591 research outputs found
Minimizing Induced Drag with Weight Distribution, Lift Distribution, Wingspan, and Wing-Structure Weight
Because the wing-structure weight required to support the critical wing section bending moments is a function of wingspan, net weight, weight distribution, and lift distribution, there exists an optimum wingspan and wing-structure weight are presented for rectangular wings with four different sets of design constraints. These design constraints are fixed lift distribution and net weight combined with 1) fixed maximum stress and wing loading, 2) fixed maximum deflection and wing loading, 3) fixed maximum stress and stall speed and 4) fixed maximum deflection and stall speed. For each of these analytic solutions, the optimum wing-structure weight is found to depend only on the net weight, independent of the arbitrary fixed lift distribution. Analytic solutions for optimum weight and lift distributions are also presented for the same four sets of design constraints. Depending on the design constraints, the optimum lift distribution can differ significantly from the elliptic lift distribution. Solutions for two example wing designs are presented, which demonstrate how the induced drag varies with lift distribution, wingspan, and wing-structure weight in the design space near the optimum solution. Although the analytic solutions presented here are restricted to rectangular wings, these solutions provide excellent test cases for verifying numerical algorithms used for more general multidisciplinary analysis and optimization
Comparison of Theoretical and High-Fidelity Aerostructural Solutions
As contemporary aerostructural research in aircraft design trends toward high-fidelity computational methods, aerostructural solutions based on theory are often neglected or forgotten. In fact, in many modern aerostructural wing optimization studies, the elliptic lift distribution is used as a benchmark in place of theoretical aerostructural solutions with more appropriate constraints. In this paper, we review several theoretical aerostructural solutions that could be used as benchmark cases for wing design studies, and we compare them to high-fidelity solutions with similar constraints. Solutions are presented for studies with 1) constraints related to the wing integrated bending moment, 2) constraints related to the wing root bending moment, and 3) structural constraints combined with constraints on either wing stall or wing loading. It is shown that for each set of design constraints, the theoretical optimum lift distribution consistently shows excellent agreement with high-fidelity results. It follows that theoretical optimum lift distributions can often serve as a good benchmark for higher fidelity aerostructural wing optimization methods. Moreover, a review of solutions for the optimum wingspan and corresponding drag reveals important insights into the effects of viscosity, aeroelasticity, and compressibility on the aerodynamic and structural coupling involved in wing design and optimization
Minimum Induced Drag for Tapered Wings Including Structural Constraints
For a wing in steady level flight, the lift distribution that minimizes induced drag depends on a tradeoff between wingspan and wing-structure weight. In 1933, Prandtl suggested that tapered wings have an advantage over rectangular wings due to this tradeoff. However, Prandtlâs solutions were obtained using assumptions that correspond to rectangular wings. Therefore, his claim was not analytically proven by his 1933 publication. Here, an approach similar to Prandtlâs is taken with more general approximations that apply to wings of arbitrary planform. This more general development is used to study Prandtlâs claim about tapered wings. Closed-form solutions for the optimum wingspan and corresponding induced drag are presented for wings having elliptic and linearly-tapered planforms with constraints of fixed wing loading and maximum stress. It is shown that induced drag is minimized with a triangular planform, which gives a reduction in induced drag of up to 24.44% over the rectangular planform and up to 11.71% over the elliptic planform. Numerical solutions for the lift distributions that minimize induced drag for each planform are also presented. It is shown that the optimum lift distribution produces up to 5.94% less induced drag than the elliptic lift distribution when the triangular planform is used
Numerical Method for Rapid Aerostructural Design and Optimization
During early phases of wing design, analytic and low-fidelity methods are often used to identify promising design concepts. In many cases, solutions obtained using these methods provide intuition about the design space that is not easily obtained using higher-fidelity methods. This is especially true for aerostructural design. However, many analytic and low-fidelity aerostructural solutions are limited in application to wings with specific planforms and weight distributions. Here, a numerical method for minimizing induced drag with structural constraints is presented that uses approximations that apply to wings with arbitrary planforms and weight distributions. The method is applied to the NASA Ikhana airframe to show how it can be used for rapid aerostructural optimization and design-space exploration. The design space around the optimum solution is visualized, and the sensitivity of the optimum solution to changes in weight distribution, structural properties, wing loading, and taper ratio is shown. The optimum lift distribution and wing-structure weight for the Ikhana airframe are shown to be in good agreement with analytic solutions. Whereas most modern high-fidelity solvers obtain solutions in a matter of hours, all of the solutions shown here can be obtained in a matter of seconds
Two-Dimensional Hydrodynamics of Pre-Core Collapse: Oxygen Shell Burning
By direct hydrodynamic simulation, using the Piecewise Parabolic Method (PPM)
code PROMETHEUS, we study the properties of a convective oxygen burning shell
in a SN 1987A progenitor star prior to collapse. The convection is too
heterogeneous and dynamic to be well approximated by one-dimensional
diffusion-like algorithms which have previously been used for this epoch.
Qualitatively new phenomena are seen.
The simulations are two-dimensional, with good resolution in radius and
angle, and use a large (90-degree) slice centered at the equator. The
microphysics and the initial model were carefully treated. Many of the
qualitative features of previous multi-dimensional simulations of convection
are seen, including large kinetic and acoustic energy fluxes, which are not
accounted for by mixing length theory. Small but significant amounts of
carbon-12 are mixed non-uniformly into the oxygen burning convection zone,
resulting in hot spots of nuclear energy production which are more than an
order of magnitude more energetic than the oxygen flame itself. Density
perturbations (up to 8%) occur at the `edges' of the convective zone and are
the result of gravity waves generated by interaction of penetrating flows into
the stable region. Perturbations of temperature and electron fraction at the
base of the convective zone are of sufficient magnitude to create angular
inhomogeneities in explosive nucleosynthesis products, and need to be included
in quantitative estimates of yields. Combined with the plume-like velocity
structure arising from convection, the perturbations will contribute to the
mixing of nickel-56 throughout supernovae envelopes. Runs of different
resolution, and angular extent, were performed to test the robustness of theseComment: For mpeg movies of these simulations, see
http://www.astrophysics.arizona.edu/movies.html Submitted to the
Astrophysical Journa
Probing Solar Convection
In the solar convection zone acoustic waves are scattered by turbulent sound
speed fluctuations. In this paper the scattering of waves by convective cells
is treated using Rytov's technique. Particular care is taken to include
diffraction effects which are important especially for high-degree modes that
are confined to the surface layers of the Sun. The scattering leads to damping
of the waves and causes a phase shift. Damping manifests itself in the width of
the spectral peak of p-mode eigenfrequencies. The contribution of scattering to
the line widths is estimated and the sensitivity of the results on the assumed
spectrum of the turbulence is studied. Finally the theoretical predictions are
compared with recently measured line widths of high-degree modes.Comment: 26 pages, 7 figures, accepted by MNRA
Large-scale instability in a sheared nonhelical turbulence: formation of vortical structures
We study a large-scale instability in a sheared nonhelical turbulence that
causes generation of large-scale vorticity. Three types of the background
large-scale flows are considered, i.e., the Couette and Poiseuille flows in a
small-scale homogeneous turbulence, and the "log-linear" velocity shear in an
inhomogeneous turbulence. It is known that laminar plane Couette flow and
antisymmetric mode of laminar plane Poiseuille flow are stable with respect to
small perturbations for any Reynolds numbers. We demonstrate that in a
small-scale turbulence under certain conditions the large-scale Couette and
Poiseuille flows are unstable due to the large-scale instability. This
instability causes formation of large-scale vortical structures stretched along
the mean sheared velocity. The growth rate of the large-scale instability for
the "log-linear" velocity shear is much larger than that for the Couette and
Poiseuille background flows. We have found a turbulent analogue of the
Tollmien-Schlichting waves in a small-scale sheared turbulence. A mechanism of
excitation of turbulent Tollmien-Schlichting waves is associated with a
combined effect of the turbulent Reynolds stress-induced generation of
perturbations of the mean vorticity and the background sheared motions. These
waves can be excited even in a plane Couette flow imposed on a small-scale
turbulence when perturbations of mean velocity depend on three spatial
coordinates. The energy of these waves is supplied by the small-scale sheared
turbulence.Comment: 12 pages, 14 figures, Phys. Rev. E, in pres
Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation
We introduce an alternative to the method of matched asymptotic expansions.
In the "traditional" implementation, approximate solutions, valid in different
(but overlapping) regions are matched by using "intermediate" variables. Here
we propose to match at the level of the equations involved, via a "uniform
expansion" whose equations enfold those of the approximations to be matched.
This has the advantage that one does not need to explicitly solve the
asymptotic equations to do the matching, which can be quite impossible for some
problems. In addition, it allows matching to proceed in certain wave situations
where the traditional approach fails because the time behaviors differ (e.g.,
one of the expansions does not include dissipation). On the other hand, this
approach does not provide the fairly explicit approximations resulting from
standard matching. In fact, this is not even its aim, which to produce the
"simplest" set of equations that capture the behavior
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