A Parallel-Effect Combination of Absorption and Adsorption Cooling as a First Step Toward Uninterrupted Hybrid Sorption Refrigeration

Abstract

The design integration of absorption and adsorption cooling systems is a recently emerging research field in which the inherent advantages of both these systems are intended to be combined so as to maximize system performance. However, a vast majority of the conventional integration approaches reported in the literature still suffer from the following drawbacks: (a) the inability to provide a continuous cooling effect of the integrated design during the switching period of the adsorption component, (b) the lack of incorporation of the mass/heat recovery cycles and its subsequent effects upon the integrated performance, and (c) the lack of functional dependence of all thermodynamic variables including heat capacities and adsorption enthalpy upon operational parameters such as temperature and pressure. This study presents the first attempt of a numerically validated performance prediction of such an integrated system with parallel functionality to facilitate a continuous cooling operation. An empirical model of mass recovery cycle has been formulated for the very first time which adequately describes the sorption dynamics during mass transfer. All thermodynamic variables have been expressed as functions of operational parameters during the cooling cycle. For a mean driving temperature predicted to be as low as 38 °C and a mean cycle time of 11.82 min, the proposed integrated design has been predicted to yield a cycle-averaged specific cooling power of 48.93 W kg⁻¹ and a minimum achievable coefficient of performance of 0.74 compared to the corresponding values of 27.64 W kg⁻¹ and 0.57 for the benchmark stand-alone silica gel/water adsorption chiller.

Appendices

Appendix 1

The expression for ${U}_{\text{SHE}}{\left({T}_{\text{weak}}^{\text{SHE}},{T}_\text{strong}^\text{SHE},{X}_{\text{weak}},{X}_\text{strong}\right)A}_{\text{SHE}}$ is given below [44]:

The solution heat exchanger is assumed to be a concentric double pipe countercurrent heat exchanger in which the strong solution is flowing within the inner pipe, while the weak solution is flowing within the annulus between the two pipes in the opposite direction to the strong solution. ${U}_{\text{SHE}}{A}_{\text{SHE}}$ can be expressed as:

${U}_{\text{SHE}}{A}_{\text{SHE}}=\left(\frac{1}{\frac{{D}_{oi}}{{D}_{ii}}\frac{1}{{h}_{i}}+\frac{1}{{h}_{o}}}\right)\left(\pi \frac{{D}_{oi}^{2}}{4}\right), {\text{where}}$where ${D}_{{\text{ii}}}$ is the inner diameter of the inner pipe ($0.875$ inches), while ${D}_{{\text{oi}}}$ is the inner diameter of the outer pipe ($1.5$ inches), and ${h}_{{\text{i}}}$ and ${h}_{{\text{o}}}$ are the heat transfer coefficients of the strong and weak solutions, respectively, and can be expressed as:

$${h}_{{\text{i}}}=\frac{0.023{Re}_\text{strong}^{0.8}{Pr}_\text{strong}^{1/3}{K}_{\text{sol}}^\text{strong}\left({T}_\text{strong}^\text{SHE},{X}_\text{strong}\right)}{{D}_{{\text{ii}}}}$$

$${h}_{{\text{o}}}=\frac{0.023{Re}_{\text{weak}}^{0.8}{Pr}_{\text{weak}}^{1/3}{K}_{\text{sol}}^{\text{weak}}\left({T}_{\text{weak}}^{\text{SHE}},{X}_{\text{weak}}\right)}{{D}_{{\text{oi}}}}$$

where the thermal conductivity of the LiBr/water solution can be expressed as:

$${K}_{\text{sol}}\left(T,X\right)=-\left(6.32\times {10}^{-9}\right)X{T}^{3}+\left(7.32\times {10}^{-9}\right){T}^{3}+\left(1.39\times {10}^{-5}\right)X{T}^{2}-\left(1.55\times {10}^{-5}\right){T}^{2}-\left(7.67\times {10}^{-3}\right)XT+\left(8.99\times {10}^{-3}\right)T+\left(8.84\times {10}^{-1}\right)X-0.88$$

$${{\text{Re}}}_{\text{weak}}\left({T}_{\text{weak}}^{\text{SHE}},{X}_{\text{weak}}\right)=\frac{4{D}_{E}{\dot{m}}_{\text{weak}}}{\pi {\mu }_{\text{sol}}\left({T}_{\text{weak}}^{\text{SHE}},{X}_{\text{weak}}\right)\left[{D}_{{\text{oi}}}^{2}-{\left({D}_{{\text{ii}}}+2{t}_{i}\right)}^{2}\right]}$$

$${{\text{Re}}}_\text{strong}\left({T}_\text{strong}^{\text{SHE}},{X}_\text{strong}\right)=\frac{4{\dot{m}}_\text{strong}}{\pi {D}_{{\text{ii}}}{\mu }_{\text{sol}}\left({T}_\text{strong}^{\text{SHE}},{X}_\text{strong}\right)}$$

where ${D}_{E}$ is the equivalent diameter (0.74 inches), ${t}_{i}$ is the thickness of inner pipe (0.0315 inches), and the viscosity of solution can be expressed as:

$${\mu }_{\text{sol}}\left(T,X\right)={10}^{-3}{e}^{\left(-35212\frac{{X}^{2}}{{T}^{2}}+\frac{372995}{{T}^{2}}+963.16\frac{{X}^{2}}{T}-\frac{609.5}{T}+3.19{X}^{2}-2.32\right)}$$

$${Pr}_{\text{sol}}\left(T,X\right)=\frac{{C}_{p}^{\text{sol}}\left(T,X\right){\mu }_{\text{sol}}\left(T,X\right)}{{K}_{\text{sol}}\left(T,X\right)}$$

where the specific heat capacity of solution can be expressed as [45]:

$\begin{aligned} & C_{p}^{{{\text{sol}}}} \left( {T,\mathop X\limits^{} } \right) = - \left( {2 \times 10^{3} } \right)\\ &\quad T\left( {C_{0} + C_{1} \mathop X\limits^{} + C_{2} \mathop X\limits^{} {}^{2} + C_{3} \mathop X\limits^{} {}^{3} + C_{4} \mathop X\limits^{} {}^{{1.1}} } \right) \\ & - \left( {6 \times 10^{3} } \right)T^{2} \left( {D_{0} + D_{1} \mathop X\limits^{} + D_{2} \mathop X\limits^{} {}^{2} + D_{4} \mathop X\limits^{} {}^{{1.1}} } \right) \\ &\quad - \left( {12 \times 10^{3} } \right)T^{3} \left( {E_{0} + E_{1} \mathop X\limits^{} } \right) \\ & - \left( {2 \times 10^{3} } \right)\frac{{\left( {F_{0} + F_{1} \mathop X\limits^{} } \right)T}}{{\left( {T - T_{0} } \right)^{3} }} \\ &\quad + \frac{{10^{3} }}{T}\left( {L_{0} + L_{1} \mathop X\limits^{} + L_{2} \mathop X\limits^{} {}^{2} + L_{3} \mathop X\limits^{} {}^{3} + L_{4} \mathop X\limits^{} {}^{{1.1}} } \right) \\ & - 10^{3} \left( {M_{0} + M_{1} \mathop X\limits^{} + M_{2} \mathop X\limits^{} {}^{2} + M_{3} \mathop X\limits^{} {}^{3} + M_{4} \mathop X\limits^{} {}^{{1.1}} } \right) \\ \end{aligned}$, where $\acute{X}= 100X$ and the values of the various coefficients are listed in the following table.

Variable	Coefficient Value
${C}_{i}, i=0,..,4$	$2.65\times {10}^{-2}$	$-2.31\times {10}^{-3}$	$7.56\times {10}^{-6}$	$-3.76\times {10}^{-8}$	$1.18\times {10}^{-3}$
${D}_{i}, i=0,..,\mathrm{2,4}$	$-8.53\times {10}^{-6}$	$1.32\times {10}^{-6}$	$2.79\times {10}^{-11}$	$-$	$-8.51\times {10}^{-7}$
${E}_{i}, i=0,..,1$	$-3.84\times {10}^{-11}$	$2.63\times {10}^{-11}$	$-$	$-$	$-$
${F}_{i}, i=0,..,1$	$-5.16\times {10}^{1}$	$1.1146$	$-$	$-$	$-$
${L}_{i}, i=0,..,4$	$-2.18\times {10}^{3}$	$-1.27\times {10}^{2}$	$-2.3646$	$1.39\times {10}^{-2}$	$1.58\times {10}^{2}$
${M}_{i}, i=0,..,4$	$-2.27\times {10}^{1}$	$2.98\times {10}^{-1}$	$-1.26\times {10}^{-2}$	$6.85\times {10}^{-5}$	$2.77\times {10}^{-1}$

Appendix 2

The expressions for ${U}_{\text{abs}}{\left({T}_{\text{abs}}\right)A}_{\text{abs}}$ and ${U}_{\text{gen}}{\left({T}_{\text{gen}}\right)A}_{\text{gen}}$ are exactly the same as those reported for ${U}_{\text{evap}}{\left({T}_{\text{evap}}\right)A}_{\text{evap}}$ and ${U}_\text{con}{\left({T}_\text{con}\right)A}_\text{con},$ respectively, in an earlier publication along with the following replacements: ${T}_{\text{evap}}={T}_{\text{gen}}$, ${T}_\text{cond}={T}_{\text{abs}}$, ${T}_{ch,i}^{\text{evap}}={T}_\text{hw,i}^{\text{gen}}$, ${T}_{ch,o}^{\text{evap}}={T}_\text{hw,o}^{\text{gen}}$, ${T}_\text{cw,i}^\text{con}={T}_\text{cw,i}^{\text{abs}}$, ${T}_\text{cw,o}^\text{con}={T}_\text{cw,o}^{\text{abs}}$, ${{\dot{m}}_{ch}^{\text{evap}}=\dot{m}}_\text{hw}^{\text{gen}}$, ${{\dot{m}}_\text{cw}^\text{con}=\dot{m}}_\text{cw}^{\text{abs}}$ [29].