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MIT International Journal of Mechanical Engineering, Vol. 4, No. 2, August 2014, pp. 115-119 115ISSN 2230- 7680 © MIT Publications

Development of Mathematical Model of Chiller System Considering Heat as well as

Pressure LossesR.S. Mukherjee

Department of Mechanical Engineering, Technocrats Institute of Technology

Department of Mechanical Engineering,

Himanai khandelwalDepartment of Mechanical Engineering,

Technocrats Institute of Technology

E-mail; [email protected]

Nomenclature

COP Coefficient of performance

h j Specific enthalpy of refrigerant at state point j (kJ/kg)

m mass flow rate (kg/s)

DPcond pressure loss in condenser (kpa)

DPevap pressure loss in evaporator (kpa)

Qcond heat rejected by condenser (kj)

Qevp heat absorbed by evaporator (kj)

Qsusloss heat loss in suction line (kj)

Qpcloss heat loss due to pressure loss in condenser (kj

Qdisloss heat loss in discharge line (kj)

Wcomp compressor work (kj/sec)

Qcomploss heat loss in compressor (kj/sec)

TWine water inlet temperature in evaporator

TWoe water outlet temperature in evaporator

INTRODUCTIONNowdays, there is a high energy consumption associated with refrigeration and air conditioning systems[1], most of these fa-cilities are based on the vapour compression cycle. In order to reduce their consumption, it is necessary both to have efficient systems and to operate them properly. To achieve these objectives, it is convenient to use complete models, which take under con-sideration a large amount of factors and facilitate the design of efficient systems. In the same way, there is also a need for models, with low computational cost, to simulate the performance of any facility and that can be used to improve the system operation and to evaluate its performance easily. Taking into account that operating the facilities properly is as important as having efficient systems, this work is focused on developing a model that can be used in any installed facility to simulate the system performance in order to optimize its operation.[2]The development of refrigeration system models which simulates the actual working of a reciprocating chiller has been the goal of many researchers [10-13]. The simplest model is the Carnot model, which represents an ideal refrigeration cycle without any

In this work, a finite-time thermodynamic model which simulates the working of an actual vapour-compression system is developed by considering heat and pressure losses using R-134a as a circulating refrigerant. The developed model is mainly based on well known physical equations and partially based on empirical and parametrical correlations. As input data uses only the main operating variables: evaporating and condensing refrigerant pressures. Mass flow rates, and inlet temperature of secondary fluid, and returns as main values. All refrigerant temperatures, secondary fluid exit temperatures, refrigerating effect, compression power consumption and COP. In this way the model allows to analyze easily the influence of the main operating variables on the energy performance. Furthermore, the model results are validated using experimental data taken from a test rig in a wide range of operating conditions. The agreement between the model predictions and the actual values is found to be within ±5%.Keywords: Vapour compression refrigeration system, RE, COP, mass flow rate.

ABSTRACT

Bhopal, M.P

vishal Saxena

M.J.P. Rohilkhand University, Bareilly, U.P.

Bhopal, M.P


irreversible losses. The Carnot model is considered to be a design goal for actual systems. It should be noted that the finite-time thermodynamic model accounts for irreversibility’s existing due to the finite temperature difference in the heat exchangers as well as the losses due to non-isentropic compression and expansion in the compressor and expansion valve of the system, respectively. The thermodynamic model can be modified by including the heat leaks to and from the system, and pressure loss as shown in Fig. 1. The model using the actual refrigerant properties can be reduced to an ideal refrigerant cycle model by eliminating pressure losses, irreversible losses in the heat exchangers and compressor of the system. In this regard, analysis of an actual system is studied in detail Reciprocating chillers are commonly used in a wide range of commercial and industrial refrigeration applications.[8] They represent a substantial fraction of the installed refrigeration systems. The chiller consists of an evaporator, reciprocating com-pressor, condenser and an expansion valve. All the components of the cycle are connected in a closed loop, as shown in Fig. 1, while the temperature-entropy diagram indicating corresponding thermodynamic processes is shown in Fig. 2. As it is known that there is always a pressure drop in both the condenser and the evaporator, for simplicity these losses are used to ignored [1] but in the present discussion., these losses are considered with other losses to create more accurate model that simulate the performance of VCRS.

LITERATURE REvIEWIn the available literature, there is a large body of work that deals with modelling vapour compression systems [3,4]. Focusing on the models based on Physics laws, Braun et al. [5] developed a model for variable speed centrifugal chillers useful for predicting power requirement and cooling capacity. Beyene et al. [6] mod-eled and simulated conventional chillers using DOE2 software, obtaining performance values to compare among different kinds of chillers. Browne and Bansal [7] presented a model for predicting vapour compression chiller performance from secondary fluids temperatures, using an elemental NTU-efficiency methodology. Khan and zubair also proposed model for refrigeration system [8]. Saiz Jabardo et al. [9] proposed a model for automotive air conditioning systems based on a NTU-efficiency model that predicts refrigerant capacity, power consumption and other important pa-rameters for the performance of the system from secondary fluids conditions and evaporating temperature. Continuing with the main objective of these works, this paper proposes a model to predict the performance of a vapour com-pression plant including the various heat as well as pressure losses.

Fig. 1: Schematic diagram of a simple refrigeration cycle considering losses

Fig. 2: Temperature entropy diagram of simple refrigeration cycle considering losses


MODEL DEvELOPMENT AND vALIDATIONConsidering the steady-state cyclic operation of the system shown in Figs. 1 and 2, refrigerant vapor enters the compressor at state 4 and saturated liquid exits the condenser at state 6. The refrigerant then flows through the expansion valve to the evapo-rator. Referring to Fig. 1, using the first law of thermodynamics and the fact that the change in internal energy is zero for a cyclic process, we getQcond + Qdis

loss + Qpcloss – (Qevp + Qsuc

loss + Qpcloss) – (Wcomp – Qcomp

loss ) = 0

1. Expansion valve:Process 6-7 is an isenthalpic process therefore h6 = h7

h6 Is calculated from table at (Pcond –DPcond) = P6

DPcond = 25% of Pcond

h6 = hf at p6, t6 = tsat at p6

2. Evaporator Heat transfer to and from the cycle occurs by convection to flowing fluid streams with finite mass-flow rates and specific heats. Therefore heat transfer rate related to effectiveness is given by ε = Qevap/Qmax

= mw. Cpw (TWine – TWee) / mw. Cpw (PWine – T7)T7 is calculated from table at T7 = Tsat at P7, P7 = Pevap + DPevap

DPevap = 30% of Pevap It is assumed that the heat leaking into the suction line[1] is Qloss

suc = mr × h4 – hd

(Qsuctinloss )evap = 50% of (Qevap)ref

5% of (Qevap)ref = (Qevap)ref – (Qevap)w

.05 mref (h4 – h7) = mref (h4 – h7) – mw.Cpw (TWine – TWoe)h4 Can be calculated from eqn, aboveT4 Can be calculated at h4, P4 from table RE = mref (h4 – h7) in kwAlso ε = 1 – exp(–NTU)

UA = Cmin.ln (1/1 – εcond)Uevap in watt/m2°C

3. CompressorThe power required by the compressor is described in terms of an isentropic efficiency, given by ha = h4 + (hb – h4)/ηisentrope

S4 = Sb and Pb = Pc, hb can be calculated from tableThus ha can be calculated in kj/kg Heat loss in compressor: Qcomp

loss = mr(ha – h4) – (hb – h4)

Assume, Scomploss = Qloss

discharge

The heat leakage from the discharge can be expressed [1] as Qcomp

loss+ Qlossdischarge = mref(ha – h1)

h1 can be calculated in kj/kgT1 can be calculated in kj/kg T1 can be calculated at h1, P1, from table.

(Wcomp)act = mref(ha – h4). kW The COP is defined as the refrigerating effect over the net work input, COP = RE / (Wcomp)act

4. Condenser The heat-transfer rate between the refrigeration cycle and the sink in the condenser is given by

(Wcomp)ref = mref (h1 – h6) kW (Qcond)ref = (Qcond)w = mwCpw (TWoc – TWinc) TWoc calculated in KNow, ε = 1 – exp(–NTU)

It is known that when one of the fluids is undergoing a phase change, based on the fact that a major portion of the heat exchang-ers in this system is in two-phase region, we can write from the heat exchanger theory Ucond = (1/A). (Cmin. ln (1/1 – Ccond)). It should be kept in mind that Cmin is the thermal capacitance rate of that fluid in the heat exchanger which is not undergoing a phase change, [20] (qureshi and zubair) therefore, Cmin = mW CPw

Ucond in watt/m 2°C.The above equations are solved by “C” program. The program gives the COP and all other system parameters as output for the given set of input data given below. Input parameters: • Operating pressure of condenser and evaporator

(Pc, Pe):1385.4 kpa and 179 kpa • Mass flow rate of water and refrigerant () :.046 kg/sec

and .008 kg/sec • Inlet water temperature in condenser and evaporator

(Twinc, TWine):18.30C

vALIDATION OF EXPERIMENTAL RESULTS WITH MATHEMATICAL MODEL RESULTOUTPUTS MATHEMATICAL

RESULTEXPERIMENTAL

RESULTERROR( %age)

T1 (0C) 70.84 70.1 .01

T6 (0C) 40.96 40.8 .003

T7 (0C) -7.3 -6.9 .05


T4 (0C) 6.37 10.3 .38

COP 2.10 2.2 .04RE (kW) 1.136 1.134 .001Wcomp (kW)

0.539 0.555 .028

Ucond (watt/m2 0C)

152.46 152.2 .001

Uevap (watt/m2 0C)

76.23 75.69 .007

Twoe (0C) 12.39 12.4 .004

Twoc (0C) 26.13 26 .005

RESULT AND CONCLUSION

Fig. 3: variation of refrigeration effect with mass flow rate

Fig. 4: variation of compressor work with mass flow rate

With the help of model, the performance of the refrigeration system can be analysed by varying the mass flow rate at constant inlet temperature of secondary fluid i.e. water. The variation also simulates the fouling condition. The study further can help in evaluating the effect of fouling on various performance param-eters. To substantiate the nature of these curves in a rigorous manner, all of them were fitted to see how close each resembles logarithmic behaviour

Fig. 3 shows the variation of refrigeration effect with the mass flow rate at different inlet temperature of water .it shows the logarithmic behaviour and with increase in temperature there is increase in refrigeration effect. Fig. 4 shows the variation of com-pressor work with mass flow rate at different inlet temperature. The variation is logarithmic and with increase in temperature the compressor work will also increaseSimilarly Fig. 5 shows the variation of coefficient of performance with increase in mass flow rate i.e. also of logarithmic behaviour and COP is not much affected when inlet temperature of both condenser and evaporator increases simultaneously.

Fig. 5: variation of coefficient of performance with mass flow rate

CONCLUSIONThe computer simulation of reciprocating refrigeration systems using the thermodynamic model involves the use of actual re-frigerant properties. Using such a model, the system COP and all other system parameters are calculated accurately (within 5.0% of the actual values). The model is demonstrated to be a useful tool for design and performance evaluation of the refrigeration systems. In this regard, the performance characteristics of a system are discussed with respect to various irreversible losses of the system.The model using the actual refrigerant properties, reduced to an ideal refrigerant cycle model by eliminating pressure losses, irreversible losses in the heat exchangers and compressor of the system. Many models have been developed for evaluating the perfor-mance of VCRS system, but none of them includes the various losses that actually occurred in the system. The chillers perfor-mance curves of an actual reciprocating refrigeration system are explained by taking into account various losses of the system.The present work expresses the following points in a suggested mathematical model: 1. It simulates the performance of VCRS with the help of

model developed accurately. 2. It considers various losses in the unit. 3. The model developed is based on input as operating pres-

sures, secondary fluid input condition and mass flow rates. 4. It can further also help in analysing the effect of fouling

in both evaporators as well as in condenser.


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