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Proceeding from the basic assumptions of the Batho-Bredt theory on twisting failure of thin-walled columns, the discrepancies most frequently encountered are analyzed. A generalized approximate method is suggested for the determination of the disturbances in the stress condition of the column, induced by the constrained warping in one of the end sections.
We study the performance of two selected RANS models (SST-$k$-$\omega$ and Baldwin-Lomax) to simulate the mean wall-shear and pressure data obtained from a distributed-roughness-related experimental campaign conducted at Ahmic Aerospace, LLC, located in Ohio, US. A structured compressible Navier-Stokes in-house solver, DPLR, is used to conduct the RANS simulations. As the final objective is to perform the studies under high-enthalpy flow conditions, such as inside the AHF facility at NASA-Ames Research Center (ARC), the current investigation focuses on the low-enthalpy cases using Ahmic's high-Reynolds-number supersonic wind tunnel as the initial step to simplify the flow physics. Furthermore, the wind tunnel simulations are conducted with perfectly-smooth walls to further simplify the problem and perform the initial testing of different solver-based RANS models. The Baldwin-Lomax model is observed to be more accurate than the SST model. However, when these RANS models and their roughness augmentation models are utilized to study their accuracy with respect to the experimental datasets, where the roughness effects are activated, both models perform well for a low roughness height case. However, as the roughness height increases, the SST model more accurately predicts the wall data (shear and pressure) than the Baldwin-Lomax model. Therefore, this present work has built a solid foundation for selecting the best RANS model to study the wall data under high-enthalpy flow conditions at the AHF facility soon.
A formation of wave energy flow was developed for motion in curved ducts. A parametric study over a range of frequencies determined the ability of circular bends to transmit energy for the case of perfectly rigid walls.
The Monte Carlo technique is proposed for the determination of the acoustical pressure-time history at chosen points in a partial enclosure, the central idea of this technique being the tracing of acoustical rays. A statistical model is formulated and an algorithm for pressure is developed, the conformity of which is examined by two approaches and is shown to give the known results. The concepts that are developed are applied to the determination of the transient field due to a sound source in a homogeneous medium in a rectangular enclosure with perfect reflecting walls, and the results are compared with those presented by Mintzer based on the Laplace transform approach, as well as with a normal mode solution.
Investigation of the ability of circular bends to transmit acoustic energy flux. A formulation of wave-energy flow is developed for motion in curved ducts. A parametric study over a range of frequencies shows the ability of circular bends to transmit energy in the case of perfectly rigid walls.
During this period, the computations of the impedance elements were completed. These include interactions between the two electric current modes, the elecric current mode and the magnetic current mode, and the two magnetic current modes. An accurate and efficient formulation of computing interactions between electric current mode and magnetic current mode was accomplished. This, together with other subroutines allows for the fill-in of all the elements in the matrix. After the fill-in of the impedance elements in the matrix, the forward problem is accomplished. That is, given the specification of the horn and the excitating waveguide mode, the radiation pattern of the antenna based on the integral equation can be obtained. An example case was run for a standard X-band gain-horn (DBG-520). The H- and E-plane patterns of this horn antenna with perfectly conducting walls are compared with the gain pattern available from the manufacturer for up to the first side lobe. Good agreements are obtained although the cross polarization has not yet been accounted for. The effect of the lossy coating on the radiation pattern was also investigated. The resulting E-plane pattern shows about 3-dB improvement in the first sidelobe and 4-dB improvement in the second sidelobe.
A quantization procedure for the electromagnetic field in a rectangular cavity with perfect conductor walls is presented, where a decomposition formula of the field plays an essential role. All vector mode functions are obtained by using the decomposition. After expanding the field in terms of the vector mode functions, we get the quantized electromagnetic Hamiltonian.
In 1983, Ambjorn and Wolfram produced plots of the energy density of the quantum mechanical electromagnetic fluctuations in a volume of vacuum bounded by perfectly conducting walls in the shape of a rectangular cavity of dimensions a(1), a(2), and a(3), as a function of the ratios a(2)/a(1) and a(3)/a(1). Portions of these plots are double-valued, in that they allow rectangular cavities with the same, value of a(2)/a(1), but different values of a(3)/a(1), to have the saint total energy. Using these double-valued regions of the plots, I show that it is possible to define a "Casimir Vacuum Energy Extraction Cycle" which apparently would allow for the endless extraction of energy from the vacuum in the Casimir cavity by cyclic manipulation of the Casimir cavity dimensions.
The EM backscatter from a two-dimensional S-shaped inlet cavity is analyzed using three different techniques, namely a hybrid combination of asymptotic high frequency and modal methods, an integral equation method, and the geometrical optics ray method, respectively. This inlet has a thin absorber coating on its perfectly conducting inner walls and the planar interior termination is made perfectly conducting. The effect of the absorber on the inner wall is treated via a perturbation scheme in the hybrid approach where it is assumed that the loss is sufficiently small for the method to be valid. The results are compared with the backscatter from a straight inlet cavity to evaluate the effect of offsetting the termination in the S-bend configuration such that it is not visible from the open end of the inlet. The envelope of the backscatter pattern for the straight inlet is always seen to peak around the forward axis due to the large return from the directly visible termination, and the pattern envelope tapers off away from the forward axis. Offsetting the termination causes the envelope of the backscatter pattern to flatten out, thereby reducing the return near the forward axis by several dB. The absorber coating reduces the pattern level of the straight inlet in directions away from the forward axis but has little effect on the peak near the axis; furthermore, the absorber coating is seen to consistently reduce the backscatter from the S-bend inlet for almost all incidence angles. The hybrid method gives excellent agreement with experimental data and with the integral equation solution, whereas, the geometrical optics ray tracing method is able to generally predict the average of the bachscatter pattern but not the pattern details.
The electromagnetic (EM) scattering from a planar termination located inside relatively arbitrarily shaped open-ended waveguide cavities with smoothly curved interior walls is analyzed using a Gaussian Beam (GB) expansion of the incident plane wave fields in the open end. The cavities under consideration may contain perfectly-conducting interior walls with or without a thin layer of material coating, or the walls may be characterized by an impedance boundary condition. In the present approach, the GB's are tracked only to the termination of the waveguide cavity via beam reflections from interior waveguide cavity walls. The Gaussian beams are tracked approximately only along their beam axes; this approximation which remains valid for relatively well focussed beams assumes that an incident GB gives rise to a reflected GB with parameters related to the incident beam and the radius of curvature of the wall. It is found that this approximation breaks down for GB's which come close to grazing a convex surface and when the width of the incident beam is comparable to the radius of curvature of the surface. The expansion of the fields at the open end depend on the incidence angle only through the expansion coefficients, so the GB's need to be tracked through the waveguide cavity only once for a wide range of incidence angles. At the termination, the sum of all the GB's are integrated using a result developed from a generalized reciprocity principle, to give the fields scattered from the interior of the cavity. The rim edge at the open end of the cavity is assumed to be sharp and the external scattering from the rim is added separately using Geometrical Theory of Diffraction. The results based on the present approach are compared with solutions based on the hybrid asymptotic modal method. The agreement is found to be very good for cavities made up of planar surfaces, and also for cavities with curved surfaces which are not too long with respect to their width.
A theory is developed in which a perfectly conducting cylindrical wall is used to describe incompressible MHD turbulence. Dynamic equations of incompressible MHD and its associated fields are expanded in a system of vector eigenfunctions of the curl. The total energy, magnetic helicity, and cross helicity have simple quadratic expressions in the expansion coefficients. The invariants are temporally constant for a truncation at a large, but finite, number of coefficients. The invariants are used to construct canonical distributions. It is noted that for all initial conditions, including quiescent ones, the mean-square velocity fields have finite values. The stability problem is transformed into a search for values of the integral variants which minimize the mean-square velocity fields. This leads to an extremal helicity principle.
Preliminary results are reported from application of a three-dimensional spectral method model to the solution of the Strauss (1976) reduced MHD equations. The investigation was focused on describing MHD turbulence in a current-carrying bounded magnetofluid. A cylindrical geometry with a square cross-section was considered, with the walls being rigid perfect conductors with free-slip boundary conditions. A uniform magnetic field and the electric current density both point in the z-direction. Initial conditions are specified which feature small amounts of random noise expressed as Fourier modes. Linearized equations are defined for tracing the movement to equlibrium conditions or other temporal development. The model is further refined with nonlinear equations to examine the effects of the appearance of disruptions. Comparisons are drawn between solutions obtained with linear and nonlinear equations, with an eye to the associated physical realities.
A finite-element Galerkin formulation was used to study the effect of material surface deposits on the reflective characteristics of straight uniform ducts with PEC (perfectly electric conducting) walls. Over a wide frequency range, the effect of both single and multiple surface deposits on the duct reflection coefficient were examined. The power reflection coefficient was found to be significantly increased by the addition of deposits on the wall.
A finite-element Galerkin formulation has been used to study the effect of material surface deposits on the reflective characteristics of straight uniform ducts with PEC (perfectly electric conducting) walls. Over a wide frequency range, the effect of both single and multiple dielectric surface deposits on the duct reflection coefficient were examined. The power reflection coefficient was found to be significantly increased by the addition of deposits on the wall.
Mixed convection in a rectangular channel (width/height = 2) with bottom-heated and top-cooled sections is studied by laser Doppler anemometry in nitrogen at Ra = 22,200 and Re = 18.75, 36, and 54. At the lower Re values, symmetry breaking is observed in steady but spatially oscillating flows that prevail over a certain distance from the leading edge of the differentially heated section. Further downstream, unsteady flows are found even for Re = 18.75. Numerical models are used to investigate the effects of adiabatic, conducting (with a conductive-convective heat transfer coefficient), and perfectly conducting side walls; channel tilts and Prandtl number dependence. Good agreement between calculations and experiment is obtained for longitudinal convective roll velocities. The transverse velocities are found to be independent of Re.
This paper presents a numerical study that investigate the effects of nonequilibrium chemistry, and in particular, wall catalycity on the separated flow region generated by an oblique shock wave impinging upon a flat plate boundary layer. To obtain a solution to this problem, the full two dimensional Navier-Stokes equations were solved using MacCormack's predictor-corrector time dependent technique on a rectangular grid. Nonequilibrium chemistry was included by utilizing the 5 species, 17 reaction modified Dunn-Kang chemical kinetics model. Separate results were obtained for: calorically perfect, chemically reacting - noncatalytic wall, and chemically reacting - fully catalytic wall cases, for a given set of flow conditions. A direct comparison of all three cases revealed a slight decrease in the peak heat transfer for the noncatalytic wall case, as compared to the calorically perfect case. On the other hand, the fully catalytic wall case had a tremendous increase in the peak surface heat transfer. It is concluded that, for the particular conditons treated here (nearly frozen flow in the free stream), the effects of the nonequilibrium chemically reacting flow on the shock-wave/boundary-layer interaction depend critically on the catalycity of the wall, having virtually no effect for the case of a noncatalytic wall, and exerting a tremendous effect for a fully catalytic wall.
A finite-element Galerkin formulation has been developed to study transverse magnetic (TM) wave propagation in 2-D S-curved ducts with both perfectly conducting and absorbing walls. The reflection and transmission at the entrances and the exits of the curved ducts are determined by coupling the finite-element solutions in the curved ducts to the eigenfunctions of an infinite, uniform, perfectly conducting duct. Example solutions are presented for a double mitred and S-ducts of various lengths. The length of the S-duct is found to significantly effect the reflective characteristics of the duct. Also, the effect of curvature on an absorbing duct is illustrated.
The performance of two axisymmetric nozzles which were designed to produce uniform, parallel flow with nominal Mach numbers of 4 and 8 is examined. A free-piston-driven shock tube was used to supply the nozzle with high-temperature, high-pressure test gas. The inviscid design procedure treated the nozzle expansion in two stages. Close to the nozzle throat, the nozzle wall was specified as conical and the gas flow was treated as a quasi-one-dimensional chemically-reacting flow. At the end of the conical expansion, the gas was assumed to be calorically perfect, and a contoured wall was designed (using method of characteristics) to convert the source flow into a uniform and parallel flow at the end of the nozzle. Performance was assessed by measuring Pitot pressures across the exit plane of the nozzles and, over the range of operating conditions examined, the nozzles produced satisfactory test flows. However, there were flow disturbances in the Mach 8 nozzle flow that persisted for significant times after flow initiation.