Far-field diffraction pattern for corner reflectors with complex reflection coefficients
Far field diffraction pattern of corner reflector for normally incident monochromatic light, considering polarization characteristics
Alley, C. O.↗
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Sharp flat plate heat transfer in helium at Mach numbers of 22.8 to 86.8 and in corner flow with air at Mach number of 19
Surface heat transfer rates were measured on a sharp flat plate at zero angle of attack in a hypersonic shock tunnel. The density and leading edge Knudsen number were varied to span the continuum to near free molecule regimes. The strong interaction parameter varied from 11 to 16,000 with Knudsen numbers from 0.56 to 17.1 respectively. Local heat transfer rates in the corner flow region produced by the intersection of two perpendicular flat plates with sharp leading edges were determined for various flow densities. The strength of the shock wave from the vertical plate was varied by adjusting the angle of attack from 0 to 5 deg. The unit Reynolds number varied from 1,000 to 17,200 and the Knudsen numbers from 1.6 to 27. The strong interaction parameter varied from 14 to 500.
Nagamatsu, H. T.↗
Diffraction of a plane wave by a three-dimensional corner
By the superposition of the conical solution for the diffraction of a plane pulse by a three dimensional corner, the solution for a general incident plane wave is constructed. A numerical program is presented for the computation of the pressure distribution on the surface due to an incident plane wave of any wave form and at any incident angle. Numerical examples are presented to show the pressure signature at several points on the surface due to incident wave with a front shock wave, two shock waves in succession, or a compression wave with same peak pressure. The examples show that when the distance of a point on the surface from the edges or the vertex is comparable to the distance for the front pressure raise to reach the maximum, the peak pressure at that point can be much less than that given by a regular reflection, because the diffracted wave front arrives at that point prior to the arrival of the peak incident wave.
Ting, L.↗
Analysis of requirements for GEOS-C laser cube-corner reflector panels
A mathematical analysis of the tradeoffs and requirements was performed to develop an improved array design which will give stronger returns at lower elevation angles and reduce pulse spread in the return. It was determined that a zenith angle of 75deg can be obtained with an array with an area of 0.28 sq m, if the array is shaped on the surface of a 45 deg cone whose axis is coincident to the satellite axis. The total weight of the truncated pyramid array with 270 cube corners is calculated to be not more than 50% greater than the GEOS 2 array, while the efficiency is increased 275%.
Minott, P. O.↗
Down-bucklng of a corner of a descending plate
A model of the earth's crust is presented as a set of rigid crustal blocks in which the crust is consumed, compressed, or created only at the boundaries of the blocks. As such the trench boundary moves with respect to the colliding plates because of down-buckling at the corner of the descending plate. It is further shown that this mechanism requires plate consumption of the descending plate at a rate faster than the relative plate motion, which in turn causes infilling of the basin behind the arc to compensate for the increased destruction. It is demonstrated that earthquake, heat flow, paleomagnetic, gravity anomaly, and geologic data derived from Japan and the Sea of Japan support the model.
Lowrey, B. E.↗
Numerical solution for the inviscid supersonic flow in the corner formed by two intersecting wedges.
The inviscid, interference corner flow generated by two intersecting wedges immersed in a supersonic stream is obtained by use of a second-order, shock-capturing, finite-difference approach. The governing equations are solved iteratively in conical coordinates to yield the flow structure consisting of multiple shock and slip surfaces. The numerical results for shock wave and slip surface position and structure, pitot pressure traverses, and surface pressure distributions are compared with experimental data obtained over a wide range of Reynolds numbers. The comparisons show the best agreement with the high Reynolds number (greater than 3,000,000) results for which the boundary layer is turbulent.
Kutler, P.↗
The statistics of laser returns from cube-corner arrays on satellite
A method first presented by Goodman is used to derive an equation for the statistical effects associated with laser returns from satellites having retroreflecting arrays of cube corners. The effect of the distribution on the returns of a satellite-tracking system is illustrated by a computation based on randomly generated numbers.
Lehr, C. G.↗
Stress intensity factors for deep cracks emanating from the corner formed by a hole intersecting a plate surface
A technique consisting of a marriage between stress freezing photoelasticity and a numerical method was used to obtain stress intensity factors for natural cracks emanating from the corner at which a hole intersects a plate surface. Geometrics studied were: crack depth to thickness ratios of approximately 0.2, 0.5, and 0.75; crack depth to crack length ratios of approximately 1.0 to 2.0. All final crack geometries were grown under monotonic loading and growth was not self similar with most of the growth occurring through the thickness under remote extension. Stress intensity plate surface K sub s factors were determined at the intersection of the flaw border with the plate surface K sub s and with the edge of the hole K sub h. Results showed that for the relatively shallow flaws K sub h approximately equal to 1.5 K sub s, for the moderately deep flaws K sub h approximately equal to K sub s, and for the deep flaws K sub h approximately equal to 0.5 K sub s, revealing a severe sensitivity of K to flaw geometry.
Mcgowan, J. J.↗
Stress intensity factors for deep cracks emanating from the corner formed by a hole intersecting a plate surface
A technique consisting of freezing photo-elasticity and a numerical method was used to obtain stress intensity factors for natural cracks emanating from the corner at which a hole intersects a plate surface. Geometries studied were: (1) crack depth to thickness ratios of approximately 0.2, (2) 0.5 and 0.75; (3) crack depth to crack length ratios of approximately 1.0 to 2.0; and (4) crack length to hole radius ratios of about 0.5 to 2.0. All final crack geometries were grown under monotonic loading and growth was not self similar, with most of the growth occuring through the thickness under remote extension. Stress intensity factors were determined at the intersection of the flaw border.
Mcgowan, J. J.↗
Numerical solutions of the supersonic, laminar flow over a two-dimensional compression corner
Numerical solutions of Navier-Stokes equations are presented for the supersonic laminar flow over a two-dimensional compression corner. A well-known time-dependent method has been used wherein the asymptotic steady solutions of the unsteady Navier-Stokes equations are obtained with the Brailovskaia (1965) finite-difference scheme.
Carter, J. E.↗
Measurement of the lidar cross sections of cube corner arrays for laser ranging of satellites
The satellite coordinate system necessary to describe the location and orientation of each cube corner in the array is discussed. The method of optical testing is described along with the gain function, and computational methods for deriving the gain function and experimental values for it. The velocity aberration is derived as a function of satellite orbit, a complete method for cross section evaluation is described, and finally the radar equation is described.
Minott, P. O.↗
Numerical solutions of supersonic and hypersonic laminar flows over a two-dimensional compression corner
An efficient time-splitting, second-order accurate, numerical scheme is used to solve the complete Navier-Stokes equations for supersonic and hypersonic laminar flow over a two-dimensional compression corner. A fine, exponentially stretched mesh spacing is used in the region near the wall for resolving the viscous layer. Good agreement is obtained between the present computed results and experimental measurement for a Mach number of 14.1, a Reynolds number of 104,000, and wedge angles of 15, 18, and 24 deg. The details of the pressure variation across the boundary layer are given, and a correlation between the leading edge shock and the peaks in surface pressure and heat transfer is observed.
Hung, C. M.↗
Cube corner retroreflector test and analysis
Cube corner retroreflectors with nominal dihedral angles of 90 deg 0 min 1.5 sec were fabricated, tested, and analyzed to determine the return energy in the annular ring of the far field diffraction pattern required by the Laser Geodynamic Satellite. Performance was assessed for variations in the dihedral angles, optical surfaces, and thermal environment. Despite relatively high independent axial and radial sensitivities, the changes caused by the anticipated thermal environment were found to be negligible; however, there were substantial variations between the analytical predictions and measured performance.-
Zurasky, J. L.↗
Computation of the inviscid supersonic flow over an external axial corner
A second-order finite-difference procedure is used to evaluate the inviscid supersonic flowfield surrounding an external axial corner composed of swept planar compression surfaces and representing the inlets on existing high-speed aircraft. The governing partial differential equations in conservation-law form are hyperbolic with respect to the axial coordinate and are solved iteratively by means of MacCormack's algorithm. The procedure treats both the peripheral shock wave and vortical singularities as discontinuities. Numerical results are presented for two parametric studies regarding the effects on the flowfield of varying the free-stream Mach number and the leading edge sweep of the horizontal wedge. Results of parametric Mach number study agree with the Mach number independence principle in that as the Mach number increases, such characteristics as shock shape, cross-flow sonic line location, and vortical singularity position approach an asymptote.
Kutler, P.↗
Diffraction of a shock wave by a compression corner. I - Regular reflection
The unsteady, two-dimensional flowfield resulting from the interaction of a moving planar shock wave with a compression corner is determined using a second-order, discontinuity-fitting, finite-difference approach. The time-dependent Euler equations are transformed to normalize the distance between the body and peripheral shock and to include the existing self-similar property of the flow. The resulting set of partial differential equations in conservation-law form is then solved in a time-dependent fashion using MacCormack's scheme. The vortical singularity, which lies on the body surface, and the single reflected shock are both treated as discontinuities in the numerical procedure. The results of the numerical simulation compare quite favorably with existing experimental interferograms and yield better flowfield resolution than previous first-order, shock-capturing, numerical solutions.
Kutler, P.↗
Numerical simulation of supersonic and hypersonic turbulent compression corner flows using relaxation models
Relaxation turbulence eddy viscosity models are incorporated to solve the complete Navier-Stokes equations for supersonic and hypersonic flows over a two-dimensional compression corner. The system of equations is solved by a time-split, second-order accurate numerical scheme. Details of relaxation process are studied, and several relaxation models are tested and compared. Good improvement in the prediction of upstream pressure propagation is obtained for a Mach number of 2.96, and Reynolds number of 10,000,000, with wedge angle of 25 deg. However, the application of the relaxation models to hypersonic flow at Mach number 8.66 and Reynolds number of 22,000,000, with highly cooled wall, shows unfavorable effects on heat transfer and skin friction in the reattachment and recompression regions.
Hung, C. M.↗
Diffraction of a shock wave by a compression corner; regular and single Mach reflection
The two dimensional, time dependent Euler equations which govern the flow field resulting from the injection of a planar shock with a compression corner are solved with initial conditions that result in either regular reflection or single Mach reflection of the incident planar shock. The Euler equations which are hyperbolic are transformed to include the self similarity of the problem. A normalization procedure is employed to align the reflected shock and the Mach stem as computational boundaries to implement the shock fitting procedure. A special floating fitting scheme is developed in conjunction with the method of characteristics to fit the slip surface. The reflected shock, the Mach stem, and the slip surface are all treated as harp discontinuities, thus, resulting in a more accurate description of the inviscid flow field. The resulting numerical solutions are compared with available experimental data and existing first-order, shock-capturing numerical solutions.
Vijayashankar, V. S.↗
Investigation of an incompressible flow along a corner by an alternating direction implicit method
The axial corner flow is analyzed for the incompressible laminar boundary layer flow. The governing equations are derived from the Navier-Stokes equations by neglecting second derivative terms of the axial direction. An alternating direction implicit method is used to solve the equations in primitive variables.
Goglia, G. L.↗