America's Fighters of the 1980s - F-16 & F-18 by Robert C. Stern

By Robert C. Stern

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16) with for a covariance function matrix element, Cui uj (ξ) = Cui uj (ξ1 , ξ2 , 0) = E {ui (0, 0, 0)uj (ξ1 , ξ2 , 0)} Note that the atmospheric turbulence covariance matrix is symmetrical, therefore C u1 u2 (ξ) = Cu2 u1 (ξ), Cu1 u3 (ξ) = Cu3 u1 (ξ) and Cu2 u3 (ξ) = Cu3 u2 (ξ). 6 is presented. This figure shows the atmospheric turbulence velocity components at origin OE , u1 (0, 0, 0) and u2 (0, 0, 0), and at P (ξ1 , ξ2 , 0), u1 (ξ1 , ξ2 , 0) and u2 (ξ1 , ξ2 , 0), decomposed in a direction along the OE P connection line and decomposed perpendicular to the connection line OE P .

7) with ∇Φ the airflow’s velocity components and n the configuration’s local normal vector (both given in the frame Faero ). 8) with Q∞ = [U∞ , V∞ , W∞ ]T , the vector of undisturbed velocity components at infinity. 1: The Aerodynamic Frame of Reference Faero , including the undisturbed velocity components [U∞ , V∞ , W∞ ]T of Q∞ . [11, 12, 8, 9]. 9)  4π  r r SB +SW +S∞ SB +SW +S∞ with SW containing both the upper and lower wake-surfaces, or SWupper and SWlower , respectively. 9) hold for a sphere at infinity (S∞ ), the configuration submerged in the airflow (SB ) and the configuration’s wake (SW = SWupper + SWlower ).

The flow equations to be solved are based on Linearized Potential Flow (LPF) formulations, see also references [11, 12]. These formulations only hold for inviscid, irrotational, incompressible flow. In estimating the aerodynamic forces and moments, however, the Computational Aerodynamics approach does have its limitations, they are governed by the fluid flow model. Starting at the highest level of fluid flow modeling, the basic equations of motion describing a fluid flow are the so-called Navier-Stokes equations.

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