forces on a cylinder in steady current wind forces on structures the in-line component of the mean...
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FORCES ON A CYLINDER IN STEADY CURRENT
WIND FORCES ON STRUCTURES
The in-line component of the mean resultant force due to pressure (the in-line mean pressure force) per unit length of cylinder is given by
rdoscpFp
2
0while that due to friction (the in-line
mean friction force) is given by
rdFf sin2
0
0
(1)
(2)
in which p is the pressure and τo is the wall shear stress on the cylindersurface (the overbar denotes time-averaging).
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
The total in-line force, the so-called mean drag, is the sum of these two forces:
fpD FFF (3)
Fp is termed the form drag and Ff the friction drag.
Relative contribution of the friction force t the total drag for circular cylinder.
For the range of Re numbers normally encountered in practice, namely Re ≥ 104, the contribution of the friction drag to the total drag forces is less than 2 – 3%. So the friction dragcan be omitted in most of the cases, and the total mean drag can be assumed to be composed of only one component, namely the form drag.
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
Regarding the cross-flow component of the mean resultant force, this force will be nil’due to symmetry in the flow. However, the instantaneous cross-flow force on the cylinder, i.e., the
instantaneous lift force, is non-zero and its value can be rather large.
AERODYNAMIC COEFFICIENT:
Pressure coefficient
2
0
21U
ppcp
where:po − static pressureρ − flowing medium densityU − inflow velocity
(4)
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
Mean drag coefficient
2
21DU
Fc DD
(5)
For the case of circular cylinder mean value FL = 0 due to symmetry of pressure distribution
2
21DU
Fc LL
(6)
Mean lift coefficient
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
Pressure cp distributions. S denotes the separtion point
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
Drag Coefficient as a Function of the Reynolds Number for a Smooth Sphere
Dimpled Golf Ball: Reduce Drag
the dimples of a golf ball (i.e., the surface roughness of the object) are used to create turbulent boundary layer flow, and hence reduce the drag force
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
Pressure distribution and wall shear stress distribution at different Re numbers for a smooth cylinder.
EFFECT OF REYNOLDS NUMBER
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
EFFECT OF SURFACE ROUGHNESS
The drag coefficient, CD, now becomes not only a function of Re number but also a
function of the roughness parameter ks/D
D
kcc s
DD Re,
in which ks is the Nikuradse equivalent sand roughness.
(7)
Drag coefficient of a circular cylinder for various surface roughness parameters ks/D.
EFFECT OF WALL PROXIMITY
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
This topic is of direct relevance with regard to pipelines − what kind of changes take place in the flow around and in the forces on a pipe suspended above the bed with
a small gap.
Flow around a) free cylinder, b) a near-wall cylinder. S = separation points.
1.Vortex shedding is suppressed for the gap-ratio values smaller thanabout e/D = 0.3.2. The stagnation point moves to a lower angular position.3. The separation point at the free-stream side of the cylinder movesupstream and that at the wall-side moves downstream.4. Suction is larger on the free-stream side of the cylinder than on thewall-side of the cylinder.
EFFECT OF WALL PROXIMITY
WIND FORCES ON STRUCTURES
FORCES ON A CYLINDER IN STEADY CURRENT
Schematic variation of mean drag coefficient with the gap ratio.
Variation of mean lift coefficient with the gap ratio.
EFFECT OF CROSS-SECTION SHAPE ON FORCE −
COEFFICIENTS
The shape of the cross-section has a large influence on the resulting force. There are two points, which need to be elaborated here. One is the Reynolds number dependence in the case of cross-sectional shapes with sharp edges. In this case, practically no Reynolds number dependence should be expected since the separation point is fixed at the sharp corners of the cross section. So, no change in force coefficients is expected with Re number for these cross-sections in contrast to what occurs in the case of circular crosssections. Secondly, non-circular cross-sections may be subject to steady lift at a certain angle of attack. This is due to the asymmetry of the flow with respect to the principle axis of the cross-sectional area.
WIND FORCES ON STRUCTURES