Coriolis Coefficients Research Articles

New in the hydraulics of channels with permeable walls: indicator of the relative value of the dissipation

The factors that have led to the creation of the scientific direction “hydraulics of variable mass” to study the fluid movement laws in channels with permeable walls are indicated. The results of applying of the dynamics of a variable mass point for describing the flow in such pipelines are presented. It is noted unjustifiability of the second Newton’s law generalization to the case of motion of a variable mass point for hydrodynamics problems. The functionality of one-dimensional and multidimensional models of fluid motion in permeable channels based on the classical equations of fluid and gas mechanics is characterized. It is substantiated the dominance of one-dimensional models in engineering computational practice, and a number of contradictions in the description of fluid dynamics are shown (with the flow visualization). On the base of the new kinematic image (instead of the generally accepted “solid jet”, when fluid particles are separated or joined), it has been obtained a one-dimensional equation of fluid motion in a permeable channel in which the friction coefficient is an indicator of the relative magnitude of the energy dissipation of the flow. The dependence of the Coriolis coefficient on the flow regime is constructed. The structure of the friction drag coefficient of a permeable channel has been studied using the vector dimension of length. It is shown that the dissipation of the flow energy in a permeable channel is higher both during outflow and inflow of liquid than in channels with solid walls at the same flow rates. The results are in demand in the development of chemical technology devices, nuclear reactors with microfuel elements, filters and heat exchangers containing channels with permeable walls.

Investigation of the Different Models of Elliptical-Lopac Gate Performance under Submerged Flow Conditions

The effect of the elliptic ratio on the hydraulic performance of the LOPAC gate has been investigated using experimental and Computational Fluid Dynamics CFD simulations (Flow-3D Hydro). Experiments and simulations were carried out at three different flow discharges, three different submerged ratios, and five different elliptic ratios. In this context, the CFD model was first calibrated and verified using the measured data, and then CFD simulation was performed. The ratio of upstream/downstream flow depth, the flow discharge coefficient, and the energy dissipation through the gate have been calculated and analyzed, and the three-dimensional features of the flow have been described. Based on the results, the elliptical LOPAC gates with circular weirs determine extreme values of the controlled flow parameters. Asymmetric recirculation downstream of the gate is sometimes observed in the model predictions. The use of Coriolis coefficients relevant to the entire cross-section, here deployed just for the circular and the traditional rectangular Lopac gates, has allowed a concise way to report and compare complex flows for any experimental condition.

On the equations of open channel flow

The traditional equations for describing open channel flow have appeared in the literature for decades and are so ingrained that they might seem to be statements of settled science. Careful derivations that detail assumptions and approximations relied upon in the formulation are mostly absent. We derive mass, momentum, and energy equations by averaging their small-scale counterparts and formulate forms that are Galilean invariant as required by continuum mechanics. Averaging is over a time increment and a spatial region in a single step, clarifying the need for closure relations. The derivation leads to the Boussinesq tensor and Coriolis vector as rigorous generalizations of the Boussinesq and Coriolis coefficients typically proposed. Examples are provided for the computation of these coefficients from published data. The approach employed here can be extended to systems such as pipe flow or shallow water equations, and the Galilean invariant forms are also suitable for entropy generation analyses.

On the Nonlinear Mathematical Model Representing the Coriolis Effect

In this study, the traveling wave solutions of a nonlinear partial differential equation (NPDE) called as Geophysics Korteweg-de Vries (GpKdV) equation are obtained using the modified exponential function method (MEFM). Coriolis effect is stated with the help of this model used in geophysics. The nonlinear model has a Coriolis coefficient representing this effect.

On Boussinesq and Coriolis coefficients and their derivatives in transient pipe flows

A rigorous analytical justification is developed for a simplification that is widely used in one-dimensional simulations of steady and unsteady flows in pipes, namely treating the flow as a 'plug flow' in which cross-sectional variations in axial velocity are neglected except for consequential shear forces on pipe walls. The proof is obtained without assuming that the flow is nearly incompressible flow and, indeed, it is found that the plug flow approximation remains good even for compressible flows at moderate, subsonic speeds. In more general analyses, explicit allowance is sometimes made for the influence of (i) the Boussinesq coefficient β and (ii) its axial rate of change ∂β/∂x. Typically, such analyses discard the terms in ∂β/∂x in the basic equations and proceed using β alone. This is done on the grounds that no method of evaluating ∂β/∂x is available. It is shown in this paper that discarding ∂β/∂x is not only unnecessary, but that it actually leads to less accurate outcomes than simply assuming plug flow. The process used to derive the analytical justification has a spin-off benefit of shedding light on alternative methods of integrating source terms over the pipe cross-section. Although the primary purpose of the paper is to demonstrate that the use of plug flow approximations can be justified rigorously for most flows, brief attention is also paid to cases where it has potential to mislead.

Determination of Boussinesq and Coriolis coefficients for pipelines operating with discharge connection along the path

Peculiarities of the diagrams of averaged fluid velocities in the cross-sections of pressure collecting perforated pipelines were determined on the basis of the experimental studies conducted by the authors.
 The most characteristic typical diagrams of averaged velocities in the pipelines cross-sections with their different design characteristics were given. A comparative analysis of the obtained diagrams with the diagrams of velocities that occur during uniform motion in pressure pipelines with solid walls was carried out. It is shown that the main difference between them occurs in the flow zones, which are located near the pipeline walls. It was explained by the connected liquid jets effect on the main flow. The degree of diagrams deformation was estimated by the value of the momentum coefficient α0 (Boussinesq coefficient) and the coefficient of kinetic energy α (Coriolis coefficient). It was determined that in the general case these coefficients will be variable in magnitude along the length of the studied pipes. Nevertheless, these coefficients are recommended to be constant in magnitude in engineering calculations. The limits of the structural characteristics of collecting perforated pipes for which this non-uniformity of the diagrams must be taken into account, and for which it can be neglected were determined on the basis of the analysis of the equation of fluid motion with a variable flow rate.

Propionitrile in the two lowest excited vibrational states in the laboratory and on Titan

The rotational spectrum of propionitrile (ethyl cyanide, C2H5CN) in the two lowest excited vibrational states, v13=1 and v21=1, was studied in detail. The compiled experimental data set consisted of published line lists, lines measured from published spectra up to 645 GHz, and new measurements at frequencies from 8 to 331 GHz. The two states are subject to considerable mutual interaction but application of a- and b-axis Coriolis coupling model to the measured A-symmetry internal rotation substate transitions was found to be successful. A total of over 1900 transitions were fitted for J values up to 76 and Ka up to 24, resulting in determined vibrational separation between the two states ΔE=6.2070246(14) cm−1, and Coriolis coefficients |ζ13,21a| = 0.378, |ζ13,21b| = 0.127, in good agreement with quantum chemistry calculations. The new line catalog was used to model ALMA spectra of Titan’s atmosphere from 2016, fitting many weak lines not previously modeled. By including the vibrationally excited lines of C2H5CN and a new partition function, we derive a disk-averaged volume mixing ratio estimate in 2016 of 7.8 ± 0.2 ppb assumed constant above 300 km.

Experimental investigations of the turbulent swirl flow in straight conical diffusers with various angles

Results of experimental investigations of the turbulent swirl flow in three straight conical diffusers with various diffuser total angles are presented in this paper. All three diffusers have the inlet diameter 0.4 m and total divergence angles 8.6?, 10.5?, and 12.6?. The incompressible swirl flow field is generated by the axial fan impeller, and for each diffuser several regimes were achieved by changing rotation number. Original classical probes were used for measurements. The distributions of the average main swirl flow characteristics along the diffuser are shown. Distributions of the inlet Boussinesq number, outlet Coriolis coefficient, ratio of the swirl and completely axial flow loss coefficients at conical diffuser on the inlet swirl flow parameter are also presented.

Laboratory Study on 3D Flow Structures Induced by Zero-Height Side Weir and Implications for 1D Modeling

AbstractSide weir flows induce complex three-dimensional (3D) structures on the flow field in the main channel. Extensive experiments at the laboratory scale were conducted in order to investigate the flow field for the particular case of a side weir with a zero height crest in both fixed bed and steady flow conditions. Detailed measurements of the flow surface, discharge, and velocity field were performed in the main channel upstream, alongside, and downstream of the side weir location. They allowed detection and analysis of the three-dimensional flow structures. Elaborations of the measurements show the implications of such three-dimensional nature of the flow on integral quantities such as Coriolis and Boussinesq coefficients as well as the specific energy and discharge coefficient that are important in the widely used one-dimensional (1D) models. Moreover, the results may help to better understand other free-surface problems similar to the side weir flow, such as lateral diversions, river bifurcations...

Kinetic energy redistribution on the hydrodynamic initial section

Scientific and technical information, regarding the issues of viscous and abnormally viscous liquid flow in geometrically heterogeneous channels is analyzed. The reasons of additional energy losses, caused by the occurrence of the inertial forces in the flow during the development of the velocity profile on the hydrodynamic initial section of channels are determined. Kinematic characteristics of unstabilized flow under various conditions of entry in the initial section are investigated. The analysis of kinetic energy redistribution in the flow is carried out. The functional dependence of the Coriolis coefficient on hydrodynamic conditions of entry in the initial section is found, and formulas to calculate its length are defined. An opportunity to identify additional pressure losses without using the hydrodynamic section method, associated with restructuring the velocity profile on its length is provided. Calculated dependences to compute the length of the flow stabilization section are defined. The obtained results of «control» over the hydrodynamic conditions of entry allow to create the optimal operating modes and improve performance characteristics of the process equipment.

Convective boundary layer wind dynamics and inertial oscillations: the influence of surface stress

AbstractInvestigating the influence of surface friction on the inertial oscillation (IO) of an extratropical, non‐growing, convective boundary layer (CBL), we paid particular attention to the stability‐dependent interactive coupling of shear‐induced turbulence and turbulent friction, which leads to a nonlinear relationship between friction and velocity. We showed that in contrast to common perception, IO damping is controlled not only by friction but also by the dependence of friction on velocity. Furthermore, we found that surface friction not only causes damping but also modifies the restoring force. Using these basic principles, we studied the oscillatory properties (equilibrium, periodicity and damping) of the CBL by means of a model based on Monin–Obukhov surface‐layer similarity (MOS) and the mixed‐layer approximation. We found that the model complies with a quadratic surface stress–velocity relationship (QS) in the neutral limit, and a linear surface stress–velocity relationship (LS) in the proximity of the free‐convective limit. Dynamically, the LS leads to a harmonic oscillation with a constant periodicity and exponential damping of the IO. However, the QS displays rather complex anharmonic behaviour; in comparison with the LS it produces a 50% stronger overall damping and a 100% larger contribution to the restoring force. Considering CBLs of arbitrary stability, we found that the MOS stress–velocity relation can be very well approximated by a much simpler linear combination of the LS and the QS which, respectively, represent the convective and the shear‐induced contributions to friction. This enabled us to link the set of the external parameters (surface roughness, surface buoyancy flux and boundary layer depth) to a set of three effective parameters: the equilibrium velocity, the convective friction constant and the neutral friction constant. Together with the Coriolis coefficient, these parameters completely determine the IO.

Energy and Momentum Velocity Coefficients for Calibrating Submerged Sluice Gates in Irrigation Canals

There is renewed interest in developing calibration methods for gates operating in submerged conditions in irrigation canals. In the present study, a new method based on a generalization of the standard energy-momentum method that accounts for variations in the energy and momentum velocity coefficients is proposed, for the following reasons. First, it was found that the assumption of uniform submerged jet velocity to account for the kinetic energy head and momentum flux is in reality equivalent to assuming a parabolic relationship between the Coriolis and Boussinesq coefficients. Second, literature investigations showed that the coefficients for the downstream side of submerged gates are notably greater than unity, and the implicit parabolic relationship between these coefficients in the standard energy-momentum method is inadequate, at least for high submergence conditions. The proposed energy-momentum method was evaluated using the data obtained from four gates operating in an irrigation canal in Southe...

Investigation of the turbulent swirl flows in a conical diffuser

Results of the theoretical and experimental investigations of the turbulent mean swirl flows characteristics change along straight conical diffuser of incompressible fluid (air) are presented in this paper. The main swirl flow characteristics review is given. In addition: the specific swirl flow energy, the energy loss, the mean circulation, the swirl flow parameter, the ratio between the swirl and axial flow loss coefficients change along the diffuser are presented. Among other values: the Boussinesq number, outlet Coriolis coefficient and swirl flow loss coefficient dependences on inlet swirl flow parameter are also given. The swirl flow specific energy and outlet Coriolis coefficient calculation procedure are presented in this paper, as well as experimental test bed and measuring procedures. The swirl flow fields were induced by the axial fan impeller. Various swirl parameters were achieved by the impeller openings and rotational speeds.

Texture and fractal methods for analyzing the characteristics of unsteady gas flows in pipelines

Turbulent structures in two-dimensional model gas flows are analyzed by estimating the fractal dimension and the texture characteristics of the gas flows. The fractal dimension is estimated using the self-similarity indices of the power spectra for the following characteristics of the gas flows: the Coriolis and Boussinesq coefficients, average pressure, hydraulic resistance coefficient, velocity loss in a pipeline element, and curvature of the gas flow. The texture characteristics are calculated using the following texture indices: energy, entropy, inertia coefficient, uniformity coefficient, cluster excess coefficient, cluster asymmetry coefficient, and also information measure of cluster correlation. Computer experiments show that, in propagation of a shock wave, the wavelet spectra of the indices of the model gas flows contain a large number of self-similar figures, which is indicative of a hierarchical structure and a fractal character of the model gas flows.

Torsional Coriolis coefficients in a ?regular? vibrational basis for molecules with one pair of internal rotors

Torsional Coriolis coefficients in a ?regular? vibrational basis for molecules with one pair of internal rotors

Torsional Coriolis coefficients in a ‘regular’ vibrational basis for molecules with one pair of internal rotors

A general method for calculating the values of torsional Coriolis coefficients of molecules with internal rotation, with respect to an internal axis system, is described. This is done in view of the important role of torsional Coriolis interactions in the mechanisms, affecting the torsional splitting patterns. We choose a set of symmetrized vibrational coordinates where the displacements of all nuclei follow rectilinear trajectories in an internal axis system. The vibrational wavefunctions associated with these coordinates represent vibrational states where the splittings of the torsional components follow regular patterns, and departures from these basis vibrational states generate anomalous patterns. General expressions for the calculation of torsional Coriolis coefficients are obtained by the methods of basic molecular mechanics, and applications to special classes of molecules are shown and commented in detail.

Physical behavior, symmetry classification and quantum numbers of vibrational–torsional states in ethane-like molecules

The symmetry species of vibrational and vibrational–torsional states of ethane-like molecules are labeled and classified by the values of quantum numbers related to the vibrational contribution to the z-axis rotational and torsional angular momenta. It is emphasized that the symmetry behavior of degenerate vibrational states of this class of molecules depends on the joint action of end-to-end and torsional Coriolis coupling by a complex mechanism, with group theoretical implications. A new vibration–torsion quantum number is defined, to account for the arbitrariness of the symmetry classification of the degenerate vibrational modes. The classification of the vibrational states of a G s+ G s combination is studied in detail. The limit case where the value of the Coriolis coefficient is equal to one in both partners of the combination is examined, accounting for the effects of end-to-end and torsional Coriolis interactions, and the results are shown to be in agreement with the predictions from group theory. The occurrence of vibrational ℓ and ℓ i splittings in a G s+ G s combination, analogous to the vibrational ℓ-doubling in E+ E combinations, is also discussed. It is pointed out that the complex mechanisms of end-to-end and torsional Coriolis coupling, which can affect the torsional splittings significantly, might contain relevant general features also applicable to other classes of molecules with internal rotation.

Mathematical Simulation of Superinertial Free Oscillations of the Black Sea in the β-Plane Approximation

New results on the numerical simulation of superinertial fee oscillations of the Black Sea for a variable Coriolis coefficient are presented.

Head and Tail Deformations, Torsional Coriolis Coupling, and E1d-E2d Vibrational Mixing in Ethane-Like Molecules

The mechanism of torsional Coriolis interaction of E1d and E2d vibrational modes in ethane-like molecules is investigated, and it is shown that this coupling can drastically affect the torsional splitting in the degenerate vibrational states. A basic point of our treatment is that the sets of coordinates of head and tail which combine with the + sign to generate E1d normal coordinates are in general different from those which combine with the − sign to generate E2d normal coordinates. It is shown that the ζγ torsional Coriolis coefficients calculated by the usual methods of normal mode analysis are related to the vibrational angular momenta within head and tail referred to the internal rotor axis systems. With knowledge of the L and L−1 matrices it is possible to transform these coefficients for reference to the molecule-fixed frame. It is peculiar that torsional Coriolis matrix elements occur between E1d and E2d vibrational components with the same x or y orientation in the molecule-fixed frame. The matrix elements of the torsional Coriolis operator and other operators responsible for the end-to-end coupling are determined, and a method for calculating vibration–torsion energies, and then torsional splittings, in degenerate vibrational states is outlined. Detailed calculations require a global model, involving all the degenerate vibrational basis states in a complex mechanism of interactions, but it is shown that useful information can be obtained by means of simplified models. Our semiempirical rule that degenerate vibrational states with a large negative value of the diagonal vibration–rotation Coriolis coefficient are likely to deviate much from the behavior of E1d or E2d vibrational states, with a sensible decrease of the torsional splittings, is confirmed.

High-resolution spectroscopic study of H2 80 Se in the ν(stretch) = 5 and 6 local-mode pairs states

High-resolution spectra of the H2 80Se molecule (50±,0), A1/B2 and (60±,0), A1/B2 (local mode pairs) stretching states were recorded using a Fourier transform spectrometry technique and also a Ti: sapphire laser photo-acoustic spectrometer with resonance cavity and multi-pass cell. The vibrational wavefunction, stretching band origins, rotational constants and Coriolis coefficients of H2 80Se molecule ν = 5 and 6 local-mode pairs were calculated by using the NMDD (normal mode with Darling—Dennison resonance included) model. These parameters were used to predict the upper state energy levels, which were used as the bases of ground state combination differences for assigning the vibration—rotational transitions of H2 80Se molecule ν = 5 and 6 local-mode pairs states. Several striking local-mode limit effects and the formation of four-fold ro-vibrational energy clusters were observed and discussed.