This chapter contains sections titled: What Is Identification? Identification: A Simple Example Description of the Stochastic Behavior of Estimators Basic Steps in the Identification Process A Statistical Approach to the Estimation Problem Exercises

An Introduction to Identification

On the generation of flight dynamics aerodynamic tables by computational fluid dynamics

In this paper we develop reduced-order models for the unsteady lift on a pitching and plunging aerofoil over a range of angles of attack. In particular, we analyse the pitching and plunging dynamics for two cases: a two-dimensional flat plate at using high-fidelity direct numerical simulations and a three-dimensional NACA 0006 aerofoil at using wind-tunnel measurements. Models are obtained at various angles of attack and they are verified against measurements using frequency response plots and large-amplitude manoeuvres. These models provide a low-dimensional balanced representation of the relevant unsteady fluid dynamics. In simulations, flow structures are visualized using finite-time Lyapunov exponents. A number of phenomenological trends are observed, both in the data and in the models. As the base angle of attack increases, the boundary layer begins to separate, resulting in a decreased quasi-steady lift coefficient slope and a delayed relaxation to steady state at low frequencies. This extends the low-frequency range of motions that excite unsteady effects, meaning that the quasi-steady approximation is not valid until lower frequencies than are predicted by Theodorsen’s classical inviscid model. In addition, at small angles of attack, the lift coefficient rises to the steady-state value after a step in angle, while at larger angles of attack, the lift coefficient relaxes down to the steady-state after an initially high lift state. Flow visualization indicates that this coincides with the formation and convection of vortices at the leading edge and trailing edge. As the angle of attack approaches the critical angle for vortex shedding, the poles and zeros of the model approach the imaginary axis in the complex plane, and some zeros cross into the right half plane. This has significant implications for active flow control, which are discussed. These trends are observed in both simulations and wind-tunnel data.

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Reduced-order unsteady aerodynamic models at low Reynolds numbers

Indicial Aerodynamics in Compressible Flow-Direct Computational Fluid Dynamic Calculations

An unsteady Euler solver is modie ed to calculate the indicial response of a rectangular wing to a step change in the angle of attack. In this new approach the grid time metrics include the velocity caused by the impulsive change in angle of attack, but the mesh is not moved accordingly. This approach avoids numerical instabilities and decouples the step change in the angle of attack from a pitch rate. Numerical results are validated by comparison with analytical results for two-dimensional indicial responses. The application of the same method to rectangular wings reveals important characteristics of the three-dimensional indicial response. It is found that the direct calculation of the indicial response using computational e uid dynamics gives quite accurate results and provides a rich database, in the absence of experimental data, to validate the approximations to indicial response.

Direct Calculation of Three-Dimensional Indicial Lift Response Using Computational Fluid Dynamics

This paper presents summarized descriptions and applications of engineering, intermediate, and high level missile aerodynamics prediction methods developed and/or used by NEAR. The engineering level method is represented by the M3HAX experimental data based code, the intermediate level method includes the analytical panel-method based SUPDL/SUBDL and modified linear theory VTXCHN codes, and the high level methods include the NEARZEUS space marching Euler flow solver. All of the methods contain models to account for fin and body vorticity effects in the aerodynamic loads. The engineering and intermediate level methods are applied to the prediction of high angle of attack pitch plane and lateral aerodynamic characteristics of missiles at arbitrary roll angle and aerodynamic loads acting on conventional and chined body shapes, and to assess effects of fin-body gap on fin loads. The intermediate level methods are also employed in the design of nonconvention al fin planforms for minimum hinge moment The Euler flow solver is applied to the prediction of rolling moments acting on a canard configuration. Comparisons with experimental data are presented It is concluded that the missile aerodynamicist and/or designer should be aware of the availability and utility of the various levels of missile aerodynamics prediction methodology.

Engineering, intermediate, and high level aerodynamic prediction methods and applications

The aim of the research described herein was to develop and verify an efficient optimization-based aerodynamic / structural design tool for missile fin and configuration shape optimization. The developed software was used to design several missile fin planforms which were tested in the wind tunnel. Specifically, this paper addresses fin planform optimization for minimizing fin hinge moments, as well as aeroelastic design (flexible fin structures) for hinge moment control. The method is also capable of shape optimization of fin-body combinations with geometric constraints. The inclusion of aerodynamic performance, geometric constraints, and structural constraints within the optimization software facilitates multidisciplinary analysis and design. The results of design studies and wind tunnel tests are described.

Multidisciplinary design optimization of missile configurations and fin planforms for improved performance

p,q,r rotational rates, rads/sec Engineering-level missile aerodynamics prediction code s fin semispan measured from body centerline MISL3 has recently been applied to a variety of configurations including two tandem-control models and to a two-fin-set model with free rolling tail fins tested at NASA Langley Research Center. Enhanced capabilities since the earlier M3HAX version include the modeling of conical changes in body diameter (flares, boattails) and arbitrary interdigitation angles between fin sets. Results presented include high angle of attack aerodynamics, induced lateral forces, tandem-control fin deflections, configurations with flares and/or boattails, estimates of free rotating fin section performance, rotational damping estimates, and updates to results presented in an earlier paper. Comparisons to independent experimental data are presented to demonstrate the unique qualities of the code. In M3F3CA , earlier MISL3 , MISSILE3 ) has been general, good agreement with experimental data is developed for aerodynamic performance prediction and obtained for a variety of configurations (body alone, for preliminary design of conventional missiles. The single-fin set, two-fin set, and three-fin set method uses the Triservice systematic fin-on-body force configurations) and flow conditions (symmetric and and moment data base which covers a Mach number asymmetric). range from 0.6 to 4.5, fin aspect ratios from 0.25 to 4.0,

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Recent Applications and Improvements to the Engineering-Level Aerodynamic Prediction Software MISL3

There are several difficulties associated with the use of Navier-Stokes/Euler solvers for calculating aerodynamic i n d i c i a l r e s p o n s e s . T h e s e p r o b l e m s h a v e been systematically addressed, and an innovative solution to them has been evaluated. A smooth ramp/Laplace domain analysis which overcomes these difficulties has been formulated and its accuracy is demonstrated. Parametric studies of the ramps required to obtain accurate indicial responses have been performed, and the range of application of the method has been investigated over a wide range of flow conditions (M-, a, Re). The results presented in this paper indicate that smooth ramps can be used in a time-accurate Navier-Stokes or Euler solver to accurately determine indicial functions using a Laplace transform approach.

A practical approach for calculating aerodynamic indicial functions with a Navier-Stokes solver

Studies of vortex-induced aerodynamic nonlinearities associated with body and fin vortices for missile configurations have been performed. As part of this effort, the vortex and fin modeling methodologies in the engineering-level and intermediate-level aerodynamic predictions codes MISL3 and MISDL have been reviewed and improved. The ability of the methods to predict detailed fin loads in the presence of external vortices is demonstrated. Both codes have been used extensively to predict missile performance including canard/wing vortex induced effects on tail fins. These effects often manifest themselves in pitching moments and most dramatically in induced rolling moments on tail fins which counter, and often times reverse, the direct roll control of canard fins. Both codes have shown the capability to capture these vortexinduced phenomena. For validation purposes, the methods were compared to detailed vortex-fin interaction studies, performed at Sandia National Laboratories, which measured fin loads influenced by a vortex generated by an upstream fin.

Daniel J. Lesieutre

Papers

Engineering, intermediate, and high level aerodynamic prediction methods and applications

Multidisciplinary design optimization of missile configurations and fin planforms for improved performance

Recent Applications and Improvements to the Engineering-Level Aerodynamic Prediction Software MISL3

A practical approach for calculating aerodynamic indicial functions with a Navier-Stokes solver

Studies of Vortex Interference Associated with Missile Configurations