# Dynamic Modeling and Simulation of a Facade-Integrated Adsorption System for Solar Cooling of Lightweight Buildings

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Literature Review

_{2}emissions [8]. The multiple different solar cooling technologies can be distinguished into two major groups [9]: on the one hand, photovoltaic modules can electrically drive compression chillers [10], and on the other hand, solar thermal collectors can thermally drive sorption chillers or desiccant cooling systems. The latter group of thermally driven technologies is studied widely and many applications are in operation [11,12,13,14]. The proposed system investigated in this work belongs to the group of thermally driven sorption chillers. Compared to the electrically driven technologies, it has two main advantages. The efficiency of the solar thermal collector is two to three times higher than the efficiency of currently available photovoltaic modules. Secondly, the proposed adsorption cooling system introduces thermal capacity to the lightweight building through its ad-/desorption potential, and thus, can limit the temperature fluctuations already without active cooling.

#### 1.3. Subject Matter

#### 1.4. Objectives of Study

- What is the achievable cooling power and cooling energy capacity?
- What is a suitable size ratio of the components?
- How can the system performance be optimized?

## 2. Model Description

#### 2.1. Adsorber

- The vapor is an ideal gas and viscous Newton-fluid;
- Local thermal equilibrium is assumed;
- Due to the low pressure, rarefaction effects in the mass and heat transport in the adsorbent bulk are considered;
- The adsorption kinetics can be described by the linear-driving-force approximation;
- The heat of adsorption depends on the water uptake;
- The temperature dependencies of the material parameters (viscosity, heat capacity, density, etc.) are accounted for.

#### 2.2. Condenser

- The energy and mass of the vapor are neglectable;
- The vapor is an ideal gas;
- The vapor is always saturated;
- Incoming vapor fully condenses;
- The water is incompressible;
- Temperature variations in the condensed water are negligibly small, but natural convection is indirectly captured through correlations for the heat transfer;
- Temperature variations in height direction of the walls are negligibly small;
- Boundary effects of the top and bottom of the casing are neglected;
- The temperature dependencies of the water (density, heat capacity, enthalpy of evaporation, etc.) are accounted for.

- The condensate film flow is always laminar and steady;
- The surface temperatures of fins and walls are isotherm;
- The vapor bulk is stagnant.

#### 2.3. Evaporator

- Energy and mass of the vapor phase are neglectable;
- The vapor is an ideal gas;
- The water is incompressible;
- Vapor pressure in the evaporator is assumed to be equal to saturation pressure;
- Outflowing vapor instantly evaporates;
- The temperature dependencies of the water (density, heat capacity, enthalpy of evaporation, etc.) are accounted for.

#### 2.4. Coupling and Boundary Conditions

#### 2.5. Operating Phases and Switching Criteria

#### 2.6. Cooling Power Control

## 3. Numerical Implementation

## 4. Results and Discussion

#### 4.1. Simulation Case Set-Up and Procedure

#### 4.2. Reference Case

#### 4.3. Parametric Studies

#### 4.3.1. Adsorber

#### 4.3.2. Condenser

Control Active | Control Inactive | ||||
---|---|---|---|---|---|

Variation | Cooling Energy | Dynamic | Max. Cooling | Cooling Energy | |

[Wh] | [min] | Power [W] | [Wh] | ||

Reference | / | 823 | 112 | $82.5$ | 1043 |

Adsorber | |||||

Collector efficiency ${\eta}_{\mathrm{sol}}$ | High | $+3.4\%$ | $+44.6\%$ | $+20.2\%$ | $+21.3\%$ |

Collector efficiency ${\eta}_{\mathrm{sol}}$ | Low | $-3.9\%$ | $-58.9\%$ | $-13.5\%$ | $-14.4\%$ |

External adsorber fins | |||||

(${w}_{\mathrm{fin},\mathrm{sht},\mathrm{A}}$ × ${L}_{\mathrm{gap},\mathrm{A}})$ | $15\mathrm{mm}$ × $15\mathrm{mm}$ | $+2.6\%$ | $+28.6\%$ | $+3.6\%$ | $+3.5\%$ |

External adsorber fins | |||||

(${w}_{\mathrm{fin},\mathrm{sht},\mathrm{A}}$ × ${L}_{\mathrm{gap},\mathrm{A}})$ | $20\mathrm{mm}$ × $20\mathrm{mm}$ | $+2.7\%$ | $+30.4\%$ | $+3.8\%$ | $+3.6\%$ |

External adsorber fins | |||||

(${w}_{\mathrm{fin},\mathrm{sht},\mathrm{A}}$ × ${L}_{\mathrm{gap},\mathrm{A}})$ | $30\mathrm{mm}$ × $30\mathrm{mm}$ | $+2.8\%$ | $+31.3\%$ | $+4.0\%$ | $+3.7\%$ |

External adsorber fins | |||||

(${w}_{\mathrm{fin},\mathrm{sht},\mathrm{A}}$ × ${L}_{\mathrm{gap},\mathrm{A}})$ | $10\mathrm{mm}$ × $20\mathrm{mm}$ | $+4.9\%$ | $+51.8\%$ | $+8.5\%$ | $+5.1\%$ |

External adsorber fins | |||||

(${w}_{\mathrm{fin},\mathrm{sht},\mathrm{A}}$ × ${L}_{\mathrm{gap},\mathrm{A}})$ | no fins | $-4.5\%$ | $-50.0\%$ | $-5.8\%$ | $-7.3\%$ |

Material of metal structures | Copper | $-1.7\%$ | $-16.1\%$ | $-3.5\%$ | $-4.4\%$ |

Material of metal structures | Steel | $-2.6\%$ | $-24.1\%$ | $-5.5\%$ | $-6.5\%$ |

Condenser | |||||

Length of outer fins ${L}_{\mathrm{fin},\mathrm{o},\mathrm{C}}$ | $11\mathrm{mm}$ | $-1.0\%$ | $-4.5\%$ | $-1.7\%$ | $-2.8\%$ |

Length of outer fins ${L}_{\mathrm{fin},\mathrm{o},\mathrm{C}}$ | $45\mathrm{mm}$ | $+1.0\%$ | $+2.7\%$ | $+1.9\%$ | $+3.0\%$ |

Width between fins ${w}_{\mathrm{fin},\mathrm{C}}$ | $25\mathrm{mm}$ | $+1.0\%$ | $+4.5\%$ | $+2.1\%$ | $+3.2\%$ |

Width between fins ${w}_{\mathrm{fin},\mathrm{C}}$ | $25\mathrm{mm}$ | $-1.0\%$ | $-4.5\%$ | $-1.7\%$ | $-2.7\%$ |

Heat transfer coefficient ${\alpha}_{\mathrm{amb},\mathrm{C}}$ | $8\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}$ | $+1.5\%$ | $+5.4\%$ | $+2.9\%$ | $+4.7\%$ |

Heat transfer coefficient ${\alpha}_{\mathrm{amb},\mathrm{C}}$ | $16\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}$ | $+1.9\%$ | $+8.0\%$ | $+4.5\%$ | $+7.4\%$ |

Facade area | $0.5{\mathrm{m}}^{2}$ | $-5.6\%$ | $-26.8\%$ | $-9.7\%$ | $-13.8\%$ |

Facade area | $2{\mathrm{m}}^{2}$ | $+2.2\%$ | $+17.0\%$ | $+7.0\%$ | $+9.1\%$ |

Evaporator | |||||

Surface area | $1.25{\mathrm{m}}^{2}$ | $+20.5\%$ | $-0.9\%$ | / | / |

Surface area | $1.5{\mathrm{m}}^{2}$ | $+31.5\%$ | $-5.4\%$ | / | / |

Surface area | $1.75{\mathrm{m}}^{2}$ | $+33.9\%$ | $+1.8\%$ | / | / |

Surface area | $2{\mathrm{m}}^{2}$ | $+35.0\%$ | $+6.3\%$ | / | / |

Surface area | $3{\mathrm{m}}^{2}$ | $+37.4\%$ | $+15.2\%$ | / | / |

Surface area | $4{\mathrm{m}}^{2}$ | $+38.5\%$ | $+19.6\%$ | / | / |

Surface area | $5{\mathrm{m}}^{2}$ | $+39.2\%$ | $+22.3\%$ | / | / |

Set point temperature ${T}_{\mathrm{set},\mathrm{E}}$ | $12.5\xb0\mathrm{C}$ | $+23.2\%$ | $-22.3\%$ | / | / |

Set point temperature ${T}_{\mathrm{set},\mathrm{E}}$ | $10\xb0\mathrm{C}$ | $+26.7\%$ | $-25.9\%$ | / | / |

Heat transfer coefficient ${\alpha}_{\mathrm{r},\mathrm{E}}$ | $14\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}$ | $+34.9\%$ | $+38.4\%$ | $+17.7\%$ | $+6.4\%$ |

Building | |||||

Compass orientation | |||||

of adsorber facade | $-90\xb0$ | $+1.9\%$ | $-214.3\%$ | $-27.0\%$ | $-18.8\%$ |

Compass orientation | |||||

of adsorber facade | $-67.5\xb0$ | $+7.5\%$ | $-45.5\%$ | $-17.9\%$ | $-17.3\%$ |

Compass orientation | |||||

of adsorber facade | $-22.5\xb0$ | $-0.7\%$ | $+12.5\%$ | $+7.8\%$ | $-0.1\%$ |

Compass orientation | |||||

of adsorber facade | $0\xb0$ | $-3.8\%$ | $+33.0\%$ | $+15.3\%$ | $-2.0\%$ |

#### 4.3.3. Evaporator

#### 4.3.4. Building

#### 4.4. Optimum Cases

#### 4.4.1. Practical Optimum Case

#### 4.4.2. Ideal Optimum Case

## 5. Conclusions and Outlook

- It was found that cooling power levels of up to $100\mathrm{W}/{\mathrm{m}}^{2}$ can be reached with a practical best-case configuration. This compares well to the values of state-of-the-art cooling ceilings. The current system is able to provide constant cooling powers of around $75\mathrm{W}/{\mathrm{m}}^{2}$ for more than 13 hours. Nevertheless, the system is not able to provide constant power levels higher than around $75\mathrm{W}/{\mathrm{m}}^{2}$ due to the finite adsorption rate of the adsorber.
- The optimal surface ratio of the component adsorber and evaporator strongly depends on the heat transfer that can be realized between room and the evaporator, which depends on the heat transfer coefficient and the set-point temperature of the evaporator. With the configuration of the reference case with a determined cooling rate of $54\mathrm{W}/{\mathrm{m}}^{2}$, the $1{\mathrm{m}}^{2}$ adsorber can be connected to up to $1.5{\mathrm{m}}^{2}$ of evaporator area. For higher cooling rates, the ratio should be 1:1, as the adsorption rate of the adsorber is limited. The surface area of the condenser has only minor influence on the cooling performance.
- The parameters with the highest impact on the cooling power and cooling energy, respectively, are the solar collector efficiency of the adsorber, the surface ratios, the orientation of the facade carrying the adsorber, the configuration of the external fins on the absorber sheet and the maximum heat flux between evaporator and adjacent room determined by the heat transfer coefficient and the temperature difference.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Cross-section view and operating principle of a high-rise building equipped in floor n (exemplarily) with the facade-integrated adsorption system for solar cooling. The main components are: A—adsorber, C—condenser, E—evaporator. The regeneration phase, in which the adsorber is heated up by solar irradiation, is shown on the left hand side and the cooling phase on the right hand side. The colored arrows indicate the main heat fluxes during the two phases.

**Figure 2.**Design scheme and model domain (dashed red box) of the adsorber (cross-section side view). The scheme is not to scale, as the height is approximately 1 m, while the width in z-direction is only approximately 10 cm. The absorber sheet is equipped with metal fins inside the air gap channel.

**Figure 3.**Design schemes and model domain (dashed red box) of the condenser (cross-section top and front view). The schemes are not to scale as the height and length are approximately 1 m, while the width in z-direction is approximately 8 cm. (

**a**) Cross-section top view of the condenser, (

**b**) cross-section front view of the condenser.

**Figure 4.**Design scheme and model domain (dashed red box) of the evaporator (cross-section side view).

**Figure 5.**Ambient temperature and solar radiation on 26 August 2016 for a site in Stuttgart, Germany. The solar radiation is determined for a vertical facade with compass orientation south-east.

**Figure 6.**Operational phases (blue boxes) and switching strategy of the adsorption system. The corresponding switching criteria are given in the black boxes.

**Figure 7.**Evolution of the water uptake inside the adsorber over 10 consecutive days with identical ambient conditions for the reference case.

**Figure 8.**Evolution of temperatures, pressures, water uptake, water masses and cooling power of the three components adsorber, condenser and evaporator over the time t for the reference case. The four operational phases are numbered, where ➀ refers to the regeneration phase, ➁ refers to the inter-cooling phase, ➂ refers to the cooling phase and ➃ refers to the inter-heating phase. The parts of the figure covered by the legend can be seen from the first half of the figures. The cooling power $\dot{q}$ is given per installed square meter of adsorber facade.

**Figure 9.**Evolution of cooling powers over the time t for different configurations analyzed in the parametric study. The parts of the figure covered by the legend can be seen from the first half of the figures. The cooling power $\dot{q}$ is given per installed square meter of adsorber facade.

**Figure 10.**Evolution of cooling powers over the time t for the practical and the ideal optimum case, see Table 6. The parts of the figure covered by the legend can be seen from the first half of the figures. The cooling power $\dot{q}$ is given per installed square meter of adsorber facade.

Previous Works by co-Author Schaefer | |||
---|---|---|---|

Model Aspect | Fundamental Adsorber Model [32,33] | Sauna Oven Application [34] | This Work |

Mass transfer inside the adsorber | ✓ | ✓ | ✓ |

Heat transfer inside the adsorber | ✓ | ✓ | ✓ |

Heat transfer fluid inside the adsorber | ✓ | - | - |

Metal plate to absorb heat | - | ✓ | ✓ |

Metal fins inside the adsorber | - | ✓ | ✓ |

Solar collector | - | ✓ | - |

Evaporator | - | - | ✓ |

Condenser | - | - | ✓ |

Operation strategy for building application | - | - | ✓ |

**Table 2.**Coefficients of the solar collector efficiency, see Equation (7).

Parameter | Evacuated Flat | Flat Plate Collector | Average |
---|---|---|---|

Plate Collector | |||

${\eta}_{0}(-)$ | $0.737$ | 0.791 | 0.764 |

${c}_{1}(\mathrm{W}/\left({\mathrm{m}}^{2}\mathrm{K}\right))$ | $0.504$ | $4.47$ | $2.487$ |

${c}_{2}(\mathrm{W}/\left({\mathrm{m}}^{2}{\mathrm{K}}^{2}\right))$ | $0.006$ | $0.007$ | $0.0065$ |

Parameter | Value |
---|---|

Geometry—Adsorber, see Figure 2 | |

width between internal fins | ${w}_{\mathrm{z},\mathrm{A}}=30\mathrm{mm}$ |

length of internal fins | ${L}_{\mathrm{z},\mathrm{A}}=50\mathrm{mm}$ |

thickness of internal fins | ${h}_{\mathrm{fin},\mathrm{z},\mathrm{A}}=3\mathrm{mm}$ |

thickness of absorber sheet | ${L}_{\mathrm{sht},\mathrm{A}}=2\mathrm{mm}$ |

width of air gap channel | ${L}_{\mathrm{gap},\mathrm{A}}=10\mathrm{mm}$ |

width between external fins | ${w}_{\mathrm{fin},\mathrm{sht},\mathrm{A}}=20\mathrm{mm}$ |

Geometry—Condenser, see Figure 3 | |

width between fins | ${w}_{\mathrm{fin},\mathrm{C}}=50\mathrm{mm}$ |

length of inner fins | ${L}_{\mathrm{fin},\mathrm{i},\mathrm{C}}=81\mathrm{mm}$ |

length of outer fins | ${L}_{\mathrm{fin},\mathrm{o},\mathrm{C}}=22.5\mathrm{mm}$ |

thickness of fins | ${h}_{\mathrm{fin},\mathrm{C}}=3\mathrm{mm}$ |

thickness of casing | ${s}_{\mathrm{C}}=3\mathrm{mm}$ |

Geometry—Evaporator, see Figure 4 | |

thickness of bottom sheet | ${s}_{\mathrm{E}}=3\mathrm{mm}$ |

Parameter | Value | Unit |
---|---|---|

Boundary conditions | ||

${T}_{\mathrm{r}}$ | 23 | °C |

${T}_{\mathrm{set},\mathrm{E}}$ | 15 | °C |

${T}_{\mathrm{amb}}$ | time-dependent, see Figure 5 | °C |

${\dot{q}}_{\mathrm{sol}}$ | time-dependent, see Figure 5 | $\mathrm{W}/{\mathrm{m}}^{2}$ |

${\eta}_{\mathrm{sol}}$ | average, see Table 2 | - |

Initial conditions | ||

${T}_{\mathrm{A},0}$ | 23 | °C |

${T}_{\mathrm{C},0}$ | 21 | °C |

${T}_{\mathrm{E},0}$ | 23 | °C |

${p}_{\mathrm{A},0}$ | $24.93$ | $\mathrm{mbar}$ |

${p}_{\mathrm{C},0}$ | $24.93$ | $\mathrm{mbar}$ |

${p}_{\mathrm{E},0}$ | $28.17$ | $\mathrm{mbar}$ |

${X}_{\mathrm{A},0}$ | $0.3393\phantom{\rule{0.222222em}{0ex}}(33.93\%)$ | $\mathrm{kg}/\mathrm{kg}$ |

${m}_{\mathrm{w},\mathrm{C},0}$ | 40 | $\mathrm{kg}$ |

${m}_{\mathrm{w},\mathrm{E},0}$ | 10 | $\mathrm{kg}$ |

Parameter | Ref. Case | Pract. Optimum | Ideal Optimum | Unit |
---|---|---|---|---|

Adsorber | ||||

${\eta}_{\mathrm{sol}}$ | Average | Average | High | % |

${L}_{\mathrm{fin},\mathrm{abs},\mathrm{A}}$ | 10 | 20 | 20 | $\mathrm{mm}$ |

${w}_{\mathrm{fin},\mathrm{abs},\mathrm{A}}$ | 20 | 10 | 10 | $\mathrm{mm}$ |

Condenser | ||||

${w}_{\mathrm{C}}$ | 50 | 50 | 25 | $\mathrm{mm}$ |

${L}_{\mathrm{fin},\mathrm{o},\mathrm{C}}$ | $22.5$ | 45 | 45 | $\mathrm{mm}$ |

${\alpha}_{\mathrm{amb},\mathrm{C}}$ | 4 | 8 | 16 | $\mathrm{W}/\left({\mathrm{m}}^{2}\mathrm{K}\right)$ |

Evaporator | ||||

${T}_{\mathrm{set},\mathrm{E}}$ | 15 | $12.5$ | $10;12.5;15$ | °C |

${\alpha}_{\mathrm{air},\mathrm{E}}$ | 7 | 7 | 14 | $\mathrm{W}/\left({\mathrm{m}}^{2}\mathrm{K}\right)$ |

${A}_{\mathrm{E}}$ | 1 | $1;1.5;2$ | 1 | ${\mathrm{m}}^{2}$ |

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## Share and Cite

**MDPI and ACS Style**

Boeckmann, O.; Marmullaku, D.; Schaefer, M.
Dynamic Modeling and Simulation of a Facade-Integrated Adsorption System for Solar Cooling of Lightweight Buildings. *Energies* **2024**, *17*, 1706.
https://doi.org/10.3390/en17071706

**AMA Style**

Boeckmann O, Marmullaku D, Schaefer M.
Dynamic Modeling and Simulation of a Facade-Integrated Adsorption System for Solar Cooling of Lightweight Buildings. *Energies*. 2024; 17(7):1706.
https://doi.org/10.3390/en17071706

**Chicago/Turabian Style**

Boeckmann, Olaf, Drin Marmullaku, and Micha Schaefer.
2024. "Dynamic Modeling and Simulation of a Facade-Integrated Adsorption System for Solar Cooling of Lightweight Buildings" *Energies* 17, no. 7: 1706.
https://doi.org/10.3390/en17071706