Effects of centrifugal and Coriolis forces on the mold-filling behavior of titanium melts in vertically rotating molds

The vertical centrifugal-casting technique is widely used in the manufacture of various irregularlyshaped castings of advanced structural alloys with thin walls, complex shapes and/or large sizes. These castings are used in the increasing applications in aero-space/aviation industries, human teeth/bone repairs with nearnet shaped components, etc. In a vertically rotating casting system, the mold-filling processes of alloy melts, coupled with solidification-heat transfer, may be much more complicated, because they are driven simultaneously by gravity, centrifugal and Coriolis forces. In the present work, an N-SNOF-equations-based model, solved using a SOLA-VOF algorithm, under a rotating coordinate system was applied to numerically investigate the impacts of centrifugal and Coriolis forces on metallic melt mold-filling processes in different vertical centrifugal-casting configurations with different mold-rotation rates using an authors＇ computer-codes system. The computational results show that the Coriolis force may cause remarkable variations in the flow patterns in the casting-part-cavities of a large horizontal-section area and directly connected to the sprue via a short ingate in a vertical centrifugal-casting process. A ＂turn-back＂ mold-filling technique, which only takes advantage of the centrifugal force in a transient rotating melt system, has been confirmed to be a rational centrifugal-casting process in order to achieve smooth and layer-by-layer casting-cavities-filling control. The simulated mold-filling processes of Ti-6AI-4V alloy melt, in a vertical centrifugal-casting system with horizontally-connected plate-casting cavities, show reasonable agreement with experimental results from the literature.

Tide simulation using the mild-slope equation with Coriolis force and bottom friction

Since the mild-slope equation was derived by Berkhoff （1972）,the researchers considered various mechanism to simplify and improve the equation,which has been widely used for coastal wave field calculation.Recently,some scholars applied the mild-slope equation in simulating the tidal motion,which proves that the equation is capable to calculate the tide in actual terrain.But in their studies,they made a lot of simplifications,and did not consider the effects of Coriolis force and bottom friction on tidal wave.In this paper,the first-order linear mild-slope equations are deduced from Kirby mild-slope equation including wave and current interaction.Then,referring to the method of wave equations’ modification,the Coriolis force and bottom friction term are considered,and the effects of which have been performed with the radial sand ridges topography.Finally,the results show that the modified mild-slope equation can be used to simulate tidal motion,and the calculations agree well with the measurements,thus the applicability and validity of the mild-slope equation on tidal simulation are further proved.

Exploring Solutions of Nonlinear Rossby Waves with Complete Coriolis Force

Nonlinear Rossby waves in a Boussinesq fluid model which includes both the vertical and horizontalcomponents of Coriolis force are studied by using the semi-geostrophic approximation and the method of travelling-wavesolution.Taylor series expansion has been employed to isolate the characteristics of the linear Rossby waves and identifythe Rossby cnoidal and solitary waves.Qualitative analysis indicates that if the disturbances are independent of latitude,the effect of horizontal components of Coriolis force disappears.

Numerical simulation and parameter optimization of Coriolis force scale measurement process based on DEM

The Coriolis force method is a recently developed and highly regarded direct measurement technique that enables high-precision measurement of bulk materials.The operational parameters and variations thereof directly influence the measurement accuracy of the equipment.In this study,a measurement correction coefficient is introduced to improve the calculation method for mass flow rate of the materials.The DEM is employed to simulate the motion of particle groups within the Coriolis force scale under different parameters,and the effects of various structural and operational parameters on the measurement results are compared.The research findings indicate that a lower rotational speed leads to more stable instantaneous measurement results,although the measurement error is relatively large.When the rotational speed exceeds 300 rpm,the measurement error remains within 15%.For materials with a radius of 1–2 mm,the variation range of precision error is approximately 0.4%.Among the structural parameters,the radius of the measurement wheel has the most significant impact on the measurement results,wherein a larger measurement wheel radius corresponds to a smaller measurement error.The horizontal angle of the blades follows as the next influential parameter,with a clockwise rotation and a horizontal angle of 30°resulting in a measurement error below 2%.

Global Mild Solution of Stochastic Generalized Navier–Stokes Equations with Coriolis Force

In this paper, we apply Littlewood-Paley theory and Ito integral to get the global existence of stochastic Navier-Stokes equations with Coriolis force in Fourier-Besov spaces. As a comparison, we also give corresponding results of the deterministic Navier-Stokes equations with Coriolis force.

Nonlinear advection,Coriolis force,and frictional influence in the South Channel of the Yangtze Estuary,China

Observation data of along-estuary and lateral current velocities over a transect located at the South Channel of the Yangtze estuary was obtained during a spring tide in August 2011.Harmonic analysis was done on the current velocities to get a mean component and a semi-diurnal component.Based on these two components,the driving mechanisms of mean lateral flow and M2 lateral tidal flow are shown and analyzed respectively.The dominant driving force of mean lateral flow is nonlinear advection and that of lateral M2 tidal flow is Coriolis force.The friction plays an important role near the bottom and surface for both lateral mean flow and M2 tidal flow.

A discussion on Corioli force effect and aftershock activity tendency of the M=8.1 Kunlun Mountain Pass earthquake on Nov. 14, 2001

Following the theory and definition of the Corioli force in physics, the Corioli force at the site of the M=8.1 Kunlun Mountain Pass earthquake on November 14, 2001, is examined in this paper on the basis of a statistical research on relationship between the Corioli force effect and the maximum aftershock magnitude of 20 earthquakes with M7.5 in Chinese mainland, and then the variation tendency of aftershock activity of the M=8.1 earthquake is discussed. The result shows: a) Analyzing the Corioli force effect is an effective method to predict maximum aftershock magnitude of large earthquakes in Chinese mainland. For the sinistral slip fault and the reverse fault with its hanging wall moving toward the right side of the cross-focus meridian plane, their Corioli force pulls the two fault walls apart, decreasing frictional resistance on fault plane during the fault movement and releasing elastic energy of the mainshock fully, so the maximum magnitude of aftershocks would be low. For the dextral slip fault, its Corioli force presses the two walls against each other and increases the frictional resistance on fault plane, prohibiting energy release of the mainshock, so the maximum magnitude of aftershocks would be high. b) The fault of the M=8.1 Kunlun Mountain earthquake on Nov. 14, 2001 is essentially a sinistral strike-slip fault, and the Corioli force pulled the two fault walls apart. Magnitude of the induced stress is about 0.06 MPa. After a comparison analysis, we suggest that the aftershock activity level will not be high in the late period of this earthquake sequence, and the maximum magnitude of the whole aftershocks sequence is estimated to be about 6.0.

A Comparative study on generalized Manev potential and Newtonian potential in perturbed restricted four-body problem

The motion of a test particle within the context of the restricted four-body problem(R4BP)driven by a new kind of potential,called the generalized Manev potential,with perturbations in the Coriolis and centrifugal forces is considered in this study.The system possesses eight libration points which were distributed on its plane of motion in different manner from those of the usual Newtonian potential.Unlike the case of the perturbed R4BP under Newtonian potential,where two of these librations are stable,all of them are unstable in linear sense under Manev potential.We found that a gradual perturbation in the centrifugal force causes the trajectories of motion to drift inward but the Coriolis force was proven to have no effect on the location of the libration points of the system.Using first order Lyapunov characteristic exponents,the dynamical behavior of the system is found irregular.We experimented with a high velocity stellar system(82 G.Eridani)to establish the applicability of the model in astrophysics.

Mathematical model of burden distribution for the bell-less top of a blast furnace

Due to the difficulty in measuring the burden trajectory directly in an actual blast furnace （BF）, a mathematical model with Coriolis force and gas drag force considered was developed to predict it. The falling point and width of the burden flow were obtained and analyzed by the model, the velocities of particles at the chute end were compared with and without the existence of Coriolis force, and the effects of chute length and chute torque on the falling point were also discussed. The simulation results are in good agreement with practical measurements with laser beams in a 2500 m3 BF.

Vortex Theory and Earth Dynamics

Morphological evidence in active tectonic areas originate from alternative mechanisms to those described consisting of subcircular shapes suggests that these geometries may by translational dynamics of complex faults. The mechanics behind endogenic forces, in particular convection currents, hasn＇t been completely explained. Differing in density from upward flows developing in atmosphere and in water, magma upwelling from the mantle can trigger endogenic vortexes in particular conditions and due to Coriolis Force. At their onset and ascent phase, vortexes apply lateral forces as result of rotation, open their way toward the surface and over time stabilize the channel. Opposite to a rising linear flow which compacts overlying materials impeding their surge, vortex flows unload the materials externally and compact them on the lateral surface of the channel, thus making it more regular and stable. Torsional movements on the surface associated to vulcanites, lateral ramps and subcircular elevations, can be observed. Other phenomena that may be consequence of vortex dynamics are the volcanic cones showing pseudo-rotations in the morphologies surrounding the crater. In this study we suggest a modeling for a vortex theory which may explain the Earth dynamics in terms of spiraling movement and magma upwelling stabilizing over time.

Effect of Stokes drift on upper ocean mixing

Stokes drift is the main source of vertical vorticity in the ocean mixed layer. In the ways of Coriolis - Stokes forcing and Langmuir circulations, Stokes drift can substantially affect the whole mixed layer. A modified Mellor-Yamada 2. 5 level turbulence closure model is used to parameterize its effect on upper ocean mixing conventionally. Results show that comparing surface heating with wave breaking, Stokes drift plays the most important role in the entire ocean mixed layer, especially in the subsurface layer. As expected, Stokes drift elevates both the dissipation rate and the turbulence energy in the upper ocean mixing. Also, ilffluence of the surface heating, wave breaking and wind speed on Stokes drift is investigated respectively. Research shows that it is significant and important to assessing the Stokes drift into ocean mixed layer studying. The laboratory observations are supporting numerical experiments quantitatively.

Design and Characterization of a Novel Z-axis Quartz Cross-fork Micromachined Gyroscope

The existing researches on quartz gyroscope mainly focus on the structure design of the tuning fork, which aim at obtaining a better vibration characterization. However, the fabrication of complicated structure is a challenge for present processes, and the imperfect fabrication process seriously affects the performances of the sensors. In this paper, a novel quartz cross-fork structure micromachined gyroscope is proposed. The sensor has a simple structure in x-y plane of quartz crystal. Unlike other quartz gyroscopes, the proposed gyroscope is based on shear stress detection to sense Coriolis’ force rather than normal stress detection. This feature can simplify the sensing electrode patterns and miniaturize the structure easily. Then the mechanical analysis of the structure is discussed. In order to obtain high sensitivities and uniform characteristics between different structures, the sensing beam is designed to be tapered, and the taper should be appreciably greater than 1°. This scheme is validated by finite element analysis software. The dynamic characteristic of the structure is analyzed by lumped parameter model. The dynamic stress in the beam and the detection sensitivity are deduced to optimize the structure parameter of gyroscope. Finally, the gyroscope is fabricated by quartz anisotropic wet etching. The prototype is characterized as follows. The drive mode frequency is 13.38 kHz, and the quality factor is about 900 in air. The scale factor is 1.45 mV/（（°） s –1 ） and the nonlinearity is 3.6% in the dynamic range of ±200°/s. Process and test results show that the proposed quartz gyroscope can achieve a high performance at atmosphere pressure. The research can simplify the fabrication of the quartz gyroscope, and is taken as a novel method for the design of quartz gyroscope.

Numerical Investigation of Submarine Hydrodynamics and Flow Field in Steady Turn

This paper presents numerical simulations of viscous flow past a submarine model in steady turn by solving the Reynolds-Averaged Navier-Stokes Equations（RANSE） for incompressible, steady flows. The rotating coordinate system was adopted to deal with the rotation problem. The Coriolis force and centrifugal force due to the computation in a bodyfixed rotating frame of reference were treated explicitly and added to momentum equations as source terms. Furthermore, velocities of entrances were coded to give the correct magnitude and direction needed. Two turbulence closure models（TCMs）, the RNG k-ε model with wall functions and curvature correction and the Shear Stress Transport（SST） k-ω model without the use of wall functions, but with curvature correction and low-Re correction were introduced, respectively. Take DARPA SUBOFF model as the test case, a series of drift angle varying between 0° and 16° at a Reynolds number of 6.53×10^6 undergoing rotating arm test simulations were conducted. The computed forces and moment as a function of drift angle during the steady turn are mostly in close agreement with available experimental data. Though the difference between the pressure coefficients around the hull form was observed, they always show the same trend. It was demonstrated that using sufficiently fine grids and advanced turbulence models will lead to accurate prediction of the flow field as well as the forces and moments on the hull.

Flow Loss Mechanism in a Supercritical Carbon Dioxide Centrifugal Compressor at Low Flow Rate Conditions

With the advantages of high efficiency and compact structure,supercritical carbon dioxide(sC02)Brayton cycles have bright prospects for development in energy conversion field.As one of the core components of the power cycle,the centrifugal compressor tends to operate near the critical point(304.13 K,7.3773 MPa).Normally,the compressor efficiency increases as the inlet temperature decreases.When the inlet temperature is close to the critical point,the density increases sharply as the temperature decreases,which results in quickly decreasing of volume flow rate and efficiency reducing.The flow loss mechanism of the sCO_(2) compressor operating at low flow rate is studied in this paper.Computational fluid dynamics(CFD) simulations for sCO_(2)compressor were carried out at various inlet temperatures and various mass flow rates.When the sCO_(2)compressor operates at low volume flow rate,the flow loss is generated mainly on the suction side near the trailing edge of the blade.The flow loss is related to the counterclockwise vortexes generated on the suction side of the main blade.The vortexes are caused by the flow separation in the downstream region of the impeller passage,which is different from air compressors operating at low flow rates.The reason for this flow separation is that the effect of Coriolis force is especially severe for the sCO_(2) fluid,compared to the viscous force and inertial force.At lower flow rates,with the stronger effect of Coriolis force,the direction of relative flow velocity deviates from the direction of radius,resulting in its lower radial component.The lower radial relative flow velocity leads to severe flow separation on the suction side near the trailing edge of the main blade.

Landau quantization effects on damping Kawahara solitons in electron–positron–ion plasma in rotating ionized medium

For the dynamics of three-dimensional electron–positron–ion plasmas,a fluid quantum hydrodynamic model is proposed by considering Landau quantization effects in dense plasma.Ion–neutral collisions in the presence of the Coriolis force are also considered.The application of the reductive perturbation technique produces a wave evolution equation represented by a damped Korteweg–de Vries equation.This equation,however,is insufficient for describing waves in our system at very low dispersion coefficients.As a result,we considered the highest-order perturbation,which resulted in the damped Kawahara equation.The effects of the magnetic field,Landau quantization,the ratio of positron density to electron density,the ratio of positron density to ion density,and the direction cosine on linear dispersion laws as well as soliton and conoidal solutions of the damped Kawahara equation are explored.The understanding from this research can contribute to the broader field of astrophysics and aid in the interpretation of observational data from white dwarfs.

Turbulent characteristics and rotation correction of wall function in rotating channel with high local rotation parameter

The turbulent fluctuation and the rotation correction of wall function law are investigated in the entrance section of a rotating channel. The one-dimensional hot wire probe and the X-type probe are utilized to measure the boundary layer at four streamwise stations. Through the analysis on the boundary layer near the leading side and trailing side, it is found that the turbulent fluctuation is promoted in the trailing side whereas suppressed in the leading side. This difference is attributed to the Coriolis instability near the trailing side. In addition, considering the local rotation parameter Rc, whose maximum absolute value is 0.014, is larger than that in previous research, whose maximum value is 0.007, the whole process of the relaminarization is captured. To understand this phenomenon better, the effects of the generation term and the Coriolis term in the transport equation of the Reynolds stress are discussed. In addition, the rotation correction of the viscous-Coriolis region and the Coriolis region are discussed, a new revising method for the wall function is proposed.

FORMATION AND INFLUENCING FACTORS OF FREE SURFACE VORTEX IN A BARREL WITH A CENTRAL ORIFICE AT BOTTOM

Based on the Navier-Stokes equations with considering the effect of the Coriolis force, the finite volume method was employed to discretize the governing equations, the SIMPLE method was adopted to solve the discretized equations, and the flow field in a barrel with an outlet at the center of the bottom was simulated. The numerical results agree well with the experimental data. From the Lagrangian, the relations among the acceleration, the Coriolis force and the viscosity force were analyzed. The results show that the Coriolis force is the major factor that causes the formation of the vortex. The flow fields in the flume under different incoming flow conditions were numerically simulated using the software Fluent. The numerical simulations show good agreement with the experiments for the shape and position of the vortex.

THE PERTURBATION SOLUTIONS OF THE FLOW IN A ROTATING CURVED ANNULAR PIPE

WT5”BZ]In this paper, the flow in a rotating curved annular pipe is examined by a perturbation method. A second order perturbation solution is presented. The characteristics of the secondary flow and the axial flow are studied in detail. The study indicates that the loops of the secondary flow are more complex than those in a curved annular pipe without rotation and its numbers depend on the ratio of the Coriolis force to centrifugal force F. As F≈-1, the secondary flow has eight loops and its intensity reaches the minimum value, and the distribution of the axial flow is like that of the Poiseuille flow. The position of the maximum axial velocity is pushed to either outer bend or inner bend, which is also determined by F. [WT5”HZ]

Vibrational characteristics of rotating soft cylinders

Rotating structural components are omnipresent in engineering structures and natural world. This work investigates the effects of the centrifugal and Coriolis forces on the free vibrational characteristics of soft cylinders rotating with respect to the axis of symmetry based on the nonlinear elasticity and linear incremental theories. The formulations indicate that the biasing deformation, instantaneous elastic moduli, and incremental equations of motion strongly depend on the rotating speed. The characteristic equation for the natural frequency is derived using the state-space method and approximate laminate technique.The numerical examples included in this work demonstrate that the centrifugal and Coriolis forces might have significant effects on the vibrational characteristics of the cylinder. Results of this work will benefit the design and control of novel engineering systems with rotating soft cylinders or shafts.

Global Well-posedness of the 3D Generalized Rotating Magnetohydrodynamics Equations

In this paper, we establish the global well-posedness of the generalized rotating mag- netohydrodynamics equations if the initial data are in χ^1-2α defined by χ^1-2α {u ∈D＇（R^3） ：fR^3｜｜^1-2αu^^（ξ）｜dξ〈＋∞}.In addition, we also give Gevrey class regularity of the solution.