Computation of Ecological Properties, Flammability Properties and Thermodynamic Properties of Sustainable Refrigerant Dimethylether (RE170) Using Martin Hou Equation of State (MHEOS)

Commonly, environmental impact of several refrigerants is investigated by computing their ecological properties such as ODP and GWP. In order to protect ozone layer and also to decrease the greenhouse effect of atmospheric environment, alternative refrigerants not only desire zero ODP but also it desires lower value of GWP. Correlations used to compute ODP and GWP of several refrigerants were taken from related literature and they are given below [18-21].

$\mathrm{ODP}_{\mathrm{i}}=\left(\alpha \mathrm{n}_{\mathrm{Br}, \mathrm{i}}+\mathrm{n}_{\mathrm{Cl}, \mathrm{i}}\right) \times \frac{\mathrm{f}_{\mathrm{i}}}{\mathrm{f}_{\mathrm{CFC}-11}} \times \frac{\tau_{\mathrm{i}}}{\tau_{\mathrm{CFC}}-11} \times \frac{\mathrm{MW}_{\mathrm{CFC}-11}}{\mathrm{MW}_{\mathrm{i}}} \times \frac{1}{3}$       (4)

where, $f$ is the halogen fractional release factor, $\alpha$  is the relative effectiveness of bromine when compared with chlorine for ozone depletion, τ is the overall lifespan, MW is the molecular weight, and n_Cl (n_Br) is the number of chlorine (bromine) atoms present in the refrigerant. CFC-11 subscripts designate quantities for CFC-11, while i subscripts indicate quantities relating to the refrigerant for which the ODP is required.

$\mathrm{GWP}=\frac{\int_{0}^{\mathrm{t}}\left(\mathrm{F}_{\mathrm{x}} \mathrm{e}^{\frac{-\mathrm{t}}{\mathrm{e}_{\mathrm{x}}} \mathrm{dt}}\right)}{\int_{0}^{\mathrm{t}}\left(\mathrm{F}_{\mathrm{CO}_{2} \mathrm{R}_{\mathrm{t}} \mathrm{d} \mathrm{t}}\right)}$       (5)

where, F_x is the radiative forcing per unit mass of species x, t is the time horizon considered, $F_{C O_{2}}$ is the radiative forcing of CO₂, R(t) is the response function that defines the deterioration of an instantaneous pulse of C_O2 and t_x is the atmospheric life cycle.

By using Eqns. (4) and (5), the values of ODP and GWP for refrigerant RE170 were computed and they are compared with literature results [16, 22]. Comparison of computed ecological properties (ODP and GWP) of refrigerant RE170 with results from related literature is given in Table 1.

Table 1. Comparison of computed ODP and GWP values of refrigerant RE170 with literature results [16, 22]

From Table 1, it is observed that the computed ODP and GWP values of refrigerant RE170 shows excellent agreement with that of literature values. The deviation of computed values of ecological properties of RE170 when compared with literature values was within 1.25 %. Therefore, the empirical correlations which were used to compute ecological properties can be considered as reliable.

The basic physical properties of refrigerant Dimethylether (RE170) were taken from related literature and they are presented in Table 2 [17].

From Table 1, it is also observed that refrigerant RE170 has zero ODP and negligible GWP. Therefore, refrigerant RE170 can be considered as an environmental friendly refrigerant. RE170 can be used as one of the mixing components with other Hydrofluorocarbons (HFCs) in order to reduce the GWP of mixture and also to improve the performance of the mixture. In this context, Shaik and Babu (2017) computed the theoretical performance of VCR cycle using four ternary refrigerant mixtures consists of R32, R134a, R290, R1270 and RE170 as replacements to R22, operating at T_e=7.2 ℃ and T_k=54.4 ℃ by considering subcooling and superheating as 5 ℃ [23]. Authors were neglected the various losses occurred in the cycle, while doing the performance study of various considered blends. The performance results of various blend studied were presented in the Table 3.

Table 2. Physical properties of refrigerant Dimethylether (RE170)

Table 3. Performance results of four ternary mixtures [23]

From Table 3, it is noticed that the performance of ternary refrigerant mixture TRM30 (R134a/RE170/R1270 55/7.5/37.5 composition mass %) was 5.35 % higher than that of R22. Apart from refrigerant TRM30, the refrigerant mixture TRM40 also has considerable increase in COP compared to R22. From this thermodynamic performance results, it is evident that mixing the RE170 with other refrigerants (R134a, R290 and R1270) enhances the performance of the system.

Methodology used to calculate refrigerant thermodynamic properties is discussed in this section and it is given below. Pressure-Enthalpy (P-h) chart used, while estimating the thermodynamic properties of pure refrigerant is shown in Figure 1 [29].

1.jpg

Figure 1. Pressure-Enthalpy chart used for estimation of pure refrigerant properties

4.2 Saturation vapour pressure

Initially, saturation vapour pressure of refrigerant is computed. The relation between saturation pressure (P_sat) and saturation temperature (T_sat) is stated by Wagner and corresponding saturation vapour pressure equation is given below [30].

$\ln \left(\frac{\mathrm{p}_{\mathrm{sat}}}{\mathrm{p}_{\mathrm{c}}}\right)=\left(\frac{1}{1-\mathrm{x}}\right)\left[\mathrm{A}_{1} \mathrm{x}+\mathrm{B}_{1} \mathrm{x}^{1.5}+\mathrm{C}_{1} \mathrm{x}^{2.5}+\mathrm{D}_{1} \mathrm{x}^{5}\right]$     (10)

where, $\mathrm{x}=1-\left(\frac{\mathrm{T}}{\mathrm{T}_{\mathrm{c}}}\right)$ ; A₁, B₁, C₁ and D₁ are constants for a specific refrigerant and the values of above constants for Wagner equation are presented in the related research article for several different refrigerants [30]. Constants of saturation vapour pressure for refrigerant RE170 is given in Table 5.

Table 5. Constants of RE170 for equation (10)

4.3 Liquid phase density

Next, refrigerant RE170 liquid density is computed. In the present study, Reid et al, equation was used to calculate the RE170 liquid density [31-32].

$\rho_{\mathrm{r}}=\frac{\rho}{\rho_{\mathrm{C}}}=1+0.85 \times\left(1-\mathrm{T}_{\mathrm{r}}\right)+(1.6916+0.984 \times \omega) \times\left(1-\mathrm{T}_{\mathrm{r}}\right)^{1 / 3}$      (11)

where, ω is acentric factor; T_r =T/T_c, ω, ρ_c and T_c are constants for a specific refrigerant and values of these constants for several different refrigerants are available in the related literature [33]. Constansts of Reid et al, density correlation for refrigerant RE170 are listed in Table 6.

Table 6. Constants of RE170 for equation (11)

4.4 Specific volume of vapour

Next, vapour specific volume of refrigerant RE170 is calculated. In the present research work, vapour specific volume of refrigerant RE170 was computed by using MHEOS [15, 34].

Table 7. Dimensionless coefficients of refrigerant RE170 for equation (12)

$\mathrm{P}=\frac{\mathrm{RT}}{\mathrm{V}-\mathrm{b}}+\frac{\mathrm{A}_{2}+\mathrm{B}_{2} \mathrm{T}+\mathrm{C}_{2} \mathrm{e}^{\frac{-5.475 \mathrm{T}}{\mathrm{T}_{\mathrm{C}}}}}{(\mathrm{V}-\mathrm{b})^{2}}+\frac{\mathrm{A}_{3}+\mathrm{B}_{3} \mathrm{T}+\mathrm{C}_{3} \mathrm{e}^{\frac{-5.475 \mathrm{T}}{\mathrm{T}_{\mathrm{C}}}}}{(\mathrm{V}-\mathrm{b})^{3}}+\frac{\mathrm{A}_{4}}{(\mathrm{V}-\mathrm{b})^{4}}+\frac{\mathrm{B}_{5} \mathrm{T}}{(\mathrm{V}-\mathrm{b})^{5}}$           (12)

where, A₂, A₃, A₄, B₂, B₃, B₅, C₂, C₃ and b are dimensionless coefficients of MHEOS for different refrigerants. Method followed to calculate above coefficients is described in the related literature [15, 34]. By solving the equation (12), dimensionless coefficients of MHEOS were obtained for given refrigerant RE170 and they are presented in Table 7.

4.5 Enthalpy of vapourization

Enthalpy of vapourization of given refrigerant is computed. Clausius-Clapeyron equation was used in this research work, in order to calculate the enthalpy of vapourization of given refrigerant RE170 [29].

$\frac{\mathrm{dP}_{\mathrm{sat}}}{\mathrm{dT}}=\frac{\mathrm{h}_{\mathrm{fg}}}{\mathrm{T} \times \mathrm{V}_{\mathrm{fg}}}=\frac{\mathrm{h}_{\mathrm{fg}}}{\mathrm{T} \times\left(\mathrm{V}_{\mathrm{g}}-\mathrm{V}_{\mathrm{f}}\right)}$         (13)

4.6 Departure method

Departure method is followed, in order to calculate the entropy and enthalpy of different refrigerants [29, 33]. Enthalpy and entropy properties (both liquid and vapour phase) of given refrigerant RE170 is computed using departure method. Generally, the reference state of entropy and enthalpy is fixed, while computing properties. İn refrigerants case, the reference state chosen is that of saturated liquid at 0 ℃. Entropy and enthalpy values allocated to the reference state of saturated liquid at 0 ℃ are usually S₁=S_f1=1.0 kJ/kg K and h₁=h_f1=200 kJ/kg, respectively [29, 33]. While comparing the computed properties of RE170 with REFPROP, the same above reference state was used in the NIST REFPROP and therefore validation of computed properties against REFPROP can be considered as reliable.

The importance of departure method is, to calculate the entropy and enthalpy at different state points as shown in Figure 1. For example, to calculate enthalpy at point 3, enthalpy departure method was applied and the corresponding departure function (h₃-h₂) is given as follows.

$\mathrm{h}_{3}-\mathrm{h}_{2}=\left(\mathrm{U}_{3}-\mathrm{U}_{2}\right)+\left(\mathrm{P}_{3} \mathrm{V}_{3}-\mathrm{P}_{2} \mathrm{V}_{2}\right)$      (14)

$\mathrm{U}_{3}-\mathrm{U}_{2}=\int_{2}^{3}\left[\mathrm{T}\left[\frac{\partial \mathrm{P}}{\partial \mathrm{T}}\right]_{\mathrm{V}}-\mathrm{P}\right] \mathrm{d} \mathrm{V}$         (15)

By solving equations (14) and (15), the h₃ value can be calculated. In order to compute the enthalpy h₄ at point 4, ideal gas heat capacity equation and difference in enthalpy term (h₄-h₃) can be used and it is given below.

$\mathrm{h}_{4}-\mathrm{h}_{3}=\int_{3}^{4} \mathrm{C}_{\mathrm{P} 0} \mathrm{d} \mathrm{T}$       (16)

İn this work, ideal gas heat capacity (C_P0) equation was taken from related article and it is presented below [33].

$\mathrm{C}_{\mathrm{P} 0}=\mathrm{F}_{0}+\mathrm{F}_{1} \mathrm{T}+\mathrm{F}_{2} \mathrm{T}^{2}+\mathrm{F}_{3} \mathrm{T}^{3}+\mathrm{F}_{4} \mathrm{T}^{4}$      (17)

where, F₀, F₁, F₂, F₃ and F₄ are constants for a specific refrigerant and values of these constants for several different refrigerants are available in related article [33]. Constants of ideal gas heat capacity for RE170 are presented in Table 8.

Table 8. Constants of RE170 for equation (17)

In order to find enthalpy h₅, once again enthalpy departure method was applied in between the state points 4 and 5. And Corresponding enthalpy departure term (h₅-h₄) is given below.

$\mathrm{h}_{5}-\mathrm{h}_{4}=\left(\mathrm{U}_{5}-\mathrm{U}_{4}\right)+\left(\mathrm{P}_{5} \mathrm{V}_{5}-\mathrm{P}_{4} \mathrm{V}_{4}\right)$      (18)

$\mathrm{U}_{5}-\mathrm{U}_{4}=\int_{4}^{5}\left[\mathrm{T}\left[\frac{\partial \mathrm{P}}{\partial \mathrm{T}}\right]_{\mathrm{V}}-\mathrm{P}\right] \mathrm{dV}$       (19)

By solving Eqns. (18) and (19), the h₅ value can be calculated. On the other hand, enthalpy of saturated liquid at state point 6 can be calculated by using the following formulas.

$\mathrm{h}_{5}-\mathrm{h}_{6}=\mathrm{h}_{\mathrm{fg}}$       (20)

$\mathrm{h}_{6}=\mathrm{h}_{5}-\mathrm{h}_{\mathrm{fg}}$       (21)

where, $h_{f g}$  can be computed using Clasius-Clayperon equation at a given temperature.

4.7 Liquid entropy

The liquid entropy of given refrigerant is determined. In order to calculate refrigerant thermodynamic properties (entropy and enthalpy) at any given temperature and pressure, the departure method was used, and the corresponding entropy of saturated liquid and enthalpy of saturated liquid was computed with the help of Clausius-Clapeyron equation. Entropy of saturated liquid for any particular refrigerant can be computed by using equations (22) and (23).

$\mathrm{S}_{\mathrm{fg}}=\mathrm{S}_{\mathrm{g}}-\mathrm{S}_{\mathrm{f}}$          (22)

$\mathrm{S}_{\mathrm{f}}=\mathrm{S}_{\mathrm{g}}-\mathrm{S}_{\mathrm{fg}}$         (23)

4.8 Vapour entropy

Vapour entropy of any particular refrigerant can be calculated using Eqns. (24) and (25).

$S_{\mathrm{fg}}=\frac{\mathrm{h}_{\mathrm{fg}}}{\mathrm{T}_{\mathrm{sat}}}$        (24)

$\mathrm{S}_{\mathrm{g}}=\frac{\mathrm{h}_{\mathrm{g}}}{\mathrm{T}_{\mathrm{sat}}}$         (25)

By using the above methodology, refrigerant RE170 thermodynamic properties were computed over wide temperature range from about 131.6 K to 398.15 K and pressure up to 51.3 bar.

4.9 Validation of results based on literature

In the present study, a MATLAB program was developed to compute the thermodynamic properties of refrigerant RE170 using MHEOS and various related correlations. The computed thermodynamic properties of RE170 have been validated with NIST-REFPROP data base, since its properties are not presented in the literature and also in the ASHRAE hand book [16]. Hence, REFRPROP can be considered as reliable source as that of ASHRAE data hand book [17]. The validation of thermodynamic properties of RE170 with REFPROP is shown in Table 9 [17].

From Table 9, it is observed that the deviation between computed values of RE170 using MHEOS and NIST REFPROP 9.1 values of RE170 was within 1.45% for the given AHRI operating conditions. Hence, the methodology used to establish thermodynamic properties of RE170 can be considered as reliable and thus it can be employed for the estimation of thermodynamic properties of any given pure refrigerant. Generally, theoretical thermodynamic performance of air conditioners was evaluated at AHRI conditions.

Table 9. Validation of computed thermodynamic properties of refrigerant RE170 with NIST REFPROP 9.1 at AHRI conditions (T_e=7.2⁰C and T_k=54.4 ℃)

4.10 Thermodynamic analysis of refrigerant RE170 using properties obtained from MHEOS

Commonly, thermodynamic properties of refrigerants are necessary in order to compute thermodynamic performance of any given refrigerants. Therefore, thermodynamic properties obtained from MHEOS for RE170 are used in the present study, to evaluate the performance parameters of given refrigerant RE170.

Theoretical thermodynamic analysis of given refrigerant RE170 was conducted based on standard VCR cycle. The P-h chart of standard VCR cycle is shown in Figure 2. The operating conditions considered, while doing thermodynamic analysis of refrigerant RE170 were taken from literature and they are expressed as $\mathrm{T}_{\mathrm{k}}=50^{\circ} \mathrm{C}, \mathrm{T}_{\mathrm{e}}=-10^{\circ} \mathrm{C}, \Delta T_{\text {sub }}=5^{\circ} \mathrm{C}$ and $\Delta T_{\text {sup }}=10^{\circ} \mathrm{C}$, respectively [22]. In the present investigation, MATLAB program was written, to compute the thermodynamic performance parameters of refrigerant RE170. Thermodynamic properties, operating conditions and various formulas were included in the MATLAB program in order to obtain the performance results.

2.jpg

Figure 2. P-h chart of standard VCR cycle

The formulas used, while doing thermodynamic analysis of refrigerants were listed below.

Refrigerant mass flow rate is calculated as

$\dot{\mathrm{m}}=\frac{\mathrm{Q}_{\mathrm{c}}}{\mathrm{c} \mathrm{E}}$        (26)

Cooling effect is calculated as

$\mathrm{CE}=\left(\mathrm{h}_{1^{''}}-\mathrm{h}_{4^{''}}\right)$         (27)

Isentropic compressor work is calculated as

$\mathrm{W}_{\mathrm{c}}=\mathrm{h}_{2^{\mathrm{''}}}-\mathrm{h}_{1^{\mathrm{''}}}$       (28)

Coefficient of performance (COP) is computed as

$\mathrm{COP}=\mathrm{CE} / \mathrm{W}_{\mathrm{c}}$        (29)

Pressure ratio is calculated as

$\mathrm{P}_{\mathrm{r}}=\left(\frac{\mathrm{P}_{\mathrm{k}}}{\mathrm{P}_{\mathrm{e}}}\right)$          (30)

Power consumed per ton of refrigeration (PPTR) is calculated as

$\mathrm{PPTR}=\dot{\mathrm{m}} \mathrm{W}_{\mathrm{c}}=3.5\left(\frac{\mathrm{h}_{2^{\prime \prime}}-\mathrm{h}_{1^{\prime \prime}}}{\mathrm{h}_{1^{\prime \prime}}-\mathrm{h}_{4^{\prime \prime}}}\right)$

$\operatorname{PPTR}=\dot{\mathrm{m}} \mathrm{W}_{\mathrm{c}}=3.5\left(\frac{\mathrm{W}_{\mathrm{C}}}{\mathrm{RE}}\right)=\left(\frac{3.5}{\mathrm{COP}}\right)$        (31)

$\dot{\mathrm{m}}=\frac{\mathrm{Q}_{\mathrm{c}}}{\mathrm{RE}}=\frac{3.5}{\mathrm{RE}}$

where, Q_c = Capacity in terms of TR, 1TR=210 kJ/min or 3.5 kW.

Volumetric cooling (refrigeration) capacity is calculated as

$\mathrm{VCC}=\rho_{1^{\prime \prime}} \times \mathrm{CE}$       (32)

Compressor discharge temperature (T_disch) can be calculated as

$\mathrm{S}_{2}=\mathrm{S}_{3}+\mathrm{C}_{\mathrm{p} 2} \times \ln \left(\frac{\mathrm{T}_{2} \mathrm{''}}{\mathrm{T}_{3} \mathrm{''}^{\mathrm{n}}}\right)=\mathrm{S}_{1^{\mathrm{''}}}$        (33)

Results obtained from the thermodynamic analysis of refrigerant RE170 were compared with literature and they are shown in Table 10.

Table 10. Comparison of results of thermodynamic analysis of refrigerant RE170 with literature results [22]

From Table 10, it is noticed that the thermodynamic performance results obtained from present MATLAB program exhibits good agreement with literature results and the deviation of program results compared with literature results is within 1.5 %. Therefore, thermodynamic properties obtained from MHEOS which are used in the thermodynamic analysis of RE170 can be treated as reliable and also the MATLAB program which was developed in this study can be treated as reliable.

In this work an attempt was made to compute ecological properties, flammability properties of RE170 and also to establish the thermodynamic properties of an ecofriendly refrigerant RE170 (Dimethylether) using MHEOS over the wide temperature range about 131.6 K to 398.15 K and pressure up to 51.3 bar. The conclusions drawn from this investigation are presented below.

• Ecological properties exhibited that refrigerant RE170 has zero ODP and very low GWP (equal to one) compared to other four studied refrigerant mixtures.
• Flammability study exhibited that refrigerant RE170 was classified into highly flammable group (ASHRAE A3) and hence safety precautions must be followed while using RE170. And also refrigerant RE170 has UFL of 25.60 vol%, LFL of 3.34 vol% and RF number of 51.05 kJ/g, respectively.

• In this study, thermodynamic properties generated were validated against NIST REFPROP database. Martin-Hou equation of state was found to be an appropriate equation of state in the operating temperature region (280-328 K) of residential air conditioner, since the deviation of all the computed and developed properties (P_sat, ρ_f, V_g, h_f, h_g, S_f and S_g) were within 1% when compared with NIST REFPROP database.
• Similarly deviation of computed thermodynamic properties of refrigerant RE170 for the temperature range (131 K to 363 K) was within 2.5 %. This study exhibited that there was considerable increase in deviation of properties as the computation approaches to critical point or critical region.
• Also in this study, mean absolute deviation (MAD) of all the computed thermodynamic properties of RE170 was found. MAD of saturation pressure and liquid density was 0.071 % and 0.25 %, respectively over the entire temperature range about 131.6 K to 398.15 K and pressure up to 51.3 bar.
• MAD of saturated vapour phase of both enthalpy and entropy was 0.31 % and 0.26 %, whereas MAD of saturated liquid phase enthalpy and entropy was 1.01 and 1.05 % over wide temperature about 131.6 K to 398.15 K and pressure up to 51.3 bar.
• MAD of vapour specific volume of RE170 was 1.49 % over the wide temperature range about 131.6 K to 398.15 K and pressure up to 51.3 bar.
• However, mean absolute deviation (MAD) of all the properties was within 1.05 % as the temperature approaches near to critical region. Hence the developed thermodynamic properties of refrigerant RE170 by using MHEOS were considered as reliable and these properties would be useful and applicable for computing and analyzing the thermodynamic performance characteristics of VCR system.
• The present study revealed that blending the refrigerant RE170 as one of the mixing components with other refrigerants not only enhances the performance of refrigerant mixture, but it also redues the GWP of refrigerant mixture.
• The Martin-Hou equation of state (MHEOS) can be conveniently used for further future research work on development of properties of any given pure refrigerants and also experimental PvT properties of any pure substance can be validated with the properties obtained from MHEOS.
• Flammability correlations used in the present study provides the essential information to the researchers to classify the any given new refrigerants into various safety categories.