An experimental study of liquid instability in a vibrating elastic tank.
Liquid instability of vibrating partially filled elastic tank, emphasizing resonant breathing mode and frequency response
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Liquid instability of vibrating partially filled elastic tank, emphasizing resonant breathing mode and frequency response
Hydrodynamic mechanism of solar corona expansion
Plane wave disturbances in infinite rotating collisionless system for wave vector normal to axis of rotation
This publication is the result of over 260 fractional-frequency-whirl stability tests on a variety of fixed-geometry journal bearings. It is intended principally as a guide in the selection and design of antiwhirl bearings that must operate at high speeds and low loads in low-viscosity fluids such as water or liquid metals. However, the various fixed-geometry configurations can be employed as well in applications where other lubricants, such as oil, are used and fractional-frequency whirl is a problem. The important parameters that effect stability are discussed for each bearing type, and design curves to facilitate the design of optimum-geometry bearings are included. A comparison of the stability of the different bearing configurations tested is also given.
A true airspeed sensor based on the precession of a vortex whistle for sensing airspeeds up to 321.9 km/hr (200 mph). In an attempt to model the complicated fluid mechanics of the vortex precession, three dimensional, inviscid, unsteady, incompressible fluid flow was studied by using the hydrodynamical linearized stability theory. The temporal stability approach was used to derive the relationship between the true airspeed and frequency response. The results show that the frequency response is linearly proportional to the airspeed. A computer program was developed to obtain the numerical solution. Computational results for various parameters were obtained. The designed sensor basically consisted of a vortex tube, a swirler, and a transducer system. A microphone converted the audible tone to an electronic frequency signal. Measurements for both the closed conduit tests and wind tunnel tests were recorded. For a specific flow rate or airspeed, larger exit swirler angles produced higher frequencies. For a smaller cross sectional area in the precessional flow region, the frequency was higher. It was observed that as the airspeed was increased the Strouhal number remained constant.
Performance tests of water-lubricated, Rayleigh step, hydrodynamic journal bearings under no load conditions to determine stability
Hydrodynamic equations for stability, and control analyses on liquid propellant space vehicles
In the past, the acoustic combustion instability was studied independently of the hydrodynamic instability induced by vortex motions. This paper is intended to combine the two different sources of energy everywhere within the spatial domain and determine the effect of one upon the other. This can be achieved by calculating the mean flow velocities and vorticities and their fluctuating parts of velocities and vortices, as well as the fluctuating pressure. The Orr-Sommerfeld equation is utilized to determine the wavenumbers and unsteady stream functions from which vortically coupled acoustic instability growth constants are calculated. This process demonstrates that there are two different frequencies, acoustic and hydrodynamic, various combinations of which contribute to either damping or amplification. It is found that stability boundaries for coupled acoustic and vortical oscillations are somewhat similar to the classical hydrodynamic stability boundaries, but they occur in the form of multiple islands.
To determine the trim range in which a seaplane can take off without porpoising, stability tests were made of a Plexiglas model, composed of float, wing, and tailplane, which corresponded to a full-size research airplane. The model and full-size stability limits are in good agreement. After all structural parts pertaining to the air frame were removed gradually, the aerodynamic forces replaced by weight forces, and the moment of inertia and position of the center of gravity changed, no marked change of limits of the stable zone was noticeable. The latter, therefore, is for practical purposes affected only by hydrodynamic phenomena. The stability limits of the DVL family of floats were determined by a systematic investigation independent of any particular sea-plane design, thus a seaplane may be designed to give a run free from porpoising.
An exact equation is derived for the dissipation function of a homogeneous, isotropic, Newtonian fluid, with terms associated with irreversible compression or expansion, wave radiation, and the square of the vorticity. This and other forms of the dissipation function are used to identify simple flows, such as incompressible channel flow, the potential vortex with rotational core, and incompressible, irrotational flow as minimally dissipative distributions. A comparison of the hydrodynamic and thermodynamic stability characteristics of a parallel shear flow suggests that an association exists between flow stability and the variation of net dissipation with disturbance amplitude, and that nonlinear effects, such as bounded disturbance amplitude, may be examined from a thermodynamic basis.
The low-speed aerodynamic and hydrodynamic characteristics of a proposed multijet water-based aircraft configuration for supersonic operation have been investigated. The design features include upward-rotating engines, body indentation, a single hydro-ski, and a wing with an aspect ratio of 3.0, a taper ratio of 0.143, 36.90 sweepback of the quarter-chord line, and NACA 65AO04 airfoil sections. For the aerodynamic investigation, with the flaps retracted, the model was longitudinally and directionally stable up to the stall. The all-movable horizontal tail was capable of trimming the model up to a lift coefficient of approximately 0.87. All flap configurations investigated had a tendency to become longitudinally unstable at stall. The effectiveness of the all-movable horizontal tail increased with increasing lift coefficient for all flap configurations investigated; however, with the large static margin of the configuration with the center of gravity at 0.25 mean aerodynamic chord, the all-movable horizontal tail was not powerful enough to trim all the various flapped configurations investigated throughout the angle-of-attack range. For the hydrodynamic investigation, longitudinal stability during take-offs and landings was satisfactory. Decreasing the area of the hydro-ski 60 percent increased the maximum resistance and emergence speed 40 and 70 percent, respectively. Without the jet exhaust, the resistance was reduced by simulating the vertical-lift component of the forward engines rotated upward. However, the jet exhaust of the forward engines increased the maximum resistance approximately 60 percent. The engine inlets and horizontal tail were free from spray for all loads investigated and for both hydro-ski sizes.
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An extended Landau-Levich model of liquid-propellant combustion, one that allows for a local dependence of the burning rate on the (gas) pressure at the liquid-gas interface, exhibits not only the classical hydrodynamic cellular instability attributed to Landau but also a pulsating hydrodynamic instability associated with sufficiently negative pressure sensitivities. Exploiting the realistic limit of small values of the gas-to-liquid density ratio p, analytical formulas for both neutral stability boundaries may be obtained by expanding all quantities in appropriate powers of p in each of three distinguished wave-number regimes. In particular, composite analytical expressions are derived for the neutral stability boundaries A(sub p)(k), where A, is the pressure sensitivity of the burning rate and k is the wave number of the disturbance. For the cellular boundary, the results demonstrate explicitly the stabilizing effect of gravity on long-wave disturbances, the stabilizing effect of viscosity (both liquid and gas) and surface tension on short-wave perturbations, and the instability associated with intermediate wave numbers for negative values of A(sub p), which is characteristic of many hydroxylammonium nitrate-based liquid propellants over certain pressure ranges. In contrast, the pulsating hydrodynamic stability boundary is insensitive to gravitational and surface-tension effects but is more sensitive to the effects of liquid viscosity because, for typical nonzero values of the latter, the pulsating boundary decreases to larger negative values of A(sub p) as k increases through O(l) values. Thus, liquid-propellant combustion is predicted to be stable (that is, steady and planar) only for a range of negative pressure sensitivities that lie below the cellular boundary that exists for sufficiently small negative values of A(sub p) and above the pulsating boundary that exists for larger negative values of this parameter.
The reported investigation has the objective to provide a basis for understanding the hydrodynamic characteristics of the continuous flow electrophoresis chamber and their effects on the separation process. Particular emphasis is placed on the role buoyancy plays in establishing the basic flow and affecting its stability. The flow and temperature field is discussed, taking into account mathematical models for the structure of the temperature field, models for the structure of the axial velocity field, a two-dimensional constant thermal conductivity model, the axial velocity field, a two-dimensional constant transport properties model, and one-dimensional velocity fields. Questions of hydrodynamic stability are considered, giving attention to the stability of a fully developed flow with an axial temperature gradient.
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.
Tests of a PB2Y-3 flying boat were made at the U.S> Naval Air Station, Patuxent River, Md., to determine its hydrodynamic trim limits of stability. Corresponding tests were also made of a 1/8-size powered dynamic model of the same flying boat in Langley tank no. 1. During the tank tests, the full-size testing procedure was reproduced as closely as possible in order to obtain data for a direct correlation of the results. As a nominal gross load of 66,000 pounds, the lower trim limits of the full-size and model were in good agreement above a speed of 80 feet per second. As the speed decreased below 80 feet per second, the difference between the model trim limits and full-scale trim limits gradually became larger. The upper trim limit of the model with flaps deflected 0 deg was higher than that of the full-size, but the difference was small over the speed range compared. At flap deflections greater than 0 deg, it was not possible to trim either the model of the airplane to the upper limit with the center of gravity at 28 percent of the mean aerodynamic chord. The decrease in the lower trim limits with increase in flap deflection showed good agreement for the airplane and model. The lower trim limits obtained at different gross loads for the full-size airplane were reduced to approximately a single curve by plotting trim against the square root of C(sub delta (sub o)) divided by C(sub V).
Using numerical hydrodynamics techniques, we perform a nonlinear stability analysis of accretion disk systems that contain thick, self-gravitating disks. The systems are initially represented by a point mass M(sub c) at the center and a geometrically thick, axisymmetric disk of mass M(sub d) that supports uniform specific angular momentum and obeys an n = 3/2, polytropic equation of state. The equilibrium disk structure is uniquely defined upon the specification of two key dimensionless system parameters: M(sub d)/M(sub c) and T/absolute value of W (the ratio of rotational kinetic energy if the disk to the gravitational potential energy of the system). The focus of this work is on the identification of systems within this two-dimensional parameter space that are marginally unstable toward the development of nonaxisymmetric distortions. The geometric form and relative pattern speed of the disk's distortion as well as the likelihood of disk fragmentation as a result of such instabilities is examined, particularly in the context of protostellar systems. The value of T/absolute value of W at which thick disks first become dynamically unstable to nonaxisymmetric distortions is found to vary significantly with the mass ratio of the accertion disk system. Nonaxisymmetric eigenmodes with four distinctly different characters are identified in systems with mass ratios in the range 0.2 less than or equal to (M(sub d)/M(sub c)) less than or equal to 5.
Self-similar models, characterized by near-equilibrium between gravity, centrifugal force and radiation pressure, are generated for geometrically thick, supercritical accretion disks analyzing their structure and stability. The assumption that hydrodynamic quantities scale as power laws in radius allows for computation of disk structure as a function of the angle from the rotation axis, given a viscosity law model to which the structure of the interior of the disk is sensitive. The behaviors of other hydrodynamic quantities near the surface depend on the viscosity law, but not on the degree of pressure support on the equator. All models are found to be unstable to local axisymmetric perturbations at high latitudes noting the role of convection in bringing the disk to marginal stability. It is recommended that future thick accretion disk models take into account both their convective nature and the dependence of their structure on the viscosity law.