Chens Model for Saturated Boiling Reference: A correlation for - - PowerPoint PPT Presentation

Chen’s Model for Saturated Boiling

NB c

h h h  

 2

t coefficien transfer heat

• f

component boiling Nucleate : t coefficien transfer heat

• f

component Convective :

NB c

h h

Reference: A correlation for boiling heat transfer to saturated fluids in convective flows, ASME Paper 63-HT-34, Presented at the 6th National Heat Transfer Conference, Boston, 1963. Chen’s Model: First of its kind – the heat transfer coefficient is the sum of two components The convective component is given by:

 

F D k k c D x G h

f f p f c

                         

4 . 8 .

1 023 .  

• Modified form of the Dittus-Boelter Equation,
• The enhancement factor F accounts for the enhanced flow and

turbulence effects due to the presence of vapor.

 

 

8 . 8 . 2 8 . 2

1 Re Re Re                   

f f

D x G F 

 

Using the above in the expression for the convective heat transfer coefficient, gives:

   

         D k h

f f c 4 . 8 . 2

Pr Re 023 .



Chen argued that

  2 2

~ and Pr ~ Pr k k f

f

   

         D k hc

   2 4 . 2 8 . 2

Pr Re 023 .

Hence, Since F is a flow parameter, it can be uniquely expressed as the function of the Martinelli parameter, thus:

1 . 1 1 213 . 35 . 2 1 . 1 1

736 .

            

tt tt tt

X for X F X for F

1 . 5 . 9 .

1                        

g f f g tt

x x X    

• As quality increases, X decreases, therefore F increases,

implying that the contribution due to evaporation increases.

The Forster-Zuber Correlation forms the basis of the heat transfer coefficient for nucleate boiling

   

          

24 . 24 . 29 . 5 . 45 . , 49 . 79 . 75 . 24 .

00122 .

g fg f f p f f e e NB

h c k p T h    

where:

     

sat e e sat e e

T p T p p T T T       ,

 

sat e e

T T T   

: the mean superheat of the fluid in which the bubble

grows, lower than the wall superheat,

 

sat w w

T T T   

Suppression factor, S, is defined as the ratio of the mean superheat to the wall superheat.

99 .

        

sat e

T T S

Using Clausius-Clapeyron Equation

75 . 24 .

                

sat e sat e

p p T T S

   

          

24 . 24 . 29 . 5 . 45 . , 49 . 79 . 75 . 24 .

) ( 00122 .

g fg f f p f f sat sat NB

h c k p T S h    

Therefore, using S in the expression for hNB, we get

• S decreases from 1 to 0 as the

quality increases, approaches unity at low flows and zero at high flows.

• Thus, contribution of nucleate boiling

goes down as the quality increases, since evaporation takes over.

Plot of S as a function of Two-Phase Reynolds number

 

25 . 1 2 17 . 1 2 6

Re Re Re 10 53 . 2 1 1 Number Reynolds Phase Two Local F S f S

f

     

  

Steps involved in calculation of the heat transfer coefficient for known values

• f heat flux, mass velocity and quality.

a. Calculate (1/Xtt). b. Calculate F, the enhancement factor from the graph or given equation. c. Calculate the convective component of the heat transfer coefficient. d. Calculate two-phase Reynolds number based on single-phase Reynolds number and value of F. e. Evaluate the suppression factor, S from the graph or equation. f. Calculate the nucleate boiling component of the heat transfer coefficient. g. Calculate as the sum of the convective component and the nucleate boiling components.

 2

h

Chen Correlation - Example

Chen's Correlation

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Quality (x) Heat Transfer Coeff. (W/m 2-K)

Convective HTC Nucleate Boiling HTC Two Phase HTC

G L D DeltaT Delta P kg/m2-s m m deg C Pa 400 3 0.0254 10 1.985E+5