A Regressive Model for Periodic Dynamic Instabilities during Condensation of R1234yf and R1234ze Refrigerants

Abstract

This paper presents the results of experimental research and mathematical modelling in terms of the influence periodic dynamic instabilities have on condensation phase change in R1234yf and R1234ze refrigerants in tubular minichannels. The main reason for this research was the fact that under the Montreal Protocol (1986), as well as Regulation No 517/2014 of the European Parliament and of the Council of 16 April 2014, the F-gases such as hydrofluorocarbons (HFC), perfluorocarbons (PFC), sulphur hexafluoride, and other agents containing fluorine have to be withdrawn. This includes one of the most commonly used refrigerants—R134a—which, since 1 January 2017, has already been withdrawn. It also includes the R404A refrigerant. R1234ze and R1234yf are suggested as substitutions for R134a. The basic parameters determining the application of those agents are their global warming potential (GWP) indicator, which is below 150, and reduction in fluorinated greenhouse gases emission by a third, simply by withdrawing them (with 2010 as a reference level). The current state of knowledge enables researchers to foresee the influence of some hydrodynamic instabilities on the condensation of fluorinated refrigerants in minichannels. Therefore, an expansion of this knowledge regarding the suggested substitutes is absolutely necessary. Research concerning the condensation in minichannels under dynamic instabilities was already conducted for the refrigerants currently being withdrawn. However, the influence of those instabilities on a phase change in the suggested pro-ecologic substitutes is not known. It is known that during the condensation of refrigerants under dynamic instabilities, the propagation of instabilities occurs in a waveform. Two-phase media are particularly susceptible to this phenomenon. Propagation of instabilities in the form of acoustic wave or wave change in other parameters such as temperature, the density of mass, or heat flux plays a special role. All of them have their own characteristics, with evidently different propagation velocities. Both mechanisms include irreversible dissipation and dispersion. The dissipative effects, by their irreversibility, cause entropy generation and dump the instability propagation in a two-phase medium. The dispersive effects influence the instability propagation that is a function of the generation frequency. Besides the experimental results, the paper contains a dimensional analysis procedure based on the Π–Buckingham theorem that has allowed for the development of a regressive model for the velocities of pressure dynamic instabilities. The experimental part of this paper was conducted using tubular minichannels with an internal diameter of d_ID = 1.40–3.3 mm.

1. Introduction

After 50 years, the era of the application of chlorinated refrigerants (freons) is coming to an end. It is a direct result of the introduction of environmental regulations. There are two significant international agreements concerning substitutes (replacement) of refrigerants used so far—the Montreal Protocol (1987) and provisions from the Earth Summit in Rio de Janeiro (1992). Under the Montreal Protocol, with subsequent amendments (Helsinki (1989), London (1990), Vienna (1995), etc.), due to their destructive influence on the stratospheric ozone layer, R12 (CFC type), R22 (HCFC type), and other freons were withdrawn in 2010. The following two indicators were introduced to describe the environmental impact of the refrigerants:

• ODP—ozone depletion potential, expressed as a ratio with the reference level R11 (ODP = 1);
• GWP—global warming potential, expressed as a ratio with the reference level CO2 (GWP = 1).

In the EU, changes were enforced by Regulation No 517/2014 of the European Parliament and of the Council of 16 April 2014. Under this regulation, the F-gases have to be withdrawn. For example, the most commonly used refrigerant—R134a—had to be withdrawn by 1 January 2017, which was related to the limiting value of the GWP indicator—150 (GWP R134a = 1430). New regulations will lead to a reduction in greenhouse gases emission by 80–90% by 2050 (reference level 1990). It will prevent climate change, and the average global temperature rise will not exceed 2 K. By 2030, the emission of fluorinated greenhouse gases should be reduced by a third (reference level 2010), simply by withdrawing them [1,2,3]. Therefore, it is necessary to investigate the influence of hydrodynamic instabilities on phase change in suggested substitutes (replacement) of withdrawn gases, especially condensation in pipe minichannels [4]. A study was also conducted to investigate the condensation heat transfer coefficient of R1234ze(E) and R134a near the critical point [5]. It was found that condensation heat transfer coefficients of R1234ze(E) and R134a decreased with an increase in reduced pressure. The influence of mass flux on refrigerants decreased with an increase in reduced pressure. The authors noted that the dominant parameter for the condensation heat transfer coefficients is the interfacial shear stress between the liquid film and the vapour core. However, the effect significantly decreases with an increase in the reduced pressure. Travis model was used to describe the HTC with good agreement. The process was also studied in relation to condensation heat transfer performance, and integrated correlations of low GWP refrigerants in plate heat exchangers were also investigated [6]. The authors analysed the effects of mass flux, heat flux, and condensation pressure according to mean vapour quality on the condensation heat transfer coefficient and frictional pressure drop for plate heat exchangers with different chevron angles. It was noted that the heat transfer coefficient increased with the heat flux, mass flux, and mean vapour quality, but it decreased with an increase in the condensation pressure. The frictional pressure drop also showed similar trends to those of the heat transfer coefficient. Authors developed integrated correlations for R124, R1233zd(E), R1234ze(E), R134a, and R410A, in agreement with research data. Investigated falling film evaporation of R1234ze (E) on horizontal enhanced tubes was presented in another study [7]. The authors found that the influence of heat flux on the heat transfer performance of falling film evaporation is influenced by spray density. The effect of evaporation temperature on the heat transfer performance of falling film evaporation is mainly reflected in the changes in the thermophysical properties of refrigerants. Measured vapour–liquid equilibrium properties of binary mixtures of the low-GWP refrigerants such as R1123 and R1234yf were presented in a paper by [8]. The authors provided a regression analysis using the binary interaction parameter of the modified Peng–Robinson equation [9]. The experimental vapour–liquid equilibrium data were reproduced by developing a correlation with one parameter of the modified Peng–Robinson equation of state. In a plate heat exchanger for organic Rankine cycle units, flow boiling heat transfer and pressure drop characteristics of R134a, R1234yf, and R1234ze were studied in a paper [10], the authors of which compared experimental data with few existing correlations and developed their own correlation with good agreement.

This paper presents the issues concerning phase changes in condensation inside minichannels, which were investigated for R134a refrigerants, as well as for their substitutes R1234ze and R1234yf, respectively. This is because the refrigerants are used as a working fluid for a wide spectrum of applications—namely, heat pumping, refrigeration, and air conditioning (both stationary and mobile) [11,12].

The results obtained by the authors of this paper are important from the point of view of designers and developers of new compact heat exchangers built on the basis of minichannels. The proposed regression equations allow taking into account the impacts of the nature of the so-called hydraulic impacts having destructive effects on structures.

2. Subject of the Research

The subjects of experimental studies were R1234ze and R1234yf isomers as substitutes for R134a refrigerants. R1234 refrigerants are fluorinated propylene isomers containing unsaturated compounds (of double bond type carbon–carbon) belonging to the group of olefins or alkenes. They are identified by the symbol R (refrigerant) and symbols HFO (hydrofluoroolefins), HFA (hydrofluoroalkines), and HFC (hydrofluorocarbons). In particular, for refrigeration applications, two isomers were distinguished—namely, 2, 3, —tetrafluoropropene ((R1234yf) and 1, 3, 3, 3—tetrafluoropropene (R1234ze(E)) [4,13,14,15]. They were proposed as direct substitutes for the R134a refrigerant, especially in car air conditioning systems (R1234yf) and as a potential substitute in systems with high evaporation temperature (R1234ze).

Investigations of the influence of periodical instabilities of dynamic character on the condensation process of R1234 isomers in pipe minichannels were carried out on a test stand, the diagram of which is presented in Figure 1 [16,17].

Figure 1. Photo of the apparatus [16,17].

Figure 1. Photo of the apparatus [16,17].

2.1. Subject of Research

The subject of the research was horizontal, tube minichannels, made of AISI 304L steel. The internal diameter of minichannels was d_iD = 1.40–3.3 mm. The length of the minichannels was L = 1000 mm. Three homogeneous refrigerants were investigated—R134a, R1234ze, and R1234yf. The section of the minichannel was cooled with water, at a flow velocity varying v = 0.002–0.02 ms⁻¹. The refrigerants were supplied with set and timed thermal and flow parameters. The minichannels were placed in a water channel 28 mm high and 24 mm wide. The structure of the test stand enabled the measurement of refrigerants’ temperature, pressure, the temperature of the channel wall, and cooling water, all along the measuring section. The scope of research was described in details in Table 1. The mass flow of the refrigerant and coolant was also measured.

2.2. Test Stand

In order to determine the local and average values of the heat transfer coefficient, the experimental data for condensation of homogeneous refrigerants data were collected in the range of parameter changes shown in Table 1.

Table 1. The scope of research.

Parameter	Values
Internal diameter di (mm)	1.40–3.3
Mass flux density G (kg·m−2s−1)	300–550
Heat flux density q (W·m−2)	35,000–80,000
Vapour quality x (-)	1–0
Refrigerant	R134a; R1234ze; R1234yf
Refrigerant/coolant flow direction	Counter-current

Table 1. The scope of research.

Parameter	Values
Internal diameter di (mm)	1.40–3.3
Mass flux density G (kg·m−2s−1)	300–550
Heat flux density q (W·m−2)	35,000–80,000
Vapour quality x (-)	1–0
Refrigerant	R134a; R1234ze; R1234yf
Refrigerant/coolant flow direction	Counter-current

The superheated vapour of refrigerant was forced into the minichannel by means of a reciprocating compressor. An exchanger was installed before the inlet of the measuring section in order to obtain the desired degree of vapour quality. The vapour quality was calculated on the basis of its thermal balance. The calculation procedure has been described in detail in [18,19]. The intensity of the heat transfer varied depending on the flow rate of the exchanger cooling medium (water). The pressure of refrigerant was measured at the inlet and outlet of the measuring section (Figure 2), with pressure sensors and an Endress + Hauser PMP 131-A1401A1W transmitter, manufactured in measuring class 0.5.

Another heat exchanger was placed to ensure a homogenous liquid at the end of the measuring section. The refrigerant flowed through the Coriolis 34XIP67 flowmeter in measuring class 0.52 after being cooled in the second heat exchanger. The mass flow rate of water was controlled by a solenoid valve. The measurement uncertainty was determined in accordance with the calculation procedure described in [20]. The value of the heat transfer coefficient uncertainty was 8%. Figure 3 shows the framework of the test stand.

The heat balance data were burdened with a ±5% measurement error of the heat flux, which confirmed the correctness of the conducted experimental research. The sensors and measuring equipment uncertainty are shown in

Table 2. The measuring device uncertainty.

Measured Variable	Device	Measuring Range	Max. Uncertainty
Refrigerant mass flow	Coriolis effect mass flow meter	0–450 (kg·h−1)	±0.15%
Absolute pressure	Piezoresistive sensor	0–25 (bar)	±0.05%
Electric power	Electrical measuring transducer	0–20 (kW)	±0.25%
K type termocouple	TP-201K-1B-100	−40–+475 (°C)	±0.2 K
T type termocouple	20102-2	−40–+133 (°C)	±0.2 K

.

3. Methodology and Experimental Research

The theory on the dispersive character of periodic instabilities is available in the literature. It explains how the frequency of disturbances influences the velocity of the pressure wave and the condensation front.

The curve shown in Figure 4 has two characteristic limits. The first limit is called the equilibrium velocity and is expressed as follows:

v_eq. = v(ω→0)

(1)

Figure 4. Pressure wave velocity as a function of frequency for conventional channels, Moody diagram [11,12,21,22].

Figure 4. Pressure wave velocity as a function of frequency for conventional channels, Moody diagram [11,12,21,22].

This represents a case in which the wave period is longer than the time of reestablishing the thermodynamic equilibrium, the so-called relaxation time, and the pressure wave travels relatively slowly. The second limit is called the frozen velocity, expressed as

v_fr = v(ω→∞)

(2)

where ω is the circular frequency (pulsation) of a disturbance, ω = 2πf; the value f determines the number of cycles of a periodic phenomenon occurring in a unit of time, with $f=\frac{1}{T}$, where T is the period between the occurrence of the same phase in a vibrating movement.

As regards physical terms, T is the wave period equal to the period of propagating vibrations, whereas k is the wavenumber defined by the following relationship developed in several publications [11,12,21,22]:

$$k=\frac{2\pi }{\lambda },$$

(3)

where λ is the wavelength.

Equation (2) represents a case in which the wave period is shorter than the relaxation time, and the pressure wave travels much faster.

The term relaxation time refers to the balanced state of a system, that is, without interactions with the environment (isolated); however, the phenomenon can be referred approximately to transients. Relaxation processes consequently lead to medium dispersity, which is reflected by the propagation of disturbances at the phase velocity calculated from the relationship developed by [21] as follows:

$$v_f\left(\omega \right)=\frac{\omega }{k\left(\omega \right)}$$

(4)

Figure 5 defines the research object with inputs on the left, outputs on the right, constants at the bottom, and noises at the top. The input values (the variables) were the internal diameter of the channel and cutoff valve timings. The output values (the results) were the mass flow rate, and pressure and temperature distributions. The constants were the equipment, inlet conditions for the cooling water, and inlet conditions for the refrigerant during the steady state. In addition, the identified noises that could not be eliminated were ambient temperature variation during the long-lasting experiments and noises originating from the laboratory power supply grid. DasyLab software was used to acquire, process, and store experimental data.

The experimental research part was conducted using the same methodology as other researchers of this subject [23,24,25]. The time evolution of signals from multiple sensors along the minichannel examples is shown in Figure 5 for pressure, the values of which were compared so that one may find a time shift between the responses.

To minimise the uncertainty of the average value, multiple time shifts were averaged for each frequency. The final results were achieved using a simple formula—namely, the distance over time shift (distance between sensors was known a priori).

$$v_i=\frac{\Delta l_i}{\Delta t_i},$$

(5)

where

• Δt_i—Time shift;
• Δl_i—The distance between sensors.

A manual estimation of time shifts (Figure 5) could be arbitrary, depending on the person who performs the reading. In order to eliminate the human factor, a curve fitting procedure was introduced. A four-parameter logistic curve was chosen as a reference curve for the pressure signals, expressed as follows:

$$y\left(\tau \right)=\frac{a}{1+{exp}^{\left(-k\cdot \left(\tau -{\tau }_o\right)\right)}}+c$$

(6)

where

• a—Gain;
• k—Shape parameter;
• τo—An inflection point;
• c—Initial value.

In addition, the following resized and shifted sinusoid was chosen as a reference curve for temperature signals:

y(τ) = a∙sin(t + t_o) + c

(7)

where

• a—Resized parameter;
• t_o—Phase;
• c—Average value.

The procedure of curve fitting was coded in Python [26,27] using the following libraries: numpy, pandas, pylab, and scipy.

The test methodology previously developed for R134a refrigerant was applied [12]. The results of pressure instability propagation rates obtained for R1234ze and R1234yf were compared with those available in the literature for R134a (Figure 6) [17].

Figure 6. Propagation velocity of pressure instabilities v_p m/s as a function of frequency ω of generated disturbances for R134a, R1234yf, and R1234ze refrigerants [17].

Figure 6. Propagation velocity of pressure instabilities v_p m/s as a function of frequency ω of generated disturbances for R134a, R1234yf, and R1234ze refrigerants [17].

4. Results of Regression Modelling

For R1234ze and R1234yf isomers, a regression function was used to describe the velocity of movement of pressure instability v_p, describing how the expected value of the explanatory variable depends on the explanatory variables. For this purpose, the procedures of dimensional analysis were used, taking into account the Π–Buckingham theory [28,29]. The magnitude of the velocity of the pressure change signal v_p caused by dynamic instability was functionally dependent on the following parameters:

v_p = f(Δp, p_o, υ, d, w, φ)

(8)

The assumed assumptions show that the velocity of movement of the induced dynamic instabilities depends on the amplitude and frequency of their generation and the physical properties of the refrigerant. The magnitude of the amplitude of pressure oscillation Δp depends on the change in the void fraction φ of the condensing refrigerant. With regard to Equation (1), dimensional analysis was applied to obtain a formula for the dimensionless propagation rate of pressure instability. The methodology of the used dimensional analysis was developed on the basis of information available in the literature [22,29]. The following form of expected dependence for periodical instability was obtained:

$$v_p^{+}=C\cdot {\mathrm{Re}}_{TPF}^a\cdot {\left(\mathsf{\Delta }{p}^{+}\right)}^b\cdot {\phi }^c$$

(9)

For R134a refrigerant, quasi-Newton and Symplex calculation modules, standard equipment in the Statistica software (Koszalin University of Technology, Poland license package), were used, and the following unknown values were obtained: C = 8726.60a = −0.697023, b = −0.512730 and c = 0.625924, with a 95% variance and a significance factor R = 0.98. The description of dimensionless pressure instability for R134a is given in the following form:

$$v_p^{+}=8726.6 · R{e}_{TPF}^{-0.697023} · {\Delta }_p^{{+}^{-0.512730}} · {\phi }^{0.625924}$$

(10)

The comparison of calculation values of $v_{p.reg}^{+}$ with experimental $v_{p.\exp }^{+}$ is shown in Figure 7, with compliance within ±25%.

The regression function for R1234yf and R1234ze refrigerants was analogously determined, as described below.

For R1234yf refrigerant, the constant values were C = 13302.44, a = −1.19212, b = −0.646647, and c = 0.299296, with a 96% variance and a significance factor R = 0.98. This results in the following relationship:

$$v_p^{+}=13302.44 · R{e}_{TPF}^{-1.19212} · {\Delta }_p^{{+}^{-0.646647}} · {\phi }^{0.299296}$$

(11)

Additionally, a comparison of results with a compliance rate of ±25% is shown in Figure 8.

The constant values for R1234ze refrigerant are C = 2.576837 × 10⁹, a = −1.90405, b = −0.295680, and c = −1.9323, with a 96% variance and a significance factor R = 0.91. This results in the following relationship:

$$v_p^{+}=2.576837\times {10}^9 · R{e}_{TPF}^{-1.90405} · {\Delta }_p^{{+}^{-0.295680}} · {\phi }^{-1.97323}$$

(12)

A comparison of results with a compliance rate of ±25% is shown in Figure 9.

5. Conclusions

This paper presented suggestions on computational models for the propagation velocities of pressure instabilities during onset and decay of condensation for currently used R134a refrigerants and their new pro-ecological substitutes R1234 isomers. The suggested computational methods were based on a regression function for which the expected value of the dependent variable depends on explanatory variables. For the investigated case, the propagation velocity of a given instability was the dependent variable, and the explanatory variables were connected to system parameters. Simple dimensional analysis procedures taking into account the Π–Buckingham theorem were used. Then, the general form of regression function that allowed the calculation of nondimensional values of v_p⁺ for refrigerants was obtained. The compliance level was satisfactory at a ±25% threshold for all of the investigated refrigerants. This score indicated a satisfactory level and confirmed that developed regression models can be used to calculate the propagation velocities of pressure instabilities resulting from dynamic instability.

The proposed computational models can be used to identify the so-called hydraulic strokes in refrigeration systems and heat pumps. Their consideration should support the design process of the so-called compact heat exchangers whose construction is based on minichannels. In particular, this applies to heat exchangers used as condensers.

It is also important that this research was carried out for new pro-ecological substitutes of F-gases, R1234 isomers, which are not only prospective but already used in refrigeration, air conditioning, and heat pump equipment.