Reduced-Frequency Approach for Calculating Dynamic Derivatives

Computing Stability Derivatives and Their Gradients for Aerodynamic Shape Optimization

“…In these figures, the extra points in the five-and seven-instance cases lie on the same sinusoidal solution predicted by the three-instance solution. This is consistent with the findings of Murman [21]. Murman observes that the ability to simulate the forced oscillation with a single frequency arises because the forcing frequency of the oscillation largely determines the frequency of the output and because there is a limited potential for energy transfer between the modes when using the Euler equations.…”

“…The time-spectral stability derivative formulation presented in the following section is similar to the methods presented by Murman [21] and Da Ronch et al [27,29] in that it uses a time-periodic approximation to the unsteady CFD solution to reduce the cost of the computation. However, the forced oscillation motions used here and the linear regression approach used to determine the derivatives in this work differ somewhat from those previously used.…”

“…Several researchers, including Weinacht [17], DeSpirito et al [18], Sahu [19], and Oktay and Akay [20], demonstrated methods using steady and unsteady CFD to predict the stability derivatives of missiles and projectiles. More recently, Murman [21] presented a method for computing stability derivatives of both missiles and full aircraft configurations using a frequency-domain CFD method. He used the frequency domain solver to produce periodic data for the forced oscillation of the configuration of interest.…”

Effect of elastic deformation on the aerodynamic characteristics of a high-speed spinning projectile

“…Currently, linear aerodynamic load distribution methods are frequently used in the aerodynamic modeling of a projectile with elastic deformation [8][9][10][11]. In addition, unsteady aerodynamic effects are measured using the aerodynamic damping coefficient [12][13][14][15]. These methods consider the relationship between the external loads of a projectile body and the local angle of attack.…”

Time-periodic incompressible flow simulation using non-linear frequency domain approach

“…Murman [23] used the procedure followed by Hall et al [15] and extended the application to 3-D Euler equations to calculate dynamic stability derivatives of some configurations in an inviscid flow. Also, the results show that in some cases for viscous flows, the solution with just a single mode would generally be irrelevant and higher (but a limited) number of modes should be considered.…”