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NASA NTRS1992

Interaction of disturbances with an oblique detonation wave attached to a wedge

The linear response of an oblique overdriven detonation to impose free stream disturbances or to periodic movements of the wedge is examined. The free stream disturbances are assumed to be steady vorticity waves and the wedge motions are considered to be time periodic oscillations either about a fixed pivot point or along the plane of symmetry of the wedge aligned with the incoming stream. The detonation is considered to be a region of infinitesmal thickness in which a finite amount of heat is released. The response to the imposed disturbances is a function of the Mach number of the incoming flow, the wedge angle, and the exothermocity of the reaction within the detonation. It is shown that as the degree of overdrive increases, the amplitude of the response increases significantly; furthermore, a fundamental difference in the dependence of the response on the parameters of the problem is found between the response to a free stream disturbance and to a disturbance emanating from the wedge surface.

Lasseigne, D. G.↗

NASA NTRS1992

Electromagnetic scattering by coated convex surfaces and wedges simulated by approximate boundary conditions

Asymptotic/high-frequency solutions are developed for analyzing the non-specular scattering mechanisms associated with coated convex surfaces and edges simulated by approximate boundary conditions. In particular, the standard impedance boundary conditions (SIBC's) and the second order generalized impedance boundary conditions (GIBC's) are employed for a characterization of the edge diffraction, creeping wave, and surface diffracted wave contributions. To study the creeping wave and surface diffracted wave mechanisms, rigorous UTD (uniform geometrical theory of diffraction) diffraction coefficients are developed for a convex coated cylinder simulated with SIBC's and GIBC's. The ray solutions obtained remain valid in the transition region and reduce uniformly to those in the deep lit and shadow regions. A uniform asymptotic solution is also presented for observations in the close vicinity of the cylinder. The diffraction coefficient for a convex cylinder are obtained via a generalization of the corresponding ones of the circular cylinder. To validate the asymptotic/high-frequency solution, integral equations are derived for both E and H-polarization and solved numerically using the method of moments. Results are presented for a single and three layered coated convex cylinder. Some insights are also provided on the accuracy of the employed GIBC's versus SIBC's for application to curved surfaces. To characterize the scattering by impedance wedges illuminated at skew incidence, diffraction coefficients are derived from an approximate solution of the governing functional difference equations. This solution exactly recovers the known ones for an impedance half plane or an arbitrary wedge at normal incidence, and to validate it for other wedge angles, a moment method code was used. Finally, to test the usefulness of the approximate skew incidence impedance wedge diffraction coefficient for three dimensional structures, equivalent currents are derived in the context of the physical theory of diffraction (PTD) for a finite length impedance wedge of arbitrary internal angles. These are incorporated in a standard general purpose PTD code and results are presented for a number of different impedance structures.

Syed, H. H.↗

NASA NTRS1992

A periodic moment method solution for TM scattering from lossy dielectric bodies with application to wedge absorber

The periodic moment method (PMM) solution for the scattering from two-dimensional lossy dielectric bodies is developed in this paper. The purpose is to design microwave wedge absorber for low reflectivity so that one can improve the performance of anechoic chamber measurements. With PMM, the reflection and transmission coefficients of periodically distributed bodies illuminated by a plane wave have been accurately calculated using a Cray Y-MP supercomputer. Through these studies, some wedge absorber configurations have been designed, fabricated, and then tested in the OSU/ESL compact range measurement facility. Two 8 in. commercial wedges, a curved wedge, and a four-layer wedge are studied in this paper. In all cases, good agreement between calculations and measurements has been obtained.

Yang, Chang-Fa↗

NASA NTRS1993

Interaction of disturbances with an oblique detonation wave attached to a wedge

The linear response of an oblique overdriven detonation to impose free stream disturbances or to periodic movements of the wedge is examined. The free stream disturbances are assumed to be steady vorticity waves and the wedge motions are considered to be time periodic oscillations either about a fixed pivot point or along the plane of symmetry of the wedge aligned with the incoming stream. The detonation is considered to be a region of infinitesimal thickness in which a finite amount of heat is released. The response to the imposed disturbances is a function of the Mach number of the incoming flow, the wedge angle, and the exothermocity of the reaction within the detonation. It is shown that as the degree of overdrive increases, the amplitude of the response increases significantly; furthermore, a fundamental difference in the dependence of the response on the parameters of the problem is found between the response to a free stream disturbance and to a disturbance emanating from the wedge surface.

Lasseigne, D. G.↗

NASA NTRS2019

CFD Simulations of the IHF Arc-Jet Flow: 9-Inch Nozzle, Flow Surveys, LEAF Wedge Calibration Data

This paper reports computational analyses and flow characterization studies in a high enthalpy arc-jet facility at NASA Ames Research Center. These tests were conducted using a wedge model placed in a free jet downstream of new 9-inch diameter conical nozzle in the Ames 60-MW Interaction Heating Facility. Both the nozzle and wedge model were specifically designed for testing in the new Laser-Enhanced Arc-jet Facility. Data were obtained using stagnation calorimeters and wedge models placed downstream of the nozzle exit. Two instrumented wedge calibration plates were used: one water-cooled and the other RCG-coated tile plate. Experimental surveys of arc-jet test flow with pitot and heat flux probes were also performed at three arc-heater conditions, providing assessment of the flow uniformity and valuable data for the flow characterization. The present analysis comprises computational fluid dynamics simulations of the nonequilibrium flowfield in the facility nozzle and test box, including the models tested, and comparisons with the experimental measurements. By taking into account nonuniform total enthalpy and mass flux profiles at the nozzle inlet as well as the expansion waves emanating from the nozzle exit and their effects on the model flowfields, these simulations approximately reproduce the probe survey data and predict the wedge model surface pressure and heat flux measurements.

Arc-jets↗

NASA NTRSDate not supplied

CFD Simulations of the AEDC H3 Arc-Jet Flow: Mach 3.3 Nozzle, Flow Surveys, Wedge Models

This paper reports computational simulations and analysis of tests in a high enthalpy arc-jet facility at Arnold Engineering Development Center. These tests were conducted using wedge models placed in a free jet downstream of a 4.5-inch diameter contoured Mach 3.3 nozzle in the H3 facility. For calibration of test conditions, one wedge calibration plate instrumented with an array of pressure and coaxial thermocouple heat flux gages, one stagnation pressure probe and two null-point heat flux calorimeters were used. The pitot pressure and null-point probe measurements give experimental surveys of the test flow, providing assessment of the flow uniformity and valuable data for flow characterization. The present analysis comprises computational fluid dynamics simulations of the nonequilibrium flowfield in the facility nozzle, into the test box and over the wedge models, and comparisons with the experimental measurements. Several issues related to testing are considered: test flow characterization, prediction of surface quantities for three wedge models, effects of model shape change and test article recession, and prediction of surface quantities for the test articles with two circular cavities. These simulations take into account non-uniform total enthalpy profiles at the nozzle inlet as well as the expansion waves emanating from the nozzle exit and their effects on the wedge model flowfields.

Arc-jet testing↗

DOE OSTI2021

Seeing the entanglement wedge

We study the problem of revealing the entanglement wedge using simple operations. We ask what operation a semiclassical observer can do to bring the entanglement wedge into causal contact with the boundary, via backreaction. In a generic perturbative class of states, we propose a unitary operation in the causal wedge whose backreaction brings all of the previously causally inaccessible ‘peninsula’ into causal contact with the boundary. This class of cases includes entanglement wedges associated to boundary sub-regions that are unions of disjoint spherical caps, and the protocol works to first order in the size of the peninsula. The unitary is closely related to the so-called Connes Cocycle flow, which is a unitary that is both well-defined in QFT and localised to a sub-region. Our construction requires a generalization of the work by Ceyhan & Faulkner to regions which are unions of disconnected spherical caps. We discuss this generalization in the appendix. We argue that this cocycle should be thought of as naturally generalizing the non-local coupling introduced in the work of Gao, Jafferis & Wall.

2D gravity↗

DOE OSTI2026

Filling the cellulosic bio-economy gap by utilizing a wedge approach combined with stakeholder collaboration

The price gap between the market and breakeven prices of cellulosic biomass for farmers represents a significant barrier to the development of a low-carbon cellulosic bioeconomy. Using a bottom-up, agent-based modeling tool that replicates the behaviors and interactions of key stakeholders, this study analyzes the emergence of a cellulosic bioeconomy at the local scale through a wedge approach that examines an integrated portfolio of multiple policy options, including subsidies for small-scale bioproducts and environmental credits. Here, the role of collaboration among multiple stakeholders, such as biomass producers (farmers), bio-refinery industry, government, and society, is assessed for filling the price gap. Using the Sangamon River Basin as a case study site, we evaluate the effectiveness of the wedge approach by comparing simulation results from multiple scenarios, each incorporating different combinations of bioeconomy wedges, with and without stakeholder collaboration. Results underscore that active collaboration among stakeholders acts as a catalyst enlarging the effectiveness of bioeconomy wedges. Including the carbon credits and environmental value in the policy portfolio is found to bridge the price gap through collective contributions from diverse stakeholders, where the cellulosic biofuel and bioproduct industry plays a pivotal role. Although this study is conducted at the local watershed scale, the methodology and findings offer valuable insights for market development in other watersheds and the potential scaling of local markets to regional and national levels.

09 BIOMASS FUELS↗

NASA NTRS1971

An Analytical Investigation of an Oscillating Wedge in a Supersonic Perfect Gas Flow

Several aspects of the oscillating wedge are investigated to evaluate both the resulting trends for the wedge and methods of analyzing unsteady flows. An existing hypersonic small disturbance theory for an oscillating thin wedge is extended and applied. A perturbation method involving linearization about the known flow is then derived and discussed. Subsequently, a finite difference technique for calculating the complete unsteady flow field of the wedge in motion is presented and discussed in conjunction with some calculated quasi-static nonlinear trends.

Bennett, R. M.↗

NASA NTRS1974

Contact and crack problems for an elastic wedge

The contact and the crack problems for an elastic wedge of arbitrary angle are considered. The problem is reduced to a singular integral equation which, in the general case, may have a generalized Cauchy kernel. The singularities under the stamp as well as at the wedge apex were studied, and the relevant stress intensity factors are defined. The problem was solved for various wedge geometries and loading conditions. The results may be applicable to certain foundation problems and to crack problems in symmetrically loaded wedges in which cracks initiate from the apex.

Erdogan, F.↗

NASA NTRS1975

Investigation of two-dimensional wedge exhaust nozzles for advanced aircraft

Two-dimensional wedge nozzle performance characteristics were investigated in a series of wind-tunnel tests. An isolated single-engine/nozzle model was used to study the effects of internal expansion area ratio, aftbody cowl boattail angle, and wedge length. An integrated twin-engine/nozzle model, tested with and without empenage surfaces, included cruise, acceleration, thrust vectoring and thrust reversing nozzle operating modes. Results indicate that the thrust-minus-aftbody drag performance of the twin two-dimensional nozzle integration is significantly higher, for speeds greater than Mach 0.8, than the performance achieved with twin axisymmetric nozzle installations. Significant jet-induced lift was obtained on an aft-mounted lifting surface using a cambered wedge center body to vector thrust. The thrust reversing capabilities of reverser panels installed on the two-dimensional wedge center body were very effective for static or in-flight operation.

Maiden, D. L.↗

NASA NTRS1980

Stress singularities at the vertex of a cylindrically anisotropic wedge

The plane elasticity problem for a cylindrically anisotropic solid is formulated. The form of the solution for an infinite wedge shaped domain with various homogeneous boundary conditions is derived and the nature of the stress singularity at the vertex of the wedge is studied. The characteristic equations giving the stress singularity and the angular distribution of the stresses around the vertex of the wedge are obtained for three standard homogeneous boundary conditions. The numerical examples show that the singular behavior of the stresses around the vertex of an anisotropic wedge may be significantly different from that of the isotropic material. Some of the results which may be of practical importance are that for a half plane the stress state at r = 0 may be singular and for a crack the power of stress singularity may be greater or less than 1/2.

Delale, F.↗

NASA NTRS1982

The crack and wedging problem for an orthotropic strip

The plane elasticity problem for an orthotropic strip containing a crack parallel to its boundaries is considered. The problem is formulated under general mixed mode loading conditions. The stress intensity factors depend on two dimensionless orthotropic constants only. For the crack problem the results are given for a single crack and two collinear cracks. The calculated results show that of the two orthotropic constants the influence of the stiffness ratio on the stress intensity factors is much more significant than that of the shear parameter. The problem of loading the strip by a rigid rectangular lengths continuous contact is maintained along the wedge strip interface; at a certain critical wedge length the separation starts at the midsection of the wedge, and the length of the separation zone increases rapidly with increasing wedge length.

Cinar, A.↗

NASA NTRS1983

The crack and wedging problem for an orthotropic strip

Cinar, A.↗

NASA NTRS1986

Analysis and measurement of electromagnetic scattering by pyramidal and wedge absorbers

By modifying the reflection coefficients in the Uniform Geometrical Theory of Diffraction a solution that approximates the scattering from a dielectric wedge is found. This solution agrees closely with the exact solution of Rawlins which is only valid for a few minor cases. This modification is then applied to the corner diffraction coefficient and combined with an equivalent current and geometrical optics solutions to model scattering from pyramid and wedge absorbers. Measured results from 12 inch pyramid absorbers from 2 to 18 GHz are compared to calculations assuming the returns add incoherently and assuming the returns add coherently. The measured results tend to be between the two curves. Measured results from the 8 inch wedge absorber are also compared to calculations with the return being dominated by the wedge diffraction. The procedures for measuring and specifying absorber performance are discussed and calibration equations are derived to calculate a reflection coefficient or a reflectivity using a reference sphere. Shaping changes to the present absorber designs are introduced to improve performance based on both high and low frequency analysis. Some prototypes were built and tested.

Dewitt, B. T.↗

NASA NTRS1989

Reflections, diffractions, and surface waves for an interior impedance wedge of arbitrary angle

The asymptotic-impedance wedge solution for plane-wave illumination at normal incidence is examined for interior wedge diffraction. An efficient method for calculating the diffraction coefficient for arbitrary wedge angle is presented. The asymptotic solution isolates the incident, singly reflected, multiply reflected, diffracted, surface-wave, and associated-surface-wave transition fields. Multiply reflected fields (of any order) from the exact solution arise as ratios of auxiliary Maliuzhinets functions; however, by using properties of these functions, the representation can be reduced to products of reflection coefficients, much more efficient for calculation. A surface-wave transition field is added to the surface wave to retain continuity of the total field at the surface wave boundaries. This formulation is equally valid for both exterior and interior wedges with uniform but different impedances on each face, for both soft and hard polarizations.

Griesser, Timothy↗

NASA NTRS1953

Impingement of water droplets on wedges and diamond airfoils at supersonic speeds

An analytical solution has been obtained for the equations of motion of water droplets impinging on a wedge in a two-dimensional supersonic flow field with a shock wave attached to the wedge. The closed-form solution yields analytical expressions for the equation of the droplet trajectory, the local rate of impingement and the impingement velocity at any point on the wedge surface, and the total rate of impingement. The analytical expressions are utilized to determine the impingement on the forward surfaces of diamond airfoils in supersonic flow fields with attached shock waves. The results presented include the following conditions: droplet diameters from 2 to 100 microns, pressure altitudes from sea level to 30,000 feet, free-stream static temperatures from 420 degrees to 460 degrees R. Also, free-stream Mach numbers from 1.1 to 2.0, semi-apex angles for the wedge from 1.14 degrees to 7.97 degrees, thickness-to-chord ratios for the diamond airfoil from 0.02 to 0.14, chord lengths from 1 to 20 feet, and angles of attack from zero to the inverse tangent of the airfoil thickness-to-chord ratio.

SURFACE CONDITIONS - WING SECTIONS↗

NASA NTRS1954

Experimental investigation at Mach numbers 1.88, 3.16, and 3.83 of pressure drag of wedge diverters simulating boundary-layer-removal systems for side inlets

The pressure drag coefficients for a number of simulated wedge diverter boundary-layer-removal systems for side inlets were obtained at Mach numbers of 1.88m 3.16, and 3.83. Wedge included angle, wedge height, and wedge axial position relative to the splitter plate were independently varied for unswept and swept splitter plate configurations immersed in the turbulent boundary layer of a flat plate. Friction and total drag coefficients for several configurations were also obtained at Mach number 3.16

Piercy, Thomas G↗