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Thermal calculation and experimental corroboration of counter-flow tube-type evaporators and condensers of heat pumps operating on zeotropic mixtures

When using renewable heat sources that have limited volumetric heat capacity, for example, air, water, gases, the temperature of which changes significantly during cooling in the evaporator and heating in the condenser, execution of cycles for heat pumps operating on zeotropic mixtures, the temperature of which also changes, makes it possible to increase their energy efficiency. The paper proposes a technique for thermal calculation of counter-flow tube-type evaporators and heat pump condensers which use media with limited volumetric heat capacity as heat sources, and zeotropic mixtures as working substances. We carried out experimental corroboration of the proposed technique for thermal calculation of counter-flow tube-type evaporators and heat pump condensers, which confirms the validity of the developed mathematical equations of heat transfer in the “medium with limited volumetric heat capacity, i.e. propane-butane zeotropic mixture” system. Average deviation of experimental data from theoretical dependencies with a confidence level of 95% is 27.6%, which makes it possible to recommend them for use in design and operational practice.


Introduction
When using renewable heat sources with limited volumetric heat capacity (VHC), for example, air, water, gases, the temperature of which changes significantly during cooling in the evaporator and heating in the condenser of the heat pump (HP), the use of substances with constant temperatures of boiling and condensation as working agents is characterized by the decrease in the energy efficiency of the HP use [1][2][3]. At the same time, the implementation of a cycle with variable temperatures of heat sources (air, water, various gases) and working agents in the evaporator and condenser makes it possible to increase energy efficiency of the heat pumps use [4][5][6]. The use of working agents consisting of zeotropic mixtures with variable boiling points in the evaporator and condenser of the heat pump is the subject of the works written by A.A. Sukhikh, K.S. Generalov, I.A. Akimov [3], Bukin V.G., Kuzmin Yu.A. [4,5], Kim M., Ogurechnikov L.A., Mezentseva N.N. [10,11] and a number of other foreign authors [6][7][8][9]. In [10], the author concluded that tzeotropic mixture composition is significantly influenced by condensation temperatures in the condenser and boiling temperatures in the HP evaporator, which in their turn depend on the changing temperatures of heated and cooled media with VHC.
Analysis of the use of working substances as components of a zeotropic mixture in heat pumps showed that mixtures of R22/R142b, R290/600 (propane and n-butane), R600a/R601 (iso-butane and n-pentane), R290/R601a (propane and iso-pentane), R600a/R601b (iso-butane and n-pentane) meet the requirements [12,13] in terms of the degree of destruction of the Earth's ozone layer and production of the greenhouse effect and are considered completely safe in this respect.
In [14][15][16][17], the authors proposed to achieve the minimum value of difference between average condensation and boiling temperatures by selecting each of the two zeotropic mixture components with close physical properties and molar concentration of its low-boiling component l ψ z based on the dependence of its saturation temperatures in the condenser and the evaporator of the heat pump on the relative amount of the boiled mixture.
It has been proved that the temperatures of heated and cooled media with limited heat capacity have a significant influence on the choice of zeotropic mixture components and molar concentration value of the liquid phase of its low-boiling component l ψ z , at which the minimum value of the difference between the average condensation and boiling temperatures and the maximum HP energy efficiency are achieved. With frequent use of heat pumps in systems for heating the external inflowing air, the final temperature of the air heated in the condenser is taken as t = 20°C. In this case, the maximum energy efficiency is achieved when using heat pumps with zeotropic mixture "R290 (propane) -R600 (n-butane)" with molar concentration value of the low-boiling component R290 (propane) in the mixture equal to l ψ z = 42 mol % [16,17]. However, the existing works do not touch upon issues of thermal calculation and its experimental corroboration for evaporators and condensers of heat pumps operating on zeotropic mixtures.

Development of thermal calculation technique to determine the length of counter-flow tubetype evaporators and condensers of heat pumps operating on zeotropic mixtures of optimal chemical composition
As a rule, horizontal and low-inclined pipes or bundles of parallel-connected horizontal pipes are used in the heat pump technology for evaporation and condensation of zeotropic mixtures intended for heating and cooling media with VHC. It is known that the processes of evaporation and condensation in horizontal pipes proceed in the reverse sequence and are described by the same heat transfer equations, and also have z enlarged flow regimes of a vapor-liquid zeotropic mixture ( Figure 1) inside the pipe [18], where z is the number and name of the flow regime: z = 1stratified-cork; z = 2ringwave; z = 3dispersed. Thus, when liquid evaporates in a horizontal pipe (z = 1; 2; 3), first there is a stratified-cork flow regime (z = 1, section 3a and 3b, Figure 1), which, with an increase in the amount of evaporated liquid, turns into a ring-wave flow regime (z = 2, section 2a and 2b, Figure 1), and upon further boiling it turns into a dispersed (z = 3, section I, Figure 1) flow regime.
At the same time, during vapor phase condensation in a horizontal pipe (z = 3; 2; 1), on the contrary, first there is a dispersed flow regime (z = 3, section I in Figure 1), which, with an increase in the amount of condensed vapor, transforms into a ring-wave flow regime (z = 2, sections 2a and 2b, Figure 1), and upon further condensation it transforms into a stratified-cork flow regime (z = 1, sections 3a and 3b, Figure 1 (1)  The length of an individual z-th section of the counter-flow tube-type evaporator with complete evaporation of the zeotropic mixture inside the pipe and the condenser with its complete condensation is determined by the formula: where G is the estimated mass flow rate of the zeotropic mixture circulating in the evaporator and condenser, kg/h; Хz.e, Xz.b are the final and initial values of the dryness degree of the vapor-liquid mixture, at which there is a transition from one flow regime to another, unit fraction; int d is the inner diameter of the flow-through tube-type evaporator and heat pump condenser, m; kz(z) is the value of the heat transfer coefficient, as a function of the heat transfer coefficient, characteristic of stratifiedcork, ring-wave and dispersed flow regimes, W/(m 2 K); th is the heat transfer agent temperature, 0 С; tz is the current temperature of the vapor-liquid mixture, changing in the temperature range from tb.z to te.z in the evaporator and from te.z to tb.z in the condenser, 0 С; tb.z, te.z are the initial and final temperatures of the evaporated or condensed vapor-liquid zeotropic mixture in the areas, respectively, with stratified-cork, ring wave and dispersed flow regimes in the flow-through tube-type evaporator or condenser with the corresponding degree of dryness Хz.e and Хz.b, 0 C; rz.av, cz.av are, respectively, the average valuesof the latent heat of vaporization and specific heat capacity of the mixture in the intervals of its evaporation or condensation, respectively, in areas with stratified-cork, ring-wave and dispersed flow regimes, kJ/kg, kJ/kgK. When obtaining formula (2), the zeotropic mixture entering the evaporator with molar content of the low-boiling component in the liquid phase l ψ z , according to [15,16], completely boils away in the temperature range from tb.z=1 to te.z=3. In this case, for each of the indicated flow regimes, the mixture evaporation temperature changes in the following ranges: stratified-cork regimete.z=1>tz=1 >tb.z=1; ringwave regimete.z=2 >tz=2 >tb.z=2; dispersed regimete.z=3 >tz=3 >tb.z=3. The supplied heat flux consists of both the heat of the mixture vaporization and the heat of its heating in the temperature range of its complete evaporation from tb to te. completely condenses in the temperature range from te.z=3 to tb.z=1. In this case, for each of the indicated flow regimes, the mixture condensation temperature changes in the following ranges: dispersed regimete.z=3 >tz=3 >tb.z=3; ring-wave regimete.z=2>tz=2>tb.z=2; stratifiedcork regimete.z=1>tz=1 >tb.z=1. The removed heat flux arises both due to mixture condensation and cooling in the temperature range of its complete condensation from te.z=3 to tb.z=1.
Specific heat capacities and latent heats of vaporization of the zeotropic mixture saturated vapor phase in the ranges of existence of stratified-cork, ring-wave and dispersed flow regimes are taken as constant and equal to their average values, that is: сz=1.av, сz=2.av, сz=3.av and rz=1.av, rz=2.av, rz=3.av.
Changing the flow regimes and the content of the low-boiling component in the vapor and liquid phases of the vapor-liquid mixture leads to a change in the value of heat transfer coefficient between the inner surface of the heat exchange pipe and the zeotropic mixture. In this case, for each of the indicated flow regimes, the content of the low-boiling component in the liquid phase l ψ z changes in the following ranges: The heat transfer coefficient kz(z) for the evaporator and the condenser varies within the same Using the equation (2) in the formula (1)   .int z  are, respectively, internal heat transfer coefficients for stratified-cork, ring-wave and dispersed flow regimes, determined according to [21], W/(m 2 K); do, dint are, respectively, the outer and inner diameters of the evaporator and condenser, m, determined using the measurement data;  is the thermal conductivity coefficient of the evaporating pipe coil, W/(mK); . o z  is the external coefficient of heat transfer from the outer surface of the evaporator and condenser pipes to the heat transfer agent for the case of its forced flow in the tubular annulus during longitudinal washing, determined according to [20], for the case when the heat transfer agent flows in the tubular annulus (a pipe with a smaller diameter is located in a pipe of a larger diameter) , W/(m 2 K).
In the stratified-cork flow regime (with a predominantly clear contrast between the vapor and liquid phases of the propane and butane mixture), the heat exchange mechanism is similar to heat transfer during high-volume boiling of liquid [20]. Defining the average value of the heat transfer coefficient   The final degree of dryness corresponding to transition boundary of stratified-cork flow regime into ring-wave flow regime was determined on the basis of the Baker diagram [18,24] and was  [20], is determined similarly as for the case of single-phase flow of dry saturated vapor:

Experimental corroboration of the thermal calculation technique for determining the length of counter-flow tube-type evaporators and condensers of heat pumps operating on zeotropic mixtures of optimal chemical composition
In order to corroborate the validity of equations (1) -(7) for determining the length  1sample pressure gauge; 2heat transfer agent flow meters; 3three-way valve; 4shut-off and control valve; 5thermal converter-sensor for determining the temperature of zeotropic mixture at the inlet and outlet of the evaporator pipe; 6prototype for determining the evaporator pipe length; 7outer case with heat transfer agent for evaporator pipe 6; 8thermal converter-sensor for determining the temperature of heat transfer agent at the inlet and outlet of case 7 of evaporator pipe 6; 9prototype for determining the condenser pipe length; 10outer case with heat transfer agent for condenser pipe 6; 11thermal converter-sensors for determining zeotropic mixture temperature in the evaporator pipe; 12thermal converter-sensors for determining the heat transfer agent temperature in case 7 of the evaporator pipe; 13multichannel temperature meters; 14laptop; 15thermal converter-sensors for determining zeotropic mixture temperature in the condenser pipe; 16thermal converter-sensors for determining the heat transfer agent temperature in case 10 of the condenser pipe 9; 17thermal valve; 18compressor with electric drive; 19turbulator and vortex flow meter of the zeotropic mixture vapor phase; 20signal processing unit; 21recorder of measured values; 22interface. Evaporative and condensing heat exchangers here are made of straight steel pipes with the inner diameter of 6,0 mm and length of 5500 mm. To reduce heat loss, the outer surface of pipes 7 and 10 was covered with thermal insulation.
The stand has a system for monitoring the equipment parameters in the process of conducting experiments and automatically taking readings from sensors placed on the experimental equipment.
Primary sensors provided the following measurement accuracy: temperature -0.1 °С; pressurenot less than 0.0025 MPa; consumptionnot less than 1.5% of the maximum value. Heat exchangers of the "pipe-in-pipe" type are installed on the stand. Considering higher intensity of heat transfer from boiling or condensed zeotropic mixture as compared to cooled or heated water, tube-type evaporators and condensers on the side of the outer surfaces had evenly placed pins obtained by deforming cutting technology. This form of finning allows implementing the principle of counterflow flow of the zeotropic mixture and hot water in the "pipe-in-pipe" heat exchanger. . z L , we used the temperature distribution analysis in the evaporator and condenser pipelines during boiling and condensation of zeotropic mixture. The obtained temperature distribution of the vaporliquid mixture was used to determine the boundary of the evaporation and condenser sections for each of the regimes with any predetermined accuracy. Zeotropic mixture boiling in the flow-through system occurs within temperature range starting at tb.z=1 and ending at te.z=3 and, vice versa, condensation begins at te.z=3 and ends at tb.z=1. To determine the boundaries of the evaporating and condensing sections of each of the regimes, it is necessary to find points on the pipeline where the temperature values of the vapor-liquid mixture tz can be found: tb.z=1; te.z=1; te.z=2; te.z=3.
The values of the initial, current and final temperatures of condensation tz in the condenser in the It should be noted that the discrepancy associated with the use of the calculation formula (8), based on the laws of Dalton, Raoul and Antoine's correlation, using the measurement data is 4,5% [15,16] for zeotropic mixtures, and for saturated hydrocarbons with the absolute pressure of up to 1,0 MPa in particular.
The equipment we used todetermine zeotropic mixture temperatures tb.z=1; te.z=1; te.z=2; te.z=3 in the tube-type evaporator and condenser, included the following elements ( Figure 2 where the lengths Lz=1, Lz=2, Lz=3 are found according to the formula (2). In order to obtain a unified theoretical line for the HP evaporator and condenser, we carried out the calculations at the same temperature differences between water and zeotropic mixture.
It can be seen from the diagram (Figure 3) that the main amount of the liquid phase Хz=2 = 68% (points 4 → 5 → 6) boils away (condenses) in the section with the ring-wave flow regime. In this case, only Lz=2.о = 45,8% (points 4 → 5 → 6) of the total length of the evaporator (condenser) falls on the section with the ring-wave flow regime. A decrease in the relative length in this section is explained by the increase in the heat transfer coefficient due to the onset of the wave-ring flow regime, when the liquid phase washes the entire inner surface of the evaporator (condenser). It also follows from the diagram (Figure 3) that in the section with the dispersed flow regime, only Хz=3 = 2% of the liquid phase boils away (points 7 → 8 → 9). In this case, the section with the dispersed flow regime accounts for more than Lz=3.о = 16,4% (points 4 → 5 → 6) of the total length of the evaporator (condenser). A sharp increase in the relative length in this section is explained by the decrease in the heat transfer coefficient, due to the onset of the dispersed flow regime, when all liquid droplets are carried away from the boiling film located on the inner surface of the pipe into the vapor core of the liquid flow, and the inner surface of the pipe is washed only by the vapor phase of the propane and butane mixture.
For reference, the diagram shows the experimental values of the relative lengths of the evaporator and condenser. In order to obtain uniform experimental values for the HP evaporator and condenser, we carried out the experiments at the same temperature differences between water and zeotropic mixture. Each experimental point shown in the diagram is taken as common for the evaporator and condenser, i.e. averaged over four measurements (n = 4) for the evaporator and over four measurements (n = 4) for the condenser. The reliability of results is taken as  = 0.9, and the value of