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At least 667 records · Page 37

A Geophysical Flow Experiment in a Compressible Critical Fluid

The first objective of this experiment is to build an experimental system in which, in analogy to a geophysical system, a compressible fluid in a spherical annulus becomes radially stratified in density through an A.C. electric field. When this density gradient is demonstrated, the system will be augmented so that the fluid can be driven by heating and rotation and tested in preparation for a microgravity experiment. This apparatus consists of a spherical capacitor filled with critical fluid in a temperature controlled environment. To make the fluid critical, the apparatus will be operated near the critical pressure, critical density, and critical temperature of the fluid. This will result in a highly compressible fluid because of the properties of the fluid near its critical point. A high voltage A.C. source applied across the capacitor will create a spherically symmetric central force because of the dielectric properties of the fluid in an electric field gradient. This central force will induce a spherically symmetric density gradient that is analogous to a geophysical fluid system. To generate such a density gradient the system must be small (approx. 1 inch diameter). This small cell will also be capable of driving the critical fluid by heating and rotation. Since a spherically symmetric density gradient can only be made in microgravity, another small cell, of the same geometry, will be built that uses incompressible fluid. The driving of the fluid by rotation and heating in these small cells will be developed. The resulting instabilities from the driving in these two systems will then be studied. The second objective is to study the pattern forming instabilities (bifurcations) resulting from the well controlled experimental conditions in the critical fluid cell. This experiment will come close to producing conditions that are geophysically similar and will be studied as the driving parameters are changed.

Hegseth, John↗

Experimental Dynamic Characterization of a Reconfigurable Adaptive Precision Truss

The dynamic behavior of a reconfigurable adaptive truss structure with non-linear joints is investigated. The objective is to experimentally examine the effects of the local non-linearities on the global dynamics of the structure. Amplitude changes in the frequency response functions are measured at micron levels of motion. The amplitude and frequency variations of a number of modes indicate a non-linear Coulomb friction response. Hysteretic bifurcation behavior is also measured at an amplitude approximately equal to the specified free-play in the joint. Under the 1 g pre-load, however, the non-linearity was dominantly characteristic of Coulomb friction with little evidence of free-play stiffening.

Hinkle, J. D.↗

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - 2

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Yee, H. C.↗

Nonlinear Analysis of the Space Shuttle Super-Lightweight External Fuel Tank

The results of buckling and nonlinear analyses of the Space Shuttle External Tank super-lightweight liquid oxygen (LOX) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests conducted on the original external tank. These results illustrate three distinctly different types of nonlinear responses for thin-walled shells subjected to combined mechanical and thermal loads. These nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of nonlinear behavior generally require a large scale high-fidelity finite element model. Results are also presented that show that a fluid filled launch vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full scale structural tests of the original standard weight external tank suggest that the finite element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the super lightweight LOX tank.

Nemeth, Michael P.↗

Steady-State Dynamic Behavior of a Flexible Rotor With Auxiliary Support From a Clearance Bearing

This paper investigates the steady-state responses of a rotor system supported by auxiliary bearings in which there is a clearance between the rotor and the inner race of the bearing. A simulation model based upon the rotor of a production jet engine is developed and its steady-state behavior is explored over a wide range of operating conditions for various parametric configurations. Specifically, the influence of rotor imbalance, clearance, support stiffness and damping is studied. Bifurcation diagrams are used as a tool to examine the dynamic behavior of this system as a function of the afore mentioned parameters. The harmonic balance method is also employed for synchronous response cases. The observed dynamical responses is discussed and some insights into the behavior of such systems are presented.

Xie, Huajun↗

Shape of Asteroid 4769 Castalia (1989 PB) from Inversion of Radar Images

The inversion of previously reported, delay-Doppler images of Castalia yields a 167-parameter, three-dimensional shape model that is bifurcated into two distinct irregular, kilometer-sized lobes. The crevice that separates the lobes has an average depth of between 100 and 150 meters and is oriented roughly perpendicular to the asteroid's longest dimension. The constrained least-squares reconstruction method introduced here can be used to determine the shape, spin vector, and radar-scattering properties of any asteroid or comet for which delay-Doppler images provide sufficient signal-to-noise ratio, orientational coverage, and spatial resolution.

Hudson, R. Scott↗

Nonlinear Analysis of the Space Shuttle Superlightweight External Fuel Tank

Results of buckling and nonlinear analyses of the Space Shuttle external tank superlightweight liquid-oxygen (LO2) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests that were conducted on the original external tank. The results illustrate three distinctly different types of nonlinear response for thin-walled shells subjected to combined mechanical and thermal loads. The nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of non- linear behavior generally require a large-scale, high-fidelity finite-element model. Results are also presented that show that a fluid-filled launch-vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full-scale structural tests of the original standard-weight external tank suggest that the finite-element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the superlightweight LO2 tank.

Nemeth, Michael P.↗

Control of an Axisymmetric Jet Using Vortex Generators

The results of an experimental investigation on the effect of vortex generators, in the form of small tabs at the nozzle exit on the evolution of a jet, are reported in this paper. Primarily tabs of triangular shape are considered, and the effect is studied up to a jet Mach number of 1.8. Each tab is found to produce a dominant pair of counter-rotating streamwise vortices having a sense of rotation opposite to that expected from the wrapping of the boundary layer. This results in an inward indentation of the mixing layer into the core of the jet. A triangular-shaped tab with its apex leaning downstream, referred to as a delta tab, is found to be the most effective in producing such vortices, with a consequential large influence on the overall jet evolution. Two delta tabs, spaced 180 deg apart, completely bifurcate the jet. Four delta tabs stretch the mixing layer into four 'fingers,' resulting in a significant increase in the jet mixing downstream. For six delta tabs the mixing layer distortion settles back to a three finger configuration through an interaction of the streamwise vortices. The tabs are found to be equally effective in jets with turbulent or laminar initial boundary layers. Two sources of streamwise vorticity are postulated for the flow under consideration. One is the upstream 'pressure hill,' generated by the tab, which constitutes the main contributor of vorticity to the dominant pair. Another is due to vortex filaments shed from the sides of the tab and reoriented downstream by the mean shear of the mixing layer. Depending on the orientation of the tab, the latter source can produce a vortex pair having a sense of rotation opposite to that of the dominant pair. In the case of the delta tab, vorticity from the two sources add, explaining the strong effect in that configuration.

Zaman, K. B. M. Q.↗

The Dynamics of Some Iterative Implicit Schemes

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations is analyzed using the theory of dynamical systems. With the aid of parallel Connection Machines (CM-2 and CM-5), the associated bifurcation diagrams as a function of the time step, and the complex behavior of the associated 'numerical basins of attraction' of these iterative implicit schemes are revealed and compared. Studies showed that all of the four implicit LMMs exhibit a drastic distortion and segmentation but less shrinkage of the basin of attraction of the true solution than standard explicit methods. The numerical basins of attraction of a noniterative implicit procedure mimic more closely the basins of attraction of the differential equations than the iterative implicit procedures for the four implicit LMMs.

Yee, H. C.↗

Joint US/Russia TU-144 Engine Ground Tests

Two engine research experiments were recently completed in Moscow, Russia using an engine from the Tu-144 supersonic transport airplane. This was a joint project between the United States and Russia. Personnel from the NASA Lewis Research Center, General Electric Aircraft Engines, Pratt & Whitney, the Tupolev Design Bureau, and EBP Aircraft LTD worked together as a team to overcome the many technical and cultural challenges. The objective was to obtain large scale inlet data that could be used in the development of a supersonic inlet system for a future High Speed Civil Transport (HSCT). The-first experiment studied the impact of typical inlet structures that have trailing edges in close proximity to the inlet/engine interface plane on the flow characteristics at that plane. The inlet structure simulated the subsonic diffuser of a supersonic inlet using a bifurcated splitter design. The centerbody maximum diameter was designed to permit choking and slightly supercritical operation. The second experiment measured the reflective characteristics of the engine face to incoming perturbations of pressure amplitude. The basic test rig from the first experiment was used with a longer spacer equipped with fast actuated doors. All the objectives set forth at the beginning of the project were met.

Acosta, Waldo A.↗

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - Part 2

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Yee, H. C.↗

Comparison of the Aeroacoustics of Two Small-Scale Supersonic Inlets

An aerodynamic and acoustic investigation was performed on two small-scale supersonic inlets to determine which inlet would be more suitable for a High Speed Civil Transport (HSCT) aircraft during approach and takeoff flight conditions. The comparison was made between an axisymmetric supersonic P inlet and a bifurcated two-dimensional supersonic inlet. The 1/14 scale model supersonic inlets were used in conjunction with a 4.1 in (10.4 cm) turbofan engine simulator. A bellmouth was utilized on each inlet to eliminate lip separation commonly associated with airplane engine inlets that are tested under static conditions. Steady state measurements of the aerodynamic flowfield and acoustic farfield were made in order to evaluate the aeroacoustic performance of the inlets. The aerodynamic results show the total pressure recovery of the two inlets to be nearly identical, 99% at the approach condition and 98% at the takeoff condition. At the approach fan speed (60% design speed), there was no appreciable difference in the acoustic performance of either inlet over the entire 0 deg to 110 deg farfield measurement sector. The inlet flow field results at the takeoff fan speed (88% design speed), show the average inlet throat Mach number for the P inlet (Mach 0.52) to be approximately 2 times that of the 2D inlet (Mach 0.26). The difference in the throat Mach number is a result of the smaller throughflow area of the P inlet. This reduced area resulted in a 'soft choking' of the P inlet which lowered the tone and overall sound pressure levels of the simulator in the forward sector by an average of 9 dB and 3 dB, respectively, when compared to the 2D inlet.

Ng, Wing↗

Development of Curved-Plate Elements for the Exact Buckling Analysis of Composite Plate Assemblies Including Transverse Shear Effects

The analytical formulation of curved-plate non-linear equilibrium equations that include transverse-shear-deformation effects is presented. A unified set of non-linear strains that contains terms from both physical and tensorial strain measures is used. Using several simplifying assumptions, linearized, stability equations are derived that describe the response of the plate just after bifurcation buckling occurs. These equations are then modified to allow the plate reference surface to be located a distance z(c), from the centroid surface which is convenient for modeling stiffened-plate assemblies. The implementation of the new theory into the VICONOPT buckling and vibration analysis and optimum design program code is described. Either classical plate theory (CPT) or first-order shear-deformation plate theory (SDPT) may be selected in VICONOPT. Comparisons of numerical results for several example problems with different loading states are made. Results from the new curved-plate analysis compare well with closed-form solution results and with results from known example problems in the literature. Finally, a design-optimization study of two different cylindrical shells subject to uniform axial compression is presented.

McGowan, David M.↗

Radar Observations of Asteroids 7 Iris, 9 Metis, 12 Victoria, 216 Kleopatra, and 654 Zelinda

We report 13-cm wavelength radar observations of the main-belt asteroids 7 Iris, 9 Metis, 12 Victoria, 216 Kleopatra, and 654 Zelinda obtained at Arecibo between 1980 and 1989. The echoes are highly polarized yet broadly distributed in Doppler frequency, indicating that our targets are smooth on decimeter scales but very rough on some scale(s) larger than about I m. The echo spectra are generally consistent with existing size, shape, and spin information based on radiometric, lightcurve, and occultation data. All of our targets possess distinctive radar signatures that reveal large- scale topography. Reflectivity spikes within narrow ranges of rotation phase suggest large flat regions on Iris, Metis, and Zelinda, while bimodal spectra imply nonconvex, possibly bifurcated shapes for Kleopatra and Victoria. Kleopatra has the highest radar albedo yet measured for a main-belt asteroid, indicating a high metal concentration and making Kleopatra the best main-belt candidate for a core remnant of a differentiated and subsequently disrupted parent body. Upon completion of the Arecibo telescope upgrade, there will be several opportunities per year to resolve main-belt asteroids with hundreds of delay-Doppler cells, which can be inverted to provide estimates of both three-dimensional shape and radar scattering properties.

Mitchell, David L.↗

Radiative Ignition and Transition to Spread Investigation (RITSI)

A total of 25 experiments was conducted in the Glovebox Facility on the Third United States Microgravity payload (USMP3) mission to study the behavior of both flaming and smoldering ignition events, the transition from ignition to the flame/smoldering spread, and the flame/smoldering growth pattern in air. Twenty one of the 25 experiments were flaming experiments and the remainder were smoldering experiments. Ignition was initiated by a heated wire across a thermally thin filter paper in the middle of the sample for the two-dimensional configuration and by a focused beam from a halogen/tungsten lamp at the center of the sample for the three-dimensional configuration. The external air flow velocity was varied from 0 cm/s to 6.5 cm/s. The ignition and subsequent flame spread events were recorded by a video camera, a 35 mm camera, and 6 thermocouples (2 in the gas phase and 4 in the sample). The results indicate that non-piloted radiative ignition of the paper by external thermal radiation tends to occur more easily than in normal gravity. In the two-dimensional configuration, the transition from ignition to downstream flame spread never occurred; only the transition to upstream spread took place. In the three-dimensional configuration, a char growth pattern emerged in the shape of a fan, with the ignited area as the center of the fan and the fan spreading in the upstream direction. The internal angle of the fan increased with an increase in external flow velocity (higher flow velocity gave a more opened fan pattern). At an external flow velocity of 5 cm/s, the flame was horseshoe-shaped and the char pattern became an elongated semicircle toward upstream. It appears that the peak upstream flame spread rate was reached at a higher external velocity than for the two-dimensional flame front. Flame spread much faster along open edges of the sample paper than along the sample face, presumably due to there being larger supply of oxygen and energy feedback at the open edges than at the surface. These results indicate the possible importance of the effect of the flame front shape such as the curvature of the flame front on spread rate and flame strength. A complex, unexpected finger-shaped char growth pattern was observed during the smoldering experiment. Higher external flow velocity increased the number of localized smoldering fronts, of the char fingers they left behind, and frequency of bifurcations from the fingers. At present, it is not clear what caused such a complex char growth pattern.

Kashiwagi, Takashi↗

The Solar-Stellar Connection (NAG5-6124: SOHO Guest Investigator Program)

The following is a final report from the SOHO Guest Investigator program to use the SUMER far-UV spectrometer to obtain imaging spectroscopy in support of the goals of the so-called "solar-stellar connection." In particular, a major emphasis was utilization of the long-slit time-resolved maps of the solar surface in bright far-UV emission lines to deduce how particular aspects of the temporally and spatially averaged line profiles trace back to individual structural features of the magnetically disturbed outer atmosphere; to help interpret the unresolved line profiles from high quality stellar observations (say, with the Space Telescope Imaging Spectrograph). The researchers served two tours of duty in the SOHO Operations Center as SUMER planners, during which time we conducted an extensive series of observing programs. These can be divided into three general categories: surface mapping, translimb spectroscopy, and active region diagnostics. We have analyzed some of the large volumes of data to the point where we have presented them in poster papers, and in invited papers at national and international meetings. Listed below are the titles of the preliminary publications we have written, including brief abstracts to indicate the main results. (1) Chromospheric structure and Dynamics-- Observations -- The chromosphere is a highly structured dynamic 'layer' of the solar outer atmosphere. Here, not only are the effects of mechanical heating first evident (moving upward in altitude from the deep photosphere), but also the amount of nonradiative energy deposited is far greater than in the albeit much hotter overlying transition region and corona. Further, the chromosphere is by far the thickest zone of the solar atmosphere with respect to the pressure scale height. A major goal of stellar astrophysics is to understand how the chromosphere is heated and why it adopts its peculiar structure. A cursory examination of solar filtergrams and high-resolution movies demonstrates that much of the chromospheric "action" must be occurring on fine spatial scales and short times; particularly in the cell interior transient brightenings, but also in the longer-lived network fragments. That regime of investigation is far removed from what one usually associates with "synoptic" measurements. Nevertheless, synoptic observations of chromospheric indices, filtergrams, and globally-averaged profile parameters not only can provide important insight concerning the crucial role of the cycle-variable part of the solar magnetic field; but they also can forge a key link with analogous measurements of the stars, where often the phenomena can be significantly exaggerated from the solar case, but high spatial resolution reconnaissance is not even a remote possibility. In addition to discussing the synoptic aspects of chromospheric structure and dynamics, I summarized new insights into the general problem of the solar chromosphere that have been obtained recently with the SUMER far-ultraviolet spectrometer on SOHO. (2) CO and the Temperature Structure of the Solar Atmosphere -- The surface layers of the Sun provide a crucial boundary condition for many of the processes that occur in the deep interior. The stratification of the outer solar atmosphere once was thought to be well understood. However, studies of thermally sensitive molecular absorptions in the infrared revealed puzzling anomalies. Strong lines of the CO fundamental vibration-rotation bands near 5 microns showed very cool temperatures at the extreme limb, and remarkable off-limb emissions extending well into the supposedly hot chromosphere. The conflicting pictures of the photosphere/chromosphere interface, from the widely separated wavelength regimes, has raised suspicions that those "layers" of the atmosphere are much more inhomogeneous than previously suspected. One proposal is that the low chromosphere is dominated by cool gas, the "COmosphere," which is threaded by a network of persistent small-scale hot magnetic filaments and occasionally disrupted by localized acoustic disturbances. The COmosphere is capped by the merged fields of the network elements in the chromospheric "canopy." (3) Translimb Spectroscopy with SOHO/SUMER -- We have used SUMER to obtain deep exposures of the 1300-1400 A spectrum, at the extreme limb and off-limb. Previous "translimb" studies in the thermal infrared had revealed remarkable extensions of cold material (T is approximately equal to 3000 K)-traced by carbon monoxide emission lines-into the heart of the hot chromosphere. A main objective of our program was to search for corresponding far-UV signatures of the "thermally-bifurcated" low chromosphere; for example, radiatively fluoresced emissions of the CO A-X 4th-positive system (collisional excitation would be negligible in cold gas). We conducted two separate observing programs with SUMER. Both made use of the 1 inch-diameter circular aperture, translated across the limb in the minimum motor step increments of 0."375, along the central meridian in the Northern polar coronal hole. The first program executed for nine hours beginning 19UT 25 Oct 1996. The full wavelength range was 1340-1400 A. It was recorded in two overlapping segments, placing key regions of the spectrum alternately on the KBr and bare parts of the detector, to help isolate 2nd-order features. Each segment was integrated for 500 s, and 32 pairs were obtained to span a 12" swath centered on the optical limb. The second program was conducted 00-09UT 01 Dec 1996. It consisted of a single wavelength setting (1300-1340 A) with exposure time 500 s, but twice the spatial coverage of the earlier series: 64 steps, for a total displacement of 24". The strong chromospheric resonance lines of atomic oxygen (1302-1305 A) and ionized carbon (1334-1335 A) were observed on the bare part of the MCP camera.

Ayres, Thomas R.↗

Dynamic Nucleation of Supercooled Melts and Measurement of the Surface Tension and Viscosity

We investigate the phenomenon of acoustic pressure-induced nucleation by using a novel approach involving the large amplitude resonant radial oscillations and collapse of a single bubble intentionally injected into a supercooled liquid. Using a combination of previously developed and proven techniques, the bubble is suspended in a fluid host by an ultrasonic field which supplies both the levitation capability as well as the forcing of the radial oscillations. We observe the effects of an increase in pressure (due to bubble collapse) in a region no larger than 100 microns within the supercooled melt to rigorously probe the hypothesis of pressure-induced nucleation of the solid phase. The use of single bubbles operating in narrow temporal and spatial scales will allow the direct and unambiguous correlation between the origin and location of the generation of the disturbance and the location and timing of the nucleation event. In a companion research effort, we are developing novel techniques for the non-contact measurements of the surface tension and viscosity of highly viscous supercooled liquids. Currently used non-invasive methods of surface tension measurement for the case of undercooled liquids generally rely of the quantitative determination of the resonance frequencies of drop shape oscillations, of the dynamics of surface capillary waves, or of the velocity of streaming flows. These methods become quickly ineffective when the liquid viscosity rises to a significant value. An alternate and accurate method which would be applicable to liquids of significant viscosity is therefore needed. We plan to develop such a capability by measuring the equilibrium shape of levitated undercooled melt droplets as they undergo solid-body rotation. The experimental measurement of the characteristic point of transition (bifurcation point) between axisymmetric and two-lobed shapes will be used to calculate the surface tension of the liquid. Such an approach has already been validated through the experimental verification of numerical modeling results. The experimental approach involves levitation, melting, and solidification of undercooled droplets using a hybrid ultrasonic-electrostatic technique in both a gaseous as well as a vacuum environment. A shape relaxation method will be investigated in order to derive a reliable method to measure the viscosity of undercooled melts. The analysis of the monotonic relaxation to equilibrium shape of a drastically deformed and super-critically damped free drop has been used to derive interfacial tension of immiscible liquid combinations where one of the component has high viscosity. A standard approach uses the initial elongation of a droplet through shear flows, but an equivalent method could involve the initial deformation of a drop levitated in a gas by ultrasonic radiation pressure, electric stresses, or even solid body rotation. The dynamic behavior of the free drop relaxing back to equilibrium shape will be modeled, and its characteristic time dependence should provide a quantitative means to evaluate the liquid viscosity.

Trinh, E. H.↗

Hydrodynamic Instability and Thermal Coupling in a Dynamic Model of Liquid-Propellant Combustion

For liquid-propellant combustion, the Landau/Levich hydrodynamic models have been combined and extended to account for a dynamic dependence of the burning rate on the local pressure and temperature fields. Analysis of these extended models is greatly facilitated by exploiting the realistic smallness of the gas-to-liquid density ratio rho. Neglecting thermal coupling effects, an asymptotic expression was then derived for the cellular stability boundary A(sub p)(k) where A(sub p) is the pressure sensitivity of the burning rate and k is the disturbance wavenumber. The results explicitly indicate the stabilizing effects of gravity on long-wave disturbances, and those of viscosity and surface tension on short-wave perturbations, and the instability associated with intermediate wavenumbers for critical negative values of A(sub p). In the limit of weak gravity, hydrodynamic instability in liquid-propellant combustion becomes a long-wave, instability phenomenon, whereas at normal gravity, this instability is first manifested through O(1) wavenumbers. In addition, surface tension and viscosity (both liquid and gas) each produce comparable effects in the large-wavenumber regime, thereby providing important modifications to the previous analyses in which one or more of these effects was neglected. For A(sub p)= O, the Landau/Levich results are recovered in appropriate limiting cases, although this typically corresponds to a hydrodynamically unstable parameter regime for p << 1. In addition to the classical cellular form of hydrodynamic stability, there exists a pulsating form corresponding to the loss of stability of steady, planar burning to time-dependent perturbations. This occurs for negative values of the parameter A(sub p), and is thus absent from the original Landau/Levich models. In the extended model, however, there exists a stable band of negative pressure sensitivities bounded above by the Landau type of instability, and below by this pulsating form of hydrodynamic instability. Indeed, nonsteady modes of combustion have been observed at low pressures in hydroxylammonium nitrate (HAN)-based liquid propellants, which often exhibit negative pressure sensitivities. While nonsteady combustion may correspond to secondary and higher-order bifurcations above the cellular boundary, it may also be a manifestation of this pulsating type of hydrodynamic instability. In the present work, a nonzero temperature sensitivity is incorporated into our previous asymptotic analyses. This entails a coupling of the energy equation to the previous purely hydrodynamic problem, and leads to a significant modification of the pulsating boundary such that, for sufficiently large values of the temperature-sensitivity parameter, liquid-propellant combustion can become intrinsically unstable to this alternative form of hydrodynamic instability. For simplicity, further attention is confined here to the inviscid version of the problem since, despite the fact that viscous and surface-tension effects are comparable, the qualitative nature of the cellular boundary remains preserved in the zero-viscosity limit, as does the existence of the pulsating boundary. The mathematical model adopts the classical assumption that there is no distributed reaction in either the liquid or gas phases, but now the reaction sheet, representing either a pyrolysis reaction or an exothermic decomposition at the liquid/gas interface, is assumed to depend on local conditions there.

Margolis, S. B.↗