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At least 541 records · Page 30

Parabolized Navier-Stokes solutions of separation and trailing-edge flows

A robust, iterative solution procedure is presented for the parabolized Navier-Stokes or higher order boundary layer equations as applied to subsonic viscous-inviscid interaction flows. The robustness of the present procedure is due, in part, to an improved algorithmic formulation. The present formulation is based on a reinterpretation of stability requirements for this class of algorithms and requires only second order accurate backward or central differences for all streamwise derivatives. Upstream influence is provided for through the algorithmic formulation and iterative sweeps in x. The primary contribution to robustness, however, is the boundary condition treatment, which imposes global constraints to control the convergence path. Discussed are successful calculations of subsonic, strong viscous-inviscid interactions, including separation. These results are consistent with Navier-Stokes solutions and triple deck theory.

Brown, J. L.↗

Enhancing Adhesion: Relative Merits of Different Approaches

Adhesive performance is improved mainly by manipulation of the bimaterials interface zone, which is only a few molecules thick. There are three approaches to enhancement of interfacial adhesion at the molecular level. They are 1) changing the nonchemically bonded interactions across the interface from weak ones to strong ones, 2) making the true interfacial area much larger than the simple geometric area, and 3) inducing chemical bonding between the two materials forming the interface. Our goal this summer was to question some of the built-in assumptions contained within these approaches and to determine the most promising approach, both theoretically and practically, for enhancing adhesion in NASA structures. Our computations revealed that all three of these approaches have, in theory, the potential to enhance molecular adhesion approximately ten-fold. Experiments, however, revealed that this excellent level of enhancement is not likely to be reached in practice. Each approach was found to be severely limited by practical problems. In addition, some of the built-in assumptions associated with these approaches were found to be insufficient or inadequate. The first approach, changing the nonchemically bonded interactions from weak to strong, Is an example of one containing inadequate assumptions. The extensive literature on intermolecular interactions, based on solution studies, shows that certain functional group pairs interact much more strongly than others. It has always been assumed that these data can be reliably extended to systems where only one member of the pair is in solution and the other Is contained in a solid surface. Our experiments this summer demonstrated that solution data do not adequately predict the strength of functional group interaction at the solid-liquid interface. Furthermore, the strong solvents needed to dissolve the monomers or polymers to which the functional groups of interest are attached compete successfully with the solid surface for the functional group. As a result, functional groups in solution cannot pair with the complementary groups in the solid surface, and the expected enhancement of nonchemically bonded interactions is not realized. The second approach, increasing the true interfacial area, is an example of one containing inadequate assumptions and suffering from numerous practical problems. First, practitioners have assumed that material removal, such as bead blasting or etching, increases true surface area (and therefore interfacial area) in a meaningful way. Our geometric analysis demonstrated that removal methods increase area by a factor of two at most. To increase interfacial area by an order of magnitude or more. a thin layer of high porosity must be added to the substrate surface prior to application of the adhesive phase. Consistent with this finding, we attempted to create a thin layer of rigid, highly porous glass on the surface of our smooth glass substrate by means of sol-gel technology. We were unable to surmount a wide variety of practical problems and obtained only collapsed, nonporous layers. Thus this approach, appealing in principle, would require long term development and is not promising in the near term. The third approach, inducing chemical bonding at the interface, is an example of one having neither inadequate assumptions nor insurmountable practical problems. When silicate glass is the substrate, there are only a few chemical reactions that can be successfully conducted to create these chemical bonds, and these reactions usually involve silicon-containing reagents. We compared the silazane reagents to the silane reagents and found through experiment that the silazanes react with the glass surface much more readily, and under milder conditions, than the silanes. The functional groups attached to the glass surface by silazane reactions were not able to be removed by solvent extraction, elevated temperature exposure, or mechanical action. This clearly indicates that the formation of chemical bonds at the interface is the most effective approach for enhancing molecular adhesion.

Penn, L. S.↗

Detonation to Deflagration-Mode Transitions in Pulsed Plasma Accelerators

PULSED plasma accelerators typically operate by storing energy in a capacitor bank and then discharging this energy through a gas. The current in such discharges will ionize the gas and produce a strong magnetic field, which interacts with the flowing current to accelerate the plasma through the Lorentz body force. For the present work, two plasma accelerator types employing this general scheme are of interest: the gas-fed pulsed plasma thruster (PPT) 1 and the quasi-steady magnetoplasmadynamic (MPD) accelerator. 2 The gas-fed pulsed plasma accelerator is generally understood as a completely transient device discharging in ∼1-10 μs. When the capacitor bank is discharged through the gas, a current sheet forms at the breech of the thruster and propagates forward under a j × B body force, entraining and accelerating propellant it encounters. This process is sometimes referred to in literature as 'snowplowing' the propellant or accelerating the gas in a detonation-mode because the current sheet representation approximates that of a strong detonation shockwave propagating through the gas. For these devices, acceleration of the initial current sheet ceases when either the current sheet reaches the end of the device and is ejected or when the current in the circuit reverses, striking a new 'crowbar' discharge at the breech and depriving the initial sheet of additional acceleration. In general, PPTs typically claim thrust efficiencies (ratio of jet kinetic energy to input electrical energy) registering in the teens or lower. 3 In the quasi-steady MPD accelerator, the pulse is lengthened to ∼1 ms or longer and maintained at an approximately constant level during discharge through the use of a pulse-forming network (PFN) of capacitors. After an initial transient discharge, which is typically short relative to the overall discharge period, the plasma assumes a relatively steady-state configuration, known as 'quasi-steady' MPD operation. 2 In this state, ionized gas flows through a stationary current channel in a manner that is sometimes referred to as deflagration-mode operation owing to the similarities to deflagration waves in gases. The plasma experiences electromagnetic acceleration as the plasma flows through the current channel towards the exit of the device. Quasi-steady MPD thrusters claim efficiencies up to 50% for certain propellants.4 There has been significant and sustained research over several decades on both gas-fed PPTs and quasi-steady MPD thrusters, however there have been pulsed thrusters that do not appear to exactly fit either classification, instead possessing a mixture of operational qualities characteristic of both thruster variants. The Coaxial High ENerGy (CHENG) thruster by Cheng, et al.5 operated on the short 10 μs timescales characteristic of PPTs, but claimed the high thrust densities, high efficiencies, and low electrode erosion rates that are more consistent with the MPD/deflagration mode of plasma acceleration. Gas-fed PPT research by Ziemer, et al. 3, 6 identified two separate regimes of performance in those thrusters. The regime at higher mass bits (termed Mode I in that work) possessed relatively constant thrust efficiency as a function of mass bit, while the second regime at very low mass bits (termed Mode II) exhibited an increase in efficiency with decreasing mass bit. Work by Poehlmann et al.7 and by Sitaraman and Raja8 sought to understand the performance of the CHENG thruster and the Mode I/Mode II performance in PPTs by modeling the acceleration using the Hugoniot Relation, with the detonation and deflagration modes of plasma acceleration representing two distinct sets of solutions to the relevant conservation laws. In these works, it was proposed that the values of the various controllable parameters determined whether the accelerator would operate in detonation or deflagration mode. Our hypothesized view of the acceleration process in the CHENG thruster and in PPTs experiencing a transition from Mode I to Mode II is inspired by observations of the transition from the PPT mode of operation to the quasi-steady MPD mode. Specifically, the quasi-steady MPD was discovered by driving a PPT to extended pulse lengths. Above a certain pulse length threshold the transient plasma current sheet transitions into a stable plasma acceleration mode that 'replicates in every observable detail steady flow self-field magnetoplasmadynamic acceleration.' 9 In the present work, instead of treating the accelerator as if it were only operating in a single mode during a pulse, we consider the initial stage of the discharge in all cases as a current sheet forming at the breach of the accelerator and moving towards the exit as a detonation wave. If the current sheet reaches the exit of the accelerator before the discharge is completed, the view of the acceleration mode transitions to the deflagration mode-type found in quasi-steady MPD thrusters. In previous work10 we presented a modeling framework that first captured the time-evolution of the current sheet (detonation) mode of the thruster and then transitioned into the quasi-steady MPD (deflagration) mode of plasma acceleration. In the present work, variations of the controllable parameters - specifically the pulsed circuit properties, the amount of mass injected into the thruster, and the relative timing between the initial gas injection and the initiation of the plasma current sheet - will be used to explore the thruster performance. A range of parameters are explored to demonstrate that standard gas-fed pulsed plasma accelerators, the CHENG thruster, and the quasi-steady MPD accelerator are variations of the same device, with the overall acceleration of the plasma depending upon the behavior of the plasma discharge during initial transient phase and the relative lengths of the detonation and deflagration modes of operation.

Polzin, Kurt A.↗

Modeling the Dynamics of the Middle Atmosphere and Lower Thermosphere Under the Influence of Gravity Waves

Our Numerical Spectral Model (NSM), which extends from the ground up into the thermosphere, is non-linear, time-dependent and has been employed for 2D and 3D applications. The standard version of the NSM incorporates Hines' Doppler Spread Parameterization for small scale gravity waves (GW), but planetary waves generated in the troposphere have also been incorporated. The NSM has been applied to describe: (1) the anomalous seasonal variations of the zonal circulation and temperature in the upper mesosphere, (2) the equatorial oscillations (quasi-biennial and semi-annual oscillations (QBO and SAO)) extending from the stratosphere into the upper mesosphere, (3) the diurnal and semi-diurnal tides, and (4) the planetary waves that are excited in the mesosphere. With the emphasis to provide understanding, we present here results from numerical experiments with the NSM that shed light on the GW processes that are of central importance in the mesosphere and lower thermosphere. These are our conclusions: (1) The large semiannual variations in the diurnal tide (DT), with peak amplitudes observed around equinox, are produced primarily by GW interactions that involve, in part, planetary waves. The DT, like planetary waves, tends to be amplified by GW momentum deposition, which reduces also the vertical wavelength, but variations in eddy viscosity associated with GW interactions are also important. (2) The semidiurnal tide (SDT) and its phase in particular, is strongly influenced by the mean zonal circulation. The SDT, individually, is also amplified by GW. But the DT filters out GW such that the GW interaction effectively reduces the amplitude of the SDT, producing a strong nonlinear interaction between the DT and SDT. (3) Without external time dependent energy or momentum sources, planetary waves (PW) are generated in the model for zonal wavenumbers 1 to 4, which have amplitudes in the mesosphere above 50 km as large as 40 m/s and periods between 50 and 2 days. The waves are generated primarily during solstice conditions, which indicates that the baroclinic instability (associated with the GW induced reversal in the latitudinal temperature gradient) is playing an important role. Numerical experiment show that GW, directly, also greatly amplify the PW. A common feature of the PW generated in summer and winter is that their vertical wavelengths throughout the mesosphere are large, which indicates that the waves are not propagating freely but are generated throughout the region. Another common feature is that the PW propagate preferentially westward in summer and eastward in winter, being launched from the westward and eastward zonal winds that prevail respectively in summer and winter at altitudes below 80 km. (4) Planetary waves generated internally by baroclinic instability and GW interaction produce large amplitude modulations of the DT and SDT. In summary we conclude that GW play major roles in generating and amplifying the dynamical components in the MLT region and, acting principally through wave filtering, produce important non-linear interactions between the components.

Mayr, H. G.↗

Strong Dependence of Atmospheric Feedbacks on Mixed-Phase Microphysics and Aerosol-Cloud Interactions in HadGEM3

We analyze the atmospheric processes that explain the large changes in radiative feed-backs between the two latest climate configurations of the Hadley Centre Global Environmental model. We use a large set of atmosphere-only climate-change simulations (amip and amip-p4K) to separate the contributions to the differences in feedback parameter from all the atmospheric model developments between the two latest model configurations. We show that the differences are mostly driven by changes in the shortwave cloud radiative feedback in the midlatitudes, mainly over the Southern Ocean. Two new schemes explain most of the differences: the introduction of a new aerosol scheme; and the development of a new mixed-phase cloud scheme. Both schemes reduce the strength of the pre-existing shortwave negative cloud feedback in the midlatitudes. The new aerosol scheme dampens a strong aerosol-cloud interaction, and it also suppresses a negative clear-sky shortwave feedback. The mixed-phase scheme increases the amount of cloud liquid water path (LWP) in the present-day, thereby reducing the radiative effciency of the increase of LWP in the warmer climate. It also enhances a strong, pre-existing, positive cloud fraction feedback. We assess the realism of the changes by comparing present-day simulations against observations, and discuss avenues that could help constrain the relevant processes.

HadGEM3↗

The Summer 1997 Eruption at Pillan Patera on Io: Implications for Ultrabasic Lava Flow Emplacement

Galileo data and numerical modeling were used to investigate the summer 1977 eruption at Pillan Patera on Io. This event, now defined as "Pillanian" eruption style, included a high-temperature (greater than 1600 C), possible ultrabasic , 140-km-high plume eruption that deposited dark, orthopyroxene-rich pyroclastic material over greater than 125,000 sq km, followed by emplacement of dark flow-like material over greater than 3100 sq km to the north of the caldera. We estimate that the high-temperature, energetic episode of this eruption had a duration of 52 - 167 days between May and September 1997, with peak eruption temperatures around June 28, 1997. Galileo 20 m/pixel images of part of the Pillan flow field show a wide-spread, rough, pitted surface that is unlike any flow surface we have seen before. We suggest that this surface may have resulted from: 1. A fractured lava crust formed during rapid, low-viscosity lava surging, perhaps including turbulent flow emplacement. 2. Disruption of the lava flow by explosive interaction with a volatile-rich substrate. or 3. A combination of 1 and 2 with or without accumulation of pyroclastic material on the surface. Well-developed flow lobes are observed, suggesting that this is a relatively distant part of the flow field.Shadow measurements at flow margins indicate a thickness of-8 - 10 m. We have modeled the emplacement of putative ultrabasic flow from the summer 1997 Pillan eruption using constraints from new Galileo data. Results suggest that either laminar sheet flows or turbulent channelized flows could have traveled 50 - 150 km on a flat, unobstructed surface, which is consistent with the estimated length of the Pillan flow field (approx. 60 km). Our modeling suggests low thermal erosion rates (less than 4.1 m/d), and that the formation of deep (greater than 20 m) erosion channels was unlikely, especially distal to the source. We calculate a volumetric flow rate of approx. 2 - 7 x 10(exp 3)cu m/s, which is greater than those for typical Mauna Loa/Kilaueaq flows but comparable to those for the (1783) Laki eruption and the inferred flow rates of the Roza flows in the Columbia River flood basalts. The differences in ultrabasic eruption styles on Earth and Io appear to be controlled by the different eruption environments; Plumes at sites of ultrabasic eruptions on Io suggest strong magma-volatile interactions on a low-gravity body lacking an atmosphere, whereas the geology at sites of komatiite eruptions on Earth suggest mostly submarine emplacement of thick flows with a pronounced lack of subaerial explosive activity.

Williams, David A.↗

The Summer 1997 Eruption at Pillan Patera on Io: Implications for Ultrabasic Lava Flow Emplacement

Galileo data and numerical modeling were used to investigate the summer 1997 eruption at Pillan Patera on Io. This event, now defined as 'Pillanian' eruption style, included a high-temperature (greater than 1600 C), possibly ultrabasic, 140-km-high plume eruption that deposited dark, orthopyroxene-rich pyroclastic material over greater than 125,000 sq km, followed by emplacement of dark flow-like material over greater than 3100 sq km to the north of the caldera. We estimate that the high-temperature, energetic episode of this eruption had a duration of 52- 167 days between May and September 1997, with peak eruption temperatures around June 28, 1997. Galileo 20 m/pixel images of part of the Pillan flow field show a widespread, rough, pitted surface that is unlike any flow surface we have seen before. We suggest that th.s surface may have resulted from (1) a fractured lava crust formed during rapid, low-viscosity lava surging, perhaps including turbulent flow emplacement; (2) disruption of the lava flow by explosive interaction with a volatile-rich substrate: or (3) a combination of 1 and 2 with or without accumulation of pyroclastic materials on the surface. Well-developed flow lobes are observed, suggesting that this is a relatively distal part of the flow field. Shadow measurements at flow margins indicate a thickness of approx. 8-10 m. We have modeled the emplacement of putative ultrabasic flows from the summer 1997 Pillan eruption using constraints from new Galileo data. Results suggest that either laminar sheet flows or turbulent channelized flows could have traveled 50-150 km on a flat. unobstructed surface, which is consistent with the estimated length of the Pillan flow field (approx. 60 km). Our modeling suggests low thermal erosion rates (less than 0.1 m/d), and that the formation of deep (greater than 20 m) erosion channels was unlikely, especially distal to the source. We calculate a volumetric flow rate of approx. 2-7 x l0(exp 3) cu m/s, which is greater than those for typical Mauna Loa/Kilauea flows but comparable to those for the (1783) Laki eruption and the inferred flow rates of the Roza flows in the Columbia River flood basalts. The differences in ultrabasic eruption styles on Earth and Io appear to be controlled by the different eruption environments: Plumes at sites of ultrabasic eruptions on Io suggest strong magma-volatile: interactions on a low-gravity body lacking an atmosphere, whereas the geology at sites of komatiite eruptions on Earth suggest mostly submarine emplacement of thick flows with a pronounced lack of subaerial explosive activity.

Williams, David A.↗

An experimental study of the sources of fluctuating pressure loads beneath swept shock/boundary-layer interactions

An experimental research program providing basic knowledge and establishing a database on the fluctuating pressure loads produced on aerodynamic surfaces beneath three dimensional shock wave/boundary layer interactions is described. Such loads constitute a fundamental problem of critical concern to future supersonic and hypersonic flight vehicles. A turbulent boundary layer on a flat plate is subjected to interactions with swept planar shock waves generated by sharp fins at angle of attack. Fin angles from 10 to 20 deg at freestream Mach numbers of 3 and 4 produce a variety of interaction strengths from weak to very strong. Miniature Kulite pressure transducers flush-mounted in the flat plate are used to measure interaction-induced wall pressure fluctuations. The distributions of properties of the pressure fluctuations, such as their ring levels, amplitude distributions, and power spectra, are also determined. Measurements were made for the first time in the aft regions of these interactions, revealing fluctuating pressure levels as high as 160 dB. These fluctuations are dominated by low frequency (0-5 kHz) signals. The maximum ring levels in the interactions show an increasing trend with increasing interaction strength. On the other hand, the maximum ring levels in the forward portion of the interactions decrease linearly with increasing interaction sweep back. These ring pressure distributions and spectra are correlated with the features of the interaction flowfield. The unsteadiness of the off-surface flowfield is studied using a new, non-intrusive technique based on the shadow graph method. The results indicate that the entire lambda-shock structure generated by the interaction undergoes relatively low-frequency oscillations. Some regions where particularly strong fluctuations are generated were identified. Fluctuating pressure measurements are also made along the line of symmetry of an axisymmetric jet impinging upon a flat plate at an angle. This flow was chosen as a simple analog to the impinging jet region found in the rear portion of the shock wave/boundary layer interactions under study. It is found that a sharp peak in ring pressure level exists at or near the mean stagnation point. It is suggested that the phenomena responsible for this peak may be active in the swept interactions as well, and may cause the extremely high fluctuating pressures observed in the impinging jet region in the present experimental program.

Settles, G. S.↗

Aerodynamic heat transfer to RSI tile surfaces and gap intersections

Review of the results of aerothermal heating tests of a simulated reusable surface insulation (RSI) tile array, performed on the sidewall of a Mach-10 hypersonic tunnel. In particular, the heating characteristics of the tile array, such as they result from heating inside the tile-expansion-space providing gaps between individual tiles, are investigated. The results include the finding that heating on the upstream face of a tile is strongly affected by the interacting longitudinal gap flow.

Dunavant, J. C.↗

Theory of type 3b solar radio bursts

During the initial space-time evolution of an electron beam injected into the corona, the strong beam-plasma interaction occurs at the head of the beam, leading to the amplification of a quasi-monochromatic large-amplitude plasma wave that stabilizes by trapping the beam particles. Oscillation of the trapped particles in the wave troughs amplifies sideband electrostatic waves. The sidebands and the main wave subsequently decay to observable transverse electromagnetic waves through the parametric decay instability. This process gives rise to the elementary striation bursts. Owing to velocity dispersion in the beam and the density gradient of the corona, the entire process may repeat at a finite number of discrete plasma levels, producing chains of elementary bursts. All the properties of the type IIIb bursts are accounted for in the context of the theory.

Smith, R. A.↗

Theory of type IIIb solar radio bursts

During the initial space-time evolution of an electron beam injected into the corona, the strong beam-plasma interaction occurs at the head of the beam, leading to the amplification of a quasi-monochromatic large-amplitude plasma wave that stabilizes by trapping the beam particles. Oscillation of the trapped particles in the wave troughs amplifies sideband electrostatic waves. The sidebands and the main wave subsequently decay to observable transverse electromagnetic waves through the parametric decay instability. This process gives rise to the elementary striation bursts. Owing to velocity dispersion in the beam and the density gradient of the corona, the entire process may repeat at a finite number of discrete plasma levels, producing chains of elementary bursts. All the properties of the type IIIb bursts are accounted for in the context of the theory.

Smith, R. A.↗

Energetic solar particle behaviour in the magnetosphere

The behavior of energetic solar flare particles in the magnetosphere is discussed. In the absence of magnetospheric motion, the problem of particle transport can be treated as simple propagation of charged particles in a stationary magnetic field configuration using, for instance, trajectory calculations in model fields. This single particle approach is the basis for the determination of intensity and anisotropy structures over the polar caps and in the geomagnetic tail from different interplanetary conditions. Particle transport on closed field lines is in addition strongly affected by resonant interaction processes as pitch angle scattering and radial diffusion.

Scholer, M.↗

Numerical solution of the Navier-Stokes equations for a family of three-dimensional corner geometries

Three-dimensional corners occur in many aerodynamic engineering situations. Supersonic flow about such geometries is characterized by strong inviscid-viscid interactions which are analyzed adequately only through the solution of the Navier-Stokes equations. In this paper numerical solution for the laminar compressible Navier-Stokes equations are presented for a family of three-dimensional corners consisting of wedge-plate and wedge-cylinder intersecting boundaries. The equations of motion are transformed to a uniform rectangular computational domain. The computational technique is the MacCormack time-split algorithm vectorized and programmed to run on the CDD CYBER 203 computer. The metric data for the transformation is obtained from the 'two-boundary technique.'

Smith, R. E.↗

The effect of microscopic turbulence on magnetosphere-ionosphere coupling

The effect of turbulence on the coupling of the magnetosphere and ionosphere has been investigated by including an effective collision frequency in the electron equation of motion. When this term is combined with the continuity equation, the ion equation of motion and Maxwell's equations, a dispersion relation for the kinetic Alfven wave including effective collisions is found. The wave-particle interaction leads to a strong damping of the wave. Inclusion of the effects of plasma sheet kinetics yields a scale size transverse to the magnetic field which corresponds to the size of visual auroral arcs.

Lysak, R. L.↗

Computation of hypersonic viscous flow around three-dimensional bodies at high angles of attack

A parabolized Navier-Stokes code capable of predicting steady viscous supersonic flows with cross-flow separation is applied to three-dimensional arbitrary geometries at high angles of attack. The numerical procedure, which is implicit, noniterative, and of second-order accuracy in the marching direction, has been used to compute complicated flow fields containing a relatively thick sonic layer and regions of strong viscous-inviscid interaction. A consistent and accurate procedure has also been developed to provide the necessary starting data through timewise integration of the equations of motion near the nose-tip region of the body. Numerical results obtained from the present method compare well with experiment for both the surface pressures and heat transfer.

Rizk, Y. M.↗

Theory of the fine structure of auroral kilometric radiation

Recent data from ISEE 1 show auroral kilometric radiation (AKR) with finely separated bands in frequency. The observation that the AKR fine structure frequency separation is about equal to the ion cyclotron frequency at the AKR source is strong evidence for the interaction of AKR and electrostatic ion cyclotron (EIC) waves in the source, as proposed by Grabbe et al. (1980) to explain the origin of AKR. It is pointed out that no other wave of frequency close to the band separation is known to exist in the auroral source region. The fine structure observed in the source region AKR is the first evidence for EIC waves in the lower source region (3000 - 5000 km attitude), as required in the theory of Grabbe et al.

Grabbe, C. L.↗

Fast magnetospheric echoes of energetic electron beams

Electron beam experiments using rocket-borne instrumentation confirmed earlier observations of fast magnetospheric echoes of artificially injected energetic electrons. A total of 234 echoes were observed in a pitch angle range from 9 to 110 deg at energies of 1.87 and 3.90 keV. Of these, 102 echoes could unambiguously be identified with known accelerator operations at 2, 4 or 8 keV energy and highest current levels resulting in the determination of transit times of typically 300 to 400 ms. In most cases, when echoes were present in both energy channels, the higher energy electrons led the lower energy ones by 50 to 70 ms. Adiabatic theory applied to these observations yields a reflection height of 3000 to 4000 km. The injection process is discussed as the strong beam-plasma interaction that occurred near the electron accelerator appears to be instrumental in generating the source of heated electrons required for successful echo detection.

Wilhelm, K.↗

Trailing edge flow conditions as a factor in airfoil design

Some new developments relevant to the design of single-element airfoils using potential flow methods are presented. In particular, the role played by the non-dimensional trailing edge velocity in design is considered and the relationship between the specified value and the resulting airfoil geometry is explored. In addition, the ramifications of the unbounded trailing edge pressure gradients generally present in the potential flow solution of the flow over an airfoil are examined, and the conditions necessary to obtain a class of airfoils having finite trailing edge pressure gradients developed. The incorporation of these conditions into the inverse method of Eppler is presented and the modified scheme employed to generate a number of airfoils for consideration. The detailed viscous analysis of airfoils having finite trailing edge pressure gradients demonstrates a reduction in the strong inviscid-viscid interactions generally present near the trailing edge of an airfoil.

Ormsbee, A. I.↗