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Interaction of plane, oblique, incident reflecting shock wave with turbulent boundary layer on cooled surface - graphs
An experimental investigation of the ignition of individual fuel drops after their interaction with an incident and a reflected shock wave near the end wall of a shock tube has been carried out. The influence of the aerodynamic shattering of the fuel drop by the convective flow on the ignition characteristics has been examined by varying the drop-end wall separation distance. Data are presented which show the ignition delay times to be a function of the various experimental conditions encountered in this study. A comparison is made with previous investigations concerning the ignition of a liquid fuel drop due only to the interaction with an incident shock wave.
Hydrodynamic variables in primary and reflected argon and nitrogen shock waves
Interaction of plane, oblique, incident reflecting shock wave with turbulent boundary layer on cooled surface - summary
Analytical and numerical calculation of the effects of radiative cooling on the flow field and heat transfer behind a reflected shock wave. The analytical solutions are developed by an expansion procedure about the Newtonian limit - i.e., the flow variables are expanded in the small parameter epsilon representing the initial density ratio across the shock front. Solutions carried out through the zeroth- and first-orders in epsilon show an accuracy to the order of epsilon squared - namely, for the specific conditions considered the analytically calculated enthalpy changes agree to within 2% with the numerically computed changes. The numerical procedure consists of a finite-difference calculation with pressure gradients neglected. The analytical calculations show that pressure-gradient effects may be neglected, except at very long times when the shocked gas has cooled by a large amount. The present calculations show much greater shock-wave attenuation than does a previous numerical computation. This difference is attributed to a better representation of the thermodynamic properties in the present calculations.
The diffraction of a TM sub o surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation, the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained by a combination of the generalized scattering matrix technique and function theoretic methods.
The diffraction of a TM sub 0 surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained via a combination of the generalized scattering matrix technique and the Wiener-Hopf procedure. Expressions for the reflection and diffraction coefficients contain integrals which can be evaluated numerically.
We have revisited the problem of propagation of toroidal and linear Alfven waves formulated by Heinemann and Olbert (1980) to compare Wentzel-Kramers-Brillouin (WKB) and non-WKB waves and their effects on the solar wind. They considered two solar wind models and showed that reflection is important for Alfven waves with periods of the order of one day and longer and that non-WKB Alfven waves are no more effective in accelerating the solar wind than in WKB waves. There are several recently published papers that seem to indicate that Alfven waves with periods of the order of several minutes should be treated as non-WKB waves and that these non-WKB waves exert a stronger acceleration force than WKB waves. The purposse of this paper is to study the origin of these discrepancies by performing parametric studies of the behavior of the waves under a variety of different conditions. In addition, we want to investigate two problems that have not been addressed by Heinimann and Olbert, namely, calculate the efficieny of Alfven wave reflection by using the reflection coefficient and identfy the region of strongest wave reflection in different wind models. To achieve these goals, we investigate the influence of temperature, electron desity distribution, wind velocity, and magnetic field strength on te waves. The obtained results clearly demonstrate that Alfven wave reflection is strongly model dependent and that the strongest reflection can be expected in models with the base temperatures higher than 10(exp 6) K and with the base densities lower than 7 x 10(exp 7)/cu cm. In these models as well as in the models with lower temperatures and higher densities Alfven waves with periods as short as several minutes have negligible reflection so that they can be treated as WKB waves; however, for Alfven waves with periods of the order of one hour or longer reflection is significant, requiring a non-WKB treatment. We also show that non-WKB, linear Alfven waves are always less effective in accelerating the plasma than WKB Alfven waves. Finally, it is evident from our results that the region of strongest wave reflection is usually located at the base of the models and hence that interpretation of wave reflection based soley on the reflection coefficient can be misleading.
We have revisited the problem of propagation of toroidal and linear Alfven waves formulated by Heinemann and Olbert (1980) to compare WKB and non-WKB waves and their effects on the solar wind. They considered two solar wind models and showed that reflection is important for Alfven waves with periods of the order of one day and longer, and that non-WKB Alfven waves are no more effective in accelerating the solar wind than WKB waves. There are several recently published papers which seem to indicate that Alfven waves with periods of the order of several minutes should be treated as non-WKB waves and that these non-WKB waves exert a stronger acceleration force than WKB waves. The purpose of this paper is to study the origin of these discrepancies by performing parametric studies of the behavior of the waves under a variety of different conditions. In addition, we want to investigate two problems that have not been addressed by Heinemann and Olbert, namely, calculate the efficiency of Alfven wave reflection by using the reflection coefficient and identify the region of strongest wave reflection in different wind models. To achieve these goals, we investigated the influence of temperature, electron density distribution, wind velocity and magnetic field strength on the waves. The obtained results clearly demonstrate that Alfven wave reflection is strongly model dependent and that the strongest reflection can be expected in models with the base temperatures higher than 10(exp 6) K and with the base densities lower than 7 x 10(exp 7) cm(exp -3). In these models as well as in the models with lower temperatures and higher densities, Alfven waves with periods as short as several minutes have negligible reflection so that they can be treated as WKB waves; however, for Alfven waves with periods of the order of one hour or longer reflection is significant, requiring a non-WKB treatment. We also show that non-WKB, linear Alfven waves are always less effective in accelerating the plasma than WKB Alfven waves. Finally, it is evident from our results that the region of strongest wave reflection is usually located at the base of the models, and hence that interpretation of wave reflection based solely on the reflection coefficient can be misleading.
The ignition of mixtures of silane, hydrogen, and oxygen diluted with nitrogen was studied in a chemical kinetic shock tube. Ignition delay time measurements were made behind reflected shock waves at pressures of 1.25 atm and 1.35 atm and temperatures ranging from approximately 800 K to 1050 K for two mixtures with silane-oxygen equivalence ratios of 1.0 and 0.5, respectively. Enhancement of the ignition by use of silane was observed experimentally by the failure of a similar mixture containing only hydrogen, oxygen, and nitrogen to ignite during the maximum test time available for these test conditions.
A new and simple type of millimeter-wave isolator using a solid-state magnetoplasma in a reflection-beam system is described. Some data are presented showing performance at 94 GHz. Practical considerations indicate that performance should be much closer to ideal at higher frequencies.
A radiometric method for the measurement of gas temperature in self-absorbing gases has been applied in the study of shock tube generated flows. This method involves making two absolute intensity measurements at identical wavelengths, but for two different pathlengths in the same gas sample. Experimental results are presented for reflected shock waves in air at conditions corresponding to incident shock velocities from 7 to 10 km/s and an initial driven tube pressure of 1 torr. These results indicate that, with this technique, temperature measurements with an accuracy of + or - 5 percent can be carried out. The results also suggest certain facility related problems.
Ideally, the reflection of a shock from the closed end of a shock tube provides, for laboratory study, a quantity of stationary gas at extremely high temperature. Because of the action of viscosity, however, the flow in the real case is not one-dimensional, and a boundary layer grows in the fluid following the initial shock wave. In this paper simplifying assumptions are made to allow an analysis of the interaction of the shock reflected from the closed end with the boundary layer of the initial shock afterflow. The analysis predicts that interactions of several different types will exist in different ranges of initial shock Mach number. It is shown that the cooling effect of the wall on the afterflow boundary layer accounts for the change in interaction type. An experiment is carried out which verifies the existence of the several interaction regions and shows that they are satisfactorily predicted by the theory. Along with these results, sufficient information is obtained from the experiments to make possible a model for the interaction in the most complicated case. This model is further verified by measurements made during the experiment. The case of interaction with a turbulent boundary layer is also considered. Identifying the type of interaction with the state of turbulence of the interacting boundary layer allows for an estimate of the state of turbulence of the boundary layer based on an experimental investigation of the type of interaction. A method is proposed whereby the effect of the boundary-layer interaction on the strength of the reflected shock may be calculated. The calculation indicates that the reflected shock is rapidly attenuated for a short distance after reflection, and this result compares favorably with available experimental results.
Problems associated with quantum mechanical reflection of miniband carriers at the ends of superlattices are examined. Moebius transformations which map miniband Bloch wave reflectivity into plane wave reflectivity and vice versa are derived. These transformations facilitate the design of blocking and antiblocking layers which are analogous to reflective and antireflective coatings on optical elements. An example of termination layer design which is easy to implement is given. Applications include superlattice infrared detector design.
A dielectrically loaded four port waveguide circulator is used with a reflected wave maser connected to a second port between first and third ports to form one of a plurality of cascaded maser waveguide structures. The fourth port is connected to a waveguide loaded with microwave energy absorbing material. The third (output signal) port of one maser waveguide structure is connected by a waveguide loaded with dielectric material to the first (input) port of an adjacent maser waveguide structure, and the second port is connected to a reflected wave maser by a matching transformer which passes the signal to be amplified into and out of the reflected wavemaser and blocks pumping energy in the reflected wave maser from entering the circulator. A number of cascaded maser waveguide structures are thus housed in a relatively small volume of conductive material placed within a cryogenically cooled magnet assembly.
A study of the reflection of Alfven waves at a horizontally inhomogeneous ionosphere has been carried out. In this study, the Alfven speed above the ionosphere is assumed to be uniform and the ionosphere is treated as a height-integrated conducting slab. Analytical and numerical results indicate that the horizontal nonuniformity of the ionospheric conductivity can lead to a rotation of the reflected wave fields and cause field-aligned currents that originate in the ionosphere. A strong conductivity nonuniformity on the direction perpendicular to the incident wave field, large Hall to Pedersen conductivity ratios, and low conductivity values lead to a large rotation of the reflected wave field in the range from a few to 40 deg. The implications of the theoretical results for some ionospheric phenomena are presented, including comments on the Harang discontinuity and sun-aligned arcs.
The reflected signature of an optical fiber Bragg grating is analyzed using the transfer function method. This approach is capable to cast all relevant quantities into proper places and provides a better physical understanding. The relationship between reflected signal, number of periods, index of refraction, and reflected wave phase is elucidated. The condition for which the maximum reflectivity is achieved is fully examined. We also have derived an expression to predict the reflectivity minima accurately when the reflected wave is detuned. Furthermore, using the segmented potential approach, this model can handle arbitrary index of refraction profiles and compare the strength of optical reflectivity of different profiles. The condition of a non-uniform grating is also addressed.
A coupled magnetospheric-ionospheric (M-I) magnetohydrodynamic (MHD) model has been used to simulate the formation of Sun-aligned polar cap arcs for a variety of interplanetary magnetic field (IMF) dependent polar cap convection fields. The formation process involves launching an Alfven shear wave from the magnetosphere to the ionosphere where the ionospheric conductance can react self-consistently to changes in the upward currents. We assume that the initial Alfven shear wave is the result of solar wind-magnetosphere interactions. The simulations show how the E region density is affected by the changes in the electron precipitation that are associated with the upward currents. These changes in conductance lead to both a modified Alfven wave reflection at the ionosphere and the generation of secondary Alfven waves in the ionosphere. The ensuing bouncing of the Alfven waves between the ionosphere and magnetosphere is followed until an asymptotic solution is obtained. At the magnetosphere the Alfven waves reflect at a fixed boundary. The coupled M-I Sun-aligned polar cap arc model of Zhu et al.(1993a) is used to carry out the simulations. This study focuses on the dependence of the polar cap arc formation on the background (global) convection pattern. Since the polar cap arcs occur for northward and strong B(sub y) IMF conditions, a variety of background convection patterns can exist when the arcs are present. The study shows that polar cap arcs can be formed for all these convection patterns; however, the arc features are dramatically different for the different patterns. For weak sunward convection a relatively confined single pair of current sheets is associated with the imposed Alfven shear wave structure. However, when the electric field exceeds a threshold, the arc structure intensifies, and the conductance increases as does the local Joule heating rate. These increases are faster than a linear dependence on the background electric field strength. Furthermore, above the threshold, the single current sheet pair splits into multiple current sheet pairs. For the fixed initial ionospheric and magnetospheric conditions used in this study, the separation distance between the current pairs was found to be almost independent of the background electric field strength. For either three-cell or distorted two-cell background convection patterns the arc formation favored the positive B(sub y) case in the northern hemisphere.