficient versus hc.
Fig. B5. Fibre wall area versus hc.
110 100 90 80 70 6.75
6.85
6.95
7.05
7.15
7.25
3
6.85
7
40 6.85
6.95
Hi
Med
Lo
ULo
7.05
7.15
4.5
Hi
Fibre length L' mm
9.5
80
Tear index mN.m2/g
2
12
ULo
7.05
7.15
7.25
7.35
3
14.5 100
Lo
6.95
Fig. B10. Formation index versus hc.
17
Med
Sp
Heat transfer coefficient kW/m2 K
120
Hi
ULo
3.4
Fig. B6. Relative fibre number versus hc.
60
Lo
3.8
2.6 6.75
7.35
Med
4.2
Heat transfer coefficient kW/m2 K
Tensile index mN.m /g
6.95
Heat transfer coefficient kW/m2 K
Heat transfer coefficient kW/m K
2 7.35
7.25
Med
Lo
ULo
Sp
Eu
2.5 2 1.5 1 0.5 150
2
175
Heat transfer coefficient kW/m K
200
225
250
275
Pressure drop Pa/m
Fig. B7. Paper tensile and tear indices versus hc.
Fig. B11. L0 versus DP/L.
40 Hi
Med
Lo
Dimentional ratio L'/P
9 ULo
8
Burst index
ULo
20
2
7 6 5 4 6.75
Lo
25
15 6.75
7.35
Med
6.85
6.95
7.05
7.15
7.25
Heat transfer coefficient kW/m2 K Fig. B8. Burst index versus hc.
7.35
35 30 25 20 15 10 150
Hi
175
200
Med
Lo
225
Pressure drop Pa/m Fig. B12. L0 /P versus DP/L.
ULo
Sp
250
Eu
275
221
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
Med
Lo
ULo
Sp
Eu
Tensile index mN.m2/g
30
Ratio P /t
17
120 Hi
25 20 15 10 150
175
200
225
250
14.5 100 12 9.5
80
7 60
40 175
275
200
0.3 Lo
ULo
Sp
Eu
Hi
0.14 0.1
0.02 150
Lo
ULo
225
Med
Lo
4.5 2 275
250
ULo
7 6
175
200
225
250
4 175
275
200
Pressure drop Pa/m
225
250
275
Pressure drop Pa/m
Fig. B14. Coarseness versus DP/L.
Fig. B18. Burst index versus DP/L.
250
30 Hi
Med
Lo
ULo
Sp
Lt. Scatt. Coeff. m2 /kg
Fibre wall area μm2
Med
5
0.06
200 175 150 125
175
200
225
250
Hi
Lo
ULo
20
15 175
275
Med
25
200
Pressure drop Pa/m
225
250
275
Pressure drop Pa/m
Fig. B15. Fibre wall area versus DP/L.
Fig. B19. Light scattering coefficient versus DP/L.
150
4.6
130
Hi
Med
Lo
ULo
Sp
110
90
175
200
225
250
Pressure drop Pa/m Fig. B16. Relative fibre number versus DP/L.
275
Hi
Formation Index
Relative fibre number
Hi
8
Burst index
Coarseness
Med
0.18
70 150
ULo
9 Hi
0.22
100 150
Lo
Fig. B17. Tensile and tear indices versus DP/L.
Fig. B13. P/t versus DP/L.
225
Med
Pressure drop Pa/m
Pressure drop Pa/m
0.26
Hi
Tear index mN.m2/g
35
Med
Lo
ULo
Sp
4.2 3.8 3.4 3 2.6 150
175
200
225
Pressure drop Pa/m Fig. B20. Formation index versus DP/L.
250
275
222
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
References [1] G.G. Duffy, M.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. [2] G.G. Duffy, M.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. [3] A.A. Robertson, S.G. Mason, The flow characteristics of dilute fibre suspensions, Tappi 40 (5) (1957) 326–333. [4] G.G. Duffy, A.L. Titchener, P.F.W. Lee, K. Moller, The mechanisms of flow of pulp suspensions in pipes, Appita 29 (5) (1976) 363–370. [5] J.W. Daily, G. Bugliarello, The effects of fibres on velocity distribution, turbulence and flow resistance of dilute suspensions, Tappi 44 (7) (1961) 497–512. [6] W. Mih, J. Parker, Velocity profile measurements and a phenomenological description of turbulent fibre suspension pipe flow, Tappi 50 (5) (1967) 237– 246. [7] R.S. Sharma, Drag reduction by fibres, Can. J. Chem. Eng. 59 (1981) 3–13. [8] G.K. Patterson, J.L. Zakin, J.M. Rodriguez, Drag reduction-polymer solutions, soap solutions, and solid particle suspensions in pipe flow, Indust. Eng. Chem. 61 (1) (1969) 22–30. [9] G. Hemstrom, K. Moller, B. Norman, STFI Meddelande Series B (NR288), 1974. [10] P.F.W. Lee, G.G. Duffy, Velocity profiles in the drag reducing regime of pulp suspension flow, Appita 30 (3) (1976) 219–226. [11] J. Middis, Heat Transfer and Pressure Drop For Flowing Wood Pulp Fibre Suspensions, PhD thesis, Chemical and Materials Engineering, The University of Auckland, Auckland, New Zealand, 1994. [12] C.A. Branch, Heat Transfer and Heat Transfer Fouling in Evaporators with Kraft Pulp Black Liquor, PhD thesis, Chemical and Materials Engineering, The University of Auckland, Auckland, New Zealand, 1991. [13] J.D. Bremford, An Investigation of the Performance of Multiple Effect Evaporators for Kraft Black Liquor, PhD thesis, Chemical and Materials Engineering, The University of Auckland, Auckland, New Zealand, 1996. [14] 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.
[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] Zhumin Lu, Boo Cheong Khoo, Hua-Shu Dou, Nhan Phan-Thien, Khoon SengYeo, Numerical simulation of fibre suspension flowthrough an axisymmetric contraction and expansion passages by Brownian configuration field method, Chem. Eng. Sci. 61 (2006) 4998–5009. [21] You Zhenjiang, Lin Jianzhong, Yu Zhaosheng, Hydrodynamic instability of fiber suspensions in channel flows, Fluid Dyn. Res. 34 (2004) 251–271. [22] 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. [23] S.M. Dinh, R.C. Armstrong, A rheological equation of state for semiconcentrated fiber suspensions, J. Rheol. 28 (1984) 207–227. [24] M. Chaouche, D.L. Koch, Rheology of non-Brownian rigid fiber suspensions with adhesive contacts, J. Rheol. 45 (2001) 369–382. [25] 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. [26] S.N. Kazi, Heat Transfer to Fibre Suspensions-Studies in Fibre Characterisation and Fouling Mitigation, PhD thesis, Chemical and Materials Engineering, The University of Auckland, Auckland, New Zealand, 2001. [27] G.G. Duffy, M.S.N. Kazi, X.D. Chen, Pressure drop measurement – a new way to monitor wood pulp quality, in: Proceedings of the 56th Annual Appita Conference, Rotorua, New Zealand, 2002. [28] J.G. Knudsen, R.G. Ehteshami, G.F. Hays, Simulation of Fouling in Heat Exchangers Using an Annular Test Section. Mitigation and Heat Exchanger Fouling, Banff, Canada, 1999.
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Validation of heat transfer data for fibre suspensions in coaxial pipe 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, Monash University, Victoria 3800, Australia b
a r t i c l e
i n f o
Article history: Received 9 September 2011 Received in revised form 12 December 2011 Accepted 17 December 2011 Available online 26 December 2011 Keywords: Pressure drop Heat transfer Synthetic fibre Natural fibre Fibre concentration Coarseness Population Annular flow
a b s t r a c t Heat transfer data obtained previously in a small coaxial pipe heat exchanger were validated using a new, larger annular-area test unit with longer calming section and axial entry flow. Water and two suspensions of long-fibre softwood Kraft pulps with fibres having different coarseness (mass/unit fibre length) values were used. Data in both systems were obtained over a range of flow rates with the fibre concentration at 0.4% and compared. Heat transfer coefficient hc was found to decrease with increasing annular gap size for both water and fibre suspension flow at equal velocities. Various fibre dimensions and fibre characteristics are also shown to vary systematically with hc at the same experimental conditions. The effect of hydrodynamic annular entry length on heat transfer and pressure loss using water and fibre suspensions (concentrations 0.2% and 0.4%) are also described. It was found that that extending the central calming extension rod made no significant difference to hc values at the low fibre concentration of 0.2%, and only small differences at the higher concentration of 0.4%. The successful validation of data from the smaller-annulus coaxial pipe heat exchanger show that the relationships among heat and momentum transfer and fibre characteristics and specific properties of paper are also valid for both heat exchangers. Ó 2011 Elsevier Inc. 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. An investigation of heat transfer and pressure drop in annular flow with and internal coaxial heater was reported previously by the present authors but there was some concern with the results as spiralling flow was observed in some instances caused by the inlet flow being perpendicular to the tube axis. The calming length was regarded as insufficient to settle the flow in the test section and the flow pattern changed with velocity. The problem was exacerbated with fibre suspensions as the small annular gap meant that there was a stronger possibility for fibre–fibre bundling at the lower flow rates. Hence it was decided to rebuild the apparatus with axial flow entry, a longer calming length, and a larger annular gap. The modified test section offered an opportunity to investigate the effects of calming length and hydraulic diameter on drag reduction and heat transfer in annular flow, that have not been reported in the literature previously. This and the validation of pre-
⇑ 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. 0894-1777/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2011.12.009
vious research into the flow of fibre suspensions in annular flow is the subject of this present work.
2. Literature review The study of heat transfer and frictional pressure loss in tubes and annular spaces has been used to provide a basis for designing heat exchangers and cooling systems in industry. Design data are available mainly for common fluids but there are no significant published data for fibre suspension systems. Duffy et al. [1] studied heat transfer to fibre suspensions in annular flow. Various Kraft softwood and hardwood pulp water suspensions were investigated using 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 [2]. They have proposed that hc could be used to monitor and therefore control pulp quality variations. It has long been known that pipe friction loss for fibre suspensions is diameter dependent [3] and decreases with increasing diameter. This is caused by the plug-like character at low flow rates [4]. The diameter effect is weaker in turbulent flow which is the
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S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
Nomenclature hydraulic diameter (m) pipe diameter (m) fanning friction factor heat flux (W/m2) Reynolds number hydraulic radius (m) wall temperature (°C)
drag reducing regime for fibre suspensions [5,6]. Sharma [7] also found lower drag reduction in bigger diameter pipes. Patterson et al. [8] also showed that the diameter effect on drag reduction is extremely weak when comparisons are made at constant velocity instead of constant Reynolds number. Hence a study of the variation in annular gap is significant as nothing has been reported in the literature. Robertson and Mason [3] 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. [9] 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 [10] 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 [11] selected 20 hydraulic diameters Dh in his studies of heat transfer to fibre suspensions in annular flow. Previous researchers Middis [11], Branch [12], and Bremford [13] used a calming length of 20 Dh whereas Hasson et al. [14] selected a value of 38Dh in their heat transfer fouling study in annular flow. More recent research [15–17,18–22], has been focussed on numerical simulation, spatial and orientation distributions of fibres in various flow fields, with some experimental validation. Some investigations have extended knowledge in the shear flow behaviour of fibre suspensions [23–25]. The aim of present work, therefore, is to generate more experimental data for future development of a model for turbulent fibre suspensions flow.
3. Experimental 3.1. Experimental set-up The measurement of heat transfer and pressure loss were performed in a new annular test section with dimensional details shown schematically in Fig. 1b, and the common flow loop in Fig. 1a. Details of the previously used test section are presented in Fig. 2. The magnitudes of the dimensional differences are stated in Table 1. The pressure drop across the test section was measured with a differential pressure transducer at the tapping points designated in Fig. 1b. The Perspex test section has a stainless steel heating rod with a calming extension rod mounted concentrically. The heater rod has four embedded E-type thermocouples, with three located close to the internal heater just below the rod surface for surface temperature measurement. The fourth thermocouple is used to activate a safety trip in the event of high surface temperatures. The power supply to the heated section is controlled by the 10 amp-rated Variac. Current and voltage are measured and the signals are transmitted to the computer data logger through a
temperature at thermocouple location (°C) fluid velocity (m/s) distance along x axis (m) density (kg/m3) shear stress (N/m2) dynamic viscosity (kg/ms) thermal conductivity (W/mK)
TTC u x
q s l k
Hewlett Packard data acquisition equipment. Further details are presented elsewhere [1,26].
Annular cooler Heater Tout
Dp cell
Dh d f q Re rh TS
Flow meter Magnetic Flow meter
Bypass
Tin
Test section
Tank
Pump
Cooling pump
Cooling water tank
Fig. 1a. Schematic diagram of the experimental flow loop.
Heater
57
20 Flow out Pressure 3 tapping 10.7 Heater element Stainles steel
370 96
820 26
3 Pressure tapping
1117
20 Extension rod Perspex outer tube Flow in 20
6
150
35
44 96
Fig. 1b. Schematic diagram of the coaxial-pipe, annular Test Section B with the larger hydraulic diameter and extended calming rod.
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S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
20
Heater
60
Flow out Pressure taping
384.5
Heater element
T S ¼ T TC q=ðk=xÞ
585.7 15 9.8
Extension rod
ð1Þ
Fibre concentration was measured at the beginning and end of each run and the measured values were always in agreement with differences less than 5%.
19.8
2
20
Different types of synthetic filaments were also investigated and details are given elsewhere [27]. Before each experiment, the pulp fibres obtained in sheets were soaked for approximately 24 h and then dispersed by the pump operating in recycle mode. Recycling was maintained for approximately 1 h to ensure optimum fibre dispersion and fibre wetting, and then for a further hour before any measurements were taken. A summary of experimental conditions is given in Table 1. Experimental corrections for the thermocouples k/x values in both the cases before and after the annular test section modifications are presented in Table 2 according to the following equation:
3.4. Data reduction
Flow in
Reynolds number:
3
Re ¼ qud=l
10.7 Fig. 2. Schematic diagram of the coaxial pipe annular Test Section A (small gap) with stainless-steel heater, short calming length extension rod, and inlet pipe normal to the annular flow direction.
Hydraulic diameter:
Dh ¼ 4r h ¼ d1 d2 2
Parameters
Test Section A (smaller pipe diameter)
Test Section B (larger pipe diameter)
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
1135.0
100.0 10.7 23.8
100.0 10.7 44.0
13.1
33.3
499.8
1021.6
82.6
82.6
3.2. Data acquisition
2
2
dm ¼
ð3Þ
d2 dm d2
4r h ¼ Table 1 Dimensions of the annular test section before and after modifications with differences highlighted.
ð2Þ
ð4Þ
2
d2 d1 2
ð5Þ
2
lnðd2 =d1 Þ
The Reynolds number Re2 of the outer portion of annular velocity profile is presented in the following equation:
Re2 ¼
4r h uq
ð6Þ
l
The friction factor f2 on the outer wall of annulus bears the same relationship to the Reynolds Number, Re2 as is given in Eq. (7) for circular tubes:
ð2:1 103 < Re < 105 Þ
f ¼ 0:079Re0:25
ð7Þ
The shear stress s2 on the outer wall of the annulus is stated in the following equation:
s2 ¼ f2 qu2 =2
ð8Þ
The shear stress s1 on the inner wall is expressed by: All temperatures, flow velocities, differential pressures, voltages and currents were recorded with an IBM compatible XT personal computer, a Hewlet Packard PCIB interface, a 61013A digital multi-meter and two 61011A relay multi-plexers. The data acquisition equipment is controlled using a BASIC program. The program allows the operator to choose between automatic and manual data acquisition modes according to the requirements. Details are stated elsewhere [1,26].
3.3. Experimental procedures Fibres used in these experiments were prepared by the Kraft chemical process. These included four pine pulps (pinus radiata), one bleached spruce Sp, a bleached eucalyptus Eu, and a market Kraft bleached pine pulp. The four pine pulps were produced from different aged trees and the fibres varied in length and coarseness (mass/unit length). They are designated in terms of coarseness: High Hi, Medium Med, Low Lo and Ultra low ULo coarseness pulps.
s1 ¼ s2 ðd2 =d1 Þ
2
2
2
2
dm d1
! ð9Þ
d2 dm
4. Results and discussion 4.1. Data reproducibility The rig with the new Test Section B (see Table 1) was calibrated using water. The procedural accuracy and reproducibility of data
Table 2 k/x values before and after modifications. Location
k/x
Values (before modification)
Values (after modification)
1 2 3
k/x1 k/x2 k/x3
25,000 12,500 14,286
20,000 14,286 20,000
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S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
Bleached Kraft pine (BK) fibre of mean length 2.53 mm and coarseness 0.246 mg/m was used in the test runs to study the effect of fibres and fibre concentration on heat transfer. The data are present as hc versus flow velocity in Fig. 5 for four different fibre concentrations (0.1–0.4%) with water as the reference. At velocities greater than about 0.5 m/s there is a spread of hc data below the water values similar to that obtained previously for pipe flow [27], as well as the data from the smaller Test Section A (see Fig. 6). At lower velocities (<0.5 m/s) there is a noticeable increase of hc above water values due to fibre–fibre interactions and some network fragment structures being formed. The thermal conductivity of fibre is less than that of water but fibres provide a solid path for heat conduction through the fibres themselves at low velocity which contributes to higher overall heat transfer coefficient values [11,27]. The data trends validate the results obtained from previous investigations. 4.3. Effect of fibre flexibility Fig. 7 shows heat transfer coefficient hc as a function of velocity for different grades of pine, spruce and eucalyptus fibres at a concentration of 0.4%. For the pine fibre suspensions, hc decreases as both fibre length and fibre coarseness (mass/unit length) decrease, in agreement with data obtained in the smaller annular Test Section A (Fig. 8). The largest relative spacing for the data is at 1.5 m/s in both annular flow systems. 4.4. Hydraulic diameter/heat transfer to water and fibre suspensions Data are presented in Fig. 9 for heat transfer coefficient as a function of flow velocity for water and two different pine fibre suspensions (Hi and ULo) in annular flow for the two different annular channel gaps or hydraulic diameters (0.0131 and 0.0333 m) [Annular Test Sections A and B]. Heat transfer coefficient values of the Hi and ULo pine fibre suspensions at 0.4% concentration are of the
Heat transfer coeff. kW/m2 K
12 Water (1) Water (2)
9
Pressure drop ( Δ P/L) Pa/m
Water (1)
250
Water (2)
200 150 100 50 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 4. Pressure drop as a function of flow velocity for two water runs. DP/L data were obtained at DT 15 °C and a bulk temperature of 30 °C.
Heat transfer coefficient kW/m2 K
4.2. Fibre concentration effect
300
12 Water
10 BK0.1 BK0.2
8
BK0.3
6
BK0.4
4 2 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 5. Heat transfer coefficient as a function of flow velocity for water and different concentrations of bleached Kraft pulp fibre suspensions (Annular Test Section B). The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
Heat transfer coefficient kW/m2 K
were studied, and the data obtained compared with results with those from Test Section A used previously. The heat transfer results are presented in Fig. 3 with hc as a function of velocity, and the pressure drop data are presented in Fig. 4. Data reproducibility in both cases was very good with an rms error <3% within the confidence level of 95% for heat transfer, an average rms error <5% within the confidence level of 95% for the pressure drop data for the two water runs.
10 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
1.2
1.4
1.6
Velocity m/s 6
Fig. 6. Heat transfer coefficient as a function of flow velocity for different concentrations of pulp Hi fibre suspensions (Annular Test Section A with the smaller annular gap.) Heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
3
0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 3. Heat transfer coefficient as a function of flow velocity for two water runs. The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
same relative order in both Test Sections A and B with respect to water. Fig. 10 depicts hc as a function of Re (based on hydraulic diameter) for water and the Hi and ULo fibre suspensions at 0.4% fibre concentration. The Reynolds number corresponding to 1.5 m/s in the smaller annular Test Section A is 24,643 whereas
Heat transfer coefficient kW/m2 K
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S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
12 10 8
Water
Hi
Med
Lo
ULo
Sp
Eu
6 4 2 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 7. Heat transfer coefficient as a function of flow velocity for water and different grades (Hi, Med, Lo and ULo) of Kraft pine fibre suspensions of concentration 0.4% (Test Section B with larger annular area). The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
higher than all hc values in the larger annular Test Section B indicating that there are higher turbulence-augmented hc values in the smaller annular area test section. For a more accurate comparison of hc values corresponding to each velocity [28], the shear stress at the wall of the inner heating rod has been calculated for both water and suspension flows. The hc values are presented as a function of shear stress in the two cases [smaller (S) and larger (L) hydraulic diameter] in Fig. 11. It is observed that hc increases with increasing wall shear stress in all cases. As mentioned above, the hc values for water and fibre suspensions are always larger in the smaller annular Test Section A. Percentage differences are similar to the values of hc obtained as a function of velocity (Fig. 9). Thus either shear stress or velocity can be chosen as a variable parameter for comparison of hc. From these investigations it is obvious that the hc increases with decreasing annular gap (hydraulic diameter of the annulus space) for water and fibre suspension flow but the trends are still systematic and of the same order of magnitude.
12 10
Water
Hi
Med
Lo
ULo
Sp
Euc
8 6 4 2 0 0
0.4
0.8
1.2
1.6
2
2.4
Velocity m/s
Heat transfer coefficient kW/m2 K
Fig. 8. Heat transfer coefficient as a function of velocity for water, Kraft pine, spruce and eucalyptus fibre suspensions of concentration 0.4% (Test Section A with the smaller annular area). Heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
12 10 8
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
4 2 0 0.4
0.8
4.6. Hydraulic diameter and pressure drop of water and fibre suspensions Frictional pressure drop as a function of velocity for water and two different fibre suspensions (Hi and ULo) are presented in Fig. 13. The magnitude of pressure drop for water and ULo and
6
0
Fig. 12 shows heat transfer coefficient hc as a function of velocity for water and Kraft pine Hi and ULo coarseness at two concentrations 0.2% and 0.4% respectively for both annular test sections. The centrally located heating rod has a removable extension rod of the same diameter to aid in providing adequate calming. Data are presented in Fig. 12 without extension rod AR., and with extension rod BR. The typical increase in hc at low velocities is seen at both concentrations, with or without the calming extension rod. It can be observed that the data sets are in close agreement over the whole range of velocities for both fibre concentrations (about 13% lower than water values). This is significant as it shows that the upstream calming rod has little effect on the values obtained. A 65% increase in calming length in terms of hydraulic diameter (38 Dh and 23 Dh) only produces a 5.8% maximum difference at higher velocities (>1 m/s).
1.2
1.6
2
2.4
Velocity m/s Fig. 9. Heat transfer coefficient as a function of flow velocity for water and Hi and ULo pine fibre suspensions in annular flow for two different hydraulic diameters Dh [0.0131(S) and 0.0333(L) m]. The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
Heat transfer coefficient kW/m2 K
Heat transfer coefficient kW/m2 K
4.5. Effect of calming length on heat transfer 14
12 10 8 6 4 2
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
0 0
15
30
45
60
75
90
3
Reynolds number x10 the corresponding value at the same velocity in the larger Test Section B is 82,934. A comparison can be made on the basis of similar Re. At the Re of 24,643, the value of hc in the smaller annular Test Section A is
Fig. 10. Heat transfer coefficient as a function of Reynolds number for water and Hi and ULo pine fibre suspensions in annular flow for two different hydraulic diameters Dh [0.0131(S) and 0.0333(L) m]. The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
215
Heat transfer coefficient kW/m2 K
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
12 10 8
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
6 4 2 0 0
3
6
9
12
15
18
Shear stress N/m2
Heat transfer coefficient kW/m2 K
Fig. 11. Heat transfer coefficient as a function of wall shear stress for water and Hi and ULo fibre suspensions in annular flow for two different hydraulic diameters Dh (0.0131 and 0.0333 m). The heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
12 WATER(AR)
10
Hi0.2(AR) ULo0.4(AR)
8
WATER(BR) Hi0.2(BR)
6
ULo0.4(BR)
4 2 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 12. Heat transfer coefficient as a function of velocity for water and pine Hi and ULo fibre suspensions at concentrations of 0.2 and 0.4, without the calming extension rod (AR), and with the extension rod (BR). Heat transfer data were obtained at DT 15 °C and a bulk temperature 30 °C.
Hi fibre suspensions of 0.4% concentration are of the same order in both the cases. DP/L for smaller hydraulic diameter is higher than those of larger hydraulic diameter at all velocities as expected. Frictional pressure drop is presented as a function of Re (based
on hydraulic diameter Dh) in Fig. 14. The Reynolds number corresponding to 1.5 m/s in the smaller annular gap is 24,643, whereas in larger annulus, it is 82,934. It is observed that the order of magnitude of DP/L for water, ULo and Hi, is similar in both the cases of the smaller and larger annular gaps. At a particular Reynolds number (24,643 corresponding to 1.5 m/s in smaller annulus), the magnitude of DP/L for water, ULo, and Hi in smaller Dh annular flow are respectively 99.7%, 99.2% and 98.8% higher than those of in the larger Dh. Further analysis of unit frictional pressure drop DP/L in the annulus test section was extended by plotting the data as a function of wall shear stress on the outer surface of the inner rod. Fig. 15 represents frictional pressure drop as a function of shear stress in the smaller and larger annular gaps for water, Hi and ULo fibre suspensions at 0.4% concentration. DP/L clearly increases with the increase of shear stress in all the cases over the entire range of investigation. It can be seen that when the shear stress level on the heater rod outer surface is equal in the two annular set-ups, DP/L levels in the smaller annular flow unit are higher than all those in the larger annular space unit (for water, ULo and Hi suspension). At a specified shear stress (9.6 N/m2) corresponding to a velocity 1.5 m/s, DP/L values are 96.8%, 96.1% and 95.3% higher in the smaller annular unit than in the larger annulus (for water, ULo and Hi suspensions respectively). These values are similar to the values obtained in the case of DP/L versus velocity (Fig. 13). It can be concluded that in the heat transfer study the observed values of hc in the smaller annulus are almost same percentages higher than those of larger annulus, irrespective of whether hc is presented as a function of velocity or shear stress. 4.7. Study of pressure drop in the test section with long and short calming lengths Fig. 16 depicts pressure drop as a function of velocity for water flow in the annular test section with both the extended BR and with virtually no calming lengths AR (after removal). The pressure drop was measured across the whole test section. At a specific velocity of 1.5 m/s, the pressure drop is about 23.5% lower than with longer calming length. The difference increases with increasing velocity. Removing the extended inlet-calming length rod from central heater reduces the constriction and calming of the inlet flow, causing fluid impact on the leading face of the heater rod that affects the magnitude of the pressure loss.
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
Pressure drop (ΔP/L) kPa/m
Pressure drop ( ΔP/L) kPa/m
10 10 8 6 4 2
8
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
6 4 2 0
0 0
0.4
0.8
1.2
1.6
2
2.4
Velocity m/s Fig. 13. Pressure drop (DP/L) as a function of velocity for water, Hi and ULo fibre suspensions in annular flow for two different hydraulic diameters Dh (0.0131 and 0.0333 m). DP/L was measured at DT 15 °C, bulk temperature 30 °C and fibre concentration of 0.4%.
0
15
30
45
60
75
90
3
Reynolds number x10
Fig. 14. Pressure drop (DP/L) as a function of Reynolds number for water and Hi and ULo fibre suspensions in annular flow for two different hydraulic diameters Dh (0.0131 and 0.0333 m). DP/L was measured at DT 15 °C, bulk temperature 30 °C and fibre concentration of 0.4%.
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Pressure drop ( ΔP/L) kPa/m
10
8
Water(L)
Water(S)
Hi 0.4(L)
Hi 0.4(S)
ULo 0.4(L)
ULo 0.4(S)
6
4
2
0 0
3
6
9
12
15
18
Shear stress N/m2 Fig. 15. Pressure drop (DP/L) as a function of shear stress for water, Hi and ULo fibre suspensions in annular flow for two different hydraulic diameters (0.0131 and 0.0333 m). DP/L was measured at DT 15 °C, bulk temperature 30 °C and fibre concentration of 0.4%.
5. Conclusions
9
Pressure drop ( Δ P/L) kPa/m
was selected which was similar to values chosen for pipeline studies. The measuring techniques and procedures used with the smaller Test Section A had been of concern initially because of observed spiral entry flow, and the potential ongoing effect of the smallerthan-normal calming entry length. The research reported here with the improved set-up of coaxial pipe heat exchanger (Test Section B), resulted in a large amount of data that compared favourably with the previous experimental data obtained from the coaxial pipe heat exchanger of different dimensions. Clearly the concerns were allayed, and the results confirm that heat transfer coefficient and pressure drop measurements are promising ways of monitoring fibre variations and hence pulp quality. Some of the extensive correlations relating both fibre characteristics and the properties of paper made from the same fibres, are presented in the Appendix A. The results of this study using a larger annular space [Test Section B] further support the validation of that the comparable data obtained with the original heat exchanger [1].
8
Water(AR)
7 Water(BR)
6 5 4 3 2 1 0 0
0.5
1
1.5
2
2.5
Velocity m/s Fig. 16. Frictional pressure drop across the test section for water as a function of velocity, before (BR) and after (AR) removing the central calming extension rod. Friction loss data were obtained at DT 15 °C and a bulk temperature 30 °C.
4.8. Summary of comparisons The trends in the data reported here obtained from the larger, annular-gap coaxial pipe heat exchanger (Test Section B) validate the results obtained from the previously-used, smaller annulargap Test Section A [1]. The larger annular gap unit with the improved entry and extended calming rod length indeed gave more accurate and in some cases slightly better correlations, but overall these extensive tests validated the previous work [1] and showed that those results could also be used with confidence.
4.9. Fibre characterisation and validation of the two heat exchangers Extensive research programmes had been carried out previously to determine how various fibre properties would modify turbulence and hence provide a means of measuring and monitoring fibre characteristics and pulp quality. It had been found in pipe flow [2] that specific fibre characteristics and some fibre properties could be assessed by both heat transfer measurements and friction loss determination. Following those studies there was a need to evaluate smaller quantities of fibre in a smaller flow loop, and hence a small coaxial pipe heat changer was used [1]. Again heat and momentum transfer measurements were used and both hc and DP/L values obtained over a range of flow conditions. A comparative condition of 1.5 m/s and 0.4% fibre concentration
The results from this present study confirm that the data obtained in a smaller, annular-space coaxial heat exchanger are valid even though the results were not as accurate as those obtained in the larger annular test unit. Heat transfer to fibre suspensions is observed to increase with decreasing hydraulic diameter for water and fibre suspensions, either at equal velocities or equal shear stress levels. Hence, either shear stress or velocity can be used to compare hc values calculated from data obtained in an annular space because experimentally, the similar Dhc were obtained in two different annular test sections with different hydraulic diameters. Heat transfer to water or to fibre suspensions of low concentrations (0.2%) does not change significantly with change of calming length but at higher fibre concentration (0.4%) the difference is detectable but still very small.
Appendix A Graphical comparison of fibre and paper properties as a function of hc and DP/L of fibre suspensions flowing through the smaller Annular Test Section A and Larger Annular Test Section B for direct comparison. (L0 = mean fibre length, D = mean fibre diameter, P = fibre perimeter, t = fibre thickness).
A.1. Smaller annular space A.1.1. Test Section A Fibre properties versus hc (see Figs. A1–A6). Paper properties versus hc (see Figs. A7–A10). Fibre properties versus DP/L (see Figs. A11–A16). Paper properties versus DP/L (see Figs. A17–A20).
Appendix B B.1. Larger annular space B.1.1. Test Section B Fibre properties versus hc (see Figs. B1–B6). Paper properties versus hc (see Figs. B7–B10). Fibre properties versus DP/L (see Figs. B11–B16). Paper properties versus DP/L (see Figs. B17–B20).
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225 Hi
2
2.5
Fibre wall area μm
2 1.5 1
Hi
Med
Lo
ULo
Sp
Euc
0.5
Med
150 125
7.2
7.4
7.6
7.8
8
7.2
7.4
7.6
7.8
8 2
Heat transfer coefficient kW/m K Fig. A5. Fibre wall area versus hc.
Fig. A1. Length L0 versus hc.
35
130
Relative fibre number
Dimentional ratio L'/ P
Sp
175
Heat transfer coefficient kW/m2 K
30 25 20 15
Hi
Med
Lo
ULo
Sp
Euc
120
Hi
Med
ULo
Sp
Lo
110 100 90 80
10
70 7.2
7.4
7.6
7.8
8
7.2
7.4
Heat transfer coefficient kW/m2 K
7.6
7.8
8
Heat transfer coefficient kW/m2 K
Fig. A2. L0 /P versus hc.
Fig. A6. Relative fibre number versus hc.
35 ULo
Lo
Med
Hi
Sp
Euc
Tensile index mN.m 2/g
120
30
Ratio P /t
ULo
100 7
25 20 15
17 14.5
100
10
12 80
9.5 7
60
Hi
Med
Lo
Ulo
Hi
Med
Lo
Ulo
4.5
40 7.2
7.4
7.6
7.8
8
2 7.5
Heat transfer coefficient kW/m2 K
7.6
7.7
7.8
7.9
8
Heat transfer coefficient kW/m2 K
Fig. A3. P/t versus hc.
Fig. A7. Paper tensile and tear indices versus hc.
0.3
9
0.26
Hi
Med
Lo
Ulo
8
0.22
Burst index
Coarseness
Lo
200
Tear index mN.m2/g
Fibre length L' mm
3
0.18 Hi
Med
Lo
ULo
Sp
Euc
0.14 0.1
7 6 5
0.06 0.02
4 7
7.2
7.4
7.6
7.8
Heat transfer coefficient kW/m2 K Fig. A4. Coarseness versus hc.
8
8.2
7.5
7.6
7.7
7.8
7.9
Heat transfer coefficient kW/m2 K Fig. A8. Burst index versus hc.
8
218
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
35 Hi
Med
Lo
ULo
30
25
Ratio P /t
Lt. Scatt. Coeff. m2 /kg
30
20
Lo
Med
Hi
Sp
Euc
25 20
15 15 10
10 7.5
7.6
7.7
7.8
7.9
8
4.9
5
5.1
2
5.2
5.3
5.4
5.5
Pressure drop kP/m
Heat transfer coefficient kW/m K
Fig. A13. P/t versus DP/L.
Fig. A9. Light scattering coefficient versus hc.
0.3
4.6 Hi
Med
Lo
ULo
Sp
0.26
4.2
Coarseness
Formation Index
ULo
3.8 3.4
Hi
Med
Lo
ULo
Sp
Euc
0.22 0.18 0.14 0.1
3 0.06 2.6 7.2
7.4
7.6
7.8
0.02
8
4.5
4.7
4.9
Heat transfer coefficient kW/m2 K Fig. A10. Formation index versus hc.
5.5
225
2.5
Hi
Med
Lo
ULo
Sp
Euc
Hi
Fibre wall area μm2
Fibre length L' mm
5.3
Fig. A14. Coarseness versus DP/L.
3
2 1.5 1 0.5
Med
Lo
ULo
Sp
200 175 150 125 100
4.5
4.7
4.9
5.1
5.3
5.5
4.7
4.9
Pressure drop kP/m
5.3
5.5
Fig. A15. Fibre wall area versus DP/L.
150
Relative fibre number
35
30
25
20
15 4.7
5.1
Pressure drop kP/m
Fig. A11. L0 versus DP/L.
Dimentional ratio L'/P
5.1
Pressure drop kP/m
4.9
Hi
Med
Lo
ULo
Sp
Euc
5.1
Pressure drop kP/m Fig. A12. L0 /P versus DP/L.
5.3
5.5
130
Hi
Med
ULo
Sp
Lo
110
90
70 4.7
4.9
5.1
5.3
Pressure drop kP/m Fig. A16. Relative fibre number versus DP/L.
5.5
219
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
3
14.5 100 12 80
9.5 7
60
Hi
Med
Hi
40 4.9
Med
Lo
ULo
Lo
4.5
ULo
Fibre length L' mm
17
Tear index mN.m 2/g
Tensile index mN.m2/g
120
2.5 2 1.5 1
Hi
Med
Lo
ULo
Sp
Eu
2 5
5.1
5.2
5.3
5.4
5.5
0.5 6.75
Pressure drop kP/m
6.85
6.95
7.05
7.15
7.25
7.35
2
Heat transfer coefficient kW/m K
Fig. A17. Tensile and tear indices versus DP/L.
Fig. B1. Length L0 versus hc.
9 Hi
Med
Lo
40
Ulo
Dimentional ratio L'/P
Burst index
8 7 6 5 4 4.9
5
5.1
5.2
5.3
5.4
5.5
Hi
Lo
ULo
Sp
Eu
30
25
20 6.75
Pressure drop kP/m
Med
35
6.85
6.95
7.05
7.15
7.25
7.35
2
Heat transfer coefficient kW/m K
Fig. A18. Burst index versus DP/L.
Fig. B2. L0 /P versus hc.
35 Hi
Med
Lo
ULo
25
30
Ratio P /t
Lt. Scatt. Coeff. m2 /kg
30
20
15
Hi
Med
Lo
ULo
Sp
Eu
25 20 15
10 4.9
5
5.1
5.2
5.3
5.4
10 6.75
5.5
Pressure drop kP/m
6.85
6.95
7.05
7.15
7.25
7.35
Heat transfer coefficient kW/m2 K
Fig. A19. Light scattering coefficient versus DP/L. Fig. B3. P/t versus hc.
0.3
4.6 4.2
Coarseness
Formation Index
0.26
3.8 3.4 3
Hi
Med
Lo
Ulo
Sp
5
5.1
5.2
5.3
Pressure drop kP/m Fig. A20. Formation index versus DP/L.
5.4
Med
Lo
ULo
Sp
Eu
0.22 0.18 0.14 0.1 0.06
2.6 4.9
Hi
5.5
0.02 6.75
6.85
6.95
7.05
7.15
7.25 2
Heat transfer coefficient kW/m K Fig. B4. Coarseness versus hc.
7.35
220
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
30 Hi
Med
Lo
ULo
Sp
Lt. Scatt. Coeff. m2/kg
Fibre wall area μm2
250 225 200 175 150 125 100 6.75
6.85
6.95
7.05
7.15
7.25
Hi
6.85
130
7.15
7.25
7.35
4.6
120
Hi
Med
ULo
Sp
Lo
Hi
Formation Index
Relative fibre number
7.05
Fig. B9. Light scattering coefficient versus hc.
Fig. B5. Fibre wall area versus hc.
110 100 90 80 70 6.75
6.85
6.95
7.05
7.15
7.25
3
6.85
7
40 6.85
6.95
Hi
Med
Lo
ULo
7.05
7.15
4.5
Hi
Fibre length L' mm
9.5
80
Tear index mN.m2/g
2
12
ULo
7.05
7.15
7.25
7.35
3
14.5 100
Lo
6.95
Fig. B10. Formation index versus hc.
17
Med
Sp
Heat transfer coefficient kW/m2 K
120
Hi
ULo
3.4
Fig. B6. Relative fibre number versus hc.
60
Lo
3.8
2.6 6.75
7.35
Med
4.2
Heat transfer coefficient kW/m2 K
Tensile index mN.m /g
6.95
Heat transfer coefficient kW/m2 K
Heat transfer coefficient kW/m K
2 7.35
7.25
Med
Lo
ULo
Sp
Eu
2.5 2 1.5 1 0.5 150
2
175
Heat transfer coefficient kW/m K
200
225
250
275
Pressure drop Pa/m
Fig. B7. Paper tensile and tear indices versus hc.
Fig. B11. L0 versus DP/L.
40 Hi
Med
Lo
Dimentional ratio L'/P
9 ULo
8
Burst index
ULo
20
2
7 6 5 4 6.75
Lo
25
15 6.75
7.35
Med
6.85
6.95
7.05
7.15
7.25
Heat transfer coefficient kW/m2 K Fig. B8. Burst index versus hc.
7.35
35 30 25 20 15 10 150
Hi
175
200
Med
Lo
225
Pressure drop Pa/m Fig. B12. L0 /P versus DP/L.
ULo
Sp
250
Eu
275
221
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
Med
Lo
ULo
Sp
Eu
Tensile index mN.m2/g
30
Ratio P /t
17
120 Hi
25 20 15 10 150
175
200
225
250
14.5 100 12 9.5
80
7 60
40 175
275
200
0.3 Lo
ULo
Sp
Eu
Hi
0.14 0.1
0.02 150
Lo
ULo
225
Med
Lo
4.5 2 275
250
ULo
7 6
175
200
225
250
4 175
275
200
Pressure drop Pa/m
225
250
275
Pressure drop Pa/m
Fig. B14. Coarseness versus DP/L.
Fig. B18. Burst index versus DP/L.
250
30 Hi
Med
Lo
ULo
Sp
Lt. Scatt. Coeff. m2 /kg
Fibre wall area μm2
Med
5
0.06
200 175 150 125
175
200
225
250
Hi
Lo
ULo
20
15 175
275
Med
25
200
Pressure drop Pa/m
225
250
275
Pressure drop Pa/m
Fig. B15. Fibre wall area versus DP/L.
Fig. B19. Light scattering coefficient versus DP/L.
150
4.6
130
Hi
Med
Lo
ULo
Sp
110
90
175
200
225
250
Pressure drop Pa/m Fig. B16. Relative fibre number versus DP/L.
275
Hi
Formation Index
Relative fibre number
Hi
8
Burst index
Coarseness
Med
0.18
70 150
ULo
9 Hi
0.22
100 150
Lo
Fig. B17. Tensile and tear indices versus DP/L.
Fig. B13. P/t versus DP/L.
225
Med
Pressure drop Pa/m
Pressure drop Pa/m
0.26
Hi
Tear index mN.m2/g
35
Med
Lo
ULo
Sp
4.2 3.8 3.4 3 2.6 150
175
200
225
Pressure drop Pa/m Fig. B20. Formation index versus DP/L.
250
275
222
S.N. Kazi et al. / Experimental Thermal and Fluid Science 38 (2012) 210–222
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