Nonlinear Modeling of Cascade Fin Aerodynamics Using Kirchhoff's Steady-State Stall Model

Abstract

U NDER stationary attached flow conditions, aerodynamic effects can be adequately described using time-invariant parameters and linear models, but the models are highly nonlinear due to dominant unsteady effects and flow separation [1,2] at higher angles of attack. The models based on computational fluid dynamic methods, wind-tunnel (WT) tests, and semiempirical formulations provide a basis for analytical investigations of the complex flow phenomena, but postulating them in an analytical form suitable for parameter estimation is difficult. An alternative approach [3,4] has been followed to describe the flow separation analytically as a function of an internal state variable in the present study. The grid fins, sometimes also called the lattice fins, are a relatively recent development in guided missile technology [5], although grid fins exhibit more effective stability and control characteristics at intermediate and large angles of attack [6,7], but their aerodynamic efficiency is quite low.Misra [8] proposed a new category of grid fins (nomenclatured as “cascade fins”) with higher aerodynamic efficiency. A cascade fin has planar members (fins) placed parallel to each other at a distance based on an optimized gap-to-chord (g=c) ratio. It is the absence of crossmembers that makes a cascade fin different from a grid fin. This Note presents the modeling of nonlinear longitudinal aerodynamics associated with single/cascade fin models [8] at high angles of attack using Kirchhoff’s steady-state stall model. The WT data pertaining to single/cascade finmodels were used to analyze the effect of endplates, the number of planar fins in the cascade, and the g=c ratio on the stall characteristics parameters during nonlinear modeling and estimation. The National Wind Tunnel Facility [8] available in the Department of Aerospace Engineering at the Indian Institute of Technology, Kanpur, was used to generate the data consisting of the variation of lift coefficient (CL) as a function of angle of attack ( ).