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Al-Khwarizmi 

Engineering   
Journal 

 
Al-Khwarizmi Engineering Journal, Vol. 14, No.2, June, (2018) 

P.P. 137- 146 

 
Theoretical Prediction of Optimum Chilled Water Distribution 

Configuration in Air Conditioning Terminal Unit 

 
Ahmed Abd Mohammed Saleh*               Ali Reyadh Shabeeb**  

Department of Mechanical Engineering/ University of Technology/ Baghdad*،**  
@yahoo.com60aamsaleh :Email*  

**Email: alishabeeb.reyadh@gmail.com 

 
(Received 2 July 2017; accepted 18 December 2017) 

https://doi.org/10.22153/kej.2018.12.006  
 

Abstract  

    
 The distribution of chilled water flow rate in terminal unit is a major factor used to evaluate the performance of 

central air conditioning unit. In this work, a theoretical chilled water distribution in the terminal units has been studied to 
predict the optimum heat performance of terminal unit. The central Air-conditioning unit model consists of cooling/ 
heating coil (three units), chilled water source (chiller), three-way and two-way valve with bypass, piping network, and 
pump. The term of optimization in terminal unit ingredient has two categories, the first is the uniform of the water flow 
rate representing in statically permanents standard deviation (minimum value) and the second category is the maximum 
heat transfer rate from all terminal units. The hydraulic and energy equations governing the performance of unit solved 
with the aid of FORTRAN code with considering the following parameters: total water flow rate, chilled water supply 
temperature, and variable valve opening. It was found that the optimum solution of three-way valve case at 8°C water 
supply temperature, 0.12 kg/s total water flow rate and valve opening order (valve 1: 100%, valve 2: 100% and valve 3: 
75%) with total heat rate (987.92 Watt) and standard deviation (1.181E-3). Also, for the two-way valve case the results 
showed that the optimum condition at 8°C water supply temperature, 0.12 kg/s total water flow rate and valve opening 
order (valve 1: 75%, valve 2: 75% and valve 3: 50%) with total heat rate and standard deviation (717Watt) and (5.69E-4) 
respectively. 
 

  .heat rate ,Standard deviation ,Terminal unit ,way valve-2 ,way valve-3 ,Optimization: Keywords 

 
1. Introduction  

      Cooling is essential for all types of buildings 
in Iraq; Most of the air- central conditioning 
(A/C) systems used in commercial and 
institutional buildings are of large capacity. These 
systems use chillers for cooling production and a 
network of chilled water piping for cooling 
distribution to the individual Air-Handling Units 
(AHUs) or Fan Coil Units (FCUs). The more 
cooling capacity of cooling system will be 
accomplished per liter of chilled water 
distribution if the chilled-water temperature 
differentials were 8.3°C or greater [1] and if the 
chilled water temperature difference between 
supply and return water to the building’s side 
becomes smaller than the designed value.  The 

energy for heat distribution system and the total 
energy consumption in district heating and 
cooling system plant increases in considerable 
degrees [2] but the high chilled water temperature, 
low supply air temperature, and high outside air 
intake ratio may results in low cooling chilled 
water return temperature and the bypass bridge is 
not necessary and can be removed in the 
consumer chilled water system with the 2-way 
valve configuration. The removal not only reduces 
first cost but also operation cost [3].  

The chilled water distribution system stability 
is the basic engineering knowledge for air 
conditioning engineer; Proper sizing of control 
valves, layouts, and self-balancing, flow 
balancing and control the speed of the pump is an 
important fundamental factor of chilled water 


 Ahmed Abd Mohammed Saleh   Al-Khwarizmi Engineering Journal, Vol. 14, No. 2, P.P. 137- 146 (2018) 

138 

distribution system [4]. Jing jing Liu.et.al 
(2012)[5] simulated the cooling coil ΔT profiles 
with different geometric configurations and 
various water side and air side conditions using an 
effectiveness-NTU model and found that the 
existing water side correlations generated 
significantly different ΔT profiles, with variant 
geometric configurations, the coil ΔT at full load 
may be higher, equal, or lower than that at part 
load, the complexity of cooling coil ΔT 
characteristics indicates that it is hard to make 
conclusions about the coil ΔT change with 
cooling loads. Jin-ping Liu.et.al (2012)[6] built a 
hydraulic calculation model of pipe network 
topology, bypass loop hydraulic calculation model 
and found that when chilled water system is 
operating in bypass circuit hydraulic adjustable 
area, pressure difference bypass valve opening 
and pump operating frequency show an 
approximately linear relation, which is under little 
affection of pipe network flow ratio.  

The aim of this work is to determine 
theoretically the optimum water flow rate 
distribution in terminal unit to achieve maximum 
heat transfer between the water and air sides 
corresponding to the main parameter effect (flow 
rate, inlet temperature, and valve opening). 
 
 
2. Governing Equations  
 

In order to investigate the water distribution 
network in HVAC system, the flow distribution 
network, pressure drop, heat transfer rate as well 
as optimization equations were solved using 
iteration method numerical technique (terminal 
units), the smallest HVAC system that could be 
found practically content three circuits model , 
figure (1a & 1b) shows the schematic diagram of 
this system. 
 

(a)  The system with 3-way valve 

  
(b)  The system with 2-way valve. 

  
Fig. 1. a and b: Schematic diagram of the system.  

 
 Ahmed Abd Mohammed Saleh   Al-Khwarizmi Engineering Journal, Vol. 14, No. 2, P.P. 137- 146 (2018) 

139 

A) Hydraulic model  
 
To calculate the head losses in the pipe: 

h� = h������	 + h���
��	                                ... (1)                                                                                                 

The frictional head loss  h������	  is given by 

Darcy-Weisbach equation, such as:  

 ℎ������ = � ℓ 
�  ��

��                                       … (2)                                                                          

where Friction factor for laminar flow is: 

� = ��
��                                                            … (3)                                                                       

and for turbulent flow friction factor is defined by 
Zigrang-Sylvester formula.: 

�
  =  −4.0 log�( )ƹ/�

,.-  −  ..(�
�� log�(( ƹ/�

,.- +  �,
��)2   

                                                                       … (4)  

where the relative pipe roughness is     
ƹ
�     , … (5)                                                                  

 (ƹ)  is the nickered roughness factor and (d) is 
tube diameter.                                                                                          
Table (1) illustrates the internal roughness of 
many types of pipes. [7] 
 

Table 1, 

Pipe internal Roughness 

 
The minor head loss  h���
��	  is given as;                 

    ℎ��34�� = 56 ��
��                                      … (6)                                                                                

where 56 is (local) loss coefficient, although 

56 is dimensionless, it is not correlated in the 
literature with the Reynolds number and 

roughness ratio but rather simply with the raw 
size of the pipe. 

Fittings such as elbows, tees, valves, and 
reducers represent a significant component of the 
pressure loss in most pipe systems, the  
calculation of pressure losses through pipe fittings 
and some minor equipment  using the K-value 
method, The resistance coefficient value (K) are 
given in table (2).[8] 
 
Table 2, 

Resistance coefficient (K) 

 
The pressure drop can be calculated by : 

∆P =  9 : h�                                                   … (7) 
The pressure drop through a 3-way & 2-way valve 

∆;<�=>? =  )@=�A
BCD 2� ∗ 1296000                       … (8) 

Table (3) illustrates the flow coefficient (5<F) of 
valves with different opening [9]. 
 
 
Table 3, 

 Flow coefficient (GHI)  

Valve  

opening    

(in)      (mm) 

Flow  

coeffici

ent  

Valve opening - Percent of Total Travel 

10 20 30 40 50 60 70 80 90 100 

 3/4 20 Kvs 2.4 4.375 6.625 9.075 11.675 14.25 16.825 18.925 20.525 21.55 

 
B) Heat transfer Model 
 
In this study, the (ε-NTU) method has been 

used for cross-flow heat exchanger with both 
fluids unmixed. 

NTU depends on both the heat exchanger 

design (UA) and the operating conditions (J�34). 

With the dimensionless number of transfer units 
(NTU) that is used for heat exchanger analysis 
and was defined as: 

KLM = N∗O
PQRS                                                   … (9)                                                                                 

Where: 

U = �
�TU                                                        … (10) 

RWX  = RW�W�Y =  R
 +  RZ�YY +  R�              … (11) 
where: 

Material ƹ  (Centimeters) 

Cast iron 0.026 
Galvanized iron 0.015 

Asphalted cast iron 0.012 

Commercial steel or wrought iron 0.046 

PVC 0.00015 

Fitting  

Nominal Pipe Size 

1/2˝ 3/4˝  1˝ 

K Value 

globe valve (Full open) 9.2 8.5 7.8 
gate valve (Full  open) 0.22 0.2 0.18 
Tee straight Through 0.54 0.5 0.46 
Tee Through branch 1.62 1.5 1.38 
Elbow 90˚ 0.81 0.75 0.69 


 Ahmed Abd Mohammed Saleh   Al-Khwarizmi Engineering Journal, Vol. 14, No. 2, P.P. 137- 146 (2018) 

140 

RWX: Overall heat resistant  

R
 ∶  Inner resistance 

RZ�YY ∶ Wall resistance 

R� ∶ Outer resistance 

The overall heat resistant  RWX consists of three 
parts: convection heat resistant of the chilled 
water, conduction heat resistant of the metal wall 
and convection heat resistant of the air.  
The overall heat resistance of chilled-water coil 
was then written as: [10] 

\]^ = �
^R  OR + 

=4(�_/�R)
�`ab=  + 

�
^_ O_                      … (12)   

Where: 

ℎ3 = c>∗Bb
�3                                                   … (13) 

ℎ� = c>∗Bd
�U                                                   … (14) 

Effectiveness ε, is defined as the ratio of the 
actual heat transfer rate for a heat exchanger to the 
maximum possible heat transfer rate. 

ε =  f
fghi                      0 ≤ ɛ ≤ 1                  … (15) 

j = 1 − lmn o?pqrst.uv w ��
cxNpt.�� P y                        … (16) 

where:                                             

J: Capacity ratio   =  PQRS
PQd�                         … (17) 

Maximum possible heat rate: 

� =  J�34 (L̂ ,3 − L�,3)                                … (18) 

The  Nusselt Number for air side is calculated as. 
[10] 

       K�  = 0.117*\l(.�.*;�(.,,                   … (19)  
and for chilled water side it is calculated by:  
For laminar: 

      K� = 1.86 ��? �	 �R
ℓ �(.,,,

                      … (20)    

For turbulent:                                   

      K�  = 0.023*\l(.�*;�(.�                       … (21) 
where 

;� = P�∗�
B                                                     … (22) 

C) Flow variation and standard deviation  

The following equation evaluates the standard 
deviation: 

�� = ��
c ∑ (���� − c3�� ���� )²               … (23) 

where, 

 (�����,�����.…flow�) are the values of the 

flow calculated and � ����  � is the average value 

of these flow, while the denominator N stands for 
the size of the sample(in the present work = 3). 

  
3. Solution Code  
     

 Using FORTRAN code with iteration method 
technique to solve the governing equations from 
equation (1) to equation (23) according to the 
flow chart see figure (2). 

 
Fig. 2.  Flow chart of the water distribution 

network. 
 
 
4. Optimization Method 
 

The ultimate goal of the optimization was to 
maximize the value of the total heat rate 
(summation of three coils) and minimize the 
variation of flow in the three circuits representing 
by the standard deviation (SD). To do that we 

suggested two factors (��) & (��) and the target 
of optimization is to find the maximum value of 

(�� ∗ ��) where: 

�� = 1 − � �¡
�¢ �                                         …  (24) 


 Ahmed Abd Mohammed Saleh   Al-Khwarizmi Engineering Journal, Vol. 14, No. 2, P.P. 137- 146 (2018) 

141 

 �� = 1 − �£�¤
�� �                                         …  (25) 

¥n¦§¨§©ª¦§�« �ª¬¦�� = �� ∗  ��              …  (26) 
 
 
5. Results  and  Discussion 

5.1 Total Heat Rate  
 

Figure (3) shows that the total heat rate of 
terminal units at different total water flow rates 
(0.06, 0.08, 0.1 and 0.12 kg/s) and various water 
supply temperatures were (8, 10, 12, 14 and 16 
°C) at 100% valves opening: (valve 1=100%, 
valve 2=100% and valve 3=100%), Note that the 
higher total heat rate occurred at minimum water 
supply temperature (8°C) and at maximum total 
water flow rate (0.12 kg/s), due to the highest 
difference in temperature between the water and 
the air when the temperature of the air is constant, 
While the increase of the heat rate is slight 
because the flow type in most cases is laminar and 

the value of heat transfer coefficient (ℎ3) is almost 
constant. The same behavior was found in figure 
(4) and (5), however changing the valve opening 
from (100-75%) or to 50% for coil No.3 only 
gave less water flow rate inside this coil, while the 
total heat rate remained approximately constant. 
The figures (6) to (9) explain the changes in other 
3-way valve opening of coil. These figures 
indicate that the total water flow rate and water 
supply temperature has a significant impact on the 
total heat rate at any valve opening for any coil. 
Figure (10) illustrates the effect of valve opening 
on the overall heat rate at water supply 
temperature (8°C) and different total water flow 
rates (0.06, 0.08, 0.1 and 0.12 kg/s). It can be 
depict that the lower total heat rate occurred at 
case (valve 1=100%, valve 2=100%, and valve 
3=50%), because coil No.3 is always has the 
higher water flow rate in comparison with other 
coils in the cycle, which makes a significant effect 
on the total heat rate. But Figure (11) to (13) 
shows that the total heat rate of terminal units 
with the same input parameter in 3-way valve 
when utilize the 2-way valve. Note in all figures  
that the higher total heat rate occurred at 
minimum water supply temperature (8°C) and 
maximum total water flow rate (0.12 kg/s). Figure 
(14) illustrates the effect of valve opening on the 
overall heat rate at water supply temperature 
(8°C) and multiple total water flow rates. It noted 
that the lower overall heat rate occurred at case 
(valve 1=100%, valve 2=100%, and valve 
3=50%) for the same reason in 3-way valve. 
 

Fig. 3. The total heat rate of terminal units at 8, 10, 

12, 14 and 16 °C water supply temperature and 

valve opening: Valve 1=100%, Valve 2=100% and 

Valve 3=100%. 

 
Fig. 4. The total heat rate of terminal units at 8, 10, 

12, 14 and 16 °C water supply temperature and 

valve opening: Valve 1=100%, Valve 2=100% and 

Valve 3=75%. 
 

Fig. 5. The total heat rate of terminal units at 8, 10, 

12, 14 and 16 °C water supply temperature and 

valve opening: Valve 1=100%, Valve 2=100% and 

Valve 3=50%. 

 
 Ahmed Abd Mohammed Saleh   Al-Khwarizmi Engineering Journal, Vol. 14, No. 2, P.P. 137- 146 (2018) 

142 

 
Fig. 6. The total heat rate  of  terminal units at 8, 10, 

12, 14 and 16 °C water supply temperature and 

valve opening: Valve 1=100%, Valve 2=75 % and 

Valve 3=100. 

 
Fig. 7. The total heat rate  of terminal units at 8, 10, 
12, 14 and 16 °C water supply temperature and 

valve opening: Valve 1=100%, Valve 2=50 % and 

Valve 3=100%. 

 
Fig. 8. The total heat rate  of  terminal units at 8, 10, 

12, 14 and 16 °C water supply temperature and 

valve opening: Valve 1=75%, Valve 2=100 % and 
Valve 3=100%. 
 

Fig. 9. The total heat rate  of terminal units at 8, 10, 

12, 14 and 16 °C water supply temperature and 

valve opening: Valve 1=50%, Valve 2=100 % and 

Valve 3=100%. 

 
Fig. 10. The total heat rate of terminal units at 8°C 

water supply temperature and valve opening: Valve 

1=100%, Valve 2=100 % and Valve 3=100-75-50%. 
 
 
Fig. 11. The total heat rate  of  terminal units at 8, 

10, 12, 14 and 16 °C water supply temperature and 

valve opening: Valve 1=100%, Valve 2=100% and 

Valve 3=100%. 
 

 Ahmed Abd Mohammed Saleh   Al-Khwarizmi Engineering Journal, Vol. 14, No. 2, P.P. 137- 146 (2018) 

143 

 
Fig. 12. The total heat rate  of  terminal units at 8, 

10, 12, 14 and 16 °C water supply temperature and 
valve opening: Valve 1=100%, Valve 2=100% and 

Valve 3=75%. 

 
Fig. 13. The total heat rate  of terminal units at 8, 

10, 12, 14 and 16 °C water supply temperature and 

valve opening: Valve 1=100%, Valve 2=100% and 
Valve 3=50%. 

 
Fig. 14. The total heat rate of terminal units at 8°C 

water supply temperature and valve opening: Valve 

1=100%, Valve 2=100 % and Valve 3=100-75-50%. 
 

5.2 Standard Deviation  

 
Figure (15) illustrates the effect of the total 

water flow rate on the flow variation representing 

in standard deviation between the terminal units at 

(8°C) inlet water supply and constant valve 

opening of coil No.1, coil No.2 and variable valve 

opening of coil No.3 (100, 75, 50%) It can be seen 

that the best standard deviation (minimum) 

occurred at case (100% - 100% - 75%). That is 

mean the amount of flow variation between coils 

is very low, because coil No.3 has the highest 

flow rate of the others, therefore decreasing the 

valve opening of coil No.3 to 75%, which 

decreases the water flow rate inside the coil and 

gives closer deviation with the other valves. 

However decreasing the valve opening of coil 

No.3 more to 50%. The flow rate in coil No.3 will 

be very low in comparison with the others, which 

leads to a great increase in standard deviation. 

Also this figure proves that the standard deviation 

increases with the increase the total water flow 

rate, but the water supply temperature does not 

affect the standard deviation. Also in 2-way valve 

figure (16) illustrates the effect of the total water 

flow rate on the flow standard deviation between 

the terminal units at (8°C) inlet water supply and 

constant valve opening of coil No.1, coil  No.2 

and variable valve opening of coil No.3 (100, 75, 

50%) . It can be seen like in 3-way valve that the 

best standard deviation (minimum) at case (100% 

- 100% - 75%). The reduction in valve opening 

reduces the standard deviation of flow because the 

decrease of valve opening means reducing the 

flow in the coil system, i.e. reducing the variation 

between the coils (reduce standard deviation) of 

flow. 

 
Fig. 15. The flow standard deviation between 
terminal units at 8 °C water supply temperature 

and valve opening: Valve 1=100%, Valve 2=100% 

and Valve 3=100-75-50%. 

 
 Ahmed Abd Mohammed Saleh   Al-Khwarizmi Engineering Journal, Vol. 14, No. 2, P.P. 137- 146 (2018) 

144 

 
Fig. 16. The flow standard deviation between 

terminal units at 8 °C water supply temperature 

and valve opening: Valve 1=100%, Valve 2=100% 

and Valve 3=100-75-50%. 

 
5.2 Predict the Optimum Case  
 
The optimum conditions are found to give the 

maximum total heat rate and minimum standard 
deviation of predetermined values, the optimum 
values of these circumstances at valve opening 
(Valve 1: 100%, Valve 2: 100% and Valve 3: 
75%), the total water flow rate 0.12 kg/s (7.2  
l/min) and the water supply temperature 8°C with 
a maximum total heat rate of (987.92 watt) and 
minimum standard deviation (0.001181), the 
optimization factor could be found by using 
equations (16), (17) and (18). From figure (17) it 
can be seen that the maximum optimum factor 
(0.919894) occurred at 8°C water supply 
temperature and (0.12 kg/s) total water flow rate. 
This case is the optimum solution of three-way 
valve cases. The same procedure can be used to 
find the optimum condition in two-way valve in 
A/C system configuration, the optimum values of 
these conditions at valve opening (Valve 1: 75%, 
Valve 2: 75% and Valve 3: 50%), the total water 
flow rate 0.12 kg/s (7.2  l/min) and the water 
supply temperature 8°C with a maximum total 
heat rate of  (717 watt) and minimum standard 
deviation (0.000569), Figure (18) shows that the 
optimization factor at each flow rate and each 
water supply temperature.  
 

Fig. 17. Optimization factor of three-way valve case. 

 
Fig. 18. Optimization factor of two-way valve case.  
 

6. Conclusions 

 
1. The total heat rate in A/C terminal unit is 

minimum at the lowest valve opening, highest 

water supply temperature and lowest total 

water flow rate, whereas the total heat rate is 

maximum at the maximum valve opening, 

highest total water flow rate and lowest water 

supply temperature. 

2. The last valve (No.3 in current model) highly 

effect on the distribution of flow rate at each 

terminal unit. Therefore, the optimum value of 

maximum total heat rate and minimum 

standard deviation occurred when valve order 

(valve 1= 100%, valve 2=100% and 

valve3=75%) in three way valve case. Also, in 

a 2-way valve the optimum value of maximum 

total heat rate and minimum standard deviation 

occurred when valve opening (valve 1= 75%, 

valve 2=75%, and valve 3=50%).  


 Ahmed Abd Mohammed Saleh   Al-Khwarizmi Engineering Journal, Vol. 14, No. 2, P.P. 137- 146 (2018) 

145 

3. The supply temperature has the greater impact 

on the total heat rate than valve opening and 

total water flow rate. 

4. The valve opening and total water flow rate 

has the significant influence on the standard 

deviation, while the water supply temperature 

does not effect on it in 3-way and 2-way valve. 

5. The diameter of the bypass pipe in 2-way 

valve system should be much lower than the 

diameters of the system. 

 
Nomenclature 
 

air- central conditioning                          A/C  

standard deviation                              SD  

 Friction factor  ƒ  

Length of the pipe with constant 
diameter in (m).  

ℓ 

Internal diameter of the pipe in (m)  d  

Average velocity of flow in (m/s) V  

Gravity constant g 
Kinematic viscosity of the fluid (m²/s) ­ 

Pressure drop in (N/m²) ∆P 

Heat transfer coefficient of water side 
(W/m².K) 

ℎ3 

Minimum Capacity rate (W/ K) J�34  
Maximum Capacity rate (W/ K) J��®  
Maximum possible heat transfer rate 
(W) 

���® 

Inlet temperature of air (K) L̂ 3 
Inlet temperature of water (K) L�3 
Specific heat (J/kg.K) Cp 
Dynamic viscosity  (N.S/m²) ¯ 

Thermal conductivity (W/m.K) K 
Overall heat transfer coefficient 

(W/m².K) 

U 

Relative pipe roughness Ƹ 
Heat transfer coefficient of air side 
(W/m².K) 

ℎ� 

Temperature difference ΔT 
Total heat rate factor F1 
Standard deviation factor F2 
maximum value of total heat rate  M 

Actual value of total heat rate Q 
The range between maximum and 
minimum value of total heat rate  

\� 

Actual value of standard deviation S 
minimum value of standard deviation Z 

The range between maximum and 
minimum value of standard deviation 

\� 

Optimum factor F 
 

7. References  

 
[1] Donald P. Fiorino,"Achieving high chilled-

water delta Ts", ASHRAE Journal Vol.41, 
(1999).  

[2] Shimoda yoshiyuki, Minoru mizuno, Shigeki 
kametani and Shin-ichi kawamura, "Evaluation 
of distribution system performance in district 
heating and cooling system." Proceedings of 
sixth International IBPSA conference, (1999). 

[3] Gang Wang, Mingsheng, Bin Zheng, and 
Mingsheng Liu. , "Impacts on building return 
water temperature in district cooling 
systems", ASME 2006 International Solar 
Energy Conference, American Society of 
Mechanical Engineers, (2006). 

[4] Thirakomen Kecha and ASHRAE Thailand 
Chapter–BOG, "Stabilizing Chilled Water 
Distribution" Ashraei Thailand Chapter 
Journal, pp. 27-31, (2007). 

[5] Jingjing Liu, Hui Li and Zhiqin Zhang, 
"Simulations of Chilled Water Cooling Coil 
Delta-T Characteristics ", Ashrae 
Transactions 118, (2012). 

[6] Jin-ping Liu, Xue-feng Liu, Ji-dong Lu, Lei 
Liu and Wei Zou, "Research on operating 
characteristics of direct-return chilled water 
system controlled by variable temperature 
difference", Energy Vol. 40. 1, PP. 236–249, 
(2012). 

[7] Benefield, Larry D., Joseph F. Judkins, and A. 
David Parr, "Treatment plant hydraulics for 
environmental engineers", Englewood Cliffs, 
New Jersey: Prentice-Hall, (1984). 

[8] Friction Losses in Pipe Fittings Resistance 
Coefficient K, 
http://www.metropumps.com/ResourcesFrictionLos
sData.pdf. 

[9] Fisher Controls International, Inc., catalog 12, 
U.S.A., (2001). 

[10] Holman J. P., "Heat Transfer", Tenth Edition, 
by the McGraw-Hill Companies, Inc., (2010). 

 
 )2018( 137-146، صفحة 2د، العد14دجلة الخوارزمي الهندسية المجلم                                                    احمد عبد محمد صالح

146 

 
  المركزيةتوزيع االمثل للماء المثلج في الوحدات الطرفية في منظومة التكييف النظري لل تخمينال

  
   **     علي رياض شبيب                 *احمد عبد محمد صالح

  الجامعة التكنولوجية/ بغداد قسم الهندسة الميكانيكية/
  yahoo.com60aamsaleh@البريد االلكتروني: *

 alishabeeb.reyadh@gmail.com البريد االلكتروني:**

  
  الخالصة

 
م أداء وحدة تكييف الهواء المركزية. في هذا العمل، تم اجراء دراسة ويتوزيع معدل تدفق المياه المثلجة في الوحدات الطرفية عامال رئيسا يستخدم لتق ديع

أداء حراري للوحدة الطرفية. يتكون نموذج وحدة تكييف الهواء المركزية من الملف التبريد /  بأفضلفي الوحدات الطرفية للتنبؤ  مثلجةنظرية لتوزيع المياه ال
صطلح خة. إن مالتدفئة (ثالث وحدات)، مصدر المياه المثلجة (المبرد)، صمام ثالثي االتجاه وصمام ثنائي االتجاه مع مجرى جانبي، وشبكة األنابيب، ومض

 أعظموالفئة الثانية هي  التحسين في الوحدة الطرفية يشمل جزئين األول هو معدل تدفق المياه المنتظم الذي يتمثل في االنحراف المعياري الثابت (القيمة الدنيا)
تم حلها بمساعدة برنامج فورتران مع االخذ  معدل نقل للحرارة من جميع الوحدات الطرفية. المعادالت الهيدروليكية ومعادالت الطاقة التي تحكم أداء الوحدة

جد أن الحل األمثل بنظر االعتبار العوامل المتغيرة االتية: إجمالي معدل تدفق المياه، ودرجة حرارة إمدادات المياه المثلجة، وفتحات صمام متغيرة. وقد و
: ١/ ثانية إجمالي معدل تدفق المياه وعند فتحة صمام (صمام  كجم ٠٫١٢ووية، درجة مئ ٨لحالة الصمام الثالثي االتجاه عند درجة حرارة امداد بالمياه تبلغ 

). أيضا بالنسبة لحالة الصمام ثنائي 1.181E-3واط) وانحراف معياري ( ٩٨٧٫٩٢٪) مع معدل حرارة كلي ( ٧٥: ٣٪ وصمام ١٠٠: ٢٪، صمام ١٠٠
م / ثانية مجموع معدل تدفق المياه وعند فتحة صمام غك ٠٫١٢و  حرارة إمدادات المياه،درجة مئوية درجة  ٨االتجاه أظهرت النتائج أن الحالة المثلى عند 

   التوالي.) على 5.69E-4(واط)،  ٧١٧() مع معدل حرارة كلي وانحراف معياري %٥٠: ٣٪ وصمام ٧٥: ٢٪، صمام ٧٥: ١(صمام