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**Basic bluff-body aerodynamics I**

Wind loading and structural response Lecture 8 Dr. J.D. Holmes Basic bluff-body aerodynamics I

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**Basic bluff-body aerodynamics**

Streamlined body - flow follows contours of body : Bluff body - flow separates : vortices formed by rolling up of shear layers - may re-attach

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**Basic bluff-body aerodynamics**

Bernoulli’s equation : applicable in inviscid (zero viscosity) and irrotational (zero vorticity) flow - outside of boundary layers and free shear layers p0 and U0 are pressure and velocity in region outside of influence of body

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**Basic bluff-body aerodynamics**

Surface pressure coefficient : in regions in which Bernoulli’s Equation is valid : U = Cp = (stagnation point) U > U0 Cp < 0 approximately valid in separated flows if U is taken as velocity in flow just outside adjacent shear layer

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**Basic bluff-body aerodynamics**

Force coefficient : reference area, A, - arbitary but often projected area Force per unit length coefficient : b = reference length - often projected width normal to wind

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**Basic bluff-body aerodynamics**

Wind axes : Body axes : = angle of attack

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**Basic bluff-body aerodynamics**

Relationship between force coefficients in two axes systems : Fx = D cos - L sin Fy = D sin - L cos

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**Basic bluff-body aerodynamics**

Dependence of pressure/force coefficients on other non-dimensional groups : Cp = f(1, 2, 3 etc…) Examples of ’s : h/zo Jensen Number (h is height of building) Iu, Iv, Iw turbulence intensities lu/h, lv/h, lw/h turbulence length scale ratios Uh/ Reynolds Number ( is kinematic viscosity) In wind tunnel testing - try to match ’s in full scale and model scale

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**Basic bluff-body aerodynamics**

Reynolds Number Re = Uh/ = aUh/ = kinematic viscosity = dynamic viscosity Reynolds Number represents a ratio of inertial forces to viscous forces in the flow full-scale values of Re cannot be matched in wind tunnel tests dependence of flow on Re - less for sharp-edged bluff bodies, and very turbulent flow

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**Basic bluff-body aerodynamics**

Jensen Number Je = h/z0 z0 = roughness length Applicable only to bluff bodies immersed in a turbulent boundary layer (full-scale or wind-tunnel) Lower values of Je - steeper mean speed profile, higher turbulence Ref. Lecture 6, Chapter 3

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**Basic bluff-body aerodynamics**

Flat plates and walls normal to flow Advertising hoardings, free-standing walls Drag force, D = (pW - pL) A pW = average pressure on windward wall pL = average pressure on leeward wall dividing both sides by (1/2) a U2A : CD = Cp,W – Cp,L = Cp,W + (– Cp,L)

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**Basic bluff-body aerodynamics**

Flat plates and walls normal to flow Smooth flow CD = 1.1 SQUARE PLATE Turbulent flow CD = 1.2 Shear layer Turbulence decreases (more negative) leeward side or ‘base’ pressure by increasing entrainment of flow from wake by ‘shear’ layers

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**Basic bluff-body aerodynamics**

Flat plates and walls normal to flow Smooth flow TWO-DIMENSIONAL PLATE CD = 1.9 No flow path around the sides (out of screen) - strong vortex generation and shedding - lower base pressure - higher drag

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**Basic bluff-body aerodynamics**

Flat plates and walls normal to flow TWO-DIMENSIONAL PLATE splitter plate CD = 1.4 Splitter plate induces re-attachment of flow - weaker, smaller vortices - lower drag

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**Basic bluff-body aerodynamics**

walls normal to flow CD = 1.2 SQUARE WALL CD = 1.1 Ground TWO-DIMENSIONAL WALL Ground Walls on ground - boundary layer flow : U taken as Uh (top of wall)

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**Basic bluff-body aerodynamics**

walls normal to flow Only slight dependency of CD on length / height (b/h)

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**Basic bluff-body aerodynamics**

two square plates in series normal to flow Spacing 0 b Combined Cd 1.1 acts like a single plate 1.5b Combined Cd 0.8 combined drag is less than single plate (critical spacing = 1.5b) Spacing Combined Cd 2.2 acts like two single plates

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**Basic bluff-body aerodynamics**

porous plate CD, = CD . Kp Kp = porosity factor, Kp 1- (1-)2 = solidity = solid area/total area Kp : not sensitive to shape of openings (plate could be a truss with linear members)

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**Basic bluff-body aerodynamics**

inclined plate Primarily normal force (negligible tangential component) CN 2 a For angle of attack, < 10 degrees, CN 2 ( in radians) reference area : plan area normal to surface Centre of pressure at h/4 from leading edge

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**Basic bluff-body aerodynamics**

inclined plate CN = 1.5 45o 0.4h As increases, centre of pressure moves towards centre of plate

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**Basic bluff-body aerodynamics**

rectangular prism (two dimensional) 3 2 1 d/b Cd Smooth flow 105<Re<106 b d Maximum Cd at d/b 0.7 For d/b > 0.7, shear layers re-attach to sides of prism - drag is lower

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**Basic bluff-body aerodynamics**

rectangular prism (two dimensional) Effect of turbulence 4 3 2 1 Iu(%) Cd 0.33 0.50 0.62 1.0 b d With increasing turbulence intensity, d/b ratio for maximum Cd falls Turbulence promotes increased curvature of shear layers - reattachment occurs at lower d/b ratio (shorter after-body length)

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**Basic bluff-body aerodynamics**

rectangular prism (two dimensional) Effect of turbulence Higher drag Lower drag Decreased radius of curvature and hence lower pressure due to increased rate of entrainment of wake fluid into the more turbulent shear layer. d/b = 0.1 b d Low turbulence High turbulence Partial reattachment lower drag Higher drag d/b 0.5

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**End of Lecture 8 John Holmes 225-405-3789 JHolmes@lsu.edu**

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