ADSORPTION SYSTEM MODELLING
3.3 Formulation
3.3.7 Measurement of system performance
The cyclic average cooling capacity (CACC) can be evaluated by the following expressions:
time Cycle
dt T
T C
time m
cycle of end
time cycle of
begin chill chill f ( chillin chillout)
CACC
, , ,
(3.19)
The cycle coefficient of performance (COP) can be calculated by the following equation:
endofcycletime
time cycle of
begin f f din dout
time cycle of end
time cycle of
begin chill chill f chillin chillout
cycle
dt T T C m
dt T
T C m
, ,
, ,
,
) (
) COP (
(3.20)
Solar COP in a cycle (COPsc) can be expressed as the following expression:
endofcycletime
time cycle of
begin cr
time cycle of end
time cycle of
begin chill chill f chillin chillout
sc n A Idt
dt T
T C
m , ( , , )
COP
(3.21)
Where, in equation (3.21) I is the solar irradiance and Acr is each collector area and n is the number of collector.
Figure 3.2: Artistic view of the solar powered adsorption cooling system 3.4 Methods and Materials
Daily hourly insolation data for Dhaka (Latitude 23°46΄N, Longitude 90°23΄E) measured by the Renewable Energy Research Centre (RERC), University of Dhaka has been used in this study. The maximum and minimum temperatures throughout the year and the sunrise and sunset time have been supplied by Bangladesh Meteorological Department (BMD). Results are produced based on solar data of Dhaka of the month of
April. The configuration of the chiller is same as Alam et al. [5]. During April in Dhaka, the sunrise time is taken as 5.5h and the sunset time is taken as 18.5h while the maximum and minimum temperature for that month is 34°C and 24°C respectively.
Solar radiation in Dhaka for the month of April is taken as 771W/m2 during day time around 11.5h to 12.0h. The climate data for several months is given in Table 3.4 [19].
A cyclic simulation computer programme for different mass allocation has been developed to predict the performance of the innovative single stage chiller with no heat recovery or mass recovery. The set of differential equations (3.2), (3.4), (3.6) and (3.14) has been solved numerically by finite difference approximation with the help of equations (3.15) to (3.18) with a time step of one second. The water vapour concentration in a bed is represented in equation (3.8). Water vapour concentration inside the bed is in very complicated form. It is not feasible to divide the concentration term into the terms of temperature for present and previous time as q is a function of pressure and temperature in very complicated nonlinear form. Therefore, initially the temperature for present step (beginning of the first day) is assumed based on the assumption. The pressure and concentration is then evaluated for the current step based on this assumption of temperature.
And then, gradually the consequent steps are calculated based on the primary concentration with the help of the finite difference approximation. At that time, the newly calculated temperature is checked with the assumed temperature if the difference is not less than convergence criteria, a new assumption is made. Once it fulfills the convergence criteria, then the process goes for the next time step. The initial temperature, concentration and pressure are set on the based on the temperature of the beginning of the day, and then the program allows to run consecutive many days unless the steady conditions arrive. All results are presented here for the 3rd day on which program reaches on steady state condition so that all results are same for next consecutive days. The tolerance for all the convergence criteria is set at 10-4.
The equation for the desorber and collector are completely dependent on each other.
Therefore, those equations are discretized by the implicit finite difference approximations which form a set of linear equations in terms of temperature and their outlet. A Gaussian elimination method is exploited to solve the system of linear equations. In the beginning all initial conditions are set on ambient temperature, however, concentrations have been taken slightly less than its saturated conditions which allow the program run steadily.
Table 3.3: The designing and the operating conditions that used in the simulation
Symbol Description Value
Abed Heat transfer area of adsorbent bed 2.46m2
Aeva Heat transfer area of evaporator 1.91m2
Acon Heat transfer area of condenser 3.73m2
Acr Area of each collector 2.415m2
Wtm Weight of heat exchanger tube metal (Cu) 51.2kg Wfm Weight of heat exchanger fin metal (Al) 64.04kg
M
Weva, Weight of heat exchanger tube (Cu) of evaporator 12.45kg
M
Wcon, Weight of heat exchanger tube (Cu) of condenser 24.28kg Wcp Weight of each collector pipe including absorber
sheet
kg 4913 . 0
Ws Weight of silica-gel in each bed 47kg
r
Weva, Weight of liquid refrigerant inside evaporator initially 50kg
r
Wcon, Weight of condensed refrigerant inside condenser 0.0kg Ubed Heat transfer coefficient of bed 1724.14W/(m2K) Ueva Heat transfer coefficient of evaporator 2557.54 W/(m2K) Ucon Heat transfer coefficient of condenser 4115.23W/(m2K)
Np Number of pipe in each collector 9
hot
m f, Total mass flow rate to CPC panel or to desorber 1.3kg/s
cool
m f, Cooling water mass flow rate to adsorber 1.3kg/s
cont
m f, Cold water mass flow rate to condenser 1.3kg/s
l
Cr, Specific heat of refrigerant in liquid phase 4.18E+03J/(kgK)
v
Cr, Specific heat of refrigerant in vapor phase 1.89E+03J/(kgK) Ccu Specific heat of copper (Cu) 386 J/(kgK) Cal Specific heat of aluminum (Al) 905 J/(kgK) Cs Specific heat of silica-gel (Si) 924J/(kgK)
Rgas Water gas constant 4.62E+02J/(kgK)
L Latent heat of refrigerant vaporization 2.5E+06 J/kg Qst Heat of adsorption (silica-gel in bed) 2.8E+06 J/kg
Ea Activation energy 2.33E+06 J/kg
Dso Diffusion coefficient 2.54E04m2/s
Rp Average radius of silica-gel particle 0.17E03m
Tcool Cooling source temperature 304.15K
in chill
T , Chilled water inlet temperature 287.15K
Table 3.4: Climate data for several months in Dhaka, Bangladesh Month Sunset
time (Hour)
Sunrise time (Hour)
Maximum temperature
(°C)
Minimum temperature
(°C)
Average of maximum radiation in a day (W/m2)
(Average on 7 years)
March 5.5h 18.5h 30.0 18.8 712
April 5.5h 18.5h 34.0 24.0 771
June 5.5h 18.5h 31.4 25.8 568
August 5.5 h 18.5h 32.5 26.6 546
October 6.5h 17.5h 31.2 25.0 536
December 6.5h 17.5h 25.9 16.4 501