Experimental investigation of flow boiling heat transfer in a large diameter horizontal tube of an ORC evaporator

ORC evaporator

transfer in a large diameter horizontal tube of an

Experimental investigation of flow boiling heat

Academic year 2019-2020

Master of Science in Electromechanical Engineering

Master's dissertation submitted in order to obtain the academic degree of

Counsellor: Alihan Kaya

Supervisors: Prof. dr. ir. Michel De Paepe, Prof. dr. ir. Steven Lecompte

Student number: 01404624

ORC evaporator

transfer in a large diameter horizontal tube of an

Experimental investigation of flow boiling heat

Academic year 2019-2020

Master of Science in Electromechanical Engineering

Master's dissertation submitted in order to obtain the academic degree of

Counsellor: Alihan Kaya

Supervisors: Prof. dr. ir. Michel De Paepe, Prof. dr. ir. Steven Lecompte

Student number: 01404624

Preface

This thesis is the result of the work done over the past year. Here I would like to thank the people who helped me with creating this master’s dissertation.

First of all, I would like to thank my counsellor ir. Alihan Kaya for his guidance throughout this year. His advice, feedback and positive approach proved to be of great value for the making of this thesis.

My gratitude goes to my promotors prof. dr. ir. Michel De Paepe and prof. dr. ir. Steven Lecompte for giving me the opportunity to make this project. Special thanks goes to Frederik Martens for the construction of the experimental test setup.

Now that I am at the end of my studies, I would like to thank my friends for their positive encouragement. Finally, I want to thank my parents, my brother Simon and my grandparents for their support over the years. They helped me a lot during the many exam periods and the making of this thesis.

Permission of use on loan

The author gives permission to make this master’s dissertation available for consultation and to copy parts of this master dissertation for personal use. In all cases of other use, the copyright terms have to be respected, in particular with regard to the obligation to state explicitly the source when quoting results from this master dissertation.

Florijn Bekaert, June 2020

Preamble

The experiments were hindered a lot by the corona crisis. From the 18th of March students were no longer allowed in the buildings of the university. Because of these measures not all flow boiling experiments could be performed by myself. The crisis delayed the measurements and limited the measured data. The initial plan was to conduct experiments with uniform heating first, process this data and then rebuild the test section to conduct experiments with non-uniform heating. The non-uniform heating experiments could not be performed because of the corona crisis. An extensive literature study was done to investigate the influence of non-uniform heat flux on heat transfer and to design a test section with non-uniform heating. This study is still included in this work because of its practical importance. Time that otherwise would be spent conducting and analyzing non-uniform heat flux experiments was used for doing a more thorough analysis of the uniform heat flux experiments.

Experimental investigation of flow boiling

heat transfer in a large diameter horizontal

tube of an ORC evaporator

by Florijn Bekaert

Master’s dissertation submitted in order to obtain the academic degree of Master of Science in Electromechanical Engineering

Academic year 2019–2020

Supervisors: Prof. Dr. Ir. Michel De Paepe, Prof. Dr. Ir. Steven Lecompte Counsellor: Ir. Alihan Kaya

Faculty of Engineering and Architecture

Department of Electromechanical, Systems and Metal Engineering Research group of Sustainable Thermo-Fluid Energy Systems

Ghent University

Abstract

A crucial component of the organic Rankine cycle (ORC) is the evaporator, in which the working fluid goes from liquid to gaseous phase. Having heat transfer data is important to design evaporators accu-rately. This can lead to better sizing of the evaporators and avoid excess costs. An evaporator with a large diameter can handle a higher mass flow rate than an evaporator with a smaller diameter, which can be a major advantage for industrial applications. In this work the heat transfer in a horizontal tube of an ORC evaporator with a large diameter is investigated. The influence of the saturation temperature, the mass flow rate and the heat flux on the heat transfer coefficient are experimentally examined on a flow boiling test facility. The behaviour of the heat transfer coefficient in function of the vapor quality while varying these factors is linked with the characteristics of nucleate boiling and convective boiling. The heating of the working fluid in the evaporator can be non-uniform when waste heat is used for direct evaporation. Extra study is done to investigate the influence of non-uniform heat flux on the heat transfer in an evaporator.

Keywords

MASTER THESIS 2019-2020 Research group Sustainable Thermo-Fluid Energy Systems Department of Electromechanical, Systems and Metal Engineering – Ghent University, UGent

EXPERIMENTAL INVESTIGATION OF FLOW BOILING HEAT TRANSFER IN A LARGE DIAMETER HORIZONTAL TUBE OF AN ORC EVAPORATOR

Florijn Bekaert, Alihan Kaya, Michel De Paepe and Steven Lecompte Department of Electromechanical, Systems and Metal Engineering

Ghent University

Sint-Pietersnieuwstraat 41, B9000 Gent, Belgium E-mail: florijn.bekaert@ugent.be

ABSTRACT

A crucial component of the organic Rankine cycle (ORC) is the evaporator, in which the working fluid goes from liquid to gaseous phase. Having heat trans-fer data is important to design evaporators accurately. This can lead to better sizing of the evaporators and avoid excess costs. An evaporator with a large diam-eter can handle a higher mass flow rate than an evap-orator with a smaller diameter, which can be a major advantage for industrial applications. In this work the heat transfer in a horizontal tube of an ORC evapora-tor with a large diameter is investigated. The influence of the saturation temperature, the mass flow rate and the heat flux on the heat transfer coefficient are ex-perimentally examined on a flow boiling test facility. The behaviour of the heat transfer coefficient in func-tion of the vapor quality while varying these factors is linked with the characteristics of nucleate boiling and convective boiling. The heating of the working fluid in the evaporator can be non-uniform when waste heat is used for direct evaporation. Extra study is done to investigate the influence of non-uniform heat flux on the heat transfer in an evaporator.

INTRODUCTION

The world in this day and age is characterized by an increasing demand of energy. Currently fossil fuels and nuclear power are still the main energy sources world-wide. These sources have some downsides. Fossil fu-els are not infinitely available and their environmental impact becomes more and more visible in the form of climate change and bad air quality. Safety and nuclear waste are the main problems of nuclear energy. One way to solve this increasing demand of energy while taking the climate, air quality and safety into account is the organic Rankine cycle (ORC). ORCs can be used to generate electricity by utilizing biomass combined heat and power, geothermal energy, solar

NOMENCLATURE

h [W/(m2_{K)] Heat transfer coefficient}

˙

m [kg/s] Mass flow rate ORC [−] Organic Rankine cycle

˙ q [W/m2_{] Heat flux} T [K] Temperature x [−] Vapor quality Subscripts av average bot bottom out outlet sat saturation side side top topside tp two-phase

Figure 1: Schematic view of an ORC [1]

power plants and waste heat recovered from exhaust gases [1]. An organic Rankine cycle is a thermody-namic cycle that converts heat into work using an or-ganic fluid. In its basic form, an ORC consists of a pump, an evaporator, an expander and a condensator as is shown on Figure 1. Because of the low boiling point of organic fluids high efficiencies can be obtained

for low temperature applications [2].

The evaporator is an important component of the or-ganic Rankine cycle. A significant part (up to 50 %) of the initial investment cost of an ORC system is due to the heat exchangers, namely the evaporator and the condenser. The evaporator also has a lot of influence on the efficiency of the ORC [3]. The pressure drop in the evaporator increases with an increase of mass ve-locity [4] [5]. An evaporator with a larger diameter has a lower mass velocity which results in a lower pressure drop. This is a major advantage for industrial appli-cations.

Having heat transfer data is important to design evap-orators accurately. This can lead to better sizing of the evaporators and avoid excess costs. An under-sized evaporator will not be able to fully evaporate the working fluid, which can cause damage to the compo-nents of the ORC, while an oversized evaporator does not improve or even deteriorates the cycle performance compared to the optimum size and increases the ma-terial/labor cost of the heat exchanger [3]. The goal of this work is to investigate the heat transfer in a horizontal tube of an ORC evaporator with a large di-ameter.

When waste heat is used for direct evaporation, the heating of the evaporator can be non-uniform. A sep-arate test section is designed to investigate the influ-ence of non-uniform heating on the heat transfer in the evaporator.

DESCRIPTION OF THE FLOW BOILING TEST FACILITY

An overview of the experimental setup is shown on Fig-ure 2. The organic fluid used in this setup is R245fa. The working fluid is first preheated by the electrical preheater, in order to obtain the wanted inlet tem-perature. Then the fluid goes through the test sec-tion in which it is heated and measurements are done. Hereafter the fluid passes a pressure safety valve that makes sure that the pressure does not exceed the criti-cal pressure, followed by the electronic expansion valve which lowers the pressure of the fluid. By controlling the expansion valve the saturation pressure can be in-creased or dein-creased. Then the fluid is condensed in the condenser, which is connected to a cooling loop. After the condenser a liquid receiver is placed where the gaseous and liquid phase are separated. The pump provides the wanted mass flow and overcomes all the pressure drops in the cycle, the bladder accumulator prevents cavitation from happening.

Flow boiling is investigated in the test section. Both a test section with uniform heating and a test sec-tion with non-uniform heating were designed, but only the test section with uniform heating was constructed. The test section consists of a carbon steel pipe with a length of 2.5 m surrounded by Winkler Serie WK 401 heating cables. The carbon steel pipe has an outer diameter of 25.4 mm and an inner diameter of 21.2

mm, the heating cables have a diameter of 3.5 mm. The diameter of the test section is larger than the di-ameters of test sections from other flow boiling ex-periments for organic Rankine cycles performed in lit-erature. The pressure drop increases when the mass velocity increases [4] [5], so an evaporator with a larger diameter has a lower pressure drop for the same mass flow rate compared to an evaporator with a smaller di-ameter because of the lower mass velocity. Because of this advantage, evaporators with large diameters are interesting for the industrial applications.

On Figure 3 the locations of the thermocouples on the test section are shown. A total of 57 thermocouples are installed at 19 axial locations. So 3 thermocouples are installed per axial location: one on the bottom of the tube, one on topside of the tube and alternating one on the left or right side.

Figure 3: Locations of the thermocouples on the test section from a side view

The uniform heat flux test section is made by wrap-ping the heating elements around the tube in order to accomplish uniform heating. A total of 13 heating elements, each with a heating power of 375 W results in a total heating power of 4875 W. Kapton polyimide film is placed over the heating elements to keep every-thing in place. Finally the test section is insulated to reduce heat losses. On Figure 4 the cross section of the uniform test section is shown.

Figure 4: Cross section of the uniform test section [6]

A non-uniform heat flux test section was designed to test the influence of the non-uniformity of the heat flux on the heat transfer. The heating elements are placed in the longitudinal direction along the tube. By separately controlling the heating elements non-uniform heating can be accomplished. On Figure 5 the cross section and an example of non-uniform heating from the bottom side are shown.

Figure 2: Scheme of the flow boiling test facility

Figure 5: Cross section non-uniform test section

RESULTS

Measurements were done to examine the influence of the saturation temperature, the mass flow rate and the heat flux on the heat transfer coefficient of the large diameter test section. The influence of these factors on the heat transfer coefficient is determined by vary-ing one factor while keepvary-ing the others as constant as possible. The heat transfer coefficient at each axial point is calculated by taking the average between the heat transfer coefficients based on the measurements of the three thermocouples at each location. The er-ror bars indicated on Figure 6, Figure 7 and Figure 8 correspond with the maximum uncertainties of the heat transfer coefficient and the vapor quality of these measurements.

Influence of the saturation temperature

Figure 6 shows the influence of the saturation temper-ature on the heat transfer coefficient. The horizontal

axis represents the vapor quality, while the vertical axis represents the heat transfer coefficient. The gen-eral trend for both low and high saturation tempera-ture is a decline of the heat transfer coefficient with increasing vapor quality.

It can noticed that the working fluid reaches a higher vapor quality in the test section when the saturation temperature is higher.

The average heat transfer coefficient increases with in-creasing saturation temperature: for a low saturation temperature the average heat transfer coefficient in the test section is htp,av= 2784 W/(m2K), for a high satu-ration temperature htp,av= 2937 W/(m2K). The sat-uration temperature has more influence for the lower vapor qualities. This is caused by the dominance of nucleate boiling at these lower vapor qualities [7] [8]. The saturation temperature has more influence for nu-cleate boiling compared to convective boiling.

The saturation temperature has a major influence on the shape of the two graphs. Initially, the heat trans-fer coefficient stays constant for the lowest vapor qual-ities in Figure 6 (a). This is because nucleate boiling is dominant at these very low vapor qualities. This is confirmed by Steiner and Taborek [9], they state that the flow boiling heat transfer coefficient becomes virtually independent of the vapor fraction for fully developed nucleate boiling. This is followed by a de-cline, which is caused by the diminishing contribution of nucleate boiling with increasing vapor quality. The higher saturation temperature increases the over-all contribution of nucleate boiling. Graph (b) in Fig-ure 6 first declines and starts to flatten after. The decline is caused by the decreasing contribution of the dominant nucleate boiling with increasing vapor qual-ity. The heat transfer coefficient stays almost

con-(a) Tsat= 372 K

(b) Tsat= 392 K

Figure 6: Influence of the saturation temperature on the heat transfer coefficient

stant for higher vapor qualities, which indicates that the decrease of nucleate boiling is compensated by the increase of convective boiling once the vapor quality reaches a value of 0.32.

Finally the measurements of the heat transfer coeffi-cient are compared with the heat transfer model of Kattan-Thome-Favrat [10]. Increasing the saturation temperature results in an increase of the heat trans-fer coefficient, which corresponds to the findings of the measurements. The overall heat transfer coefficient is higher for the Kattan-Thome-Favrat model than for the measurements and has a different shape. The dif-ferences between the Kattan-Thome-Favrat model and the measurements are to be expected, since this heat transfer model was made for different operational con-ditions and fluids. The differences between the mea-surements and the Kattan-Thome-Favrat heat transfer model show the need for new heat transfer models and flow pattern maps that correspond with the findings of the measurements.

Influence of the mass flow rate

The influence of the mass flow rate on the heat trans-fer coefficient is shown on Figure 7. The heat transtrans-fer coefficient is calculated for a low, medium and high mass flow rate while keeping the heat flux and the

sat-uration temperature constant.

The average heat transfer coefficient in the test sec-tion increases with increasing mass flow rate: htp,av= 1433 kW/(m2_{K) (low ˙m), h}

tp,av = 2188 kW/(m2K) (medium ˙m) and htp,av= 3476 kW/(m2K) (high ˙m). It has to remarked that these values are calculated over different ranges of vapor qualities: xts,out = 0.97 (low ˙m), xts,out= 0.54 (medium ˙m) and xts,out= 0.35 (high ˙m). When the averages of the heat transfer co-efficients are calculated over the same vapor quality range of 0 to 0.35, smaller differences are found: htp= 1949 kW/(m2K) (low ˙m), htp = 2468 kW/(m2K) (medium ˙m) and htp = 3476 kW/(m2K) (high ˙m). An increase of mass flow rate still results in an increase of the average heat transfer coefficient over this range, but the differences are smaller. These reduced differ-ences are caused by the important contribution of nu-cleate boiling at these lower vapor qualities. This cor-responds with observations of Charnay [7] and Steiner and Taborek [9].

The graph with low mass flow shown on Figure 7 (a) starts with a steep decline first until the vapor quality becomes 0.51. The steep decline at low vapor quality is caused by the importance of nucleate boiling at low vapor qualities. Increasing the vapor quality decreases the contribution of nucleate boiling which results in an overall decrease of the heat transfer coefficient. When the vapor quality raises above 0.51 the decrease of nu-cleate boiling is compensated by the increase of convec-tive boiling, which results in the constant heat transfer coefficient.

Figure 7 (b) shows the heat transfer coefficient in func-tion of the vapor quality for medium mass flow rate. Increasing the mass flow rate increases the convective boiling heat transfer which results in an overall in-crease of the heat transfer coefficient. Nucleate boiling is still an important heat transfer mechanism for these low vapor qualities, which results in the heat transfer coefficient initially staying almost constant. After the flow reaches a vapor quality of 0.20, the heat transfer coefficient starts to decrease because of the decreasing contribution of nucleate boiling.

The heat transfer coefficient in function of the vapor quality for a high mass flow is shown on Figure 7 (c). There are some fluctuations in this graph, but the heat transfer coefficient is overall slowly descend-ing with increasdescend-ing vapor quality. The increased mass flow rate increases the convective boiling heat transfer which results in an increase of the total heat transfer coefficient. An increase of vapor quality reduces the contribution of nucleate boiling which is only partially compensated by the increase of convective boiling con-tribution. This results in the overall slow decrease of the heat transfer coefficient.

The measurements are compared to the heat trans-fer model of Kattan-Thome-Favrat [10]. The average heat transfer coefficient increases when the mass flow rate is increased for the Kattan-Thome-Favrat model similar to the measurements. The heat transfer

coef-ficient values are overall higher and the shape for the Kattan-Thome-Favrat heat transfer model differs from the measurements.

(a) ˙m = 0.036 kg/s

(b) ˙m = 0.065 kg/s

(c) ˙m = 0.098 kg/s

Figure 7: Influence of the saturation temperature on the heat transfer coefficient

Influence of the heat flux

Figure 8 shows the heat transfer coefficient in function of the vapor quality for two different heat fluxes. A higher heat flux results in a wider vapor quality range, as can be expected for a higher heat input.

The general trend is that an increase of the heat flux leads to an increase of the heat transfer coeffi-cient: the average heat transfer coefficient for a heat

(a) ˙q = 23.42 kW/m

(b) ˙q = 29.28 kW/m

Figure 8: Influence of the heat flux on the heat transfer coefficient

flux of 23.42 kW/m2_{is h}

tp,av= 1980 W/(m2K), for a heat flux of 29.28 kW/m2 _{the average heat flux} trans-fer coefficient becomes htp,av= 2504 W/(m2K). This is mainly caused by the increase of nucleate boiling heat transfer when the heat flux is increased. Since the vapor qualities only reach a value of 0.50 (low ˙q) and 0.64 (high ˙q), the dominant heat transfer mech-anism is nucleate boiling for both cases. The major influence of heat flux on nucleate boiling is also the reason that the difference between the two graphs is the largest for the lower vapor qualities. The heat flux has less influence on convective boiling, which has more contribution for higher vapor qualities.

Figure 8 (a) shows the heat transfer coefficient in func-tion of the vapor quality for a low heat flux. First the heat transfer coefficient stays constant for the lowest vapor qualities, because of the dominance of nucleate boiling here [9]. Hereafter the heat transfer coefficient linearly decreases with increasing vapor quality, be-cause of the decreasing contribution of nucleate boil-ing.

Figure 8 (b) shows the heat transfer coefficient in func-tion of the vapor quality for a high heat flux. Because the heat flux is higher the nucleate boiling is almost fully developed for lower vapor qualities. According to

Steiner and Taborek [9] the flow boiling heat transfer coefficient becomes virtually independent of the va-por fraction for fully developed nucleate boiling. At the same time the convective boiling increases with increasing vapor quality, which could cause the heat transfer coefficient to increase for the lowest vapor qualities. A change of flow pattern could also be a cause of this increase of the heat transfer coefficient. Hereafter the decrease of the contribution of nucleate boiling starts to become more important, which first causes a plateau and then a rapid decline of the heat transfer coefficient. The decline becomes less steep for the higher values of the vapor quality, which indi-cates that increasing contribution of convective boiling starts to become dominant.

Similar to the measurements, an increase of the heat flux leads to an increase of the heat transfer co-efficient in the Kattan-Thome-Favrat heat transfer model. The values of the heat transfer coefficient are overall higher for the Kattan-Thome-Favrat heat transfer model than for the measurements and the shape of the graphs is different. This again shows that heat transfer models are only an approximation of the reality and that they should be used and interpreted with caution.

CONCLUSION

The goal of this thesis was to investigate flow boiling heat transfer in a large diameter horizontal tube of an ORC evaporator.

Both a test section with uniform heating and a test section with non-uniform heating were designed, but only the test section with uniform heat flux was con-structed. One of the elements that made this exper-imental test facility unique was the large diameter of the test section, which is interesting for industrial ap-plications. Test sections of other similar experimental studies had smaller diameters.

The influence of the saturation temperature, mass flow rate and heat flux on the heat transfer coefficient was examined by conducting experiments in the flow boiling test facility.

The experiments showed that the average heat transfer coefficient increased when the saturation temperature was increased. At lower vapor qualities the saturation temperature had more influence than at higher vapor qualities. This could be linked with the dominance of nucleate boiling over convective boiling at lower vapor qualities. In general the heat transfer coefficient de-creased with increasing vapor quality, because of the decreasing contribution of nucleate boiling and con-vective boiling becoming dominant.

Increasing the mass flow rate resulted in a higher heat transfer coefficient overall. Comparing the average heat transfer coefficients over different vapor quality ranges showed that nucleate boiling was less influenced by the mass flow rate than convective boiling

An increase of the heat flux resulted in an increase of

the average heat transfer coefficient, which was linked to the increase of nucleate boiling heat transfer. Espe-cially at lower vapor qualities where nucleate boiling is dominant the heat flux had a major influence. These experimental results were each time compared with the model of Kattan-Thome-Favrat. The results of the measurements differed from the heat transfer model in each case. This showed that heat transfer models should be used with caution and that they are only an approximation of the reality.

REFERENCES

[1] S. Quoilin, M. V. D. Broek, S. Declaye, P. De-wallef, and V. Lemort, “Techno-economic survey of organic rankine cycle (ORC) systems,” Re-newable and Sustainable Energy Reviews, vol. 22, pp. 168–186, 2013.

[2] I. Vankeirsbilck, B. Vanslambrouck, S. Gusev, and M. De Paepe, “Organic Rankine cycle as ef-ficient alternative to steam cycle for small scale power generation,” pp. 785–792, 2011.

[3] A. Kaya, M. Lazova, ¨O. Ba˘gcı, S. Lecompte, B. Ameel, and M. De Paepe, “Design Sensitivity Analysis of a Plate-Finned Air-Cooled Condenser for Low-Temperature Organic Rankine Cycles,” Heat Transfer Engineering, vol. 38, no. 11-12, pp. 1018–1033, 2017.

[4] J. R. Thome, “Engineering Data Book III,” pp. 1– 34, 2006.

[5] H. M¨uller-Steinhagen and K. Heck, “A simple friction pressure drop correlation for two-phase flow in pipes,” Chemical Engineering and Process-ing, vol. 20, no. 6, pp. 297–308, 1986.

[6] B. Baert, “Experimental investigation of flow boiling in horizontal tubes at low-temperature subcritical ORC conditions,” 2017.

[7] R. Charnay, “Experimental study of flow boiling in horizontal minichannels at high saturation tem-perature,” 2015.

[8] A. Greco and G. P. Vanoli, “Evaporation of refrig-erants in a smooth horizontal tube: Prediction of R22 and R507 heat transfer coefficients and pres-sure drop,” Applied Thermal Engineering, vol. 24, no. 14-15, pp. 2189–2206, 2004.

[9] D. Steiner and J. Taborek, “Flow boiling heat transfer in vertical tubes correlated by an asymp-totic model,” Heat Transfer Engineering, vol. 13, no. 2, pp. 43–69, 1992.

[10] N. Kattan, J. R. Thome, and D. Favrat, “Flow boiling in horizontal tubes: Part 1-development of a diabatic two-phase flow pattern map,” Journal of Heat Transfer, vol. 120, no. 1, pp. 140–147, 1998.

Contents

Preface iv

Permission of use on loan v

Preamble vi

1 Introduction 1

2 Literature study 3

2.1 Organic Rankine cycle . . . 3

2.2 Two-phase flow boiling in horizontal tubes . . . 4

2.2.1 Flow patterns . . . 5

2.2.2 Heat transfer mechanisms . . . 9

2.2.3 Two-phase flow boiling heat transfer correlations . . . 9

2.2.4 Influencing factors on the heat transfer coefficient . . . 13

2.2.5 Two-phase flow boiling pressure drop correlations . . . 17

2.3 Non-uniform heat flux . . . 20

2.3.1 Waste heat . . . 20

2.3.2 Direct evaporation . . . 20

2.3.3 Theoretical background . . . 21

2.3.4 Experimental studies in the literature related to non-uniform heat flux . . 22

3 Flow boiling test facility 25 3.1 General description . . . 25

3.1.1 Scheme of the flow boiling test facility . . . 25

3.1.2 R245fa as a working fluid . . . 27

3.2 Components . . . 27

3.2.1 Preheater . . . 27

3.2.2 Test section . . . 27

3.2.3 Proportional relieve valve . . . 30

3.2.4 Electronic expansion valve . . . 30

3.2.5 Condenser . . . 30

3.2.6 Liquid receiver . . . 30

3.2.7 Subcooler . . . 31

3.2.8 Pump . . . 31 xiv

CONTENTS xv

3.2.9 Bladder accumulator . . . 32

3.2.10 Cooling loop . . . 32

3.3 Measuring equipment . . . 32

3.3.1 Mass flow sensor . . . 32

3.3.2 Temperature sensor . . . 33

3.3.3 Pressure sensor . . . 33

3.3.4 Cameras for flow pattern analysis . . . 33

3.4 Data acquisition . . . 34

4 Measurements 35 4.1 Measurement method . . . 35

4.2 Measurements of the heat transfer coefficient . . . 35

4.2.1 Influence of the saturation temperature . . . 36

4.2.2 Influence of the mass flow rate . . . 41

4.2.3 Influence of the heat flux . . . 48

5 Conclusion and perspectives 52 5.1 Conclusion . . . 52

5.2 Perspectives . . . 53

A Data reduction 57 A.1 Mass velocity . . . 57

A.2 Heat flux . . . 57

A.3 Volumetric heat flux . . . 57

A.4 Pressure in the test section . . . 58

A.5 Inner wall temperature . . . 58

A.6 Vapor quality . . . 58

A.7 Heat transfer coefficient . . . 59

A.8 Heat loss estimation . . . 60

B Accuracy of measurements 63 B.1 Measurement uncertainties . . . 63

B.1.1 Geometrical . . . 63

B.1.2 Temperature . . . 63

B.1.3 Pressure . . . 64

B.1.4 Mass flow rate . . . 65

B.1.5 Preheater power . . . 65

B.1.6 Test section heating . . . 66

B.1.7 Overview . . . 66

B.2 Uncertainty analysis . . . 66

B.2.1 Pressure in the test section . . . 66

B.2.2 Mass velocity . . . 67

B.2.3 Heat flux . . . 67

CONTENTS xvi

B.2.5 Inner wall temperature . . . 68

B.2.6 Latent heat of vaporization . . . 68

B.2.7 Vapor quality . . . 68

B.2.8 Heat transfer coefficient . . . 68

List of Figures

2.1 Schematic view of an ORC without recuperator (left) and with recuperator (right)

[2] . . . 4

2.2 Temperature-entropy process diagram of an ORC with R245fa [6] . . . 4

2.3 Flow pattern map for horizontal gas-liquid flow according to Baker [7] . . . 5

2.4 The Kattan–Thome–Favrat flow-pattern map (solid lines) compared to the Steiner map (dashed lines) evaluated for R410A at Tsat = 5°C in a 13.84 mm internal diameter tube at different heat fluxes [10] . . . 6

2.5 Flow pattern map for R245fa according to Wojtan et al. [11] . . . 8

2.6 Flow regimes evaporating two-phase flow inside a horizontal tube [6] . . . 8

2.7 Two-phase heat transfer coefficient ration versus the heat flux ratio for different powers n [12] . . . 10

2.8 Simplification of the the stratified, annular, intermittent, stratified-wavy and an-nular with partial dryout flow patterns [8] . . . 13

2.9 Influence of the saturation temperature on the heat transfer coefficient for R-245fa at 300 kg/m²s and 700 kg/m²s with a heat flux of 50 kW/m² (I:intermittent flow and A: annular flow) [6] . . . 15

2.10 Influence of the mass velocity on the heat transfer coefficient for R-245fa at 60°C, 80°C, 100°C and 120°C with a heat flux of 50 kW/m² (I: intermittent flow and A: annular flow) [6] . . . 16

2.11 Influence of the heat flux on the heat transfer coefficient for R-245fa at 60°C, 80°C, 100°C and 120°C with a mass velocity of 500 kg/m²s (I: intermittent flow and A: annular flow) [6] . . . 18

2.12 Layout of ORC-WHR system with indirect evaporation structure (left); Layout of ORC-WHR system with direct evaporation structure (right) [21] . . . 21

2.13 Schematic of the test facility [26] . . . 23

2.14 Schematic of the test section [26] . . . 24

2.15 Schematic diagram of non-uniform test section [26] . . . 24

2.16 Non-uniform heat flux distribution of cross section [26] . . . 24

3.1 Scheme of the flow boiling test facility . . . 26

3.2 Schematic of the preheater . . . 28

3.3 Locations of the thermocouples on the test section from a side view . . . 28

3.4 Cross section of the uniform test section [27] . . . 29

3.5 Photograph uniform test section . . . 29 xvii

LIST OF FIGURES xviii

3.6 Schematic of the non-uniform test section . . . 29

3.7 Cross section non-uniform test section . . . 30

3.8 Schematic of liquid receiver . . . 31

3.9 Sliding vane pump working principle . . . 31

3.10 Sliding vane pump characteristic [27] . . . 32

3.11 Scheme of cooling loop [29] . . . 33

4.1 Influence of the saturation temperature on the heat transfer coefficient . . . 38

4.2 Flow pattern map of R245fa for different saturation temperatures (S=stratified, SW=stratified-wavy, I=intermittent, A=annular, D=dryout, M=mist flow) . . . 39

4.3 Heat transfer coefficient in function of the vapor quality according to the heat transfer model of Kattan-Thome-Favrat for different saturation temperatures . . 40

4.4 Influence of the mass flow rate on the heat transfer coefficient . . . 43

4.4 Influence of the mass flow rate on the heat transfer coefficient (cont.) . . . 44

4.5 Flow pattern map of R245fa for different mass flow rates (S=stratified, SW=stratified-wavy, I=intermittent, A=annular, D=dryout, M=mist flow) . . . 44

4.5 Flow pattern map of R245fa for different mass flow rates (S=stratified, SW=stratified-wavy, I=intermittent, A=annular, D=dryout, M=mist flow) (cont.) . . . 45

4.6 Heat transfer coefficient in function of the vapor quality according to the heat transfer model of Kattan-Thome-Favrat for different mass flow rates . . . 46

4.6 Heat transfer coefficient in function of the vapor quality according to the heat transfer model of Kattan-Thome-Favrat for different mass flow rates (cont.) . . . 47

4.7 Influence of the heat flux on the heat transfer coefficient . . . 49

4.8 Flow pattern map of R245fa for different heat fluxes (S=stratified, SW=stratified-wavy, I=intermittent, A=annular, D=dryout, M=mist flow) . . . 50

4.9 Heat transfer coefficient in function of the vapor quality according to the heat transfer model of Kattan-Thome-Favrat for different heat fluxes . . . 51

A.1 Cross section of the test section . . . 60

List of Tables

2.1 Constants Kandlikar correlation . . . 11

2.2 Fluid dependent parameter Ff l [17] . . . 12

2.3 R-245fa properties at 60°C and 120°C [6] . . . 13

3.1 Physical properties R245fa . . . 27

B.1 Uncertainties of pressure sensors . . . 65

B.2 Calibration mass flow meter . . . 65

B.3 Maximal uncertainties of the measuring equipment . . . 66

B.4 Measuring points . . . 69

B.5 Uncertainties for the different measuring points . . . 69

B.6 Uncertainty of the vapor quality . . . 70

B.7 Uncertainty of the heat transfer coefficient . . . 70

List of symbols

MATHEMATICAL SYMBOLS

Symbol Description Unit

A area m²

Bi Biot number

-Bo Boiling number

-Co Convection number

-D diameter m

e thickness of the tube wall m

F r Froude number –

F Reynolds number factor

-f Darcy friction factor

-G mass velocity kg/(m²s)

g gravitational constant m/s²

Gr Grashof number

-h heat transfer coefficient W/(m²K)

h specific enthalpy J/kg h height m k conductivity W/(mK) k spring constant N/m L length m ˙

m mass flow rate kg/s

n power factor -N u Nusselt number -p pressure Pa P r Prandtl number -˙ Q heating power W

q general physical quantity

-˙

q heat flux W/m²

˙

q00 volumetric heat flux W/m³

R thermal resistance K/W Re Reynolds number -S suppression factor -T temperature K W e Weber number -xx

xxi

x vapor quality

-X general physical quantity

-y distance from the test section inlet m

δ error

-δ liquid film thickness mm

∆ difference -λ thermal conductivity W/(mK) ν kinematic viscosity m²/s ρ density kg/m³ θ angle rad φ two-phase multiplier -µ viscosity µPa·s σ surface tension mN/m ABBREVIATIONS Symbol Description A annular AC alternating current BSL best-straight-line CS capacitance sensor D dryout

DAQ data acquisition system

FS full scale

HSC high speed camera

I intermittent

M mist

ORC organic Rankine cycle PID proportional–integral–derivative RTD resistance temperature detector

S stratified

SG sight glass

SW stratified-wavy

TEB thermal error band TWC triple point of water cell WHR waste heat recovery

SUBSCRIPTS

Symbol Description

abs absolute

acc accuracy

acc accumulator

xxii av average b bulk bot bottom cal calibration cb convective boiling cr critical cond condenser dif difference dry dry fb flow boiling fl fluid fric/fr friction g vapor h hydraulic i inner in inlet ins insulation l liquid lg liquid-vapor

line line pressure lm logarithmic mean

loss heat loss

m measured mom momentum nb nucleate boiling non non-linear o outer out outlet pb pool boiling ph preheater

regr linear regression

rel relation s solid side side sat saturated sc subcooling sp single-phase stat static temp temperature top top tot total tp two-phase ts test section

xxiii twc triple point of water cell

vap/V vapor

w wall

wet wet

Chapter 1

Introduction

The world in this day and age is characterized by an increasing demand of energy. This increase is caused by the evolution and growing need of technology. The development of new technologies goes hand in hand with the increase of energy demand. Currently fossil fuels and nuclear power are still the main energy sources worldwide. These sources have some downsides. Fossil fuels are not infinitely available and their environmental impact becomes more and more visible in the form of climate change and bad air quality. Safety and nuclear waste are the main problems of nuclear energy.

One way to solve this increasing demand of energy while taking the climate, air quality and safety into account is the organic Rankine cycle (ORC). The organic Rankine cycle is a thermodynamic cycle that consists of the same components as a Rankine cycle, but instead of water an organic fluid is used. Because of the lower boiling point higher efficiencies can be obtained for low temperature applications [1]. ORCs can be used to generate electricity by utilizing biomass combined heat and power, geothermal energy, solar power plants and waste heat recovered from exhaust gases [2].

A crucial component of the organic Rankine cycle is the evaporator, in which the working fluid is heated and evaporated by a heat source. A significant part (up to 50 %) of the total initial investment cost of an ORC system is due to the heat exchangers, namely the evaporator and the condenser. The evaporator has a lot of influence on the efficiency of the ORC [3], which is why good knowledge of the evaporation process is crucial. The pressure drop in the evaporator increases with an increase of mass velocity [4] [5]. An evaporator with a larger diameter has a lower mass velocity which results in a lower pressure drop. This is a major advantage for industrial applications.

Having heat transfer data is important to design evaporators accurately. This can lead to better sizing of the evaporators and avoid excess costs. An undersized evaporator will not be able to fully evaporate the working fluid, which can cause damage to the components of the ORC, while an oversized evaporator does not improve or even deteriorates the cycle performance compared to the optimum size and increases the material/labor cost of the heat exchanger [3]. The goal of this work is to investigate the heat transfer in a horizontal tube of an ORC evaporator with a large diameter, both by literature study and experiments.

CHAPTER 1. INTRODUCTION 2 When waste heat is used for direct evaporation in the evaporator, the heating of the evaporator can be non-uniform. Extra literature study is done to investigate the influence of non-uniform heat flux on the heat transfer inside an evaporator.

Chapter 2

Literature study

This chapter starts with a discussion of the working principle of the organic Rankine cycle. Hereafter two-phase flow boiling in horizontal tubes is discussed. The final section expands on non-uniform heat flux for the specific case where waste heat is used for direct evaporation in the evaporator.

2.1 Organic Rankine cycle

An organic Rankine cycle (ORC) is a thermodynamic cycle that converts heat into work using an organic fluid. In its basic form, an ORC consists of a pump, an evaporator, an expander and a condensator as is shown on the left side of Figure 2.1. The pump increases the pressure of the fluid before sending it through the evaporator. In the evaporator the enthalpy of the fluid is increased until the fluid is saturated and reaches a superheated gaseous state at the end of the evaporator. In order to increase the enthalpy in the evaporator, a heat source is needed. Hereafter the gas goes through an expander that generates power and lowers the pressure. After this, a condenser brings the fluid back to a liquid phase using external cooling. Figure 2.2 shows a typical temperature-entropy diagram of an ORC with R245fa as working fluid. where 1-2 represents the pumping of the fluid, 2-3 represents the evaporation process, 3-4 is the part where the fluid goes through the expander and 4-1 represents the condensation process.

A more efficient organic Rankine cycle can be obtained by adding a recuperator. The recuperator is used to preheat the working fluid before entering the evaporator, as can be seen on the right side of Figure 2.1. The advantage of using a recuperator is that less heat needs to be added by the evaporator, which results in a higher efficiency.

An organic Rankine cycle is preferred over a standard Rankine cycle for low temperature appli-cations. The reason for this is the lower evaporation temperature of organic fluids.

One interesting application where organic Rankine cycles are used is the recuperation of waste heat. Typical for waste heat recuperation is the non-uniform heating of the evaporator that is caused by direct evaporation. This is discussed in the section ’Non-uniform heat flux’.

CHAPTER 2. LITERATURE STUDY 4

Figure 2.1: Schematic view of an ORC without recuperator (left) and with recuperator (right) [2]

Figure 2.2: Temperature-entropy process diagram of an ORC with R245fa [6]

2.2 Two-phase flow boiling in horizontal tubes

As the working fluid goes through the evaporator, the enthalpy and the vapor quality are increased throughout the evaporator. The process of fluid flowing in a tube while being externally heated is called flow boiling. Depending on the mass flow and the vapor quality, different flow patterns are obtained. The flow pattern has a lot of influence on the heat transfer coefficient and its correlations.

CHAPTER 2. LITERATURE STUDY 5 There is a big difference between flow boiling in a horizontal tube and a vertical tube. In this master thesis the focus will be on horizontal tubes, since the test section of the experimental set-up consists of a horizontal tube.

2.2.1 Flow patterns

A lot of research about flow pattern maps and correlations is done by different authors [6]. Baker [7] developed one of the first flow pattern maps for horizontal tubes, for the application of oil and gas flowing in large diameter pipes. This adiabatic flow pattern map was based on the superficial gas and liquid velocities relative to water-air mixtures. A flow pattern map according to Baker for oil and gas is shown on Figure 2.4.

Figure 2.3: Flow pattern map for horizontal gas-liquid flow according to Baker [7] In 1998 Kattan et al. [8] created a flow pattern map for tubes with a smaller diameter which is used in heat exchangers and is a modification of the flow pattern map of Steiner [9] [10]. A method capable of predicting the onset of the dryout at the top of the tube in evaporating annular flows was included in this model. The axes of this map are the vapor quality x and the mass velocity G, which are typical parameters related to flow boiling. On Figure 2.4 the Kattan and Steiner flow pattern map for R410A are compared.

CHAPTER 2. LITERATURE STUDY 6

Figure 2.4: The Kattan–Thome–Favrat flow-pattern map (solid lines) compared to the Steiner map (dashed lines) evaluated for R410A at Tsat= 5°C in a 13.84 mm internal diameter tube at

different heat fluxes [10]

the map. Based on their void fraction measurements, the stratified-wavy region was divided into three subzones: slug, slug/stratified-wavy and stratified-wavy. This map incorporates annular-to-dryout and dryout-to-mist flow transition curves. It also takes into account the influence of the heat flux on the annular-to-dryout and dryout-to-mist flow transition curves using a non-dimensional ratio ˙q/ ˙qcrit. This type of flow pattern map is used as a reference for the

measurements in chapter 4. A flow pattern map for R245fa is shown on Figure 2.5.

There are 8 different flow patterns in horizontal flow boiling that are generally being recognized by most sources. These are shown on Figure 2.6.

• Bubbly flow: The flow consists of a continuous liquid phase with a vapor phase dis-tributed as discrete bubbles. Vapor bubbles mostly occur in the top half of the tube at low liquid velocities. The flow becomes more uniform distributed over the cross-section with increasing velocity.

• Plug flow: Vapor plugs occur mostly in the upper half of the tube. This type occurs at low vapor flow rates and moderate liquid flow rates. The nose of the plug has a characteristic spherical cap and the vapor in the plug is separated from the tube wall by a thin film of liquid. Smaller plugs can be entrained in the wake of a large plug.

CHAPTER 2. LITERATURE STUDY 7 • Stratified flow: The bottom part of the tube is filled with liquid, the top part is gaseous

with straight separation. This type occurs at very low liquid and vapor velocities.

• Stratified-wavy flow: The straight separation between the liquid and gaseous part be-comes disrupted by waves travelling in the direction of the flow. This happens when the vapor velocity is increased.

• Slug flow: The waves of the liquid-gas boundary become larger which results in an upper part that is alternately wet and dry. The vapor-liquid interface at the front and the tail of the slug is not always clearly definable. This happens when increasing the vapor velocity.

• Intermittent flow: Unsteady flow patterns like plug and slug flow are sometimes grouped together as intermittent flow. The entire tube periphery is frequently wetted and a vapor-liquid interface is often undefinable.

• Annular flow: The circumference of the tube is liquid while the center of the tube is gaseous. The film will be thicker at the base of the tube. The film thickness and its distribution depend on the vapor velocity.

• Partial dry-out flow: With liquid flow thinning out, dry spots start to appear at the top of the tube. When more liquid is vaporizing, the upper part of the tube remains constantly dry and eventually the bottom section of the tube periphery dries out.

• Mist flow: When the liquid ring formed in annular flow is fully evaporated, it is called mist flow. Small droplets are entrained in the vapor core.

The type of flow pattern will have a big impact on the heat transfer coefficient, so the flow pattern inside the tube is of great importance. As can be seen from Figure 2.5, the flow pattern mainly depends on two factors: the mass velocity and the vapor quality.

Two-phase flow boiling heat transfer correlations can be based on the flow pattern occurring. One such a correlation is the Kattan-Thome-Favrat heat transfer correlation and is discussed in the last section of the following paragraph.

CHAPTER 2. LITERATURE STUDY 8

Figure 2.5: Flow pattern map for R245fa according to Wojtan et al. [11]

CHAPTER 2. LITERATURE STUDY 9

2.2.2 Heat transfer mechanisms

It is important to have a good understanding what the heat transfer mechanisms are. When the working fluid flows through an evaporator, a transition takes place from liquid to gaseous phase. This type of heat transfer is called two-phase flow boiling heat transfer. In literature it is assumed that flow boiling heat transfer is the combined effect of nucleate boiling and convective boiling.

Nucleate boiling has a lot of similarities with pool boiling, but in nucleate boiling there is fluid flow that has an influence on the growth and departure of the bubbles. As long as the heat flux has a smaller value than the critical heat flux there is an increase of the heat transfer with increasing heat flux [4]. An increasing mass flow rate and increasing vapor quality decrease the relative effect of nucleate boiling compared to convective boiling. This is due to the thinner thermal boundary layer of forced convection compared to natural convection at high mass flow rate and high vapor qualities.

Convective boiling is similar to single-phase convective heat transfer, but in convective boiling there is also the influence of the two-phase state of the flow. The average density decreases and the velocity increases with the formation of vapor. This results in an increase of importance of convective boiling when compared to single-phase forced convection.

Steiner and Taborek [12] developed an equation to calculate the local two-phase heat transfer co-efficient as a function of the nucleate boiling coco-efficient hnband the convective boiling coefficient

hcb:

htp= [(hnb)n+ (hcb)n]1/n (2.1)

In Figure 2.7 the results of equation 2.1 are shown for different values of n. n = 1 corresponds with the sum of hnb and hcb, n = ∞ corresponds with the maximum hnb and hcb.

It has to be remarked that in Figure 2.7 the convective boiling is independent of the heat flux, which is a common assumption for flow boiling prediction methods [6] [13]. It also assumed that hnb is a function of the heat flux which follows from the similarity with pool boiling. In the

section below the different heat transfer correlations are summarized and explained.

2.2.3 Two-phase flow boiling heat transfer correlations

There are many different heat transfer correlations that are applicable for different operational scenarios and circumstances. Five of those correlations are discussed here: the correlations of Shah [14], Chen [15], Gungor-Winterton [16], Kandlikar [17] and Kattan-Thome-Favrat [8].

Shah correlation

Shah [14] made a distinction between 4 regimes of flow boiling: pure nucleate boiling, bubble suppression, pure convective boiling with surface fully wet and convective boiling with partly dry surface.

CHAPTER 2. LITERATURE STUDY 10

Figure 2.7: Two-phase heat transfer coefficient ration versus the heat flux ratio for different powers n [12]

In the pure nucleate boiling regime, the logical assumption was made that nucleate boiling is dominant.

In the bubble suppression regime both bubble nucleation and convective effects are significant. With increasing vapor quality, bubble nucleation gets suppressed more and more.

In the case of a horizontal flow, a distinction is made between a fully wet regime and a partly wet regime using the liquid Froude number:

F rl=

G2

ρ2_{· g · D} (2.2)

The Froude number is a dimensionless number defined as the ratio of the flow inertia to the external field (gravity). If F rl < 0.04, part of the tube surface is dry and the heat transfer

coefficient is lower than in vertical tubes [14].

For each regime the two-phase heat transfer coefficient is calculated by taking the maximum of the nucleate boiling and the convective boiling heat transfer coefficient:

CHAPTER 2. LITERATURE STUDY 11 The nucleate boiling coefficient can be calculated using a correlation depending on the boiling number and the convective heat transfer coefficient can be calculated from the correlation of Dittus and Boelter [18].

Chen correlation

The Chen correlation [15] starts from equation 2.1 with power n = 1, but multiplies the terms with a suppression factor S and a Reynolds number factor F:

htp = hpb· S + hsp· F (2.4)

Since convective boiling has a larger influence than the single-phase convection, F is usually bigger than 1. The suppression factor S varies between zero and one, expressing the relative importance of nucleate boiling.

This correlation is only useful for vertical flow. The nucleate pool boiling factor can be deter-mined using the Forster-Zuber correlation and the forced convection factor using the Dittus-Boelter correlation [18].

Gungor-Winterton correlation

The Gungor-Winterton correlation [16] is, contrary to the Chen correlation, applicable for both horizontal and vertical flow and can be used for subcooled and saturated boiling. The Gungor-Winterton correlation starts from the Chen correlation and uses iteration to calculate the sup-pression factor and the Reynolds number factor. The pool boiling heat transfer in this correlation is determined using the Cooper correlation [19].

Kandlikar correlation

The Kandlikar correlation [17] is a general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. It can be applied for different fluids by the usage of the fluid dependent parameter Ff l. Kandlikar proposed the following correlation:

hT P

hl

= C1· CoC2 · (25F rlo)C5 + C3· BoC4 · Ff l (2.5)

The values of C1, ..., C5 are given in Table 2.1:

Table 2.1: Constants Kandlikar correlation

Constant Convective region Nucleate boiling region

C1 1.1360 0.6683

C2 -0.9 -0.2

C3 667.2 1058.0

C4 0.7 0.7

C5 0.3 0.3

It has to be remarked that C5= 0 for vertical tubes and for horizontal tubes with F rl> 0.04.

CHAPTER 2. LITERATURE STUDY 12 Table 2.2: Fluid dependent parameter Ff l [17]

Fluid Ff l Water 1.00 R-11 1.30 R-12 1.50 R-1381 1.31 R-22 2.20 R-113 1.30 R-114 1.24 R-152a 1.10 Nitrogen 4.70 Neon 3.50 Kattan-Thome-Favrat correlation

Kattan-Thome-Favrat [8] [11] used the flow pattern to calculate the heat transfer coefficient. After determining the flow pattern, the needed geometrical parameters are determined from the simplified flow patterns, which are shown on Figure 2.8.

The heat transfer coefficient htp was calculated as a combination of the heat transfer coefficient

for the wet and dry perimeter separately: htp=

θdryhV + (2π − θdry)hwet

2π (2.6)

With θdry being the dry angle, hV the heat transfer coefficient of the dry perimeter and hwet

the heat transfer coefficient of the wet perimeter, which is calculated from the asymptotic model with the exponent n = 3:

hV = 0.023Re0.8V P r0.4V kV D (2.7) hwet = [(hcb)3+ (hnb)3]1/3 (2.8) hcb= CRemLP rmL kL δ (2.9)

With δ the liquid film thickness, C and m are determined in Kattan et al. [8] and the nucleate boiling heat transfer coefficient hnb can be calculated from the correlation of Cooper [19].

The measurements of chapter 4 are compared with the model of Kattan-Thome-Favrat. This heat transfer model was chosen because it is more accurate than the models of Shah and Gungor-Winterton [8] and more advanced than the model of Kandlikar. The Chen correlation is not used since it is only useful for vertical flow.

CHAPTER 2. LITERATURE STUDY 13

Figure 2.8: Simplification of the the stratified, annular, intermittent, stratified-wavy and annular with partial dryout flow patterns [8]

2.2.4 Influencing factors on the heat transfer coefficient

In the following section the influence of the saturation temperature, mass velocity and heat flux on the heat transfer coefficient are discussed. Experiments to investigate the influence of these factors for minichannels were done by Charnay et al. [6]. Flow boiling experiments with R245fa were done while varying the saturation temperature within a range of 60 to 120°C.

Influence of the saturation temperature

Varying the saturation temperature from 60°C to 120°C will have a major influence on the heat transfer coefficient. The influence of the saturation temperature at a constant heat flux for two different mass velocities (G = 300 kg/m²s and G = 700 kg/m²s) is shown on Figure 2.9. For both mass velocities it can be stated that a higher saturation temperature results in a larger heat transfer coefficient over a wide range of vapor quality until dryout inception.

Table 2.3: R-245fa properties at 60°C and 120°C [6]

Pred [-] ρL[kg/m³] ρV[kg/m³] µL[µPa.s] µV[µPa.s] λL[mW/m.K] σ[mN/m]

60°C 0.13 1237 25.7 265 12 79 9.59

120°C 0.53 998 119.7 125 15 61 2.64

For Figure 2.9 (a) where G = 300 kg/m²s it is shown that the influence of the saturation temperature has more influence when the vapor quality is low. At these low vapor qualities small

CHAPTER 2. LITERATURE STUDY 14 bubbles have a major influence on the heat transfer. An increase of the saturation temperature leads to a surface tension decrease, a vapor density increase and an liquid density decrease. An overview of the properties of R245fa at 60°C and 120°C is shown in Table 2.3. The changes of these properties lead to an intensification of the nucleate boiling heat transfer, which results in a general increase of the heat transfer coefficient.

At 60°C and 80°C the heat transfer is mainly due to nucleate boiling. The heat transfer coefficient is almost constant over the vapor quality range.

At a saturation temperature of 100°C the graph has a plateau which corresponds to the inter-mittent flow pattern. With increasing vapor quality the heat transfer coefficient decreases slowly until reaching dryout, after which there is large decrease of the heat transfer coefficient.

For a saturation temperature of 120°C there is a decrease of the heat transfer coefficient over the whole vapor quality range. The decrease of the heat transfer coefficient is twofold. First, the decrease of the heat transfer coefficient results from the reduction of the nucleate boiling contribution. The contribution of nucleate boiling is especially important in the low vapor qual-ity regions for high saturation temperatures, but is also of importance at higher vapor qualities where annular flow occurs. Second, the convective boiling contribution is not sufficient at high saturation temperature to lead to an increase of the heat transfer coefficient with increasing vapor quality. Table 2.3 shows that an increasing saturation temperature results in an increase of the vapor density, which results in a lower flow velocity, and a decrease of liquid film con-ductivity. This implicates lower conduction and convection through the liquid film and thus a reduced contribution of the convective boiling too at high saturation temperatures.

The heat transfer coefficient as a function of the vapor quality for a mass velocity of 700 kg/m²s for the same 4 saturation temperatures (60°C-80°C-100°C-120°C) is shown on Figure 2.9 (b). At 60°C and 80°C a plateau occurs for intermittent flow which corresponds with low vapor qualities, this indicates dominance of nucleate boiling. Increasing vapor quality in the annular flow region results in a gradual increase of the heat transfer coefficient. Convective boiling becomes more important but does not completely suppress nucleate boiling. The contribution of convective boiling becomes more important with an increase of the mass velocity.

At 100°C and 120°C there is a strong decrease of the heat transfer coefficient with increasing vapor quality for the intermittent flow regime. This decrease is possibly caused by the bubbles frequency reduction, because small bubbles tend to merge together to form bigger bubbles with increasing vapor quality. A minimum of the heat transfer coefficient is reached at the transition between intermittent and annular flow. The vapor quality at this minimum is xmin.

After reaching this minimum point the flow becomes annular flow and a plateau occurs for the heat transfer coefficient. This plateau results from the decrease of the nucleate boiling and the increase of convective boiling. The heat transfer coefficient falls when dryout flow starts to occur. Figure 2.9 (b) also shows that dryout occurs at a lower vapor quality for a higher saturation temperature.

CHAPTER 2. LITERATURE STUDY 15

Figure 2.9: Influence of the saturation temperature on the heat transfer coefficient for R-245fa at 300 kg/m²s and 700 kg/m²s with a heat flux of 50 kW/m² (I:intermittent flow and A: annular flow) [6]

Influence of the mass velocity

The mass velocity has the largest influence on the heat transfer in convective boiling. The influence of the mass velocity on the heat transfer for constant heat flux and four different saturation temperatures is shown on Figure 2.10.

At 60°C the general trend is that an increased mass velocity results in an increase of heat transfer coefficient. For low vapor qualities the flow pattern is intermittent and the mass flow has little influence. In this region is nucleate boiling dominant. For annular flow the heat transfer coefficient increases with increasing vapor quality for all mass flows except for 300

CHAPTER 2. LITERATURE STUDY 16 kg/m²s, where the heat transfer coefficient stays almost constant. The dominant heat transfer mechanism for these higher vapor qualities is convective boiling, which explains the influence of the mass velocity.

At 80°C and 100°C the influence of the mass flow rate depends on the occurring flow regime. For intermittent flow (lower vapor qualities) a higher mass velocity results in a smaller heat transfer coefficient. Nucleate boiling is here the dominating heat transfer mechanism.

For annular flow regime (higher vapor qualities) a higher mass velocity results in a higher heat transfer coefficient. Convective boiling is here dominant.

At 120°C the heat transfer coefficient decreases with increasing mass velocity as is shown in Figure 2.10 (d). This behaviour is especially interesting for the annular flow region. In contrast to the saturation temperatures of 80°C and 100°C nucleate boiling is the dominating flow regime in the annular flow region, which explains this behaviour.

Figure 2.10: Influence of the mass velocity on the heat transfer coefficient for R-245fa at 60°C, 80°C, 100°C and 120°C with a heat flux of 50 kW/m² (I: intermittent flow and A: annular flow) [6]

CHAPTER 2. LITERATURE STUDY 17

Influence of the heat flux

The effect of the heat flux on the heat transfer coefficient is shown on Figure 2.11 for a mass velocity of 500 kg/(m²·s) and for four saturation temperatures: 60°C, 80°C, 100°C and 120°C. The general trend is that an increase of heat flux leads to an increase of the heat transfer coefficient.

At 60°C the heat flux has more influence in intermittent flow (low vapor qualities) than in annular flow (high vapor qualities). Once the flow becomes annular the influence of the heat flux reduces. This behaviour can (once again) be explained by the dominance of nucleate boiling during the intermittent flow regime while convective boiling becomes more and more important and starts suppressing nucleate boiling with increasing vapor quality. This effect is more noticeable for low heat flux (10 kW/m²) than for the higher heat fluxes.

At 80°C and 100°C the heat flux influences the heat transfer coefficient over the whole range of vapor qualities until dryout inception. Figure 2.11 (b) and (c) indicate that the suppression of the nucleate boiling occurs at a higher vapor quality.

At 120°C the characteristic is entirely different for the heat flux of 10 kW/m² compared to the other two heat fluxes.

• For a heat flux of 10 kW/m² the heat transfer coefficient stays almost constant during the intermittent flow regime and starts increasing with increasing vapor quality in annular flow. The contribution of convective boiling to the heat transfer increases with increasing vapor quality, which results in an increase of the heat transfer coefficient.

• For 30 kW/m² and 50 kW/m² the general trend is a decrease of the heat transfer coeffi-cient with increasing vapor quality. Nucleate boiling becomes the dominant heat transfer mechanism for higher heat flux values. The nucleate boiling decreases with increasing vapor quality which results in an overall decrease of the heat transfer coefficient. Dryout inception will happen at a lower vapor quality for a higher heat flux.

2.2.5 Two-phase flow boiling pressure drop correlations

The pressure drop has a major influence on the design of the heat exchanger and the organic Rankine cycle in general. Since the test section has a large diameter, the mass velocity is lower compared to tubes with a smaller diameter, which results in a smaller pressure drop. No measurements were done to analyze the pressure drop, but because of its importance the theory behind the two-phase pressure drop is discussed here.

A pump needs to compensate to total pressure drop accumulated over the whole cycle. When there is a large pressure drop, a more powerful pump is needed which can result in a lower efficiency and a higher cost.

For two-phase flows the total pressure drop is sum of three types of pressure drop [4]: the static pressure drop ∆pstat, the momentum pressure drop ∆pmomand the friction pressure drop ∆pf ric.

CHAPTER 2. LITERATURE STUDY 18

Figure 2.11: Influence of the heat flux on the heat transfer coefficient for R-245fa at 60°C, 80°C, 100°C and 120°C with a mass velocity of 500 kg/m²s (I: intermittent flow and A: annular flow) [6]

The static pressure drop is the pressure drop due to the change in gravitational potential energy. For horizontal heat exchangers, this type of pressure drop will have no influence.

The momentum pressure drop is the result of the change in kinetic energy of the flow. The kinetic energy of a fluid increases when passing through an evaporator.

The third and most significant term is the frictional pressure drop. There exist a lot of different correlations to determine the frictional pressure drop. Because of the importance of the friction term, two correlations are elaborated on: the Friedel correlation [20] and the Muller-Steinhagen and Heck correlation [5].

Friedel correlation

The Friedel correlation method [4] utilizes a two-phase multiplier:

∆pf ric= ∆pL· Φ2f r (2.11)

CHAPTER 2. LITERATURE STUDY 19

∆pL= 4fL(L/di) ˙m2total(1/2ρL) (2.12)

With fLbeing the liquid friction factor which can be derived from the Reynolds number.

The two-phase multiplier is calculated with the following function: Φ2_{f r} = E + 3.24 · F · H

F r_H0.045W e0.035_L (2.13) With E, F and H being dimensionless numbers in function of x, ρL, ρG, fL, fG, µL, µG, F rH being

the Froude number and W eL being the liquid Weber number.

This method is typically recommended when the ratio of µL

µG is less than 1000 and is applicable

to vapor qualities from 0 ≤ x ≤ 1.

Müller-Steinhagen and Heck

Müller-Steinhagen and Heck [4] [5] proposed a two-phase frictional pressure gradient correlation that is in essence an empirical interpolation between all liquid flow and all vapor flow. The two-phase multiplier is calculated with the following function:

 dp dz



f rict

= G(1 − x)1/3+ Bx3 (2.14)

With the factor G being:

G = A + 2(B − A)x (2.15)

The factors A and B are the frictional pressure gradients for all the flow liquid (dp/dz)Land all

the flow vapor (dp/dz)G.

This method gives the best results in a comparison of competing methods to a large database that covered air-oil, air-water, water-steam and several refrigerants and is applicable for 0 ≤ x ≤ 1.

CHAPTER 2. LITERATURE STUDY 20

2.3 Non-uniform heat flux

The specific case where waste heat is used as a heat source for direct evaporation in an organic Rankine cycle is discussed in this section. The heating of the evaporator can be non-uniform in this situation, which can have a major impact on the heat transfer.

First waste heat as heat source is discussed, followed by an explanation of direct evaporation. Then some theoretical background of non-uniform heat flux is given and finally an experimental study is discussed.

2.3.1 Waste heat

Waste heat can be defined as unused heat given to the surroundings by a heat engine in a ther-modynamic process in which it converts heat to useful work. The two main sources of waste heat are internal combustion engines and industrial processes. Depending on the temperature, waste heat is divided into two categories: low temperature waste heat (<250°C) and high temperature waste heat (>250°C). The focus will be on the low temperature waste heat, for which organic Rankine cycles are used. What makes waste heat so interesting as a source of energy is the availability and the cost. There are a lot of sources of waste heat and waste heat is completely lost in the atmosphere if not used. Using waste heat as a energy source is one solution to the increasing energy demand in the world.

Waste heat can be used both directly and indirectly for the evaporation in an ORC. This is discussed in the next paragraph.

2.3.2 Direct evaporation

Direct evaporation uses waste heat directly to evaporate the working fluid without the use of an intermediate cycle. Indirect evaporation uses an intermediate secondary cycle between the waste heat source and the ORC with a different working fluid, usually a thermal oil or cooling water. Both an ORC with direct evaporation (right) and an ORC with indirect evaporation (left) are shown on Figure 2.12, in which the waste heat of the exhaust gasses from an internal combustion engine are used.

An advantage of indirect evaporation is the possibility to mitigate the incoming heat peaks coming from the waste heat. For some applications the working fluid cannot exceed certain temperatures in order to keep the installation safe. Indirect evaporation is already well re-searched and well documented.

Direct evaporation has a lower capability of damping a variable heat source, so for some appli-cations this can be a potential risk. The big advantage of direct evaporation is the absence of a secondary cycle, which results in a much simpler design and a potential lower price. Other ad-vantages are the reduced footprint and the potential for a higher thermal efficiency [21]. Direct evaporation using waste heat can result in a non-uniform heat flux. Theoretical background and an experimental study about non-uniform heat flux are discussed next.