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Research Papers: Fundamental Issues and Canonical Flows

Study on Kelvin–Helmholtz Instability With Heat and Mass Transfer

[+] Author and Article Information
Mukesh Kumar Awasthi

Department of Mathematics,
University of Petroleum and Energy Studies,
Dehradun 248007, India
e-mail: mukeshiitr.kumar@gmail.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 20, 2013; final manuscript received April 30, 2014; published online September 10, 2014. Assoc. Editor: Ali Beskok.

J. Fluids Eng 136(12), 121202 (Sep 10, 2014) (8 pages) Paper No: FE-13-1569; doi: 10.1115/1.4027599 History: Received September 20, 2013; Revised April 30, 2014

The effect of heat and mass transfer on the Kelvin–Helmholtz instability between liquid and vapor phases of a fluid has been studied using three different theories: a purely irrotational theory based on the dissipation method, a hybrid irrotational-rotational theory, and an inviscid potential flow theory. These new results are compared with previous results from viscous irrotational theory. The stability criterion is given in terms of the critical value of relative velocity. The system is shown to be unstable when the relative velocity is greater than the critical value of relative velocity; otherwise, it is stable. It is observed that heat and mass transfer has a destabilizing effect on the stability of the system while vapor fraction has a stabilizing effect.

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References

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Awasthi, M. K., and Agrawal, G. S., 2011, “Viscous Potential Flow Analysis of Rayleigh–Taylor Instability With Heat and Mass Transfer,” Int. J. App. Math. Mech., 7(12), pp. 73–84.
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Figures

Grahic Jump Location
Fig. 1

Equilibrium configuration of the system

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Fig. 2

Stability diagram for the water, ammonia, and propane according to the data of Table 1 when α∧ = 1 and β = 0.5

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Fig. 3

The neutral stability curves for relative velocity for the water-vapor system for different theories: (a) IPF, (b) HM, (c) VPF, and (d) DM

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Fig. 4

The critical relative velocity versus heat transfer coefficient for the water-vapor system when β = 0.5

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Fig. 5

The critical relative velocity versus viscosity ratio of two fluids for the water-vapor system for different values of σ∧ when α∧ = 1 and β = 0.5

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Fig. 6

The relative velocity versus wave number for the water-vapor system for different values of ρ∧ when α∧ = 1 and β = 0.5

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Fig. 7

The critical relative velocity versus heat transfer coefficient for the water-vapor system for different values of density and viscosity ratio of two fluids when β = 0.5

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