# Hybrid Adsorption-Compression Systems for Air Conditioning in Efficient Buildings: Design through Validated Dynamic Models

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## Abstract

**:**

## 1. Introduction

- thermophysical models, making use of the constitutive equations of the system, that can be solved through a numerical or iterative approach;
- black box models, that are based on a completely empirical approach;
- grey box models, combining a semi-empirical approach with the physical models for one or more components.

## 2. System Description

- if solar energy is not available, cold energy is produced directly from the vapour compression chiller, that can be directly connected to the dry cooler.
- If there is a mismatch between the solar availability and user demand, in order to exploit the renewable source, cold energy can be produced using the cascade system and stored in a sensible or latent cold storage.
- During winter, the heating demand of the building can be satisfied by direct connection to the solar collectors (if solar energy is available) or by the heat pump.
- Domestic hot water can be supplied by the solar collectors, coupled to a small water buffer or a back-up system (i.e., existing gas boiler in case of retrofitting).

## 3. Model Description: Adsorption Module

#### 3.1. Generalities and Assumptions

- all components are lumped models with uniform properties;
- the heat transfer fluid inside the heat exchangers is incompressible;
- pressure drops inside the heat exchangers are constant;
- gravity is neglected;
- the thermal masses of vacuum vessels are neglected;
- there are no heat losses to the environment;
- there is no direct heat exchanger due to conduction between the components;
- there are no inert gases inside the closed volume.

#### 3.2. Heat Exchange Model

#### 3.3. Adsorption Model

_{sorb}, pressure p

_{ads}in the adsorber, as well as the heat of adsorption [60]. Among them, for the SAPO-34 sorbent considered, the Dubinin-Ashtakov (DA) correlation was selected [61]:

_{0}and n are empirical constants and A is the adsorption potential:

#### 3.4. VLE Model

## 4. Model Description: Compression Chiller

#### 4.1. Assumptions

- All components are lumped, with constant properties.
- One dimensional flow in each component with uniform velocity profile.
- No pressure loss inside the heat exchangers. Instead, lumped pressure loss models in both refrigerant and water pipelines were employed.
- Heat losses to the ambient are neglected for every component.
- Neglected dynamics for the compressor.
- Constant electromechanical efficiency of the compressor motor.
- Existence of subcooling and superheating at the outlet of the condenser and the evaporator respectively.
- Heat transfer coefficients vary with their nominal values according to the mass flow rate to nominal mass flow rate ratio.

#### 4.2. Heat Exchangers Models

#### 4.3. Compressor Model

#### 4.4. Thermostatic Expansion Valve model (TEXV)

## 5. Model Validation

#### 5.1. Adsorption Module

^{®}(by Mitsubishi Chemical Corporation, Tokyo, Japan), with grain size 0.710–0.800 mm, published in [74], were used. The results are shown in Figure 7, where the temporal evolution of the dimensionless uptake for simulation and experiments are compared. The dimensionless uptake represents the ratio between the uptake at each instant and the uptake at equilibrium in the temperature-pressure conditions tested. Commonly, the value of time needed to complete 63% of the adsorption reaction and the time needed to reach 80% of maximum uptake are used for sizing and evaluation analysis on dynamic properties of sorbents. It is possible to conclude that the model can actually reproduce with good accuracy such conditions, thus being a useful tool. The maximum deviation with experiments is around 7.5%, which is within uncertainty of measurement and is concentrated in the part of the curve with low loading, where the experimental conditions are affected by several external factors, such as vibrations due to the switching of the hydraulic circuits and so on.

#### 5.2. Compression Chiller

## 6. Hybrid System Integrated Model: Results

- the temperature of the heat source is higher than a user-defined value (in the present case, 75 °C);
- the temperature in the chilled water circuit (evaporator secondary circuit) of the adsorption unit is lower than T
_{amb}− 5 °C, the condition under which direct connection of the compression unit with the external sinks becomes more favorable.

#### 6.1. Results in Dynamic Conditions

#### 6.2. Sensitivity Analysis

#### 6.3. Applications of the Model

- (a)
- lookup tables, useful for example as input data in a TRNSYS or Energy Plus model for annual energy evaluation or to test different control strategies at system level;
- (b)
- analytical equations, correlating the EER/COP to the operating conditions. Such equations can be re-used in a simplified model to be applied for optimization of control strategies.

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | Adsorption potential, kJ |

b | Equilibrium constant, kg/J |

c_{p} | Specific heat, kJ/kg K |

D | Diffusion coefficient, m^{2}/ s |

e | efficiency |

E | Adsorption equilibrium coefficient, kJ/kg |

h | Specific enthalpy, kJ/kg |

H | Enthalpy, kJ |

K | Flow coefficient, bar^{-1/2} kg/s |

L | Length, m |

m | Mass, kg |

$\dot{m}$ | Mass flow, kg/s |

N | Adsorption equilibrium exponent |

p | Pressure, Pa |

P | Electric power, kW |

Q | Energy, kJ |

$\dot{Q}$ | Thermal Power, kW |

r | Radius, m |

R | Universal gas constant, kJ/(kg K) |

rpm | Rotations, 1/min |

RS | Relative size, kW/kW |

S | Surface, m^{2} |

slip | Motor slip factor |

t | Time, s |

T | Temperature, °C |

U | Internal energy, kJ |

V | Volume, m^{3} |

w | Uptake, kg/kg |

W | Work, kW |

w_{0} | Equilibrium constant, kg/kg |

x | Vapour quality |

y | Control signal |

Greek letters | |

α | Heat transfer coefficient, W/(m^{2}K) |

β | Adsorption rate constant, 1/s |

ε | Heat Exchanger effectiveness |

$\kappa $ | Hybrid/compression chiller pressure ratio, bar/bar |

ρ | Density, kg/m^{3} |

γ | Mean Void Fraction |

Subscripts | |

ads | adsorption |

amb | ambient |

c | channel |

comp | compressor |

cond | condenser |

ev | evaporator |

el | electric |

eq | equilibrium |

hyb | hybrid |

in | inlet |

is | isentropic |

l | liquid |

mot | motor |

nom | nominal |

out | outlet |

ref | refrigerant |

s | swept |

sat | saturation |

sf | secondary fluid |

sorb | adsorbent |

sync | synchronous |

th | thermal |

v | vapour |

vol | volumetric |

Abbreviations | |

CV | Control Volume |

EER | Energy Efficiency Ratio, kW/kW |

HEX | Heat EXchanger |

HTF | Heat Transfer Fluid |

NTU | Number of Heat Transfer Units |

SB | SubCooled |

SH | SuperHeated |

TEXV | Thermostatic EXpansion Valve |

TP | Two Phase |

## Appendix A

_{set}:

**Table A1.**Parameters of equilibrium equation [11].

Phase | A [kJ/kg] | w_{0} [kg/kg] | E [kJ/kg] | n |
---|---|---|---|---|

Adsorption | <450 | 0.31 | 388.8 | 3 |

>450 | 265 | 0.8 | ||

Desorption | <200 | 0.3 | 400 | 3.5 |

>200 < 305 | 810 | 1.8 | ||

>305 < 410 | 410 | 6 | ||

>410 | 410 | 1.2 |

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

${\alpha}_{ads}$ | 120 W m^{−2} K^{−1} | [40,63] |

${c}_{{p}_{sorb}}$ | 10^{3} J kg^{−1} | [80] |

D | 3.3 ·10^{−10} m^{2} s^{−1} | Experimental data fitting parameter |

h_{ads} | 2.6 ·10^{6} J kg^{−1} | [61] |

f_{v} | 10^{−5} m s | [34] |

f_{p} | 0.1 kg s^{−1} | [34] |

m_{sorb} | 20 kg | Provided by the component manufacturer |

m_{metal,ads} | 24.5 kg | Provided by the component manufacturer |

V_{HTF,ads} | 10.5 l | Provided by the component manufacturer |

${\dot{m}}_{ads}$ | 0.5 kg s^{−1} | Provided by the component manufacturer |

m_{ref} | 6 l | Provided by the component manufacturer |

α_{HTF,cond} | 3000 W m^{−2} K^{−1} | Calculated from experimental data reported in [16] |

α_{HTF,evap} | 1500 W m^{−2} K^{−1} | Calculated from experimental data reported in [16] |

α_{ref,cond} | 1000 W m^{−2} K^{−1} | Calculated from experimental data reported in [16] |

α_{ref,evap} | 500 W m^{−2} K^{−1} | Calculated from experimental data reported in [16] |

m_{metal,cond} | 25 kg | Provided by the component manufacturer |

m_{metal,evap} | 25 kg | Provided by the component manufacturer |

V_{HTF,cond} | 3.8 l | Provided by the component manufacturer |

V_{HTF,evap} | 3.8 l | Provided by the component manufacturer |

${\dot{m}}_{cond}$ | 1.8 kg s^{−1} | Provided by the component manufacturer |

${\dot{m}}_{evap}$ | 0.5 kg s^{−1} | Provided by the component manufacturer |

## Appendix B

Parameter | Description | Value | Source | |
---|---|---|---|---|

Heat Exchanger Models | ||||

Evaporator | Condenser | |||

$N$ | Number of plates | 24 | 30 | HEX Manufacturer |

${S}_{c}\left({\mathrm{m}}^{2}\right)$ | Cross sectional area of a channel | 2.08·10^{−4} | 2.08·10^{−4} | HEX Manufacturer |

$S\left({\mathrm{m}}^{2}\right)$ | Heat transfer area | 1.32 | 1.68 | HEX Manufacturer |

${M}_{wall}\left(\mathrm{kg}\right)$ | Total wall mass | 12 | 16 | HEX Manufacturer |

${c}_{wall}\left(\mathrm{J}/\mathrm{kgK}\right)$ | Wall specific heat capacity | 490 | 490 | HEX Manufacturer |

${\dot{m}}_{nom}\left(\mathrm{kg}/\mathrm{s}\right)$ | Refrigerant nominal flow rate for the refrigerant | 0.078 | 0.078 | Chiller Manufacturer |

${\dot{m}}_{sf,nom}\left(\mathrm{kg}/\mathrm{s}\right)$ | Water nominal flow rate | 0.63 | 0.78 | Chiller Manufacturer |

${a}_{SH,nom}$ $\left(\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}\right)$ | Nominal heat transfer coef. SH CV | 450 | 500 | Calculated |

${a}_{TP,nom}$ $\left(\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}\right)$ | Nominal heat transfer coef. TP CV | 5000 | 3400 | Calculated |

${a}_{SB,nom}\left(\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}\right)$ | Nominal heat transfer coef. in SB CV | − | 500 | Calculated |

${a}_{sf,nom}\left(\mathrm{W}/{\mathrm{m}}^{2}\mathrm{K}\right)$ | Nominal heat transfer coef. for water | 7100 | 8400 | Calculated |

$\gamma $ | Mean Void Fraction | 0.96 | 0.8 | Calculated |

$\Delta {p}_{nom}\left(\mathrm{bar}\right)$ | Nominal lumped pressure drop for the whole refrigerant line | 0.2 | 0.2 | Chiller Manufacturer |

${\Delta}_{p}{}_{sf,nom}\left(\mathrm{bar}\right)$ | Nominal lumped pressure drop on the water side | 0.196 | 0.12 | Chiller Manufacturer |

Compressor Model | ||||

${V}_{s}$ (cm³/rev) | Compressor Swept Volume | 51 | Chiller Manufacturer | |

${N}_{p}$ | Magnetic poles of compressor motor | 2 | Chiller Manufacturer | |

$slip$ | Slip factor of compressor motor | 0.029 | Chiller Manufacturer | |

${e}_{v,n}$ | Volumetric efficiency on nominal conditions | 0.945 | Calculated | |

${e}_{is,n}$ | Isentropic on nominal conditions | 0.683 | Calculated | |

TEXV Model | ||||

${S}_{full}$ (mm^{2}) | TEXV full open cross sectional area | 2.25 | Calculated | |

${T}_{SH}^{\left(set\right)}\left(\xb0\mathrm{C}\right)$ | TEXV Set point | 4.2 | Standard Value |

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**Figure 1.**The hybrid system proposed: (1) solar thermal collectors field. (2) photovoltaic panels. (3) adsorbers of the adsorption chiller. (4) adsorption chiller condenser. (5) adsorption chiller evaporator. (6) vapour compression chiller condenser. (7) vapour compression chiller evaporator. (8) compressor. (9) dry cooler for heat rejection to the ambient.

**Figure 2.**Layout of the model of the adsorption module with the indication of fluid ports and thermal ports as in the model implementation in Dymola.

**Figure 3.**Schematics of the adsorber (left) and its implementation, with input and output variables and energy flows for the adsorber during adsorption (middle) and desorption (right).

**Figure 4.**Representation of the evaporator/condenser (left) and its implementation, with input and output variables and energy flows for the evaporator (middle) and condenser (right).

**Figure 9.**Compression chiller validation results in terms of relative errors (%) for the evaporator capacity and the EER under various inlet water temperatures.

**Figure 10.**Dymola layout of the hybrid integrated model. 1: sorption module; 2: compression chiller; 3: control unit; 4: 3-way valve for switching between heating and cooling mode of the compression chiller; 5: 3-way valves to switch between the hydraulic connections of the units and the direct connection of the compression chiller to the heat rejection (medium temperature) circuit.

**Figure 11.**Boundary conditions for the dynamic simulation of the hybrid system - temperature and cooling demands for a reference day in Aglantzia (CY).

**Figure 12.**Temperatures in the circuits of the sorption module and heat pump for the reference conditions. The outlet of the evaporator of the adsorption unit (light green) also represents the inlet of the condenser in the vapour compression chiller; the inlet of the of the evaporator of the adsorption unit (dark green) also represents the outlet of the condenser in the vapour compression chiller.

**Figure 13.**Thermal powers in the components of the sorption module and the vapour compression chiller for the reference conditions.

Reference | Components/Systems Modelled | Type of Model | Simulation Tool | Validation |
---|---|---|---|---|

[37] | Adsorption chiller | Grey-box (coupled heat and mass transfer model of the adsorber and lumped parameters model for the other components) | COMSOL/MATLAB | Yes |

[38,39] | Adsorber, Adsorption chiller | Physical dynamic | Modelica | Yes |

[34] | Adsorption chiller | Physical dynamic | Modelica | Yes |

[40] | Adsorption material | Physical dynamic | COMSOL | Yes |

[41] | Adsorption reactor | Physical dynamic | FEMLAB | No |

[42] | System for adsorption refrigeration-desalination | Physical dynamic | Simulink | No |

[43] | Coated adsorber | Physical–governing equations simplified to an ODE system | Not specified | Yes, with a numerical model of a 2-bed chiller |

[21,44,45,46,47] | Adsorption chiller | Black box | TRNSYS | Models based on experimental data or datasheets |

[48] | Adsorption-sensible storage | Grey box | TRNSYS/MATLAB | No |

[49] | Air-water heat pump with R410a | Physical steady-state and dynamic | Modelica | Yes |

[50] | Air-air heat pump with R134a | Physical dynamic | Modelica | Yes |

[32] | CO2 heat pump | Physical dynamic | Modelica | No |

[31] | Ground-source heat pump | Physical dynamic | Modelica | Yes |

[35] | Variable speed heat pump | Grey box | Modelica/Dymola | Yes |

[51] | Air-water heat pump | Grey box | MATLAB/Simulink | No |

[52] | Water-water and air-water heat pumps | Exergy modelling | - | Yes |

[24,44] | Air-water heat pumps | Black box | TRNSYS | No |

[25,53] | Air-water heat pumps | Black box | IDA-ICE | No |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Palomba, V.; Varvagiannis, E.; Karellas, S.; Frazzica, A. Hybrid Adsorption-Compression Systems for Air Conditioning in Efficient Buildings: Design through Validated Dynamic Models. *Energies* **2019**, *12*, 1161.
https://doi.org/10.3390/en12061161

**AMA Style**

Palomba V, Varvagiannis E, Karellas S, Frazzica A. Hybrid Adsorption-Compression Systems for Air Conditioning in Efficient Buildings: Design through Validated Dynamic Models. *Energies*. 2019; 12(6):1161.
https://doi.org/10.3390/en12061161

**Chicago/Turabian Style**

Palomba, Valeria, Efstratios Varvagiannis, Sotirios Karellas, and Andrea Frazzica. 2019. "Hybrid Adsorption-Compression Systems for Air Conditioning in Efficient Buildings: Design through Validated Dynamic Models" *Energies* 12, no. 6: 1161.
https://doi.org/10.3390/en12061161