Simulation energy consumption

8/11/2019 Simulation energy consumption

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Journal of Thermal Science Vol.23, No.3 (2014) 285289

Received: September 2013 HAO Xuejun, Associate Professor

This paper was supported by a Grant-in-Aid for Scientific Research through grant number KM200610016003 from the Beijing Mu-

nicipal Commission of Education.www.springerlink.com

DOI: 10.1007/s11630-014-0708-4 Article ID:1003-2169(2014)03-0285-05

Simulation Analysis of Factors Influencing Chiller EER

HAO Xuejun, WANG Tong

Beijing University of Civil Engineering and Architecture, Beijing 100044, PR China

Science Press and Institute of Engineering Thermophysics, CAS and Springer-Verlag Berlin Heidelberg 2014

This study constructed a mathematic model of a variable frequency centrifugal chiller using Simulink software.By running the simulation, it was discovered that when the other factors are constant, the EEREnergy Efficiency

Ratio of the chiller increases with decreases in the temperature of the cooling water and increases in the tem-

perature of the chilled water. The effect of changes in the cooling water temperature on the EER of the chiller is

stronger than that of changes in the chilled water temperature. In addition, as the chiller load decreases, the EER

increases until reaching a maximum, after which it decreases. Furthermore, the EER of chillers working under a

constant flow rate is slightly higher than that of those working under varying flow rates.

Keywords:Chiller, Simulation, EER

Introduction

The EER of a chiller is an important index, reflecting

its efficiency and therefore energy consumption. Many

factors directly affect the EER, such as the temperature

of the cooling water, the chiller load, the flow rate, and

the temperature of the chilled water. However, the change

in the EER for a given change in these parameters has

not been quantified. In this paper, using a simulation, a

model of variable-frequency centrifugal chiller was con-

structed (variable-frequency centrifugal chillers are com-

mon). In this paper, the EER was analyzed as a function

of three different parameters: cooling water temperature,chilled water flow, and chilled water temperature.

Description of the mathematical model of a vari-

able-frequency centrifugal chiller

There are two important hypotheses for the mathe-

matical modeling of a variable-frequency centrifugal

chiller in this paper.Because chillers can maintain the chilled water tem-

perature near the value set by the automatic control

equipment, this paper assumes that the temperature of the

chilled water is constant.

This paper neglects the heat transferred through the

wall of the pipe and compressor. Specifically, this paper

considered the load of the condenser to be equal to the

sum of the refrigerating capacity and compressor power.

Mathematical model of the evaporator

In a centrifugal chiller, the evaporator is generally a

full liquid evaporator. To keep the evaporator liquid levelconstant, it is generally equipped with a float ball valve,

which controls the flow rate of the refrigerant according

to the liquid level of the evaporator. Thus, in this paper,

the liquid level of the evaporator is considered constant.

Applying energy conservation, the amount of heat lost

be the chilled water is equal to the amount of heat trans-

ferred from the chilled water side to the refrigerant side.

That is,


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286 J. Therm. Sci., Vol.23, No.3, 2014

1 20 Z1 2

1

2

C M (T T ) K A

ln

z zz

z z

z z

T TQ

T T

T T

(1)

where Tz1, Tz2inlet and outlet chilled water tem-perature, respectively, C;

Q0refrigerating capacity of the evaporator, W;

Cspecific heat capacity of water, J/(kgC);

Mflow rate of water, kg/s;

Aeffective heat transfer area of the evaporator,

m2;

Kheat transfer coefficient of the evaporator,

W/(m2K).

Formula (1) can be rewritten as

1 2

1

K A

C M

z K A

C M

T T eT

e

(2)

where Tzevaporation temperature of the refrig-

erant, C.

Furthermore, the boiling heat transfer coefficient of

the refrigerant side is [2]

0.5 0.25 0.450

0

16.4 p ( )b zs

hd

(3)

where hbzboiling heat transfer coefficient of the

refrigerant side;

heat flux, W/m2;

p0evaporation pressure, kPa;

sdistance between tubes, m;d0pipe outer diameter, m.

The following formula was used to calculate the con-

vective heat transfer coefficient of the chilled water side [3]:

When Re2100 (laminar region),

1/3 0.141.86 ( ) [Re Pr ( )]i ii ii i

hd d

(4)

When 2100


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HAO Xuejun et al. Simulation Analysis of Factors Influencing Chiller EER 287

efficiency of the compressor.

In formulas (11) - (13), each coefficient associated

with the actual compressor models can be fitted by the

related parameters in the compressor sample. Further-

more, according to mass conservation, the flow rate ofthe compressor is approximately equal to the flow rate of

the evaporatorMo.Because the actual compression process is not isen-

tropic, the actual energy provided is greater than the the-

oretical energy provided:

,2 1( )

c th

ad

WW h h

(14)

where Wactual energy provided, J/kg;

Wc, ththeoretical energy provided, J/kg;

adadiabatic efficiency of the compressor, set as

0.8;

h2enthalpy of the refrigerant at the compressoroutlet, J/kg;

h1enthalpy of the refrigerant at the compressor

inlet, J/kg.

Mathematical model of the condenser

The condenser of the centrifugal chiller is generally

comprised of a horizontal shell and tube condensers. The

flow rate of cooling water is constant. In addition, the

assumption at the beginning of this section shows that the

heat dissipation of condenser is

0eQ Q N (15)

where Qeheat dissipation of the condenser, w.

According to energy conservation, the heat gain from

the cooling water is equal to the heat transferring from

the chilled water to the refrigerant sides.

2 1

2 1

2

1

ln

e ee e e

e e

e e

K A T TQ C M T T

T T

T T

(16)

where Te1, Te2inlet and outlet water temperature of

the condenser, respectively, C.

The condensation heat transfer coefficient of the re-

frigerant side[2] is1

3 2 3

0.65Cg r

hl

(17)

wherehccondensation heat transfer coefficient of the

refrigerant side;

heat flux, w/m2;

thermal conductivity of the refrigerant, w/(mK);

density of the refrigerant, kg/m3;

lstereotype size, m;

kinetic viscosity of the refrigerant, m/s2.

Furthermore, the cooling water side convective heat

transfer coefficient hican be obtained from equations (4)

- (6), and the water side heat transfer coefficient of re-

frigerant side can be obtained from equation (7).

Solving the mathematical model using Simulink

The simulation software used in this paper is Simulink.

By creating the corresponding block diagram with Simu-

link software, the mathematical model can be solved.

Figure 1 shows the block diagram of the centrifugal

Fig. 1 Highest-level block diagram of the centrifugal chiller model


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288 J. Therm. Sci., Vol.23, No.3, 2014

chillers model created in this paper. As observed in the

diagram, the block diagram mainly includes four modules:

the condenser sub-module, the evaporator sub-module, the

compressor sub-module, and a load sub module to calcu-

late the hourly return water temperature and the flow rateof chilled water according to the refrigerating load. Be-

cause the model must iteratively solve numerous equa-

tions at each time step, a do-while module and memory

module are used in the block diagram. First, according to

the hourly load values and the conditions (variable or

constant flow conditions), the program uses the load sub-

module to calculate the hourly return water temperature

Tz1and chilled water flow Mof the chiller and sends the

data to the sub-module of the evaporator. Furthermore,

the sub-module of the evaporator can calculate the re-

frigerating capacity Q0, the flow rate of the vapor dis-

charged from the evaporator M0, the evaporation tem-

perature Te, and the evaporation pressure P1 based onthese two values and sends the flow rate of the vapor

discharged from evaporator M0 and the evaporating

pressure P1 to the centrifugal compressor sub-module.

First, the compressor sub-module calculates the power of

the compressor according to these values as well as the

assumptive initial rotational speed and sends it out. Next,

the condensing load of the condenser Qeis calculated by

adding the power value W to the refrigerating capacity of

the evaporatorQ0in this program, which is then sent to

the sub-module of the condenser. The sub-module of the

condenser can calculate the condensing temperature Td

and condensing pressureP2according these values. Thesub-module of the condenser then sends this pressure

information to the sub-module of the compressor. Next,

the sub-module of the compressor can calculate the theo-

retical energy head Wc, th in accordance with the ideal

constant entropy process using the internally stored data

of the pressure-enthalpy diagram according to the con-

densing pressureP2and the evaporating pressure P1. The

actual energy head W can then be calculated using equa-

tion (14). Substituting this value into equation (11), the

program can calculate a new value of rotational speed N

and send it out. There is an iterative loop structure in the

outermost layer of the model. If the relative error be-

tween the speed value Nin the previous iteration step andthe speed value in this step is greater than 1%, then the

iterative loop structure will send the new speed value N

to the compressor sub-module and perform a new inter-

action. In addition, the memory sub-module can provide

an initial rotational speed for the compressor sub-module.

Above is the general working process of the model.

Performance analysis of variable-frequency cen-

trifugal chillers

Effect of cooling water temperature on the chiller EER

For chillers, the temperature of the cooling water

changes throughout the air-conditioning season. To ana-

lyze how the cooling water temperature affects the chiller

EER, the supply and return water temperature of chilled

water and the flow of the chilled water are taken as con-

stant. By running the simulation, the curve of the chillerEER with the cooling water temperature can be obtained,

as shown in Figure 2. As observed in the figure, when the

temperature of the cooling water decreases, the EER of

the chiller increases. The relationship between these pa-

rameters is nearly linear. This linear relationship is

mainly due to the fact that when the supply and return

water temperature of chilled water and the flow of the

chilled water are constant, the refrigerating capacity of

the chiller and the evaporating pressure is constant;

however, a decrease in the temperature of the cooling

water will lead to a decrease in the condensing pressure.

Thus, the compressor energy head will decrease, as willthe total power.

Fig. 2 EER as a function of cooling water temperature

Effect of flow rate of chilled water on the chiller EER

As seen in Figure 3, whether the chilled water is under

constant or variable flow conditions, the EER of the

chiller increase and then decrease as the chiller load de-

creases. As the load decreases, the chiller EER decreases

more rapidly. The figure shows that the maximum EER

does not occur under the full load condition. In addition,

the chiller EER is lower for the variable flow conditions

than the constant flow conditions. When the chiller ap

proaches the full load condition, the EER is very close

for both flow conditions; however, as the load continuesto decrease, the difference between them increases.

However, overall, both conditions are still very close to

each other. Thus, for the variable-flow primary pump

system, the total energy consumption is not much higher

than that for the constant flow system.

Effect of chilled water temperature on the chiller EER

When the chilled water temperature changes, the EER

also changes. To analyze how a change in the chilled

water temperature will affect the chiller EER, the differ-

ence between the supply and return temperature of the

chilled water is set to 5C, and the flow of the chilled


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HAO Xuejun et al. Simulation Analysis of Factors Influencing Chiller EER 289

Fig. 3 EER as a function of relative chiller load

Fig. 4 EER as a function of chilled water temperature

water as well as the chilled water temperature are as-

sumed to be constant. The simulation provides the chiller

EER as a function of the chilled water temperature, as

shown in Figure 4. As the chilled water temperature in-

creases, the chiller EER will also increase in a nearly

linear fashion. Furthermore, Figures 2 and 4 show that

the effect of the cooling water temperature on the EER is

greater than that of the chilled water temperature.

Conclusions

Through the analysis of chillers simulation, the fol-

lowing conclusions can be obtained:

(1) With the other parameters held constant, as the

cooling water temperature decreases, the chiller EER

increases in a nearly linear fashion.

(2) With the other factors held constant, as the chiller

load decreases, the chiller EER first increases and sub-

sequently decreases. Moreover, as the load continues todecrease, the EER will decrease more rapidly. In addition,

the EER of the chiller running under variable flow condi-

tions is slightly lower than that of the chiller running un-

der constant flow conditions.

(3) With the other factors held constant, as the chilled

water temperature increases, the chiller EER also in-

creases in a nearly linear fashion. In addition, the effect

of the cooling water temperature on the EER is greater

than that of the chilled water temperature.

Acknowledgment

This paper was supported by a Grant-in-Aid for Scien-

tific Research through grant number KM200610016003

from the Beijing Municipal Commission of Education.

References

[1] Li Ying, Xue Haibin Zhu Boli, Liu Chunhui: Simulink

dynamic system modeling and simulation, [M] 2nd Edi-

tion, Xi'an: Xidian University Press, pp.1390, 2009

[2] Zhang Qisen, Shi Wenxing, Tian Changqing: Air condi-

tioning refrigeration technology, [M] 4th Edition, Beijing:

China Building Industry Press, pp.74118, 2007

[3] PING Laizhou, ZHANG Rongke: Air cooler, [M] Version

1, Beijing: China Petrochemical Press, pp. 2530, 2010

[4] CAI Zengji, LONG Tianyu: Fluid mechanics with pumps

and fans, [M] 4th Edition, Beijing: China Building Indus-

try Press, pp. 287326, 2006

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