Thermodynamic analysis of a direct expansion solar-assisted heat pump system working with R290 as a drop-in substitute for R22

Abstract

The thermodynamic analysis of direct expansion solar-assisted heat pump system working with R290 as a drop-in substitute for R22 was carried out under the metrological conditions of Calicut, India. A prototype of a DXSAHP system consists of a compressor, an air-cooled condenser with evaporator–collector and thermostatic expansion valve. The experiments were carried during the winter months of 2016. The artificial intelligence technique artificial neural network integrated with genetic algorithm model was presented to predict energy and exergy performance of a system. The energy performance ratio of a system was found to be 5.75% higher and reduced heating capacity of about 6.8% when compared to R22. Similarly, the second law analysis (exergy analysis) of a total system working with R290 was found to be better when compared to baseline refrigerant. The selected alternative working fluid is a hydrocarbon and has zero ozone depletion and negligible global warming potential. Hence, R290 can be used as a drop-in substitute for R22 in DXSAHP systems.

Appendices

Appendix A

The following typical values are considered for uncertainty calculation.

$\hbox {T}_{1}$ = 10.51$\,\pm \,$0.01$^\circ$C    $\hbox {T}_{2}$ = 81.62$\,\pm \,$0.01$^\circ$C    $\hbox {T}_{3}$ = 48.12$\,\pm \,$0.01$^\circ$C    $\hbox {T}_{4}$ = 8.68$\,\pm \,$0.01$^\circ$C

$\hbox {T}_{\mathrm{ciat}}$ = 34.46$\,\pm \,$0.01$^\circ$C    $\hbox {T}_{\mathrm{coat}}$ = 47.32$\, \pm \,$0.01$^\circ$C    $\hbox {T}_{\mathrm{o}}$ = 34.46$\,\pm \,$0.01$^\circ$C

$\hbox {P}_{1}$ = 4.80$\,\pm \,$0.05 bar $\hbox {P}_{2}$ = 1.68$\,\pm \,$0.02 bar $\hbox {P}_{3}$ = 1.62$\,\pm \,$0.05 bar $\hbox {P}_{4}$ = 4.15$\,\pm \,$0.05 bar

$\hbox {Q}_{\mathrm{c}}$ = 3468 W $\hbox {V}_{\mathrm{air}}$ = 3.5$\,\pm \,$0.1 m/s $\hbox {m}_{\mathrm{r}}$ = 0.03$\,\pm \,$0.0001 kg/s I = 860 $\,\pm \,$ 5 W/m$^2$

$\hbox {m}_{\mathrm{air}}$ = 0.228$\,\pm \,$0.01 kg/s PC = 1268$\,\pm \,$1 W

The uncertainty associated in the performance parameters is computed using the following relations:

I. Energy performance parameters

• 1. Power consumption

  Power consumption = f (T$_{1}$, P$_{1}$, m$_{\mathrm{r}}$ )

  $$\begin{aligned} \frac{\delta {\mathrm{PC}}_{\mathrm{comp}}}{{\mathrm{PC}}_{\mathrm{comp}}}= \left[ \left( \frac{\delta T_1}{T_1} \right) ^2+ \left( \frac{\delta P_1}{P_1} \right) ^2+\left( \frac{\delta m_\mathrm{r}}{m_\mathrm{r}} \right) ^2\right] ^{1/2} \end{aligned}$$

  Substituting the values

  $$\begin{aligned} \frac{\delta {\mathrm{PC}}_{\mathrm{comp}}}{{\mathrm{PC}}_{\mathrm{comp}}} =2.09\% \end{aligned}$$

• 2. Heating capacity

  Heating capacity = f (T$_{\mathrm{ciat}}$, T$_{\mathrm{coat}}$, T$_{3}$, m$_{\mathrm{air}}$)

  $$\begin{aligned} \frac{\delta Q_\mathrm{c}}{Q_\mathrm{c}}=\left[ \left( \frac{\delta T_{\mathrm{ciat}}}{T_{\mathrm{ciat}}}\right) ^2+ \left( \frac{\delta T_{\mathrm{coat}}}{T_{\mathrm{coat}}}\right) ^2+\left( \frac{\delta T_{3}}{T_{3}} \right) ^2 +\left( \frac{\delta m_{\mathrm{air}}}{m_{\mathrm{air}}} \right) ^2 \right] ^{1/2} \end{aligned}$$

  Substituting the values

  $$\begin{aligned} \frac{\delta Q_\mathrm{c}}{Q_\mathrm{c}} =3.38\% \end{aligned}$$

• 3. Energy performance ratio

  Heating capacity = f (Q$_{\mathrm{c}}$, PC$_{\mathrm{comp}}$)

  $$\begin{aligned} \frac{\delta \mathrm{EPR}}{\mathrm{EPR}}=\left[ \left( \frac{\delta \mathrm{PC}_{\mathrm{comp}}}{\mathrm{PC}_{\mathrm{comp}}} \right) ^2 + \left( \frac{\delta Q_\mathrm{c}}{Q_\mathrm{c}}\right) ^2\right] ^{1/2} \end{aligned}$$

  Substituting the values

  $$\begin{aligned} \frac{\delta \mathrm{EPR}}{\mathrm{EPR}}=3.47\% \end{aligned}$$

II. Exergy-efficiency assessment parameters

• Compressor

• Exergy efficiency of compressor = f (T$_{1}$, P$_{1}$,T$_{2}$, P$_{2}$, PC, T$_{\mathrm{o}}$, m$_{\mathrm{r}}$)

  $$\begin{aligned} \frac{\delta \varepsilon _{\mathrm{comp}}}{\varepsilon _{\mathrm{comp}}}= \left[ \left( \frac{\delta T_1}{T_1} \right) ^2+ \left( \frac{\delta P_1}{P_1} \right) ^2+\left( \frac{\delta T_2}{T_2} \right) ^2+\left( \frac{\delta P_2}{P_2} \right) ^2+\left( \frac{\delta T_\mathrm{0}}{T_0} \right) ^2+\left( \frac{\delta m_{\mathrm{r}}}{m_{\mathrm{r}}} \right) ^2\right] ^{1/2} \end{aligned}$$

• Substituting the values

  $$\begin{aligned} \frac{\delta \varepsilon _{\mathrm{comp}}}{\varepsilon _{\mathrm{comp}}} =4.58\% \end{aligned}$$

• Condenser

• Exergy efficiency of compressor = f (T$_{2}$, P$_{2}$,T$_{3}$, P$_{3}$, PC, T$_{\mathrm{o}}$, T$_{\mathrm{ciat}}$, T$_{\mathrm{coat}},$ m$_{\mathrm{r}}$, m$_{\mathrm{air}}$)

  $$\begin{aligned} \frac{\delta \varepsilon _{\mathrm{cond}}}{\varepsilon _{\mathrm{cond}}} &= \left[ \left( \frac{\delta T_2}{T_2} \right) ^2+\left( \frac{\delta P_2}{P_2} \right) ^2 +\left( \frac{\delta T_3}{T_3} \right) ^2+\left( \frac{\delta P_3}{P_3} \right) ^2+\left( \frac{\delta m_{\mathrm{air}}}{m_{\mathrm{air}}} \right) ^2+\left( \frac{\delta m_{\mathrm{r}}}{m_{\mathrm{r}}} \right) ^2\right. \\&\left. +\left( \frac{\delta T_{\mathrm{ciat}}}{T_{\mathrm{ciat}}} \right) ^2+\left( \frac{\delta T_{\mathrm{coat}}}{T_{\mathrm{coat}}} \right) ^2+\left( \frac{\delta T_\mathrm{0}}{T_\mathrm{0}} \right) ^2\right] ^{1/2} \end{aligned}$$

• Substituting the values

  $$\begin{aligned} \frac{\delta \varepsilon _{\mathrm{cond}}}{\varepsilon _{\mathrm{cond}}} =6.22\% \end{aligned}$$

• Expansion valve

• Exergy efficiency of compressor = f (T$_{3}$, P$_{3}$,T$_{4}$, P$_{4}$ T$_{o}$, m$_{\mathrm{r}}$)

  $$\begin{aligned} \frac{\delta \varepsilon _{txv}}{\varepsilon _{txv}}= \left[ \left( \frac{\delta T_3}{T_3} \right) ^2+\left( \frac{\delta P_3}{P_3} \right) ^2+\left( \frac{\delta T_4}{T_4} \right) ^2+\left( \frac{\delta P_4}{P_4} \right) ^2+\left( \frac{\delta T_\mathrm{0}}{T_\mathrm{0}} \right) ^2+\left( \frac{\delta m_\mathrm{r}}{m_\mathrm{r}} \right) ^2\right] ^{1/2} \end{aligned}$$

• Substituting the values

  $$\begin{aligned} \frac{\delta \varepsilon _{\mathrm{txv}}}{\varepsilon _{\mathrm{txv}}}=3.33\% \end{aligned}$$

• Collector–evaporator

• Exergy efficiency of compressor = f (T$_{4}$, P$_{4}$,T$_{1}$, P$_{1}$ T$_{\mathrm{o}}$, I)

  $$\begin{aligned} \frac{\delta \varepsilon _{\mathrm{sol.col}}}{\varepsilon _{\mathrm{sol.col}}}= \left[ \left( \frac{\delta T_4}{T_4} \right) ^2+ \left( \frac{\delta P_4}{P_4} \right) ^2+\left( \frac{\delta T_1}{T_1} \right) ^2+\left( \frac{\delta T_1}{T_1} \right) ^2+\left( \frac{\delta T_{\mathrm{ciat}}}{T_{\mathrm{ciat}}} \right) ^2+\left( \frac{\delta I}{I} \right) ^2\right] ^{1/2} \end{aligned}$$

• Substituting the values

  $$\begin{aligned} \frac{\delta \varepsilon _{\mathrm{sol.col}}}{\varepsilon _{\mathrm{sol.col}}} =1.36\% \end{aligned}$$

• Total system

  $$\begin{aligned}&\hbox {Exergy efficiency of compressor=f} \left( \left( \frac{\delta \varepsilon _{\mathrm{comp}}}{\varepsilon _{\mathrm{comp}}}\right) , \left( \frac{\delta \varepsilon _{\mathrm{cond}}}{\varepsilon _{\mathrm{cond}}}\right) , \left( \frac{\delta \varepsilon _{\mathrm{txv}}}{\varepsilon _{\mathrm{txv}}}\right) ,\left( \frac{\delta \varepsilon _{\mathrm{sol.col}}}{\varepsilon _{\mathrm{sol.col}}}\right) \right) \\&\frac{\delta \varepsilon _{\mathrm{total.sys}}}{\varepsilon _{\mathrm{total.sys}}}= \left[ \left( \frac{\delta \varepsilon _{\mathrm{comp}}}{\varepsilon _{\mathrm{comp}}}\right) ^2+ \left( \frac{\delta \varepsilon _{\mathrm{cond}}}{\varepsilon _{\mathrm{cond}}}\right) ^2+\left( \frac{\delta \varepsilon _{\mathrm{txv}}}{\varepsilon _{\mathrm{txv}}}\right) ^2+\left( \frac{\delta \varepsilon _{\mathrm{sol.col}}}{\varepsilon _{\mathrm{sol.col}}}\right) ^2\right] ^{1/2} \end{aligned}$$

• Substituting the values

  $$\begin{aligned} \frac{\delta \varepsilon _{\mathrm{total.sys}}}{\varepsilon _{\mathrm{total.sys}}} =6.58\% \end{aligned}$$