Hi Designing Water Cooled Condenser Tube Bundles!.

Hi Designing Water Cooled Condenser Tube Bundles!.

In application a water cooled condenser must reject the heat removed from the chilled water circuit plus the compressor work at specified water flow and entering & leaving temperatures. Water-cooled condenser has water on the tube side & refrigerant on the shell side. The unit compressor capacity and power consumption are functions of the refrigerant saturation temperature, among other operating parameters.

For the tube bundle, determine the flow areas and heat transfer areas.

A_f=N_t*(π*D_i²/4)/N_p, tube side flow area, ft²

A_o=N_t*π*D_o*L, shell side heat transfer area, ft²

A_i=N_t*π*D_i*L, tube side heat transfer area, _ft2

A_ia= N_t*a_i*L, tube side heat transfer area for fouling, ft²

a_i=actual enhanced tube side area/ft, ft²/ft

B= A_o/ A_i

WhereB₂=A_o/ A_ia

N_t=number of tubes

N_p=number of tube passes

D_i=inside tube diameter, ft

D_o=outside tube diameter, ft

L=length of tube, ft

There are two equations that apply

Q=U_o*A_o*LMTD

and

Q=m_w*c_p*( Tw_o -Tw_i)

Where

Q=Capacity, BTU/ Hr

U_o=Overall Heat Transfer Coefficient, BTU/ (Hr-Ft²-^oF)

LMTD=Log Mean Temperature Difference, ^oF

LMTD=(Tw_o-Tw_i)/ln((T_s-Tw_i)/ (T_s-Tw_o))

m_w=Mass Flow of water, Lb/Hr

c_p=Specific heat of water, BTU/(Lb-^oF)

T_s=Refrigerant saturation temperature, ^oF

Tw_i=Entering Water Temperature, ^oF

Tw_o=Leaving Water Temperature, ^oF

The overall heat transfer coefficient is a function of the refrigerant side coefficient, the tube metal resistance, the water side coefficient and the fouling resistance.

U_o=1/((1/h_o')+(B/h_i)+(B₂*R_f))

Where

h_o'=refrigerant side heat transfer coefficient, BTU/(hr-ft²-^oF)

Note: The metal wall resistance is commonly included with the refrigerant side heat transfer coefficient. No fouling resistance allowance is needed on the refrigerant side.

h_i=water side heat transfer coefficient, BTU/(hr-ft²-^oF)

R_f=water side fouling resistance, (hr-ft²-^oF)/BTU

A common engineering problem is to determine the refrigerant saturation given the condenser heat rejection, the water flow rate and the entering water temperature. The solution for T_s is as follows:

Using the two equations that determine Q

U_o*A_o*LMTD=m_w*c_p*(Tw_o-Tw_i)

Substituting the equation for LMTD

U_o*A_o*( Tw_o-Tw_i)/ln((T_s-Tw_i)/ (T_s-Tw_o))=m_w*c_p*(Tw_o-Tw_i)

U_o*A_o/ln((T_s-Tw_i)/ (T_s-Tw_o))=m_w*c_p

ln((T_s-Tw_i)/ (T_s-Tw_o))= U_o*A_o/m_w*c_p

Define

C= U_o*A_o/m_w*c_p

Then

ln((T_s-Tw_i)/ (T_s-Tw_o))=C

(T_s-Tw_i)/ (T_s-Tw_o)=e^C

T_s-Tw_i =e^C* T_s - e^C * Tw_o

e^C * Tw_o- Tw_i= e^C* Ts-Ts

T_s=(e^C*Tw_o- Tw_i)/( e^C -1)

Designers can perform these calculations using spreadsheets or computer programs to determine the operating saturation temperature for a given tube bundle in a chiller application, or to size heat exchanger tube bundles to meet the required heat rejection, saturation temperatures and water temperatures.