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Heat transfer in supercritical fluids under pulse heating regime
International Journal of Heat and Mass Transfer 57 (2013) 126–130
Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer in supercritical fluids under pulse heating regime Sergey B. Rutin, Pavel V. Skripov ⇑ Institute of Thermal Physics, Ural Branch, Russian Academy of Sciences, Amundsena St. 106, Ekaterinburg 620016, Russian Federation
a r t i c l e
i n f o
Article history: Received 13 August 2012 Accepted 8 October 2012 Available online 3 November 2012 Keywords: Pulse heating Supercritical fluids Heat transfer intensity
a b s t r a c t The peculiarities of the heat transfer in supercritical fluids under short characteristic times scale has been studied experimentally. The constant heating power mode for the technique of controlled pulse heating of a wire probe was used for isobaric penetrating into the region of supercritical temperatures. The pressure range was (1–6)p/pc and the temperature range was (0.6–1.6)Tc, where subscript ‘‘c’’ corresponds to the critical point of a substance. The characteristic pulse length was 10 ms; the heat flux density through the probe surface was from 1 MW/m2 to 10 MW/m2. A sharp decrease in the heat transfer intensity for supercritical fluids with respect to that of subcritical liquids has been obtained. A high sensitivity of the heat transfer pattern to the reduced pressure values was revealed as well. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction In spite of a long history of studying the properties of supercritical fluids (SCFs) and heat exchange problems associated with their use as working fluids, many unresolved issues remain in this area of knowledge. Search for relevant solutions is motivated by the fact that hundreds of thermal power stations in the world operate on supercritical water, and the design projects for nuclear reactors cooled by supercritical water are currently discussed. In the fundamental book written by Pioro and Duffey [1], the data on heat exchange in SCFs over the past 50 years were analyzed. It has been shown that attempts to build up the theoretical model capable to describe all the modes of heat transfer in SCFs that were observed in the experiments so far failed. With all the virtues of experimental studies discussed in [1], they contain an irremovable obstacle, which follows from the fact of abnormally high compressibility of SCFs and leads to a significant in magnitude density distribution in the gravitational field. Galitzine [2], apparently, was among the first who faced an unusual density distribution of SCF up to 25% by volume of the measuring cell. In this experiment, the observation time was not too short, being about 1.5 h. Generally, in quasi-static experiments aimed at engineering applications, the action of several factors manifests itself, which extremely complicates the interpretation of the results. These factors include abnormal compressibility, nonlinearity of the properties and parameters of heat exchange (see, for example, [3,4]), the influence of gravitational field, as well as various kinds of instabilities, including the hydrodynamic instability. In order to overcome the effects of gravity, some experiments were carried out in outer space [5]. If the issues of the gravity effect on the results of ⇑ Corresponding author. Tel.: +7 343 3745442; fax: +7 343 2678800. E-mail address: [email protected] (P.V. Skripov). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.10.027
quasi-static experiments, whose main purpose is to determine the critical indices, are the subject of discussion (see [6] and references therein), the effect of gravity on the results of experiments aimed at engineering applications is beyond question [1]. The specificity of SCFs behavior makes us to search new approaches for their study. The general idea of a technique presented in this paper is as follows: to create special experimental conditions in which the influence of gravity and macroscopic convection would be minimized and the temperature changing would be done over a wide range. The problem was solved by the use of the method of controlled pulse heating of a wire probe – resistance thermometer [7–9], which made it possible to compare the intensity of heat exchange of the probe with the environment in a wide range of sub- and supercritical states under strictly defined conditions of heating. The fundamental features of the technique are the high values of heat flux density and the relatively small length of the probing pulse. The range of pulse lengths was chosen from considerations on the one hand, of the sufficiency of the thickness of the heated layer for increasing sensitivity of the method and reducing influence of the heat capacity of the probe (which requires an increase in pulse length) and on the other hand, of minimizing the impact of macroscopic convection and gravity (which requires a decrease in pulse length). A compromise solution satisfying both conditions was the time range of the order of one to tens milliseconds. Indirect verification of the absence of the influence of gravity was performed as follows: the cell with the probe was positioned in the vertical and horizontal positions. In this case, the differences in the observed patterns of heat transfer were not identified. 2. Experimental An appropriate selection of the control algorithm is a key point in solving the problem, since it determines the possibility of simple
S.B. Rutin, P.V. Skripov / International Journal of Heat and Mass Transfer 57 (2013) 126–130
and clear interpreting the measurement results. Paper [10] may be cited as an example of appropriate choice of the method, where the authors managed to obtain new results related to the problems of superintensive bubble boiling. Analysis of variants has shown that such algorithm is a control of the electric power released in the heater-probe. The essence of the control algorithm can be written as follows:
UðtÞ ¼ k PðtÞ; where U(t) is the input pulse of the controlling voltage, P(t) is the power released at the probe in the course of heating, t is time, k is a constant coefficient. For U(t) = const, we have constant heating power mode. The main unit of apparatus is a fast PI controller with negative feedback, which allows maintaining the selected shape and amplitude of the electric power with high accuracy. In a series of
127
experiments at the chosen form of the controlling voltage pulse, the energy imparted to the probe–environment system at any time from the beginning of the pulse will be repeated with high accuracy. Thereby, the practical basis for direct comparison of the intensity of heat transfer by different samples under identical conditions of heat release in the probe is created. The rest of the apparatus is intended for recording the experimental data, calculations of the required quantities and for graphical representation of both the recorded and calculated data. As for the well-known transient hot-wire (THW) technique [11,12], the probe serves as a heater and a resistance thermometer simultaneously. The values of changing in time voltage drops across a standard resistor and the probe are the quantities recorded in the experiment. Calculated quantities are the current through the probe, the power released at the probe, the resistance of the probe and it’s averaged over the bulk temperature T as
Fig. 1. Characteristic probe temperature curves at the constant heating power mode for isopropanol (Fig. 1a). Pressure serves as a parameter. The insert illustrates the actual power values in the course of experiment. The derivatives of probe temperature with respect to time at the same pressures (Fig. 1b).
128
S.B. Rutin, P.V. Skripov / International Journal of Heat and Mass Transfer 57 (2013) 126–130
functions of time. A platinum wire applied in thermometry was used to make the probe. The diameter of the probe was 20 lm; its length was 1–2 cm. The probe was immersed in the fluid under investigation and hermetically sealed in the measuring cell. Pulse heating of the probe in the investigated medium was performed under isobaric conditions. The patterns of the probe temperature rise in time T(t) observed in the experiments give information about the heat exchange of the probe with the medium and make it possible to calculate the thermal resistance of the probe–environment system for any moment of time [7,8]. All presented results were obtained in the constant power mode that allows their clearest interpretation. In the experiments, the probe temperature rise in time for given values of the heating power and pressure was monitored. From these data we calculated
the heat flux density through the probe surface q = (P PPt)/pdl and the thermal resistance Rk(t) = DT(t)/q at a given exposure, where d and l are diameter and length of the probe, DT(t) is a temperature rise, PPt(t) is the power spent on heating the probe. In our experiments, the PPt value did not exceed 0.1P. The error of the probe surface area measurement pdl is an order of magnitude greater than that of other variables, so a relative version of the method was applied. In this case, since the measurements are performed at the same probe, the surface area is excluded from the calculations. Systematic error that is inherent in THW techniques due, in particular, to the end corrections and probe heat capacity is also substantially compensated. In the approximation of zero heat capacity of the probe that is appropriate in our experimental conditions, the problem reduces to finding
Fig. 2. Characteristic probe temperature curves at the constant heating power mode for diethyl malonate (Fig. 2a). Pressure serves as a parameter. The insert illustrates the actual power values in the course of experiment. The derivatives of probe temperature with respect to time at the same pressures (Fig. 2b).
S.B. Rutin, P.V. Skripov / International Journal of Heat and Mass Transfer 57 (2013) 126–130
the DTi/DT0 ratio for selected values of P and t, where the indices ‘‘i’’ and ‘‘0’’ refer to a number of pressure values, one of which (‘‘0’’) was chosen as the base pressure. The absolute values of P and T in our experiments are determined with estimated error of ±0.65% and ±1.0%, respectively. The error of determination of the relative thermal resistance (Rki/Rk0) appears to be on the order of 0.1%. Experimental procedure and the estimation of errors were discussed in detail elsewhere [7]. With regard to SCFs, measurement procedure was as follows: a cell with a probe filled with the investigated liquid was placed in a pressure chamber. Pressure served as a parameter in the experiments. The pressure range was chosen taking into account the pc value of the studied substance. The pressure was produced by hydraulic press and measured with a manometer. As explained above, the constant power mode is used with pulse length of about 10 ms. Characteristic thickness of the heated layer by the end of the pulse was (23) 105 m. The power value was chosen so that the probe was at supercritical temperature for not less than half of the pulse length. For each of the substances chosen power value remained unchanged until the end of the measurements. For each pressure the probe temperature rise T(t) for the chosen power level P(t) was recorded and then the relative thermal resistance of a substance reduced to its base value was calculated. The greatest pressure in the experiment was chosen as the ‘‘base’’ one. Raw files recorded during the measurement were smoothed using a cubic spline. From the smoothed T(t) files, the derivatives were calculated using software, their analysis provides additional information about the perturbations of heat transfer process in the transition to supercritical region.
3. Results and discussion Figs. 1 and 2 show the results of experiments for isopropanol and diethyl malonate, and Figs. 3 and 4 show the calculations of their relative thermal resistance (RTR) for different reduced pressures. As seen, the actual power values fall within a band of ±0.01%. Although these substances belong to different classes of organic compounds, a similarity of patterns of heat transfer is
129
observed in the given experimental conditions. When crossing the vicinity of the critical temperature during isobaric heating, the T(t) curves are deflected in the higher temperatures direction, indicating a decrease in heat transfer intensity. The derivatives oT/ot are also sharply deflected upward with respect to their extrapolated values into supercritical region. At p (1–2)pc, the maximums are formed on the graphs of derivatives. In general, the data presented in Figs. 1 and 2 lead to the following conclusion. A significant extension of the ‘‘beam’’ of T(t) curves indicates an abnormally high sensitivity of the intensity of heat transfer to pressure at supercritical parameters. The scale of such an extension exceeds the scale characteristic for subcritical temperatures by an order of magnitude. The pressure range (2.5–3)pc is likely to be transitional one. At exceeding these values of pressure, the T(t) curves and their derivatives take the form typical for the region of subcritical pressures. Maximums on the derivatives become more sloping and degenerate almost completely in the (2.5–3)pc region. We attribute this fact to a significant decrease in non-linearity of heat transfer parameters with increasing p/pc value. For the calculations of RTR, the maximum pressure in the experiment was chosen as the base one. In either case, the base pressure was about 6pc. For this choice, the determined variable on approaching from above to the critical pressure will have a positive value. Figs. 3 and 4 show the results of RTR calculations. For isopropanol, an increase in RTR was about 30% as the pressure decreased from the base one to (1.02)pc and for diethyl malonate, it was about 22% with decreasing pressure from the base one to (1.07)pc, which exceeds the change in RTR for subcritical temperatures in our experiments by an order of magnitude. The revealed sharp decrease in heat transfer intensity in the immediate vicinity of the critical temperature, as discussed above, is formally contradictory to the well-known concept of the critical enhancement of heat transfer in this region. We attribute this experimental fact to a substantial distinction of our approach to the experiments with SCFs. Our procedure made it possible to almost completely ‘‘switch off’’ the effect of gravity and macroscopic convection, which is unfeasible in the quasi-static experiments. It is correct to assume that heat transfer observed in our experiments
Fig. 3. The change in isopropanol thermal resistance in the course of pulse heating at different pressures (Rki) reduced to thermal resistance at the most high pressure (Rk0).
130
S.B. Rutin, P.V. Skripov / International Journal of Heat and Mass Transfer 57 (2013) 126–130
Fig. 4. The change in diethyl malonate thermal resistance in the course of pulse heating at different pressures (Rki) reduced to thermal resistance at the most high pressure (Rk0).
is a purely conductive. In our experiments, a radiation component of heat transfer is small due to the short length of the probe pulse, and it can be neglected.
4. Conclusion Application of the method of controlled pulse heating in the study of heat transfer in SCFs made it possible to obtain qualitatively new results: - Effect of the sharp decrease in heat transfer intensity in the isobaric approaching to the region of supercritical temperatures was found. The extent of this effect was surprisingly large; in this case, the closer is the pressure to the critical value, the greater is the sensitivity of heat transfer pattern to the reduced pressure. - The (2.5–3)pc pressure range is taken to be transitional one. At exceeding these pressures the heating curves and their derivatives take the form characteristic of the subcritical pressure region. Two hypotheses concerning the transition region can be formulated. First, at pressures above 2.5pc the heat exchange in actual heat-exchanging devices will not contain the typical instabilities and deteriorated modes peculiar to SCFs near the critical temperature. Taking into account the significant decrease in thermal resistance with increasing p/pc value (see Figs. 3 and 4), checking this hypothesis in the specially designed experiments becomes quite reasonable. Second, this transition zone can be considered as a transition between the gas-like and liquid-like states of SCFs, realizing the conventionality of these terms. Similarity of heat transfer processes for both studied compounds and the fact that heat transfer pattern at pressures above the transition region is indistinguishable from those for ordinary liquids at subcritical parameters point to such a possibility. To check this supposition and its possible generalization to a class of liquid
dielectrics, we plan to perform experiments with a set of substances with various properties.
Acknowledgments The study was partially supported by RFBR, research project No. 10-08-00538-a and by CRDF – UrB RAS Project No. RUE1-7033-EK11. References [1] I.L. Pioro, R.B. Duffey, Heat transfer and hydraulic resistance at supercritical pressures in power engineering applications, ASME, New York, 2007. [2] B. Galitzine, Ueber den Zustand der Matherie in der Nähedes kritischen Punktes, Ann. d. Phys. u. Chem. 50 (1893) 521–545. [3] E. Schmidt, Wärmetransport durch natürliche konvektion in stoffen bei kritischem zustand, Int. J. Heat Mass Transfer 1 (1) (1960) 92–101. [4] A. Bruch, A. Bontemps, S. Colasson, Experimental investigation of heat transfer of supercritical carbon dioxide flowing in a cooled vertical tube, Int. J. Heat Mass Transfer 52 (11–12) (2009) 2589–2598. [5] M.R. Moldover, Low-gravity experiments in critical phenomena, in: G.A. Hazelrigg, J.M. Reynolds (Eds.), Opportunities for academic research in a low-gravity environment. Progress in Astronautics and Aeronautics, American Institute of Astronautics and Aeronautics, New York, 108, 1986, 57–79. [6] D.Yu. Ivanov, Critical Behavior of Nonideal Systems, WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim, 2008. pp. 9–42. [7] S.B. Rutin, P.V. Skripov, Apparatus for studying heat transfer in nanofluids under high-power heating, J. Eng. Thermophys. 21 (2) (2012) 144–153. [8] P.V. Skripov, A.P. Skripov, The phenomenon of superheat of liquids: in memory of Vladimir P. Skripov, Int. J. Thermophys. 31 (4–5) (2010) 816–830. [9] P.V. Skripov, Method of controlled pulse heating: applications for complex fluids and polymers, in: S. Rzoska, A. Drozd-Rzoska, V. Mazur (Eds.), NATO Science for Peace and Security Series – A, Metastable Systems under Pressure, Springer, Dordrecht, 2010, pp. 323–335. [10] S.A. Zhukov, S.Yu. Afanas’ev, S.B. Echmaev, Concerning the magnitude of the maximum heat flux and the mechanisms of superintensive bubble boiling, Int. J. Heat Mass Transfer 46 (18) (2003) 3411–3427. [11] M.J. Assael, K.D. Antoniadis, W.A. Wakeham, Historical evolution of the transient hot-wire technique, Int. J. Thermophys. 31 (6) (2010) 1051–1072. [12] R.A. Perkins, H.M. Roder, C.A. Nieto de Castro, A high-temperature transient hot-wire thermal conductivity apparatus for fluids, J. Res. Natl. Inst. Stand. Technol. 96 (3) (1991) 247–269.
Contents lists available at SciVerse ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer in supercritical fluids under pulse heating regime Sergey B. Rutin, Pavel V. Skripov ⇑ Institute of Thermal Physics, Ural Branch, Russian Academy of Sciences, Amundsena St. 106, Ekaterinburg 620016, Russian Federation
a r t i c l e
i n f o
Article history: Received 13 August 2012 Accepted 8 October 2012 Available online 3 November 2012 Keywords: Pulse heating Supercritical fluids Heat transfer intensity
a b s t r a c t The peculiarities of the heat transfer in supercritical fluids under short characteristic times scale has been studied experimentally. The constant heating power mode for the technique of controlled pulse heating of a wire probe was used for isobaric penetrating into the region of supercritical temperatures. The pressure range was (1–6)p/pc and the temperature range was (0.6–1.6)Tc, where subscript ‘‘c’’ corresponds to the critical point of a substance. The characteristic pulse length was 10 ms; the heat flux density through the probe surface was from 1 MW/m2 to 10 MW/m2. A sharp decrease in the heat transfer intensity for supercritical fluids with respect to that of subcritical liquids has been obtained. A high sensitivity of the heat transfer pattern to the reduced pressure values was revealed as well. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction In spite of a long history of studying the properties of supercritical fluids (SCFs) and heat exchange problems associated with their use as working fluids, many unresolved issues remain in this area of knowledge. Search for relevant solutions is motivated by the fact that hundreds of thermal power stations in the world operate on supercritical water, and the design projects for nuclear reactors cooled by supercritical water are currently discussed. In the fundamental book written by Pioro and Duffey [1], the data on heat exchange in SCFs over the past 50 years were analyzed. It has been shown that attempts to build up the theoretical model capable to describe all the modes of heat transfer in SCFs that were observed in the experiments so far failed. With all the virtues of experimental studies discussed in [1], they contain an irremovable obstacle, which follows from the fact of abnormally high compressibility of SCFs and leads to a significant in magnitude density distribution in the gravitational field. Galitzine [2], apparently, was among the first who faced an unusual density distribution of SCF up to 25% by volume of the measuring cell. In this experiment, the observation time was not too short, being about 1.5 h. Generally, in quasi-static experiments aimed at engineering applications, the action of several factors manifests itself, which extremely complicates the interpretation of the results. These factors include abnormal compressibility, nonlinearity of the properties and parameters of heat exchange (see, for example, [3,4]), the influence of gravitational field, as well as various kinds of instabilities, including the hydrodynamic instability. In order to overcome the effects of gravity, some experiments were carried out in outer space [5]. If the issues of the gravity effect on the results of ⇑ Corresponding author. Tel.: +7 343 3745442; fax: +7 343 2678800. E-mail address: [email protected] (P.V. Skripov). 0017-9310/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.10.027
quasi-static experiments, whose main purpose is to determine the critical indices, are the subject of discussion (see [6] and references therein), the effect of gravity on the results of experiments aimed at engineering applications is beyond question [1]. The specificity of SCFs behavior makes us to search new approaches for their study. The general idea of a technique presented in this paper is as follows: to create special experimental conditions in which the influence of gravity and macroscopic convection would be minimized and the temperature changing would be done over a wide range. The problem was solved by the use of the method of controlled pulse heating of a wire probe – resistance thermometer [7–9], which made it possible to compare the intensity of heat exchange of the probe with the environment in a wide range of sub- and supercritical states under strictly defined conditions of heating. The fundamental features of the technique are the high values of heat flux density and the relatively small length of the probing pulse. The range of pulse lengths was chosen from considerations on the one hand, of the sufficiency of the thickness of the heated layer for increasing sensitivity of the method and reducing influence of the heat capacity of the probe (which requires an increase in pulse length) and on the other hand, of minimizing the impact of macroscopic convection and gravity (which requires a decrease in pulse length). A compromise solution satisfying both conditions was the time range of the order of one to tens milliseconds. Indirect verification of the absence of the influence of gravity was performed as follows: the cell with the probe was positioned in the vertical and horizontal positions. In this case, the differences in the observed patterns of heat transfer were not identified. 2. Experimental An appropriate selection of the control algorithm is a key point in solving the problem, since it determines the possibility of simple
S.B. Rutin, P.V. Skripov / International Journal of Heat and Mass Transfer 57 (2013) 126–130
and clear interpreting the measurement results. Paper [10] may be cited as an example of appropriate choice of the method, where the authors managed to obtain new results related to the problems of superintensive bubble boiling. Analysis of variants has shown that such algorithm is a control of the electric power released in the heater-probe. The essence of the control algorithm can be written as follows:
UðtÞ ¼ k PðtÞ; where U(t) is the input pulse of the controlling voltage, P(t) is the power released at the probe in the course of heating, t is time, k is a constant coefficient. For U(t) = const, we have constant heating power mode. The main unit of apparatus is a fast PI controller with negative feedback, which allows maintaining the selected shape and amplitude of the electric power with high accuracy. In a series of
127
experiments at the chosen form of the controlling voltage pulse, the energy imparted to the probe–environment system at any time from the beginning of the pulse will be repeated with high accuracy. Thereby, the practical basis for direct comparison of the intensity of heat transfer by different samples under identical conditions of heat release in the probe is created. The rest of the apparatus is intended for recording the experimental data, calculations of the required quantities and for graphical representation of both the recorded and calculated data. As for the well-known transient hot-wire (THW) technique [11,12], the probe serves as a heater and a resistance thermometer simultaneously. The values of changing in time voltage drops across a standard resistor and the probe are the quantities recorded in the experiment. Calculated quantities are the current through the probe, the power released at the probe, the resistance of the probe and it’s averaged over the bulk temperature T as
Fig. 1. Characteristic probe temperature curves at the constant heating power mode for isopropanol (Fig. 1a). Pressure serves as a parameter. The insert illustrates the actual power values in the course of experiment. The derivatives of probe temperature with respect to time at the same pressures (Fig. 1b).
128
S.B. Rutin, P.V. Skripov / International Journal of Heat and Mass Transfer 57 (2013) 126–130
functions of time. A platinum wire applied in thermometry was used to make the probe. The diameter of the probe was 20 lm; its length was 1–2 cm. The probe was immersed in the fluid under investigation and hermetically sealed in the measuring cell. Pulse heating of the probe in the investigated medium was performed under isobaric conditions. The patterns of the probe temperature rise in time T(t) observed in the experiments give information about the heat exchange of the probe with the medium and make it possible to calculate the thermal resistance of the probe–environment system for any moment of time [7,8]. All presented results were obtained in the constant power mode that allows their clearest interpretation. In the experiments, the probe temperature rise in time for given values of the heating power and pressure was monitored. From these data we calculated
the heat flux density through the probe surface q = (P PPt)/pdl and the thermal resistance Rk(t) = DT(t)/q at a given exposure, where d and l are diameter and length of the probe, DT(t) is a temperature rise, PPt(t) is the power spent on heating the probe. In our experiments, the PPt value did not exceed 0.1P. The error of the probe surface area measurement pdl is an order of magnitude greater than that of other variables, so a relative version of the method was applied. In this case, since the measurements are performed at the same probe, the surface area is excluded from the calculations. Systematic error that is inherent in THW techniques due, in particular, to the end corrections and probe heat capacity is also substantially compensated. In the approximation of zero heat capacity of the probe that is appropriate in our experimental conditions, the problem reduces to finding
Fig. 2. Characteristic probe temperature curves at the constant heating power mode for diethyl malonate (Fig. 2a). Pressure serves as a parameter. The insert illustrates the actual power values in the course of experiment. The derivatives of probe temperature with respect to time at the same pressures (Fig. 2b).
S.B. Rutin, P.V. Skripov / International Journal of Heat and Mass Transfer 57 (2013) 126–130
the DTi/DT0 ratio for selected values of P and t, where the indices ‘‘i’’ and ‘‘0’’ refer to a number of pressure values, one of which (‘‘0’’) was chosen as the base pressure. The absolute values of P and T in our experiments are determined with estimated error of ±0.65% and ±1.0%, respectively. The error of determination of the relative thermal resistance (Rki/Rk0) appears to be on the order of 0.1%. Experimental procedure and the estimation of errors were discussed in detail elsewhere [7]. With regard to SCFs, measurement procedure was as follows: a cell with a probe filled with the investigated liquid was placed in a pressure chamber. Pressure served as a parameter in the experiments. The pressure range was chosen taking into account the pc value of the studied substance. The pressure was produced by hydraulic press and measured with a manometer. As explained above, the constant power mode is used with pulse length of about 10 ms. Characteristic thickness of the heated layer by the end of the pulse was (23) 105 m. The power value was chosen so that the probe was at supercritical temperature for not less than half of the pulse length. For each of the substances chosen power value remained unchanged until the end of the measurements. For each pressure the probe temperature rise T(t) for the chosen power level P(t) was recorded and then the relative thermal resistance of a substance reduced to its base value was calculated. The greatest pressure in the experiment was chosen as the ‘‘base’’ one. Raw files recorded during the measurement were smoothed using a cubic spline. From the smoothed T(t) files, the derivatives were calculated using software, their analysis provides additional information about the perturbations of heat transfer process in the transition to supercritical region.
3. Results and discussion Figs. 1 and 2 show the results of experiments for isopropanol and diethyl malonate, and Figs. 3 and 4 show the calculations of their relative thermal resistance (RTR) for different reduced pressures. As seen, the actual power values fall within a band of ±0.01%. Although these substances belong to different classes of organic compounds, a similarity of patterns of heat transfer is
129
observed in the given experimental conditions. When crossing the vicinity of the critical temperature during isobaric heating, the T(t) curves are deflected in the higher temperatures direction, indicating a decrease in heat transfer intensity. The derivatives oT/ot are also sharply deflected upward with respect to their extrapolated values into supercritical region. At p (1–2)pc, the maximums are formed on the graphs of derivatives. In general, the data presented in Figs. 1 and 2 lead to the following conclusion. A significant extension of the ‘‘beam’’ of T(t) curves indicates an abnormally high sensitivity of the intensity of heat transfer to pressure at supercritical parameters. The scale of such an extension exceeds the scale characteristic for subcritical temperatures by an order of magnitude. The pressure range (2.5–3)pc is likely to be transitional one. At exceeding these values of pressure, the T(t) curves and their derivatives take the form typical for the region of subcritical pressures. Maximums on the derivatives become more sloping and degenerate almost completely in the (2.5–3)pc region. We attribute this fact to a significant decrease in non-linearity of heat transfer parameters with increasing p/pc value. For the calculations of RTR, the maximum pressure in the experiment was chosen as the base one. In either case, the base pressure was about 6pc. For this choice, the determined variable on approaching from above to the critical pressure will have a positive value. Figs. 3 and 4 show the results of RTR calculations. For isopropanol, an increase in RTR was about 30% as the pressure decreased from the base one to (1.02)pc and for diethyl malonate, it was about 22% with decreasing pressure from the base one to (1.07)pc, which exceeds the change in RTR for subcritical temperatures in our experiments by an order of magnitude. The revealed sharp decrease in heat transfer intensity in the immediate vicinity of the critical temperature, as discussed above, is formally contradictory to the well-known concept of the critical enhancement of heat transfer in this region. We attribute this experimental fact to a substantial distinction of our approach to the experiments with SCFs. Our procedure made it possible to almost completely ‘‘switch off’’ the effect of gravity and macroscopic convection, which is unfeasible in the quasi-static experiments. It is correct to assume that heat transfer observed in our experiments
Fig. 3. The change in isopropanol thermal resistance in the course of pulse heating at different pressures (Rki) reduced to thermal resistance at the most high pressure (Rk0).
130
S.B. Rutin, P.V. Skripov / International Journal of Heat and Mass Transfer 57 (2013) 126–130
Fig. 4. The change in diethyl malonate thermal resistance in the course of pulse heating at different pressures (Rki) reduced to thermal resistance at the most high pressure (Rk0).
is a purely conductive. In our experiments, a radiation component of heat transfer is small due to the short length of the probe pulse, and it can be neglected.
4. Conclusion Application of the method of controlled pulse heating in the study of heat transfer in SCFs made it possible to obtain qualitatively new results: - Effect of the sharp decrease in heat transfer intensity in the isobaric approaching to the region of supercritical temperatures was found. The extent of this effect was surprisingly large; in this case, the closer is the pressure to the critical value, the greater is the sensitivity of heat transfer pattern to the reduced pressure. - The (2.5–3)pc pressure range is taken to be transitional one. At exceeding these pressures the heating curves and their derivatives take the form characteristic of the subcritical pressure region. Two hypotheses concerning the transition region can be formulated. First, at pressures above 2.5pc the heat exchange in actual heat-exchanging devices will not contain the typical instabilities and deteriorated modes peculiar to SCFs near the critical temperature. Taking into account the significant decrease in thermal resistance with increasing p/pc value (see Figs. 3 and 4), checking this hypothesis in the specially designed experiments becomes quite reasonable. Second, this transition zone can be considered as a transition between the gas-like and liquid-like states of SCFs, realizing the conventionality of these terms. Similarity of heat transfer processes for both studied compounds and the fact that heat transfer pattern at pressures above the transition region is indistinguishable from those for ordinary liquids at subcritical parameters point to such a possibility. To check this supposition and its possible generalization to a class of liquid
dielectrics, we plan to perform experiments with a set of substances with various properties.
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