388 Wind Tunnels and Experimental Fluid Dynamics Research Wind Tunnel 20 20 Noise suppression effect [dB] 10 0 -10 Hp [mm] 30 50 100 -20 -30 150 -40 0 100 200 300 x/L ∼ ∼ 400 500 389 21 Active PassivePassive Control of Flow Past a Cavity Active and and Control of Flow Past a Cavity flow 50 295 block 27 Hb x 4.2 Small block on the floor ∞ 5 Conclusion ≤ 390 Wind Tunnels and Experimental Fluid Dynamics Research Wind Tunnel 22 90 without block 80 SPL [dB] with block 70 60 50 40 0 500 1000 1500 Frequency [Hz] Frequency [Hz] 2,000 1,500 1,000 500 0 0.1 0.2 0 0.1 0.2 Time [s] 0.3 0.4 0.5 0.3 0.4 0.5 Frequency [Hz] 2,000 1,500 1,000 500 0 Time [s] power 1 391 23 Active PassivePassive Control of Flow Past a Cavity Active and and Control of Flow Past a Cavity 10 Hb [mm] 8 6 4 2 0 0.0 0.2 0.4 0.6 x/L 6 Acknowledgments 0.8 1.0 392 24 7 References Wind Tunnels and Experimental Fluid Dynamics Research Wind Tunnel Active PassivePassive Control of Flow Past a Cavity Active and and Control of Flow Past a Cavity 393 25 394 26 Wind Tunnels and Experimental Fluid Dynamics Research Wind Tunnel 18 Aerodynamic Parameters on a Multisided Cylinder for Fatigue Design Byungik Chang West Texas A&M University USA 1 Introduction Cantilevered signal, sign, and light support structures are used nationwide on major interstates, national highways, local highways, and at local intersections for traffic control purposes Recently, there have been a number of failures of these structures that can likely be attributed to fatigue In Iowa, USA (Dexter 2004), a high-mast light pole (HMLP), which is typically used at major interstate junctions, erected for service in 2001 along I-29 near Sioux City collapsed in November 2003 (see Figure 1 (a)) Fortunately, the light pole fell onto an open area parallel to the interstate and injured no one Figure 1 (b) shows another highmast lighting tower failure in Colorado, USA (Rios 2007) that occurred in February of 2007 Similar to the failure in South Dakota, fracture initiated at the weld toe in the base plate to pole wall connection, and then propagated around the pole wall until the structure collapsed It appears that these structures may have been designed based on incomplete and/or insufficient code provisions which bring reason to reevaluate the current codes that are in place A luminary support structure or HMLP is generally susceptible to two primary types of wind loading induced by natural wind gusts, or buffeting and vortex shedding, both of which excite the structure dynamically and can cause fatigue damage (AASHTO 2009) Vortex shedding is a unique type of wind load that alternatively creates areas of negative pressures on either side of a structure normal to the wind direction This causes the structure to oscillate transverse to the wind direction When the vortex shedding frequency (i.e., the frequency of the negative pressure on one side of the structure) approaches the natural frequency of the structure, there is a tendency for the vortex shedding frequency to couple with the frequency of the structure (also referred to as “lock-in” phenomenon) causing greatly amplified displacements and stresses 2 Background and objectives While vortex shedding occurs at specific frequencies and causes amplified vibration near the natural frequencies of the structure, buffeting is a relatively “broad-band” excitation and includes frequencies of eddies that are present in the natural wind (usually up to 2 Hz) as well as those caused by wind-structure interactions The dynamic excitation from buffeting can be significant if the mean wind speed is high, the natural frequencies of the structure are below 1 Hz, the wind turbulence intensity is high with a wind turbulence that is highly 396 Wind Tunnels and Experimental Fluid Dynamics Research Fig 1 A collapsed high-mast light pole; (a) Iowa (Dexter 2004), (b) Colorado (Rios 2007) correlated in space, the structural shape is aerodynamically odd with a relatively rough surface, and the mechanical damping is low In practice, a structure is always subject to both vortex shedding and buffeting excitations But unlike vortex shedding, where amplified dynamic excitation occurs within a short range of wind speeds, buffeting loads keep increasing with higher wind speeds For multisided slender support structures, the current American Association of State Highway and Transportation Officials (AASHTO) Specification does not provide all the aerodynamic parameters such as the static force coefficients, their slopes with angle of attack, Strouhal number, the lock-in range of wind velocities and amplitude of vortexinduced vibration as a function of Scruton number, etc, that are needed for proper evaluation of aerodynamic behavior Thus, wind tunnel testing was required to obtain these parameters Buffeting, self-excited and vortex shedding responses are those significant parameters in the design of a slender support structure 412 Wind Tunnels and Experimental Fluid Dynamics Research Fig 1 Physical significance of thermal layer Where: θ= δ i +1  T ( x , t )dx (10) δi Then the temperature distribution T(x,t) is known: qw q ⋅ ( δ i + 1 (t ) − δ i (t ) ) − w ⋅ x + 3⋅k k qw qw 2 + ⋅x − ⋅ x3 k ⋅ ( δ i + 1 (t ) − δ i (t ) ) 3 ⋅ k ⋅ δ i2 1 (t ) − δ i2 (t ) + (11) δ i = 12 ⋅ α ⋅ ti (12) δ i + 1 = 12 ⋅ α ⋅ ti + 1 (13) T ( x , t ) = Ti + ( ) Where: When δ ( t ) is greater than the thickness L, the semi-infinite body approximation cannot be considered The heat conduction differential equation is integrated over the thickness L: L L ∂ 2T 1 ∂T  ∂x 2 dx =  α ∂t dx 0 0 (14) Giving the following energy integral equation: ∂T ∂T 1 d (x = L) − ( x = 0) = ⋅ (θ − Ti ⋅ L ) ∂x ∂x α dt (15) The origin of the x axis is on the external surface where aerodynamic heating is applied At x=L adiabatic boundary conditions are considered (see figure 2) The boundary conditions are: −k ⋅ ∂T ( x = 0) = q w − σ ⋅ ε ⋅ (Ts (t )4 − Te (t )4 ) ∂x ∂T (x = L) = 0 ∂x (16) A New Methodology to Preliminary Design Structural Components of Re-Entry and Hypersonic Vehicles 413 Fig 2 Schematic representation of the thermal problem Where Te is the ambient temperature and Ts is the temperature at x=0 For the same arguments explained above, the temperature distribution chosen is a quadratic one: T (x, t) = a + b ⋅ x + c ⋅ x2 (17) As mentioned before the thermal layer has now no physical significance Then it is necessary to introduce a new time-dependent parameter Two kind of parameters can be considered: 1 Ts(t) 2 r = Ts(t)+TL(t) Where TL(t) is the temperature at x=L In paragraph 2 it will be demonstrated that the second approach gives better results with respect to the first one when compared to one-dimensional finite element model results In fact, in the second approach the solution of the energy integral equation has an information on the temperature distribution of the previous time step since the parameter r represents the sum of the temperature values at the extreme points of the body On the contrary in the first approach it is not possible to give any information on the previous temperature distribution The energy integral equation is: −α ⋅ ∂T d ( x = 0) = (θ − Ti ⋅ L ) ∂x dt (18) Where: L θ =  T ( x , t )dx (19) 0 When boundary conditions are applied, the integral equation becomes: ( A + B ⋅ Ts (t )3 ) ⋅ dTs + C ⋅ Ts (t )4 = D dt (20) For the second case: − ( A + B ⋅ r(t )3 ) ⋅ − − dr + C ⋅ r (t )4 = D dt (21) 414 Wind Tunnels and Experimental Fluid Dynamics Research The terms B ⋅ Ts (t )3 and B ⋅ r(t )3 are neglected when: 4 σε 3 Ts L