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Condensation
CONDENSERSPower plant – water is boiled in boiler and condensed in condenserOil refinery - oil is evaporated in distillati...
CONDENSATION HEAT TRANSFER• Film condensation• Dropwise condensation                                   FILM CONDENSATION  ...
• Condensate film thickness are thin – heat transfer coefficients are large• Example - steam at a saturation temperature o...
DROPWISE CONDENSATION                               80°C                                       DropletsIf the condensate d...
Droplets slide down when they reach a certain size, clearing the surface andexposing it to vapor.There is no liquid film i...
Bonding a polymer such as teflon to the surface is expensive and adds additionalthermal resistanceGold plating is also exp...
LAMINAR FLOW CONDENSATION ON A VERTICAL WALL                                                             Tsat          g  ...
LAMINAR FLOW CONDENSATION ON A VERTICAL WALLConsider a vertical wall exposed to a saturated vapour at pressure p and satur...
0                     x                     Laminar film of                       condensate                              ...
ASSUMPTIONS• Laminar flow and constant properties are assumed for the liquid film• Gas is assumed to be pure vapour and at...
Steady state two dimensional incompressible flow                     u   u    P        2u  2u                   ...
 v   v                                             2v               L u  v                   x                 ...
x2     L v  g  L   v   C1 x  C 2                          2    C2  0   C1  g  L   v                      ...
Local mass flow rate per unit width  (y)                                                                            y...
 L g  L   v   3                                y                                               L           3  ...
T  C1 x  C 2              x   T  Tsat              x  0 T  Tw  C 2  Tw                                           ...
Heat flux into the wall = Heat flux across the film                                                      Q k l Tsat  Tw ...
Rate of heat transfer from the vapour             = Heat releasead as vapour is condensedto the plate through the liquid f...
4     L k l Tsat  Tw                                                    y                         4    L g  L  ...
1                                                                                                                     ...
Effect of subcoolingRohsenow refined• avoided linear temperature profile• Integral analysis of temperature distribution ac...
JAKOB NUMBERIs a measure of degree of subcooling experienced by the liquid film                               C p ,L Tsat...
Reynolds Number               L um Dh                   4 Ac 4b         Re            ; um       ; Dh           4...
4  L g 3                                     2  L   v  Re                                    3 L                 ...
Hydraulic diameter                         D                                        P  2LPL                  P D      ...
Wavy Laminar flow over vertical platesAt Reynolds number greater than about 30, it is observed that waves form at theliqui...
Turbulent flow over vertical plates (Re > 1800)Labuntsov proposed the following relation                                  ...
Non-dimensionalised heat transfer coefficients for the wave-free laminar and             turbulent flow of condensate on v...
Problem: Saturated steam at atmospheric pressure condenses on a 2 m high and 3 mwide vertical plate that is maintained at ...
1                                          1              g                  9.81  965 .3  965 .32314  1000 ...
1                                                1                                                                       ...
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Condensation

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Condensation

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Condensation

  1. 1. Condensation
  2. 2. CONDENSERSPower plant – water is boiled in boiler and condensed in condenserOil refinery - oil is evaporated in distillation column and condensedinto liquid fuels like gasoline and keroseneDesalination plant – water vapor is produced by evaporation frombrine and condensed as pure waterCondensation – enthalpy of phase change to be removed by a coolantEnthalpy of phase change is relatively large, for water (2.5 106 J/kg)and associated heat transfer rates are also largeHeat transfer to phase interface – convective process – complicated byan irregular surface – bubbles and drops
  3. 3. CONDENSATION HEAT TRANSFER• Film condensation• Dropwise condensation FILM CONDENSATION Condensate wets the surface and forms a liquid film on the surface that slides down under the influence 80° C of gravity. Surface is blanketed by a liquid film of increasing thickness, and this “liquid wall” between the solid surface and the vapor serves as a resistance to heat transfer Liquid film
  4. 4. • Condensate film thickness are thin – heat transfer coefficients are large• Example - steam at a saturation temperature of 305 K condenses on a 2 cm – O.Dtube with a wall temperature of 300 K•Average film thickness - 50m (0.05 mm) and the average heat transfer coefficient –11,700 W/m2.K• If the condensate flow rate is small, the surface of the film will be smooth and theflow laminar because • Temperature difference is small • Wall is short• If the condensate flow rate is high, waves will form on the surface to give wavylaminar flow•If the condensate flow rate is yet higher, the flow becomes turbulent
  5. 5. DROPWISE CONDENSATION 80°C DropletsIf the condensate does not wet the wall, because either it is dirty or it has beentreated with a non-wetting agent, droplets of condensate nucleate at small pits andother imperfections on the surface, and they grow rapidly by direct vaporcondensation upon them and by coalescenceWhen the droplets become sufficiently large, they flow down the surface under theaction of gravity and expose bare metal in their tracks, where further dropletnucleation is initiatedTHIS IS CALLED DROPWISE CONDENSATION
  6. 6. Droplets slide down when they reach a certain size, clearing the surface andexposing it to vapor.There is no liquid film in this case to resist heat transfer.Heat transfer rates that are more than 10 times larger than those associated withfilm condensation can be achieved with dropwise condensationMost of the heat transfer is through drops of less than 100m diameterThermal resistance of such drops is small; hence, heat transfer coefficients fordropwise condensation are large; values of upto 30000 W/m2.K have beenmeasured.Hence, dropwise condensation is preferred over filmwise condensationConsiderable efforts are put for non-wetting heat exchanger surfacesIf the surface is treated with non-wetting agent (stearic acid) to promote dropwisecondensation, the effect lasts only few days, until the promoter is washed off oroxidised.Continuous adding of the promoter to the vapour is expensive and contaminates thecondensate.
  7. 7. Bonding a polymer such as teflon to the surface is expensive and adds additionalthermal resistanceGold plating is also expensiveBecause of lack of sustainability of dropwise condensation, present day condensersare designed based on filmwise condensationFilmwise condensation – conservative estimate
  8. 8. LAMINAR FLOW CONDENSATION ON A VERTICAL WALL Tsat g Tw Laminar Vapor reservoir Cold wall Wavy T Tw x T  x 0 Tsat Velocity Vapor Turbulent Liquid Vapor Liquid TwTemperature of the liquid-vapour interface is the saturation temperature that corresponds to TsatVapour in the descending jet is colder than the vapour reservoir and warmer than the liquid in the film attached to the wall
  9. 9. LAMINAR FLOW CONDENSATION ON A VERTICAL WALLConsider a vertical wall exposed to a saturated vapour at pressure p and saturation temperature Tsat = Tsat(P).The wall could be flat or could be the outside surface of a vertical tubeIf the surface is maintained at a temperature Tw < Tsat, vapour will continuously condense on the wall, and if the liquid phase wets the surface well, will flow down the wall in a thin filmProvided the condensation rate is not too large, there will be no discernable waves on the film surface, and the flow in the film will be laminar• Fluid dynamics of the flow of a thin liquid film• Heat transfer during the flow of a thin liquid film
  10. 10. 0 x Laminar film of condensate  x 0 T Tsat u Zero shear , 0 v y u Tw v x = δ(y) Interface T = Tsat Tsat  Tw x y H y + dy From reservoir of hg d saturated vapor   d T  Tsat H + dH
  11. 11. ASSUMPTIONS• Laminar flow and constant properties are assumed for the liquid film• Gas is assumed to be pure vapour and at a uniform temperature equal to Tsat. The merit of this simplification is that it allows us to focus exclusively on the flow of the liquid film and to neglect the movement of the nearest layers of vapour• Shear stress at the liquid-vapour interface is assumed to be negligible• With no temperature gradient in the vapour, heat transfer to the liquid-vapour interface can occur only by condensation at the interface and not by conduction from the vapour
  12. 12. Steady state two dimensional incompressible flow  u u  P   2u  2u  L u  v     x   L  2  2   y  x  x y   v v  P   2v  2v  L u  v     x   L  2  2    L g  y  y  x y  x ~ ;y ~ L u  v , Hence , x  momentum equation vanishes Neglected, y<<x  v v  dP  v  v 2 2 L u  v     x   L  2  2    L g  y  dy  x y  dP  pressure imposed from the inviscid potion   v g  Hydrostatic pressure dy  v v   2v  L  u  v    L   v g   L 2  x  y   x
  13. 13.  v v   2v L u  v   x   L   v g   L 2    y      x   SINKING EFFECT FRICTION INERTIAAssuming inertia is negligible  2v  L 2   L   v g  0 xBoundary conditions x0 v0 v x  0 xIntegrating v  L  g   L   v  x  C1 x x2  L v  g  L   v   C1 x  C 2 2 x  0 v  0  C2  0 v v x   0  L  g  L   v x  C1  g  L   v   C1 x x
  14. 14. x2  L v  g  L   v   C1 x  C 2 2 C2  0 C1  g  L   v  x2  L v  g   L   v   g   L   v  x 2 g  L   v   x2  v  x    L  2  g  L   v  2   x 1  x 2  vx , y        L  2    Film thickness is unknown function of (y)
  15. 15. Local mass flow rate per unit width  (y)     y    y     Lv dx 0  g  L   v   x 1  x 2    y    L  2      dx L  2   0    g  L   v  2  x 2 1  x 3     y   L     3  L  2 6      0  L g  L   v  2       y      L 2 6  L g  L   v  2    y   L 3  L g  L   v   3   y  L 3
  16. 16.  L g  L   v   3   y  L 3 b L g L   v   3 m  b  y    L 3B – width of the plate perpendicular to the plane of paperFlow rate is proportional to the sinking effect - g(L-v)Flow rate is inversely proportional to the liquid viscosity (Friction)HEAT TRANSFER PROBLEMFilm velocity is lowTemperature gradients in the y-direction are negligible since both wall and filmsurface are isothermal d 2T 0 dx 2 dT  C1 ; T  C1 x  C 2 dx
  17. 17. T  C1 x  C 2 x   T  Tsat x  0 T  Tw  C 2  Tw Tsat  Tw T  C1 x  Tw  Tsat  C1  Tw  C1   T  Tsat  Tw  x  Tw This is a linear temperature profile similar to the conduction in a planewall
  18. 18. Heat flux into the wall = Heat flux across the film Q k l Tsat  Tw    hTsat  Tw    dT kl dx w A  kl dT k l Tsat  Tw  h dx w   k  l Tsat  Tw  Tsat  Tw   kl h Determination of film thickness  L g  L   v   b L g L   v   3 m  b  y   3   y  ;  L 3 L 3  b L g L   v  3 2 d Rate of condensation of  b  y   dm dy L 3 dy vapour over a vertical distance dy
  19. 19. Rate of heat transfer from the vapour = Heat releasead as vapour is condensedto the plate through the liquid film   dmh  k b dy Tsat  Tw dQ  fg l  dm k l b Tsat  Tw   dy h fg   b L g  L   v  3 2 d k l b Tsat  Tw  b  y   dm  dy L 3 dy h fg   L g  L   v  3 2 d k T  Tw  l sat L 3 dy h fg   L k l Tsat  Tw   3 d  dy  L g  L   v h fg 4  L k l Tsat  Tw   yC y  0,   0C  0 4  L g  L   v h fg
  20. 20. 4  L k l Tsat  Tw   y 4  L g  L   v h fg 1  4 k 4 T  T  4   y    L l sat w y   L g  L   v h fg    1   g   L   v h fg k l4  4 h   L kl    4 L k l Tsat  Tw  y    1 1   L g    L  L   v h fg k l3  4  g L  L   v h fg k l3  4 L 1 1hL    dy    1  L y 4 dy L 0 4 L Tsat  Tw  y   4 L Tsat  Tw      0
  21. 21. 1     g L  L   v h fg k l3  4  hL  0.943  4 T  T L   L sat w  1 b L g L   v   3  4 k 4 T  T  4 m  b  y      y    L l sat w y L 3   L g  L   v h fg    3 b L g  L   v   4 L k l4 Tsat  Tw  4 m   y 3 L   L g  L   v h fg   All liquid properties evaluated at Tsat  Tw Tf  2
  22. 22. Effect of subcoolingRohsenow refined• avoided linear temperature profile• Integral analysis of temperature distribution across the filmTemperature profile whose curvature increases with the degree of subcoolingCp,L(Tsat-Tw) hfg  h fg  0.68C p ,L Tsat  Tw Replace in previous equations h fg by hfgAll liquid properties evaluated at Tsat  Tw Tf  2hfg and v are evaluated at the saturation temperature Tsat
  23. 23. JAKOB NUMBERIs a measure of degree of subcooling experienced by the liquid film C p ,L Tsat  Tw  Ja  h fg hfg  h fg  0.68C p ,L Tsat  Tw  hfg  h fg 1  0.68 Ja 
  24. 24. Reynolds Number  L um Dh  4 Ac 4b Re  ; um  ; Dh    4 L  L P b  4 4 Re   L   L  L  L 4 Re  L  L g  L   v   3   y  L 3 4 4  L g  L   v   3 Re   L 3 L L 4  L g 3 2 4 g 3  L   v  Re   3 L 2 3 L 2
  25. 25. 4  L g 3 2  L   v  Re  3 L 2    x  L  l kl k   h hx  L 3 hx  L  havg 4 3   2  kL  3 4 g L  k L  2 4 g LRe  2        3  L  hx  L  3 L  3 2   havg  4  1 1   g 3 havg  1.47 k l Re 3   2   l 
  26. 26. Hydraulic diameter D P  2LPL P D Ac  2 LAc  L Ac   D 4 Ac Dh   4 4 Ac P 4ADh  c  4 Dh   4 P P
  27. 27. Wavy Laminar flow over vertical platesAt Reynolds number greater than about 30, it is observed that waves form at theliquid vapour interface although the flow in liquid film remains laminar. The flow inthis case is Wavy LaminarKutateladze (1963) recommended the following relation for wavy laminarcondensation over vertical plates 1  g Re k l 3 hvert ,wavy    1.08 Re 1.22  2   5.2  l  30  Re  1800 ,  v   l 0.82  1  3.70 Lk l Tsat  Tw   g  3     Re vert ,wavy  4.81    l hfg  2    l     
  28. 28. Turbulent flow over vertical plates (Re > 1800)Labuntsov proposed the following relation 1 Re k l  g 3   hvert ,turbulent   8750  58 Pr  0.5 Re 0.75  253   l2    Film condensation on an inclined Plates hinclined  hvert cos  Condensate  1 1  1 2 hL   l2  3  kl  g      Re L0.44     3 5.82  10  6 Re L.88 PrL  0     
  29. 29. Non-dimensionalised heat transfer coefficients for the wave-free laminar and turbulent flow of condensate on vertical plates 1 Pr = 10 5 3 2h( vl2 g )1 3 kl 1 Wave-free Wavy Turbulent laminar laminar 0.1 10 30 100 1000 1800 10,000 Re
  30. 30. Problem: Saturated steam at atmospheric pressure condenses on a 2 m high and 3 mwide vertical plate that is maintained at 80C by circulating cooling water throughthe other side. Determine (a) the rate of heat transfer by condensation to the plate(b) the rate at which the condensate drips off the plate at the bottomSolution: saturated steam at 1 atm condenses on a vertical plate. The rats of heattransfer and condensation are to be determinedAssumptions: 1. steady operating conditions exist 2. The plate is isothermal. 3. Thecondensate flow is wavy laminar over the entire plate (will be verified). 4. Thedensity of vapour is much smaller than the density of the liquid v<<lProperties: The properties of water at the saturation temperature of 100C are hfg =2257 103 J/g and v = 0.6 kg/m3. The properties of liquid water at the filmtemperature 90C are T  Tw 100  80 T f  sat   90 2 2 hfg  h fg  0.68C p ,L Tsat  Tw   l  965 .3 kg / m 3 3  l  0.315  10 Pa .s hfg  2257 103  0.68 4206 100 80   l  l  0.326  10  6 m 2 / s l hfg  2314103 J / kg C pl  4206 J / kg .K k l  0.675 W / m .K Pr  1.9628
  31. 31. 1 1  g     9.81  965 .3  965 .32314  1000   v h fg k l3  4 0.675 3  4  L L    hL  0.943  0.943   4  T  T L   4  0.315  10  3 100  80 4   L sat w    W hL  2656 .2 m2KQ  hL As Tsat  Tw   2562 .2  2  3  100  80   307464 W Q  mh  307464  m  2314  10 3  m  0.1329 kg / s   sf 4 4 m 4  0.1329 Re        562.5 L  L  b  0.315  10 3  3 
  32. 32. 1 1  1 2 hL   l2  3  kl  g      Re L0.44     3 5.82  10  6 Re L.88 PrL  0      1 1   hL  0.326  10   6 2  3      562 .5  0.44   1 2 5.82  10  6  562 .50.88  1.9628 3   0.675   9.81        W hL  7691 .4 m2K Q  hL As  Tsat  Tw   7691.4  2  3   100  80   2307420 W    Q  mhsf  2307420  m  2314  103  m  0.9972 kg / s   4 4 m 4  0.9972  Re    b  0.315  103  3   4221  L L     This confirms that condensation is in turbulent regionComments: This Reynolds number confirms that condensation is in Wavy laminardomain

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