Experimental Study and Numerical Simulation of Cellular Structures and Mach Reflection of Gaseous Detonation Wave

In this paper the Deflagration to Detonation Transition (DDT) process of gaseous H-2-O-2 mixture and Mach reflection of gaseous detonation wave on a wedge have been conducted experimentally. The cellular pattern of DDT process and Mach reflection were obtained from experiments with wedge angle theta = 10(0) similar to 40(0) and initial pressure of gaseous mixture 16kPa similar to 26.7kPa. The 2-D numerical simulations of DDT process and Mach reflection of detonation wave were performed by using the simplified ZND model and improved space-time conservation element and solution element (CE/SE) method. The numerical cellular structures were compared with the cellular patterns of soot track. Compared results were shown that it is satisfactory. The characteristic comparisons on Mach reflection of air shock wave and detonation wave were carried also out and their differences were given.

The Droplet Group Micro-Explosions, Viscosity and Atomization Characteristics of W/O Emulsions

The spray of emulsified fuel, composed of diesel fuel, water and methanol can make micro-explosion under high temperature conditions, and the viscosity and the atomization characteristics of emulsion have significant effects on the micro- explosion of emulsions. To clarify the combustion mechanism of water-in-oil emulsion sprays, combustion bomb experiments were carried out, and the droplet group micro- explosions in W/O fuel emulsion sprays in a high-pressure, high-temperature bomb were observed clearly by a multi-pulsed, off-axis, image-plane ruby laser holocamera and continuously by a high-speed CCD camera.The viscosity and atomization characteristics of emulsions were also studied experimentally. The experimental results show that the higher concentration of the aqueous phase (water-methanol) (<50%) increases the viscosity of the emulsions, especially for higher agent concentration, and higher aqueous phase concentration and higher viscosity results in lager Sauter Mean Diameter (SMD). The experiment results also show that the different kinds of emulsifying agents, with different Hydrophile-Lipophile Balance (HLB) values, have significant influence on the viscosity of the emulsions.

IP Simulation of Micro Gas Flows under 3-D Head Sliders

Gas film lubrication of a three-dimensional flat read-write head slider is calculated using the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method, respectively. The pressure distributions on the head slider surface at different velocities and flying heights obtained by the two methods are in excellent agreement. IP method is also employed to deal with head slider with three-dimensional complex configuration. The pressure distribution on the head slider surface and the net lifting force obtained by the IP method also agree well with those of DSMC method. Much less (of the order about 10(2) less) computational time (the sum of the time used to reach a steady stage and the time used in sampling process) is needed by the IP method than the DSMC method and such an advantage is more remarkable as the gas velocity decreases.

Design, Construction and Testing of a Hydraulic Power Take-Off for Wave Energy Converters

This paper presents the construction, mathematical modeling and testing of a scaled universal hydraulic Power Take-Off (PTO) device for Wave Energy Converters (WECs). A specific prototype and test bench were designed and built to carry out the tests. The results obtained from these tests were used to adjust an in-house mathematical model. The PTO was initially designed to be coupled to a scaled wave energy capture device with a low speed and high torque oscillating motion and high power fluctuations. Any Energy Capture Device (ECD) that fulfils these requirements can be coupled to this PTO, provided that its scale is adequately defined depending on the rated power of the full scale prototype. The initial calibration included estimation of the pressure drops in the different components, the pressurization time of the oil inside the hydraulic cylinders and the volumetric efficiency of the complete circuit. Since the overall efficiency measured during the tests ranged from 0.69 to 0.8 and the dynamic performance of the PTO was satisfactory, the results are really promising and it is believed that this solution might prove effective in real devices.

Wave Sensor Technologies, St Petersburg, Florida, March 7-9, 2007: workshop proceedings

The Alliance for Coastal Technologies (ACT) convened a workshop on "Wave Sensor Technologies" in St. Petersburg, Florida on March 7-9, 2007, hosted by the University of South Florida (USF) College of Marine Science, an ACT partner institution. The primary objectives of this workshop were to: 1) define the present state of wave measurement technologies, 2) identify the major impediments to their advancement, and 3) make strategic recommendations for future development and on the necessary steps to integrate wave measurement sensors into operational coastal ocean observing systems. The participants were from various sectors, including research scientists, technology developers and industry providers, and technology users, such as operational coastal managers and coastal decision makers. Waves consistently are ranked as a critical variable for numerous coastal issues, from maritime transportation to beach erosion to habitat restoration. For the purposes of this workshop, the participants focused on measuring "wind waves" (i.e., waves on the water surface, generated by the wind, restored by gravity and existing between approximately 3 and 30-second periods), although it was recognized that a wide range of both forced and free waves exist on and in the oceans. Also, whereas the workshop put emphasis on the nearshore coastal component of wave measurements, the participants also stressed the importance of open ocean surface waves measurement. Wave sensor technologies that are presently available for both environments include bottom-mounted pressure gauges, surface following buoys, wave staffs, acoustic Doppler current profilers, and shore-based remote sensing radar instruments. One of the recurring themes of workshop discussions was the dichotomous nature of wave data users. The two separate groups, open ocean wave data users and the nearshore/coastal wave data users, have different requirements. Generally, the user requirements increase both in spatial/temporal resolution and precision as one moves closer to shore. Most ocean going mariners are adequately satisfied with measurements of wave period and height and a wave general direction. However, most coastal and nearshore users require at least the first five Fourier parameters ("First 5"): wave energy and the first four directional Fourier coefficients. Furthermore, wave research scientists would like sensors capable of providing measurements beyond the first four Fourier coefficients. It was debated whether or not high precision wave observations in one location can take the place of a less precise measurement at a different location. This could be accomplished by advancing wave models and using wave models to extend data to nearby areas. However, the consensus was that models are no substitution for in situ wave data.[PDF contains 26 pages]

Simulation of gas flow over a micro cylinder

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum /particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.

Fluctuation characteristics of arc voltage and jet flow in a non-transferred dc plasma generated at reduced pressure

A torch with a set of inter-electrode inserts between the cathode and the anode/nozzle with a wide nozzle exit was designed to generate plasma jets at chamber pressures of 500–10 000 Pa. The variation of the arc voltage was examined with the change in working parameters such as gas flow rate and chamber pressure. The fluctuation in the arc voltage was recorded with an oscilloscope, and the plasma jet fluctuation near the torch exit was observed with a high-speed video camera and detected with a double-electrostatic probe. Results show that the 300 Hz wave originated from the tri-phase rectified power supply was always detected under all generating conditions. Helmholtz oscillations over 3000 Hz was detected superposed on the 300 Hz wave at gas flow rates higher than 8.8 slm with a peak to valley amplitude lower than 5% of the average voltage value. No appreciable voltage fluctuation caused by the irregular arc root movement is detected, and mechanisms for the arc voltage and jet flow fluctuations are discussed.

Nonlinear dispersive wave problems

The nonlinear partial differential equations for dispersive waves have special solutions representing uniform wavetrains. An expansion procedure is developed for slowly varying wavetrains, in which full nonlinearity is retained but in which the scale of the nonuniformity introduces a small parameter. The first order results agree with the results that Whitham obtained by averaging methods. The perturbation method provides a detailed description and deeper understanding, as well as a consistent development to higher approximations. This method for treating partial differential equations is analogous to the "multiple time scale" methods for ordinary differential equations in nonlinear vibration theory. It may also be regarded as a generalization of geometrical optics to nonlinear problems.

To apply the expansion method to the classical water wave problem, it is crucial to find an appropriate variational principle. It was found in the present investigation that a Lagrangian function equal to the pressure yields the full set of equations of motion for the problem. After this result is derived, the Lagrangian is compared with the more usual expression formed from kinetic minus potential energy. The water wave problem is then examined by means of the expansion procedure.

Wave propagation in an inhomogeneous medium

This paper is in two parts. In the first part we give a qualitative study of wave propagation in an inhomogeneous medium principally by geometrical optics and ray theory. The inhomogeneity is represented by a sound-speed profile which is dependent upon one coordinate, namely the depth; and we discuss the general characteristics of wave propagation which result from a source placed on the sound channel axis. We show that our mathematical model of the sound- speed in the ocean actually predicts some of the behavior of the observed physical phenomena in the underwater sound channel. Using ray theoretic techniques we investigate the implications of our profile on the following characteristics of SOFAR propagation: (i) the sound energy traveling further away from the axis takes less time to travel from source to receiver than sound energy traveling closer to the axis, (ii) the focusing of sound energy in the sound channel at certain ranges, (iii) the overall ray picture in the sound channel.

In the second part a more penetrating quantitative study is done by means of analytical techniques on the governing equations. We study the transient problem for the Epstein profile by employing a double transform to formally derive an integral representation for the acoustic pressure amplitude, and from this representation we obtain several alternative representations. We study the case where both source and receiver are on the channel axis and greatly separated. In particular we verify some of the earlier results derived by ray theory and obtain asymptotic results for the acoustic pressure in the far-field.

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Experimental, Numerical and Analytical Studies of the MHD-driven plasma jet, instabilities and waves

This thesis describes a series of experimental, numerical, and analytical studies involving the Caltech magnetohydrodynamically (MHD)-driven plasma jet experiment. The plasma jet is created via a capacitor discharge that powers a magnetized coaxial planar electrodes system. The jet is collimated and accelerated by the MHD forces.

We present three-dimensional ideal MHD finite-volume simulations of the plasma jet experiment using an astrophysical magnetic tower as the baseline model. A compact magnetic energy/helicity injection is exploited in the simulation analogous to both the experiment and to astrophysical situations. Detailed analysis provides a comprehensive description of the interplay of magnetic force, pressure, and flow effects. We delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms.

When the experimental jet is sufficiently long, it undergoes a global kink instability and then a secondary local Rayleigh-Taylor instability caused by lateral acceleration of the kink instability. We present an MHD theory of the Rayleigh-Taylor instability on the cylindrical surface of a plasma flux rope in the presence of a lateral external gravity. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring at a two-dimensional planar interface.

In the experiment, this instability cascade from macro-scale to micro-scale eventually leads to the failure of MHD. When the Rayleigh-Taylor instability becomes nonlinear, it compresses and pinches the plasma jet to a scale smaller than the ion skin depth and triggers a fast magnetic reconnection. We built a specially designed high-speed 3D magnetic probe and successfully detected the high frequency magnetic fluctuations of broadband whistler waves associated with the fast reconnection. The magnetic fluctuations exhibit power-law spectra. The magnetic components of single-frequency whistler waves are found to be circularly polarized regardless of the angle between the wave propagation direction and the background magnetic field.

Dynamic characterization of micro-particle systems

Ordered granular systems have been a subject of active research for decades. Due to their rich dynamic response and nonlinearity, ordered granular systems have been suggested for several applications, such as solitary wave focusing, acoustic signals manipulation, and vibration absorption. Most of the fundamental research performed on ordered granular systems has focused on macro-scale examples. However, most engineering applications require these systems to operate at much smaller scales. Very little is known about the response of micro-scale granular systems, primarily because of the difficulties in realizing reliable and quantitative experiments, which originate from the discrete nature of granular materials and their highly nonlinear inter-particle contact forces.

In this work, we investigate the physics of ordered micro-granular systems by designing an innovative experimental platform that allows us to assemble, excite, and characterize ordered micro-granular systems. This new experimental platform employs a laser system to deliver impulses with controlled momentum and incorporates non-contact measurement apparatuses to detect the particles’ displacement and velocity. We demonstrated the capability of the laser system to excite systems of dry (stainless steel particles of radius 150 micrometers) and wet (silica particles of radius 3.69 micrometers, immersed in fluid) micro-particles, after which we analyzed the stress propagation through these systems.

We derived the equations of motion governing the dynamic response of dry and wet particles on a substrate, which we then validated in experiments. We then measured the losses in these systems and characterized the collision and friction between two micro-particles. We studied wave propagation in one-dimensional dry chains of micro-particles as well as in two-dimensional colloidal systems immersed in fluid. We investigated the influence of defects to wave propagation in the one-dimensional systems. Finally, we characterized the wave-attenuation and its relation to the viscosity of the surrounding fluid and performed computer simulations to establish a model that captures the observed response.

The findings of the study offer the first systematic experimental and numerical analysis of wave propagation through ordered systems of micro-particles. The experimental system designed in this work provides the necessary tools for further fundamental studies of wave propagation in both granular and colloidal systems.

Wave uplift pressures on horizontal platforms

The major objective of the study has been to investigate in detail the rapidly-varying peak uplift pressure and the slowly-varying positive and negative uplift pressures that are known to be exerted by waves against the underside of a horizontal pier or platform located above the still water level, but not higher than the crests of the incident waves.

In a "two-dimensional" laboratory study conducted in a 100-ft long by 15-in.-wide by 2-ft-deep wave tank with a horizontal smooth bottom, individually generated solitary waves struck a rigid, fixed, horizontal platform extending the width of the tank. Pressure transducers were mounted flush with the smooth soffit, or underside, of the platform. The location of the transducers could be varied.

The problem of a d equate dynamic and spatial response of the transducers was investigated in detail. It was found that unless the radius of the sensitive area of a pressure transducer is smaller than about one-third of the characteristic width of the pressure distribution, the peak pressure and the rise-time will not be recorded accurately. A procedure was devised to correct peak pressures and rise-times for this transducer defect.

The hydrodynamics of the flow beneath the platform are described qualitatively by a si1nple analysis, which relates peak pressure and positive slowly-varying pressure to the celerity of the wave front propagating beneath the platform, and relates negative slowly-varying pressure to the process by which fluid recedes from the platform after the wave has passed. As the wave front propagates beneath the platform, its celerity increases to a maximum, then decreases. The peak pressure similarly increases with distance from the seaward edge of the platform, then decreases.

Measured peak pressure head, always found to be less than five times the incident wave height above still water level, is an order of magnitude less than reported shock pressures due to waves breaking against vertical walls; the product of peak pressure and rise-time, considered as peak impulse, is of the order of 20% of reported shock impulse due to waves breaking against vertical walls. The maximum measured slowly-varying uplift pressure head is approximately equal to the incident wave height less the soffit clearance above still water level. The normalized magnitude and duration of negative pressure appears to depend principally on the ratio of soffit clearance to still water depth and on the ratio of platform length to still water depth.

Magnetic field and pressure effects in a saturated gas laser amplifier

Theoretical and experimental studies of a gas laser amplifier are presented, assuming the amplifier is operating with a saturating optical frequency signal. The analysis is primarily concerned with the effects of the gas pressure and the presence of an axial magnetic field on the characteristics of the amplifying medium. Semiclassical radiation theory is used, along with a density matrix description of the atomic medium which relates the motion of single atoms to the macroscopic observables. A two-level description of the atom, using phenomenological source rates and decay rates, forms the basis of our analysis of the gas laser medium. Pressure effects are taken into account to a large extent through suitable choices of decay rate parameters.

Two methods for calculating the induced polarization of the atomic medium are used. The first method utilizes a perturbation expansion which is valid for signal intensities which barely reach saturation strength, and it is quite general in applicability. The second method is valid for arbitrarily strong signals, but it yields tractable solutions only for zero magnetic field or for axial magnetic fields large enough such that the Zeeman splitting is much larger than the power broadened homogeneous linewidth of the laser transition. The effects of pressure broadening of the homogeneous spectral linewidth are included in both the weak-signal and strong-signal theories; however the effects of Zeeman sublevel-mixing collisions are taken into account only in the weak-signal theory.

The behavior of a He-Ne gas laser amplifier in the presence of an axial magnetic field has been studied experimentally by measuring gain and Faraday rotation of linearly polarized resonant laser signals for various values of input signal intensity, and by measuring nonlinearity - induced anisotropy for elliptically polarized resonant laser signals of various input intensities. Two high-gain transitions in the 3.39-μ region were used for study: a J = 1 to J = 2 (3s₂ → 3p₄) transition and a J = 1 to J = 1 (3s₂ → 3p₂) transition. The input signals were tuned to the centers of their respective resonant gain lines.

The experimental results agree quite well with corresponding theoretical expressions which have been developed to include the nonlinear effects of saturation strength signals. The experimental results clearly show saturation of Faraday rotation, and for the J = 1 t o J = 1 transition a Faraday rotation reversal and a traveling wave gain dip are seen for small values of axial magnetic field. The nonlinearity induced anisotropy shows a marked dependence on the gas pressure in the amplifier tube for the J = 1 to J = 2 transition; this dependence agrees with the predictions of the general perturbational or weak signal theory when allowances are made for the effects of Zeeman sublevel-mixing collisions. The results provide a method for measuring the upper (neon 3s₂) level quadrupole moment decay rate, the dipole moment decay rates for the 3s₂ → 3p₄ and 3s₂ → 3p₂ transitions, and the effects of various types of collision processes on these decay rates.