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ABSTRACT
The algorithm for the accurate and relevant numerical solution technique given in part I of this article is used to obtain the results for shear-driven annular condensing flows in horizontal channels—with or without transverse gravity. The unsteady wave simulation capability is used to implement a unique non-linear stability analysis. The steady and unsteady simulations’ results for millimeter scale (hydraulic diameter 4–8 mm), modest mass-flux (5–120 kg/m2/s), and refrigerant vapors (FC-72, R113, etc.) are used to mark the approximate location beyond which the annular regime typically transitions to a non-annular regime. These are used to develop correlations for local heat transfer coefficients and the approximate length that marks the transition from annular to non-annular regimes.
Nomenclature
| Cp | = | specific heat, J/(kg/K) |
| Frx | = | Froude number in x-direction U/(gxLc)1/2 |
| Fry | = | Froude number in y-direction U/(gyLc)1/2 |
| G | = | inlet mass flux, kg/(m2/s) |
| gx | = | gravity component in x-direction, m/s2 |
| gy | = | gravity component in y-direction, m/s2 |
| h | = | cross-section height of the chanel, m |
| Ja | = | condensate liquid Jakob number, Cp1· ΔT / hfg(pin) |
| k | = | conductivity, W/(m-K) |
| L | = | length of the channel or test-section, m |
| = | local interfacial mass flux, kg/m2-s | |
| p0 | = | steady inlet pressure (also pin), kPa |
| Pr1 | = | condensate liquid Prandtl number, µ1 · Cp1/k1 |
| Rein | = | inlet vapor Reynolds number, ρ2ULc/µ2 |
| t | = | non-dimensional time |
| = | mean condensing surface temperature,°C | |
| Tsat(p) | = | saturation temperature at pressure p,°C |
| U | = | average inlet vapor velocity in the x-direction, m/s |
| w | = | cross-sectional width of the channel, m |
| x,y | = | non-dimensional distances along and perpendicular to the condensing surface |
| xA | = | non-dimensional length of the annular regime |
| Δ | = | physical value of condensate thickness, m |
| µ | = | viscosity, kg/(m-s) |
| ρ | = | density, kg/m3 |
| Subscripts | = | |
| 1 or L | = | represents liquid phase of the flow variable |
| 2 or V | = | represents vapor phase of the flow variable |
| Superscripts | = | |
| p | = | represents physical variable, e.g., xp—physical distance along x axis |
| i | = | value of the flow variable at the interface |
Nomenclature
| Cp | = | specific heat, J/(kg/K) |
| Frx | = | Froude number in x-direction U/(gxLc)1/2 |
| Fry | = | Froude number in y-direction U/(gyLc)1/2 |
| G | = | inlet mass flux, kg/(m2/s) |
| gx | = | gravity component in x-direction, m/s2 |
| gy | = | gravity component in y-direction, m/s2 |
| h | = | cross-section height of the chanel, m |
| Ja | = | condensate liquid Jakob number, Cp1· ΔT / hfg(pin) |
| k | = | conductivity, W/(m-K) |
| L | = | length of the channel or test-section, m |
| = | local interfacial mass flux, kg/m2-s | |
| p0 | = | steady inlet pressure (also pin), kPa |
| Pr1 | = | condensate liquid Prandtl number, µ1 · Cp1/k1 |
| Rein | = | inlet vapor Reynolds number, ρ2ULc/µ2 |
| t | = | non-dimensional time |
| = | mean condensing surface temperature,°C | |
| Tsat(p) | = | saturation temperature at pressure p,°C |
| U | = | average inlet vapor velocity in the x-direction, m/s |
| w | = | cross-sectional width of the channel, m |
| x,y | = | non-dimensional distances along and perpendicular to the condensing surface |
| xA | = | non-dimensional length of the annular regime |
| Δ | = | physical value of condensate thickness, m |
| µ | = | viscosity, kg/(m-s) |
| ρ | = | density, kg/m3 |
| Subscripts | = | |
| 1 or L | = | represents liquid phase of the flow variable |
| 2 or V | = | represents vapor phase of the flow variable |
| Superscripts | = | |
| p | = | represents physical variable, e.g., xp—physical distance along x axis |
| i | = | value of the flow variable at the interface |
Acknowledgment
This work was supported by NSF Grants CBET-1033591 and CBET-1402702.