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Heat and Mass Transfer

, Volume 55, Issue 8, pp 2117–2135 | Cite as

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

  • Yubo Wang
  • Liejin GuoEmail author
Original
  • 81 Downloads

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

cf,D

Viscous drag coefficient

cw

Propagation speed of interface wave

D

Diameter

F

Complex potential of the flow

FD,visc

Viscous drag force

f

Dimensionless function, fluid

fi

Interface friction factor

kA

Modulus of wave

p

Coordinator transition number

R

Radius of curvature

Re

Reynolds number

ReG

Reynolds number of gas phase

ReL

Reynolds number of liquid phase

ReG,M

Modified Reynolds number of gas phase

rλ

r a /r d

rλA

λ/A

s

Algebraic sum of coefficients

U

Velocity component in x direction

UG

Gas velocity

UL

Liquid velocity

u

Velocity component in x direction

u*

Friction velocity

v

Velocity component in y direction

x,y

Rectangular spatial coordinates

yx

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

λa

Wave length of ascending semi period

λd

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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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Multiphase Flow in Power EngineeringXi’an Jiaotong UniversityXi’anChina

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