Quasi Steady Air Loads Report: Flat Plate With Central Load

Transcription

1 Quasi Steady Air Loads Report: Flat Plate With Central Load Sorin Pirau, Alexander Forbes, Brandon Liberi, Vrishank Raghav, Narayanan Komerath Experimental Aerodynamics and Concepts Group Daniel Guggenheim School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia USA Contact: February 24, 2015

2 Report Number ADLP February 24,

3 Summary The variation of quasi-steady air loads with attitude on a flat plate model with a cylindrical load centered on its upper surface, is described. The loads are ensemble-averaged with 1-degree resolution using the Continuous Rotation technique, with a stepper motor rotating at 0.99 RPM above a 6- DOF load cell. The azimuthal variation is reduced to a Fourier series. A truncated series of Fourier coefficients is listed. This is seen to represent the load variations with adequate accuracy for use in dynamic simulation. Cases included those at zero pitch and at -10 degrees pitch. 2

4 Contents 1 Description 4 2 Model Geometry 5 3 Results-Fourier Coefficients m/s (20 Mph), Flat Edge facing the flow, Pitch -10 deg m/s (20 Mph), Sharp Edge facing the flow, Pitch -10 deg m/s (30 Mph), Flat Edge facing the flow, Pitch -10 deg m/s (30 Mph), Sharp Edge facing the flow, Pitch -10 deg

5 Chapter 1 Description The Flat plate is composed of plexi-glass, with an aluminum cylinder placed on top, which connects the flat plate to a thin cylindrical rod of length m (10.5in) and diameter of m (3/8 in). The aluminum cylinder ensures that the metal rod is flush to the surface of the flat plate and there are no gaps between the rod and the flat plate to interact with the flow. It is to be noted that the metal rod goes through the flat plate and into the aluminum cylinder, and thus only m (8.625in) of the metal rod is exposed to the airflow. The cylindrical rod is used as a mounting strut for the model. A continuous rotation method is used in order to obtain load data about the flat plate for incrimental changes in yaw. The model is rotated at an RPM of 0.99 for 10 revolutions, after which the data obtained is phase averaged and ensemble averaged to a resolution of 1 degree. After the data is averaged, Fast Fourier Transform can be used on the data to estimate the coefficients of a trigonometric polynomial that interpolates each individual set of data, Cx, Cy, Cz, CMx, CMy, CMz. Only the first 20 coefficients are used, thus during simulations, it is more efficient to interpolate/calculate the load values from the Fourier coefficients than by looking up and extracting the required values from a data set. This paper lists the coefficients for these Fourier series representations so that they may be used instead of the actual data points. In order to interpolate the data, a trigonometric polynomial of the form shown in Equation 1.1 was used. y = a 0 + b 0 + a 1 cos(2π(x/360)) + b 1 sin(2π(x/360) + a 2 cos(2π(2x/360)) + b 2 sin(2π(2x/360) a 2 0cos(2π(20x/360)) + b 2 0sin(2π(20x/360) (1.1) The conditions for which the flat plate was tested are listed before each data set and the geometric dimensions of the flat plate are listed in Chapter 2 of this report. The flat plate was tested for two configurations at two different velocities/reynolds numbers. It was found through close examination of the flat plate, that one of the long sides of the flat plate had a flat edge where it was cut and the other side had a sharp/angled edge. Therefore the flat plate was tested at a -10 deg initial pitch, first with the flat edge facing the flow, and second with the sharp edge facing the flow. Figure 1.1: Flatplate model 4

6 Chapter 2 Model Geometry Table 2.1: Experimental Velocities Tested Experimental Velocities Tested Velocity (mph) Velocity (m/s) Table 2.2: Model Geometry Model Geometry Flat Plate Length (m) Flat Plate Width (m) Flat Plate Height (m) Area Used for Coefficients (m 2 ) Moment Arm Used for Coefficients (m)

7 Chapter 3 Results-Fourier Coefficients m/s (20 Mph), Flat Edge facing the flow, Pitch -10 deg Table 3.1: Experimental Conditions Experimental Conditions Tempterature (F) 74.2 Pressure (inhg) Density Calculated (kg/m 3 ) Density Used (kg/m 3 ) Table 3.2: A-Fourier Coefficients A-Fourier Coefficients Number CD CY CZ CMX CMY CMZ E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-06 6

8 Table 3.3: B-Fourier Coefficients B-Fourier Coefficients Number CD CY CZ CMX CMY CMZ E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-06 7

9 8

10 9

11 10

12 m/s (20 Mph), Sharp Edge facing the flow, Pitch -10 deg Table 3.4: Experimental Conditions Experimental Conditions Tempterature (F) 74.2 Pressure (inhg) Density Calculated (kg/m 3 ) Density Used (kg/m 3 ) Table 3.5: A-Fourier Coefficients A-Fourier Coefficients Number CD CY CZ CMX CMY CMZ E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-06 11

13 Table 3.6: B-Fourier Coefficients B-Fourier Coefficients Number CD CY CZ CMX CMY CMZ E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-05 12

14 13

15 14

16 15

17 m/s (30 Mph), Flat Edge facing the flow, Pitch -10 deg Table 3.7: Experimental Conditions Experimental Conditions Tempterature (F) 74.2 Pressure (inhg) Density Calculated (kg/m 3 ) Density Used (kg/m 3 ) Table 3.8: A-Fourier Coefficients A-Fourier Coefficients Number CD CY CZ CMX CMY CMZ E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-06 16

18 Table 3.9: B-Fourier Coefficients B-Fourier Coefficients Number CD CY CZ CMX CMY CMZ E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-05 17

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20 19

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22 m/s (30 Mph), Sharp Edge facing the flow, Pitch -10 deg Table 3.10: Experimental Conditions Experimental Conditions Tempterature (F) 74.2 Pressure (inhg) Density Calculated (kg/m 3 ) Density Used (kg/m 3 ) Table 3.11: A-Fourier Coefficients A-Fourier Coefficients Number CD CY CZ CMX CMY CMZ E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-06 21

23 Table 3.12: B-Fourier Coefficients B-Fourier Coefficients Number CD CY CZ CMX CMY CMZ E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-05 22

24 23

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