Basic bluff-body aerodynamics II Wind loading and structural response Lecture 9 Dr. J.D. Holmes Basic bluff-body aerodynamics II

Basic bluff-body aerodynamics Pressures on prisms in turbulent boundary layer : -0.20 -0.10 -0.23 -0.18 x Sym.about CL -0.2 -0.5 -0.8 -0.6 -0.7 0.7 0.5 0.0 Wind leeward wall roof side wall windward wall drag coefficient (based on Uh )  0.8

Basic bluff-body aerodynamics Pressures on prisms in turbulent boundary layer : x 0.4 0.3 x 0.9 x 0.5 x Windward wall x -0.6 x -0.6 -0.5 -0.6 -0.7 Wind Side wall -0.5 -0.4 to –0.49 Leeward wall -0.6 -0.56 to –0.59 x Wind Roof shows effect of velocity profile nearly uniform

Basic bluff-body aerodynamics Circular cylinders : Complexity due to interacting effects of surface roughness, Reynolds Number and turbulence in the approach flow Flow regimes in smooth flow : Re < 2  105 Cd = 1.2 Sub-critical Laminar boundary layer Separation Subcritical regime : most wind-tunnel tests - separation at about 90o from the windward generator

Basic bluff-body aerodynamics Circular cylinders : Complexity due to interacting effects of surface roughness, Reynolds Number and turbulence in the approach flow Flow regimes in smooth flow : Re  5  105 Cd  0.4 Super-critical Laminar Turbulent Separation Supercritical : flow in boundary layer becomes turbulent - separation at 140o - minimum drag coefficient

Basic bluff-body aerodynamics Circular cylinders : Complexity due to interacting effects of surface roughness, Reynolds Number and turbulence in the approach flow Flow regimes in smooth flow : Re  107 Cd  0.7 Post-critical Turbulent Separation Post-critical : flow in boundary layer is turbulent - separation at about 120o

Basic bluff-body aerodynamics Circular cylinders : Pressure distributions at sub-critical and super-critical Reynolds Numbers 20 60 100 140 1.0 0.5 -0.5 -1.0 -1.5 -2.0 -2.5 U q degrees q Cp Drag coefficient mainly determined by pressure on leeward side (wake)

Basic bluff-body aerodynamics Circular cylinders : Effect of surface roughness : increasing surface roughness 1.2 0.8 0.4 U b 104 2 4 8 105 2 4 8 106 2 4 8 107 k/b = 0.02 k/b = 0.007 k/b = 0.002 Sanded surface Smooth surface Cd Re Increasing surface roughness : decreases critical Re - increases minimum Cd

Basic bluff-body aerodynamics Circular cylinders : Effect of aspect ratio on mean pressure distribution : Cp b h Silos, tanks in atmospheric boundary layer Decreasing h/b : increases minimum Cp (less negative)

Basic bluff-body aerodynamics Fluctuating forces and pressures on bluff bodies : Sources of fluctuating pressures and forces : Freestream turbulence (buffeting) - associated with flow fluctuations in the approach flow Vortex-shedding (wake-induced) - unsteady flow generated by the bluff body itself Aeroelastic forces - forces due to the movement of the body (e.g. aerodynamic damping)

Basic bluff-body aerodynamics Buffeting - the Quasi-steady assumption : Fluctuating pressure on the body is assumed to follow the variations in wind velocity in the approach flow : p(t) = Cpo (1/2) a [U(t)]2 Cpo is a quasi-steady pressure coefficient Expanding : p(t) = Cpo (1/2) a [U + u(t) ]2 = Cpo (1/2) a [U2 + 2U u(t) + u(t)2 ] Taking mean values : p = Cpo (1/2) a [U2 + u2]

Basic bluff-body aerodynamics Buffeting - the Quasi-steady assumption : Small turbulence intensities : (e.g. for Iu = 0.15, u2 = 0.0225U2 ) p  Cpo (1/2) aU2 =Cp (1/2) aU2 i.e. Cpo is approximately equal to Cp Fluctuating component : p' (t) = Cpo (1/2) a [2U u'(t) + u'(t)2 ] Squaring and taking mean values :  Cp2 (1/4) a2 [4U2 ]= Cp2 a2 U2 u2

Basic bluff-body aerodynamics Peak pressures by the Quasi-steady assumption : Time p(t) Quasi-steady assumption gives predictions of either maximum or minimum pressure, depending on sign of Cp

Basic bluff-body aerodynamics Vortex shedding : On a long (two-dimensional) bluff body, the rolling up of separating shear layers generates vortices on each side alternately Occurs in smooth or turbulent approach flow may be enhanced by vibration of the body (‘lock-in’) cross-wind force produced as each vortex is shed

Basic bluff-body aerodynamics Vortex shedding : Strouhal Number - non dimensional vortex shedding frequency, ns : b = cross-wind dimension of body St varies with shape of cross section circular cylinder : varies with Reynolds Number

Basic bluff-body aerodynamics Vortex shedding - circular cylinder : vortex shedding not regular in the super-critical Reynolds Number range

Basic bluff-body aerodynamics Vortex shedding - other cross-sections : 0.08 2b 2.5b ~10b 0.12 0.06 0.14

Basic bluff-body aerodynamics fluctuating pressure coefficient : fluctuating sectional force coefficient : fluctuating (total) force coefficient :

Basic bluff-body aerodynamics fluctuating cross-wind sectional force coefficient for circular cylinder : 105 106 107 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Fluctuating side force coefficient Cl Reynolds number, Re dependecy on Reynolds Number

Basic bluff-body aerodynamics Quasi-steady fluctuating pressure coefficient : Quasi-steady drag coefficient :

Basic bluff-body aerodynamics Correlation coefficient for fluctuating forces on a two-dimensional body : Correlation length : y is separation distance between sections

Basic bluff-body aerodynamics Correlation length for a stationary circular cylinder (smooth flow) : 6 4 2 104 105 106 Reynolds number, Re Correlation length / diameter cross-wind vibration at same frequency as vortex shedding increases correlation length

Basic bluff-body aerodynamics Total fluctuating force on a slender body : L We require the total mean and fluctuating forces on the whole body

Basic bluff-body aerodynamics Total fluctuating force on a slender body : mean total force : F = fi yi instantaneous total fluctuating force : F(t) =  fi  (t) yi = f1 (t) y1 + f2 (t) y2 + ……………….fN (t) yN Squaring both sides : [F(t)]2 = [ f1 (t) y1 + f2 (t) y2 + ……………….fN (t) yN]2 = [f1 (t) y1]2 + [f2 (t) y2]2 ..+ [fN (t) yN]2 + f1 (t) f2(t) y1y2 + f1 (t) f3(t) y1y3 +...

Basic bluff-body aerodynamics Total fluctuating force on a slender body : Taking mean values : As yi, yj tend to zero : writing the integrand (covariance) as : This relates the total mean square fluctuating force to the sectional force

Basic bluff-body aerodynamics Total fluctuating force on a slender body : Introduce a new variable (yi - yj) : Special case (1) - full correlation, (yi-yj) = 1 : fluctuating forces treated like static forces Special case (2) - low correlation, correlation length l is much less than L : mean square fluctuating force is proportional to the correlation length - applicable to slender towers

Basic bluff-body aerodynamics Total fluctuating force on a slender body : The double integral : is represented by the volume under the graph : yi yj Symmetric about diagonal since (yj-yi) = (yi-yj ). Along the diagonal, the height is 1.0 On lines parallel to the diagonal, height is constant

Basic bluff-body aerodynamics Total fluctuating force on a slender body : Consider the contribution from the slice as shown : Volume under slice = (z)(L-z)2 Length of slice = (L-z)2 z/2 z /2 L yi-yj=0 yi-yj= z yj yi Total volume = (reduced to single integral)

End of Lecture 9 John Holmes 225-405-3789 JHolmes@lsu.edu