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

Chen’s Model for Saturated Boiling Reference: A correlation for boiling heat transfer to saturated fluids in convective flows, ASME Paper 63-HT-34, Presented at the 6 th National Heat Transfer Conference, Boston, 1963 . Chen’s Model: First of its kind – the heat transfer coefficient is the sum of two components   h h h  2 c NB h : Convective component of heat transfer coefficien t c h : Nucleate boiling component of heat transfer coefficien t NB The convective component is given by:   0 . 8    0 . 4      c k G 1 x D        p f h 0 . 023 F      c       k D   f f

• 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.   0 . 8   0 . 8 Re Re       2 2 F     0 . 8   Re    G 1 x D f        f Using the above in the expression for the convective heat transfer coefficient, gives:       k    0 . 8 0 . 4 f 0 . 023 Re Pr h    c 2 f   D Pr ~ Pr and k f ~ k Chen argued that   f 2 2

      k     0 . 8 0 . 4 2 Hence , h c 0 . 023 Re Pr     2 2   D Since F is a flow parameter, it can be uniquely expressed as the function of the Martinelli parameter, thus: 1   F 1 for 0 . 1 X tt 0 . 736   1 1      F 2 . 35 0 . 213 for 0 . 1     X X tt tt 0 . 5 0 . 1         0 . 9  1 x        g f X       tt   x     f g • 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    0 . 79 0 . 49 0 . 45 k c        0 . 24 0 . 75 f f p , f   h 0 . 00122 T p    NB e e 0 . 5 0 . 29 0 . 24 0 . 24   h   f fg g where:             T T T , p p T p T e e sat e e sat      : the mean superheat of the fluid in which the bubble T T T   e e sat    T T T grows, lower than the wall superheat, w w sat Suppression factor, S , is defined as the ratio of the mean superheat to the wall superheat. 0 . 99    T  e   S    T sat

Using Clausius-Clapeyron Equation 0 . 24 0 . 75       T p  e e     S       T p sat sat Therefore, using S in the expression for h NB , we get    0 . 79 0 . 49 0 . 45 k c        0 . 24 0 . 75  f f p , f  h 0 . 00122 ( S ) T p    NB sat sat 0 . 5 0 . 29 0 . 24 0 . 24   h   f fg g • 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

   S f Local Two Phase Reynolds Number 1   S    6 1 . 17 1 2 . 53 10 Re  2  1 . 25 Re Re F  2 f Steps involved in calculation of the heat transfer coefficient for known values of heat flux, mass velocity and quality. a. Calculate (1/X tt ). 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 h  2 boiling components.

Chen Correlation - Example Chen's Correlation 5000 4500 Heat Transfer Coeff. (W/m 2 -K) 4000 3500 3000 Convective HTC 2500 Nucleate Boiling HTC 2000 Two Phase HTC 1500 1000 500 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Quality (x) G L D DeltaT Delta P m m deg C Pa kg/m2-s 400 3 0.0254 10 1.985E+5