ap-3-12.dvi


Acta Polytechnica Vol. 52 No. 3/2012

Heat Exchangers for Condensation and Evaporation Applications

Operating in a Low Pressure Atmosphere

Petr Kraćık1, Jǐŕı Posṕı̌sil1, Ladislav Šnajdárek1

1
Brno University of Technology, FME, Department of Power Engineering,
Technická 2896/2, 616 69 Brno, Czech Republic

Correspondence to: kracik@fme.vutbr.cz

Abstract

This paper presents a state-of-the-art study of a heat transfer process in liquid spraying heat exchangers placed in a vac-
uum chamber. The experimental case studied here describes the behavior of a falling film evaporation and condensation
mode on horizontal tube bundles. The study aims to obtain the heat transfer coefficient and its correlations by means
of a mathematical model.

Keywords: liquid spraying, heat exchangers, vacuum chamber.

1 Introduction

The use of cooling increases year by year, not only in the food, chemical and engineering industries, but especially
in shopping centers, in office buildings and in homes. Cold compressor cooling systems, which consume a lot
of energy, are the most widely produced systems. An alternative way of cooling that consumes approximately
one-fifth of the energy is by using absorption units. The absorption cycle is supplied directly by heat from
gas burners, or is indirectly generated by power plants in the form of waste heat. The use of waste heat leads
primarily to fuel saving. If the cold that is produced is used to increase thermal comfort in the summer season,
the use of waste heat can spread heat production more equally throughout the year. This can result in a stable
output of power units throughout the year, increasing the reliability and therefore the lifetime of power units.

The heat exchanger is an essential component of the absorption cycle that provides optimum heat transfer.
In this paper, the authors attempt to determine the surface heat transfer coefficient of a spray-water cooled
exchanger located in a vacuum chamber. The vacuum is generated by a rotary vane vacuum pump. This basic
research follows a study of the heat transfer coefficient on a tube bundle at atmospheric pressure, which is being
carried out in the Dept. of Power Engineering at the Energy Institute of the Faculty of Mechanical Engineering
of the Technical University in Brno.

2 Description of the vacuum apparatus

The chamber is a cylindrical airtight vessel with three visors, in which a tube bundle is placed. The chamber is
connected to three closed loops. Two of these loops are designed for pressure up to 1.0 MPa, and they are used
for transporting a cooling/heating fluid (depending on the type of experiment — condensation/evaporation).
The third loop is used for transporting a liquid spray. Each loop is equipped with a pump, a regulation valve,
a flow meter and a plate heat exchanger. The plate heat exchanger can be connected to a boiler filled with
hot water, for heating the liquid or with cold water in the case of cooling. Each of the pressure loops is also
equipped with an expansion vessel, which serves to compensate the pressure differences, and with a safety valve
that releases the liquid when there is overpressure. For visual control, each of the loops is equipped with a
pressure gauge and a thermometer.

The temperature condition of the media in the individual loops is measured by thermocouples at the inlets
or outlets of the container. For a more accurate approximation of the heat stratification in the tube bundle,
there are four thermocouples: two for each loop that is not transporting liquid spray.

The mounting plate for the tube bundle is divided into two halves. Each half has been drilled with different
spacing of the holes to provide large variability of the tube arrangements. The tube bundle is composed of
copper tubes and sprinkler pipes, one over each vertical row of copper tubes. The copper tubes are 12.0 mm in

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Acta Polytechnica Vol. 52 No. 3/2012

Figure 1: Diagram of the vacuum apparatus

diameter. The sprinkler pipe is a tube 940.0 mm in length, with 9.2 mm spacing of the sprinkling holes 1.0 mm
in diameter.

The pressure in the chamber is measured by three pressure gauges. The first utilizes mercury, and is used
for visual inspection. The second is a digital gauge, and it can measure the entire desired pressure range. The
third is a digital vacuum gauge, with an absolute pressure range of 0 kPa to 25 kPa, and serves for accurate
low-pressure measurements.

3 Mathematical description

Under the conservation of energy, the heat balance between the right-closed pressurized loop (marked with
suffix ‘B’) and the under-pressured loop (marked with suffix ‘V’) must be guaranteed:

Q̇5 + Q̇1 = Q̇6 + Q̇2 + ΔQ̇56 + ΔQ̇12 [W] (1)

⇒ Q̇B = Q̇6 − Q̇5 [W] (2)
⇒ Q̇V = Q̇1 − Q̇2 [W] (3)

provided that: T6 > T5 a T1 > T2 [
◦C] (4)

The heat transfer red through the copper tube wall:

Q̇S = Q̇B + ΔQ̇56 = Q̇V − ΔQ̇12 [W] (5)
• derivation equations of heat transfer through a circular wall
The heat passage of the wall is composed of conduction, convection and also radiation. At lower temper-

atures, the heat transmitted by radiation is negligible, and is therefore not considered in the calculation. The
calculation is based on Newton’s principle of heat transfer and the Fourier heat conduction principle, provided
there is a parallel arrangement of pipes. Walls do not contain internal sources, and the heat flow is in the radial
direction relative to the tube.

The heat passage is determined by substituting into the general equations and integrating them

Q̇S =
2 · π · n · L(tout − tin)

1
Hin·rin +

1
λS

·
[
ln
(

rin
rout

)]
+ 1

Hout·rout
[W] (6)

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Acta Polytechnica Vol. 52 No. 3/2012

Figure 2: Sign parameters for calculating the heat transfer

Where selected members of the equation express the heat transfer coefficient:

uS =
2 · π

1
Hin·rin +

1
λS

·
[
ln
(

rin
rout

)]
+ 1

Hout·rout
[W · m−1 · K−1] (7)

The heat exchangers do not have a balanced temperature gradient at the inlet and outlet refrigerant. This is
therefore replaced by the meanlogarithmic temperature gradient. Thus the final equation for the heat passage
circular wall in the radial direction is:

Q̇S = kS · n · L · ΔTln [W] (8)
• calculation of the heat transfer on the outside of the tube
The heat transfer coefficient on the outside of the tube is derived from the heat passage equation:

Hout =
1

2 · π · rout ·
[

1
kS

− 1
2·π·Hin·rin −

1
2·π·λS · ln

(
rin
rout

)] [W · m−2 · K−1] (9)
Equal (5) and (8) must be valid for the heat passage equations, which results in the heat transfer coefficient:

Q̇S = Q̇B + ΔQ̇56 = kS · n · L · ΔTln W] (10)

kS =
Q̇S

n · L · ΔTln
=

V̇V · ρV (pv; T̄) · cp(pv; T̄) · (T1 − T2)
n · L · ΔTln

[W · m−1 · K−1] (11)

The investigated apparatus is among loops “A” and “V”, and the logarithmic temperature gradient is expressed
as:

ΔTln =
ΔT1 − ΔT2
ln
(

ΔT1
ΔT2

) = (T1 − T6) − (T2 − T5)
ln
(

T1−T6
T2−T5

) [K] (12)
The last unknown in equation (9) is the coefficient of heat transfer inside the tube. It can be calculated using
the Nusselt number, which is defined as the ratio of the heat transfer by convection and by conduction. [1,2]

Nu =
Hout · L

λ
⇒ Hout1 =

NuD · λin
din

[W · m−2 · K−1] (13)

The following criteria are accepted for calculating the Nusselt number:
1. The Reynolds number for fully developed turbulent flow is:

Re =
win · din

ν
≥ 10 000 [–] (14)

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Acta Polytechnica Vol. 52 No. 3/2012

2. The Prandtl number ranges between:

0.6 ≤
(
Pr =

ν

a

)
≤ 160 [–] (15)

3. The ratio of the length to its diameter pipe:

L

d1
≥ 10 [–] (16)

The Nusselt number is stated as:

NuD = 0.023 · Re0.8D · Prn [–] (17)
where coefficient “n” (in the case of heating fluid in the pipe) is equal to 0.4 [–] and in the case of cooling fluid
in the pipe,it is equal to 0.3 [–]. The fluid velocity is calculated from the volume flow as:

V̇B = Sin · win ⇒ win =
4 · V̇B
π · din

(18)

• comparison between the falling-film mode map and data in the literature
The Reynolds number expressed for the jet-droplet mode [4]:

Re = 0.084 · Ga0.302mod [–] (19)
The Galileo number is stated as a reciprocal Kapitza number:

Gamod =
1

Ka
=

ρ · σ3
μ4 · g [–] (20)

We compare the experimentally obtained values from the vacuum apparatus with the values obtained by Jacobi
and Hu [4] using the criteria number (19), (20). This data was obtained from atmospheric apparatus with a
comparable configuration of the heat exchanger, as shown in Figure 3.

Figure 3: Experimental results for the jet-droplet transition mode

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Acta Polytechnica Vol. 52 No. 3/2012

4 Evaluation of measured data

The measurements of temperature, pressure and other variables that are required for calculating any coefficient
in the equations above are obtained with inaccuracies. The values are always inaccurate, due to the environment,
the selected measuring method, or the condition of the measuring devices. There is always some tolerance within
which the final value is spread. Before we start evaluating the measured data, we have to determine the limits
from the calibration measurements. The limits determined by the quadratic sum of the type A uncertainties
represents a statistical evaluation of the measured data set and the type B uncertainty of which is determined by
the instrument manufacturer or calibration of the measuring devices. The uncertainty of the indirectly measured
physical quantities derived from the measured data set is coupled with a similar equation. The T-type enclosed
thermocouples that were used, with an ungrounded end and with increased accuracy, were calibrated in an
Omega CL1000 dry block probe calibrator, which controls the temperature set by PID regulation with accuracy
of 0.15 ◦C.

Due to the calibration curve, we decided to use a single error for all thermocouples which consists of the
measured maximum peak, or the minimum peak (which achieved a maximum statistical error of 0.006 ◦C) and
dry block probe calibrator errors. Figure 4 plots the calibration curves of the T-thermocouples used in the
measuring loops with factory inaccuracies uB,T (19)

uB,T = ± 0.65 [◦C] (21)

Figure 4: Segment of the calibration curve using thermocouples

The vacuum (under-pressure) was measured using a TED 6 digital gauge with pressure inaccuracy 0.5 % of
the measured absolute pressure range:

uB,pv = ± 0.005 · (0 . . 100) = ±0.50 [kPa] (22)

The flow rates and the spraying loop were measured using a FLOMAG3000 inductive flowmeter within accura-
cies:

uB,V = ± 0.003 · (0 . . 30.67) = ± 0.092 [l · min−1] (23)
Figure 5 plots the investigated heat transfer coefficients on the outside of the tube.

The measurements were performed for three levels of absolute pressure: 6.2 kPa, 19.2 kPa and 30.2 kPa.
The derived points were interspersed with the exponential curve that best described the increasing heat transfer
coefficient trend, with an increasing flow rate in spite of the fact that a lower correlation was still sufficient at
a pressure level of 6.2 kPa.

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Acta Polytechnica Vol. 52 No. 3/2012

Figure 5: Heat transfer coefficients on the outside of the tube

5 Conclusion

On a vacuum compiled apparatus, we measured the temperature, pressure and flow meter values, from which
the heat transfer coefficient was deduced. The increasing heat transfer coefficient trend on the outside of the
tube depends on the ambient pressure reduction that is achieved. This trend corresponds to the theory and to
the current state of knowledge on spraying exchangers. In the vacuum apparatus will continue implementing
to the influence of surface treatment tubes and design to increase the heat transfer coefficient.

Acknowledgement

This work has been financially supported by the Czech Science Foundation under the Grant P101/10/1669.

References

[1] Incropera, F. P., Dewittl, D. P., Bergman, T., Lavine, A.: Fundamentals of Heat and Mass Transfer,
6th Edition, 2007, Hardcover, 1 024 p. ISBN 978-0-471-45728-2.

[2] J́ıcha, M.: Přenos tepla a látky, Brno. CERM, 2001, 160 p. ISBN 80-214-2029-4.

[3] Karṕı̌sek, Z.: Matematika IV: statistika a pravděpodobnost. 3rd, Brno : CERM, 2007, 170 p. ISBN
978-802-1433-809.

[4] Jacoby, A., Hu, X.: The Intertube Falling-Film Modes: Transition, Hysteresis, and Effects on Heat Transfer,
Urbana, IL 61801, (217) 333–3115, 1995.

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