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International Journal of Refrigeration 30 (2007) 1358e1367 www.elsevier.com/locate/ijrefrig
Comparison of experimental pressure drop data for two phase flows to prediction methods using a general model Alfonso William Mauroa,*, Jesu´s Moreno Quibe´nb, Rita Mastrulloa, John R. Thomeb a
Laboratorio di Tecnica del Freddo, DETEC, Faculty of Engineering, Universita` degli Studi di Napoli Federico II, 80125 Naples, Italy b Laboratory of Heat and Mass Transfer (LTCM), Faculty of Engineering Science (STI), E´cole Polytechnique Fe´de´rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland Received 8 September 2006; received in revised form 3 March 2007; accepted 6 April 2007 Available online 27 April 2007
Abstract In this paper, existing and new two phase pressure drop data are used to run an extensive comparison to predictive methods. The database used is for seven refrigerants (R22, R134a, R404A, R407C, R410A, R417A, and R507A) over a wide range of operating conditions. The procedure used for the comparison is a model of general validity since it is independent of the data reduction procedure. Four quoted methods and a new one by Moreno Quibe´n and Thome are used. The statistical analysis showed that the methods by Gro¨nnerud and by Moreno Quibe´n and Thome are equally the best. Segregating the data by flow regimes and taking into account for the prediction of the data trends, the method by Moreno Quibe´n and Thome is able to give reliable predictions in all the range of vapour qualities, especially in the regions of the intermittent flow and dry-out. Ó 2007 Elsevier Ltd and IIR. All rights reserved. Keywords: Cooling; Heat exchanger; Horizontal tube; Smooth tube; Two-phase flow; R-22; R-134a; R-404A; R-407C; R-410A; R-507A; Pressure drop; Modelling
Comparaison des donne´es expe´rimentales sur la chute de pression lors de l’e´coulement diphasqiue et des me´thodes de pre´vision s’appuyant sur un mode`le ge´ne´ral Mots cle´s : Re´frige´ration ; E´changeur de chaleur ; Tube horizontal ; Tube lisse ; E´coulement diphasique ; R-22 ; R-134a ; R-404A ; R-407C ; R-410A ; R-507A ; Chute de pression ; Mode´lisation
1. Introduction
* Corresponding author. Tel.: þ39 (0) 81 7682304; fax: þ39 (0) 81 2390364. E-mail address:
[email protected] (A.W. Mauro). 0140-7007/$35.00 Ó 2007 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2007.04.008
Many industrial processes are related to two phase flows such as fluid motion in pipes or channels and heat exchange in evaporators and condensers. Predictions in local heat transfer coefficients and local pressure gradients are required
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Nomenclature Greeks a r s D
void fraction density (kg m3) surface tension (N m1) finite variation
Letters d g h p q x z D ER
derivative gravitational acceleration (m s2) specific enthalpy (kJ kg1) static pressure (kPa, bar) heat flux (kW/m2) vapour quality abscissa along the tube (m) internal diameter (mm) error function
for industrial equipment in order to reduce the costs, optimize performance and save energy. In past years, the complexity of two phase phenomena led to many experiments for airewater and vapoureliquid mixtures, refrigerant blends and other two phase flows. At the same time, in response to a growing need for more accurate procedures for engineering calculations, a great number of predictive methods were developed and implemented, but no general prediction methods are still available. Often predictive methods are empirical and not of general application since they have a restricted range of underlying conditions and have been developed for specific fluid combinations, crosssectional geometry, and tube orientation or flow regime. These methods result in errors in predictions that are often too large for that required in engineering calculations. Tribbe and Mu¨ller-Steinhagen [1] presented an extensive comparison of 35 two phase pressure drop predictive methods compared to a large database for the following fluid combinations: aireoil, cryogenics, steamewater, airewater and several refrigerants. They ran a statistical comparison for this large database also segregating the data by fluid. They found that statistically the method of Mu¨ller-Steinhagen and Heck [2] gave the best and most reliable results. Several studies about statistical comparisons of the most reliable predictive methods were published; nevertheless, this kind of analysis is not enough to carry out a comprehensive comparison. A work published by Ould-Didi et al. [3] showed a comparison between some leading predictive methods and experimental data obtained for five different refrigerants segregating the experimental data by flow regimes. Overall, they found that the Gro¨nnerud [4] and the Mu¨ller-Steinhagen and Heck [2] methods to be equally the best, while the Friedel [5] method was the third best in a comparison of seven leading predictive methods. Segregating the data by flow regimes using the flow pattern map by Kattan [6], the authors found that predictive methods work differently varying the flow regime, since
FS G L T
full scale mass velocity (kg/m2) tube length (m) temperature ( C)
Subscripts corr correlation exp experimental in referred to inlet section mom momentum out referred to outlet section sat saturation condition G referred to gas phase L referred to liquid phase LV difference between bubble and dew points
the models are not able to capture completely the effects of the variations in flow structure. Recently, Moreno Quibe´n and Thome [7,8] published a work in which they made a comprehensive study to run accurate experiments. Then using a new flow pattern map by Wojtan et al. [9], they built a flow pattern based model for predicting pressure drops. In the present work, the first objective is to highlight the steps for the correct use of predictive methods and the errors that could be produced by the incorrect use of predictive methods. As a second step, a general procedure for comparison of experimental data to predictive methods is shown and an extensive comparison to an existing database and new experimental data is carried out. 2. A general procedure for comparison of predicted two phase pressure drop values versus experimental data The evidence from two phase pressure gradient measurements in a tube is that the local pressure gradient is a function of the following parameters: mass velocity, local fluid properties, geometry and configuration of the tube. The distribution of the two phases inside the test section also plays an important role. The dependence on the latter parameter is not always explicit. The most of the predictive methods use a unique expression for the calculation, that take into account for this effect. The change in flow regimes causes a different distribution of the gas and liquid phases in the cross-section and along the fluid path. Consequently, the expression of the pressure gradient function changes. Hence, it can be assumed that the main parameters influencing the local pressure gradient are: dp ðzÞ ¼ f ðG; local fluid properties; dz geometry and configuration of the tubeÞ
ð1Þ
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This function need different expressions for each flow regime. In design calculations for evaporators, it is necessary to calculate the pressure drop for a fixed geometry and configuration of a tube (orientation, cross-sectional area, surface aspect and length) at fixed operating conditions (mass velocity, fluid properties at the tube inlet and heat flux along the tube surface). The local fluid properties are a function of the static pressure and the vapour quality. The procedure is to integrate a function as in Eq. (1). For smooth circular tubes, the integral function reduces to: ð zout dp Dpðzout ; zin Þ ¼ ðfluid; G; p; x; diameterÞdz ð2Þ zin dz It is important to notice that, in general, all the independent variables of the integral could change along the fluid path and their variation along the tube should be known. In practice, the diameter is often constant along the tube; hence, for steady state conditions, the mass velocity of the fluid is constant. Assuming negligible the effects of the static pressure variations along the evaporator are usually neglegible for the calculations, here the effect of the vapour quality variations is highlighted. Fixing the vapour quality at the inlet of the tube, it is possible to determine the vapour quality at a fixed position, z, from an energy balance: ðz ðz dx 4 _ qðzÞdz ð3Þ xðzÞ ¼ xðzin Þ þ ðzÞdz ¼ xin þ hLV GD zin zin dz The local vapour quality is influenced by the heating conditions upstream. To reach complete evaporation of the refrigerant in a smooth horizontal tube for fixed working conditions (mass velocity, fluid properties at the inlet, diameter and length), different heat flux distribution are possible. For fixed operating conditions varying the heat flux at the tube surface, different values of the local vapour quality will determine different values of the integral pressure drop. Finally, the integral function of the pressure drop for a finite length tube is a function of the following parameters: Dp ¼ gðfluid; G; pin ; xin ; D; length; heating conditionsÞ
ð4Þ
In diabatic experiments where the pressure drops are measured over a finite length of tube it is not possible to obtain directly the local pressure gradient from the experimental data. The pressure gradient over a finite length of tube coincides with the local pressure gradient when the integrating function in Eq. (2) is constant. This is possible only when all the independent variables of the function in Eq. (1) are constant, i.e. for almost constant vapour quality (adiabatic measurements in steady state conditions). Consequently, the direct (‘‘local’’) comparison between predictive methods and experimental data is correct only when the experiments are related to adiabatic measurements. Otherwise, it is mandatory to integrate the local function as required in Eq. (2) fixing all the parameters required in Eq. (4) and then it is
possible to compare the integral values to experimental data (‘‘integral comparison’’).
3. Remarks about the data reduction and comparison of pressure gradient measurements For diabatic two phase pressure drop measurements the data reduction procedures try to estimate the local values of the pressure gradient function from integral measurements. These measurements are dependent on the mean heat flux and the heat flux distributions. Many authors assume that the integral measurement of the pressure gradient for diabatic measurements coincides with the value of the local pressure gradient function at the mean vapour quality between the inlet and the exit of the measurement tube. In general, this is an approximation that is exact only assuming that the local pressure gradient is a linear function of the vapour quality and that the vapour quality is a linear function of the fluid path (constant heat flux). In this case the integral value depends only on the mean value of the vapour qualities at the inlet and the outlet. This data reduction procedure is not general since it requires the following assumptions: constant heat flux along the tube and linear dependence of local pressure gradient on the vapour quality. In experiments the last circumstance is usually verified up to the transition to annular flow regime; otherwise only a small variation of the vapour quality can give a good approximation. Since near the transition to the dry-out, the local pressure gradient function usually achieves a maximum, for measurements spanning the maximum, the integral value of the pressure gradient depends on the heat flux. In a first approximation the local pressure gradient function near the maximum is a linear and continuous function, as follows: dp ðxÞ ¼ ða cÞx þ b; with b ¼ c ¼ 0 for 0 x xmax ; dz b > 0 and c > a for xmax < x 1 ð5Þ where xmax is the value of the vapour quality corresponding to the maximum of the local pressure gradient function. For constant heat flux, the integral value over the maximum is: Dp ðx þ xin Þ cðxout - xmax Þ2 ðzin ; zout Þ ¼ a out ðx þ xin Þ Dz 2 4 xout out 2
ð6Þ
This integral value depends not only on the mean value of the vapour qualities, but also on the position of the maximum of the local pressure gradient function and on the vapour quality at the outlet. In particular, for fixed operating conditions and fixed mean vapour quality between the inlet and the outlet, increasing the heat flux diminishes the vapour quality at the inlet and, consequently, the value of the integral pressure gradient. This is confirmed also by experiments
A.W. Mauro et al. / International Journal of Refrigeration 30 (2007) 1358e1367
Fig. 1. Experimental pressure gradient data versus vapour quality for different heat fluxes for R410A, D ¼ 13.8 mm, L ¼ 2.03 m and G ¼ 300 kg/m2 s at 9.4 bar from ref. [10].
as reported in Fig. 1 that depicts the frictional integral pressure gradient data obtained at different heat fluxes for R410A, D ¼ 13.8 mm, L ¼ 2.03 m, G ¼ 300 kg/m2 s at 9.4 bar [10]. The pressure gradient function is independent of the heat flux in the region before the peak, since it is an almost linear function of the vapour quality. In the experiments where the vapour quality of the peak in the pressure gradient function is between the inlet and the outlet vapour qualities, increasing the heat flux shifts the peaks to lower vapour qualities, as the position of the maximum and the transition from annular flow to dry-out. The integral pressure gradient is lower than the local pressure gradient value at the mean vapour quality and it diminishes increasing the heat flux, as expected from Eq. (6). At the same time, the data reduction procedure for diabatic measurements affects the values and the trends of the experimental data and it is important to take this into account before running a comparison. For example, Fig. 2 shows two different data reductions for experimental measurements [11] obtained at the same operating conditions and with the same heating method. The first set of data is obtained by fixing liquid saturated conditions at the inlet and the pressure gradients from the liquid saturated condition to the actual vapor quality are reported as a function of the vapour quality. The second set of data is obtained by measuring the pressure drop between two vapour qualities and the pressure gradients are reported as a function of the mean vapour quality. The data reported are both integral measurements, but there are differences in values and trends, expecially for high vapor qualities. The reason is that the variation of the vapour quality over the measurement length is larger in the first case and the data are referred to different vapour qualities.
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Fig. 2. Pressure gradients for R22, G ¼ 350 kg/m2 s and p ¼ 5.8 bar at 18 kW/m2 for a horizontal smooth tube with an I.D. of 6.00 mm: comparison between different data reduction methods (data from ref. [11]).
4. The experimental database The database used for the present comparison is the data available at Federico II University of Napoli. It was developed for R22, its substitute R134a and other refrigerant blends (R404A, R407C, R410A and R507A). In this paper, new experimental data for the refrigerant R417A, a drop-in substitute of R22, are also reported. Table 1 reports the operating conditions in terms of saturation pressure (at the inlet of the test section), mass velocity and vapour quality. The number of data for each operating condition is eight and there are more then 150 different operating conditions over a wide range of evaporating pressure and mass velocities. 5. Experimental test section, measurement method and data reduction The measurement test section is a horizontal smooth stainless steel tube of 6000 mm length and 6.00 mm I.D., heated uniformly by Joule effect. Two phase pressure drops were directly measured using a differential pressure transducer working over the range from 0 to 100 kPa within an accuracy of 0.075% FS. The differential transducer was calibrated before use. Eight pressure taps are located along the tube. They can be connected alternatively to a manifold in order to measure separately the pressure drop between the inlet and several points during evaporation. The local vapour quality was calculated by an energy balance over the test section from the inlet to the actual measurement station. The direct electrical power was measured by an ampermeter and a voltmeter with an accuracy in power measurement of 0.2%. The mass flow
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Table 1 Ranges of operating conditions for the experimental database Refrigerants
Number of experimental data Psat (bar) Tsat ( C) G (kg/m2 s) q (kW/m2) Vapour quality (%)
R22
R134a
R404A
R407C
R410A
R417A
R507A
193 4.9/10.1 6.5/19.9 380/1100 10/40 3e98
252 2.2/11.9 7.1/46.2 280/1080 5/38 5e94
63 3.3/11.7 18.4/22.1 290/1080 5/40 8e93
85 3.8/10.8 12.0/21.4 360/1100 5/40 2e94
121 4.8/12.2 15.2/14.0 360/1150 5/42 4e85
200 3.3/8.6 16.0/19.2 190/750 6/33 3e96
248 4.0/12.3 13.8/22.8 350/1100 8/38 2e90
rate was measured by a Coriolis meter with an accuracy of 0.2%. The inlet conditions were measured in the subcooled region measuring the static pressure and the temperature of the flow. The absolute error in vapour quality measurement was 3.0%. All thermophysical properties were calculated using REFPROP [12]. A more detailed description of the test facility and its operating range are reported in ref. [13]. From this measurement technique, the total pressure drop during evaporation from saturated liquid condition to a fixed outlet vapour quality is available. The measured pressure drop is the sum of frictional and momentum pressure drops. The momentum pressure drop is calculated by the following expression: # # ) (" " ð1 xÞ2 x2 ð1 xÞ2 x2 2 Dpmom ¼ G þ þ rL ð1 aÞ rG a rL ð1 aÞ rG a out
in
ð7Þ In a recent work by Wojtan [14] it was found that the Steiner [15] version of the Rouhani and Axelsson [16] drift flux model is very accurate for predicting void fractions. The recommended expression is: " ! x x 1x þ ð1 þ 0:21ð1 xÞÞ a¼ rG rG rL #1 1:18ð1 xÞ½gsðrL rG Þ0:25 ð8Þ þ G2 r0:5 L The frictional pressure drop was calculated by subtracting the momentum contribution from the total pressure drop. Finally, the pressure gradients were calculated by dividing the frictional pressure drop between the satured liquid condition and the actual vapour quality by the length of the tube corresponding to the actual measurement section. The data were reported at the vapour quality at the exit of the measurement test length. According to the procedure suggested by Moffat [17] the uncertainty propagation analysis showed that the uncertainty in the momentum pressure drop measurement is high, especially for low vapour qualities. For the frictional pressure gradients, 50.1% of the
reported experimental data are obtained with an uncertainty less than 5% and 95.2% with an uncertainty less than 15%. The data with an uncertainty greater then 15% are excluded from the statistical analysis. 6. The comparison of the experimental data to the predictive methods In this section the comparison of the experimental database against the following predictive methods is presented: Moreno Quibe´n and Thome [8], Friedel [5], Mu¨ller-Steinhagen and Heck [2], Gro¨nnerud [4] and Jung and Radermacher [18]. The procedure used to calculate the predicted values is the integral method described above. Fig. 3 depicts the direct comparison of the whole experimental database to the predictive methods. To measure the accuracy of the predictions, a statistical analysis was run. To run the statistical comparison, the experimental data were normalised with respect to the predicted ones and the following error function was used: ER ¼
Dpexp Dpcorr
1
1 þ if Dpexp < Dpcorr
ð9Þ
This error function returns zero, when the predicted value and the experimental one coincide; otherwise it is positive, when the experimental value is lower than that predicted and it is negative in the opposite case. For each experimental data point, the error function was calculated for all predictive methods. A statistical analysis of the values of the error function was carried out calculating the mean value and the standard deviation both for the whole database and for the data segregated by flow regimes. The mean value of the selected error function will be zero for a symmetric distribution, i.e. when the experimental data are equally overestimated and underestimated and positive when the mean of the predictions are conservative with respect to the experimental data. The standard deviation is calculated to measure the scatter of the data distribution. The results for the whole database and for the data segregated by flow regimes are reported in Table 2. To segregate the data by flow regime the
A.W. Mauro et al. / International Journal of Refrigeration 30 (2007) 1358e1367
Fig. 3. Direct integral comparison of the experimental data against predicted values.
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Table 2 Results of the statistical comparison Number of data points
Moreno Quibe´n and Thome
Friedel
Gro¨nnerud
Mu¨ller-Steinhagen and Heck
Jung and Radermacher
All data
Mean value of ER (%) Standard deviation of ER (%)
1110
7 30
4 36
14 30
12 33
27 31
Intermittent flow regime
Mean value of ER (%) Standard deviation of ER (%)
510
10 33
17 33
11 31
3 33
27 35
Annular flow regime
Mean value of ER (%) Standard deviation of ER (%)
360
1 22
31 19
9 23
34 18
19 21
Dry-out flow regime
Mean value of ER (%) Standard deviation of ER (%)
129
14 26
21 28
35 21
16 28
41 21
overall results. But this was affected by the data distribution with respect to the flow regimes. The analysis for each flow regime showed different results. The methods predict the integral pressure drop with a different error depending on the flow regime. The Friedel method was never the best for any flow regime and this is not surprising since in the mean this method underpredicted experimental data in the intermittent region and overpredicted in the annular and dry-out flow regimes. In the intermittent region, the method by
flow pattern map by Wojtan et al. [9] was used. The experimental data were filtered choosing only the tests with the same flow regime at the inlet and at the outlet of the test section. Then they were reduced calculating the pressure drop between two consecutive measurement stations and dividing by the corresponding length. Hence, the predicted values are calculated integrating the equations of each method at these conditions. For the entire database, the Friedel method [5] and Moreno Quibe´n and Thome method [7,8] gave the best
(a)
(b)
2
2
R22 D=6.00 [mm] G=353 [kg/m2s] p=5.06 [bar] q=18.3 [kW/m2]
R22 D=6.00 [mm] G=586 [kg/m s] p=8.18 [bar] q=27.2 [kW/m ]
700
700
560 M
420 I 280
D
A
Slug
140 0 0.0
0.4
0.6
0.8
I 420 280
0 0.0
1.0
SW 0.2
20 15
Moreno and Thome Friedel Grönnerud Müller−Steinhagen and Heck Jung−Radermacher Experimental data
10 5 0 0.0
0.2
0.4
0.6
vapor quality
0.4
0.6
0.8
1.0
0.8
1.0
vapor quality
0.8
1.0
integral pressure gradient [kPa/m]
integral pressure gradient [kPa/m]
25
M
Slug
vapor quality 30
D
A
140
SW 0.2
G [kg/m2s]
G [kg/m2s]
560
15 12 9
Moreno and Thome Friedel Grönnerud Müller−Steinhagen and Heck Jung−Radermacher Experimental data
6 3 0 0.0
0.2
0.4
0.6
vapor quality
Fig. 4. Flow pattern map and direct integral comparison of the experimental data against predicted values.
(a)
(b) R410A D=6.00 [mm] G=360 [kg/m2s] p=7.16 [bar] q=35.4 [kW/m2] 600 M 480 D
360 I
A
240 120
360 240
A
I
Slug
120
Slug
0 0.0
SW
SW 0.2
0.4
0.6
0.8
0 0.0
1.0
0.2
0.4
10 Moreno and Thome Friedel Grönnerud Müller−Steinhagen and Heck Jung−Radermacher Experimental data
8 6 4 2 0 0.0
0.2
0.4
0.6
0.8
1.0
0.8
1.0
vapor quality
0.6
0.8
1.0
integral pressure gradient [kPa/m]
vapor quality integral pressure gradient [kPa/m]
1365
R407C D=6.00 [mm] G=361 [kg/m2s] p=9.91 [bar] q=16.9 [kW/m2] 600 M 480 D
G [kg/m2s]
G [kg/m2s]
A.W. Mauro et al. / International Journal of Refrigeration 30 (2007) 1358e1367
15 Moreno and Thome Friedel Grönnerud Müller−Steinhagen and Heck Jung−Radermacher Experimental data
12 9 6 3 0 0.0
0.2
0.4
vapor quality
0.6
vapor quality
(c)
(d)
R417A D=6.00 [mm] G=405.2 [kg/m2s] p=5.8 [bar] q=17.7 [kW/m2] 600
R507A D=6.00 [mm] G=794 [kg/m2s] p=10.8 [bar] q=32.8 [kW/m2] 900
M 720
D
360
A
I
Slug
G [kg/m2s]
G [kg/m2s]
480
240 120 0 0.0
0.4
0.6
0.8
360
I
Slug
SW 0 0.0
1.0
0.2
Moreno and Thome Friedel Grönnerud Müller−Steinhagen and Heck Jung−Radermacher Experimental data
4
0 0.0
0.2
0.4
0.6
vapor quality
0.8
1.0
integral pressure gradient [kPa/m]
integral pressure gradient [kPa/m]
16
8
0.4
0.6
0.8
1.0
0.8
1.0
vapor quality
vapor quality
12
A
180
SW 0.2
M
D 540
30 24 18
Moreno and Thome Friedel Grönnerud Müller−Steinhagen and Heck Jung−Radermacher Experimental data
12 6 0 0.0
0.2
0.4
0.6
vapor quality
Fig. 5. Direct integral comparison of the experimental data against predicted values at selected operating conditions.
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Mu¨ller-Steinhagen and Heck [2] and by Moreno Quibe´n and Thome [7,8] gave the more reliable predictions. Predictions by Moreno Quibe´n and Thome method were the best in the annular and dry-out flow regimes, where the predictions of other methods were quite poor. To overcome the limits of the statistical analysis, a further step was to evaluate how well the predictive methods captured the trends of the integral pressure drop function. For this reason a direct comparison of the integral function for the methods and the experimental data was carried out. To highlight the main results of the comparison, Fig. 4 depicts an example of the flow pattern map, the corresponding integration of the predictive methods and the experimental data at some representative operating conditions. It is clear that the Moreno Quibe´n and Thome method best captures the trends of the integral pressure gradient function in all the range of vapour qualities. The Gro¨nnerud [4] and Jung and Radermacher [18] methods capture the trend well up to the annular region, not the region of higher vapour qualities, where dry-out occurs, a range of application of prime importance for direct expansion evaporators. The other methods are not very successful in predicting the trends of the integral pressure gradient function. It is clear that Friedel method overpredicts experimental data in the low vapour quality region and underpredicts them in the annular flow regime, so in the statistical analysis for the whole database it seems to be the best. To point out the sensitivity of the methods to the variations of the operating parameters, Fig. 5 depicts the integral comparison of the experimental data to the predicted values varying refrigerant, evaporating pressure and mass velocity. It is evident that, of the selected methods, the one by Moreno Quibe´n and Thome is able to capture the trends of the integral function in all the flow regimes varying the operating conditions and the fluids, even if sometimes there is a difference between the predicted and the measured values, especially at very high mass flow rates and at the higher pressures, which were not represented in its original database. 7. Conclusions The approach to compare experimental two-phase pressure drop data against predictive methods can be ‘‘local’’ or ‘‘integral’’, as specified above. In the first case, a correct procedure for the comparison requires that the experiments be carried out over adiabatic test sections. For diabatic measurements it is mandatory to integrate a method over the same conditions as in experiments. This requires the knowledge of not only the evaporation pressure, the mass velocity, the diameter of the tube and the fluid but also the inlet conditions of the fluid, the length of the tube and the heating conditions (variation of the heat flux along the tube). Different procedures could result in large errors in the predicted calculations of these data, especially when making incorrect data reductions of diabatic measurements in order to find the local pressure gradient function. In this work, an integral comparison of a database from University of Naples to
some leading predictive methods was carried out. The statistical analysis showed the methods by Moreno Quibe´n and Thome [7,8] and Gro¨nnerud [4] to be statistically the best. The analysis of the methods when segregating the data by flow regimes and by analyzing how well the methods replicated the actual experimental trends a direct comparison showed that the method by Moreno Quibe´n and Thome is able to give reliable predictions in the annular, intermittent and dry-out flow regimes, while the Gro¨nnerud method worked well up to the annular flow regime. The other methods yielded remarkable differences in the annular and dry-out flow regimes. None of these methods is so far able to capture well the effect of large variations in evaporating pressure and mass velocity. Acknowledgments This work was developed thanks also to the short mobility term program for Ph.D. students by the Magnifico Rettore of Federico II University of Naples (2006).
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