3 Thermal-hydraulic constraints

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					    #3 Thermal-hydraulic constraints
 From: N. Todreas & M. Kazimi, “Nuclear Systems I:
 Thermal-hydraulic fundamentals” (1989)
• Core pressure drop (p. 382) – determined by p of the main
  pump; this constraint fixes the pressure drop over the
  reactor core (p)
             p = pinlet + prods + pgrids
    pinlet : over the bottom nozzle of the FA (can vary with
          radial position in core by adjusting inlet orifice size)
    prods: turbulent-flow correlation (e.g., Dittus-Boelter) – a
      function of m , De
                     
    pgrids: depends of type and number of spacer grids on FA

                                                            1
• Fuel-rod vibration – driven by turbulence and (in PWRs)
  by cross flow
  - less important in BWRs because vapor phase at top of
  rods dampens vibrations
  - importance: wear (fretting) of cladding metal due to
  rubbing against grid holder
  - in lieu of a detailed vibration analysis, an axial flow
  velocity constraint is often used
• Critical heat flux (pp. 25, 554) – rod-to-coolant heat flux
  (or the LHR) that results in a drastic reduction in the
  heat-transfer coefficient (h)

                                                              2
  Critical Heat Flux (CHF)
• CHF is sometimes called
the boiling crisis

• In PWRs, the CHF is called
Departure from Nucleate
Boiling, or DNB                         vapor     vapor


• In BWRs, the CHF is called
dryout (at critical bundle power)

• measures of rod power:
q’’’ = volumetric heat source
q’’ = heat flux to coolant
q’ = linear heat rate (LHR)
                                    q'  (D) '   / 4Dpelletq' ' ' 3
                                          q'            2
                  DNB in PWRs
• Consider a single channel (one fuel rod and associated
  coolant)
• The LHR at which DNB occurs decreases with z

                        from a correlation

                                   z < zDNB, single-phase
                                         heat transfer
                                   (with nucleate boiling)

                                     z > zDNB, film
                                     boiling; poor heat
                                     transfer
                                                       4
   The W-3 Correlation for DNB (p. 558)
    q’DNB = p-term x G-term x De-term x h-term
    p = system pressure; G = mass flux; De = equivalent
           diameter of channel; h = enthalpy rise, inlet  z
  p-term = (a - bp) + (a’ –b’p)exp[(a” – b”p)xe]
  G-term = [(c – dxe+ gxe|xe|)G + s]
  De term = (c’ – d’xe)(j + kemD )e        xe = “thermodynamic”
                                            steam quality (p.141)
  h term = u + v(hf – hin)
        h ( z)  h f
  xe 
                                             z
                                         1
         hg  hf          h ( z)  hin 
                                            q'rod (z' )dz'
                                         m L / 2
 quality if equilibrium prevails
                                                  xe can be < 0!
hg and hf evaluated at system pressure                             5
 Two-phase flow properties (BWRs)
                             
                             mv , v v
                        
                        m , v 


    Flow quality (Eq 5.35): x  mv / m
                                    

    Void fraction (Eq 5.10): α  Vv / V  A v / A
    Slip Ratio (Eq 5.48):               S = vv /v
                                                     1
            ρvvv Av                1 x ρ v 
   x                       α  1       S
      ρv vv Av  ρ v A             x ρ 

Avg. velocity = G/[v + (1- ) ]
                                                          6
               Dryout (p.560)

• No liquid film on wall – substantial decrease
  in heat transfer
• Hensch-Gillis correlation:
  - gives the critical quality at which dryout
  occurs
   - critical quality controled of by mass flux G
  and by upstream conditions
   - See Memo #2 for details


                                                    7
   Phase-change constraints in LWRs (p. 560)
• Instead of prescribing q’cr, the
  ratio q’cr/q’rod or q’cr/q’FA is used
• This is called the “critical power
  ratio”, or CPR
• For BWRs, The minimum CPR
  is prescribed:
            q             ~
     MCPR  (' cr / q'FA ) 1.2

For PWRs, this is the Minimum
  Departure from Nucleate
  Boiling Ratio:

           q              ~
   MDNBR  (' cr / q'rod ) 2.35
                                          8
Components of MDNBR




                      9
              BWR Thermal power for MCPR


                                                   
    A flow  (P 2   4 D 2 ) N rod     G
                                                  M
                                                                    q 
                                                                      crit
                                             A flow N bun


                         
h out  h in  f p,core Q / M         Steam tables                  xout
                                                                              compare

                                          
                                          Q  f p,core
           
     input Q                                                    =      q 
                                      DL  N bun  N rod


              
    increment Q                          no                 MCPR  q  q ?
                                                                          crit

                                                                 yes
                                                                    exit            10