NEAR Publications

• Papers on Nonlinear Indicial Theory
• Papers on Volterra-Wiener Theory
• Papers on Linear Indicial Theory

Papers on modeling using nonlinear indicial theory:

• Data Based Aerodynamic Modeling Using Nonlinear Indicial Theory,
  Patrick H. Reisenthel and Matthew T. Bettencourt
  [available as AIAA Paper 99-0763] [PDF file, 600 KB]

ABSTRACT: Nonlinear indicial response theory addresses the need for high-fidelity prediction of nonlinear phenomena such as unsteady aerodynamics. The present paper describes a particular implementation of nonlinear indicial theory in which it is assumed that the indicial and critical-state responses of a nonlinear system can be parameterized based on the instantaneous motion state. These parameterized indicial and critical-state responses form a kernel which can be determined in principle from experiment, computation, or analysis. The application described in this paper considers a 65degree delta wing undergoing forced roll oscillations at a high angle of attack. A new extraction algorithm is applied to identify the system's kernel of indicial and critical-state responses. It is shown that, using this kernel, one can accurately predict the unsteady aerodynamic response of the wing to novel maneuvers.
 

• Extraction of Nonlinear Indicial and Critical State Responses from Experimental Data,
  Patrick H. Reisenthel and Matthew T. Bettencourt
  [available as AIAA Paper 99-0764] [PDF file, 504 KB]

ABSTRACT: Practical application of nonlinear indicial theory is of interest for the rapid, yet high-fidelity, modeling of unsteady aerodynamic phenomena. The present paper addresses the question of how to extract nonlinear indicial and critical-state responses from empirical data which were not specifically designed for this purpose. The extraction algorithm is presented, and the results are illustrated on the case of the rolling moment response of a 65-degree delta wing undergoing forced roll oscillations.
 

• An Analysis of Fin Motion Induced Vortex Breakdown,
  Patrick H. Reisenthel, Wensheng Xie, Ismet Gursul and Matthew T. Bettencourt
  [available as AIAA Paper 99-0136] [PDF file, 360 KB]

ABSTRACT: New experimental and theoretical results describe the dynamic hysteresis of the vortex breakdown location over a delta wing, due to an imposed unsteady pressure gradient. Unlike previous studies, in which both the pressure gradient and the circulation of the vortex are simultaneously changed as a result of varying angle of attack, the time-dependent pressure gradient is generated here at a fixed angle of attack, through the root bending motion of a vertical fin placed near the trailing edge of a 75-degree delta wing. Nonlinear indicial theory was used to analyze the results. The theoretical predictions corroborate two key experimental observations, namely the flattening of the hysteresis loops and the shift of the average location of vortex breakdown with increasing frequency.
 

• Semiconductor Modeling Using the Indicial Prediction System,
  Patrick H. Reisenthel and Matthew T. Bettencourt
  [available as NEAR TR 541]

ABSTRACT: The Indicial Prediction System applies nonlinear indicial theory to solve complex problems, such as those associated with nonlinear aerodynamic phenomena during rapid maneuver of aircraft. While originally developed for flight simulation applications, IPS is a versatile general purpose tool which is applicable to nonlinear problems in other fields. The example addressed in the present study concerns the high frequency (between 50 and 400 MHz) transient behavior of a Zener diode near the threshold. The method was used to extract the indicial responses of the system, and these responses were, in turn, used to predict inexpensively the diode's response to novel excitation schedules. In a parallel effort, we have demonstrated that the IPS code can be parallelized efficiently. Most importantly, the parallelization effort needs only be confined to specific shared objects.
 

• A Nonlinear Indicial Prediction Tool for Unsteady Aerodynamic Modeling,
  Patrick H. Reisenthel, Matthew T. Bettencourt, James H. Myatt and Deborah S. Grismer
  [available as AIAA Paper 98-4350] [PDF file, 432 KB]

ABSTRACT: The present paper describes a new tool kit which can be used to model the time-dependent response of nonlinear systems. The Indicial Prediction System (IPS) applies nonlinear indicial theory to solve complex unsteady problems, such as those associated with nonlinear aerodynamic phenomena during maneuver of aircraft. The functionality of this system and its capabilities are described through numerous examples. An important demonstration of the method is its application to the prediction of the aerodynamic loads on a 65-degree delta wing undergoing forced body-axis rolling motions at high angles of attack.
 

• Development of a Nonlinear Indicial Model Using Response Functions Generated by a Neural Network,
  Patrick H. Reisenthel
  [available as AIAA Paper 97-0337] [PDF file, 352 KB]

ABSTRACT: In order to predict the dynamics of maneuvering aircraft or missiles at high rotational rates and high angles of attack, it is essential to accurately and efficiently model the nonlinearities associated with post-stall aerodynamics, including bifurcations and hysteresis. Nonlinear indicial theory offers a viable alternative which can fulfill the need for the efficient and accurate modeling of nonlinear "plant" characteristics. The present paper describes recent applications of linear and nonlinear indicial response models for aerodynamic prediction of maneuvering flight vehicles.
 

• Application of Nonlinear Indicial Modeling to the Prediction of a Dynamically Stalling Wing,
  Patrick H. Reisenthel
  [available as AIAA Paper 96-2493] [PDF file, 392 KB]

ABSTRACT: A nonlinear indicial prediction model was developed to predict the time-dependent unsteady aerodynamic loads associated with flight maneuvers at high angles of attack and high pitch rates. This model is based on nonlinear indicial theory and on efficient parameterization of the indicial and critical-state responses. The parameterization is based only on "local" information, such as instantaneous angle of attack and pitch rate. The present paper describes the application of this nonlinear indicial model to the prediction of the unsteady aerodynamic loads associated with a rectangular wing undergoing dynamic stall. The wing data used to validate the prediction is approximated by an artificial neural network which was trained to reproduce in detail the aerodynamic characteristics of the wing. It is shown that only a finite number of indicial and critical-state responses is necessary in order to accurately construct the flow responses for novel maneuvers.
 

• Development of a Nonlinear Indicial Model for Maneuvering Fighter Aircraft,
  Patrick H. Reisenthel
  [available as AIAA Paper 96-0896] [PDF file, 472 KB]

ABSTRACT: A nonlinear indicial prediction model was developed to predict the unsteady aerodynamic response associated with maneuvering flight vehicles at high angles of attack. The model is based on nonlinear indicial response theory and key simplifications thereof using functional interpolation of parameterized responses. This paper presents the initial development of the method and its application to a model problem involving the "Cobra" maneuver by a full-scale fighter aircraft.
 

Related papers on Volterra series modeling:

• Prediction of Unsteady Aerodynamic Forces Via Nonlinear Kernel Identification,
  Patrick H. Reisenthel
  [PDF file, 1464 KB]

ABSTRACT: Aeroelastic studies play a critical role in aircraft safety and design and, to accelerate the design process and reduce life cycle costs, nonlinear aerodynamic effects must be considered from the onset. The Volterra theory of nonlinear systems provides a mathematically rigorous approximation technique to describe these unsteady aerodynamic effects. A critical problem, however, is the difficulty of identifying the Volterra kernels. The present paper demonstrates the use of a time-domain Volterra kernel identification method which uses physically realizable inputs, is robust with respect to noise, and minimizes or eliminates the need for analytical assumptions. This technology provides a rational means of simulating nonlinear aerodynamic behavior in multidisciplinary analyses and will facilitate the incorporation of high-fidelity tools into the preliminary design phase of aerospace vehicles.
 

Related papers on linear indicial theoretical applications:

• Towards a Semi-Analytic Tool for the Prediction of Dynamic Stall,
  Patrick H. Reisenthel
  [available as AIAA paper 94-0537]

ABSTRACT: Direct numerical simulations are used to analyze in detail the vorticity dynamics of the leading edge region of a NACA0012 airfoil pitched about its 1/4 chord. The results presented in this paper illustrate how the formalism of indicial theory can be used to predict the integrated vorticity fluxes and the vorticity accumulation during unsteady maneuver. In particular, the flow response to large amplitude nonlinear motions is shown to be predicted reasonably accurately, provided that the indicial functions of the flow are inferred in the Laplace domain and stretched to account for quasi-static nonlinearity. The implication of this work is the possibility of developing a fast semi-analytical prediction method for incipient leading edge stall, which will be accurate within certain classes of maneuvers.
 

• A Practical Approach for Calculating Aerodynamic Indicial Functions with a Navier-Stokes Solver,
  Daniel J. Lesieutre and Patrick H. Reisenthel
  [available as AIAA paper 94-0059]

ABSTRACT: There are several difficulties associated with the use of Navier-Stokes / Euler solvers for calculating aerodynamic indicial responses. These problems have 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 (Mach number, angle of attack, Reynolds number). 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.
 

• Unsteady Simulation of Flexible Missiles Flying Low Over the Sea,,
  Daniel J. Lesieutre, Patrick H. Reisenthel, Marnix F. E. Dillenius, Danilo Viazzo, Steve Fisher, Sudarshan Bhat, and Samuel C. McIntosh
  [available as AIAA paper 94-0720]

ABSTRACT: A detailed investigation into the factors affecting transonic missile flight low over the sea has been performed. The simulation program developed in this effort models a flexible missile flying low over the sea and includes unsteady aerodynamics and detailed models of the control system, sensors, and structure. Unsteady aerodynamics are included in the simulation through the implementation of indicial theory. An extended six-degree-of-freedom model has been developed which includes control fin deflections and body elastic modes as additional system states. A sea wave / wind gust model has been developed which acts as an unsteady forcing function on the missile during its flight. The states of the system (6-DOF, fin deflections, and flexible body modes) are coupled and integrated together in the simulation. Unsteady aerodynamics can affect the performance of the missile directly or by excitation of the flexible body modes which can cause accelerations and spurious inputs at sensor locations.
 

• Application of Indicial Theory to the Prediction of Unsteady Separation,
  Patrick H. Reisenthel and David Nixon
  [available as AIAA paper 91-1742]

ABSTRACT: Several key aspects characterizing the time-dependent behavior of boundary layer separation are shown to be accurately predicted, based on the application of Duhamel's convolution integral and the knowledge of the step response of the flowfield to perturbations in Mach number and Reynolds number.
 

• Prediction of Aeroelastic Effects for Sea Skimming Missiles with Flow Separation,
  Patrick H. Reisenthel, Daniel J. Lesieutre and David Nixon
  [available as AIAA paper 91-1052]

ABSTRACT: This paper concerns the application of a recently developed computational capability to the prediction of unsteady vortex effects on a deformable body. The body under consideration is a flexible missile-type configuration undergoing structural oscillations induced by periodic gusts. These gusts represent the effect of sea-state on a "sea-skimming" missile, for which considerable phase lags between aerodynamic loads and the excitation may exist. This paper is devoted to the prediction of amplitudes and phase lags at Mach 0.8. An important result of this work is the demonstration that indicial theory may be used to predict the time-dependent characteristics of the unsteady aerodynamic loads of a three-dimensional body with fins.
 

• Prediction of Unsteady Transonic Flow Around Missile Configurations,,
  Patrick H. Reisenthel and David Nixon
  [available as AIAA paper 91-0601]

ABSTRACT: The Transonic Small Disturbance equation was supplemented with a transport equation for the streamwise vorticity and a vector potential equation to predict vortex effects over missile configurations. The flow separation phenomenon was modeled using normal vorticity jets placed along the separation line. The strength and location of the separating vorticity was determined from empirical criteria. Time-accurate calculations performed using a modified version of the CAP-TSD code in subsonic, transonic, and supersonic flow suggest that it is possible to compute realistic angle of attack configurations using CAP-TSD, thus showing considerable potential for aeroelastic applications and unsteady aerodynamics.