Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Mechanical measurement system
Reexamination Certificate
1999-05-24
2001-11-27
Hoff, Marc S. (Department: 2857)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Mechanical measurement system
C114S06700A
Reexamination Certificate
active
06324480
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method for analyzing the effects of interposing bubbles at the ship-water interface on reducing the skin-friction of a cruising ship.
2. Description of the Related Art
As a method for reducing skin-friction in a cruising ship, there is an approach of introducing bubbles in the outer surface region of the ship. Many theoretical models for analyzing the effects of bubbles in reducing the skin-friction assume that a void fraction distribution (distribution of bubbles in the boundary layer) is known before calculating various flow parameters in the flow fields surrounding the ship, therefore, it is essential to clarify the mechanism of producing the void fraction distribution to provide an accurate estimation of friction reduction effects. To apply such a friction reduction method to analysis of bubbly flow effects on an actual ship, it becomes necessary to estimate, during the course of computing various parameters in a flow field, the void fraction from a given volume of bubbles being supplied. Therefore, study of void fraction distribution is also critical from the viewpoints of practical application of bubbly flow for reducing the skin-friction.
The present inventors had disclosed an analytical method for obtaining dynamics of bubbles on the hull surface based on the mixing length theory, in a Japanese Patent Application, First Publication, Hei 8-144646. This was followed by a Japanese Patent Application, First Publication, Hei 9-292999, in which a technique was disclosed to simulate the bubble distribution patterns on hull surfaces. It was further disclosed in Japanese Patent Applications, First Publications, Hei 9-142818 and Hei 10-55453 (U.S. patent application Ser. No. 078,950)that a turbulent flow model in the turbulent boundary layer near the hull surface can be constructed by extending the mixing length theory to a bubbly flow field in the turbulent flow model, it offered an analytical methodology to logically explain past experimental results, and demonstrated that the friction reduction effects in different flow fields can be analytically reproduced, by adjusting the operative wall constant &kgr;
1
in the wall law for bubbly flow to indicate the bubble mixing length, in accordance with the extent of flow fields, i.e., the thickness of the turbulent boundary layer produced.
However, in the technique disclosed in the aforementioned Japanese Patent Applications, First Publications, Hei 9-142818 and Hei 10-55453, emphasis was on simplifying the analytical process so that there were aspects of the model which were not fully examined in developing the theoretical framework. For example, it was considered that the following points need to be examined more closely in the future.
(1) Although bubble movement in y-direction (gravitational direction) was discussed quantitatively, it has not been made clear why the bubble can be assumed to remain stationary in x-direction (fluid flow direction) of the turbulent flow. Also, a question was unresolved as to the assumption of a constant magnitude of slip.
(2) When introducing an apparent the mixing length change l
mb
, it was necessarily, for mathematical simplification, to suppose that either of the two turbulent flow velocities u′
L
, v′
L
becomes completely zero and the other becomes affected by damping. In other words, a question remained in the assumption that the fluid shear decrement &tgr;
t
caused by a bubble is given by changes in the turbulent stress (Reynolds stress).
(3) Empirically, a wall constant &kgr;
1
for bubbly flow (a constant in the wall law when a micro-bubble is present in the turbulent layer) was assumed to decrease in proportion to (&lgr;
m
/d
b
)&agr;
⅔
, where &lgr;
m
is an apparent turbulence scale, d
b
is a bubble diameter and &agr; is a local void fraction. But, it was unclear whether the operative wall constant &kgr;
1
would be negative at very small d
b
, and similarly, whether &kgr;
1
would be negative at low &lgr;
m
.
(4) It was thought reasonable to assume that &lgr;
m
∝v
L
/U
&tgr;
(=y/y
+
), (proportional to the length of the bottom surface) where v
L
is the dynamic viscosity of liquid and U
&tgr;
is a the frictional velocity, but a question remained whether it is reasonable to assume that y/y
+
∝&dgr; where &dgr; is the thickness of the turbulent boundary layer.
(5) It was assumed that mixing of a bubble reduces friction, but was not certain that this was sufficient. Is there not a need to consider an increment in the shear stress caused by kinetic mass exchange resulting from motion of the bubble?
SUMMARY OF THE INVENTION
It is an object of the present invention to provide a mathematical model to yield a superior analysis of the effects of bubbly flow on reducing the skin-friction in a cruising ship.
The object has been achieved in a method for analyzing effects of generating bubble jets in a flow field near a ship surface on reducing skin-friction in a cruising ship comprising the steps of: obtaining a shear stress decrement &tgr;
&tgr;
produced by having a bubble in the flow field in terms of a resistive force &Dgr;R
v
acting on the bubble derived from movements of the bubble in a fluid flow direction, x-direction, along the cruising ship as well as in a direction at right angles to a ship wall surface, y-direction, in accordance with a definition of a high frequency band region in which a product of a bubble time-constant T and a turbulence frequency &ohgr;
L
in the flow field is greater than 1; obtaining an operative wall constant &kgr;
1
in the wall law when there is a bubble having a parametric bubble diameter d
b
, by assuming that the shear stress decrement is generated by a decrease in a mixing length; and obtaining a solution for skin-friction ratio, C
f
/C
f0
, in the high frequency band region, according to an expression relating the operative wall constant &kgr;
1
to a local friction factor C
f
for bubbly flow, and an expression relating a normal wall constant &kgr; in the wall law in non-bubbly flow to a a local friction factor C
f0
in non-bubbly flow.
The object has also been achieved in a method for analyzing effects of generating bubble jets in a flow field near a ship surface on reducing skin-friction in a cruising ship comprising the steps of: performing a Fourier transform of kinetic equations (1) and (2) for a bubble moving in x- and y-directions, representing a fluid flow direction and a direction at right angles to the ship surface, respectively, in terms of an added mass of a bubble m
A
, a bubble diameter d
b
, a dynamic liquid viscosity coefficient v
L
, and obtaining an expression for a gain in x-direction G
x
and an expression for a gain in y-direction G
y
comprised by a bubble time-constant T and a turbulence frequency &ohgr;
L
, based on equations (3) and (4) respectively; obtaining from equation (16) a resistive force &Dgr;R
v
, acting on a bubble in a high frequency band region where a product of a bubble time-constant T and a turbulence frequency &ohgr;
L
is greater than 1, in terms of a normal wall constant &kgr; in the wall law in non-bubbly flow, a fluid density &rgr;
L
, a dynamic fluid viscosity coefficient v
L
, and a time-averaged velocity in x-direction u
L
, by assuming that a turbulence cycle 2&pgr;/&ohgr;
L
in the flow field is equal to the integral time-scale T.
L
; obtaining a shear stress decrement &tgr;
t
caused by the resistive force &Dgr;R
v
from equation (17); obtaining a mixing length decrement l
mb
from equation (27) in terms of an empirical constant &agr;, a bubble diameter d
b
, a dynamic viscosity coefficient &agr;
L
, a frictional velocity U
&tgr;
and a near-wall local void fraction &agr;
W
, by comparing the equation (17) with equation (22) which expresses a shear stress decrement &tgr;
t
that is assumed to be produced by a mixing length decrement l
mb
; obtaining a revising wall constant &kgr;
2
in the wall law as in equation (33) by using the equation (27), and obtaining
Kato Hiroharu
Takahashi Yoshiaki
Yoshida Yuki
Hoff Marc S.
Ishikawajima-Harima Heavy Industries Co. Ltd.
Pearne & Gordon LLP
Pretlow Demetrius
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