Raymond C. Maple

Pylon Fuel Injector Design for a Scramjet Combustor

Abstract : This paper covers the initial development of an in-stream fuel injector concept for a circular hydrocarbon scramjet combustor. Three scramjet fuel injection pylon configurations are established--a basic pylon, a ramp pylon, and an alternating wedge pylon. The first pylon configuration is a baseline. The latter two configurations introduce streamwise vorticity into the flow to increase mixing action. Operating conditions and design considerations are discussed and the fuel injector configurations are presented. A testing methodology relating flight conditions to cold flow conditions is addressed. Initial Computational Fluid Dynamic simulations without fuel injection are presented for a wind tunnel cold flow test point. Two parameters used for comparison among the pylons are axial vorticity generation and total pressure loss. It is found the ramp and alternating wedge pylons increase streamwise vorticity in the flow over the basic pylon. The alternating wedge pylon increases streamwise vorticity the most. It is also found the ramp and alternating wedge pylons result in slightly increased total pressure losses due to the induced streamwise vorticity.

Adaptive Harmonic Balance Solutions to Euler' s Equation

A new adaptive harmonic balance method is presented and applied to a variety of subsonic and supersonic onedimensional e owe elds containing strong moving shocks. The adaptive method augments the frequency content in each cell as required to capture the local e ow physics. Augmentation automatically adjusts with grid density, resulting in lower frequency content on coarse grids that cannot adequately resolve high-frequency terms. A study of the effect of augmentation thresholds, increments, and scheduling on the performance and accuracy of the adaptive method is presented, and optimal parameters identie ed. When optimal parameters are used, the new adaptive harmonic balancemethod produces solutions equivalent to a nonadapted harmonic balance solution, but with up to a 50% reduction in run time.

Uncertainty Quantification with a B-Spline Stochastic Projection

Presented is a new stochastic algorithm for computing the probability density functions and estimating bifurcations of nonlinear equations of motion whose system parameters are characterized by a Gaussian distribution. Polynomial and Fourier chaos expansions, which are spectral methods, have been used successfully to propagate parametric uncertainties in nonlinear systems. However, it is shown that bifurcations in the time domain are manifested as discontinuities in the stochastic domain, which are problematic for solution with these spectral approaches. Because of this, a new algorithm is introduced based on the stochastic projection method but employing a multivariate B spline. Samples are obtained by choosing nodes on the stochastic axes. These samples are used to build an interpolating function in the stochastic domain. Monte Carlo simulations are then very efficiently performed on this interpolating function to estimate probability density functions of a response. The results from this nonintrusive and non-Galerkin approach are in excellent agreement with Monte Carlo simulations of the governing equations, but at a computational cost 2 orders of magnitude less than a traditional Monte Carlo approach. The probability density functions obtained from the stochastic algorithm provide a rapid estimate of the probability of failure for a nonlinear pitch and plunge airfoiL.

Computational Aeroelastic Analysis of Micro Air Vehicle With Experimentally Determined Modes

This paper presents the results of a combined computational and experimental aeroelastic analysis of a Micro Air Vehicle. This MAV has a 24 inch wing span, and is designed for local area reconnaissance. The fuselage and leading edge of the wings are made of carbon flber, with nylon parachute material spanned by carbon flber ribs making up the rest of the wing. Wind tunnel data for the MAV with a rigid carbon flber wing and a ∞exible carbon flber ribbed nylon wing are used to validate the computational approach. The general aeroelastic algorithm consists of coupling a structural model based on experimentally determined mode shapes and a conventional deforming grid CFD solution. The mode shapes used in the structural model are measured using laser vibrometry on the harmonically excited vehicle. The aeroelastic algorithm is used to calculate static structural deformations coupled with a steady ∞ow solution, as well as the dynamic structural response coupled with a time accurate ∞ow solution. Quantitative comparisons of the statically deformed results are made with wind-tunnel testing, and a qualitative analysis of the dynamic response is also presented.

Computational Aeroelastic Analysis of Store-Induced Limit-Cycle Oscillation

Limit-cycle oscillation was simulated for a rectangular wing referred to as the Goland + wing. It was found that the aerodynamic nonlinearity responsible for limit-cycle oscillation in the Goland + wing was shock motion and the periodic appearance/disappearance of shocks. The Goland + structural model was such that in the transonic flutter dip region, the primary bending and twisting modes were in phase and coupled to produce a single-degree-of-freedom, torsional flutter mode about a point located ahead of the leading edge of the wing. It was determined that the combination of strong trailing-edge and lambda shocks which periodically appear/disappear, limited the energy flow into the structure. This mechanism quenched the growth of the flutter, resulting in a steady limit-cycle oscillation. Underwing and tip stores were added to the Goland + wing to determine how they affected limit-cycle oscillation. It was found that the aerodynamic forces on the store transferred additional energy into the structure increasing the amplitude of the limit-cycle oscillation. However, it was also found that the underwing store interfered with the airflow on the bottom of the wing, which limited the amplitude of the limit-cycle oscillation.

Split-domain harmonic balance solutions to Burger's equation for large-amplitude disturbances

A new split-domain harmonic balance approach is presented. The split-domain approach combines the conventional multidomain harmonic balance approach with a split-operator technique in a unique way to solve periodic unsteady e ow problems efe ciently. The new technique is applied to Burger’ s equation to obtain solutions for two large-amplitude periodic boundary conditions— a single-frequency sine wave and a simulated wake function. Solutions containing strong moving discontinuities are obtained with Fourier series containing up to 48 frequencies for various grid densities. The split-domain harmonic balance solutions are compared with conventional time-accurate solutions. The differences between the two are found to be asymptotic with respect to the number of Fourierfrequenciesincluded.In addition, theharmonicbalanceapproachwasfound to besensitiveto grid density.

Predicting Uncertainty Propagation in a Highly Nonlinear System with a Stochastic Projection Method

Presented is a new stochastic algorithm for computing the probability distribution functions and bifurcation diagrams of highly nonlinear equations of motion whose input parameters are characterized by a Gaussian distribution. It is shown that bifurcations in the time domain are manifested as discontinuities in the stochastic domain, which are problematic for solution with a traditional polynomial chaos expansion approach. Because of this, a new algorithm is introduced based on the stochastic projection method but employing a multivariate B-spline. Samples are obtained by choosing nodes on the stochastic axes. These samples are used to build an interpolating function in the stochastic domain on which Monte Carlo simulations are performed. This non-intrusive, non-Galerkin approach produces results that are in excellent agreement with Monte Carlo simulations of the governing equations but at a computational cost two orders of magnitude less than a traditional Monte Carlo approach.

The Role of Viscosity in Store-Induced Limit-Cycle Oscillation

Aircraft with stores can exhibit an aeroelastic phenomenon characterized by limited amplitude, self-sustaining oscillations produced by aerodynamic-structure interactions known as limit-cycle oscillation. In order to study this phenomenon, a first order accurate code has been developed to interface a modal structural model with a commercial, parallel, Navier-Stokes fluid solver with a deforming grid capability. The commercial solver chosen was FLUENT 6.1 by FLUENT Inc. Initial testing of this code has been completed on the Goland+ and AGARD 445.6 wings. Limit-cycle oscillation was successfully obtained with the Goland+ wing. Grid refinement was found to slightly decrease the oscillating frequency. The Spalart-Allmaras turbulence model was used in one Goland+ test case. However, due to the length of the run times, conclusions can not yet be drawn. A tip store and underwing stores were successfully added to the Goland+ wing. These stores did not affect the limit-cycle oscillation. The code was also used to get a preliminary look at a documented F-16C limit-cycle oscillation flight test scenario.

Estimating the Probability of Failure of a Nonlinear Aeroelastic System

A limit-cycle oscillation (LCO) can be characterized by a subcritical or supercritical bifurcation, and bifurcations are shown to be discontinuities in the stochastic domain. The traditional polynomial-chaos-expansion method, which is a stochastic projection method, is too inefficient for estimating the LCO response surface because of the discontinuities associated with bifurcations. The objective of this research is to extend the stochastic projection method to include the construction of B-spline surfaces in the stochastic domain. The multivariate B-spline problem is solved to estimate the LCO response surface. A Monte Carlo simulation (MCS) is performed on this response surface to estimate the probability density function (PDF) of the LCO response. The stochastic projection method via B-splines is applied to the problem of estimating the PDF of a subcritical LCO response of a nonlinear airfoil in inviscid transonic flow. A probability of failure based upon certain failure criteria can then be computed from the estimated PDF. The stochastic algorithm provides a conservative estimate of the probability of failure of this aeroelastic system two orders of magnitude more efficiently than performing an MCS on the governing equations.

Examining the Influence of Structural Flexibility on Flapping Wing Propulsion

Abstract : The influence of structural deformations on the aerodynamic response of a flapping wing configuration was examined using Navier-Stokes based simulation. Two deformation modes, torsion and bending, were considered for an elastic axis along the leading edge of the wing. Both deformation modes influence the velocity and acceleration profile of the wing surface, altering the unsteady aerodynamic phenomena produced by the dynamic wing motion. The spanwise feathering rotation, or torsional response, alters the motion of the wing near the wing root. This variation in the acceleration profile influences the non-circulatory aerodynamic response and the local wake structures produced near the wing root during pronation and supination. Increased lifting forces and enhanced aerodynamic efficiencies were observed for a moderate increase in torsional exibility. Peak bending deformations near the wing tip also occur during pronation and supination, altering the velocity and acceleration profiles of the wing as the circulatory aerodynamic phenomena undergo a transition as the wing changes direction of motion. Because of the timing of the bending deformations, small tip deformations may have a significant influence on overall aerodynamic performance.