HEAT TRANSFER IN A COMPACT HEAT
EXCHANGER CHANNEL
J. M. Corberán
1, E. Cuadros
1, K. González
1, A. Franco
21Department of Applied Thermodynamics, Universidad Politécnica de Valencia, Spain 2Dipartmento di Fisica Tecnica, Universita degli Studi di Padova, Italy
Abstract
A test rig for the study of flow boiling of hydrocarbons in compact heat exchangers has been built at the Universidad Politécnica de Valencia. This paper deals with the procedure to estimate the two phase local heat transfer coefficient along the test section.
There are a number of difficulties in estimating the heat transfer coefficient from the measured temperatures, the main problem being the estimation of the fluid temperature evolution considering that due to the existence of the fins it is not possible to measure it along the channel but just at the inlet and outlet.
The paper presents the data reduction process developed to estimate the heat transfer coefficient of a pure hydrocarbon or mixture under boiling vertical flow conditions, i.e. smoothing of the wall temperature measurements, estimation of the heat losses to the ambient through the insulation, estimation of the longitudinal heat conduction along the test section, estimation of the evolution of the fluid pressure and temperature, and finally, the estimation of the heat transfer coefficient.
Nomenclature
A area (m2)
h enthalpy (J/kg)
hconv heat transfer coefficient (W/m2K) k
l
mass flow rate (kg/s)
thermal conductivity (W/mK) length (m)
Q heat transfer (W/m2) t thickness (m) T temperature (K)
UA overall heat transfer conductance (W/K) z longitudinal coordinate (m) η fin efficiency β fin parameter Subscripts: w wall f fin cond conduction conv convection elec electrical loss loss to the ambient
Abbreviations:
HTC heat transfer coefficient
1 Introduction
A test rig located at the Universidad Politécnica de Valencia was built to study the flow boiling in compact heat exchangers with different fin geometries using hydrocarbons (pure or mixtures) as working fluid. The test rig is mainly composed of a pressurising loop and a circulating loop which ensure independent metering of the fluid flow rate and absolute pressure as well as the setting of the inlet conditions.
The test section is located in the circulating loop and consists of a single finned channel (simulating the typical channel of a compact heat exchanger). The preheated fluid enters into the test section in single phase. Then, it is heated up with electrical resistances producing the boiling of the fluid. For safety conditions the outlet quality is limited to 70%.
Figure 1 shows the test section and its corresponding cross section. The test section consists of two parts: bottom and top, measuring approximately 600 mm in length each, separated by an
intermediate instrument plate. The channel can contain different fin pads. In the case illustrated in figure 1, the bottom part is divided in two halves: one with perforated fins and another one with serrated fins (of short serration length), while the upper part is all continuous with serrated fins with short serration length. The dimensions of the fluid channel are approximately 75 mm x 6.5 mm. The test section is made of aluminium and the wall thickness is 7 mm. The internal fins are also made of aluminium and are brazed to the walls. The hydraulic diameter of the channels including the fins is around Dh = 2 mm.
Figure 1: Test section (left side). Cross section and fluid cell (right side).
Mass flow rate is measured by a Coriolis mass flow meter, with an accuracy of ±0.6% at = 20 kg/m2s up to ±0.2% at = 350 kg/m2s. All temperatures are measured by T-type thermocouples (copper/constantan), all made from the same wire in order to reduce the scattering among temperature readings, which was experimentally checked to be lower than 0.03 K. The temperature is measured against a reference cold junction; the temperature of the cold junction, in turn, is measured with an RTD, and is calibrated to provide an accuracy of ±0.1 K over the entire temperature range.
Two flat electrical resistances, whose design assures a uniform heat flux density, are employed to heat the fluid stream through the test section walls into the fluid. The test section is made of aluminium in order to insure the best possible distribution of the heat.
This arrangement presents some typical problems; the most important being that the temperature and pressure of the fluid cannot be easily measured along the channel due to the fins, so that some special instrument plate must be placed in between different parts of the test section in order to measure both pressure and temperature of the fluid. In our case this is done at the bottom of the test section, at the middle (between the upper and bottom parts), and at the top of the test section. The temperature of the wall is much easier to measure and it is done thanks to thermocouples placed through small transverse holes (thermowells as indicated in figure 1) at both sides of the test section, and all along it (80 readings from bottom to top). Therefore, the main problem of this experimental procedure is the estimation of the fluid temperature evolution under boiling conditions, considering that fluid temperature is only measured at the inlet, middle and outlet positions, as well as the pressure, and it is not possible to exactly pinpoint the starting point of the boiling process.
Another, secondary but still important difficulty is the estimation of the longitudinal conduction effect on the heat balance around each portion of test section. Other, less important, factors
affecting the accuracy of the estimation of the HTC along the test section are the evaluation of the heat losses through the outer thermal insulation and also the smoothing of the wall temperature measurements.
In the following, a data reduction methodology addressing all these difficulties is outlined and a few examples of obtained results are shown. The developed methodology basically follows the following steps.
1. Smoothing of the wall temperature readings
2. Estimation of the pressure evolution along the channel
3. Local estimation of the heat transfer to the fluid and of the outlet fluid properties at each test section portion, from bottom to top of the test section with evaluation of the local HTC.
2
Smoothing of the wall temperature readings
Although the best care was put on the calibration of the thermocouples, the wall temperature readings showed a certain degree of scattering. This scattering is mainly due to two reasons; the first it is of course the uncertainty of the measurement, the second is the position of the thermocouple tips in the thermo wells. Figure 2 shows a sample of wall temperature measurements along the test section. At each position there are two readings; from both sides of the test section. The peak in temperature at the bottom part of the test section is due to the fact that the initial part of it is in single phase, so that the fluid temperature and consequently the wall temperature both increase monotonically with the distance. When boiling starts, the fluid temperature evolves between bubble and dew temperatures and it is controlled by the pressure evolution. Wall temperature follows the fluid temperature becoming almost constant in the case of the figure.
The thermowells consisted of a square passage of 1.5mm side going across the test section from side to side in the transversal direction (figure 1). The remaining aluminium layer between the passages and the fluid channel is 1mm thick. The passages were first filled in with a high conductive paste and then, the thermocouple wires (1.1mm) were inserted into the holes in a way that the measuring tip of the thermocouple was approximately located at the middle of the passage. This manual procedure gave good results but presented two main difficulties; first the thermocouple tip can be located in any position inside the passage; i.e. inside the paste or touching the walls; second, it could be in a place where an air bubble in the paste exists or it is close to it. The high conductivity of the test section (aluminium) reduces to the minimum the spatial temperature differences, however when the heat fluxes are high the described irregularities certainly generate some scattering in the readings. Therefore the first step of the data reduction procedure was the filtering of the wall temperature readings.
The data reduction methodology presented here was developed under MATLAB environment. The different techniques available in it were explored to filter (smooth) the wall temperature scattering. The standard tool for this task is called smoothing and has the following format (1):
y=smooth (xdata, ydata, span, method)
The user is able to employ different methods, i.e. “loess, moving, sgolay, lowess and rlowess”; and also choose the number of neighbour points: “span”. The span defines a window of neiboring points to include in the smoothing calculation for each data points. This window moves across the data set as the smoothed response value is calculated for each predicter value, The optimal span value depends on the data set and the smoothing method. The span value in the command line is the percentage of the total number of data points in the data set, which are employed to compute each smoothed value. For example a span of 0.1 uses 10% of the data points. Matlab supports these smoothing methods:
• Lowess and Loess: Locally weighted scatter plot smooth. These methods use linear least squares fitting and first-degree polynomial (lowess) or a second-degree polynomial (loess). • Savitzky-Golay filtering: A generalized moving average where you derive the filter coefficients
by performing an unweighted linear least squares fit using a polynomial of the specified degree. Figure 2 shows the results obtained by employing the different available methods (with span=0.25), and figure 3 shows the influence of the span on the smoothing results employing the “loess” method.
After a comprehensive study about the influence of the different available methods on a large set of experimental data, the best compromise between smoothing and fidelity to the measurements seemed to be the “loess” method. Concerning the span, a value of 0.2 was considered as the best option. Greater values did introduce too much smoothing meanwhile lower values had almost negligible effect.
Figure 2: Influence of the smoothing method
3
Pressure evolution estimation
Pressure is measured at the bottom, middle and top positions with absolute pressure transducers and the pressure drop along the bottom and upper parts of the test section is measured with two differential pressure transducers. The temperature of the connecting lines is measured to evaluate the liquid density and thus the liquid head in order to accurately evaluate the pressure difference in between the pressure tapings. The absolute pressure readings are just employed to have the absolute reference pressure of the fluid. Given that the data is redundant, the absolute pressure read at the top (outlet) of the test section is employed as the reference. Then, the pressure at each cell of the test section is calculated taking into account the proportional part of the pressure difference obtained from the differential pressure transducers. This procedure is based on the assumption of a linear distribution of the pressure along the test section.
4
Fluid temperature evolution estimation
As explained above, fluid temperature is only measured at bottom, middle and top of the test section. For the determination of the fluid properties, the channel is considered as divided in small cells, each one corresponding to a thermocouple location (see figure 1), in a way that the thermocouple reading corresponds to the wall temperature at the cell while the fluid temperature is defined at the inlet and outlet sections of the fluid cell.
Based on the pressure distribution assumed along the heat exchanger, the fluid pressure at inlet and outlet of each fluid cell is evaluated along the channel. The data reduction analysis then progress from bottom to top following t e conse vation energy prin iple along each ch r c ell (see figure 1).
where and, represent the heat transferred by longitudinal conduction at the inlet and outlet cross sections of the test section respectively, is the heat generated by electrical mats in the cell, is the heat lost through the outer insulation around the cell, is the mass flow rate, and and are the fluid enthalpies at the inlet and outlet sections of the cell. The fluid properties at the inlet of the test section (bottom) are all known so the enthalpy of the fluid can be evaluated.
The heat transferred by longitudinal c nductio on at position i, , is given by the Fourier’s law:
Where Acond is the area of heat conduction, i.e. the cross section of the test section. A numerical
approximation of the first derivative of the wall temperature is required in order to estimate the heat flux by longitudinal conduction. Given that the wall temperature is known at the centre of the fluid cell (centre of the wall cell) a good approximation of the first derivative at the inlet section is obtained just using the centred temp ture d ffe e between the wall temperatures of the considered cell and the previous one: era i renc
∆
The heat lost through the outlet insulation is characterised by a UA model as a function of the temperature difference between the wall temperature and the ambient temperature around the test section which is also registered during tests. The UA value was adjusted thanks to a series of special calorimetric tests keeping the fluid under single phase conditions and the wall at constant temperature all along the heat exchanger.
Once the enthalpy of the fluid is evaluated at the outlet of a fluid cell, knowing the pressure and assuming thermodynamic equilibrium, the other fluid properties can be evaluated, i.e. vapour fraction, composition on the liquid and vapour phases, and temperature.
For the fluid properties evaluation, the software SUPERTRAPP from NIST is employed. It is software specifically developed for the thermodynamic and transport properties evaluation of hydrocarbons, pure fluids and fluid mixtures containing up to 20 components. The components are selected from a database of 210 components, mostly hydrocarbons (2).
In general, the effect of longitudinal conduction is not very important at the regions where the phase change occurs; since in that case the temperature of the wall is almost constant along the channel. However, its influence on the heat transfer coefficient (HTC) evaluation could be important in areas where wall temperature variations occur, as a study performed combining measurements with a 3D detailed calculation of the wall temperature distribution along the test section, showed (3). This study allowed to realise that the effect of longitudinal conduction can be locally important in several places: inlet and outlet of each part of the test section due to the discontinuity of the heated area, and in the places where the fin pad was changed (some of the test sections incorporated two different fin pads in the same part, for instance the bottom one in figure 1). The inclusion of the longitudinal conduction effect as described above is easy to be implemented in the data reduction procedure and helps to diminish the uncertainty on the HTC evaluation in the mentioned places. The fluid at the entrance of the test section is always subcooled so its temperature and pressure define the state of the fluid. As the calculation of the outlet enthalpy progresses upwards, the saturation (bubble line) calculated with the local pressure is checked. When the fluid crosses the saturation line the boiling is considered to have started and the vapour faction, the temperature and compositions are then controlled by pressure and enthalpy.
It is important to notice that the measured temperature at the inlet of the test section is the one employed to estimate the conditions of the fluid at the inlet of the test section, in contrast with the fluid temperature measured at middle and top sections, which are not employed in the data reduction procedure. The developed procedure allows the estimation of the temperature of the fluid at the middle and top measurement stations. The program then checks the difference between the estimated values and the measured ones and reports about them. The differences found are always small (around 1K) so that the global procedure can be qualified as very consistent. The differences are attributed to the difficulties in measuring in a two phase flow, to the non satisfaction of the equilibrium hypothesis, and also to the fact that the mixing length for the fluid upstream the measurements are too short. Conversely, the measurement of the fluid at the inlet of the test section is always done in a single phase flow and the mixing length upstream from the re-heater device is very long. This is the reason why the fluid temperature measured at the inlet is preferred as the reference for the calculations. The described procedure also allows for the estimation of the pressure variation due to gravity and acceleration and therefore the estimation of the pressure gradient due to friction.
5
Heat Transfer Coefficient Analysis
Once the fluid temperature has been estimated all along the test section, the HTC can be evaluated at each cell from the net heat transferred to the fluid and the temperature difference between the wall and the fluid temperatures. The heat transferred to h id is equal to the enthalpy increase and can be written in the following form: t e flu
2 1
where, hconv is the HTC, A1 is the primary area of the cell (corresponding to the channel perimeter), A2 is the secondary area of the cell (fin area), η is the fin efficiency, e is the distance between the thermo well and the channel surface, and kw is the thermal conductivity of the material of the test
section.
Given that the fin efficiency is a function of HTC through the fin parameter , the equation becomes implicit and must be solved iteratively.
6
Results and conclusions
An example of the fluid and wall temperature profiles and the corresponding HTC are shown in figure 4 for a mixture of 90% pentane and 10% isooctane. It shows the final results obtained for both the fluid and wall temperatures as a result of the described data reduction procedure. As can be observed, the boiling starts little after x/L=0.3 with a sudden increase of HTC. The wall temperature presents a sudden drop which, in fact, is a result of the HTC rise given that heat flux is almost constant. The fluid temperature at the bottom part of the test section increases monotonically in single phase until the bubble point is reached, and then almost keeps constant all along the channel, with a slight trend to increase due to the glide of the mixture which compensates part of the saturation temperature decrease produced by the pressure drop. The estimated point for the starting of the boiling process boiling obtained by following the described procedure agrees very well with the experimentally observed increase in the heat transfer results for pure pentane. However, for mixtures, as can be seen on the figure, the start of the boiling process takes place much beyond the mixture bubble point.
Figure 4: Wall and fluid Temperature profile on the left and HTC on the right
The HTC is comparatively low at the single phase region, and then starts to grow when boiling starts. Only the upper region of the bottom part of the test section is under two phase flow boiling, leading to a high HTC peak value. The HTC of the upper part of the test section is quite high because it contains a serrated fin with long serration length. The HTC is increasing as the vapour fraction increases. The HTC of the short serration length fin pad is logically higher than the one corresponding to the long serration length. Experience has shown that the obtained results at the inlet and outlet of the each part of the test section (see figure 4) always present an important deviation compared with those corresponding to the central areas. Therefore, in the end the results obtained at the two first and last points of each part of the test section are discarded.
Finally, figure 5 shows a comparison between the HTC results for the indicated mixture and the ones obtained for pure pentane at approximately the same inlet conditions, mass flow and heat flux. As can be observed, the boiling of the mixture starts much later given that the bubble temperature is higher than the pentane saturation temperature. Also, it is clearly visible the important degradation of the HTC due to the mixture effect.
Figure 5: HTCs for pure pentane and a mixture of 90% pentane and 10% isooctane
The described data reduction procedure has been employed during a series of test campaigns performed at the Universidad Politécnica de Valencia (Spain) for HTFS AspenTech Ltd (U.K.) to characterise the HTC of hydrocarbon flow boiling in channels with different fin pads. At the initial stage of the work the usual hypothesis of negligible longitudinal conduction and heat losses was considered. Since its application, the described procedure has shown to produce good results significantly reducing the scattering on the evaluated HTCs.
Acknowledgements
This research is related with the experimental estimation of Heat Transfer Coefficients of boiling hydrocarbons through characteristic channels of compact heat exchangers, performed at the Universidad Politécnica de Valencia (Spain) for HTFS AspenTech Ltd (U.K.). The authors wish to express their most sincere gratitude to HTFS AspenTech Ltd. for their financial and technical support.
References
(1) 1994-2005 The MathWorks, Inc. Curve fitting toolbox. User manual
(2) National Institute of Standard and Technologies. SUPERTRAPP, NIST Thermophysical Properties of Hydrocarbon Mixtures Database: Version 3.2, http://www.nist.gov/srd/nist4.htm (3) J.M. Corberán, E. DaRiva, E.L. Cuadros. Influence of longitudinal heat conduction on the
constant-heat flux apparatus for experimental determination of the heat transfer coefficient. Under review in International Journal of Thermal Sciences, 2007.
