# Theoretical and experimental research on interfacial shear stress and interfacial friction factor of gas-liquid two-phase wavy stratified flow in horizontal pipe

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## Abstract

The external flow field over wave interface is reached by the aid of conformal transformation thought, and velocity boundary layer of inner flow field is deduced also, which gives fundamental description of shear stress over wave interface. The viscous drag coefficient is induced with considering the characteristics of interface wave, such as wave height, wave length and ratio between wave lengths of both ascending and descending semi periods, which significantly impact the velocity gradient over the wave interface that accounts for the differences in distribution of local shear stress. The influence of fluid flow is studied also, which gives support that the earlier separating point of the fluid flow over wave interface the stronger depression to the turbulent perturbation is made, and a reduced drag force arrived. There are otherness and commonness between fluid flow over wave interface and interface appearing in air-water wave stratified flow, and a new model is proposed to intrinsically construct the interfacial friction factor encountered in wave stratified flow. The models for viscous drag coefficient and interfacial friction factor are tested, different models are studied, predicted values are compared with experimental data and that computed by solving there-dimension unsteady Navier-Stokes equations, which gives proof that the values predicted by newly proposed models well fit the real values.

## Keywords

Wave interface Wave stratified flow Viscous drag coefficient Interfacial friction factor Velocity boundary layer model## Nomenclature

*A*Cross-sectional area, projected area, wave height

*a*Radius of circle cylinder

*C*Coefficient

*c*_{f,D}Viscous drag coefficient

*c*_{w}Propagation speed of interface wave

*D*Diameter

*F*Complex potential of the flow

*F*_{D,visc}Viscous drag force

*f*Dimensionless function, fluid

*f*_{i}Interface friction factor

*k*_{A}Modulus of wave

*p*Coordinator transition number

*R*Radius of curvature

*Re*Reynolds number

*Re*_{G}Reynolds number of gas phase

*Re*_{L}Reynolds number of liquid phase

*Re*_{G,M}Modified Reynolds number of gas phase

*r*_{λ}*r*_{ a }*/r*_{ d }*r*_{λA}*λ/A**s*Algebraic sum of coefficients

*U*Velocity component in

*x*direction*U*_{G}Gas velocity

*U*_{L}Liquid velocity

*u*Velocity component in

*x*direction*u*^{*}Friction velocity

*v*Velocity component in

*y*direction*x*,*y*Rectangular spatial coordinates

*y*_{x}Section profile of circle cylinder

## Greek symbols

*α*Phase holdup, radius angle

*θ*Radius angle, phase position angle

*λ*Wave length of interface wave

*τ*Shear stress

*ρ*Density

*μ*Dynamic viscosity

*ν*Kinematic viscosity

*λ*_{a}Wave length of ascending semi period

*λ*_{d}Wave length of descending semi period

*ζ*Complex coordinate

*ψ*Stream function

*η*Dimensionless variable

*Γ*Velocity circulation

## Subscripts

*G*Gas phase

*i*Interface

*L*Liquid phase

## Notes

### Acknowledgements

The authors gratefully acknowledge the financial supports by National Natural Science Foundation of China (No.51527808).

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