Weak locally homogeneous turbulence in idealized flow through a cone
Weak locally homogeneous turbulence in idealized flow through cone
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Weak locally homogeneous turbulence in idealized flow through cone
Weak locally homogeneous turbulence in idealized distorting mean flow in cone, obtaining two point correlation equations
In laboratory and natural plasmas of practical interest, the spatial scale Δ d at which magnetic field lines lose distinguishability differs enormously from the scale a of magnetic reconnection across the field lines. In the solar corona, plasma resistivity gives a/Δ d ~ 10 12 , which is the magnetic Reynold number R m . The traditional resolution of the paradox of disparate scales is for the current density j associated with the reconnecting field Brec to be concentrated by a factor of Rm by the ideal evolution, so j ~ B rec /µ 0 Δ d . A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of arbitrarily chosen magnetic field lines, Δ max /Δ min , when calculated at various points in time. Reconnection becomes inevitable where Δ max /Δ min ~ R m . A simple model of the solar corona will be used for a numerical illustration that the natural rate of increase in time is linear for the current density but exponential for Δ max /Δ min . Reconnection occurs on a time scale and with a current density enhanced by only ln(a/Δ d ) from the ideal evolution time and from the current density B rec /µ 0 a. In both resolutions, once a sufficiently wide region, Δ r , has undergone reconnection, the magnetic field loses static force balance and evolves on an Alfv´enic time scale. The Alfv´enic evolution is intrinsically ideal but expands the region in which Δ max /Δ min is large.
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The importance of the wall effect on packed beds in the adsorption and desorption of carbon dioxide, nitrogen, and water on molecular sieve 5A of 0.127 cm in radius is examined experimentally and with one-dimensional computer simulations. Experimental results are presented for a 22.5-cm long by 4.5-cm diameter cylindrical column with concentration measurements taken at various radial locations. The set of partial differential equations are solved using finite differences and Newman's method. Comparison of test data with the axial-dispersed, non-isothermal, linear driving force model suggests that a two-dimensional model (submitted to Separation Science and Technology) is required for accurate simulation of the average column breakthrough concentration. Additional comparisons of test data with the model provided information on the interactive effects of carrier gas coadsorption with CO2, as well as CO2-H2O interactions.
The experimental results of CO2 adsorption and desorption in a packed column indicated that the concentration wave front at the center of the packed column differs from those which are close to the wall of column filled with adsorbent material even though the ratio of column diameter to the particle size is greater than 20. The comparison of the experimental results with one dimensional model of packed column shows that in order to simulate the average breakthrough in a packed column a two dimensional (radial and axial) model of packed column is needed. In this paper the mathematical model of a non-slip flow through a packed column with 2 inches in diameter and 18 inches in length filled with 5A zeolite pellets is presented. The comparison of experimental results of CO2 absorption and desorption for the mixed and central breakthrough of the packed column with numerical results is also presented.
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Ideal relativistic fluids adiabatic flow, investigating heat exchange effects within framework of special relativity
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Two cases are considered. The first is concerned with mean flows of the Blasius type wherein the instabilities are represented by Tollmien-Schlichting waves. It is shown that the latter are generated fairly far downstream of the edge and are the result of a wave length reduction process that tunes the free stream disturbances to the Tollmien-Schlichting wave length. The other case is concerned with inflectional, uni-directional, transversely sheared mean flows. Such idealized flows provide a fairly good local representation to the nearly parallel flows in jets. They can support inviscid instabilities of the Kelvin-Helmholtz type. The various mathematically permissible mechanisms that can couple these instabilities to the upstream disturbances are discussed.
This paper describes the generation of instability waves downstream of a leading edge by an imposed upstream disturbance. Two cases are considered. The first is concerned with mean flows of the Blasius type wherein the instabilities are represented by Tollmien-Schlichting waves. It is shown that the latter are generated fairly far downstream of the edge and are the result of a wave length reduction process that tunes the free stream disturbances to the Tollmien-Schlichting wave length. The other case is concerned with inflectional, uni-directional, transversely sheared mean flows. Such idealized flows provide a fairly good local representation to the nearly parallel flows in jets. They can support inviscid instabilities of the Kelvin-Helmholtz type. The various mathematically permissible mechanisms that can couple these instabilities to the upstream disturbances are discussed. The results are compared to some acoustic measurements and conclusions are drawn about the generation of the instabilities in these flows.
Ideally, quantum anomalous Hall systems should display zero longitudinal resistance. Yet in experimental quantum anomalous Hall systems elevated temperature can make the longitudinal resistance finite, indicating dissipative flow of electrons. Here, we show that the measured potentials at multiple locations within a device at elevated temperature are well-described by solution of Laplace's equation, assuming spatially-uniform conductivity, suggesting non-equilibrium current flows through the two-dimensional bulk. Extrapolation suggests that at even lower temperatures current may still flow primarily through the bulk rather than, as had been assumed, through edge modes. In conclusion, an argument for bulk current flow previously applied to quantum Hall systems supports this picture.
The thermodynamic properties of nitrogen gas do not thermodynamically approximate an ideal, diatomic gas at cryogenic temperatures. Choice of a suitable equation of state to model its behavior is discussed and the equation of Beattie and Bridgeman is selected as best meeting the needs for cryogenic wind tunnel use. The real gas behavior of nitrogen gas is compared to an ideal, diatomic gas for the following flow processes: isentropic expansion; normal shocks; boundary layers; and shock wave boundary layer interactions. The only differences in predicted pressure ratio between nitrogen and an ideal gas that may limit the minimum operating temperatures of transonic cryogenic wind tunnels seem to occur at total pressures approaching 9atmospheres and total temperatures 10 K below the corresponding saturation temperature, where the differences approach 1 percent for both isentropic expansions and normal shocks. Several alternative cryogenic test gases - air, helium, and hydrogen - are also analyzed. Differences in air from an ideal, diatomic gas are similar in magnitude to those of nitrogen. Differences for helium and hydrogen are over an order of magnitude greater than those for nitrogen or air. Helium and hydrogen do not approximate the compressible flow of an ideal, diatomic gas.
While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is co-located with a flow stagnation point, the introduction of asymmetry typically leads to non-ideal flows across the null point. To understand this behavior, we present exact expressions for the motion of three-dimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows non-ideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a null-null pair or the reverse, the instantaneous velocity of separation or convergence of the null-null pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating null-null pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating null-null pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of non-ideal behavior elsewhere along the field line.
Conservative dissipative difference schemes for computing one dimensional flow are introduced, and the recognition and representation of flow discontinuities are discussed. Multidimensional methods are outlined. Second order finite volume schemes are introduced. Conversion of difference schemes for a single linear convection equation into schemes for the hyperbolic system of the nonlinear conservation laws of ideal compressible flow is explained. Approximate Riemann solvers are presented. Monotone initial value interpolation; and limiters, switches, and artificial dissipation are considered.
The real gas behavior of nitrogen, the gas normally used in transonic cryogenic tunnels, is reported for the following flow processes: isentropic expansion, normal shocks, boundary layers, and interactions between shock waves and boundary layers. The only difference in predicted pressure ratio between nitrogen and an ideal gas which may limit the minimum operating temperature of transonic cryogenic wind tunnels occur at total pressures approaching 9 atm and total temperatures 10 K below the corresponding saturation temperature. These pressure differences approach 1 percent for both isentropic expansions and normal shocks. Alternative cryogenic test gases were also analyzed. Differences between air and an ideal diatomic gas are similar in magnitude to those for nitrogen and should present no difficulty. However, differences for helium and hydrogen are over an order of magnitude greater than those for nitrogen or air. It is concluded that helium and cryogenic hydrogen would not approximate the compressible flow of an ideal diatomic gas.
The ideal MHD equations are reduced to a single equation under the assumption of axisymmetric flow. A variational principle from which the equation is derivable is given. The characteristics of the equation are briefly discussed. The equation is used to rederive the theorem of Gussenhoven and Carovillano.