Application of CFD techniques toward the validation of nonlinear aerodynamic models

Applications of Computational fluid dynamics (CFD) methods to determine the regimes of applicability of nonlinear models describing the unsteady aerodynamic responses to aircraft flight motions are described. The potential advantages of computational methods over experimental methods are discussed and the concepts underlying mathematical modeling are reviewed. The economic and conceptual advantages of the modeling procedure over coupled, simultaneous solutions of the gasdynamic equations and the vehicle's kinematic equations of motion are discussed. The modeling approach, when valid, eliminates the need for costly repetitive computation of flow field solutions. For the test cases considered, the aerodynamic modeling approach is shown to be valid

The role of time-history effects in the formulation of the aerodynamics of aircraft dynamics

The scope of any aerodynamic formulation proposing to embrace a range of possible maneuvers is shown to be determined principally by the extent to which the aerodynamic indicial response is allowed to depend on the past motion. Starting from the linearized formulation, in which the indicial response is independent of the past motion, two successively more comprehensive statements about the dependence on the past motion are assigned to the indicial response: (1) dependence only on the recent past and (2) dependence additionally on a characteristic feature of the distant past. The first enables the rational introduction of nonlinear effects and accommodates a description of the rate dependent aerodynamic phenomena characteristic of airfoils in low speed dynamic stall; the second permits a description of the double valued aerodynamic behavior characteristic of certain kinds of aircraft stall. An aerodynamic formulation based on the second statement, automatically embracing the first, may be sufficiently comprehensive to include a large part of the aircraft's possible maneuvers. The results suggest a favorable conclusion regarding the role of dynamic stability experiments in flight dynamics studies

Numerical simulation of steady supersonic flow

A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques

Aerodynamic characteristics of the standard dynamics model in coning motion at Mach 0.6

A wind tunnel test was conducted on the Standard Dynamics Model (a simplified generic fighter aircraft shape) undergoing coning motion at Mach 0.6. Six component force and moment data are presented for a range of angle of attack, sideslip, and coning rates. At the relatively low non-dimensional coning rate employed (omega b/2V less than or equal to 0.04), the lateral aerodynamic characteristics generally show a linear variation with coning rate

On the formulation of the aerodynamic characteristics in aircraft dynamics

The theory of functionals is used to reformulate the notions of aerodynamic indicial functions and superposition. Integral forms for the aerodynamic response to arbitrary motions are derived that are free of dependence on a linearity assumption. Simplifications of the integral forms lead to practicable nonlinear generalizations of the linear superpositions and stability derivative formulations. Applied to arbitrary nonplanar motions, the generalization yields a form for the aerodynamic response that can be compounded of the contributions from a limited number of well-defined characteristic motions, in principle reproducible in the wind tunnel. Further generalizations that would enable the consideration of random fluctuations and multivalued aerodynamic responses are indicated

Feasibility study for a secondary Na/S battery

The feasibility of a moderate temperature Na battery was studied. This battery is to operate at a temperature in the range of 100-150 C. Two kinds of cathode were investigated: (1) a soluble S cathode consisting of a solution of Na2Sn in an organic solvent and (2) an insoluble S cathode consisting of a transition metal dichalcogenide in contact with a Na(+)ion conducting electrolyte. Four amide solvents, dimethyl acetamide, diethyl acetamide, N-methyl acetamide and acetamide, were investigated as possible solvents for the soluble S cathode. Results of stability and electrochemical studies using these solvents are presented. The dialkyl substituted amides were found to be superior. Although the alcohol 1,3-cyclohexanediol was found to be stable in the presence of Na2Sn at 130 C, its Na2Sn solutions did not appear to have suitable electrochemical properties

Mathematical modeling of the aerodynamic characteristics in flight dynamics

Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated

Quantifying the Effect of Non-Larmor Motion of Electrons on the Pressure Tensor

In space plasma, various effects of magnetic reconnection and turbulence cause the electron motion to significantly deviate from their Larmor orbits. Collectively these orbits affect the electron velocity distribution function and lead to the appearance of the "non-gyrotropic" elements in the pressure tensor. Quantification of this effect has important applications in space and laboratory plasma, one of which is tracing the electron diffusion region (EDR) of magnetic reconnection in space observations. Three different measures of agyrotropy of pressure tensor have previously been proposed, namely, $A\varnothing_e$, $D_{ng}$ and $Q$. The multitude of contradictory measures has caused confusion within the community. We revisit the problem by considering the basic properties an agyrotropy measure should have. We show that $A\varnothing_e$, $D_{ng}$ and $Q$ are all defined based on the sum of the principle minors (i.e. the rotation invariant $I_2$) of the pressure tensor. We discuss in detail the problems of $I_2$-based measures and explain why they may produce ambiguous and biased results. We introduce a new measure $AG$ constructed based on the determinant of the pressure tensor (i.e. the rotation invariant $I_3$) which does not suffer from the problems of $I_2$-based measures. We compare $AG$ with other measures in 2 and 3-dimension particle-in-cell magnetic reconnection simulations, and show that $AG$ can effectively trace the EDR of reconnection in both Harris and force-free current sheets. On the other hand, $A\varnothing_e$ does not show prominent peaks in the EDR and part of the separatrix in the force-free reconnection simulations, demonstrating that $A\varnothing_e$ does not measure all the non-gyrotropic effects in this case, and is not suitable for studying magnetic reconnection in more general situations other than Harris sheet reconnection.Comment: accepted by Phys. of Plasm

Corrections to Fermi's Golden Rule in ϕ→KKˉ\phi \to K\bar{K} Decays

We analyze the decays $\phi \to K\bar{K}$ utilizing a formulation of transition rates which explicitly exhibits corrections to Fermi's Golden Rule. These corrections arise in systems in which the phase space and/or matrix element varies rapidly with energy, as happens in $\phi \to K\bar{K}$, which is just above threshold. We show that the theoretical corrections resolve a puzzling $5\sigma$ discrepancy between theory and experiment for the branching ratio $R = \Gamma (\phi \to K^+K^-)/\Gamma(\phi \to K^0\bar{K}^0)$

Loop Groups and Discrete KdV Equations

A study is presented of fully discretized lattice equations associated with the KdV hierarchy. Loop group methods give a systematic way of constructing discretizations of the equations in the hierarchy. The lattice KdV system of Nijhoff et al. arises from the lowest order discretization of the trivial, lowest order equation in the hierarchy, b_t=b_x. Two new discretizations are also given, the lowest order discretization of the first nontrivial equation in the hierarchy, and a "second order" discretization of b_t=b_x. The former, which is given the name "full lattice KdV" has the (potential) KdV equation as a standard continuum limit. For each discretization a Backlund transformation is given and soliton content analyzed. The full lattice KdV system has, like KdV itself, solitons of all speeds, whereas both other discretizations studied have a limited range of speeds, being discretizations of an equation with solutions only of a fixed speed.Comment: LaTeX, 23 pages, 1 figur