16-05-2012, 05:42 PM
Frictional Resistance
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1 Froude’s skin friction experiments
Frictional resistance contributes to about 80 – 85 % in the newly built slow speed ships
and 50 % in high speed ships. Corrosion and fouling still increases the frictional
resistance
Early experiments were contributed by William Froude, a British hydrodynamist
conducted experiments Torquay , England on planks varied in lengths from 0.61 m to
15.2 m and speed range 0.5 m/s to 4..1 m/s to know the variation of frictional resistance
on body length and surface roughness grounds
f, n depend on length and nature of surface roughness.
Experiment outcomes : Specific resistance per unit area - large plank
small plank
Fact is due to forward motion of fluid particles in the flow over the larger plank.
For a given surface ‘n’ decreased from 2 to 1.88 as length increased
For a given length ‘n’ increased to 2 from 1.88 as surface roughness increased
For a given surface ‘f ‘decreased as length increased
For a given length ‘f ‘ increased with surface roughness
Application of frictional coefficients from experiments : Specific resistance per unit area
decrease with increase in additional lengths is so small and can be treated as a constant
increase or neglected after lengths greater than 15.2 m
Equivalent plank concept for calculating frictional resistance for model/ships. R.E Froude
extended this concept upto 366m (without experimental basis).Froude’s experiments does
not highlight flow regime.(laminar , turbulent flow regime)
2 Two dimensional Frictional resistance formulation
Osborn Renold’s experiments for flow in glass tube. Resistance experienced by the fluid
over a given length of pipe was measured by finding loss of pressure head. Different flow
velocities, diameters and kinematic viscosity were incorporated during his tests.
He found out the flow regimes and behavior of frictional resistance with respect to
critical velocity Vc
Vc = 2000u / D
Frictional resistance was V for flow regime below Vc
Frictional resistance was V2 for flow regime higher than Vc
Vc D/u = 2000 resemblance to Cf = f( VL/u )
Flow regimes were successfully explained by Renold’s experiments for laminar flow (no
transverse flow ) and turbulent flow(transverse flow)
Laminar regime has relatively low frictional resistance and turbulent regime has higher
resistance
Blasius was first to propose the friction coefficient formula Cf for laminar flow regime
(he stated the experiments on planks were laminar) He theoretically calculated the
momentum transfer to the fluid by the flow over a plank and compared it with the
experimental results. His calculations were accurate for laminar flow regime only.
Blasius formula
For Blasius proposed formula the frictional resistance is proportional to V1.5 in the
laminar regime (below 4.5 E6 and beyond this flow was unstable)
Later individual works by Prandtl and Von Karman proposed a friction coefficient
formula in the turbulent regime
Prandtl and Von Karman
formula
For Prandtl and Von Karman proposed formula the frictional resistance is proportional to
V1.8in the turbulent regime.
Transition lines between the flow regimes was incorporated from experimental
knowledge
3 Development of two dimensional Frictional resistance formulations
EMB existence in Washington has occurred (presently NSSWC , earlier DTMB) and
model tests on planks at higher Re were conducted
Kempf has done experimentations and the results were utilized by Schoenherr to propose
a model ship correlation friction line
International Conference of Ship Tank Superintendents ( ICSTS ,1932 , Europe) laid a
formula for calculation of frictional resistance based on ship length and speed
American Towing Tank conference ( ATTC , USA , 19477 ) laid Schoenherr formula as
friction line and later modified for correlation allowance for roughness
Hughes proposed a friction line formula which was very good in the turbulent regime but
low coefficient values were criticized.
International Towing Tank Conference ( ITTC , Europe , 1957 ) modified the Hughes
formula to behave better when compared to ATTC and Hughes low coefficient values
Initially ITTC modified Hughes formula to have better friction line for Re < 10E7 but
later Gravelle showed that ITTC 1957 lines can also be successfully used for Re > 10E7
ITTC suggests the use of either ATTC ( or modified) , ITTC 1957 for Re > 10E8 and for
Re < 10E7 ITTC 1957 friction line is better than ATTC ( or modified)