REPORT ON WIND TUNNEL MEASUREMENT OF WIND DRAG ACTING ON TRIANGULAR MAST STRUCTURE

Transcription

1 REPORT ON WIND TUNNEL MEASUREMENT OF WIND DRAG ACTING ON TRIANGULAR MAST STRUCTURE Budapest University of Technology and Economics 178 Department of Fluid Mechanics H-1111 Budapest, Bertalan L. utca 4-6. Tel: Fax: lajos@simba.ara.bme.hu January 004

2 PANNON GSM (H-004 Budaörs, Baross u. 165, further on Customer) commissioned the Department of Fluid Mechanics of Budapest University of Technology and Economics (further on Department) to carry out wind tunnel experiments in order to determine the wind drag acting on a triangular mast structure used by the Customer. The measurements and the data processing have been finished. The results and the conclusions are summarized in this report. 1. The aims and objectives of the investigation The wind load acting on masts, towers can be decisive concerning the overall load of the structure, so exact knowledge of the forces can contribute to economic design and use of these structures. The relevant European Standard (ENV :1997 includes the method of calculation of wind drag. The objective of this experimental investigation included also the checking and verification of the proposed method for a given structure geometry used by the Customer. The length of the modeled equilateral triangular mast section (panel) having equal areas on each face is 10 m, the distance between cylindrical legs of mm in diameter was 3.5 m at the lower end and.5 m at the upper end. Besides cylindrical legs the modeled structure included bracing members of quadratic (60x60mm) cross section. (The drawing of one face of the 1:6 scale model is shown on Fig. 1.). Figure 1. The 1:6 scale model of one face of the equilateral triangular mast section. The wind tunnel and the model Model experiments have been carried out in the test section of the horizontal wind tunnel of the Department. This is a recirculating (Goettingen type) wind tunnel with open test section (Fig..). The nozzle diameter is.6 m, the length of

3 3 the test section is 5.7 m. The maximum wind velocity is 60 m/s. The turbulence intensity in the empty test section is Tu = 0.5%. The model was put in a uniform flow of two different turbulence levels: smooth, low turbulence (Tu = 0.5%) flow, and turbulent flow of 5% turbulence intensity. This turbulence intensity corresponds to the turbulence of atmospheric boundary layer corresponding to relatively undisturbed open-country environment and far above the ground. The turbulence intensity was enhanced by a grid fixed in the outlet cross section of the nozzle (see Fig. 3.) Figure. The horizontal recirculating wind tunnel used Fig. 3. shows also the 1:6 scale model of the mast section model in the wind tunnel: the legs were connected on both ends to a three-bladed support plates, that was fixed to the balance via a shaft. In order to ensure a D (twodimensional) flow, the model was fixed between two nearly elliptical end-plates (see Fig. 3.). The drag acting of the three-bladed support plates fixed to a cylindrical beam was measured separately and the net drag forces acting on the support plates was distracted from the drag force acting on the mast section model, support plates combination. The shafts of the two support plates were connected to the balance shown in Fig. 4.. The balance consisted vertical rods at both ends of the model connecting via - spherical joints the frames and the shafts of the support plates. (So the model could swing on the rods and rotate around the axis.) The shafts of the model were fixed by two horizontal rods provided with - spherical joints at their ends to two load cells measuring the drag forces. The cells were calibrated before and after the measurements. In order to fix the model against rotation around its axis, the shaft of the model was fixed by a special grasping part fixed to the horizontal bar. So the moment of air forces did not generate horizontal force component, influencing the drag measurement.

4 4 Figure 3. 1:6 scale model of the mast section in wind tunnel and the turbulence generator grid in the nozzle Figure 4. Measurement of the drag of support plate and the drag measuring system

5 3. Measurement of drag force and data processing 5 The measurement of drag force F D was carried out by two calibrated load cells and the force data were captured for 0 s with 500 Hz frequency and processed by PC. The wind velocity in the test section (v ref [m/s]) was determined by measuring the difference of the total pressure (head, p t [Pa]) in the inlet of nozzle by a row of Pitot tubes shown in Fig. 5. and the static pressure (p 0 [Pa]): p t -p 0. The pressure difference was measured with pressure transducers (0 s, 400 Hz) This pressure difference was correlated at both turbulence intensities by calibration with the dynamic pressure (p dyn [Pa]) in the test section, measured with standard Pitot-static tube and Betz-micromanometer calibrated by the Hungarian Office of Measurements. Figure 5. Pitot tubes at the inlet of the wind tunnel nozzle. The atmospheric pressure p 0 [Pa] and the temperature of the air in wind tunnel were also measured and the air density was determined by using the ideal gas law: p 3 0 ρ = [kg / m ], RT where R = 87 [J/kg/K] is the gas-constant for air. Knowing the density and the dynamic pressure in the test section the reference velocity can be determined: v =. ρ ref p d The drag forces measured by the two load cells were added and the resultant drag force F D was divided by the dynamic pressure. This quotient is equal to R WS, called total wind drag in ENV :1997 E European Prestandard, Eurocode 3: Design of steel structure, Part 3-1: Towers, masts and chimneys Tower and masts Par. A.. Wind drag (in the following Standard) made available for the Department by the Customer. R F D WS = = Kθ CN AS, eq. (A.) in Standard. pdyn

6 6 where K θ is the wind incident factor, A S [m ] is the area projected normal to the face of the structural components of the considered face, C N is the overall normal drag coefficient. For triangular structures Ac + Ac,sup Af Kθ = + 5 A A F F ( 1 0.1sin 1, θ) eq. (A.3b), where A c [m ] and A f [m ] the projected area of the circular-section and flat-sided section members, respectively, θ is the angle of incidence of the wind to the normal direction of the face. in our case A F =A S and A c,sup = 0, since the largest Reynolds number referring to d =0,08 m diameter of cylindrical legs and v ref,max = 35 m/s is: Re v d ν ref = = < A C + A f c N = CNF CNc eq. (A.4) with A c,sup = 0, AF AF where C = 1,76 C [1 C φ + φ ] eq. (A.5a) and C NF 1 Nc = C1 (1 Cφ) + (C1 + 0,875) φ eq. (A.5b), where C 1 = 1,9 and C =1,4 for triangular structures. φ is the ratio of total projected area of the structural components in the windward face (A S ) visible when viewed normal to the face, to the area enclosed by the boundaries of the frame projected normal to face (in the following solidity). In our case φ = 0,156. The Standard was used for the case under consideration and the results obtained (and checked as well as agreed by the Customer) is summarized in Table 1.. Table 1. Calculation of wind drag according to the Standard Wind incidence θ Leg diameter D 0,08 0,08 0,08 0,08 0,08 Length of a leg L 1,6576 1,6576 1,6576 1,6576 1,6576 Length of the bracing members L b 4,46 4,46 4,46 4,46 4,46 Cross section of junction plates A f (plates) 0, , , , ,00391 Projected area of flanges A f (flange) 0, , , , , Overlaps 0,007 0,007 0,007 0,007 0,007 Projected area of cylinders A c 0,0986 0,0986 0,0986 0,0986 0,0986 Projectedflat area A f (sum) 0, , , , , Total projected area of the face 0,8813 0,8813 0,8813 0,8813 0,8813 Projected area of structures A F =A c +A f 0, , , , ,13736 Solidity φ 0, , , , , Wind incident factor K θ 1 0, , , , C Nf,695563,695563,695563,695563, C Nc 1,5586 1,5586 1,5586 1,5586 1,5586 C N 1,9339 1,9339 1,9339 1,9339 1,9339 R WS =F e /p din =A F xk θ xc N R WS 0,6419 0,6938 0,5991 0, ,5566

7 7 4. Results of measurements First the effect of wind velocity (Reynolds number) on the total wind drag R WS was investigated at θ = 0 wind direction and at laminar and turbulent (0,5% and 5% turbulence intensity) flow: the velocity was varied between 15 and 35 m/s, i.e. the Reynolds number related to the diameter of the cylindrical components (legs). The result is shown on Fig.6.. It can be seen that the effect of Reynolds number in the investigated range is particularly in case of less turbulent flow modest, the decrease of the drag is at low turbulence R WS = 0,310 0,306 (1,3%), 0,3145 0,30 (4%) when Re increases from 8000 to R WS [m ] laminar turbulent 0.00 E+4 3E+4 4E+4 5E+4 6E+4 7E+4 Re [-] Figure 6. Reynolds number effect The results of measurements are shown on Fig. 7., where R WS is plotted against the wind incidence θ in case of laminar and turbulent flow (Tu=0,5% and 5%) at v ref =15, 0 and 5 m/s wind velocities. Also the total wind load data calculated according to the Standard (last row of the Table above) were plotted with dotted line in Fig. 7. The following observations can be formulated on the basis of Fig. 7. and Table 1.: a) The increase of turbulence intensity from 0,5% to 5% causes 1-4% increase in wind drag. As expected the turbulence intensity and the velocity caused

8 8 the largest difference at 30%, where one face of the structure is in the wake of a leg, because the characteristics of the wake, determining the drag of structural elements downstream the leg, are mostly influenced by the turbulence and the Reynolds number (in turbulent flow the length of separation bubbles decrease). b) In contrast to the calculated drag values decreasing monotonously with the angle of incidence from R WS = 0,64 to 0,56 (i.e. the change is about 3%, the measured drag changes quite considerably: the maximum R WS = 0,31 (turbulent flow, v = 5m/s) is at angle of incidence θ = 0 0 (18% more than the calculated), then it decreases and reaches its minimum at θ = 30 0 R WS = 0,55 (% less than the calculated) and increases again to R WS = 0,304 at θ = U=15 m/s lam. U=0 m/s lam. U=5 m/s lam. U=15 m/s turb. U=0 m/s turb. U=5 m/s turb R WS [m ] calculated Angle of incidence, θ [o] Figure 7. Total wind drag as function of wind direction, turbulence intensity and wind velocity.

9 5. Discussion 9 Let s carry out a short transformation of the expression given on the basis of the Standard in Kapitel 3 of the Report. When copying eq. (A.5a) and transforming eq. (A.5b) we get: C C Nc NF = C (1 C φ) + (C + 0,875) φ = C (1 C φ + 1,46 φ ) and 1 1 = 1,76 C [1 C φ + φ ] eq. (A.5a). 1 1 As an approximation φ and 1,46 φ (in our case =0,04 and 0,035, respectively) can be neglected with respect to 1-C φ = 0,78 (3,1 and 4,5% error, respectively and in sum about 3.7% error) and when inserting C 1 and C values in eq. (A4) we obtain: A f Ac ( 1 1,4φ) 1,76 + C N = 1,9. AF AF Let us regard this relation. When taking φ 0 and separate the drag acting on cylindrical and flat parts we get: a) The drag coefficient (1,9) acting on cylindrical parts corresponds nearly to 3/x1,=1,8, where 1, is the sub-critical drag coefficient of cylinder, and there are altogether 3 legs in the structure, but only two is considered when regarding the reference face. So the effect of the third leg is slightly (with 1.5%) overestimated in the calculation. b) Since all of three legs are exposed to the wind in the wind direction range the reduction of drag on all legs seems not to be relevant. In this range the calculation underestimated the forces acting on legs by 0%. In the angle range only one of three legs are influenced by other structural elements, but all of them are multiplied by the term 1-C φ=1-1,4φ, taking the shadowing effect into consideration. In our case with φ=0,156 the rear leg drag calculated according to standard is [1,9(1-1,4φ)]- x1,=0,57 which is certainly smaller than the reality. c) The drag coefficient of flat structure elements is 1,9x1,76=3,34, i.e. the drag on flat structural parts of two faces downstream the reference face is considered as ((1-1,4φ)3,34-)/ = 0,3, i.e. 5% of the drag acting on flat sided structural elements in reference face. Since in oblique wind direction their cross section facing the wind changes it is difficult to make acceptable estimation. Nevertheless this value seems to be rather low, particularly if we consider that the real degree of incidence of wind on the bracing members is much smaller, than 60 0, which relates to two oblique panels. d) At angle φ=30 0 a minimum should exist, since one face of the structure is in the wake of a leg which is not reflected in the equations proposed by the standard. Let us make a simple estimation: The full drag acts on all legs (but in case of φ=30 0 only on legs) and the drag acting on the flat sided elements of oblique panels can be approximated with c D = cos α, where α is the angle between the wind direction and the direction normal to face under consideration. The

10 10 shadowing effect is neglected, but the drag of structural elements in undisturbed and disturbed flow (c Nu and c Nd ) will be calculated separately. At this model: A f /A F =0,34 and A s /A F =0,676 In case of φ=0 c = cnu + cnd = (0,676 1, + 0,34 ) + (0,676 / 1, + 0,34 cos 60) = 1, ,73 i.e. R = c A =,189 0,1374 0, 3. (Measured: R WS = 0,308-0,314) N = WS N F = At φ=30 cn = cnu + cnd = (0,676 1, + 0,34 cos 30 ) + (0,34 cos 30 ) = 1,97 + 0,486 = 1,783, i.e. R = c A = 1,783 0,1374 0, 45 (Measured: R WS = 0,47-0,58) At φ=60 WS N F = cn = cnu + cnd = (0,676 1, 1,5 + 0,34 cos 60) + (0,34 ) = 1, ,648 =,189 i.e. R = c A =,189 0,1374 0, 3 (Measured: R WS = 0,93-0,305) WS N F =,189, The simple calculation resulted in wind drag values close to the measured ones, following the trends in the change of wind drag with respect to angle of incidence. Budapest, 6. February 004. (Dr. Tamás Lajos) Professor, Head of Department