Search results for: Coriolis

Authors: N. H. Z. Abidin, N. F. M. Mokhtar, S. S. A. Gani

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The influence of diffusion of the thermal or known as Soret effect in a heated Binary fluid model with Coriolis force is investigated theoretically. The linear stability analysis is used, and the eigenvalue is obtained using the Galerkin method. The impact of the Soret and Coriolis force on the onset of stationary convection in a system is analysed with respect to various Binary fluid parameters and presented graphically. It is found that an increase of the Soret values, destabilize the Binary fluid layer system. However, elevating the values of the Coriolis force helps to lag the onset of convection in a system.

Keywords: Benard convection, binary fluid, Coriolis, Soret

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Authors: N. F. M. Mokhtar, N. Z. A. Hamid

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This paper reports an analytical investigation of the stability and thermal convection in a horizontal anisotropic porous medium in the presence of Coriolis force and magnetic field. The Darcy model is used in the momentum equation and Boussinesq approximation is considered for the density variation of the porous medium. The upper and lower boundaries of the porous medium are assumed to be conducting to temperature perturbation and we used first order Chebyshev polynomial Tau method to solve the resulting eigenvalue problem. Analytical solution is obtained for the case of stationary convection. It is found that the porous layer system becomes unstable when the mechanical anisotropy parameter elevated and increasing the Coriolis force and magnetic field help to stabilize the anisotropy porous medium.

Keywords: anisotropic, Chebyshev tau method, Coriolis force, Magnetic field

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Authors: Evgeniia Shavrina, Yan Zeng, Boo Cheong Khoo, Vinh-Tan Nguyen

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The present paper is aimed at providing a review of error sources in cryogenic metering by Coriolis flowmeters (CFMs). Whereas these flowmeters allow accurate water metering, high uncertainty and low repeatability are commonly observed at cryogenic fluid metering, which is often necessary for effective renewable energy production and storage. The sources of these issues might be classified as general and cryogenic specific challenges. A conducted analysis of experimental and theoretical studies shows that material behaviour at cryogenic temperatures, composition variety, and multiphase presence are the most significant cryogenic challenges. At the same time, pipeline diameter limitation, ambient vibration impact, and drawbacks of the installation may be highlighted as the most important general challenges of cryogenic metering by CFM. Finally, the techniques, which mitigate the impact of these challenges are reviewed, and future development direction is indicated.

Keywords: Coriolis flowmeter, cryogenic, multicomponent flow, multiphase flow

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Authors: Mario P. Walker, Masaaki Okuma

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Ships are subjected to motions which can disrupt on-board operations and damage equipment. Roll motion, in particular, is of great interest due to low damping conditions which may lead to capsizing. Therefore finding ways to reduce this motion is important in ship designs. Several techniques have been investigated to reduce rolling. These include the commonly used anti-roll tanks, fin stabilizers and bilge keels. However, these systems are not without their challenges. For example, water-flow in anti-roll tanks creates complications, and for fin stabilizers and bilge keels, an extremely large size is required to produce any significant damping creating operational challenges. Additionally, among these measures presented above only anti-roll tanks are effective in zero forward motion of the vessels. This paper proposes and investigates a method to reduce rolling by inducing Coriolis effect using water-flow in the radial direction. Motion in the radial direction of a rolling structure will induce Coriolis force and, depending on the direction of flow will either amplify or attenuate the structure. The system is modelled with two degrees of freedom, having rotational motion for parametric rolling and radial motion of the water-flow. Equations of motion are derived and investigated. Numerical examples are analyzed in detail. To demonstrate applicability parameters from a Ro-Ro vessel are used as extensive research have been conducted on these over the years. The vessel is investigated under free and forced roll conditions. Several models are created using various masses, heights, and velocities of water-flow at a given time. The proposed system was found to produce substantial roll reduction which increases with increase in any of the parameters varied as stated above, with velocity having the most significant effect. The proposed system provides a simple approach to reduce ship rolling. Water-flow control is very simple as the water flows in only one direction with constant velocity. Only needing to control the time at which the system should be turned on or off. Furthermore, the proposed system is effective in both forward and zero forward motion of the ship, and provides no hydrodynamic drag. This is a starting point for designing an effective and practical system. For this to be a viable approach further investigations are needed to address challenges that present themselves.

Keywords: Coriolis effect, damping, rolling, water-flow

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Authors: L. A. Ostrovsky, Yu. A. Stepanyants

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Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described.

Keywords: Earth rotation, internal waves, nonlinear waves, solitons

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Authors: A. Giniatoulline

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A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid

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Authors: Medine Demir, Volker John

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Fluid equations in a rotating frame of reference have a broad class of important applications in meteorology and oceanography, especially in the large-scale flows considered in ocean and atmosphere, as well as many physical and industrial applications. The Coriolis and the centripetal forces, resulting from the rotation of the earth, play a crucial role in such systems. For such applications it may be required to solve the system in complex three-dimensional geometries. In recent years, the Navier--Stokes equations in a rotating frame have been investigated in a number of papers using the classical inf-sup stable mixed methods, like Taylor-Hood pairs, to contribute to the analysis and the accurate and efficient numerical simulation. Numerical analysis reveals that these classical methods introduce a pressure-dependent contribution in the velocity error bounds that is proportional to some inverse power of the viscosity. Hence, these methods are optimally convergent but small velocity errors might not be achieved for complicated pressures and small viscosity coefficients. Several approaches have been proposed for improving the pressure-robustness of pairs of finite element spaces. In this contribution, a pressure-robust space discretization of the incompressible Navier--Stokes equations in a rotating frame of reference is considered. The discretization employs divergence-free, $H^1$-conforming mixed finite element methods like Scott--Vogelius pairs. However, this approach might come with a modification of the meshes, like the use of barycentric-refined grids in case of Scott--Vogelius pairs. However, this strategy requires the finite element code to have control on the mesh generator which is not realistic in many engineering applications and might also be in conflict with the solver for the linear system. An error estimate for the velocity is derived that tracks the dependency of the error bound on the coefficients of the problem, in particular on the angular velocity. Numerical examples illustrate the theoretical results. The idea of pressure-robust method could be cast on different types of flow problems which would be considered as future studies. As another future research direction, to avoid a modification of the mesh, one may use a very simple parameter-dependent modification of the Scott-Vogelius element, the pressure-wired Stokes element, such that the inf-sup constant is independent of nearly-singular vertices.

Keywords: navier-stokes equations in a rotating frame of refence, coriolis force, pressure-robust error estimate, scott-vogelius pairs of finite element spaces

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Authors: A. Giniatoulline

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A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid

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Authors: Ahmad Forouzantabar, Mohammad Azadi, Alireza Alesaadi

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This paper describes a sliding mode controller for autonomous underwater vehicles (AUVs). The dynamic of AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of AUV and improve trajectory tracking. Moreover, the proposed controller can profoundly attenuate the effects of uncertainties and external disturbances in the closed-loop system. Using the Lyapunov theory the boundedness of AUV tracking errors and the stability of the proposed control system are also guaranteed. Numerical simulation studies of an AUV are included to illustrate the effectiveness of the presented approach.

Keywords: lyapunov stability, autonomous underwater vehicle, sliding mode controller, electronics engineering

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Authors: Mohamed Abdel Sabour, Mohamed Nouh, Ian Stevans, Essam Elkholy

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We study the period change of six Cepheids using 19376 accurate flux observations of the Solar Mass Ejection Imager (SMEI) onboard the Coriolis spacecraft. All observations for the six Cepheids have been derived as templates for each star, independent of the specific sites utilized to establish and update the O-C values. Sometimes, sinusoidal patterns are superimposed on the star's O-C changes, which cannot be regarded as random fluctuations in the pulsation period. Random period changes were detected and computed using Eddington's and Plakidis's approaches. A comparison of the observed and predicted period change reveals a good agreement with some published models and a very substantial divergence with others. Between the reported period change and that estimated by the current technique, a linear fit with a correlation coefficient of 90.08 percent was obtained. The temporal rate of period change in Cepheid stars might be connected to how well these stars' mass losses are known today.

Keywords: cepheids, period change, mass loss, O-C changes, period change, mass loss, O-C

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Authors: Alpana Goel, Kawalpreet Kalra

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The study of level structures of deformed nuclei is the most complex topic in nuclear physics. For the description of level structure, a simple model is good enough to bring out the basic features which may then be further refined. The low lying level structures of these nuclei can, therefore, be understood in terms of Two Quasiparticle plus axially symmetric Rotor Model (TQPRM). The formulation of TQPRM for deformed nuclei has been presented. The analysis of available experimental data on two quasiparticle rotational bands of deformed nuclei present unusual features like signature dependence, odd-even staggering, signature inversion and signature reversal in two quasiparticle rotational bands of deformed nuclei. These signature effects are well discussed within the framework of TQPRM. The model is well efficient in reproducing the large odd-even staggering and anomalous features observed in even-even and odd-odd deformed nuclei. The effect of particle-particle and the Coriolis coupling is well established from the model. Detailed description of the model with implications to deformed nuclei is presented in the paper.

Keywords: deformed nuclei, signature effects, signature inversion, signature reversal

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Authors: Samuel David Dunstan

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An elementary observation of a laminar cylindrical Poiseulle-Couette flow profile reveals no distinction in the parabolic streamwise profile from one without a cross-stream flow in whatever reference frame the observation is made. This is because the laminar flow is in solid-body rotation, and there is no intrinsic fluid rotation. Hence the main streamwise Poiseuille flow is unaffected. However, in turbulent (unsteady) cylindrical Poiseuille-Couette flow, the rotational reference frame must be considered, and any observation from an external inertial reference frame can give outright incorrect results. A common misconception in the study of fluid mechanics is the position of the observer does not matter. In this DNS (direct numerical simulation) study, firstly, turbulent flow in a pipe with axial rotation is established. Then in turbulent flow in the concentric pipe, with inner wall rotation, it is shown how the wall streak direction is oriented by the rotational reference frame. The Coriolis force here is not so fictitious after all!

Keywords: concentric pipe, rotational and inertial frames, frame invariance, wall streaks, flow orientation

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Authors: A. Giniatoulline

Abstract:

We consider the internal oscillations of the ocean which are caused by the gravity force and the Coriolis force, for different models with changeable density, heat transfer, and salinity. Traditionally, the mathematical description of the resonance effect is related to the growing amplitude as a result of input vibrations. We offer a different approach: the study of the relation between the spectrum of the internal oscillations and the properties of the limiting amplitude of the solution for the harmonic input vibrations of the external forces. Using the results of the spectral theory of self-adjoint operators in Hilbert functional spaces, we prove that there exists an explicit relation between the localization of the frequency of the external input vibrations with respect to the essential spectrum of proper inner oscillations and the non-uniqueness of the limiting amplitude. The results may find their application in various problems concerning mathematical modeling of turbulent flows in the ocean.

Keywords: computational fluid dynamics, essential spectrum, limiting amplitude, rotating fluid, spectral theory, stratified fluid, the uniqueness of solutions of PDE equations

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Authors: Nouri Sabrina, Benzeghiba Mohamed, Ghezal Abderrahmane

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Numerical parametric study is conducted to study the effects of ampoule rotation on the flows and the dopant segregation in vertical Bridgman (VB) crystal growth. Calculations were performed in unsteady state. The extended Darcy model, which includes the time derivative and Coriolis terms, has been employed in the momentum equation. It was found that the convection, and dopant segregation can be affected significantly by ampoule rotation, and the effect is similar to that by an axial magnetic field. Ampoule rotation decreases the intensity of convection and stretches the flow cell axially. When the convection is weak, the flow can be suppressed almost completely by moderate ampoule rotation and the dopant segregation becomes diffusion-controlled. For stronger convection, the elongated flow cell by ampoule rotation may bring dopant mixing into the bulk melt reducing axial segregation at the early stage of the growth. However, if the cellular flow cannot be suppressed completely, ampoule rotation may induce larger radial segregation due to poor mixing.

Keywords: numerical simulation, heat and mass transfer, vertical solidification, chemical segregation

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Authors: Nouri Sabrina

Abstract:

Numerical parametric study is conducted to study the effects of ampoule rotation on the flows and the dopant segregation in Vertical Bridgman (VB) crystal growth. Calculations were performed in unsteady state. The extended darcy model, whıch includes the time derivative and coriolis terms, has been employed in the momentum equation. It is found that the convection, and dopant segregation can be affected significantly by ampoule rotation, and the effect is similar to that by an axial magnetıc field. Ampoule rotation decreases the intensity of convection and stretches the flow cell axıally. When the convectıon is weak, the flow can be suppressed almost completely by moderate ampoule rotation and the dopant segregation becomes diffusion-controlled. For stronger convection, the elongated flow cell by ampoule rotation may bring dopant mixing into the bulk melt reducing axial segregation at the early stage of the growth. However, if the cellular flow cannot be suppressed completely, ampoule rotation may induce larger radial segregation due to poor mixing.

Keywords: rotating vertical solidification, Finite Volume Method, heat and mass transfer, porous medium, phase change

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Authors: Ruquan You, Haiwang Li, Zhi Tao

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A time-resolved particle image velocimetry (PIV) system is developed to investigate the boundary layer flow with the effect of rotating Coriolis and buoyancy force. This time-resolved PIV system consists of a 10 Watts continuous laser diode and a high-speed camera. The laser diode is able to provide a less than 1mm thickness sheet light, and the high-speed camera can capture the 6400 frames per second with 1024×1024 pixels. The whole laser and the camera are fixed on the rotating facility with 1 radius meters and up to 500 revolutions per minute, which can measure the boundary flow velocity in the rotating channel with and without ribs directly at rotating conditions. To investigate the effect of buoyancy force, transparent heater glasses are used to provide the constant thermal heat flux, and then the density differences are generated near the channel wall, and the buoyancy force can be simulated when the channel is rotating. Due to the high temporal and spatial resolution of the system, the proper orthogonal decomposition (POD) can be developed to analyze the characteristic of the turbulent boundary layer flow at rotating conditions. With this rotating facility and PIV system, the velocity profile, Reynolds shear stress, spatial and temporal correlation, and the POD modes of the turbulent boundary layer flow can be discussed.

Keywords: rotating facility, PIV, boundary layer flow, spatial and temporal resolution

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Authors: Dmitry Lukyanov, Sergey Shevchenko, Alexander Kukaev

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Modern MEMS gyroscopes have strengthened their position in motion control systems and have led to the creation of tactical grade sensors (better than 15 deg/h). This was achieved by virtue of the success in micro- and nanotechnology development, cooperation among international experts and the experience gained in the mass production of MEMS gyros. This production is knowledge-intensive, often unique and, therefore, difficult to develop, especially due to the use of 3D-technology. The latter is usually associated with manufacturing of inertial masses and their elastic suspension, which determines the vibration and shock resistance of gyros. Today, consumers developing highly dynamic objects or objects working under extreme conditions require the gyro shock resistance of up to 65 000 g and the measurement range of more than 10 000 deg/s. Such characteristics can be achieved by solid-state gyroscopes (SSG) without inertial masses or elastic suspensions, which, for example, can be constructed with molecular kinetics of bulk or surface acoustic waves (SAW). Excellent effectiveness of this sensors production and a high level of structural integration provides basis for increased accuracy, size reduction and significant drop in total production costs. Existing principles of SAW-based sensors are based on the theory of SAW propagation in rotating coordinate systems. A short introduction to the theory of a gyroscopic (Coriolis) effect in SAW is provided in the report. Nowadays more and more applications require passive and wireless sensors. SAW-based gyros provide an opportunity to create one. Several design concepts incorporating reflective delay lines were proposed in recent years, but faced some criticism. Still, the concept is promising and is being of interest in St. Petersburg Electrotechnical University. Several experimental models were developed and tested to find the minimal configuration of a passive and wireless SAW-based gyro. Structural schemes, potential characteristics and known limitations are stated in the report. Special attention is dedicated to a novel method of a FEM modeling with piezoelectric and gyroscopic effects simultaneously taken into account.

Keywords: FEM simulation, gyroscope, OOFELIE, surface acoustic wave, wireless sensing

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Authors: Md Monir Hossain, Anne Staples, Kuya Takami, Tomonari Furukawa

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Tire noise has a significant impact on ride quality and vehicle interior comfort, even at low frequency. Reduction of tire noise is especially important due to strict state and federal environmental regulations. The primary sources of tire noise are the low frequency structure-borne noise and the noise that originates from the release of trapped air between the tire tread and road surface during each revolution of the tire. The frequency response of the tire changes at low and high frequency. At low frequency, the tension and bending moment become dominant, while the internal structure and local deformation become dominant at higher frequencies. Here, we analyze tire response in terms of deformation and rolling velocity at low revolution frequency. An Abaqus FEA finite element model is used to calculate the static and dynamic response of a rolling tire under different rolling conditions. The natural frequencies and mode shapes of a deformed tire are calculated with the FEA package where the subspace-based steady state dynamic analysis calculates dynamic response of tire subjected to harmonic excitation. The analysis was conducted on the dynamic response at the road (contact point of tire and road surface) and side nodes of a static and rolling tire when the tire was excited with 200 N vertical load for a frequency ranging from 20 to 200 Hz. The results show that frequency has little effect on tire deformation up to 80 Hz. But between 80 and 200 Hz, the radial and lateral components of displacement of the road and side nodes exhibited significant oscillation. For the static analysis, the fluctuation was sharp and frequent and decreased with frequency. In contrast, the fluctuation was periodic in nature for the dynamic response of the rolling tire. In addition to the dynamic analysis, a steady state rolling analysis was also performed on the tire traveling at ground velocity with a constant angular motion. The purpose of the computation was to demonstrate the effect of rotating motion on deformation and rolling velocity with respect to a fixed Newtonian reference point. The analysis showed a significant variation in deformation and rolling velocity due to centrifugal and Coriolis acceleration with respect to a fixed Newtonian point on ground.

Keywords: natural frequency, rotational motion, steady state rolling, subspace-based steady state dynamic analysis

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Authors: Seema Paul, Jesper Oppelstrup, Roger Thunvik, Vladimir Cvetkovic

Abstract:

Lake Victoria is the second largest fresh water body in the world, located in East Africa with a catchment area of 250,000 km², of which 68,800 km² is the actual lake surface. The hydrodynamic processes of the shallow (40–80 m deep) water system are unique due to its location at the equator, which makes Coriolis effects weak. The paper describes a St.Venant shallow water model of Lake Victoria developed in COMSOL Multiphysics software, a general purpose finite element tool for solving partial differential equations. Depth soundings taken in smaller parts of the lake were combined with recent more extensive data to resolve the discrepancies of the lake shore coordinates. The topography model must have continuous gradients, and Delaunay triangulation with Gaussian smoothing was used to produce the lake depth model. The model shows large-scale flow patterns, passive tracer concentration and water level variations in response to river and tracer inflow, rain and evaporation, and wind stress. Actual data of precipitation, evaporation, in- and outflows were applied in a fifty-year simulation model. It should be noted that the water balance is dominated by rain and evaporation and model simulations are validated by Matlab and COMSOL. The model conserves water volume, the celerity gradients are very small, and the volume flow is very slow and irrotational except at river mouths. Numerical experiments show that the single outflow can be modelled by a simple linear control law responding only to mean water level, except for a few instances. Experiments with tracer input in rivers show very slow dispersion of the tracer, a result of the slow mean velocities, in turn, caused by the near-balance of rain with evaporation. The numerical and hydrodynamical model can evaluate the effects of wind stress which is exerted by the wind on the lake surface that will impact on lake water level. Also, model can evaluate the effects of the expected climate change, as manifest in changes to rainfall over the catchment area of Lake Victoria in the future.

Keywords: bathymetry, lake flow and steady state analysis, water level validation and concentration, wind stress

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Authors: Adonis Menezes, J. C. Passos

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The current panorama of technology in heat transfer and the scarcity of information about the convective boiling of CO₂ and hydrocarbon in small diameter channels motivated the development of this work. Among non-halogenated refrigerants, CO₂/ R744 has distinct thermodynamic properties compared to other fluids. The R744 presents significant differences in operating pressures and temperatures, operating at higher values compared to other refrigerants, and this represents a challenge for the design of new evaporators, as the original systems must normally be resized to meet the specific characteristics of the R744, which creates the need for a new design and optimization criteria. To carry out the convective boiling tests of CO₂, an experimental apparatus capable of storing (m= 10kg) of saturated CO₂ at (T = -30 ° C) in an accumulator tank was used, later this fluid was pumped using a positive displacement pump with three pistons, and the outlet pressure was controlled and could reach up to (P = 110bar). This high-pressure saturated fluid passed through a Coriolis type flow meter, and the mass velocities varied between (G = 20 kg/m².s) up to (G = 1000 kg/m².s). After that, the fluid was sent to the first test section of circular cross-section in diameter (D = 4.57mm), where the inlet and outlet temperatures and pressures, were controlled and the heating was promoted by the Joule effect using a source of direct current with a maximum heat flow of (q = 100 kW/m²). The second test section used a cross-section with multi-channels (seven parallel channels) with a square cross-section of (D = 2mm) each; this second test section has also control of temperature and pressure at the inlet and outlet as well as for heating a direct current source was used, with a maximum heat flow of (q = 20 kW/m²). The fluid in a biphasic situation was directed to a parallel plate heat exchanger so that it returns to the liquid state, thus being able to return to the accumulator tank, continuing the cycle. The multi-channel test section has a viewing section; a high-speed CMOS camera was used for image acquisition, where it was possible to view the flow patterns. The experiments carried out and presented in this report were conducted in a rigorous manner, enabling the development of a database on the convective boiling of the R744 in macro and micro channels. The analysis prioritized the processes from the beginning of the convective boiling until the drying of the wall in a subcritical regime. The R744 resurfaces as an excellent alternative to chlorofluorocarbon refrigerants due to its negligible ODP (Ozone Depletion Potential) and GWP (Global Warming Potential) rates, among other advantages. The results found in the experimental tests were very promising for the use of CO₂ in micro-channels in convective boiling and served as a basis for determining the flow pattern map and correlation for determining the heat transfer coefficient in the convective boiling of CO₂.

Keywords: convective boiling, CO₂/R744, macro-channels, micro-channels

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