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Research Papers: Evaporation, Boiling, and Condensation

# Direct Numerical Simulation of Condensing Stratified Flow

[+] Author and Article Information
Djamel Lakehal

Institute of Energy Technology, ETH Zurich, Switzerland; ASCOMP GmbH, Zurich, Switzerlandlakehal@ascomp.ch

Marco Fulgosi

Institute of Energy Technology, ETH Zurich, Switzerland

Institute of Energy Technology, ETH Zurich, Switzerland; ASCOMP GmbH, Zurich, Switzerland

J. Heat Transfer 130(2), 021501 (Feb 06, 2008) (10 pages) doi:10.1115/1.2789723 History: Received February 14, 2007; Revised July 24, 2007; Published February 06, 2008

## Abstract

The paper discusses the results of a detailed direct numerical simulation study of condensing stratified flow, involving a sheared steam-water interface under various thermal and turbulent conditions. The flow system comprises a superheated steam and subcooled water flowing in opposite directions. The transport equations for the two fluids are alternately solved in separate domains and then coupled at the interface by imposing mass, momentum, and energy jump conditions with phase change. The effects induced by changes in the interfacial shear were analyzed by comparing the relevant statistical flow properties. New scaling laws for the normalized heat transfer coefficient (HTC), $K+$, have been derived for both the steam and liquid phases. The steam-side law is found to compare with the passive-scalar law obtained hitherto by (Lakehal(2003, “Direct Numerical Simulation of Turbulent Heat Transfer Across a Mobile, Sheared Gas-Liquid Interfaces  ,” ASME J. Heat Transfer, 125, pp. 1129–1139) in that HTC scales with $Pr−3∕5$. A close inspection of the transfer rates on the liquid side reveals a consistent relationship between $K+$, the local wave deformation or curvature and the interfacial shear stress. The surface divergence model of Banerjee (2004, “Surface Divergence Models for Scalar Exchange Between Turbulent Streams  ,” Int. J. Multiphase Flow, 30(8), pp. 965–977) is found to apply in the liquid phase, too.

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## Figures

Figure 3

Instantaneous contours of the normalized HTC and of the interfacial shear stress in the vapor phase

Figure 4

Instantaneous contours of the normalized HTC and of the interfacial shear stress in the liquid phase

Figure 5

Probability distribution of “strongly coherent” uw¯ events versus normalized HTC at the interface. Lines and symbols are used to identify R1 and R2, respectively. (—) and (●), I quadrant events; (---) and (◻), II quadrant events; (⋯) and (◇), III quadrant events; (-∙-) and (▵), IV quadrant events.

Figure 6

Probability distribution of strongly coherent uw¯ events versus normalized HTC at the interface. Lines and symbols are used to identify C11 and C12, respectively. (—) and (●), I quadrant events; (---) and (black ◻), II quadrant events; (⋯) and (black ◇), III quadrant events; (-∙-) and (black ▵), IV quadrant events.

Figure 7

Probability distribution of strongly coherent uw¯ events versus normalized HTC at the interface. Lines and symbols are used to identify C21 and C22, respectively. (—) and(●), I quadrant events; (- - -) and (black ◻), II quadrant events; (⋯) and (black ◇), III quadrant events; (-∙-) and (black ▵), IV quadrant events.

Figure 8

Vapor-side dimensional heat transfer velocity plotted versus the shear and friction velocities

Figure 9

Liquid-side dimensional heat transfer velocity versus the shear and friction velocities

Figure 10

Effect of liquid subcooling and interfacial waviness

Figure 11

Comparison of the liquid-side DNS data with other correlations

Figure 12

Comparison of the surface term with the dilation contribution to the Hunt–Graham blocking theory

Figure 13

HTC parametrization by means of the SDM model

Figure 14

Comparison of the computed interfacial friction factors with the values obtained using Eq. 16

Figure 1

Sketch of the simulated vapor-liquid stratified flow

Figure 2

jpdf of normalized interfacial shear stress and HTC (Case R2)

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