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Yuki Yoshida Yoshiaki Takahashi Hiroharu Kato Akira Masuko Osamu Watanabe 《Journal of Marine Science and Technology》1997,2(1):1-11
For the theoretical consideration of a system for reducing skin friction, a mathematical model was derived to represent, in a two-phase field, the effect on skin friction of the injection of micro air bubbles into the turbulent boundary layer of a liquid stream. Based on the Lagrangian method, the equation of motion governing a single bubble was derived. The random motion of bubbles in a field initially devoid of bubbles was then traced in three dimensions to estimate void fraction distributions across sections of the flow channel, and to determine local bubble behavior. The liquid phase was modeled on the principle of mixing length. Assuming that the force exerted on the liquid phase was equal to the fluid drag generated by bubble slip, an equation was derived to express the reduction in turbulent shear stress. Corroborating experimental data were obtained from tests using a cavitation tunnel equipped with a slit in the ceiling from which bubbly water was injected. The measurement data provided qualitative substantiation of the trend shown by the calculated results with regard to the skin friction ratio between cases with and without bubble injection as function of the distance downstream from the point of bubble injection.List of symbols
B
law of wall constant
-
C
f
local coefficient of skin friction
-
C
f0
local coefficient of skin friction in the absence of bubbles
-
d
b
bubble diameter [m]
-
g
acceleration of gravity [m/s2]
-
k
1 k4
proportional coefficient
-
k
L
turbulent energy of the liquid phase [m2/s2]
-
L
representative length [m]
-
l
b
mean free path of a bubble [m]
-
m
A
added mass of a single bubble [kg]
-
m
b
mass of a single bubble [kg]
-
N
x
,N
y
,N
z
force perpendicular to the wall or ceiling exerted on a bubble adhering to that wall or ceiling [N]
-
P
absolute pressure [Pa]
-
Q
G
rate of air supply [/min]
-
q
L
(i)
turbulent velocity at the ith time increment [m/s]
-
R>
ex
Reynolds number defined by Eq. 32
-
T
*L
integral time scale of the liquid phase [s]
-
U
velocity of the main stream [m/s]
-
,¯v,¯w
time-averaged velocity components [m/s]
-
u,v,w
turbulent velocity components [m/s]
-
û
L
,vL
root mean square values of liquid phase turbulence components in thex- and y-directions [m/s]
-
V
volume of a single bubble [m3]
-
X,Y,Z
components of bubble displacement [m]
-
x
s
,y
s
,z
s
coordinate of a random point on a sphere of unit diameter centered at the coordinate origin
-
root mean square of bubble displacement in they-direction in reference to the turbulent liquid phase velocity [m]
-
local void fraction
-
m
mean void fraction in a turbulent region
-
regular random number
- R
v
increment of the horizontal component of the force acting on a single bubble, defined by Eq. 22 [N]
- t
time increment [s]
- 1
reduction of turbulent stress [N/m2]
-
L
rate of liquid energy dissipation [m2/s3]
-
m
coefficient defined by Eq. 30
-
law of wall constant in the turbulent region in absence of bubbles
-
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law of wall constant in the turbulent region in presence of bubbles 相似文献
2.
Seiichiro Yagi Hideki Kumamoto Osamu Muragishi Yukichi Takaoka Taichiro Shimoda 《Marine Structures》2009,22(1):12-23
SEA-Arrow (sharp entrance angle bow like an arrow) has no protrusion of the bulbous bow to reduce bow waves and has a transverse stiffening system in the narrow bow space to apply the buffer bow concept. This system has lower longitudinal stiffness than a conventional longitudinal stiffening system and therefore has buffer characteristic in ship-to-ship collision. A comparative collision study of SEA-Arrow and the conventional bulbous bow was conducted using elasto-plastic finite element analysis. A collision scenario where the striking ship hits the side shell of tanker midship perpendicularly was selected. The results showed that the buffer bow characteristic of SEA-Arrow is superior to that of the conventional bulbous bow, since much more energy is dissipated by the plastic deformation of striking and struck ships until the inner shell of struck ship ruptures. 相似文献
3.
Vehicle dynamics integrated control for four-wheel-distributed steering and four-wheel-distributed traction/braking systems 总被引:2,自引:0,他引:2
E. Ono Y. Hattori Y. Muragishi K. Koibuchi 《Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility》2006,44(2):139-151
In this article, vehicle dynamics integrated control algorithm using an on-line non-linear optimization method is proposed for 4-wheel-distributed steering and 4-wheel-distributed traction/braking systems. The proposed distribution algorithm minimizes work load of each tire, which is controlled to become the same value. The global optimality of the convergent solution of the recursive algorithm can be proved by extension to convex problems. This implies that theoretical limited performance of vehicle dynamics integrated control is clarified. Furthermore, the effect of this vehicle dynamics control for the 4-wheel-distributed steering and 4-wheel-distributed traction/braking systems is demonstrated by simulation to compare with the combination of the various actuators. 相似文献
4.
九州新干线 800 系电动车组的开发 总被引:2,自引:0,他引:2
介绍了九州新干线800系电动车组的开发概况、基本设计理念、内外部设计,以及车体、转向架、制动装置等的结构. 相似文献
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