AME 60634 Int. Heat Trans. D. B. Go Two-Phase: Overview • Two-Phase – two-phase heat transfer describes phenomena where a change of phase (liquid/gas) occurs during and/or due to the heat transfer process – two-phase heat transfer generally considers processes that occur at a solid/fluid interface and are therefore a sub-field of convection – because of the change of phase, the latent heat (h fg ) of the fluid must be considered – the surface tension (σ) is another parameter that plays an important role • Boiling – heat transfer process where a liquid undergoes a phase change into a vapor (gas) • Condensation – heat transfer process where a vapor (gas) liquid undergoes a phase change into a liquid
Transcript
AME 60634 Int. Heat Trans.
D. B. Go
Two-Phase: Overview • Two-Phase
– two-phase heat transfer describes phenomena where a change of phase (liquid/gas) occurs during and/or due to the heat transfer process
– two-phase heat transfer generally considers processes that occur at a solid/fluid interface and are therefore a sub-field of convection
– because of the change of phase, the latent heat (hfg) of the fluid must be considered
– the surface tension (σ) is another parameter that plays an important role
• Boiling – heat transfer process where a liquid undergoes a phase change into a
vapor (gas)
• Condensation – heat transfer process where a vapor (gas) liquid undergoes a phase
change into a liquid
AME 60634 Int. Heat Trans.
D. B. Go
Boiling: Overview • Boiling
– associated with transformation of liquid to vapor (phase change) at a solid/liquid interface due to convection heat transfer from the solid
– agitation of the fluid by buoyant vapor bubbles provides for large convection coefficients è large heat fluxes at low-to-moderate surface-to-fluid temperature differences
• Modified Newton’s Law of Cooling
€
" " q s = h Ts −Tsat( ) = hΔTe
€
Ts
€
Tsat
€
ΔTe ≡ Ts −Tsat( )
surface temperature
saturation temperature of liquid
excess temperature
AME 60634 Int. Heat Trans.
D. B. Go
Boiling: Overview • Flow Cases
– Pool Boiling • liquid motion is due to natural convection and bubble-induced mixing
– Forced Convection Boiling (Flow Boiling/2-Phase Flow) • liquid motion is induced by external means and there is also bubble-induced
mixing
• Temperature Cases – Saturated Boiling
• liquid temperature is slightly higher than saturation temperature
– Subcooled Boiling • liquid temperature is less than saturation temperature
AME 60634 Int. Heat Trans.
D. B. Go
Boiling: The Boiling Curve • Boiling Curve
– identifies different regimes during saturated pool boiling
– critical heat flux (CHF) (ΔTe ~ 30 °C) • maximum attainable heat flux in nucleate boiling • water at atmospheric pressure
– CHF ~ MW/m2
– hmax ~ 10000 W/m2-K
• Transition (30 °C < ΔTe < 120 °C) & Film Boiling (ΔTe > 120 °C) • heat transfer is by conduction and radiation across the vapor blanket • liquid/surface contact is impaired by presence of vapor columns • q”s decreases with increasing ΔTe until the Leidenfrost point corresponding to the
minimum heat flux for film boiling and then proceeds to increase • a reduction in the surface heat flux below the minimum heat flux results in a abrupt
reduction in surface temperature to the nucleate boiling regime
• Heat flux controlled heating: burnout potential • if the heat flux at the surface is controlled it can potentially increase beyond the CHF • this causes the surface to be blanketed by vapor and the surface temperature can
spontaneously achieve a value that potentially exceeds its melting point (ΔTe > 1000 °C)
• if the surface survives the temperature shock, conditions are characterized as film boiling
AME 60634 Int. Heat Trans.
D. B. Go
• Due to complexity of fluid mechanics and phase-change thermodynamics, boiling heat transfer correlations are empirical
• Rohsenow Correlation: Nucleate Boiling – note: can be as much as 100% inaccurate!
• Critical Heat Flux
Boiling: Pool Boiling Correlations
€
" " q s = µlh fgg ρl − ρv( )
σ
&
' (
)
* +
12 cp,l
Cs, f h fg Prln
&
' (
)
* +
3
ΔTe( )3subscripts: l è saturated liquid state
v è saturated vapor state
€
µl ≡ viscosity; cp,l ≡ specific heat; g ≡ acceleration due to gravityσ ≡ surface tension; hfg ≡ latent heat of vaporization; ρ ≡ density
€
" " q max = 0.149h fgρvσg ρl − ρv( )
ρv2
&
' (
)
* +
14 correction factor required for
surfaces with small characteristic lengths
AME 60634 Int. Heat Trans.
D. B. Go
Boiling: Pool Boiling Correlations
€
" " q s = µlh fgg ρl − ρv( )
σ
&
' (
)
* +
12 cp,l
Cs, f h fg Prln
&
' (
)
* +
3
ΔTe( )3Rohsenow Correlation
AME 60634 Int. Heat Trans.
D. B. Go
• Minimum Heat Flux
• Film Boiling – correlation for spheres & cylinders
– total average heat transfer coefficient due to cumulative & coupled effects of convection (due to boiling) and radiation across the vapor layer
Boiling: Pool Boiling Correlations
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NuD =h convD
kv
= Cg ρl − ρv( ) $ h fgD3
ν vkv Ts −Tsat( )
&
' (
)
* +
14
⇒ C =0.62 cylinder0.67 sphere
- . /
€
" " q min = 0.09h fgρvσg ρl − ρv( )ρl + ρv( )2
&
' ( (
)
* + +
14
reduced latent heat
€
" h fg = h fg + 0.80cp,v Ts −Tsat( )
€
h 4 3 = h conv4 3 + h rad( ) h 1 3( )
€
h = h conv + 0.75h rad ⇒ h conv > h rad
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h rad =εσ Ts
4 −Tsat4( )
Ts −Tsat
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σ ≡Stefan - Boltzmann constant
Leidenfrost point
AME 60634 Int. Heat Trans.
D. B. Go
Condensation: Overview • Condensation
– occurs when the surface temperature is less than the saturation temperature of an adjoining vapor
– heat is transferred from vapor the surface to the surface
• Film Condensation – entire surface is covered by the condensate which flows
continuously from the surface and presents a thermal resistance to heat transfer from the vapor to the surface
• typically due to clean, uncontaminated surfaces • can be reduced by using short vertical surfaces & horizontal
cylinders
• Dropwise Condensation – surface is covered by drops ranging from a micron to large
agglomerations – thermal resistance is lower than that of film condensation – surface coatings may inhibit wetting and stimulate dropwise
condensation
AME 60634 Int. Heat Trans.
D. B. Go
Condensation: Film Condensation • Vertical Plate
– thickness and flow rate of condensate increase with increasing x
– generally, the vapor is superheated (Tv,∞>Tsat) and may be part of a mixture that contains noncondensibles
– a shear stress at the liquid/vapor interface induces a velocity gradient in the vapor as well as the liquid
€
δ
€
˙ m
• Laminar Flow Analysis – assume pure vapor – assume negligible shear stress at liquid/vapor interface
– negligible advection in the film
€
∂u∂y y=δ
= 0
AME 60634 Int. Heat Trans.
D. B. Go
Condensation: Film Condensation • Vertical Plate: Laminar Flow Analysis
– film thickness
– flow rate per unit width
– average Nusselt number
– heat transfer rate
– condensation rate
€
δ x( ) =4klµl Tsat −Ts( )xgρl ρl − ρv( )hfg
%
& '
(
) *
14
€
Γ ≡˙ m b
=gρl ρl − ρv( )δ 3
3µl
€
NuL =h LLkl
= 0.943gρl ρl − ρv( ) $ h fgL3
klµl Tsat −Ts( )
%
& '
(
) *
14
€
" h fg = h fg 1+ 0.68Ja( )
€
Ja =cp Ts −Tsat( )
hfg
modified latent heat
Jakob number
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q = h L As Tsat −Ts( )
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˙ m = q" h fg
AME 60634 Int. Heat Trans.
D. B. Go
Condensation: Film Condensation • Vertical Plate: Turbulence
– transition may occur in the film and three flow regimes may be delineated
– wave-free laminar region (Reδ<30)
– wavy laminar region (30<Reδ<1800)
– turbulent region (Reδ>1800)
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Reδ =4Γµl
=4 ˙ m µlb
=4ρlumδ
µl
€
Reδ =4gρl ρl − ρv( )δ 3
3µl2
€
h L ν l2 g( )
1 3
kl
=1.47Reδ−1 3
€
h L ν l2 g( )
1 3
kl
=Reδ
1.08Reδ1.22− 5.2
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h L ν l2 g( )
1 3
kl
=Reδ
8750 − 58Pr−0.5 Reδ0.75− 253( )
AME 60634 Int. Heat Trans.
D. B. Go
Condensation: Film Condensation • Vertical Plate: Calculation Procedure
– assume a flow regime and use the corresponding equation for to determine Reδ
– if Reδ value is consistent with flow regime assumption, calculate total heat rate and mass flow rate
– if Reδ value is inconsistent with flow regime assumption, iterate on flow regime assumption until it is consistent
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h L
AME 60634 Int. Heat Trans.
D. B. Go
Condensation: Film Condensation • Radial Systems: Single Tubes/Spheres
€
h D = Cgρl ρl − ρv( ) $ h fgkl
3
µl Tsat −Ts( )D
%
& '
(
) *
14
Tube: C =0.729
Sphere: C=0.826
AME 60634 Int. Heat Trans.
D. B. Go
Condensation: Film Condensation • Radial Systems: Vapor Flow in a Horizontal Tube
– if vapor flow rate is low, condensation in both circumferential and axial directions
– for high flow rates, flow is two-phase annular flow €
