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Dissipative energy flow controllers are designed for interconnected modal subsystems. Active feedback controllers for vibration suppression are then viewed as either an additional subsystem or a dissipative coupling. These controllers, which are designed by the LQG positive real control approach, maximize energy flow from a specified modal subsystem.
The application is treated in sufficient detail to facilitate as much as possible its application by the engineer who is less familiar with the subject. The present work was undertaken with two objects in view. In the first place, it is considered as a contribution to the water analogy of gas flows, and secondly, a large portion is devoted to the general theory of the two-dimensional supersonic flows.
Apparatus, systems and methods for implementing flow cages and flow cage assemblies in association with high pressure fluid flows and fluid valves are provided. Flow cages and flow assemblies are provided to dissipate the energy of a fluid flow, such as by reducing fluid flow pressure and/or fluid flow velocity. In some embodiments the dissipation of the fluid flow energy is adapted to reduce erosion, such as from high-pressure jet flows, to reduce cavitation, such as by controllably increasing the flow area, and/or to reduce valve noise associated with pressure surge.
The study examines the magnetic structure and energy dissipation at low-Mach-number, quasi-parallel collisionless shocks on the basis of observations obtained by the ISEE 1 and 2 spacecraft at seven crossings of the earth's dayside bow shock. All the shocks exhibit a fairly short-scale-length ramp where the principal jumps in the electron temperature, ion temperature, and magnetic field strength take place. Large-amplitude LF transverse waves in the magnetic field are present in and downstream from the ramp, with more modest waves upstream. The amplitude of the downstream waves is typically larger than can be accounted for by shock compression of the upstream waves. The electron heating represents about 6 percent of the dissipated bulk flow energy, consistent with observations in other parameter regimes, and suggesting that the dominant electron heating process is the same. It is suggested that the low-Mach-number shocks are reforming but do not exhibit downstream variability because of the relatively low levels of reflected ions.
A versatile computer program is presented which achieves a rapid, numerical solution of the Reynolds equation for a flat sector thrust pad bearing with either compressible or liquid lubricants. Program input includes a range in values of the geometric and operating parameters of the sector bearing. Performance characteristics are obtained from the calculated bearing pressure distribution. These are the load capacity, center of pressure coordinates, frictional energy dissipation, and flow rates of liquid lubricant across the bearing edges. Two sample problems are described.
Results from the Imp 7 satellite reveal antisolar magnetosheath ion flows of 10 to the 18th to 10 to the 20th ergs/sec when they are integrated over the observed flow cross-sectional area. These results extend, in energy and spatial regions sampled, the earlier work of West and Buck (1976). The results show the existence of energized protons in the downstream magnetosheath which at energies above 50 keV carry an energy flow of the same magnitude as the extrapolated (above 1 keV) results of Baker and Stone (1977). Possible sources of the energy flow include dissipation processes due to a magnetopause electric field, leakage of magnetospheric particles through the magnetopause into the magnetosheath, bow shock acceleration, and magnetosheath acceleration.
Longitudinal turbulence intensities, autocorrelations, energy spectra and peak energy dissipation frequencies for organic solvents flowing in smooth round tubes
Methods to analyze the generation, transport, and dissipation of energy to study geophysical fluid flows are discussed. Energetics analyses are pursued in several directions: (1) the longitudinal and time dependence on the energy flow to the stratosphere was examined as a function of geographical sector; (2) strong and weak energy flows were correlated by medium range forecasts; (3) the one dimensional spectral results (Fourier services around latitude circles) were extended to spherical harmonics over a global domain; (4) the validity of vertical velocities derived from mass convergence was examined for their effect on the conversion of eddy available potential energy to eddy kinetic energy.
The defining characteristic of turbulent flows is their ability to dissipate energy, even in the limit of zero viscosity. The Euler equations, if constrained in such a way that the velocity derivatives remain bounded, conserve energy. But when they arise as the limit of the Navier-Stokes (NS) equations, when the Reynolds number goes to infinity, there is persuasive empirical evidence that the gradients become singular as just the right function of Re for the dissipation to remain non-zero and to approach a well defined limit. It is generally believed that this limiting value of the dissipation is a property of the Euler equations themselves, independent of the particular dissipative mechanism involved, and that it can be normalized with the large scale properties of the turbulent flow (e.g. the kinetic energy per unit volume u'(exp 2)/2, and the integral scale L) without reference to the Reynolds number or to other dissipative quantities. This is usually taken to imply that the low wave number end of the energy spectrum, far from the dissipative range, is also independent of the particular mechanism chosen to dispose of the energy transfer. In the following sections, we present some numerical experiments on the effect of substituting different dissipation models into the truncated Euler equations. We will see that the effect is mainly felt in the 'near dissipation' range of the energy spectrum, but that this range can be quite wide in some cases, contaminating a substantial range of wave numbers. In the process, we will develop a 'practical' approximation to the subgrid energy transfer in isotropic turbulence, and we will gain insight into the structure of the nonlinear interactions among turbulent scales of comparable size, and into the nature of energy backscatter. Some considerations on future research directions are offered at the end.
This work evaluates the interaction of a simulated spectrum of convectively generated gravity waves with realistic middle atmosphere mean winds. The wave spectrum is derived from the nonlinear convection model described by Alexander et al. that simulated a two-dimensional midlatitude squall line. This spectrum becomes input to a linear ray tracing model for evaluation of wave propagation as a function of height through climatological background wind and buoyancy frequency profiles. The energy defined by the spectrum as a function of wavenumber and frequency is distributed spatially and temporally into wave packets for the purpose of estimating wave amplitudes at the lower boundary of the ray tracing model. A wavelet analysis provides an estimate of these wave packet widths in space and time. Without this redistribution of energies into wave packets the Fourier analysis alone inaccurately assumes the energy is evenly distributed throughout the storm model domain. The growth with height of wave amplitudes is derived from wave action flux conservation coupled to a convective instability saturation condition. Mean flow accelerations and wave energy dissipation profiles are derived from this analysis and compared to parameterized estimates of gravity wave forcing, providing a measure of the importance of the storm source to global gravity wave forcing. The results suggest that a single large convective storm system like the simulated squall line could provide a significant fraction of the zonal mean gravity wave forcing at some levels, particularly in the mesosphere. The vertical distributions of mean flow acceleration and energy dissipation do not much resemble the parameterized profiles in form because of the peculiarities of the spectral properties of the waves from the storm source. The ray tracing model developed herein provides a tool for examining the role of convectively generated waves in middle atmosphere physics.
This work evaluates the interaction of a simulated spectrum of convectively generated gravity waves with realistic middle atmosphere mean winds. The wave spectrum is derived from the nonlinear convection model described by Alexander et al. [1995] that simulated a two-dimensional midlatitude squall line. This spectrum becomes input to a linear ray tracing model for evaluation of wave propagation as a function of height through climatological background wind and buoyancy frequency profiles. The energy defined by the spectrum as a function of wavenumber and frequency is distributed spatially and temporally into wave packets for the purpose of estimating wave amplitudes at the lower boundary of the ray tracing model. A wavelet analysis provides an estimate of these wave packet widths in space and time. Without this redistribution of energies into wave packets the Fourier analysis alone inaccurately assumes the energy is evenly distributed throughout the storm model domain. The growth with height of wave amplitudes is derived from wave action flux conservation coupled to a convective instability saturation condition. Mean flow accelerations and wave energy dissipation profiles are derived from this analysis and compared to parameterized estimates of gravity wave forcing, providing a measure of the importance of the storm source to global gravity wave forcing. The results suggest that a single large convective storm system like the simulated squall line could provide a significant fraction of the zonal mean gravity wave forcing at some levels, particularly in the mesosphere. The vertical distributions of mean flow acceleration and energy dissipation do not much resemble the parameterized profiles in form because of the peculiarities of the spectral properties of the waves from the storm source. The ray tracing model developed herein provides a tool for examining the role of convectively generated waves in middle atmosphere physics.
Results from direct numerical simulations of several homogeneous flows and fully developed turbulent channel flow indicate that the probability distribution function (pdf) of relative helicity density exhibits at most a 20 percent deviation from a flat distribution. Isotropic flows exhibit a slight helical nature but the presence of mean strain in homogeneous turbulence suppresses helical behavior. All the homogeneous turbulent flows studied show no correlation between relative helicity density and the dissipation of turbulent kinetic energy. The channel flow simulations indicate that, except for low-dissipation regions near the outer edge of the buffer layer, there is no tendency for the flow to be helical. The strong peaks in the relative helicity density pdf and the association of these peaks with regions of low dissipation found in previous simulations by Pelz et al.(1985) are not observed.
Triple Doppler radar observations are presented of downdrafts and turbulence within three convective cloud systems that formed over the South Park region of central Colorado. Downdrafts and turbulence are treated together here because of the relationship suggested by the fact that both can be produced by the mixing of cloudy and dry environmental air. What is more, overlays of estimated turbulent kinetic energy dissipation on general flow patterns yield additional information (including the locations of entrainment) on circulations within convective clouds. The relationship between downdrafts and turbulence is established, and examples are presented of weak to moderate downdrafts and turbulence within three convective storms. The differences in downdraft strength and turbulence intensity in the three cases examined are analyzed.
A dynamical equation for the energy dissipation rate is used together with a model spectrum to predict the velocity derivative skewness at a high Reynolds number. The objective is to determine the best choice of the exponent, m, so that the resulting model spectrum can be used to estimate statistical properties of the fine scales of turbulence. Skewness data suggest that m = 2 is the best model for laboratory-scale flows and m = 1 is a poor model for a broad range of Reynolds numbers.
The size segregation of flowing or shaken grains is a commonly observed phenomenon in industrial processes and in nature. In systems that do not involve much agitation of the grains, several mechanisms that involve gravity have been identified as leading to such segregation. In highly agitated flows, there is a mechanism independent of gravity that is available to drive separation of different grains. This is associated with spatial gradients in the energy of their velocity fluctuations. Because collisions between grains inevitably dissipate energy, collisional granular shear flows are usually of limited extent in the direction transverse to the flow. One consequence of this is that shear flows are strongly influenced by their boundaries. Because grains, on average, slip relative to boundaries, a bumpy or frictional boundary can convert slip energy into fluctuation energy. However, because each collision between a grain and the boundary dissipates fluctuation energy, there is a competition between production and dissipation. In principle, it is possible to design the geometry of the boundary - for example, the size and spacing of the bumps - so that the boundary either produces or dissipates fluctuation energy. This permits the control of the component of the spatial gradient of the fluctuation energy that is normal to the boundary. The gradients in fluctuation energy established by such boundaries may be exploited to drive the separation by size or other properties in a binary mixture of spherical grains. Microgravity makes the visual observations possible by permitting us to employ moderate rates of shear. On earth, the effects of gravity can be minimized by shearing so rapidly that the particle pressure overwhelms gravity. However, in this event, separation takes place too rapidly for visual observation, buoyancy and/or condensation associated with the centripetal acceleration must be accounted for, and the particles can be severely damaged. Because, in the absence of gravity, the only available time scale is proportional to the speed of the moving boundary, this speed can be made arbitrarily slow to permit observations and to avoid particle damage, without altering the phenomenon under study. The primary goal of this research is to carry out a physical experiment in which particle segregation is induced and maintained in a collisional flow of a binary mixture of two different types of spheres.
True dissipation occurs mainly at the highest wavenumbers where the eddy sizes are comparatively small. These high wavenumbers receive their energy through the spectral cascade of energy starting with the largest eddies spilling energy into the smaller eddies, passing through each wavenumber until it is dissipated at the microscopic scale. However, a small percentage of the energy does not spill continuously through the cascade but is instantly passed to the higher wavenumbers. Consequently, the smallest eddies receive a certain amount of energy almost immediately. As the spectral energy cascade continues, the highest wavenumber needs a certain time to receive all the energy which has been transferred from the largest eddies. As such, there is a time delay, of the order of tau, between the generation of energy by the largest eddies and the eventual dissipation of this energy. For equilibrium turbulence at high Reynolds numbers, there is a wide range where energy is neither produced by the large eddies nor dissipated by viscosity, but is conserved and passed from wavenumber to higher wavenumbers. The rate at which energy cascades from one wavenumber to another is proportional to the energy contained within that wavenumber. This rate is constant and has been used in the past as a dissipation rate of turbulent kinetic energy. However, this is true only in steady, equilibrium turbulence. Most dissipation models contend that the production of dissipation is proportional to the production of energy and that the destruction of dissipation is proportional to the destruction of energy. In essence, these models state that the change in the dissipation rate is proportional to the change in the kinetic energy. This assumption is obviously incorrect for the case where there is no production of turbulent energy, yet energy continues to cascade from large to small eddies. If the time lag between the onset on the energy cascade to the destruction of energy at the microscale can be modeled, then there will be a better representation of the dissipation process. Development of an energy cascade time scale equation is discussed.
Kinetic energy budgets are computed during a cold air outbreak in association with strong jet stream activity over the eastern United States. The period is characterized by large generation of kinetic energy due to cross-contour flow. Horizontal export and dissipation of energy to subgrid scales of motion constitute the important energy sinks. Rawinsonde data at 3 and 6 h intervals during a 36 h period are used in the analysis and reveal that energy fluctuations on a time scale of less than 12 h are generally small even though the overall energy balance does change considerably during the period in conjunction with an upper level trough which moves through the region. An error analysis of the energy budget terms suggests that this major change in the budget is not due to random errors in the input data but is caused by the changing synoptic situation. The study illustrates the need to consider the time and space scales of associated weather phenomena in interpreting energy budgets obtained through use of higher frequency data.
Certain cases of turbulence as a postinstability state of a fluid in motion modeled by the introduction of multivalued velocity fields are examined. The turbulence is regarded as occurring in the form of random pulsations which grow until the external energy input in the average flow is balanced by the dissipated energy of pulsations by means of turbulent friction. Closed form analytic solutions are shown to be possible when the considered velocity fields, the pulsation velocity and the fluid velocity, are decoupled.