Experimental study on enhancement condensation heat transfer in tube by foam metal in presence of non-condensable gas

Condensation heat transfer in tube is widely applied in industrial production, and the heat transfer process is often weakened by non-condensable gas (NCG) in actual production. Enhancing condensation heat transfer is beneficial to improve production efficiency, which has always been a hot topic in current research. Foam metal material with large specific surface area and good thermal conductivity is an ideal material to enhance heat transfer. In order to study enhancement heat transfer effect and optimize structure of foam metal, this paper investigated condensation heat transfer in tube strengthened by foam metal in presence of NCG experimentally. Section shape of foam metal is annular, and the pores per inch (PPI) of foam metals is 10, 15, 20 respectively. The effects of PPI value, steam/air mixture mass flow, and NCG mass fraction on heat transfer coefficient (HTC) and flow resistance are studied. The results reveal the following: (1) Compared with smooth tube, the foam metal enhances heat transfer significantly, and HTC increases by 1.5-2.3 times. (2) At same steam/air mixture mass flow, 10PPI foam metal tube has the highest HTC compared to others. (3) With increase of NCG mass fraction and PPI value, pressure drop increases and the HTC decreases. Based on experimental data, pressure drop and HTC correlations are developed. This paper provides an important technical basis for foam metal material application in enhancement heat transfer area.


Introduction
Condensation heat transfer (CHT) in tube applies in industrial production widely, and enhancement of heat transfer is beneficial to improve production efficiency, which has always been a hot topic in current research.Foam metal material with large surface area and good thermal conductivity is an ideal material to enhance heat transfer.Currently, heat transfer enhancement using foam metal mainly concentrates on boiling and single-phase convection heat transfer [1][2][3].The research on CHT in foam metal is comparatively few.So, it is very important to research CHT in foam metal tubes.
Moreover flow CHT often contains NCG in practical process.The NCG layer can impede condensation heat transfer and reduce local HTC.The effect of NCG on flow CHT in smooth tube has been researched maturely.Lee et al. [4] studied the effect of NCG on flow CHT in vertical tube.Zhang et al. [5] optimized the condenser structure to increase the HTC in presence of NCG.Comparatively, the effect of NCG on flow CHT in intensified heat exchange tube has been rarely researched.Therefore it is meaningful to consider effect of NCG for condensation heat transfer of foam metal tube.
This paper studied the CHT in tube strengthened by foam metal in presence of NCG experimentally.
The effects of PPI value, steam/air mixture mass flow, and NCG mass fraction on HTC and flow resistance are analyzed.

Experimental platform
The experimental platform includes vapor/air loop, cooling water loop and data sensors, as presented in Figure 1.In vapor/air loop, boiler is used to produce saturated steam, and the vortex flowmeter is applied to measure the saturated steam mass flow.The air supplied by air compressor is applied as noncondensable gas, and the glass rotameter is applied to measure air volume flow.The steam and air are evenly mixed in mixer.Then the steam/air mixture flow into experimental section and conduct countercurrent heat transfer with cooling water.In cooling water loop, the cooling water is provided by constant temperature water tank.The cooling water mass flow is obtained from turbine flowmeter.The signals of temperature, flow rate and differential pressure are collected by AGILENT data acquisition instrument.The total length of double pipe heat exchanger is 1 m.The diameter of outer pipe is 65 mm, which is made from plexiglass.The surface of outer pipe is covered with insulation cotton.The inner tube is foam metal tube, and the outer diameter is 22 mm, as presented in Figure 2. Foam metal thickness is 2 mm, which manufactured by high temperature sintering technology.

Data calculation
The inlet air mass fraction φ is calculated by: ( ) where Gv and Ga are saturated steam and air mass flow.
The heat flux q is defined as: where Am is heat exchange tube area, mcw is cooling water mass flow.
The HTC h is calculated by: where Tv is steam/air mixture average temperature, Tw is wall average temperature.

Influence of experimental conditions on heat transfer
Constant experimental conditions are inlet steam pressure (0.3MPa), cooling water average temperature (50℃), and foam metal PPI (10).Fig. 3 shows effect of inlet NCG mass fraction on HTC in foam metal pipe.The HTC decreases along with NCG mass fraction.Because NCG gathers on gas-liquid interface and increases heat and mass transfer resistance.Moreover vapor partial pressure decreases along with NCG mass fraction.Therefore, saturated temperature of vapor and mass transfer driving force also decrease.
When NCG mass fraction is lower than 0.03, HTC decreases very fast with increasing NCG mass fraction.Because foam skeleton can catch NCG effectively.There have lots of NCG adhering on gasliquid interfaces.When the gas-liquid interfaces have enough NCG, the rest of NCG flow with turbulence, which have little effect on condensation heat and mass transfer.Therefore decreasing rate of HTC becomes slow at high mass fraction.
Effect of inlet NCG mass fraction on HTC in smooth tube is presented in Figure 4.The average heat transfer coefficient also decreased obviously at low NCG mass fraction.Comparing Figure 3 with 4, the decreasing rate of HTC in foam metal tube is higher than smooth pipe at low NCG mass fraction.Because the foam skeleton can catch NCG effectively better.There have more NCG adhering on gasliquid interfaces compared to smooth tube.Constant experimental conditions are inlet steam pressure (0.3MPa) and cooling water average temperature (50℃).The tube is filled with 10PPI annular foam metal.Figure 5 illustrates influence of steam/air mixture mass flow on HTC.In the process of flow condensation, shear force generates at twophase interface because of velocity difference at two phase.Shear force can make NCG layer and condensation film thinner.Heat and mass transfer resistance are reduced.Moreover the shear force increases with steam/air mixture mass flow.Therefore the HTC increases along with steam/air mixture mass flow.
The constant experimental conditions are inlet steam pressure (0.3MPa), cooling water average temperature (50℃), and inlet NCG mass fraction (3%).Foam metal PPI is 20, 15 and 10 respectively.Fig. 6 presents influence of PPI value on HTC.The HTC of 10 PPI foam metal tube is highest at same steam/air mixture mass flow.Although metal skeleton area of 10 PPI foam metal tube is less than others, cell size of 10 PPI is relatively large.Condensate liquid film can't block the hole in foam metal.Therefore the gas-liquid interfaces and effective heat transfer area all increase.HTC of 10 PPI foam metal pipe is superior to others.Compared with smooth tube, the foam metal enhances heat transfer significantly, and HTC increases by 1.5-2.3times.

Heat transfer correlation development
Average HTC h in foam metal tube is the compositive influence of smooth pipe and foam metal.Therefore h is expressed as follow: ( 6) where β is annular foam metal effect coefficient.ho is average HTC of smooth pipe with NCG.ho is calculated according to Ren [6] correlation.β is mainly related to foam metal structure and NCG mass fraction.Basing on those elements, β can be expressed as follow [7]: where Asm is smooth pipe area.Afm is total area of foam metal tube.
Based on empirical data, k1 ~ k3 are fitted by: 0.022, 15.325, -8.518.Then, the heat transfer correlation can be calculated by: ( ) The experimental and calculated h for annular foam metal tubes are compared and the maximum error is 14%.

Effect of experimental conditions on pressure drop
The constant experimental conditions are inlet steam pressure (0.3MPa) and cooling water average temperature (40℃).The tube is filled with 10PPI annular foam metal.Fig. 7 illustrates effect of inlet NCG mass fraction on pressure drop.Pressure drop increases along with inlet NCG mass fraction.Because steam/air mixture velocity increases along with inlet NCG mass fraction.Moreover the gasliquid interfaces also fluctuate strongly.
The constant experimental conditions are inlet steam pressure (0.3MPa) and cooling water average temperature (50℃).The PPI value is 10. Figure 8    The constant experimental conditions are inlet steam pressure (0.3MPa), cooling water average temperature (50℃), and inlet NCG mass fraction (9%).Foam metal PPI are 20, 15 and 10. Figure 9 shows influence of PPI value on flow resistance.Pressure drop increases along with PPI value.Foam metal skeleton surface has abundant gas-liquid interfaces.The composition and velocity of gas-liquid fluid undergo complex changing at interface.The metal-foam skeleton can break and tow the mixing bubbles.When the PPI value increases, there has more metal-foam skeleton that impedes steam/air mixture flow.Therefore the pressure drop increases with PPI value.

Pressure drop correlation development
According to whole liquid phase multiplier method.Pressure drop correlation is expressed as follow [8]: where a and b are foam metal structure coefficient.
Based on Chisholm's formula [9], 2  is calculated as follows: ( ) ( ) where C is decided by steam/air mixture mass flow, NCG mass fraction, steam quality, and PPI value.C can be calculated by [10]： ( ) where df is average diameter of foam metal.
Based on empirical data, c1~c5 are fitted by: -1.84, -2.335, 0.206, -0.068, 3.543.Then, pressure drop can be calculated by: The experimental and calculated ΔP for annular foam metal tubes are compared and the maximum error is 17%.

Conclusions
The flow CHT in annular foam metal tube with NCG is investigated experimentally.The experimental conditions include inlet steam pressure from 0.1 to 0.4MPa, steam/air mass flow from 20 to 90kg/h, and cooling water temperature from 20 to 65℃.Foam metal PPI is 20, 15 and 10 respectively.Conclusions can be summarized: (1) Compared with smooth tube, the foam metal enhances heat transfer significantly, and HTC increases by 1.5-2.3times.
(2) At same steam/air mixture mass flow, 10PPI foam metal tube has the highest HTC compared to others.
(3) With increase of NCG mass fraction and PPI value, pressure drop increases and HTC decreases.Based on empirical data, pressure drop and HTC correlations are developed.

Figure 3 .
Figure 3. Influence of NCG mass fraction on HTC in foam metal tube.

Figure 4 .
Figure 4. Influence of NCG mass fraction on heat transfer coefficient in smooth pipe.

Figure 5 .
Figure 5. Influence of steam/air mixture mass flow on HTC in foam metal tube.

Figure 6 .
Figure 6.Influence of PPI value on HTC.
presents effect of steam/air mixture mass flow on flow resistance.Pressure drop increases along with steam/air mixture mass flow.Because turbulent enhances with steam/air mixture mass flow.

Figure 7 .
Figure 7. Influence of inlet NCG mass fraction on pressure drop in foam metal tube.

Figure 8 .
Figure 8. Influence of steam/air mixture mass flow on pressure drop in foam metal tube.

Figure 9 .
Figure 9.Effect of foam metal PPI value on pressure drop.