Heat transfer in a round channel with circulation of a non-azeotropic mixture

05015


Introduction
The use of mixtures as refrigerants and heat carriers in various energy systems has become widespread [1-3].The thermophysical properties of the mixture differ from the properties of individual components.It should be noted that vaporization in one-component liquids and non-azeotropic mixtures proceeds differently.The volatility coefficient for the components of a nonazeotropic mixture varies significantly.During nucleate boiling of a non-azeotropic mixture, a light-boiling component releases intensively, which leads to a change in its concentration both in the liquid and vapor phases.This causes a change in the local partial pressure and an increase in the temperature gradient between the wall and the temperature of mixture saturation.In addition, boiling of a non-azeotropic mixture is characterized by the diffusion processes due to the concentration gradient in the superheated liquid layer near the wall and near the liquid-vapor interface.Both factors lead to a significant decrease in the heat transfer intensity during boiling [4].The studies on vaporization during circulation of a nonazeotropic and azeotropic alcohol-water mixture in the range of mass flow rates of 300-800 kg/m 2 s and a heat flux density of 9000 W/m 2 are presented in [5,6].
The experimental studies on subcooled alcoholwater mixture boiling are described in [7].It is shown that at subcooled quasi-pool boiling, the critical heat fluxes of mixtures depend strongly on the mass concentration of alcohol.Alcohol-water mixtures accelerate vaporization beginning and increase heat fluxes due to the Marangoni effect created by the difference in concentrations at the vapor-liquid interface.The paper [8] presents the results of experimental determination of the heat transfer coefficient during flow boiling of a non-azeotropic R455A mixture and the pressure drop in a smooth round horizontal stainless steel tube with an inner diameter of 6 mm.The results show an increase in the heat transfer coefficient with an increase in the heat flux.As the saturation temperature increases, the heat transfer coefficient decreases.It is shown that the pressure drop increases with the mass flow and decreases with the saturation temperature of the mixture.The authors of [9] describe the results of experimental determination of the heat transfer coefficient and the pressure gradient when a non-azeotropic mixture boils in a horizontal tube.Comparisons were made with a single-component refrigerant.The effect of mass flow and vapor quality on the heat transfer coefficient was also investigated.As a result, the value of the heat transfer coefficient varied in proportion to the vapor quality and the saturation pressure.The results of experiments show that the values of heat transfer and pressure gradient for a nonazeotropic mixture are significantly higher than for a single-component refrigerant.The authors of [10] studied experimentally the characteristics of heat transfer during flow boiling of R1234ze (E)/R152a (40/60 wt.%) in a horizontal smooth copper tube with an inner diameter of 6 mm.The effect of mass flow, saturation temperature, heat flux, and vapor quality on the heat transfer coefficient at boiling and critical vapor quality was evaluated.It is found that the boiling point increases with heat flux or saturation temperature, but it first decreases and then increases with increasing mass flow.It was shown that the boiling point initially remained almost constant, but then it decreased with increasing vapor quality.The authors of describe experimental studies with a non-azeotropic R454C mixture.The effect of operating parameters in terms of mass flow, heat flux and saturation pressure is discussed.Mass velocity and heat flux have a positive effect on the heat transfer coefficient for in-flow boiling, while the saturation pressure has a negative effect on boiling performance.
This paper presents investigation results on the intensity of heat transfer to a non-azeotropic alcoholwater mixture with forced circulation in a round heated channel.

Set-up and method description
The study was carried out using the test set-up shown schematically in Fig. 1.The studies were carried out in a stainless steel channel (1).The inner diameter of the channel was 7.6 mm; the wall thickness was 0.2 mm.The channel was heated by direct heat release in the wall due to the electric current (Iheater).The length of the channel was 4 m.
Thirteen thin-film platinum resistance thermometers HEL-700 (2) were mounted along the channel length on the outer side of the wall to measure the wall temperature.Three of them were mounted along the upper generatrix of the channel, and other 10 thermometers were mounted along the lower generatrix.To measure the difference of the flow temperature along the channel length, the thermometers were installed at the inlet to the heated part of the channel (Tin) and behind the heated part of the channel (Tout).Pressure sensors were installed at the beginning (Pin) and at the end (Pout) of the channel.The pressure was also measured in a storage vessel (Pvessel); the liquid from this vessel was supplied to the working section and a single-or twophase flow returned there after passing through the channel of the working section.A heat exchanger (3) was installed in this vessel to evacuate the working section heat from the closed system.A cryothermostat (4) was used to organize coolant circulation through the heat exchanger.The studied mixture circulation was carried out by an immersion centrifugal pump (5) located directly in the storage vessel.A turbine flow meter ( 6) was installed at the working section inlet.Behind the working section, in the return path, a glass optical section (7), registering the two-phase flow formation, was mounted.The working section and the return path were thermally insulated using a foamed rubber material with a thermal conductivity coefficient of 0.038 W/m 2 K at 20С.The side surface of the storage vessel was thermally insulated with polyethylene foam.The experiments were carried out under conditions of inherent vapors in a closed volume.For this purpose, the set-up cavity underwent vacuum evacuation before filling the vessel with the test liquid.During the experiment, the following values were measured: -wall temperature distribution along the channel length; -the liquid temperature at the heated channel inlet and outlet behind the heated region; -the absolute pressure at the channel inlet, at the channel outlet and in the upper part of the storage vessel; -the voltage drop along the channel length and the amount of electric current through the channel; the volumetric flow rate of liquid at the channel inlet.
Data were collected using two precision ADC modules of brand LTR114.

Results and discussions
The studies presented in this paper were carried out using a non-azeotropic alcohol-water mixture with a mass concentration of ethanol of 20%.In this series of experiments, the absolute pressure in the vessel was maintained within 0.050.001MPa.The range of liquid mass flow rates through the channel was 44-46 kg/m 2 s, the heat flux density was 1260-11981 W/m 2 .The Reynolds number varied in the range of 240 -400, and the Grashof number in the range of 11000 -300000.The distribution of the wall temperature along the channel length at various thermal loads and close mass flow rates of mixture are shown in Fig. 2.
the diagram, different symbols show the experimental data of the wall temperature distribution along the working section length at 5 different heat flux densities.The heat flux value in W/m 2 is indicated in captions.The temperatures measured along the lower generatrix of the channel are given by light symbols, and those measured along the upper generatrix of the channel are given by filled symbols.The temperature at a coordinate of 4 m corresponds to the thermometer readings outside the heated wall and is determined by the temperature of mixture at the channel outlet.For each heat flux density, the calculated lines of liquid heating in the channel are plotted in the diagram Tcalc.The value of the heat flux density for each line is indicated in captions.Liquid heating was calculated on the basis of a single-phase flow at the corresponding mass flow rate and heat capacity of mixture at an average temperature.Based on the assumption of a linear change in pressure along the channel length and pressure sensor readings Pin and Pout, as well as the assumption of concentration constancy along the channel length, the equilibrium temperature lines are plotted for three values of mixture mass concentration: 0% (single-component water), 20% (test mixture) and 95% (alcohol, azeotropic mixture).These lines are landmarks for the existence of a two-phase flow.Below the 95% limit, only a single-component liquid can exist; above the 0% limit, the vapor phase is predominant.Under conditions of a slight non-equilibrium of the processes, the temperature of the two-phase mixture will approach the equilibrium temperature of mixture corresponding to given local pressure and local concentration.
As it can be seen from the diagram, for different heat flux densities, temperature distributions along the channel differ.At a heat flux density of 1260 and 3065 W/m 2 (mass flow rate of 44 kg/m 2 s), liquid heating along the channel length (thermometer reading at X=4 m) does not exceed the equilibrium temperature for alcohol (mass concentration of 95%).Thus, a singlephase flow occurs in the channel, and the wall temperature distribution is linear.At that, the local temperature difference between the wall on the upper generatrix of the channel and the calculated temperature of liquid at the corresponding coordinate of the channel is more than twice the temperature difference on the lower generatrix of the channel.At the given heat flux densities, the vapor phase is not observed in the optical section.
At heat flux density q = 5035 W/m 2 (mass flow rate of 46 kg/m 2 s), the calculated value of single-phase liquid heating at the channel outlet exceeds not only the equilibrium temperature for the mixture under study, but also the equilibrium temperature for water.In the diagram, this is observed from the behavior of temperature distribution along the channel length.Thus, the conditions for vapor phase formation are implemented in the channel.In the diagram, this is observed from the character of temperature distribution along the channel length.At coordinate X = 3 m, the calculated liquid heating reaches the equilibrium temperature of the studied mixture.Before this coordinate, the wall temperature distribution is linear, almost equidistant to the line of calculated heating, and this characterizes single-phase heat transfer.After coordinate X = 3 m, stabilization of the wall temperature is observed, which characterizes the intensive process of vaporization.A significant amount of the vapor phase is observed in the optical section (Fig. 3a).The temperature of the two-phase flow at the channel outlet corresponds to the equilibrium temperature of the mixture.The temperature difference on the upper generatrix in the regime of single-phase heat transfer (X < 3 m) is significantly higher than the temperature difference on the lower generatrix.In the region of heat transfer with phase transition (X > 3 m), the temperature difference on the upper generatrix is significantly lower than the temperature difference on the lower generatrix.At heat flux densities q = 9098 and 11981 W/m 2 (mass flow rates of 44 and 46 kg/m 2 s, respectively), the character of temperature distribution along the channel length is similar to the distribution at q = 5035 W/m 2 .The heating of liquid to the equilibrium temperature of the studied mixture under study occurs at X = 1.5 and 1.15 m, respectively.However, the temperature of the two-phase flow at the channel outlet exceeds the mixture equilibrium temperature.This effect is explained by intense vaporization (Fig. 3b, c) over a long channel length, which causes the loss of a significant part of the volatile component by the liquid phase, and this leads to an increase in the saturation temperature.
The heat transfer coefficient to a subcooled singlephase liquid is determined through the temperature difference between the wall and the flow core, and in the case of two-phase heat transfer, the temperature difference between the wall and the liquid saturation temperature is used.Therefore, to determine the temperature difference, it is necessary to separate the regions of single-phase and two-phase heat transfer.In this case, we take the coordinate X1, corresponding to the point of intersection of the line of calculated liquid heating with the line of the equilibrium temperature of the 20% alcohol-water mixture, as the boundary.The local temperature difference in the region X < X1 is determined as the difference between the wall temperature and the calculated liquid temperature.Since the concentration of mixture changes during of a highly volatile component, this effect should be taken into account to some extent.This work assumes a linear change in the equilibrium temperature from coordinate X1 to coordinate X = 4 m with a change in the liquid temperature at the channel outlet, Tout.The temperature difference is determined as the difference between the wall temperature and the equilibrium temperature of mixture with a variable concentration of the volatile component, determined by the method described above.The heat transfer coefficients  calculated by this method are shown in (Fig. 4).The local heat transfer coefficients on the lower generatrix of the channel, calculated for the region of single-phase convection, are shown in the diagram with blue symbols.The region where the phase transition occurs is shown with yellow symbols.The heat transfer coefficients calculated from the readings of thermometers on the upper generatrix of the channel are shown with green symbols.As it can be seen from the diagram, in the region of single-phase convection, the heat transfer coefficient increases with an increase in the heat flux density.At the same time, on the upper generatrix of the channel, the heat transfer coefficient is two or more times lower than that on the lower generatrix.In the phase transition region, on the contrary, the heat transfer coefficient on the upper generatrix is significantly higher than on the lower generatrix.
An increase in the saturation temperature at the channel outlet indicates evaporation of a significant amount of mixture with a significantly higher concentration of the volatile component.The vapor quality at the channel outlet can be approximately estimated based on the heat and mass balance.Since, after reaching the X1 coordinate, the entire volume of liquid in the channel warms up to the saturation temperature; then all the heat released is spent on phase transformations.If we neglect the arising fluctuations of the flow velocity in the channel and assume the constancy of the mass flow rate over the channel crosssection, then we can determine the value of enthalpy at the channel outlet.The value of specific enthalpy i for q = 5035, 9098 and 11981 W/m 2 is 371 kJ/kg, 596 and 717, respectively.The mass vapor quality  is determined based on this enthalpy and tabulated enthalpy data for the liquid and vapor phases on the equilibrium line [12], and the mass concentration of the volatile component in liquid Cx and vapor phases Cy is calculated using the vapor quality under the condition of an equilibrium state.The concentration is used to determine the equilibrium temperature Ts, which corresponds to the pressure at the channel outlet.These values are given in Table 1.The Table also shows the experimentally measured temperature at the outlet of the channel, in its unheated part Tout .According to the comparison of the measured temperature Tout and the calculated temperature Ts, the calculation is in good agreement (within 0.25C) with the experiment.Consequently, at mass flow rates of 44-46 kg/m 2 , conditions close to equilibrium are observed in the channel.

Conclusions
With a single-phase flow of an alcohol-water mixture in a round channel, the heat transfer coefficient on the upper generatrix of the channel is significantly lower than the heat transfer coefficient on the lower generatrix.Under conditions of phase transition, the heat transfer coefficient on the upper generatrix of the channel is significantly higher than the heat transfer coefficient on the lower generatrix of the channel.The heat transfer coefficient on the lower generatrix in the single-phase flow is approximately twice as high as in the two-phase flow.With intense vaporization over a considerable length of the channel, the entrainment of the volatile component leads to an increase in the equilibrium temperature of the liquid phase, which indicates a significant decrease in the volatile component concentration.It is shown that at a mass flow rate of 44 -46 kg/m 2 , the calculation of a change in the mixture composition, carried out under the conditions of liquid and vapor phase equilibrium, corresponds satisfactorily to the experimental data.

Table 1 .
Measured and calculated parameters.