Influence of pore density and porosity on the wet air flow in metal foam under different operation conditions

Accepted Manuscript

Influence of pore density and porosity on the wet air flow in metal foam under different operation conditions Zhancheng Lai , Haitao Hu , Guoliang Ding , Xiaomin Weng PII: DOI: Reference:

S0140-7007(17)30510-8 10.1016/j.ijrefrig.2017.12.010 JIJR 3852

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

16 June 2017 29 November 2017 15 December 2017

Please cite this article as: Zhancheng Lai , Haitao Hu , Guoliang Ding , Xiaomin Weng , Influence of pore density and porosity on the wet air flow in metal foam under different operation conditions, International Journal of Refrigeration (2017), doi: 10.1016/j.ijrefrig.2017.12.010

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Highlights New heat transfer and pressure drop data of wet air flow in metal foam were obtained.

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Effect of PPI and porosity on the wet air flow in metal foam was analyzed.

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Comprehensive performance of metal foam under dehumidifying condition was analyzed.

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Optimal metal foam with 20 PPI and 85% porosity for wet air was recommended.

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Influence of pore density and porosity on the wet air flow in metal foam under different operation conditions Zhancheng Lai, Haitao Hu*, Guoliang Ding, Xiaomin Weng Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, Shanghai 200240, China, Corresponding author, Fax: 86-21-34206295; Email: [email protected].

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*

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Abstract

In order to optimize the parameters of metal foam heat exchanger operating under dehumidifying conditions, the influence of pore density and porosity on the heat transfer and pressure drop

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characteristics of wet air in metal foam under different conditions were investigated experimentally. The experimental conditions cover PPI (number of pores per inch) of metal foam from 5 to 40 and

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porosity from 85% to 95%. The results show that, as PPI increases, the global heat transfer coefficient

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always increases under low relative humidity conditions, while it initially increases then decreases under high relative humidity conditions, presenting a maximum increment of 12%-21% at 20 PPI. As

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the porosity increases from 85% to 95%, the global heat transfer coefficient of wet air in metal foam

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decreases maximally by 32%, and the pressure drop of wet air in metal foam decreases by 47%.

Key words: Metal foam; Pore density; Porosity; Heat transfer; Pressure drop; Dehumidifying condition;

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Nomenclature Area (m2)

b

Slope of saturated enthalpy line (kJ·kg-1·K-1)

Cp

specific heat at constant pressure (kJ·kg-1·K-1)

D

Hydraulic diameter of the flow passage cross

ΔT

section of tested metal foam sample (m)

u

Temperature difference (K) Velocity (ms-1)

Greek symbols

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A

d

Humidity ratios of wet air

δ

Copper plate thickness，m

F

Flow configuration factor, non-dimensional

λ

Thermal conductivity (Wm-1K-1)

f

Friction factor, non-dimensional



Density (kgm-3)

Heat transfer coefficient based upon the

γ

Specific latent heat of vaporization

henthalpy

-1

(kJ·kg-1)

h

Heat transfer coefficient (Wm-2K-1)

i

Enthalpy (kJ·kg-1)

j

Colburn j factor, non-dimensional

k

thermal conductivity (WmK-1)

L

Length (m)

m

Mass (Kg)

Nu

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enthalpy difference (kg·s )

Superscripts and Subscripts air

c

copper

w

water

v

vapor

Nusselt number, non-dimensional

in

inlet

PPI

Number of pores per inch

out

outlet

Pr

Prandtl number，non-dimensional



global

∆p

Pressure drop (Pa)

dry

dry air

Q

Heat exchange (W)

LM

logarithmic mean

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PT

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a

Reynolds number，non-dimensional

T

Temperature (K)

s dehumid

saturated dehumidifying

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Re

1. Introduction Open-cell metal foam has been widely used in heat exchangers due to its advantages of high porosity, large specific surface area, high effective thermal conductivity and high heat transfer capacity (Boomsma et al., 2003; Calmidi and Mahajan, 1999; Han et al., 2012a; Zhao, 2012). For refrigeration 3

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and air conditioning systems, heat exchangers always work under dehumidifying conditions (Mazzei et al., 2005; Wu and Webb, 2002; Zhang et al., 2010), and the metal foam heat exchangers provide higher heat transfer capacity by 56%-196% than the conventional fin-and-tube heat exchangers (Dai et al., 2012a; De Schampheleire et al., 2013a; Hu et al., 2016). As wet air flows in metal foams under

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dehumidifying conditions, the condensate accumulated on the fiber surface may restrict the air flow and occupy heat transfer area (Han et al., 2012b; Hu et al., 2016), which has a profound impact on the heat exchanger performance (Hu et al., 2017). For metal foams with various pore density and porosity,

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the metal fiber diameter and specific area are different, and the condensate rate will be different under different dehumidifying conditions, leading to the different heat transfer and pressure drop characteristics of wet air in metal foam (Korte and Jacobi, 2001). It can be deduced that, there must be

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an optimal metal foam structure corresponding to the best performance under specific dehumidifying condition. In order to realize the optimal design of metal foam heat exchanger, the influence of metal

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foam pore density and porosity on the heat transfer and pressure drop characteristics of wet air under

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dehumidifying conditions should be known. For the heat transfer and pressure drop characteristics of wet air under dehumidifying conditions,

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the existing research focuses on the fin-and-tube heat exchangers, and there are only two published

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papers on wet air in metal foams (Han et al., 2012b; Hu et al., 2016). The research results on wet air in fin-and-tube heat exchangers show that, the influence of fin patterns on the heat transfer performance is different for diverse relative humidity (Chang and Wang, 1997; Lin et al., 2002; Wang et al., 2000; Yun and Lee, 2000), and both heat and mass transfer rates increase when the fin pitch decreases (Phan et al., 2011; Pirompugd et al., 2006; Wang et al., 1997); the j-factor increases as the tube diameter decreases (Yun et al., 2009), and the influence of geometrical parameters on the performance becomes less 4

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significant with the increasing tube row number (Halici et al., 2001; Ma et al., 2009; Pirompugd et al., 2006). The research results on wet air in metal foam heat exchangers show that, as the relative humidity of inlet air increases, the heat transfer rate and pressure drop of wet air in metal foam increase maximally by 67% and 62%, respectively, and the heat transfer capacity of copper foam heat exchanger

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is enhanced by 56%-196% compared to that of the fin-and-tube heat exchanger (Hu et al., 2016); the drainage performance of metal foam is as good as or better than that of louver-fin heat exchanger, and the heat transfer coefficient under wet condition is slightly higher than that under dry condition (Han et

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al., 2012b). However, the metal foam with only one porosity was used in the above researches (Han et al., 2012b; Hu et al., 2016), and the influence of metal foam pore density and porosity was not discussed.

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There is no publication on the influence of pore density and porosity on the performance of metal foam under dehumidifying conditions. However, there are researches on the influence of metal foam

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PPI and porosity on dry air flow in metal foam, including the heat transfer characteristics(Arbak et al.,

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2017; Kim et al., 2000; Mancin et al., 2012; Zhao et al., 2004) and pressure drop characteristics (Dukhan, 2006; Hsieh et al., 2004; Kim et al., 2000; Mancin et al., 2012; Zhao et al., 2004). The

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research results show that, both the heat transfer coefficient and pressure drop increase with the

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increasing PPI (Hwang et al., 2002; Kim et al., 2000; Mancin et al., 2012) and decreasing porosity (Dukhan, 2006; Hsieh et al., 2004); PPI has a more significant effect on the heat transfer than porosity (Zhao et al., 2004); the optimal porosity based on the balance between pressure drop and heat transfer varies from 0.85 to 0.95 (Zhao et al., 2004); the thermal entry length is found to be inversely proportional to the pore density, while the 40PPI metal foam produced the largest heat transfer (Arbak et al., 2017). For metal foam under dehumidifying conditions, the condensate occurred and 5

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accumulated on the fiber surface, and the quantity of condensate increases with the increasing relative humidity (Hu et al., 2016). The latent heat transfer and condensate retention make the heat transfer and pressure drop characteristics in metal foam under dehumidifying conditions much different from that for dry air. Therefore, the existing research results on the influence of pore density and porosity for dry

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air conditions cannot be extended to the dehumidifying conditions. The purpose of this study is to experimentally obtain the heat transfer and pressure drop characteristics of wet air flow in metal foams, and to analyze the influence of pore density and porosity

2. Experimental rig and test samples

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2.1 Experimental apparatus

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on the wet air flow in metal foam under dehumidifying conditions.

The experimental apparatus for investigating the heat transfer and pressure drop characteristics of

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wet air in metal foam is schematically shown in Fig. 1. The experimental apparatus consists of a wet air

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side system, a cooling water system and a data acquisition system. The experimental apparatus was introduced in detail in the literature (Hu et al., 2016).

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In the experimental apparatus, the dry air from the air compressor and the pure water vapor from

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the humidifier are mixed to generate the wet air with a certain relative humidity. The relative humidity of wet air is adjusted by the electrical heating power of the humidifier, and the temperature of wet air is controlled by the air conditioner box; the flow rate of wet air is adjusted by the open degree of the valve and measured by the volume flow meter with an uncertainty of ±0.2 L·min-1. Two relative humidity and temperature sensors with uncertainties of ±0.1°C and ±0.8% are installed at the airside of the test section, and two calibrated thermocouples with an uncertainty of ±0.1°C are installed at the 6

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cooling water side of test section. The flow rate of cooling water is measured by a volumetric flow meter with an uncertainty of ±0.02 L·min-1, and the pressure drop of wet air is measured by a

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differential pressure transducer with an uncertainty of ±0.3Pa.

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Fig. 1. Schematic diagram of experimental rig

2.2 Test samples

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In order to investigate the influence of PPI and porosity on the heat transfer and pressure drop

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under dehumidifying conditions, the metal foam test samples with various PPI and porosity values should be designed and prepared. In the present study, the test sample consists of a copper plate and a piece of copper foam, as shown in Fig. 2. The copper foam has the height of 140 mm, the length of 38 mm, and the thickness of 15 mm. The copper plate has the same height of 140mm, the length of 60 mm and the thickness of 5 mm. To reduce the thermal contact resistance between copper foam and copper plate, the brazing bonding method (De Jaeger et al., 2012) is used. The copper-based amorphous solder 7

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with melting point at 640oC is placed between copper foam and copper plate. Then the copper foam, solder and copper plate are welded together at 700oC in a vacuum furnace. The brazing bonding method has the smallest thermal contact resistance than other methods (De Jaeger et al., 2012), and the thermal contact resistance only accounts for lower than 1% of the total thermal resistance of test

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sample. Therefore, the brazing bonding method is used and the thermal contact resistance caused by

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brazing bonding can be neglected.

Fig. 2. Metal foam test example

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The photos and schematic diagram of test section are shown in Fig. 3. The test sample is installed

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through several screws. Wet air with specific temperature and relative humidity flows through metal foam with a fixed speed, while cooling water flows behind the copper plate and works as the cooling

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source. The front of the test section is covered with a transparent plexiglass plate with low thermal conductivity, and the other parts of the test section are covered with heat-insulating foam to reduce the heat loss of the experiment apparatus.

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(b) photo of top view

(c) schematic diagram of top view

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(a) photo of the front view

Fig. 3. Photos and schematic diagram of test section

2.3 Experimental conditions

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Seven types of metal foams (shown in Fig. 4) were tested for analyzing the influence of the PPI and porosity of metal foam. The PPI of metal foams covers 5, 10, 15, 20 and 40, and porosity of metal foams covers 85%, 90% and 95%. PPI (pore number per inch) and porosity are two independent

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parameters for specifying a metal foam structure (Dukhan and Ali, 2012). The PPI could be measured

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by counting the number of cells on specific length (Dukhan and Ali, 2012); porosity is the ratio of the air volume to the total foam volume and could be obtained by measuring the solid volume and the total

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foam volume (De Schampheleire et al., 2013b). The uncertainties of the measured PPI and porosity are

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within ±3% and ±2%, respectively. For metal foam with a certain PPI and porosity, the fiber diameter and specific surface area could be calculated based by Calmidi model (Calmidi, 1998). The values of

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PPI, porosity, fiber diameter and specific surface area of the tested metal foams are listed in Table 1.

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Fig. 4. Metal foams in the experiment

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The experimental conditions of the wet air include the inlet air temperature of 27 oC, 30oC, 32oC,

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35oC; inlet air relative humidity of 30%, 50%, 70%, 90%; inlet air velocity of 0.5 m·s-1, 0.75 m·s-1, 1.0 m·s-1; and cooling water temperature of 6oC, 12oC, 18oC, as shown in Table 2. Table 1 Structure parameters of tested metal foams

PPI

Fiber

Specific surface

diameter(mm)

area(m2/m3)

95%

458

porosity

0.612

10

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Composition

95%

0.306

916

15

95%

0.219

1282.4

20

95%

0.153

1832

20

90%

0.178

2591.3

20

85%

0.189

3173.6

40

95%

0.077

3664

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5

100%wt

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PT

copper

Table 2 Experimental conditions in the present study Value

PPI of metal foam

5, 10, 15, 20, 40

Porosity of metal foam

85%, 90%, 95%

Inlet air temperature (°C)

27, 30, 32, 35

Relative humidity

30%, 50%, 70%, 90%

Air velocity (m∙s-1)

0.5, 0.75, 1.0

Cooling water temperature (°C)

6, 12, 18

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Parameter

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3. Data reduction and uncertainties 3.1 Data reduction The flow characteristics of the wet air in metal foam include the pressure drop and heat transfer. The pressure drop is measured by differential pressure transducer connected to both side of metal foam,

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and the heat transfer is calculated with the temperature, relative humidity and wet air flow rate of wet air. According to the ASHRAE33-78 standard (Standard, 1978), the maximum difference between Qa and Qw must be smaller than 5%. The total heat transfer of the wet air is calculated as the average of heat transfer on air side (Qa) and heat transfer on water side (Qw), as shown in Equation (1):



1 Q Q w 2 a



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Q

(1)

The heat transfer on air side (Qa) and heat transfer on water side (Qw) are calculated (Yu et al., 2013) by Equations (2)-(5):

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Qw  mw Cpw Tw, in  Tw ,out 



(2)



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Qa  mw, dehumid w  ma,dryCpa Ta ,in  Ta, out  + ma, dry din  mw, dehumid Cpv Ta, in  Ta, out  +mw, dehumidCpv Ta ,in  Ta ,dew  (3)





Qsensbile  ma,dryCpa Ta ,in  Ta, out  + ma, drydin  mw, dehumid Cpv Ta, in  Ta, out  +mw, dehumidCpv Ta ,in  Ta ,dew  (4)

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Qlatent =mw, dehumid w  ma ,dry  din  dout   w

(5)

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In Eq.(5), the humidity ratio of wet air at the inlet (din) and outlet (dout) of the test section

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could be calculated by Equation (6):

d  0.622

 ps p   ps

(6)

For the wet conditions, the logarithmic mean enthalpy difference (LMED) method is used to calculate the heat transfer coefficient, as shown in Equations (7)-(12):

Q  henthalpy AiLM

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(7)

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iLM  F

henthalpy A



 i i ln  a ,in w, out i  a ,out  iw, in

  

1 1   b o ha Aa / Cpa a  hw Aw / b w kAw

 hair, s  b   T Tw

(9)

(10)

 f w Re  1000 Pr     w w  2  w  hw  2   fw (Prw 3  1)   lw 1.07  12.7 2   2

(11)

(12)

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f w  1.58ln Rew  3.28

(8)

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1

 ia ,in  iw, out   ia ,out  iw, in 

where, the water side heat transfer coefficient hw is calculated based on Gnielinski model (Gnielinski, 1976).

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In Eq. (9), ηo is the fin efficiency of the metal foam heat exchanger. In the existing literatures, the

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fin efficiency of metal foam fins was calculated based on the surface area of metal foam and the effective straight fin efficiency for calculating the local heat transfer coefficient (Dai et al., 2012b; Han

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et al., 2012b), while the base area of metal foam heat exchanger was used for calculating the global

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heat transfer coefficient to analyze the influence of metal foam structure (Ji et al., 2015; Mancin et al., 2012). Therefore, in the present study, the global heat transfer coefficient of wet air (ha) is used for

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comparing the performance of metal foams with various structures, and it can be calculated by Eq. (13) (Ji et al., 2015; Mancin et al., 2012).

0 ha Aa  h a Ab a s e

(13)

The Colburn j factor and friction factor f is calculated by Equations (14)-(15)(Yun and Lee, 2000)：

j

Nua Rea  Pra1/3 12

(14)

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f 

2pD u2 L

(15)

3.2 Experimental uncertainties The experimental uncertainties are estimated according to the analysis method of error

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propagation (Moffat, 1988). The maximum uncertainty of heat transfer coefficient, Colburn j factor and friction factor f are ±13.5%, ±14.0% and ±4.8%, respectively. The maximum uncertainty of the comprehensive performance index j·f -1/3 is ±15.6%. The uncertainties of the measured and calculated parameters are listed in Table 3. The uncertainties of heat transfer rates and heat transfer coefficient are calculated by Eqs. (14) -(17):

Qa

2

  m   d    m   T    m    dout   T    m   T   d                           m   d   m   T   m   dout   T   m   T   d  2

2

2

2

 Qw Qw



2

 mw2 mw2 Q

h

2

2

Tw2,in Tw2,out  Tw2,out  Tw2,in

T

w,out

 Tw,in 

2

(16)

(17)

(18)

1  1      Q 2    i 2 h Q  i   

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2

4

1   Q  Qw    a   2  Qa Qw 

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Q



2

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 Qa

2

(19)

Table 3 Uncertainties of the measured and calculated parameters Instrument

Range

Uncertainty

Instrumentation calibration

Temperature and humidity sensor (ROTRONICHC2-SH)

-50~100oC

±0.1℃

Air relative humidity

Instrumentation calibration

Temperature and humidity sensor (ROTRONICHC2-SH)

0~100%

±0.8%RH

Air flow rate

Instrumentation calibration

Float flow meter (LZ series)

1.2~12m3h-1

±0.2Lmin-1

Airside pressure drop

Instrumentation calibration

Differential pressure transducer (OMEGA PX655-0.5DI)

0~127 Pa

±0.3Pa

Water flow rate

Instrumentation calibration

Volumetric flow meter (OMEGA FLR1011)

0.2~2Lmin-1

±0.02Lmin-1

Water temperature

Instrumentation calibration

T-type thermocouple

0~60oC

±0.1℃

Heat transfer coefficient

Water flow rate, water temperature, air flow rate, air temperature, air relative humidity

Calculated

Colburn j factor

Water flow rate, water temperature, air flow rate, air temperature, air relative humidity

Calculated

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Air temperature

Major source of uncertainty

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Parameters

13

144.3-558.6 Wm-2‧ k-1

±13.5%

0.097-0.471

±14.0%

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Friction factor f

Airside pressure drop, air flow rate

Calculated

9.8-64.39

±4.8%

Comprehensive performance index j∙f -1/3

Water flow rate, water temperature, air flow rate, air temperature, air relative humidity, airside pressure drop

Calculated

0.038-0.14

±15.6%

4. Experimental results and discussion 4.1 Effect of PPI on heat transfer coefficient of wet air in metal foam

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Figure 5 shows the influence of PPI on the global heat transfer coefficient of wet air in metal foam under various experimental conditions.

The influence of PPI on heat transfer coefficient of wet air in metal foam is different at various

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relative humidity, as shown in Fig. 5(a). At low relative humidity (30% and 50%), the heat transfer coefficient of wet air always increases as PPI increases; while at high relative humidity (70% and 90%), the heat transfer coefficient of wet air initially increases then decreases as PPI increases,

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presenting a maximum increment of 16%~21% for 20PPI metal foam. The reason for this

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phenomenon is explained with the different heat transfer area of metal foams. At low relative humidity (30%, 50%), the heat transfer area always increases as PPI increases, leading to the

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increment of heat transfer coefficient. While at high relative humidity (70%, 90%), more accumulated

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condensate in metal foam occupy the heat transfer area, and the thermal resistance caused by the liquid film between the humid air and the solid ligaments are increased, resulting in the decrement of

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heat transfer coefficient as PPI increases from 20 to 40. The influence of PPI on heat transfer coefficient shows similar tendency at various inlet air

temperatures, air velocities, and cooling water temperatures, as shown in Fig. 5(b)-(d). As PPI increases from 5 to 40, the heat transfer coefficient of wet air initially increases then decreases, presenting maximum increments of 12%-19% for 20PPI metal foam.

14

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o

Tair=35 C Vair=1 ms

RH=30% RH=50% RH=70% RH=90%

450 400

500

-1

o

Tair=27 C

o

Tcooling water=6 C

450

Tair=30 C

400

Tair=32 C

RH =70 % o Tcooling water=6 C

o

Vair=1 ms

o

-1

o

Tair=35 C

h (Wm K )

350

250

200

200

150

150

100 5

10

15 PPI

20

100

40

5

(a) Relative humidity 500 Vair=0.5 ms 450

Vair=0.75 ms Vair=1 ms

400

-1

20

o

o

RH=70 % -1 Vair=1 ms

Tcooling water= 12 C o

Tcooling water= 18 C

400

200

-2

250

300



-2

300



-1

h (Wm K )

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350

-1

40

Tair=35 C

o

450

RH =70 % o Tcooling water=6 C

350

h (Wm K )

15 PPI

Tcooling water= 6 C

o

Tair=35 C

-1

10

(b) Air temperature 500

-1

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-2

250

300



-2

300



-1

-1

h (Wm K )

350

250 200

150

150

100

100

10

15 PPI

20

40

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5

10

15 PPI

20

40

(d) Cooling water temperature

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(c) Air velocity

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Fig.5. Effect of PPI on heat transfer coefficient of wet air in metal foams under various

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experimental conditions

Figure 6 shows the photographs of the condensate droplets in metal foams with low and high

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PPIs. It can be seen from the figure that, the quantity of condensate droplets accumulated in low PPI

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metal foam is much smaller than that in high PPI metal foam. In low PPI metal foam, the condensate droplets suspend on the metal fibers or the connection points; while in high PPI metal foam, the droplets in adjacent cells of metal foam combine together and enclose many cells. As PPI increases, the cell diameter decreases, and the condensate droplets are more easily to bridge over the metal fibers and accumulate in metal foam cells, leading to the deterioration of heat transfer performance for wet air in metal foams. 15

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(a) condensate droplet in low PPI metal foam (5PPI) (b) condensate droplets in high PPI metal foam (40PPI)

Fig. 6 Photographs of the condensate droplets in metal foams with different PPIs 4.2 Effect of PPI on pressure drop of wet air in metal foam

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Figure 7 shows the influence of PPI on pressure drop of wet air flow in metal foam under various experimental conditions. As PPI increases, the pressure drop always increases, and the maximum increments are within 272%-486% under various conditions. The reason for the increment of pressure

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drop is explained as follow. Firstly, as PPI increased, the length and diameter of metal fiber is

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decreased, and the pore size is decreased, resulting in the increase of flow disturbance and resistance. Secondly, with the increase of PPI, the heat transfer area of metal foam is increased and the cell

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volume of metal foams is decreased, which leads to more accumulated condensate adhered to the

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fiber surface, blocking the flow path and resulting in the increment of pressure drop. 1400

1000

o

o

Tcooling water=6 C Vair=1 ms

-1

1200

o

Tair=27 C

o

Tair=35 C

Pressure drop per unit length (Pam )

RH=30% RH=50% RH=70% RH=90%

-1

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-1

Pressure drop per unit length (Pam )

1400

800 600 400 200

Tair=30 C

1200

o

Tair=32 C 1000

RH =70 % o Tcooling water=6 C Vair=1 ms

-1

o

Tair=35 C

800 600 400 200 0

0 5

10

15

20

5

40

10

15 PPI

PPI

(a) Relative humidity

(b) Air temperature 16

20

40

ACCEPTED MANUSCRIPT 1400

1400 -1

1000

-1

o

Tcooling water= 6 C

RH =70 % o Tcooling water=6 C

800 600 400 200

1200

o

Tcooling water= 12 C o

Tcooling water= 18 C

1000

600 400 200 0

10

15

20

RH=70 % -1 Vair=1 ms

800

0 5

o

Tair=35 C

5

40

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Vair=1 ms

-1

-1

Vair=0.75 ms

1200

o

Tair=35 C

Pressure drop per unit length (Pam )

-1

Pressure drop per unit length (Pam )

Vair=0.5 ms

10

15

20

40

PPI

PPI

(c) Air velocity

(d) Cooling water temperature

Fig.7 Effect of PPI on pressure drop of wet air in metal foams under various experimental conditions

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The influence of PPI on the pressure drop is more obvious under high relative humidity conditions. As the PPI increases from 5 to 40, the pressure drops of wet air flow in metal foam at relative humidities of 30%, 50%, 70% and 90% increase by 272%, 306%, 378% and 400%,

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respectively. At high relative humidity conditions, more condensate water is accumulated on metal

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foam surface, resulting in a larger pressure drop increment. The influence of PPI on pressure drop is smaller at high air flow velocity conditions. As PPI

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increases from 5 to 40, the pressure drops of wet air flow in metal foams at air velocities of 0.5m·s -1

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and 1m·s-1 are increased by 486% and 378%, respectively. The reason for the smaller influence of PPI on the pressure is that the high air flow velocity could help to blow out the condensate water. The

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pressure drop of 40PPI metal foam is relatively high because of its small cell size and large condensate retention. 4.3 Effect of porosity on heat transfer coefficient of wet air in metal foam Figure 8 shows the influence of porosity on the global heat transfer coefficient of wet air in metal foams under various experimental conditions. As porosity increases from 85% to 95%, the heat transfer coefficient of wet air is decreased by 22%-32%. 17

ACCEPTED MANUSCRIPT 700

700

RH=30% T =35 oC air RH=50% o Tcooling water=6 C RH=70% -1 RH=90% Vair=1 ms

600

o

Tair=27 C RH =70 % o o T =30 C Tcooling water=6 C

600

air

o Tair=32 C Vair=1 ms

-1

o

-1

h (Wm K )

-2

-2

-1

400





400

300

300

200

200

100

100 85%

90%

85%

95%

(a) Relative humidity 700

Vair=0.75 ms

600

-1

o

Tair=35 C

o

RH =70 % o Tcooling water=6 C

Tcooling water= 12 C RH=70 % -1 o Tcooling water= 18 C Vair=1 ms

600

500 -1

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h (Wm K )

500 -2

-2

-1

h (Wm K )

Vair=1 ms

o

Tcooling water= 6 C

o

Tair=35 C -1

95%

(b) Air temperature

700 -1

90%

porosity

porosity

Vair=0.5 ms

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h (Wm K )

Tair=35 C

500

500

400





400

300

300

200

200

100

100

90%

porosity

95%

M

85%

90%

95%

porosity

(d) Cooling water temperature

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(c) Air velocity

85%

Fig.8 Effect of porosity on heat transfer coefficient of wet air in metal foams under various

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experimental conditions

The influence of porosity on heat transfer coefficient of wet air is more obvious under high

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relative humidity conditions. With the increment of porosity from 85% to 95%, the heat transfer

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coefficient of wet air is reduced by 22%, 24%, 25% and 30% at relative humidity of 30%, 50%, 70% and 90%, respectively. The reason for this phenomenon can be explained as follow. The heat transfer coefficient (h) is the total heat transfer coefficient, and it is the sum of sensible and latent heat transfer coefficients. As the porosity increases, the thermal conduction and the sensible heat transfer increase due to the increasing fiber diameter, and the latent heat transfer increases due to the increasing number of nucleating point, resulting in the increment of total heat transfer coefficient. Under high 18

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relative humidity conditions, the latent heat transfer is enhanced, resulting in more obvious influence of porosity. Figure 9 shows the sensible heat transfer rate, latent heat transfer rate and the mass transfer rate of wet air in metal foams. It can be seen in the figure, as the porosity increases, both the sensible and

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latent heat transfer rates of wet air in metal foam are decreased; as the inlet air relative humidity increases, the sensible heat transfer of wet air is slightly decreased, while the latent heat transfer is significantly increased, resulting in the increment of total heat transfer. 80

60

PPI=20

60

Tair=35 oC

50

Vair=1 ms-1 Tcooling water=6 oC

Qlatent (W)

Qsensible (W)

50

70

40 30 20

80

0.30

70

0.27

60

0.24

PPI=20

Tair=35 oC

0.21

Vair=1 ms-1 Tcooling water=6 oC

40

0.18 0.15

30

0.12 0.09

20

40 30 20

0.06

10

10 0 30%

50%

70%

90%

RH

0.03

M

0

30%

50%

70%

0.00

90%

RH

(b)latent heat transfer

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(a)sensible heat transfer

  

50

Qa (W)

70

0.33

  

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  

Mhumid (gs-1)

80

10

Tair=35 oC

PPI=20 Vair=1 ms

-1

Tcooling water=6 oC

0

30%

50%

70%

90%

RH

(c)total heat transfer

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Fig. 9 Heat transfer characteristics of wet air in metal foams at different relative humidity 4.4 Effect of porosity on pressure drop of wet air in metal foam

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Figure 10 shows the influence of porosity on pressure drop of wet air flow in metal foams under

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various experimental conditions. The influence of porosity on the pressure drop of wet air is more obvious at high relative humidity and high air velocity conditions due to the larger condensate water quantity in metal foam. As porosity increases from 85% to 95%, the pressure drop of wet air flow in metal foam decreases by 32%-47%. The reason for this phenomenon is that, as porosity decreases, the fiber diameter is increased, the air volume in metal foam is smaller. The larger cross section area of metal fibers could cause more flow obstruction, which contributes to the larger pressure drop. The 19

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increase of copper volume and heat transfer area also enhanced the heat transfer in metal foam, resulting in more condensate and larger pressure drop. 900

700

o

o

Tcooling water=6 C Vair=1 ms

800

Tair=27 C RH =70 % o o T =30 C Tcooling water=6 C

-1

700

o Tair=32 C Vair=1 ms

600

600

Tair=35 C

500 400 300 200

air

o

500 400 300 200 100

100

0

0 85%

90%

85%

95%

porosity

95%

(b) Air temperature

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900

Vair=0.75 ms

700

Vair=1 ms

o

Tair=35 C -1

-1

RH =70 % o Tcooling water=6 C

600 500

M

400 300 200 100 0 85%

90%

o

Tcooling water= 6 C

800

o

Tcooling water= 12 C

-1

800

-1

Pressure drop per unit length (Pam )

900

Vair=0.5 ms

ED

-1

90%

porosity

(a) Relative humidity

Pressure drop per unit length (Pam )

-1

CR IP T

800

o

Tair=35 C -1

RH=30% RH=50% RH=70% RH=90%

Pressure drop per unit length (Pam )

-1

Pressure drop per unit length (Pam )

900

700

o

Tcooling water= 18 C

o

Tair=35 C RH=70 % -1 Vair=1 ms

600 500 400 300 200 100

0 85%

95%

90%

95%

porosity

PT

porosity

(c) Air velocity

(d) Cooling water temperature

conditions

AC

CE

Fig.10 Effect of porosity on pressure drop of wet air in metal foams under various experimental

4.5 Effect on the comprehensive performance of metal foam under dehumidifying conditions To evaluate the performance of metal foam heat exchanger, both the heat transfer and pressure

drop characteristics should be considered. The comprehensive performance index (j·f -1/3) is used to evaluate the performance of heat exchanger, as did in the literatures (Qu et al., 2012; Webb, 1981; Yilmaz et al., 2001; Yun and Lee, 2000). 20

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Figure 11 shows the effect of PPI on the comprehensive performance index of metal foam. As PPI increases from 5 to 20, the comprehensive performance index changes slightly because the increment ranges of the heat transfer coefficient of wet air are close to that of pressure drop; while as PPI further increases from 20 to 40, the comprehensive performance index (j·f -1/3) sharply decreases

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due to the decrement of heat transfer coefficient and the large increment of pressure drop. The metal foam with 20PPI provides the largest comprehensive performance index under the present experimental conditions. 0.20

Tair=35 C

o

Tcooling water=6 C Vair=1 ms

RH=70% o Tcooling water=6 C

Tair=27 C o

o

Tair=30 C

-1

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0.15

0.20

o

RH=30% RH=50% RH=70% RH=90%

o

Tair=32 C

0.15

Vair=1 m/s

o

-1/3

0.10

jf

jf

-1/3

Tair=35 C

0.05

0.00 5

10

15

20

0.00

40

5

(a) Relative humidity Vair=0.5 ms Vair=1 ms

0.20

RH= 70% o Tcooling water=6 C

Tcooling water=12 C RH=70 % -1 o T =18 C Vair=1 ms

-1

o

0.15

jf

jf

0.10

0.05

AC

o

Tcooling water=6 C

CE

-1/3

PT

Vair=0.75 ms

0.15

-1

20

Tair=35 C

o

-1

15

40

(b) Air temperature

-1/3

0.20

10

PPI

ED

PPI

M

0.05

0.10

o

Tair=35 C

cooling water

0.10

0.05

0.00

0.00 5

10

15

20

40

5

PPI

10

15

20

40

PPI

(c) Air velocity

(d) Cooling water temperature

Fig.11 Comprehensive performance index of metal foam with different PPI under various experimental conditions

21

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Figure 12 shows the effect of porosity on the comprehensive performance index of metal foam under various experimental conditions. As porosity increases from 85% to 95%, the comprehensive performance index (j·f -1/3) always decreases. Due to its largest heat transfer coefficient, the metal foam with porosity of 85% has the largest comprehensive performance index under the present

0.20

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experimental conditions. 0.20

o

RH=30% RH=50% RH=70% RH=90%

0.15

Tair=35 C

Tair=35 C

o

o

Tair=30 C

o

Tcooling water=6 C Vair=1 ms

o

Tair=27 C

o

0.15

-1

Tcooling water=6 C

o

Vair=1 ms

Tair=32 C

-1

o

-1/3

jf

0.10

0.05

0.10

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jf

-1/3

Tair=35 C

0.05

0.00

0.00

85%

90%

95%

85%

0.20 -1

Vair=0.75 ms Vair=1 ms

-1

o

Tcooling water=6 C

RH= 70% o Tcooling water=6 C

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Tcooling water=12 C RH=70 % -1 o Tcooling water=18 C Vair=1 ms

-1/3

jf

0.10

0.05

0.00

0.00

85%

o

Tair=35 C

o

0.15

ED

0.10

0.05

-1

0.20

o

Tair=35 C

PT

jf

-1/3

0.15

95%

(b) Air temperature

M

(a) Relative humidity Vair=0.5 ms

90%

porosity

porosity

90%

85%

95%

90%

95%

porosity

porosity

(c) Air velocity

(d) Cooling water temperature

Fig.12 Comprehensive performance index of metal foam with different porosity under various conditions

According to the analysis based on the j·f

-1/3

comprehensive performance index, under the

experimental conditions in this study, the metal foam with PPI of 20 and porosity of 85% provides the largest comprehensive performance index. 22

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5. Conclusion The influence of PPI and porosity on the heat transfer and pressure drop characteristics of wet air in metal foam were experimentally analyzed. The experimental conditions cover PPI from 5 to 40, porosity from 85% to 95%, relative humidity from 30% to 90%, air temperature from 27oC to 35oC,

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inlet air velocity from 0.5 m·s-1 to 1.0 m·s-1, and cooling water temperature from 6 oC to 18oC. The research results show that:

1) As porosity increases from 85% to 95%, the heat transfer coefficient decreases by 22-32%,

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and the pressure drop decreases by 32%-47%.

2) As PPI increases from 5 to 40, the pressure drop in metal foam increases by 272%-486%; at low relative humidity, the heat transfer coefficient always increases; while at high relative humidity,

12%-21% for 20PPI metal foam.

M

the heat transfer coefficient initially increases then decreases, presenting a maximum increment of

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3) As the inlet air relative humidity increases, the sensible heat transfer of wet air is slightly

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decreased, while the latent heat transfer is significantly increased, resulting in the increment of total heat transfer. The influences of porosity and PPI on the heat transfer coefficient of wet air in metal

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foams are more obvious under higher relative humidity conditions due to the enhanced latent heat

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transfer.

4) The condensate accumulated in metal foams under dehumidifying conditions could occupy

heat transfer area and block the flow path, resulting in the deterioration of metal foam performance. As pore density increases, the deterioration caused by condensate becomes more obvious, resulting in the decrement of heat transfer coefficient. 5) The j·f -1/3 comprehensive performance index of metal foam is slightly changed as PPI increases 23

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from 5 to 20, and sharply decreased as PPI increases from 20 to 40; while it is decreased from 85% porosity to 95% porosity.

Acknowledgements

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This study is supported by National Natural Science Foundation of China (No.51576122, No.51674165), Natural Science Foundation of Shanghai (No.15ZR1422000).

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