Abstract
This chapter reviews in-tube boiling and condensing flows, a subset of the area of phase-change heat transfer, with emphasis on their annular regime realizations in innovative devices. This review, in the light of numerous and excellent existing books and reviews, is also relevant because of recently reported experimental and technological approaches that make it feasible for annular/stratified regimes to cover the entire lengths of millimeter-scale flow-boilers and flow-condensers. The review chapter’s content also relates to new ways of addressing challenges that have emerged in the area of high heat-flux (500–1000 W/cm2 or greater) cooling of data centers, super computers, laser weapons, and other devices. The chapter summarizes current knowledge base and provides a design example each for steady annular operations of flow-boilers and flow-condensers. Furthermore, the chapter deals with some recent breakthroughs in the simulation of annular boiling/condensing flows and how such approaches can be extended – in conjunction with well-planned and parallel experiments – to further develop the science and innovative applications associated with steady or pulsatile operations of annular flow-boilers and flow-condensers.
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Abbreviations
- A:
-
Cross-sectional area, m2
- Bl:
-
Boiling number \( \left({\overline{\mathrm{q}}}_{\mathrm{w}}^{"}/\mathrm{G}{\mathrm{h}}_{\mathrm{fg}}\right) \)
- \( \tilde{\mathrm{Bl}} \) :
-
Alternate boiling number \( \left({\mathrm{q}}_{\mathrm{w}}^{"}\cdot {\mathrm{D}}_{\mathrm{h}}/\left({\upmu}_{\mathrm{L}}\cdot {\mathrm{h}}_{\mathrm{fg}}\right)\right) \)
- Bo:
-
Bond number (g(ρL − ρV)D2/σ)
- C:
-
Lockhart-Martinelli constant
- Cp :
-
Specific heat, J/kg-K
- CHF:
-
Critical heat-flux
- Dh :
-
Hydraulic diameter, m
- f:
-
Friction factor
- frP :
-
Heated perimeter fraction (PH/PF)
- Frx :
-
Froude number in x-direction (|gx| Dh/U2)
- Fry :
-
Froude number in y-direction (|gy| Dh/U2)
- G:
-
Mass flux, kg/m2s
- gx :
-
Gravity component in x-direction, m/s2
- gy :
-
Gravity component in y-direction, m/s2
- h:
-
Height of the channel, m
- hfg :
-
Heat of vaporization, J/kg
- Ja:
-
Liquid Jakob number, (CpLΔT/hfg)
- k:
-
Conductivity, W/m-K
- L:
-
Length of the channel or test section, m
- \( {\dot{\mathrm{M}}}_{\mathrm{in}} \) :
-
Total mass flow rate, kg/m2-s
- \( {\dot{\mathrm{M}}}_{\mathrm{L}} \) :
-
Liquid mass flow rate, kg/m2-s
- \( {\dot{\mathrm{M}}}_{\mathrm{v}} \) :
-
Vapor mass flow rate, kg/m2-s
- p0 or pin :
-
Steady inlet pressure (also pin), kPa
- P:
-
Mechanical power, W
- PrL :
-
Liquid Prandtl number (μLCpL/kL)
- \( {\overline{\mathrm{q}}}_{\mathrm{w}}^{"} \) :
-
Mean wall heat-flux, W/m2
- ReT :
-
Reynolds number representing nondimensional (GDh/μV)
- S:
-
Suppression factor
- Su:
-
Suratman number (\( \upsigma {\uprho}_{\mathrm{V}}{\mathrm{D}}_{\mathrm{h}}/{\upmu}_{\mathrm{V}}^2 \))
- t:
-
Time
- \( {\overline{\mathrm{T}}}_{\mathrm{w}} \) :
-
Mean wall temperature, °C
- Tsat(p0):
-
Saturation temperature at pressure p0, °C
- u:
-
Velocity, m/s
- We:
-
Liquid Weber number (ρLU2Dh/σ)
- X:
-
Vapor quality
- \( \widehat{\mathrm{x}} \) :
-
Nondimensional distance (≡x/Dh)
- xA :
-
Nondimensional length of the annular regime
- Xtt :
-
Lockhart-Martinelli parameter
- μ:
-
Viscosity, kg/m-s
- ρ:
-
Density, kg/m3
- ϵ:
-
Void fraction
- Φg :
-
Two-phase multiplier
- σ:
-
Surface tension, kg/s2
- Δ:
-
Physical value of liquid film thickness, m
- Ψq :
-
Nondimensional heat-flux
- θw :
-
Nondimensional temperature
- cb:
-
Represents macroscale convective boiling
- CHF1:
-
Represents dry-out instability
- CHF2:
-
Represents inverted annular flow related instability
- cr:
-
Represents “critical value”
- L:
-
Represents liquid phase of the flow variable
- nb:
-
Represents macro-scale nucleate boiling
- V:
-
Represents vapor phase of the flow variable
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Acknowledgment
This work was supported by NSF grant CBET-1402702. All figures, which are schematics in their nature, are contributions of Mr. Patcharapol Gorgitrattanagul, a graduate student at MTU.
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Narain, A., Prasad, H.P.R., Koca, A. (2017). Internal Annular Flow Condensation and Flow Boiling: Context, Results, and Recommendations. In: Kulacki, F. (eds) Handbook of Thermal Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-32003-8_51-1
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