Experimental research on laminar flow performance of phase change emulsion

Applied Thermal Engineering 26 (2006) 1238–1245 www.elsevier.com/locate/apthermeng

Experimental research on laminar flow performance of phase change emulsion Binjiao Chen a, Xin Wang a, Yinping Zhang b

a,* ,

Hui Xu a, Rui Yang

b

a Department of Building Science, Tsinghua University, Beijing 100084, China Department of Chemical Engineering, Tsinghua University, Beijing 100084, China

Received 4 January 2005; accepted 10 October 2005 Available online 15 December 2005

Abstract Phase change emulsion (PCE) is a kind of novel heat transfer fluid with greater apparent specific heat and stronger heat transfer capacity than water. The laminar rheological characteristics of a type of PCE developed by us were experimentally studied. And the advantage of applying this kind of PCE as a heat transportation fluid was discussed. The results show that: (a) its viscosity is about 5.57 times of that of water, which is much lower than those reported in the literature; (b) it can be considered as Newtonian fluid from its rheological characteristics and its friction factor conforms to the rule of 64/Re; and (c) for given heat transportation quantity, due to which greater apparent specific heat, the mass flow rate and the pump consumption for the PCE decrease greatly compared with water.  2005 Elsevier Ltd. All rights reserved. Keywords: Phase change emulsion; Laminar flow; Rheological characteristics; Friction factor; Pump consumption

1. Introduction Latent functionally thermal fluids (LFTF) are a novel kind of heat storage and heat transfer fluids that include phase change micro-capsule slurry and phase change emulsion (PCE). Phase change micro-capsule slurry was prepared by in situ polymerization with polystyrene, polymethylmethacrylate, polyethylmethacrylate as encapsulation material, respectively [1]. It is more stable than PCE, however itÕs very difficult to prepare massproducedly. In PCE, the phase change material (PCM) particles with size of micron are dispersed in water by stirring and surfactant, adapted to prepare mass-producedly. In the tube experiment, abundant fluid is needed, thus PCE is studied firstly. Because of phase *

Corresponding author. Tel.: +86 10 6277 2518; fax: +86 10 6277 3461. E-mail address: [email protected] (Y. Zhang). 1359-4311/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2005.10.040

change of the particles, such a kind of emulsion is of much greater apparent specific heat than conventional single-phase fluids, and the heat transfer rate between the emulsion and the duct wall may be enhanced greatly. For given heat transportation quantity, therefore, the mass flow rate and the pump consumption for PCE can also be reduced greatly than that for water. Due to those, PCE has many potentially important applications in the fields of heating, cooling and power compiled system and heat exchanging, etc. [2–8]. In recent years, much fundamental research on PCE has been performed [4–19]. Hu and Zhang [10] found that the heat transfer rate of the emulsion was about 2 times of that of water by simulation. Roy and AvanicÕs experimental result [15] shows that the dimensionless wall temperature decreases 30.8% at the dimensionless axial distance (x/R)/(RePr) = 0.06, using emulsion of c = 30% by volume. However, the viscosities of the emulsions reported in the literature are too high. The

B. Chen et al. / Applied Thermal Engineering 26 (2006) 1238–1245

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Nomenclature c cp D dm f Hm K L m m_ N n Dp p Q q R Re r rB

mass concentration (wt%) specific heat (kJ/(kg K)) duct diameter (mm) mass average diameter (lm) friction factor heat of fusion (kJ/kg) consistency index (Pa sn) duct length (m) mass (kg) mass flow rate (kg/s) pump consumption (W) rheological index pressure drop (Pa) pressure (Pa) volumetric flow rate (m3/s) heat transfer rate (W) inner radius of a pipe (mm) the Reynolds number radial coordinate (mm) maximum radius of yield shear stress (mm)

apparent viscosities of the emulsions prepared by Inaba and Morita [16] are 31.1 mPa s (c = 5.0%) and 2.5 Pa s (c = 40.0%) at 278.15 K, which are about 20.7 and 1666.7 times of that of water (1.519 mPa s). The apparent viscosities of the emulsions prepared by Zhao and Shi [17] are 24.5 mPa s (c = 16.3%) and 150 mPa s (c = 49.8%) at 278.15 K, which are about 16.3 and 100 times of that of water. The high viscosities of the PCEs would lead to large pump energy consumption. Based on the predication, the high pump energy consumption of the PCEs presented in the literature weakens/deteriorates the advantages of enhanced heat transfer, resulting in their unfeasibility. A kind of novel PCE with low viscosity was prepared by the authors and some thermal physical properties of the PCE were measured [20]. The results show that the PCE of 30 wt% has high value of heat of fusion, acceptable viscosity and stability among the PCEs tested (c = 5–40 wt%). Thus, the PCE of 30 wt% was chosen for the flow experiment in the present paper. Its viscosity is 8.46 mPa s at 278.15 K, about 5.57 times of that of water, which is much lower than those reported in Refs. [16–18] (they are 31.1 mPa s, 24.5 mPa s and 10.4 mPa s, respectively). As melting point is 277.7 K, it can be used as the working fluid in the cooling system. For given heat transportation quantity, it may greatly reduce the mass flow rate, the pipe diameter and the pump energy consumption. An experimental system was built to study the flow characteristics of the PCE in PCMÕs liquid state such

T Tm DT Dt U u

temperature (K) melting point (K) temperature difference (K) time range (s) mean velocity (m/s) velocity (m/s)

Greek symbols d absolute error g stiffness coefficient (Pa s) gN pump consumption ratio l dynamic viscosity (Pa s) q density (kg/m3) s shear stress (Pa) sW wall shear stress (Pa) sB yield shear stress (Pa) Subscripts f fluid (water) p PCE

as the laminar rheological behavior, the friction factor and the pump consumption. The rheological behavior was analyzed by the virtual rheological curve, and the differences between different fitted forms (i.e., the Newtonian fluid form, the pseudoplastic fluid form and the Bingham fluid form) were compared. The results show that: the PCE can be considered as a Newtonian fluid; the viscidity of the emulsion conforms to the classical function (f = 64/Re) for laminar flow; the flow rate and the pump consumption of the PCE system decrease greatly for the same heat transportation quantity compared with water, due to phase change.

2. PCE preparation The PCE was made of micro-particles of C14H30 (Tm = 278.9 K, Hm = 229 kJ/kg) and water by using phase incursion method (PIM) [20] (Fig. 1). Fig. 2 shows the phase difference microscope (PDM) image of the PCE. Some thermal physical properties of the PCE of 30 wt% are listed in Table 1. The phase change temperature and the heat of fusion of the PCE were measured by differential scanning calorimeter (DSC). The heating/ cooling rate of the tests by DSC is 5 C/min. The diameters of the micro-particles of the PCE of 30 wt%, measured by a particle characterization system (Malvern Mastersizer Micro-Plus), are shown in Fig. 3. The mass average diameter is 50.97 lm, and the relative measurement error is 48%.

1240

B. Chen et al. / Applied Thermal Engineering 26 (2006) 1238–1245

Percent (%)

12

8 dm=50.97µm

4

0 0

1

6

22

89

Diameter (µm) Fig. 3. Diameters of the micro-particles of the PCE of 30 wt%.

3. Experiment for flow characteristics Fig. 1. Photo of phase change emulsion developed by the authors.

Fig. 2. PDM image of the PCE of 30 wt%.

Table 1 Thermal physical properties of the PCE C14H30 c (wt%)

Density Melting point Heat of fusion Specific heat q (kg/m3) Tm (K) Hm (kJ/kg) cp (kJ/(kg K))

30

926.0

277.7

73.47

3.67

3.1. Experimental apparatus The experimental apparatus for measuring the PCE flow characteristics is shown in Fig. 4. The major components of the system were a PCE reservoir (280 mm · 180 mm · 400 mm), a refrigerator, a blender, a filter, a pump, an AC power supply, a test duct, a digital differential manometer (produced by LvGao Ltd., Shanghai), and a flow meter (composed of a triple valve, an electronic balance and a fluid collector). The PCE in the reservoir could be maintained at a constant temperature by an evaporator in the reservoir. The blender was used to stir the PCE and make it uniform. The bypass pipe was used to adjust the flow rate. The mass flow rate of the PCE was measured by weighing method. Perspex pipe, 2.0 m in length and 10.0 mm or 14.0 mm in inner diameter, was used as the test duct. The others in the pipeline were copper pipes with 15 mm inner diameter (DN15). There were two pressure measuring points, 66D to the entrance and 5D to the exit, thus the fluid flow could be regarded as fully developed flow between the two pressure measuring points [21]. At the bottom of the reservoir and the two lowest points of the system, three drain pipes were fixed. In order to decrease the influence of ambient temperature on the measured viscosity of the PCE, the test duct was thermally insulated. During the experiments, the inlet and outlet temperature difference of the test section and the inlet fluid temperature fluctuation were less than 0.2 C. Seven T-type thermocouples were set in the middle of the reservoir, at the entry and exit of the test duct, and in the front and back of the pump. All thermocou-

B. Chen et al. / Applied Thermal Engineering 26 (2006) 1238–1245

1241

Fig. 4. Schematic of the experimental system.

ples were calibrated and their measurement error was less than 0.1 C. All the temperature data were recorded by a HP-34970A Data Logger.

Thus, the wall shearing rate is [22]: 

3.2. Measuring principle and error analysis

    Þ du 8U 3 1 d lnð8U D þ ¼ dr w D 4 4 d ln sw

ð6Þ

where The force and geometry for the controlled volume of flow is shown in Fig. 5. The wall shear stress is: ðp1  p2 Þ  R Dp  D ¼ 2L 4L The shearing rate, related with velocity, is:

du ¼ f ðsÞ dr

ð2Þ

Integrating Eq. (2) over r to R yields: Z R uðrÞ ¼ f ðsÞ dr

ð3Þ

r

The shear stress s at r is: If it is Newtonian/pseudoplastic fluid, we have r s ¼ sw R If it is Bingham fluid, we have ( sB r < rB sw  sB s¼ sB þ ðr  rB Þ r P rB R  rB

ð7Þ

Eq. (6) shows the generalized Mooney–Rabinowitsh wall shearing rate relationship for all kinds of fluids. The velocity distributions and virtual rheological curves of three kinds of fluids whose performance are independent of time are shown in Fig. 6. In Ref. [22], the virtual rheological curves of the three kinds of fluids, describing the relationship of the mean shearing rate and the shear stress, were discussed. The rheological parameters can be obtained from these curves.

ð1Þ

sw ¼



8U 4Q 32m ¼ 3¼ D pR pqD3  Dt

Newtonian fluid:   du s¼l  dr   du 8U ¼l sw ¼ l  dr w D

ð4Þ

ð5Þ

ð8Þ ð9Þ

In Fig. 6(a), the dynamic viscosity l is the slope of the curve. τ

p

p2

1

r

ρ

R

L

2

1

Fig. 5. Sketch diagram of flow.

B. Chen et al. / Applied Thermal Engineering 26 (2006) 1238–1245

u

u rB

u

τB τw

τw

τw

τw

τw

lg(τw)

[

Ig K(

4 τ 3 B 0

0 8U/D (a) Newtonian fluid

0

[

1242

3n+1 n 4n )

lg(8U/D)

8U/D (b) Bingham fluid

(c) Pseudoplastic fluid

Fig. 6. Schematic diagram of the velocity distributions and virtual rheological curves of the three kinds of fluids.

Bingham fluid:   du s ¼ sB þ g  dr "    4 # 8U sw 4 sB 1 sB ¼ 1 þ D 3 sw 3 sw g

ð10Þ

8U 4 þ sB D 3

ð12Þ

In Fig. 6(b), the stiffness coefficient g is the slope of the curve, and 43 sB is the interception of the curve. Pseudoplastic fluid:  n du s¼K  dr  n  n 8U 3n þ 1 sw ¼ K D 4n n    3n þ 1 8U lg sw ¼ lg K þ n lg 4n D

ð13Þ ð14Þ

5

sw Dp  D 2 p  Dp  D  q  Dt f ¼ qU 2 ¼ ¼ q  L U2 8  L  m2

Unit

Measuring instrument

Maximum relative error (%)

Pressure drop, Dp

Pa

1

Duct diameter, D Test section length, L Mass, m Time range, Dt

m m kg s

Digital differential manometer Square caliper Meter rule Electronic balance Stopwatch

0.5 0.1 0.01 0.1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2  2  2ffi dsw dDp dD dL ¼ þ þ ð17Þ Dp D L sw ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s

 2  2  2 d 8U dm dD dDt D ¼ þ9 þ ð18Þ 8U m D Dt D ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 2  2  2  2  2ffi df dDp dD dDt dL dm ¼ þ 25 þ4 þ þ4 f Dp D Dt L m

ð19Þ ð15Þ

n is the slope of the line, and the term, In Fig. n6(c),  lg Kð3nþ1 , is the interception. Þ 4n In order to describe the flow performance of PCE, the friction factor of the emulsion f is defined as follows [22]: 2

Parameter

ð11Þ

Considering that there is sB  sw in the high shear stress area, the high order terms can be ignored: sw ¼ g

Table 2 Relative measurement errors

The relative measurement errors of the wall shear stress, the mean shearing rate and the friction factor are less than 1.1%, 1.5%, and 2.9%, respectively.

4. Results and discussion

2

ð16Þ

4.1. Rheological property

8

The main measured parameters such as pressure drop Dp, duct diameter D, test section length L, and mass flow rate (mass m and time range Dt) are listed in Table 2. Hence, by using Eqs. (1), (7), and (16), the relative measurement errors of the wall shear stress, the mean shearing rate, and the friction factor can be written as follows:

In order to validate the reliability of the experimental system and the results, water was firstly tested. The water viscosity conforms to the classical formula (f = 64/Re) for laminar flow, and the Blasius formula [23] (f = 0.3164/Re0.25) for turbulent flow (Fig. 7). Therefore, the experimental system can be considered reliable.

B. Chen et al. / Applied Thermal Engineering 26 (2006) 1238–1245 10 0

1243

1.5

Newtonian Fluid Bingham Fluid Pseudoplastic Fluid e /R 64 f=

τw (Pa)

1.0

f

-1

10

f=0.3

164/R

e 0.25

0.5

0.0

-2

10

10 1

10 2

10 3

0

10 4

50

100

200

250

300

Fig. 9. Comparison of the different fitting functions.

Fig. 7. Relationship of the friction factor and Re for water.

In the experiments, the PCE was very stable and never blocked the duct. The virtual rheological curves at different temperatures for the PCE of 30 wt% are shown in Fig. 8. Take the experimental data at T = 301.15 K for an example. By fitting them, the function of s ¼ f ð du Þ dr for the three types of fluids can be obtained: If it is Newtonian fluid, we have   du s ¼ 0:0044  dr

ð20Þ

If it is Bingham fluid, we have   du s ¼ 0:0044  þ 0:0249 dr

ð21Þ

If it is Pseudoplastic fluid, we have  0:983 du s ¼ 0:0049  dr

ð22Þ

Eqs. (20)–(22) are shown in Fig. 9. It is seen that the PCE can be considered as Newtonian fluid, because there is little difference between them. For example, when 8U/D = 200 l/s, the wall shear stresses calculated by the three functions above are 0.880 Pa, 0.905 Pa and 0.895 Pa, respectively. The maximum relative deviation is 2.8%. As for the experimental data at T = 283.15 K, the fitted equation can be written as   du s ¼ 0:0070  ð23Þ dr The relationship of the friction factor and Re for the PCE of 30 wt% is shown in Fig. 10. The result shows that the experimental data conforms to the formula, f = 64/Re. Fig. 11 shows the relationship of the dynamic viscosity and the temperature. The experimental data for one month and one and a half month later superpose the original curve, which indicates that the PCE is stable under 10 1

2.0

c=30% (T=283.15K, DN10) c=30% (T=301.15K, DN14)

T=283.15K T=301.15K

f=

64

1.5

0

/R

e

f

10 τw (Pa)

150

8U/D (1/s)

Re

1.0

-1

10 0.5

-2

10

0.0 0

100

200

300

8U/D (1/s) Fig. 8. Virtual rheological curves at different temperatures for the PCE of 30 wt%.

101

10 3

10 2

104

Re Fig. 10. Relationship of the friction factor and Re for the PCE of 30 wt%.

1244

B. Chen et al. / Applied Thermal Engineering 26 (2006) 1238–1245 9.0

60 One day One month later(stillness) One month and a half later(stillness) Fitted value

8.5 8.0 7.5

N (×10-3 W/m)

μ (mPa.s)

7.0 6.5 6.0 5.5 5.0

pure water c=30%

50

40

30

20

4.5 10 4.0 3.5 3.0 275

0 280

285

290

295

300

305

0.0

0.1

0.2

0.3

T (K) Fig. 11. Relationship of the dynamic viscosity and the temperature.

the experiment condition. Fitting the experimental data by Andrade formula (l = A · exp(B/Tx) (x = 1 for hydrocarbon)) [24], when 280 K < T < 300 K, we have

0.4

0.5

0.6

0.7

0.8

u (m/s) Fig. 12. Relationship of the pump consumptions and the flow velocities (DN10).

60

6

l ¼ 1:27  10 expð2448:8=T Þ ð24Þ The maximum relative error between the experimental data and the fitted value is 4.8%.

In order to analyze the application feasibility of the PCE system, the pump consumptions of a conventional (water) system and a PCE system are compared. In order to simulate a cooling system in the field of heating, ventilating, and air-conditioning (HVAC), it is assumed that the working temperature ranges are 3– 10 C for the cooled water system and the PCE system. The equivalent specific heat of the PCE for the range 3– 10 C is 14.2 kJ/(kg K). For given heat transportation quantity, the mass flow rate ratio of the PCE to the water is q cp;f 4:2 m_ p cp;p DT ¼ 0:29 ð25Þ ¼ q ¼ ¼ cp;p 14:2 m_ f cp;f DT In the case of the same pump efficiency and the same duct diameter, the pump consumption ratio of the PCE to the water is Qp Dpp U p Dpp Np g gN ¼ ¼ ð26Þ ¼ Qf Dpf Nf U f Dpf g Fig. 12 shows the relationship of the pump consumptions and the flow velocities. From it, it is seen that at the same flow velocity, the pump consumption per unit pipe length for the PCE is more than that for water. For example, when the flow velocity is 0.4 m/s, the pump consumption ratio is only 1.67.

N (× 10-3 W/m )

4.2. Feasibility discussions

50

40

30

20

10 pure water c=30%

0 0

1000

2000

3000

4000

5000

6000

q (W)

Fig. 13. Relationship of the pump consumptions and the heat transportation rates (DN10).

Fig. 13 shows the relationship of the pump consumptions and the heat transportation rates. From it, it is seen that for the same heat transportation rate, the pump consumption of water is more than that of the PCE. For example, when the heat transportation rate is 1500 W and the inner diameter is 10 mm, the pump consumption ratio per unit pipe length for the PCE to that for water is 0.12; when the pump consumption per meter of pipe is 0.04 W/m, the heat transportation rate ratio of the PCE to water is 2.83.

5. Conclusions The flow characteristics of the PCE of 30 wt% such as the flow stability, the rheological behavior for laminar

B. Chen et al. / Applied Thermal Engineering 26 (2006) 1238–1245

flow, the friction factor characteristics and the pump consumption are investigated in this paper. The results show: (1) by analyzing the virtual rheological curves and comparing the different fitted forms, the PCE can be considered as a Newtonian fluid; (2) the viscidity of the emulsion conforms to the classical function (f = 64/Re) for laminar flow; (3) the dynamic viscosity of the emulsion can be expressed by Andrade formula, and the relative error between the experimental value and the fitted value is less than 4.8%; (4) the viscosity of the PCE developed by the authors is about 5.57 times of that of water and lower than those reported in the literature; (5) the flow rate and the pump consumption of the PCE system decrease greatly for the same heat transportation quantity compared with water, due to phase change; (6) the PCE developed by the authors has good application feasibility in practice and more research on its application in practice should be conducted in the near future.

[7]

[8]

[9]

[10]

[11]

[12]

[13]

Acknowledgements [14]

This work was supported by the National Natural Science Foundation of China (Grant number: 50436020), the Science and Technology Project of Beijing (Grant number: H021820040620), and the Open Project of Key Lab in Beijing (Grant number: KF200506).

[15]

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