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Strong vortex/boundary layer interactions. I - Vortices high

Detailed measurements with hot-wires and pressure probes are presented for the interaction between a turbulent longitudinal vortex pair with 'common flow' down, and a turbulent boundary layer. The interaction has a larger value of the vortex circulation parameter, and therefore better represents many aircraft/vortex interactions, than those studied previously. The vortices move down towards the boundary layer, but only the outer parts of the vortices actually enter it. Beneath the vortices the boundary layer is thinned by lateral divergence to the extent that it almost ceases to grow. Outboard of the vortices the boundary layer is thickened by lateral convergence. The changes in turbulence structure parameters in the boundary layer appear to be due to the effects of 'extra-rate-of-strain' produced by lateral divergence (or convergence) and by free-stream turbulence. The effect of the interaction on the vortices (other than the inviscid effect of the image vortices below the surface) is small. The flow constitutes a searching test case for prediction methods for three-dimensional turbulent flows.

Cutler, A. D.↗

Application of Circulation Control Technology to Airframe Noise Reduction

This report is a summary of the work performed by Georgia Tech Research Institute (GTRI) under NASA Langley Grant NAG-1-2146, which was awarded as a part of NASA's Breakthrough Innovative Technologies (BIT) initiative. This was a three-year program, with a one-year no-cost extension. Each year's study has been an integrated effort consisting of computational fluid dynamics, experimental aerodynamics, and detailed noise and flow measurements. Year I effort examined the feasibility of reducing airframe noise by replacing the conventional wing systems with a Circulation Control Wing (CCW), where steady blowing was used through the trailing edge of the wing over a Coanda surface. It was shown that the wing lift increases with CCW blowing and indeed for the same lift, a CCW wing was shown to produce less noise. Year 2 effort dealt with a similar study on the role of pulsed blowing on airframe noise. The main objective of this portion of the study was to assess whether pulse blowing from the trailing edge of a CCW resulted in more, less, or the same amount of radiated noise to the farfield. Results show that a reduction in farfield noise of up to 5 dB is measured when pulse flow is compared with steady flow for an equivalent lift configuration. This reduction is in the spectral region associated with the trailing edge jet noise. This result is due to the unique advantage that pulsed flow has over steady flow. For a range of frequencies, more lift is experienced with the same mass flow as the steady case. Thus, for an equivalent lift and slot height, the pulsed system can operate at lower jet velocities, and hence lower jet noise. The computational analysis showed that for a given time-averaged mass flow rate, pulsed jets give a higher value of C(sub l) and a higher L/D than equivalent steady jets. This benefit is attributable to higher instantaneous jet velocities, and higher instantaneous C(sub mu) values for the pulsed jet. Pulsed jet benefits increase at higher frequencies. However, these advantages are somewhat offset by the unsteadiness in the loads, which will cause structural vibrations and fatigue. Additional studies must be done, perhaps with multiple jets on the upper and lower surfaces, to smooth out the fluctuations in lift while retaining the benefits. The rest of the effort was devoted to examining ways of reducing flap edge noise by blowing air through a Coanda nozzle over a rounded tip of the flap. In this case, we were successful in moving the tip vortex away from the tip, but the device producing the blowing was noisy and we were unable to examine the noise benefits, although we believe that the movement of the tip vortex far from the tip should provide noise benefits. It should be noted that in an effort to understand the fluid dynamics and the aeroacoustics of a jet blowing over a Coanda surface, we also carried out a very extensive study of the high aspect ratio slot jets. A first-ever set of far-field noise spectra were measured for jets exhausting from slots with aspect ratios in the range 100 to 3000. Parallel measurements of velocity profiles, length scales and convection velocities were measured to understand the noise generation of high aspect ratio jets. Attempts were also made to develop jet noise prediction schemes for such jets. Much of the work done under this effort has been described in five conference papers and two doctoral theses. The first year s work on the use of steady blowing was described in two AIAA papers presented at the 2001 AIAA Aerospace Sciences Meeting in Reno. Subsequent work was presented at the 9th AIMCEAS Aeroacoustics Conference and Exhibit held at Hilton Head May 12-13. Another paper is to be presented at the 2004 AIAA Aerospace Sciences Meeting in Reno in January 2004. All six papers are included with this report as Appendices. The bulk of the experimental work done in an effort to produce a pulsed flow that is free of upstream noise is also attached as an Appendix.

Ahuja, K. K.↗

Observations on the structure of an edge-tone flowfield

The unsteady flowfield in the region in which a rectangular jet interacts with the leading edge of a 20-deg wedge is investigated experimentally. Edge-tone flowfields at Mach 0.8 in the blowdown facility at Stanford University are recorded by phase-locked Schlieren photography using the apparatus and techniques described by Krothapalli and Horne (1984); detailed surface-pressure and velocity measurements are obtained at Mach 0.23 in the NASA Ames anechoic-chamber facility and presented graphically. It is shown that the jet-edge interaction produces a secondary vortex at the leading edge when an established shear layer or primary vortex is present, and that the primary and secondary vortices then evolve from a counterrotating vortex pair to a large single vortex which migrates along the wedge surface (in agreement with the observations of Rockwell et al., 1986). From a comparison with data on airfoil-trailing-edge flows (Satyanarayana, 1977) it is inferred that an instantaneous zero pressure differential is present at the leading edge of the wedge.

Krothapalli, A.↗

Review: knots and other new topological effects in liquid crystals and colloids

Abstract Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.

Physics↗

Control of forebody three-dimensional flow separations

Some experiments involving the development of the turbulent symmetric vortex flow about the lee side of a 5 deg semiangle conical forebody at high relative incidence are discussed. The cone was immersed in a Mach 0.6 airstream at a Reynolds number of 13.5 million based on the 1.4 - m axial length of the cone. Novel means of controlling the degree of asymmetry using blowing very close to the nose were investigated. Small amounts of air injected normally or tangentially to the cone surface, but on one side of the leeward meridian and beneath the vortex farthest from the wall, were effective in biasing the asymmetry. With this reorientation of the forebody vortices, the amplitude of the side force could be reduced to the point where its direction was reversed. This phenomenon could be obtained either by changing the blowing rate at constant incidence or by changing incidence at constant blowing rate. Normal injection was more effective than tangential injection. An organized and stable flow structure emerged with the jet vortices positioned above the forebody vortices.

Peake, D. J.↗

Smoke Generator For Studies Of Vortices In Flight

Smoke-generating system used to identify vortex-core and vortex-core-breakdown locations in flights. Housed in forebody of airplane, includes multiple pyrotechnic smoke cartridges fired simultaneously or in sequence. Firing of cartridges controlled from cockpit, and smoke produced ducted to desired locations on or near surface of aircraft. Useful for other aerodynamic flight research in which necessary to visualize local flows. Nonaerospace applications include research in reduction of aerodynamic drag on vehicles and reduction of turbulence related to structures or other obstacles.

Richwine, David M.↗

The Science Behind the NASA/NOAA Electronic Theater 2002

Details of the science stories and scientific results behind the Etheater Earth Science Visualizations from the major remote sensing institutions around the country will be explained. The NASA Electronic Theater presents Earth science observations and visualizations in a historical perspective. Fly in from outer space to Temple Square and the University of Utah Campus. Go back to the early weather satellite images from the 1960s see them contrasted with the latest US/Europe/Japan global weather data. See the latest images and image sequences from NASA & NOAA missions like Terra, GOES, NOAA, TRMM, SeaWiFS, Landsat 7 visualized with state-of-the art tools. A similar retrospective of numerical weather models from the 1960s will be compared with the latest "year 2002" high-resolution models. See the inner workings of a powerful hurricane as it is sliced and dissected using the University of Wisconsin Vis-5D interactive visualization system. The largest super computers are now capable of realistic modeling of the global oceans. See ocean vortexes and currents that bring up the nutrients to feed phitoplankton and zooplankton as well as draw the crill fish, whales and fisherman. See the how the ocean blooms in response to these currents and El Nino/La Nina climate regimes. The Internet and networks have appeared while computers and visualizations have vastly improved over the last 40 years. These advances make it possible to present the broad scope and detailed structure of the huge new observed and simulated datasets in a compelling and instructive manner. New visualization tools allow us to interactively roam & zoom through massive global images larger than 40,000 x 20,000 pixels. Powerful movie players allow us to interactively roam, zoom & loop through 4000 x 4000 pixel bigger than HDTV movies of up to 5000 frames. New 3D tools allow highly interactive manipulation of detailed perspective views of many changing model quantities. See the 1m resolution before and after shots of lower Manhattan and the Pentagon after the September 11 disaster as well as shots of Afghanistan from the Space Imaging IKONOS as well as debris plume images from Terra MODIS and SPOT Image. Shown by the SGI-Octane Graphics-Supercomputer are visualizations of hurricanes Michelle 2001, Floyd, Mitch, Fran and Linda. Our visualizations of these storms have been featured on the covers of the National Geographic, Time, Newsweek and Popular Science. Highlights will be shown from the NASA's large collection of High Definition TV (HDTV) visualizations clips New visualizations of a Los Alamos global ocean model, and high-resolution results of a NASA/JPL Atlantic ocean basin model showing currents, and salinity features will be shown. El Nino/La Nina effects on sea surface temperature and sea surface height of the Pacific Ocean will also be shown. The SST simulations will be compared with GOES Gulf Stream animations and ocean productivity observations. Tours will be given of the entire Earth's land surface at 500 m resolution from recently composited Terra MODIS data, Visualizations will be shown from the Earth Science Etheater 2001 recently presented over the last years in New Zealand, Johannesburg, Tokyo, Paris, Munich, Sydney, Melbourne, Honolulu, Washington, New York City, Pasadena, UCAR/Boulder, and Penn State University. The presentation will use a 2-CPU SGI/CRAY Octane Super Graphics workstation with 4 GB RAM and terabyte disk array at 2048 x 768 resolution plus multimedia laptop with three high resolution projectors. Visualizations will also be featured from museum exhibits and presentations including: the Smithsonian Air & Space Museum in Washington, IMAX theater at the Maryland Science Center in Baltimore, the James Lovell Discovery World Science museum in Milwaukee, the American Museum of Natural History (NYC) Hayden Planetarium IMAX theater, etc. The Etheater is sponsored by NASA, NOAA and the American Meteorological Society. This presentation is brought to you by the University of Utah College of Mines and Earth Sciences and, the Utah Museum of Natural History.

Hasler, A. Fritz↗

The Effect of Predicted Vehicle Displacement on Ground Crew Task Performance and Hardware Design

NASA continues to explore new launch vehicle concepts that will carry astronauts to low- Earth orbit to replace the soon-to-be retired Space Transportation System (STS) shuttle. A tall vertically stacked launch vehicle (> or =300 ft) is exposed to the natural environment while positioned on the launch pad. Varying directional winds and vortex shedding cause the vehicle to sway in an oscillating motion. Ground crews working high on the tower and inside the vehicle during launch preparations will be subjected to this motion while conducting critical closeout tasks such as mating fluid and electrical connectors and carrying heavy objects. NASA has not experienced performing these tasks in such environments since the Saturn V, which was serviced from a movable (but rigid) service structure; commercial launchers are likewise attended by a service structure that moves away from the vehicle for launch. There is concern that vehicle displacement may hinder ground crew operations, impact the ground system designs, and ultimately affect launch availability. The vehicle sway assessment objective is to replicate predicted frequencies and displacements of these tall vehicles, examine typical ground crew tasks, and provide insight into potential vehicle design considerations and ground crew performance guidelines. This paper outlines the methodology, configurations, and motion testing performed while conducting the vehicle displacement assessment that will be used as a Technical Memorandum for future vertically stacked vehicle designs.

Atencio, Laura Ashley↗

Study of Near-Stall Flow Behavior in a Modern Transonic Fan with Composite Sweep

Detailed flow behavior in a modern transonic fan with a composite sweep is investigated in this paper. Both unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) methods are applied to investigate the flow field over a wide operating range. The calculated flow fields are compared with the data from an array of high-frequency response pressure transducers embedded in the fan casing. The current study shows that a relatively fine computational grid is required to resolve the flow field adequately and to calculate the pressure rise across the fan correctly. The calculated flow field shows detailed flow structure near the fan rotor tip region. Due to the introduction of composite sweep toward the rotor tip, the flow structure at the rotor tip is much more stable compared to that of the conventional blade design. The passage shock stays very close to the leading edge at the rotor tip even at the throttle limit. On the other hand, the passage shock becomes stronger and detaches earlier from the blade passage at the radius where the blade sweep is in the opposite direction. The interaction between the tip clearance vortex and the passage shock becomes intense as the fan operates toward the stall limit, and tip clearance vortex breakdown occurs at near-stall operation. URANS calculates the time-averaged flow field fairly well. Details of measured RMS static pressure are not calculated with sufficient accuracy with URANS. On the other hand, LES calculates details of the measured unsteady flow features in the current transonic fan with composite sweep fairly well and reveals the flow mechanism behind the measured unsteady flow field.

Hah, Chunill↗

The structure and dynamics of reacting plane mixing layers

Experimental studies of the combusting mixing layers formed over a rearward facing step and between two parallel streams are reported. The steady behavior of the mean properties of the reacting flows is similar to that of nonreacting flows except for the global effects of thermodynamic property changes. Vortices form by the two-dimensional K-H instability and grow by subharmonic combination until the layer begins to interact with the walls. Unsteady behavior occurs when there are resonator interactions with the K-H instability or the instability associated with the recirculation vortex in the rearward facing step flow.

Keller, J. O.↗

Angular fractals in thermal QFT

We show that thermal effective field theory controls the long-distance expansion of the partition function of a d-dimensional QFT, with an insertion of any finite-order spatial isometry. Consequently, the thermal partition function on a sphere displays a fractal-like structure as a function of angular twist, reminiscent of the behavior of a modular form near the real line. As an example application, we find that for CFTs, the effective free energy of even-spin minus odd-spin operators at high temperature is smaller than the usual free energy by a factor of 1/2 d . Near certain rational angles, the partition function receives subleading contributions from “Kaluza-Klein vortex defects” in the thermal EFT, which we classify. We illustrate our results with examples in free and holographic theories, and also discuss nonperturbative corrections from worldline instantons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Wind load analysis of a new linear Fresnel receiver assembly design

A linear Fresnel collector includes a low-profile reflector array and a receiver assembly with one or more absorber tubes and an optional secondary reflector. This combined optical system concentrates sunlight and converts it into thermal energy. The design of a receiver assembly is critical to the performance of a linear Fresnel collector. A position deviation of a few centimeters for the receiver assembly can result in notably reduced performance, thus leading to a direct loss in revenue associated with thermal power production. Wind load is one of the most significant environmental factors that can alter the optical - and therefore thermal - performance of a solar power system due to displacements after installation. At the same time, an over-designed receiver assembly may add unnecessary construction cost to a typically high-cost-constrained system. Thus, wind load analysis is particularly important when considering optimal engineering design of a receiver assembly and its supporting structure to cost-effectively mitigate the impacts of wind. In this study, a detailed computational fluid dynamics (CFD) model is adopted to derive the wind load of a commercial linear Fresnel receiver assembly. This wind load is then used as a reference to optimize the detailed engineering design. The CFD model is first carefully developed and benchmarked within a critical regime toward turbulence. The drag force, lift force, and vortex-shedding frequencies are derived at both the operating and survival wind-speed limits for target project deployment locations. The wind load analysis results provide a valuable reference for future engineering design and prototyping.

17 WIND ENERGY↗

The 3D flow field around an embedded planet

3D modifications to the well-studied 2D flow topology around an embedded planet have the potential to resolve long-standing problems in planet formation theory. We present a detailed analysis of the 3D isothermal flow field around a 5 Earth-mass planet on a fixed circular orbit, simulated using our graphics processing unit hydrodynamics code PEnGUIn. We find that, overall, the horseshoe region has a columnar structure extending vertically much beyond the Hill sphere of the planet. This columnar structure is only broken for some of the widest horseshoe streamlines, along which high altitude fluid descends rapidly into the planet’s Bondi sphere, performs one horseshoe turn, and exits the Bondi sphere radially in the midplane. A portion of this flow exits the horseshoe region altogether, which we refer to as the “transient” horseshoe flow. The flow continues as it rolls up into a pair of up–down symmetric horizontal vortex lines shed into the wake of the planet. This flow, unique to 3D, affects both planet accretion and migration. It prevents the planet from sustaining a hydrostatic atmosphere due to its intrusion into the Bondi sphere, and leads to a significant corotation torque on the planet, unanticipated by 2D analysis. In the reported simulation, starting with a Σ∼r{sup −3/2} radial surface density profile, this torque is positive and partially cancels with the negative differential Lindblad torque, resulting in a factor of three slower planet migration rate. Finally, we report 3D effects can be suppressed by a sufficiently large disk viscosity, leading to results similar to 2D.

79 ASTRONOMY AND ASTROPHYSICS↗

Stratospheric column NO2 measurements from three Antarctic sites

The significance of stratospheric odd-nitrogen compounds in Antarctic ozone depletion studies has prompted an increase in Antarctic activities. Although several species are being studied, work has concentrated on the acquisition of NO2 data. Ground-based measurements of stratospheric column NO2 have been made at Arrival Heights, Antarctica, since spring 1982, with some gaps in the data base. Additional data has been acquired since February 1986 at Pole Station and Halley Bay, thus providing a chain of stations across the continent. The technique used is that of absorption spectroscopy in several wavelength regions, although here only those measurements are reported in the 430 to 450 nm region where strongly structured absorption been determined experimentally. However, theory features due to NO2 are identified in scattered sunlight in the zenith sky. Operation of a moon-tracking system at Arrival Heights has provided some additional data during the polar night. Previous analyses have shown that the NO2 column observed from the ground is strongly influenced by the season, and by the location of the site with respect to that of the polar vortex. The column amount correlates strongly with stratospheric temperature at about 70 mbar. The present data set further illustrates these features, and demonstrates both the strengths and qualifications apparent in the technique.

Keys, J. G.↗

Head-on collision of viscous vortex rings

The head-on collision of two identical axisymmetric viscous vortex rings is studied through direct simulations of the incompressible Navier-Stokes equations. The initial vorticity distributions considered are those of Hill's spherical vortex and of rings with circular Gaussian cores, each at Reynolds numbers of about 350 and 1000. The Reynolds number is defined by Gamma/Nu, the ratio of circulation to viscosity. As the vortices approach each other by self-induction, the radii increase by mutual induction, and vorticy cancels through viscous cross-diffusion across the collision plane. Following contact, the vorticity distribution in the core forms a head-tail structure (for the cases considered). The characteristic time of vorticity annihilation is compared with that of a 3D collision experiment and 3D numerical simulations. It is found that the annihilation time is somewhat longer in the axisymmetric case than it is in the symmetry plane of the experiment and 3D numerical simulation. By comparing the annihilatiom time with a viscous timescale and a circulation timescale, it is deduced that both the strain rate due to local effects and to 3D vorticity realignment are important.

Stanaway, S.↗

Space Shuttle AFRSI OMS pod environment test using model 81-0 test fixture in the Ames Research Center 9x7-foot supersonic wind tunnel (OS-314A/B/C)

A test was conducted in the NASA/Ames Research Center 9x7-foot Supersonic Wind Tunnel to help resolve an anomaly that developed during the STS-6 orbiter flight wherein sections of the Advanced Flexible Reusable Surface Insulation (AFRSI) covering the OMS pods suffered some damage. A one-third scale two-dimensional shell structure model of an OMS pod cross-section was employed to support the test articles. These consisted of 15 AFRSI blanket panels form-fitted over the shell structures for exposure to simulated flight conditions. Of six baseline blankets, two were treated with special surface coatings. Two other panels were configured with AFRSI sections removed from the OV099 orbiter vehicle after the STS-6 flight. Seven additional specimens incorporated alternative designs and repairs. Following a series of surface pressure calibration runs, the specimens were exposed to simulated ascent and entry dynamic pressure profiles. Entry conditions included the use of a vortex generator to evaluate the effect of shed vortices on the AFRSI located in the area of concern.

Collette, J. G. R.↗

Discrete-vortex simulation of pulsating flow on a turbulent leading-edge separation bubble

Studies are made of the turbulent separation bubble in a two-dimensional semi-infinite blunt plate aligned to a uniform free stream with a pulsating component. The discrete-vortex method is applied to simulate this flow situation because this approach is effective for representing the unsteady motions of the turbulent shear layer and the effect of viscosity near the solid surface. The numerical simulation provides reasonable predictions when compared with the experimental results. A particular frequency with a minimum reattachment is related to the drag reduction. The most effective frequency is dependent on the amplified shedding frequency. The turbulent flow structure is scrutinized. This includes the time-mean and fluctuations of the velocity and the surface pressure, together with correlations between the fluctuating components. A comparison between the pulsating flow and the non-pulsating flow at the particular frequency of the minimum reattachment length of the separation bubble suggests that the large-scale vortical structure is associated with the shedding frequency and the flow instabilities.

Sung, Hyung Jin↗

Report of the Panel on Aerodynamics

Progress in aerodynamics over the past 50 years has been evidenced by the development of increasingly sophisticated and efficient flight vehicles throughout the flight spectrum. Advances have generally arisen in an evolutionary manner from experience gained in wind tunnel testing, flight testing, and improvements in analytical and computational capabilities. As a result of this evolutionary development, both military and commercial vehicles operate at a relatively high efficiency level. This observation plus the fact that airplanes have not changed appreciably in outward appearance over recent years has led some skeptics to conclude incorrectly that aerodynamics is a mature technology, with little to be gained from further developments in the field. It is of interest to note that progress in aerodynamics has occurred without a thorough understanding of the fundamental physics of flow, turbulence, vortex dynamics, and separated flow, for example. The present understanding of transition, turbulence, and boundary layer separation is actually very limited. However, these fundamental flow phenomena provide the key to reducing the viscous drag of aircraft. Drag reduction provides the greatest potential for increased flight efficiency from the standpoint of both saving energy and maximizing performance. Recent advances have led to innovative concepts for reducing turbulent friction drag by modifying the turbulent structure within the boundary layer. Further advances in this basic area should lead to methods for reducing skin friction drag significantly. The current challenges for military aircraft open entirely new fields of investigation for the aerodynamicist. The ability through very high speed information processing technology to totally integrate the flight and propulsion controls can permit an aircraft to fly with "complete abandon," avoiding departure, buffet, and other undesirable characteristics. To utilize these new control concepts, complex aerodynamic phenomena will have to be understood, predicted, and controlled. Current requirements for military aircraft include configuration optimization through a widened envelope from subsonic to supersonic and from low to high angles of attack. This task is further complicated by requirements for control of observables. These challenging new designs do not have the luxury of a large experimental data base from which to optimize for various parameter combinations. Consequently, there exists a strong need for better techniques, both experimental and computational, to permit design optimization in a complete sense.

Bradley, Richard G.↗