Calculation of Average Drag

Actual average drag, defined by

Drag=(1/2)*Cd*rho*V2*A,
can be predicted from the model average drag by equating drag coefficients, thus using the relationship
Drag=Dragm*(rho/rhom)*(V/Vm)2.

Values from the actual wind tunnel test and from the model simulation are given below:

Actual
Acanopy = 5 ft2
rhoair = 0.00237
V = 58.6 ft/s


Model
Acanopy-m = 5 ft2
rhoair-m = 1.0
Vm = 1.0 ft/s

Average drag was calculated using results from both the CFD simulation and the FSI simulation.




Average Drag for CFD Simulations

Values for average drag calculated from CFD simulations of four different mesh refinements, as well as for average drag calculated from the wide domain CFD simulation, are shown below. The value for average drag calculated from the Parks wind tunnel tests is also shown.


Average Drag for CFD Simulations
Source Average Drag (lbs)
Sim. Type Num. Elements Drag
CFD 100000 69.4
CFD 500000 78.9
CFD 2000000 84.9
CFD 2600000 90.3
CFD Wide Domain 44.1
Parks Wind Tunnel 44

Shown above at right is a plot of drag histories for the four CFD simulations of differing mesh refinements. The histories show similar trends, and again demonstrate that drag appears to converge with increased mesh refinement.



Average Drag for FSI Simulations

Values for average drag calculated from FSI simulations of two different mesh refinements, as well as for average drag calculated from the wide domain FSI simulation, are shown below. The value for average drag calculated from the Parks wind tunnel tests is also shown.


Average Drag for FSI Simulations
Source Average Drag (lbs)
Sim. Type Num. Elements Drag
FSI 500000 88.7
FSI 2000000 94.7
FSI Wide Domain 43.5
Parks Wind Tunnel 44

Shown above at right is a plot of drag histories for the two FSI simulations of differing mesh refinements. The histories show similar trends, and due to the similarity of the FSI drag histories with the CFD drag histories, it is guessed with confidence that were more FSI simulations to be conducted with higher mesh refinements, convergence to some value of average drag would be seen.