Docstoc

Mr. Vijayan's presentation - Sli

Document Sample
Mr. Vijayan's presentation - Sli Powered By Docstoc
					2nd RCM on the IAEA CRP on Natural Circulation Phenomena, Modelling and
     Reliability of Passive Safety Systems that Utilize Natural Circulation



   Effect of noncondensable gas on steam
       condensation in a vertical tube


            N.K. Maheshwari, P.K. Vijayan and D. Saha

                  Reactor Engineering Division,
                Bhabha Atomic Research Centre,
                Trombay, Mumbai, INDIA - 400 085



                        Corvallis, USA
    Oregon State University, August 29 to September 02, 2005
Effect of noncondensable gas on Steam Condensation in a vertical tube



      Objectives
       Development of a theoretical model for the
        calculation of the condensation heat transfer
        coefficient in presence of noncondensable gas
        flowing inside vertical tube
       Comparison of various models for condensate
        film heat transfer coefficient including the effect of
        film roughness
       Comparison of the heat transfer coefficients
        obtained from theoretical studies and experiments



                                                                . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube
                                     Cooling surface


                                                          Condensate film

                                                                  Gaseous state

                                                  Wnc,i           Steam/Air
                           Heat                                    Noncondensable
                           going                             Wnc,b Gas Concentration
                           out
                                                             Tb     Saturation bulk
                                                                    temperature


                                                  Ti                Gas/ vapour
                                                                    boundary layer

                                                             Interface



                    Fig.1 Schematic Illustration of the Model

                                                                      . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

    Theoretical Model
      Heat transfer through gas /vapor boundry layer

      dQ  dm cond H fg  h g dA(Tb  Ti )                                  (1)
      Heat transfer through condensate film
       dQ  h f dATi  Tw                                                 (2)
       Heat balance at boundary layer
      h (T - T )  m // H  h (T - T )                                      (3)
       f i w        cond fg  g b i
       Condensation heat transfer is defined as

       h       (T - T )  m // H                                            (4)
           cond b i        cond fg
           Condensation heat transfer is defined as

      h (T  T )  h
       f i    w
                         T T h T T
                     cond b  i
                                 
                                g b  i
                                                                                   1
                                                                                 
            cond  h g Tb  Ti 
                                                                   1         1
           h                                             h =                  
       =                                         (5)        tot  h     h      h         (6)
                                                                 f     cond   g

                                                                             . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube


    A mass balance at the interface is done to yield the following equation


                W 
     m //   ρD v   W  m// 
                                   
      cond       y    v, i  tot i
                    i

    As the condensate surface is impermeable to the noncondensables, Eq.
    can be simplified as,

                     W 
         //     ρD    v    1  W 
       m
         cond                      v, i 
                      y 
                          i             

                   W     W 
                                   
                    v, b      v, i 
              = h
                  m            
                     1  W 
                          v, i 


                                                                   . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube



    where hm is the mass transfer coefficient. The above equation can be
    recast, in terms of Sherwood number (hmd/ρD) , as

                 //
               m cond,x d         Wnc,i,x                        (7)
      Sh x 
                  ρD        Wnc,i,x  Wnc,b,x 

    Following modifications are carried out to account for the
    • Film Waviness/ripple effect on condensate film heat transfer coefficient
    • Condensate film roughness effect on condensation and convective
      heat  transfer
    • Suction effect
    • Developing flow effect on heat and mass transfer


                                                                   . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

    Condensate film model
    Two models for calculating the film heat transfer coefficient are used
    In the first model the Nusselt equation for film heat transfer coefficient
    is modified (McAdams (1954)) as,
               kl
     hf  β                                                      (8)
              δx 
     Where, β accounts for the increase in heat transfer due to film waviness
     and rippling. The correction is used only if film Reynolds number is
     greater than 30.
     For estimating the film thickness following eq. is used (siddique (1992))

                  2π gρ l (ρ l  ρ v )  Rδ3 5δ 4 
     m cond (x)                        3  24                 (9)
                         μl                      
     Knowing the local condensate flow rate the local film thickness can be
     calculated

                                                                       . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

   The second model to calculate the heat transfer coefficient in the
   condensate film is due to Blangetti et al. [4]. The model provides a
   weighted correction to the laminar Nusselt film solution. The Nusselt
   theory neglects interfacial shear and convective effects leading to a linear
   temperature distribution in the condensate film. Blangetti et al. (1982)
   considers that the condensate film thickness  depends on the local mass
   flow rate and the interfacial shear stress g, as
            gρl (ρl  ρ g ) 3 ρl τ g 2
        Γ                 δ       δ                             (10)
                 3μ l          2μ l
      The Nusselt number can be estimated
        Nu            1
             x, la         δ   for laminar condensate film
        Beyond laminar zone
             h L
        Nu  f  (Nu 4  Nu4 )1/4
                     x, la      x, tu      , where      Nu           aRe b Prc (1  eτ f )
              k                                               x, tu      f             g
                l                    1/3
                              μ2 
             δ                     
        δ       and      L l                                                (11)
             L                ρ2g 
                              l 
        δ is condensate film thickness

                                                                                  . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

      Film roughness considerations
      Film roughness increases the heat transfer from the gas phase by
      influencing the turbulence pattern close to the interface and
      disrupting the gaseous laminar sublayer. Using the corrections
      suggested by Norris [20] for the roughness of the heat transfer
      surface,
                           n                               n
                     fr                            fr 
       Nu = Nu                       Sh  Sh          
          or     os  f      and
                                          or     os  f         (12)
                       s                             s

      Moody correlation is used for friction factor to account for film
      roughness
                                     2ε 100 
                                                 1/3 
        f  1.375 10 3 1 + 21.544                              (13)
         r                           d    Re      
                                                    

      Where ε = δ/2 (Siddique (1992)) and Re is the bulk mixture Reynolds
      number



                                                                     . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

       To account for the film roughness an alternate model proposed by
       Wallis for interfacial friction in the vertical annular flow is used

                      δ
        f  f (1  300 )             δ is condensate film thickness       (14)
         r   s        d

        Suction effect considerations
        Kays and Moffat experimentally obtained the following correlation
        for sucked boundary layer,

          St       (1  B )
               ln        h
         St           B
            o           h
                               Nu                 B h  m cond /G  St
                                                          //
          Where,       St                and
                              RePr
                                        G∞ is the local mixture mass flux in the tube
       St/Sto defines the ratio of Stanton number with suction to that without
       suction at the same Reynolds and Prandtl numbers

                                                                         . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube
     The equation is recast
                                          1                     1
                  //                                    
                 m     Re Pr                       G
       Nu   exp   cond x  - 1                          
                                               m //
                                                                           (15)
                   G  Nu                           Re Pr 
         x
                 
                         ox  
                                
                                                cond x 
                                                            
            
     Using the analogy between heat and mass transfer, the above Eq. can be
     written as
                                        1                      1
                m // Re Sc                             
                                                   G
      Sh   exp cond x  - 1                                          (16)
        x                                   m //
                G Sh                               Re Sc 
                                               cond x 
                      ox                              

     Gnielinski correlation is used for Nusselt number without suction

                (f /2)(Re - 1000)Pr      
      Nu                                
                   s                             Re is the local mixture Reynolds
        ox                                     number in the bulk fluid
           1 + 12.7(f /2)1/2 (Pr2/3 - 1) 
                     s                                                    (17)


                                                                        . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube
      The local condensation mass flux can be given as
               G Sh          Re Sc D ρ1  ω 
        //         ox ln 1    x              
      m                                           Where, Sc=ρD/μ
                                    G d
        cond    Re Sc                          
                  x                                          (18)

     Where, ω is the ratio of the noncondensable gas mass fraction in the
     bulk to that at the liquid/gas interface

     Developing flow considerations
     Reynolds et al. suggested the following correlations for the thermal
     entrance zone,
                       0.8 (1 + 7  104 Re- 3/2 ) 
        Nu  Nu 1                                 Where, Nu=hg d/K
           ot     o                x              
                                     d            
                                                                       (19)
                       0.8 (1 + 7  104 Re- 3/2 ) 
         Sh  Sh 1                                 Where,
           ot     o                x              
                                     d              Sh=hmd/ρD
                                                                       (20)
        x is the distance from the inlet of the tube

                                                                   . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

   Input data for the Computation
         Temperature, noncondensable gas mass fraction, steam mass flow
            rate at inlet, wall temperature (Tw) , total pressure (Pt)

   Solution procedure
   Step 1.  Assuming ∆Tb, the bulk temperature at (j+1)th step is calculated
            as
             T (j  1)  T (j) - ΔT
               b          b        b
    Step 2. The local noncondensable gas mass fraction is evaluated from
            the Gibbs-Dalton ideal gas mixture equation using the partial
            pressure of steam corresponding to the bulk temperature.

    Step 3.   As the noncondensable gas flow rate is constant, the local steam
              flow rate is calculated as

                                    1  W       (j  1) 
                                          b, nc         
               m (j  1)  m
                s            nc, in  W        (j  1)            (21)
                                        b, nc           


                                                                   . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

    Step 4. The local condensate flow rate at (j+1)th location can be found as
            follows,
              m          (j  1)  m           - m (j  1)                (22)
                  cond                 s, in      s

    Step 5. The local condensate film thickness δ(x) can be found from
            the relationship containing the expression for mcond and δ

            The local film heat transfer coefficient, hf can be calculated by
            equation either (8) or (11)
    Step 6. By using a trial value of Ti and Tw the local heat flux is then
            calculated as follows,
              q ( j  1 )  h (T - T )                              (23)
               w               f i w
    Step 7. The total heat transfer for the jth step is calculated as

              Δ Q  [ m ( j ) - m (j  1) ] H (T )  m (j  1) C (Δ T )
                       s         s           fg i     s         ps   b
                     m         C     (Δ T )
                         nc, in pnc        b                              (24)


                                                                           . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

    Step 8. The step length ΔL is calculated using the following equation
                                   2 ΔQ j
                ΔL(j) 
                         πd q // ( j ) + q // (j + 1)                (24)
                             w
                                           w         
                                                      
    Step 9. To get m// cond , hcond and hg, eqs. (18), (4) and (15) are used
    Step 10. The heat balance at the interface yields the following eq.


                 h (T - T )  m // H  h (T - T )
                  f i w        cond fg  g b i                       (25)

             If the heat balance is not satisfied then improve the value of Ti
             and return to step 6.

    Step 11. The value of Tw is then calculated from the stored wall
             temperature profile. If these values differ by more than 0.10C
             from the trial value, the guessed value of Tw is improved. The
             overall heat transfer coefficient htot is then calculated.


                                                                     . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube



   Step 12   Repeat the calculations from step 5 to step 12 for other space
             steps till the end of the tube has been reached

        The theoretical formulation has been tested against In-house as well
        as literature data

              •    Maheshwari (2003)
              •    Siddique (1992)
              •    Tanrikut (1998)




                                                                 . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube


          Test section characteristics for the selected database

        Characteristics           Maheshwari    Siddique   Tanrikut

        Test tube material            SS           SS          SS

        Tube length ( m )             1.7         2.54       2.15

        Cooled segment of the         1.6         2.44       2.15
        tube ( m )

        Inner diameter ( m )        0.04276       0.046      0.033

        Thickness ( m )             0.00277      0.0024      0.003

        Measurement error            31%          18%        NA




                                                                     . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

                                Test inlet conditions

                   Case no.    Pressure   Steam flow        Non-         Mixture
      Reference                  (Pa)     rate (kg/s )   condensable     Reynolds
                                                         mass fraction   number
                                                             (%)


     Maheshwari    E19701     266000.0       0.004           11.5          9755
                   E19704     266000.0       0.004            23          10549



       Siddique   RUN # 47    214238.6     0.008863           9.8         18873
                  RUN # 52    221140.6     0.008635          35.4         22733



       Tanrikut   RUN-6.4.1   390600.0     0.01526            52          45195
                  RUN-4.4.1   398200.0     0.02987           27.8         85898




                                                                         . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

                                                 10

                                                 9

                                                 8                  With McAdams modifier and Moody corr.
            Heat transfer coefficient (kW/m K)
                                                                    With Blangetti model and Moody corr.
            2



                                                                    With Blangetti model and Wallis corr.
                                                 7                  experiment

                                                 6                      Case No. E19701
                                                                        flow rate of steam =0.004 kg/s
                                                                        Mass fraction of air =11.5%
                                                 5
                                                                        Total pressure       =0.266 MPa
                                                                        Reynolds number =9755
                                                 4

                                                 3

                                                 2

                                                 1

                                                 0
                                                      0.0   0.2   0.4       0.6     0.8      1.0     1.2   1.4   1.6     1.8
                                                                             Distance from inlet (m)


                                                      Variation of total heat transfer coefficient
                                                          along the length of the tube

                                                                                                                       . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

                                                     10



                                                                      McAdams modifier and Moody corr.
                                                                      Blangetti model and Moody corr.
                                                     8                Blangetti model and Wallis corr.
          Total heat transfer coefficient (kW/m K)
         2



                                                                      Experiment

                                                                       Case No. RUN 52
                                                                       flow rate of steam =0.008635 kg/s
                                                     6                 Mass fraction of air =35.4%
                                                                       Total pressure       =0.221 MPa
                                                                       Reynolds number =22733


                                                     4




                                                     2




                                                     0
                                                              0.0       0.5             1.0              1.5   2.0
                                                                              Distance from inlet (m)


                                                          Variation of total heat transfer coefficient
                                                                along the length of the tube


                                                                                                                     . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube
                                                           0                   2                   4             6      8
                                                      8                                                                     8
                                                          McAdams model and Moody corr. (rms error 44%)
                                                          Blangetti model and Wallis corr. (rms error 64%)




                                                                                                       0%
           Theoritical heat transfer coef. (kW/m K)




                                                                                                     +2
                                                      6                                                                     6
           2




                                                                                                                    %
                                                      4                                                          -20        4




                                                      2                                                                     2




                                                      0                                                                     0



                                                           0                   2                   4             6      8
                                                                                                             2
                                                                    Heat transfer coef. (measured) (kW/m K)

         Comparison between experimental and theoretical
           heat transfer coefficients (Maheshwari's data)



                                                                                                                        . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

                                      0.009
                                                                With McAdams modifier and Moody corr.
                                                                With Blangetti model and Moody corr.
                                      0.008                     With Blangetti model and Wallis corr.
                                                                Experiment
                                                                  Case No. RUN 52
                                      0.007
                                                                  flow rate of steam =0.008635 kg/s
                                                                  Mass fraction of air =11%
             Steam flow rate (kg/s)



                                                                  Total pressure       =.485 MPa
                                      0.006


                                      0.005


                                      0.004


                                      0.003


                                      0.002


                                      0.001
                                              0.0   0.2   0.4   0.6   0.8     1.0     1.2    1.4      1.6   1.8   2.0
                                                                      Distance from inlet (m)


           Variation of steam mass flow rate along the length of the tube

                                                                                                                        . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

                                                                  0.000         0.002             0.004             0.006          0.008   0.010
                                                              0.010                                                                            0.010
                                                                          With McAdams model and Moody corr. (rms error 13.5%)
                                                                          With Blangeti model and Wallis corr. (rms error 16.7%)
         Mass flow of steam calculated theoretically (kg/s)




                                                                                                                       0%
                                                              0.008                                                                            0.008




                                                                                                                     +2
                                                              0.006                                                                   %        0.006
                                                                                                                                   -20



                                                              0.004                                                                            0.004




                                                              0.002                                                                            0.002




                                                              0.000                                                                            0.000
                                                                  0.000         0.002             0.004             0.006          0.008   0.010
                                                                                Mass flow rate of steam calculated experimentally (kg/s)


                                                                Comparison between experimental and theoretical
                                                                steam flow rate insde the tube(Maheshwari's data)


                                                                                                                                               . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

                                                      80

                                                                    McAdams modifier and Moody corr.
                                                                         hf
                                                                         hg
                                                      60                 hcond

                 Heat transfer coefficient (kW/m K)
                2
                                                                    Blangetti model and Wallis corr.
                                                                          hf
                                                                          hg
                                                                          hcond
                                                      40

                                                                    Case No. E19701
                                                                    flow rate of steam =0.004 kg/s
                                                                    Mass fraction of air =11%
                                                                    Total pressure       =.266 MPa
                                                      20            Reynolds number =9755




                                                      0


                                                             0.0             0.5                 1.0   1.5
                                                                             Distance from inlet (m)
                                                           Variation of heat transfer coefficient
                                                           along with the length of the tube

                                                                                                             . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

                                                  60
                                                                 McAdam modifier and Moody corr.
                                                  55
                                                                      hf
                                                  50                  hg
                                                                      hcond
              Heat transfer coefficient (W/m K)   45
                                                                 Blangetti model and Wallis corr.
             2


                                                  40                   hf
                                                                       hg
                                                  35                   hcond
                                                  30

                                                  25              Case No. RUN-6.4.1
                                                                  flow rate of steam =0.01526 kg/s
                                                  20              Mass fraction of air =52%
                                                                  Total pressure       =.3906 MPa
                                                  15              Reynolds number =45195

                                                  10

                                                   5

                                                   0

                                                  -5
                                                         0.0      0.5              1.0               1.5   2.0
                                                                        Distance from inlet (m)


                                                       Variation of heat transfer coefficient
                                                       along with the length of the tube


                                                                                                                 . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

                                               100

                                                90         McAdam modifier and Moody corr.
          Heat transfer coefficient (kW/m K)                    hf
                                                                hg
         2


                                                80
                                                                hcond

                                                70         Blangetti model and Wallis corr.
                                                                 hf
                                                60               hg
                                                                 hcond                Case No. RUN-4.4.1
                                                                                      flow rate of steam =0.0298 kg/s
                                                50                                    Mass fraction of air =27.8%
                                                                                      Total pressure       =0.398 MPa
                                                40                                    Reynolds number =85898

                                                30

                                                20

                                                10

                                                 0

                                                     0.0         0.5             1.0             1.5             2.0
                                                                       Distance from inlet (m)
                                                     Variation of heat transfer coefficient
                                                      along with the length of the tube


                                                                                                                        . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

  Conclusions

  • The heat transfer coefficient decreases sharply at the initial length and then slowly
    as the mass fraction of noncondensable gas increases along the length
  • The prediction of total heat transfer coefficient by all models is close to the
    experimental data up to Reynolds number 90000. The Blangetti model and Wallis
    correlation predicts higher local heat transfer coefficient compared to those
    predicted with McAdams modifier and Moody correlation and with Blangetti
    model and Moody correlation

  • The decrease in mass flow of steam along the length of the tube with Blangetti
    model and Wallis correlation is more compared to the model with McAdams
    modifier and Moody correlation and with Blangetti model and Moody correlation.
    The predicted steam flow rate with McAdams modifier and Moody correlation
    gives the lowest deviation when compared with the Maheshwari’s experimental
    data.




                                                                           . . . RCM-2
Effect of noncondensable gas on Steam Condensation in a vertical tube

   •   The thermal resistance offered by gas/vapor boundary layer to
       condensation is higher than that offered by condensing film for low
       inlet Reynolds number. But this phenomenon may get reversed at
       higher Reynolds number. As the inlet mixture Reynolds number
       increases, the condensation heat transfer coefficient increases due to
       the higher turbulence in the gas/vapor boundary layer.


                                Thank you




                                                                  . . . RCM-2

				
DOCUMENT INFO