Experiments in Fluids

, Volume 41, Issue 1, pp 79–89 | Cite as

Solitary waves on inclined films: their characteristics and the effects on wall shear stress

Research Article
First Online:
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Abstract

The properties of solitary waves, developing from inlet disturbances of controlled frequency along an inclined film flow, are systematically studied experimentally and computationally. Time-variations of film height and wall shear stress are measured, using respectively a capacitance probe and an electrodiffusion sensor. Computational data are provided from simulations performed by a Galerkin finite element scheme. The height and spacing of solitary humps, their phase velocity and the wavelength of the preceding capillary ripples are reported as functions of the Reynolds number (10<Re<100) and the inlet frequency (0.5 Hz< f<2.5 Hz). The wall shear stress modulation imposed by the passage of solitary waves is studied experimentally and computationally as a function of Re. Distinct nonlinear characteristics are noted, including a steep maximum and a negative minimum, with the effects intensifying at intermediate Re. All computer predictions are found to be in good quantitative agreement with the experimental data.

Keywords

Solitary Wave Wall Shear Stress Good Quantitative Agreement Wall Shear Stress Distribution Parabolic Velocity Profile 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

a

wave height, =h max−h min (m)

A

amplitude of inlet disturbance (m)

c

wave phase velocity (m s−1)

f

frequency (Hz)

g

gravitational acceleration, = 9.81 m s−2

h

film thickness (m)

Hc

mean free surface curvature (m−1)

Ka

Kapitza number, =σ/[ρ (g sinφ)1/3ν4/3]

l

length of the solitary waves (m), =c/f

L

length of the strip segment in the mean flow direction (m)

ks

steady flow calibration constant of the electrodiffusion probe (A s1/3)

kt

dynamic calibration constant of the electrodiffusion probe (A s1/2)

\(\underline{n}\)

unit vector normal to the free surface

Q

mean volumetric flow rate per unit span of the plate (m2 s−1), =u N h N

q

instantaneous volumetric flow rate per unit span of the plate (m2 s−1)

Re

Reynolds number, =Q/ν

t

time (s)

u

velocity parallel to the plate (m s−1)

\(\underline{u}\)

dimensionless velocity vector

x

streamwise distance from the liquid distributor (m)

y

distance normal to the plate (m)

W

width of the strip segment (m)

φ

inclination angle of the plate (deg)

ν

kinematic viscosity (m2 s−1)

ρ

density (kg m−3)

σ

surface tension (N m−1)

\(\underline{\underline T}\)

dimensionless stress tensor

τw

wall shear stress (Pa)

Subscripts

min

minimum value

max

maximum value

N

Nusselt value

sub

substrate value

t

partial derivative with respect to time

x

partial derivative with respect to streamwise distance

Superscripts

−

average value

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Notes

Acknowledgments

This work was partly supported by the Grant Agency of the Academy of Sciences of the Czech Republic under project No. A4072914, by the European Commission in the frame of MCTS programme HPMT-CT-2000-00074, by the General Secretariat of Research and Technology of Greece through programme PENED2001 and by the Greek Ministry of Education through programme PYTHAGORAS II.

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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • J. Tihon
    • 1
  • K. Serifi
    • 2
  • K. Argyriadi
    • 2
  • V. Bontozoglou
    • 2
  1. 1.Institute of Chemical Process FundamentalsAcademy of Sciences of the Czech RepublicPrague 6Czech Republic
  2. 2.Department of Mechanical and Industrial EngineeringUniversity of ThessalyVolosGreece

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