CALCULATION AND EXPERIMENTAL VERIFICATION OF HEAT TRANSFER COEFFICIENT FOR LOW PRESSURE METHANOL

EVAPORATOR

Tomasz HAŁON(*), Bartosz ZAJĄCZKOWSKI(*), Zbigniew KRÓLICKI(*), Karolina WOJTASIK(*)

(*)Wrocław University of Technology, Katedra Termodynamiki, Teorii Maszyn i Urządzeń Cieplnych, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław.

bartosz.zajaczkowski@pwr.edu.pl

ABSTRACT

Natural refrigerants are attracting attention due to their environmental neutrality. They have good thermal properties, but their evaporation pressures at near room temperatures are just a few kPa. There is limited information regarding evaporation of methanol at low-pressures. Empirical correlations for boiling heat transfer coefficient that were developed at atmospheric pressure levels tend to give high errors. In this paper we show an experimental data for pool boiling of methanol in pressure region 0.3–18 kPa and heat fluxes 10–45 kW/m2. The results are compared to calculations based on eight empirical heat transfer coefficient correlations. Since all of them yielded noticable errors, we suggested new constants for the power law equation that allow more accurate prediction of heat transfer coefficient.

1. INTRODUCTION

Growing demand for environmentally friendly refrigerants recently returned natural fluids, such as methanol, water or butane into spotlight (Bailey et al., 2006). Strong concern is also put on sustainable and energy efficient refrigeration technologies. In this field adsorption refrigeration is a novel, fast-developing branch of cooling technologies. Adsorption refrigerators are driven by heat instead of electricity for compressors. The biggest advantage of those systems is that they can be powered at temperature as low as 60-65oC (Askalany et al., 2013). The data on low-pressure boiling of natural refrigerants can be used by heat pipe industry (Bailey et al., 2006), in electronic equipment cooling (Pal and Joshi, 2006), as well as in sorption refrigeration systems. One of the factors that determine the adsorbent-adsorbate pair is the temperature of cooling. Natural refrigerants used in adsorption refrigerators are typically water or alcohols. They are environmentally friendly and usually characterized by thermal properties exceeding those of synthetic refrigerants. If the device is designed for ice-making, then the only choice is methanol (or other alcohol) paired with suitable adsorbent, e.g. active carbon (Halon et al., 2013; Schnabel et al., 2008). Unfortunately, in the temperature range used in domestic refrigeration or air conditioning (approx. -20oC to 15oC) methanol boils at sub-atmospheric pressures (a few kPa) yielding considerably lower heat transfer coefficient (Mcgillis et al., 1991; Schnabel et al., 2008). In order to design an evaporator, i.e. determine its dimensions and cooling capacity, it is necessary to estimate heat transfer coefficient for refrigerant boiling under near vacuum conditions. However, with a few exceptions, most of research was conducted for refrigerants boiling at atmospheric or higher pressures (Mcgillis et al., 1991; Prasad et al., 2007). Prasad et al. (Prasad et al., 2007) evaluated heat transfer coefficient for methanol boiling on heated, copper coated and uncoated tubes in pressure range from 27.95 kPa to 97.23 kPa. The authors proposed a dimensional equation based on their experimental results. Bailey et al (Bailey et al., 2006) measured heat transfer coefficient and critical heat flux for methanol during boiling on a horizontal surface. The analyzed pressure range was 20 kPa to 500 kPa. Presented results show that at critical heat flux the correlation of Zuber/Kutateladze gives good resemblance to experimental data, but only if constant K takes value of 1.7

instead of 1.3 used by Zuber. Alam and Agarwal (Alam and Agarwal, 2009) measured heat transfer coefficient for methanol over a plain and coated surfaces for pressures from 44 to 97 kPa. They have established that empirical constants for the power law equation depend upon liquid type, surface characteristic and its coating type. In cited article they did not provide the values of those constants. In this paper we evaluate eight correlations for boiling heat transfer coefficient of methanol and compare them with an experimental data using the mean absolute deviation (MAD) and the mean relative deviation (MRD).

2. CALCULATION OF HEAT TRANSFER COEFFICIENT FOR BOILING METHANOL

Heat transfer during boiling is a complicated process, dependent from many variables, like type of boiling medium, material, type and finish of heating wall, presence of additives or contaminations, pressure, temperature, presence of dissolved gases or presence of gases trapped in wall cavities. Despite many studies, boiling mechanism is not fully understood and thus no general formula for boiling HTC in a wide area of conditions exists. There are many empirical or semi-empirical correlations for boiling HTC. Eight popular were chosen and shown in table 2 along with authors own proposition. Most correlations tend to give high deviations for small and medium heat fluxes, where natural convection has bigger effect on heat transfer than bubble nucleation (Mcgillis et al., 1991; Schnabel et al., 2008). It was shown that for water at low pressure (Mcgillis et al., 1991), vapor specific volume and surface tension enlarges the minimal wall superheat for the onset of nucleate boiling regime. The same phenomenon is forecasted for methanol. Table 1. Known correlations for heat transfer coefficient. Name Number Correlation Reference Power law (1) h = C ∙ q! ∙ p!

By Prasad et al. (p from 27.95 kPa to 97.23 kPa): C=0.4963, m=0.7, n=0.32, Pressure in kPa

(Prasad et al., 2007)

McNelly (2) h = 0.225

q ∙ c!r

!.!" p ∙ λ′σ

!.!" ρ′ρ"− 1

!.!!

(Fazel and Roumana, 2010)

Mostinsky (3) h = 0.1276 ∙ p!"!.!" ∙ q!.! ∙ F!

Pressure correction factor: F! = 1.8p!!.!" + 4p!!.! + 10p!!"

Pressures in bar.

(Fazel and Roumana, 2010)

Stephan – Abdelsalam

(4) h = 0.0546

λ′d!

ρ"ρ′

!.! q ∙ d!λ′ ∙ T!"#

!.!"r ∙ d!!

a′!

!.!"# ρ! − ρ"ρ′

!.!!

Bubble departure diameter:

d! = 0.0146 ∙ β2σ

g(ρ′ − ρ”)

β for water is 45o and for other fluids 35o

(Thome, 2006)

Kutateladze (5) h = 2.742 ∙ φ ∙ p!.! ∙ q!.! For methanol, where φ = 0.36 correlation is:

h = 0.98712 ∙ p!.! ∙ q!.! Pressures in bar.

(Fazel and Roumana, 2010)

Kruzylin (6) h = 0.082 ∙

λ′lPr!!,! ∙ K!!.! ∙ K!

!!  

Bubble departure frequency:

(Fazel and Roumana, 2010)

K! =ρ′ ∙ c! ∙ σ ∙ T!"#r! ∙ ρ”! ∙ l

Number of bubble creation zones:

K! =q ∙ r ∙ ρ”

g ∙ (ρ′ − ρ”) ∙ λ ∙ T!"#

Characteristic linear dimension (bubble departure dimension)

l =σ

g ∙ (ρ′ − ρ”)

Kiczgin and Tobielewicz

(7) h = 3.25 ∙ 10!!

λ′lRe!.! ∙ Pr!.! ∙ Ga!.!"# ∙ K!!.!

Characteristic linear dimension (bubble departure dimension)

l =σ

g ∙ (ρ′ − ρ”)

Nondimensional number by Kutateladze:

K! =p!"# ∙ lσ

Galileo number:

Ga =g ∙ ρ′! ∙ l!

µμ!

(Kichigin and Tobilevich, 1955)

Labuncov (8) h = 0.125 ∙

λ′l∙ (Re ∙ K!)!.!" ∙ Pr

!!

Characteristic linear dimension (bubble departure dimension)

l =c!∙ρ′ ∙ σ ∙ T!r! ∙ ρ”!

Bubble departure frequency:

K! =ρ′ ∙ c! ∙ σ ∙ T!r! ∙ ρ”! ∙ l

(Fazel and Roumana, 2010)

3. EXPERIMENTAL SETUP

Experimental setup (in Fig. 1) is made of a glass cylinder (inner diameter 77 mm) filled with methanol. The bottom brass round plate is connected to the heating coil that is controlled with autotransformer. The surface roughness (Ra) was estimated on the basis of used surface treatment (emery paper 180) to be 0.05 mm. The upper cover is a brass plate with soldered cooling coil (made of copper). The condenser is ensuring constant pressure pe – it was connected to cooling water or nitrogen (for saturation temperatures Tsat lower than 0oC). Temperature is controlled with a set of thermocouples that are connected to the temperature recorder. Wall temperature sensor is positioned 1 mm under the surface and its readings are modified by heat conduction equation. During experiments, cylinder was wrapped by 2 cm thick polyethylene foam insulation to minimize heat losses and maintain stable boiling conditions. Heat gains and losses were calculated, but neglected because their contribution to total heat added through heater was on the level of fraction of percent. The glass cylinder wall thickness was checked with EN 13480-3-2002. Photographs of the setup are presented in Fig. 2. During preparation of experimental setup 30 ml of methanol (99.8%) was injected to the open vessel (under atmospheric pressure). All ports were then sealed and air was evacuated by vacuum pump until absolute pressure of about 2 kPa was reached. After methanol reached equilibrium conditions, the vessel was evacuated once more in order to take out any non-condensable gasses that could have been dissolved in tested refrigerant. During all experiments, methanol was not changed in the vessel.

Fig. 1. Schematic presentation of an experimental setup that allows determination of the boiling heat transfer

coefficient at sub-atmospheric pressures.

Fig. 2. Experimental setup for the analysis of boiling at sub-atmospheric pressures.

Power of the heater was controlled using autotransformer (100 and 200 W). After about 60 minutes required for stabilization of boiling, the temperature of heating wall and the pressure inside the vessel were read.

Heat transfer coefficient ℎ  was then calculated according to Newton’s law of cooling in eq. (9). As for heat loss from heater, the heat balance was made for heating plate. For the purpose of calculating heat transfer coefficient – losses from the plate were subtracted from heat shown by autotransformer. ℎ = 𝑞 ∙ (𝑇! − 𝑇!"#)!! (9) Saturation temperature Tsat and other thermodynamic properties of methanol were obtained from CoolProp library (Bell et al., 2014). Experiments were conducted for two different heat powers Q: 100 and 200 W in pressure pe range between 0.3 – 18 kPa. Measurement error was calculated using finite differential method (Onan et al., 2014).

4. RESULTS AND DISCUSSION

Values of experimental heat transfer coefficient h have flat characteristic in given pressure region. They change from the lowest to the highest value by up to 30%. In measured pressure psat and heat transfer density q, the heat transfer coefficient h is lower than 1 kW/m2K and differs between 686 to 973 W/m2K for q = 43 kW/m2 and from 543 to 704 W/m2K for q = 21 kW/m2. Comparison between measured data and results of correlations gathered in table 1 is shown in fig. 3 and fig. 4 for q = 21 kW/m2 and for q = 43 kW/m2 respectively. It shows that most correlations give over-predicted values in comparison with measurements. The most accurate results are given by Kutateladze correlation. Mean Absolute Deviation (MAD) and Mean Relative Deviation (MRD) for all correlations is shown in table 2. The MAD shows correlation accuracy, while MRD checks if it is over-prediction or under-prediction. Equations for MAD and MRD are shown as eq. (10) and (11) respectively (Fang et al., 2013). 𝑀𝐴𝐷 = !

!∙ ! ! !"#$%&'#$!! ! !"#$%&"'

! ! !"#$%&"'

!!!! (10)

𝑀𝑅𝐷 = !!∙ ! ! !"#$%&'#$!! ! !"#$%&"'

! ! !"#$%&"'

!!!! (11)

Table 2. Values of Mean Absolute Deviation (MAD) and Mean Relative Deviation (MRD) for given

correlations Correlation Number MAD MRD Power Law with our constants (1) 0.06 0.02 Power Law with Prasad et al. constants

(1) 0.64 -0.64

McNelly (2) 3.4 3.4 Mostinsky (3) 1.54 1.54 Stephan-Abdelsalam (4) 6.1 6.1 Kutateladze (5) 0.42 -0.42 Kruzhylin (6) 1.62 1.62 Kiczgin and Tobielewicz (7) 1.78 1.78 Labuncov (8) 2.82 2.82

Fig. 3 Heat transfer coefficient h measured in experiment and compared with calculation results for q = 21

kW/m2.

Fig.4 Heat transfer coefficient h measured in experiment and compared with calculation results for q = 43

kW/m2. MAD and MRD values confirm observations from diagrams. As seen on diagrams, the most accurate correlation is the one proposed by Kutateladze with 42% MAD and under-prediction of 42%. After that there is one correlation having MAD lower than 100% - it is the power law correlation with parameters proposed for higher pressures by Prasad et al. with 64% MAD. For given conditions (pressure from 0.3 kPa to 18 kPa, methanol), heat transfer coefficient was proven to be mostly related to heat transfer density. The least square method was used in order to obtain the best possible resemblance of correlation to experimental results. It have shown that constants for power law correlation from eq. (1) are as follows: C = 9.11, m = 0.373, n = 0.065. Power Law with parameters proposed by us – has the mean absolute deviation of 6% with small averaged over-prediction of 2%.

5. CONCLUSIONS

Boiling of methanol at sub-atmospheric conditions yields heat transfer coefficient lower than it is predicted by most correlations. The best prediction is given by Kutateladze equation (0.42 MAD). It is also the only one that under-predicts the HTC, thus there is no risk of creating too small heat exchangers.

Heat transfer coefficient depends mostly on heat flux density q, but in checked pressure region it does not show big dependency from pressure. We have proposed our own constants for power law equation from eq. (1). It estimates the heat transfer coefficient with MAD of 6% and MRD of +2% in given conditions. The formula with those constants is ℎ = 9.11 ∙ 𝑞!.!"! ∙ 𝑝!.!"#. Heat transfer coefficient for pool boiling of methanol in pressure region 0.3–18 kPa and heat fluxes 10–45 kW/m2 is lower than 1 kW/m2K. This is the order of magnitude similar to heat transfer coefficient for forced convection. This proves observations of McGillis et al. (Mcgillis et al., 1991) that the nucleate boiling starts with higher wall superheats than in atmospheric conditions.

6. LIST OF SYMBOLS

h – heat transfer coefficient, W/(m2K) p – pressure, Pa q – heat transfer density, W/m2

C – empirical constant, - m – empirical constant, - n – empirical constant, - cp – specific heat, J/(kgK) r – latent heat of vaporization, J/kg Fp – pressure correction factor, dp – bubble diameter, m T – temperature, K l - Characteristic linear dimension (bubble departure dimension), m Pr – Prandtl number, - Ga – Gallileo number, - Re – Reynolds number, - g – gravity acceleration, m/s2

MAD – mean absolute deviation, - MRD – mean relative deviation, - Kq – Number of bubble creation zones, - Ku – Bubble departure frequency, - Kp – Nondimensional number by Kutateladze , - Greek symbols λ – heat conductivity, W/(mK) σ – surface tension, N/m α – thermal diffusivity, m2/s µ - dynamic viscosity, Pa s ρ – density, kg/m3

Subscripts/Superscripts ‘ – concerning liquid ‘’ – concerning vapor w – concerning wall sat – saturation conditions kr – critical conditionsa r - reduced

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