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Mr. De La Rosa's presentation - International Atomic Energy Agency

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Mr. De La Rosa's presentation - International Atomic Energy Agency Powered By Docstoc
					UNIVERSIDAD POLITECNICA DE VALENCIA - CIEMAT         2° RCM of the IAEA’s CRP Oregon State University, Corvallis, USA Aug-Sept 2005




                                               Effect of Non-Condensables on Natural Circulation Passive Safety Systems



                                                                      José Luis Muñoz-Cobo, Luis Herranz,
                                                                     Juan Carlos de la Rosa, Alberto Escrivà

                                                                      Presented by Juan Carlos de la Rosa

                                                                        Instituto de Ingeniería Energética
                                                                       Universidad Politécnica de Valencia
                                                                          Edificio I4 Camino de Vera s/n
                                                                              46022 Valencia - SPAIN
                                                                              delarosablul@yahoo.es



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                                                                                                           Main Contents



                                                  General Presentation of the UPV
                                                  Main aspects of the developed work
                                                  Condensation inside vertical tubes in presence of NC gases
                                                  Condensation on Finned Tubes Heat Exchangers in presence of NC
                                                   gases




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UNIVERSIDAD POLITECNICA DE VALENCIA - CIEMAT


                                                                                             General Presentation of the UPV



                                               The UPV is one of the leading Technical Universities in Spain with 35000
                                               Students and 2500 Faculty lecturers, Professors and Researchers:
                                               The Institute of Energy Engineering belongs to the UPV and has 60
                                               researchers that works in the following areas:

                                                       Thermal Engineering
                                                       Nuclear Engineering and Thermalhydraulics
                                                       Electric Engineering
                                                       Renewable Energy Sources




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                                                                                                 General Presentation of the UPV




                                                Thermalhydraulics and Nuclear Engineering Group – Participation in Projects
                                                           related with Natural Circulation Passive Safety Systems
                                                 CEE-TEPSS Technology Enhancement of Passive Safety Systems 1996-
                                                  1999, European Fourth Framework.
                                                 CONGA (Subcontract with CIEMAT). Containment Behaviour in the Event
                                                  of Core Melt with Gaseous and Aerosol Releases 1996-1999.
                                                 CEE-NACUSP Natural–Circulation and Stability Performance of BWR
                                                  1999-2004. Fifth European Framework Project.
                                                 EPP-1000, Small and Large Break LOCA Analysis in collaboration with
                                                  ANSALDO and DTN. 1999-2000.




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                                                                                         Main Aspects of the developed work


                                               By means of the proposed PIRT -which has to be finished and consolidated in
                                               this 2° RCM-,
                                               the UPV and Ciemat have already made the following issues:
                                               1.    Related with the 2° Phenomena of the proposed PIRT -Tracking of
                                                     Non-Condensables-, we have studied the main different models
                                                     which simulate the condensation inside vertical tubes in the
                                                     presence of NC gases. Also, we have made a model for the
                                                     condensation on finned tubes heat exchangers in presence of NC
                                                     gases, which gives a good agreement. The main prototypes of
                                                     passive safety reactors which can incorporate this models in its
                                                     simulations are the ESBWR and SBWR for the Passive
                                                     Containment Cooling Condensers (PCCC), and the SWR-1000 for
                                                     the Finned Tubes Heat Exchanger.
                                               2.    Related with the 3° Phenomena of the Proposed PIRT -
                                                     Condensation on the containment structures-, we have developed
                                                     an analytical model for the condensation on the containment
                                                     structures, explicitly done for the AP600 passive safety reactor.
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                                                                                            Main Aspects of the developed work



                                               3.   Finally, related with the 9° Phenomena of the proposed PIRT -
                                                    Liquid Temperature stratification-, we have studied the Stratification
                                                    that occurs in the hot legs of a Pressurized Water Reactor (PWR)
                                                    using commercial codes (like CFX) and developing new codes (like
                                                    TUBO3D).




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                                                                        Condensation inside vertical tubes in presence of NC gases



                                               The ESBWR and the SBWR extract the containment heat by means of
                                               the passive containment cooling condensers (PCCC). Each condenser is
                                               formed by a set of vertical tubes connected to common lower and upper
                                               headers or drums, and submerged into a water pool. A tube drains the
                                               steam plus non-condensable mixture from the containment and drives it
                                               to a distributor that transports the mixture by natural circulation to the
                                               upper headers of the PCCCs. Once the gas enters into the tubes, the
                                               steam condenses on the walls of the tubes, and the condensation heat is
                                               transferred to the PCCC pool.

                                               The condensate is drained by gravity to the lower header, where
                                               accumulates at the lower part of the lower drum where it is removed by
                                               gravity through the drain line which is directly connected to the reactor
                                               vessel. The non-condensed steam plus the non-condensable gases are
                                               discharged through the vent line into the wetwell pool.
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                                               Condensation inside vertical tubes in presence of NC gases




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                                               Condensation inside vertical tubes in presence of NC gases




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                                                                        Condensation inside vertical tubes in presence of NC gases


                                               The main objective is to propose several models which can be easily
                                               implemented in the existing thermal-hydraulics codes, like RELAP, TRAC-
                                               BF, and TRACE.
                                               There exists two main paths to arrive to construct a model:
                                               1.   The first one is an a priori or analytical method, which sees the
                                                    physical system as a white box. This means that the model will be
                                                    constructed by means of the conservation equations along with
                                                    closure relations, and/or using the heat and mass transfer analogy.
                                               2.   The second one is an a posteriori or semi-empirical method, which
                                                    sees the physical system as a black box, in a way that the model will
                                                    be constructed based on an analytical previous model, making the
                                                    correct adaptation to the real physical system by means of an
                                                    empirical correlation.




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                                                                       Condensation inside vertical tubes in presence of NC gases



                                               Following this aim, we have compared three models:

                                               1.   The University of California at Berkeley model, called the UCB
                                                    model, developed by Vierow and Schrock, all together with the
                                                    improved UCB model, called UCBA, and developed by Kuhn.
                                               2.   The Second model is the one from the Middle East Technical
                                                    University at Ankara, called the METU-TAEA model, and performed
                                                    by Anglar and Tanrikut.
                                               3.   Finally, the third analyzed model is the UPV-FIT model, performed
                                                    by José Luis Muñoz Cobo et al.




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                                                                            Condensation inside vertical tubes in presence of NC gases



                                               All these models belong to the second way to construct a model, that is, they use
                                               an empirical factor to account for the phenomena not implemented in the source
                                               analytical model.
                                               As we have previously said, these simple models are based on obtaining the real
                                               heat transfer coefficient (HTC) by means of one previously obtained analytically, in
                                               our case, through the Nusselt theory:

                                                                        h exp (z)       h exp (z)  N (z)
                                                              f (z)                
                                                                        h th (z)               kl

                                                In this way, the positive and negative aspects of each model will depend on the
                                               phenomena not included analytically, that is, in the degree of dependence that
                                               each one has with the experiments that were used to get the degradation factor.




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                                                                            Condensation inside vertical tubes in presence of NC gases

                                               The UCB model


                                                                        h exp (z)       h exp (z)  N (z)
                                                              f (z)                
                                                                        h th (z)               kl

                                               We can obtain a Nusselt number for the laminar and turbulent region
                                               which will be used to calculate the film thickness:

                                                          h N le                                 h N le
                                                     Nu          1.1 Re l1/3           Nu            0.0195 Re 1/3
                                                                                                                    l
                                                           kl                                     kl




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                                                                             Condensation inside vertical tubes in presence of NC gases

                                                    The UCB model

                                                    The degradation factor must account for two kind of phenomena not
                                                    included in the Nusselt theory:
                                                                              f UCB  f1 f     2


                                               1.   The enhancement of the HTC produced by the shrinkage caused by the
                                                    transfer of momentum from the gas mixture to the condensate film:

                                                                           f1  1  2.88105 Re1.18
                                                                                                g


                                               2.   The degradation produced by the NC effect, which would almost
                                                    counterbalances the forces created by the depression that occurs when
                                                    the steam condensates in the interface:
                                                                               f2  1  C Mb
                                                                                           nc


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                                                                             Condensation inside vertical tubes in presence of NC gases

                                               The UCBA model

                                                This model was improved by the Khun-Schrock-Peterson correlation
                                               denoted as UCBA, that takes on account the waviness of the condensate
                                               layer and the interfacial shear stress, but the model is more complex
                                               because involves to solve the Nusselt liquid film boundary layer equation
                                               with specified shear stress at the interface and it is not as direct as the
                                               Vierow Schrock model, because it is necessary to iterate to solve this
                                               equation.
                                                                       f UCBA  f1 f      2
                                               In this model

                                               where                              f 2  1.0  C 2, UCBA M a        for M nc  0.1
                                                                        1
                                                                     
                                               f1  1.0  C1, UCBA Re l
                                                                                                          nc
                                                                        2        f 2  1.0  M b                 for      M nc  0.1
                                                                                                nc



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                                                                          Condensation inside vertical tubes in presence of NC gases

                                               The METU-TAEA model

                                               In this case, the degradation factor is given by:

                                                                    f MET  f1 f    2


                                                Where f1 is the enhancement factor of the HTC produced by the
                                               shrinkage caused by the transfer of momentum from the gas mixture to
                                               the condensate film. Also, this enhancement factor takes into account the
                                               effect produced by the onset of disturbance waves at the interface at
                                               relatively low condensate Reynolds numbers:
                                                                  f1  fSHEAR fOTHER



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                                                                          Condensation inside vertical tubes in presence of NC gases

                                               The METU-TAEA model

                                               with
                                                                   1
                                                        fSHEAR 
                                                                   2

                                                where δ1 is the film thickness without interfacial shear stress, and δ2 is
                                               the film thickness with interfacial shear stress. We note that the interfacial
                                               shear stress is influenced by both the interface velocity and the mixture
                                               side velocity. For this reason fOTHER is correlated as:

                                                         fOTHER  1  C1 RelZ1  C2 Reg 2
                                                                                      Z




                                                Where C1, C2, Z1, and Z2, are constants of the model, Rel and Reg are the
                                               Reynolds numbers of the condensate and the gas plus NC mixture
                                               respectively.

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                                                                         Condensation inside vertical tubes in presence of NC gases

                                               The METU-TAEA model

                                               As the NC gases are being accumulated in the interface creating a
                                               gradient concentration, the Fick’s law assures that a mass transfer of NC
                                               gases will produce from the interface to the bulk. According to Aglar and
                                               Tanrikut, this can be expressed with the help of the Sherwood number.
                                               Then, the degradation factor can be written in the following expression:


                                                          f 2  1  C3 y nc Sh 
                                                                                Z3




                                                where C3, and Z3 are model constants, ync is the NC molar fraction and
                                               Sh is the Sherwood number.




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                                                                            Condensation inside vertical tubes in presence of NC gases

                                               The UPV-FIT model

                                               This model only depends empirically on the NC mass fraction, because
                                               the other phenomena not included in the Nusselt theory -waviness and
                                               shear stress effects- have been implemented through δ, in a way that its
                                               influence has not been accounted for experimentally. This goal has been
                                               achieved introducing a different δ from the one of Nusselt. In this way,
                                               instead of:
                                                                     h exp (z)       h exp (z)  N (z)
                                                           f (z)                
                                                                     h th (z)               kl
                                               We have:
                                                                      h exp (z)       h exp (z) δ(z)
                                                            f(z)                 
                                                                      h th (z)              kl



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                                                                            Condensation inside vertical tubes in presence of NC gases


                                               The UPV-FIT model

                                               Where
                                                                                       1.259  4 / 3
                                                   =                                          N
                                                                                                                                 1/ 3
                                                                                                                                
                                                                                                             c1 + c2        
                                                               2                 3
                                                         p    aj     j-1
                                                                      x p + li        b j x p 1 + mi  p
                                                                                             j-
                                                                                                                        xp       
                                                        
                                                              j=1               j=1                                             
                                                                                                                                 
                                                                  dΓ
                                               δ is obtained solving
                                                                  dδ
                                                where the interfacial shear stresses and the wavy effects of the
                                               condensate layer
                                                have been introduced, and δN is the one obtained from the Nusselt
                                               theory.

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                                                                         Condensation inside vertical tubes in presence of NC gases


                                               The UPV-FIT model

                                               In this way, we can use a degradation factor that only takes account for the
                                                     NC mass fraction:
                                                            f UPV-4P = f 1 (Re g ) f 2 (M NC)

                                               Where
                                                                  f1 = 1

                                               and
                                                             f2 = 1 - P1 M P2 + P3 e- ( P4 M NC )
                                                                           NC




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                                                                         Condensation inside vertical tubes in presence of NC gases


                                               Comparisons

                                                First, we compare the results of the UCBA and METU-TAEA models,
                                               defining an average of the absolute values of the relative differences in %
                                               between the calculated hcal and experimental hexp heat transfer
                                               coefficients as:
                                                                           1 n (h cal,i  h exp,i )
                                                                   r (%)                         100
                                                                           n i 1    h exp,i



                                               The second comparison is made with all the models for the NC effect,
                                               using the Vierow and Schrock experiments. Also, we evaluated a mixed
                                               model defined as           k
                                                                  h model            f 2, UCBA (M NC )
                                                                               UPV

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                                                                                Condensation inside vertical tubes in presence of NC gases

                                                                                                    r (%)
                                                        Pure Steam
                                                                                       fexp>1.4              fexp<1.4

                                                       METU-TAEA                         5.26                 7.18

                                                          UCBA                                      10.57




                                                                                                    r (%)
                                               Steam plus NC gas correlations
                                                     are based on Mnc                  Mnc<0.1               Mnc>0.1

                                                       METU-TAEA                        10.23                 18.39

                                                          UCBA                          12.41                 20.58




                                                                                                   r (%)

                                                Mixture of Steam plus NC.                          5<y
                                               The correlations are based on                        nc
                                                            Sh.                      ync Sh <5      Sh       ync Sh > 25
                                                                                                    <
                                                                                                    25

                                                                                                    16.
                                                       METU-TAEA                      17.22                     9.16
                                                                                                    17

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                                                                   Condensation inside vertical tubes in presence of NC gases


                                                                             r (%)                       Mnc


                                                        UCB
                                               Model             UPV-4P          UPV-VS model   UPV-2P
                                                        model

                                               Run 4     3.8       23.1                22.3      21.7    0.0086
                                               Run 5    14.6       14.9                12.2      19.1    0.023
                                               Run 6    30.2       38.2                24.9      39.0    0.110
                                               Run 7    14.1       13.7                 9.1      23.7    0.025
                                               Run 8    18.3       18.5                 9.3      31.6    0.024
                                               Run 11   37.4       18.2                41.2      14.8    0.110
                                               Run 12   17.6       20.7                15.7      19.0    0.091
                                               Run 13   18.4       21.4                15.6      23.4     0.13
                                               Run 19   147.2      27.9               181.6      21.6     0.11
                                               Run 21   11.9       17.4                 5.7      17.6    0.061
                                               Run 22   35.1       39.7                30.7      46.6    0.037
                                               Run 23   26.3       18.9                10.3      19.7    0.051
                                               Run 24   25.7       35.6                26.7      40.2    0.051
                                               Run 26   48 .3      57.1                79.9      47.7     0.08
                                               Run 28   32.3       18.7                17.2      25.0    0.039

                                                                Average relative error r (%)

                                                        32.1       25.6               33.4      27.3
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                                                                        Condensation inside vertical tubes in presence of NC gases


                                               Conclusions

                                               The actual models which can be implemented in the Thermal-Hydraulic
                                               Codes to simulate the Condensation inside tubes in presence of NC
                                               gases, are all semi-empirical models.

                                                The problem of this kind of model construction is that we almost can not
                                               enhance it, that is, as the models use an empirical factor to account for
                                               the phenomena not included in the Nusselt theory, it is almost
                                               impracticable to get a better approach.

                                                 The next phase will be to implement them in a Thermal-Hydraulic Code
                                               like TRAC, RELAP, or TRACE, and to compare its results between them,
                                               and with the models now implemented in the Thermal-Hydraulic Codes.


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                                                            Condensation on Finned Tubes Heat Exchangers in presence of NC gases


                                               The finned tube HX consists in bundles of finned tubes cooled internally by
                                               natural circulation as displayed in the figure below .




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                                                             Condensation on Finned Tubes Heat Exchangers in presence of NC gases


                                                The working principle of FTCCC can be explained as follows: if the
                                               temperature in the drywell atmosphere increases over the one in the
                                               dryer-separator storage pool, then the steam condenses on the tubes and
                                               heat up the water inside the HX finned tubes. This water of less density
                                               moves upward by natural circulation due to the slope of the exchangers
                                               tubes, and flows through the outlet line, discharging the higher
                                               temperature cooling water in the pool. The outlet line ends at a higher
                                               elevation level than the inlet line, so the lifting forces are increased for the
                                               whole system.
                                                If the medium on the heat exchanger after an accident is a nitrogen-
                                               steam mixture, then the natural convection flow over the finned tubes is
                                               downward toward the core flooding pool, because the density of the
                                               nitrogen-steam mixture increases with decreasing temperature. However,
                                               the opposite is true for a hydrogen–steam mixture.
                                                These passive HX condenses the steam inside the containment and
                                               transport the heat by natural circulation to a large pool with capability to
                                               act as a heat sink at least during 72 hours.
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                                               Condensation on Finned Tubes Heat Exchangers in presence of NC gases




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                                                                Condensation on Finned Tubes Heat Exchangers in presence of NC gases



                                                  The total thermal resistance from the bulk gas to the coolant is formulated
                                                   as a parallel combination of the convective and condensation gas
                                                   resistances coupled in series to those of condensate layer, the wall, and
                                                   the coolant.
                                                  The condensate layer thermal resistance is calculated by means of an
                                                   Adamek based condensation model.
                                                  The Murata model is implemented to compute the fin’s efficiency, because
                                                   it is calculated through a direct expression, and not using an iteration
                                                   procedure as the Adamek model requires.
                                                  The gas mixture (Steam plus NC) thermal resistance is formulated based
                                                   on a diffusion layer theory formulated by Peterson, which uses the heat
                                                   and mass transfer analogy.
                                                  The model results are compared with available experimental data of the
                                                   thermal-hydraulic phase (steam+non-condensable gases) of the
                                                   experiments of the CONGA project of the European Community.


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                                                                 Condensation on Finned Tubes Heat Exchangers in presence of NC gases



                                               The overall heat flux from the containment bulk gas mixture at
                                               temperature Tb, to the coolant circulating inside the finned tube at
                                               temperature Tc, is given by Newton’s law of cooling:
                                                            q  h T (Tb  Tc )

                                               To compute the total HTC, we use the electrical analogy:
                                                                                                                       1
                                                                                                   Rg c ond 
                                                                                                                A0 hgcond  cond
                                                    Tc            Twi           Twe         Tcli
                                                                                                                           Tb


                                                         Rcool          Rwall         Rcl
                                                                                                                       1
                                                                                                    Rgconv 
                                                                                                                A0 hgconv  conv



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                                                               Condensation on Finned Tubes Heat Exchangers in presence of NC gases



                                               And the total HTC is:

                                                          1                1                
                                                                                              
                                                     hT 
                                                          A0  R cool  R wall  R cl  R gas 
                                                                                             

                                               where

                                                                  1              1
                                                     R cool            
                                                              A 0 h cool  L k cool Nu cool
                                               and
                                                                 dr 
                                                             ln  
                                                                d 
                                                     R wall   in 
                                                             2  kwL


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                                                            Condensation on Finned Tubes Heat Exchangers in presence of NC gases



                                                For the Condensate Layer Thermal Resistance we use the Adamek’s
                                               model, which is based on calculating the total mass condensation rate.
                                               For this goal, the finned tube is divided into 3 circumferential zones,
                                               according to the amount of condensate that we have in the interfin space:




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                                                                Condensation on Finned Tubes Heat Exchangers in presence of NC gases



                                                   The heat transfer coefficient for the condensate layer is:

                                                                                    
                                                                      4 N f L h pfg M1 / 2
                                                             h cl 
                                                                            A 0 T

                                                  M1/2 denotes the total mass condensation rate per one half fin at one side
                                                   of the tube.
                                                  L is the condensing length of the tube.
                                                  Nf is the number of fins per unit length.
                                                  ΔT is the difference of temperatures between the temperature at the
                                                   liquid-gas interface and the temperature at the surface of the tube.




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                                                                   Condensation on Finned Tubes Heat Exchangers in presence of NC gases



                                                   The heat transfer coefficient for the gas diffusion layer is:

                                                   q  q conv  q cond  ( h g,conv Θ conv  h g,cond Θ cond ) (Tb  Tcli ) 
                                                    gi    g,         g,

                                                         Nu k g          Sh k cond        
                                                               Θ conv            Θ cond  (Tb  Tcli )
                                                         d                  d             

                                                  hg,cond is the condensation heat transfer coefficient for the gas.
                                                  Θcond is the suction factor for condensation.
                                                  hg,conv is the convection heat transfer coefficient for the gas.
                                                  Θconv is the suction factor for convection.

                                                  These suction factors are caused by the boundary-layer shrinkage
                                                   produced by the transfer of momentum from the gas mixture to the
                                                   condensate film.
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                                                                Condensation on Finned Tubes Heat Exchangers in presence of NC gases



                                               The convection HTC of the gas mixture is related to the Nusselt number,
                                               where the Nusselt number depends on the convection regime:

                                                  Nu  h gconv d f / k g
                                                The Sherwood number is obtained from the same correlations quoted
                                               earlier and using the heat and mass transfer analogy, which allows Sh to
                                               be correlated as the Nu, provided that the Prandtl number of the gas
                                               mixture Prg, is substituted by the Schmidt number:

                                                           g
                                                  Sc g 
                                                                (g D)



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                                                                    Condensation on Finned Tubes Heat Exchangers in presence of NC gases



                                                   Finally, the Condensation Conductivity, taken from Peterson, is given by
                                                   the following expression:
                                                                                  2
                                                                    Davg h 2 Cg M st X st, avg
                                                         k cond 
                                                                           pfg
                                                                             2
                                                                          R Tavg         X nc,avg


                                                  D denotes the air-steam diffusion coefficient taken at Tavg temperature.
                                                  hpfg is the specific enthalpy of phase change plus the subcooling energy to
                                                   the average condensate temperature.
                                                  Cg is the gas mixture molar concentration.
                                                  Mst is the molecular weight of the steam.
                                                  Tavg is the average temperature in the boundary layer.
                                                  Xst,avg and Xnc,avg are the molar fraction logarithmic averages of the steam
                                                   and non-condensable respectively.
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UNIVERSIDAD POLITECNICA DE VALENCIA - CIEMAT


                                                                        Condensation on Finned Tubes Heat Exchangers in presence of NC gases


                                               Comparisons
                                                The results of the experiments performed at JRC by De Santi and at PSI
                                               by Suckow, are compared with the results of the program FINSTUBOAE
                                               that contains the model for finned tube condensation explained before.

                                                                                                                                   PWR    PWR     PWR    PWR     PWR
                                                              BWR     BWR     BWR    BWR    PWR    PWR    PWR
                                                                                                                                   HX1    HX2     HX3    HX4     HX5

                                                                                                                     q”exp         1.2    2.01    2.16   1.99    1.82
                                                               A1      A2      A3     A6     A4     A5     A7
                                                                                                                   q”predicted     1.4    1.35    1.71   1.62    1.67
                                                  q”exp        8.9     8.4     7.5    8.2    2.0   2.19    2.0     Error %         16.6   -32.5   -21.   -18.5   -8.2
                                                q”predicted    8.7     7.8     8.1    8.3   2.15   2.25   2.26
                                                                                                                 ΔTexperim(ºC)            5.51    5.72   5.43    5.13
                                                Error %        -2.2    -7.1    8.     1.2    7.5    2.7    13
                                               ΔTexp(ºC)      13.8    12.7    11.0   12.1    4.9    5.7    6.2   ΔTpredicted(ºC)   2.32   3.65    4.64   4.41    4.52
                                               ΔTpred(ºC)     13.0    11.8    12.4   12.7    6.0    6.3    6.3
                                                                                                                   Error %                -31.    -19.   -18.8   -11.9
                                               Error %        -5.8    -7.1    12.7   4.7    22.4   10.5   1.6

                                                                       De Santi experiments                                                        Suckow
                                               experiments


                            37
UNIVERSIDAD POLITECNICA DE VALENCIA - CIEMAT


                                                             Condensation on Finned Tubes Heat Exchangers in presence of NC gases

                                               Conclusions

                                                The model to simulate the behaviour of the Finned Tubes Heat
                                               Exchanger in presence of NC gases is constructed analytically.

                                                As we can observe, the results given by this model are better than the
                                               ones obtained with the models for condensation inside tubes, all of which
                                               were constructed semi-empirically.

                                                Our model keeps a non-dependency of any specific group of
                                               experiments, which permits a broad range of use of our model to different
                                               containment conditions.

                                                Although this model has been obtained analytically, it rests partially in
                                               some empirical correlations for the non-dimensional numbers as Nusselt
                                               or Sherwood number.



                            38
UNIVERSIDAD POLITECNICA DE VALENCIA - CIEMAT


                                                             Condensation on Finned Tubes Heat Exchangers in presence of NC gases

                                               Conclusions

                                                As the model is constructed analytically, it can be enhance by
                                               suppressing or getting better the empirical correlations or the simplificative
                                               hypothesis, as the followings:

                                                  1.   The use of the Clausis-Clapeyron equation, which implies a
                                                       saturated condition of the vapor at the entrance.
                                                  2.   To include the convection energy due to the NC gases, which
                                                       actually is not considered.
                                                  3.   To include the conduction therm in the Heat Transfer of the
                                                       boundary layer to the interface.
                                                  4.   To solve Fick’s law considering the variation of the total gas
                                                       density.

                                               The next step will be study the influence of aerosols deposition in the
                                               Heat Transfer and implement it in the FORTRAN FINSTUBOAE program.

                            39

				
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posted:12/12/2011
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