scholarly journals Synchronization Theory-Based Analysis of Coupled Vibrations of Dual-Tube Coriolis Mass Flowmeters

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6340
Author(s):  
Zhong-Xiang Li ◽  
Chun Hu ◽  
De-Zhi Zheng ◽  
Shang-Chun Fan
Keyword(s):  
Numerical Solutions ◽  
Frequency Doubling ◽  
Nonlinear Effects ◽  
Coupled Vibrations ◽  
Dual Beam ◽  
Set Up ◽  
Fourth Order Method ◽  
Measuring Signal ◽  
Signal Sources ◽  
Synchronization Theory

Certain nonlinear influences are found in dual-tube Coriolis mass flowmeters (CMFs). According to experimentation, a nonlinearity dominated by frequency-doubling signals can be observed in the measuring signal. In general, such nonlinear effects are simplified as linear systems or neglected through processing. In this paper, a simplified model has been constructed for dual-beam CMFs based on the theory of nonlinear dynamics, with the spring–damper system as the medium for the dual-beam coupled vibrations. Next, the dynamics differential equation of the coupled vibrations is set up on the basis of the Lagrangian equation. Furthermore, numerical solutions are obtained using the Runge–Kutta fourth-order method. The study then fits discrete points of the numerical solutions, which are converted into the frequency domain to observe the existence of frequency-doubling signal components. Our findings show that frequency-doubling components exist in the spectrogram, proving that these nonlinear influences are a result of the motions of coupled vibrations. In this study, non-linear frequency-doubling signal sources are qualitatively analyzed to formulate a theoretical basis for CMFs design.

Nonlinear Sloshing in Fixed and Vertically Excited Containers

2002 ◽  
Author(s):  
Jannette B. Frandsen ◽  
Alistair G. L. Borthwick
Keyword(s):  
Perturbation Theory ◽  
Free Surface ◽  
Small Perturbation ◽  
Numerical Solutions ◽  
Vertical Direction ◽  
Nonlinear Effects ◽  
Breaking Waves ◽  
Surface Flow ◽  
Nonlinear Behaviour ◽  
Computational Domain

Nonlinear effects of standing wave motions in fixed and vertically excited tanks are numerically investigated. The present fully nonlinear model analyses two-dimensional waves in stable and unstable regions of the free-surface flow. Numerical solutions of the governing nonlinear potential flow equations are obtained using a finite-difference time-stepping scheme on adaptively mapped grids. A σ-transformation in the vertical direction that stretches directly between the free-surface and bed boundary is applied to map the moving free surface physical domain onto a fixed computational domain. A horizontal linear mapping is also applied, so that the resulting computational domain is rectangular, and consists of unit square cells. The small-amplitude free-surface predictions in the fixed and vertically excited tanks compare well with 2nd order small perturbation theory. For stable steep waves in the vertically excited tank, the free-surface exhibits nonlinear behaviour. Parametric resonance is evident in the instability zones, as the amplitudes grow exponentially, even for small forcing amplitudes. For steep initial amplitudes the predictions differ considerably from the small perturbation theory solution, demonstrating the importance of nonlinear effects. The present numerical model provides a simple way of simulating steep non-breaking waves. It is computationally quick and accurate, and there is no need for free surface smoothing because of the σ-transformation.

Preliminary results of numerical simulation of submarine landslide-generated waves

2021 ◽  
Author(s):  
Ramtin Sabeti ◽  
Mohammad Heidarzadeh
Keyword(s):  
Numerical Simulation ◽  
Numerical Modelling ◽  
Numerical Solutions ◽  
Numerical Technique ◽  
Source Region ◽  
Three Dimensional ◽  
Terminal Velocity ◽  
Sensitivity Analyses ◽  
Physical Experiments ◽  
Set Up

<p>Landslide-generated waves have been major threats to coastal areas and have led to destruction and casualties. Their importance is undisputed, most recently demonstrated by the 2018 Anak Krakatau tsunami, causing several hundred fatalities. The accurate prediction of the maximum initial amplitude of landslide waves (<em>η<sub>max</sub></em>) around the source region is a vital hazard indicator for coastal impact assessment. Laboratory experiments, analytical solutions and numerical modelling are three major methods to investigate the (<em>η<sub>max</sub></em>). However, the numerical modelling approach provides a more flexible and cost- and time-efficient tool. This research presents a numerical simulation of tsunamis due to rigid landslides with consideration of submerged conditions. In particular, this simulation focuses on studying the effect of landslide parameters on <em>η<sub>max</sub>.</em> Results of simulations are compared with our conducted physical experiments at the Brunel University London (UK) to validate the numerical model.</p><p>We employ the fully three-dimensional computational fluid dynamics package, FLOW-3D Hydro for modelling the landslide-generated waves. This software benefit from the Volume of Fluid Method (VOF) as the numerical technique for tracking and locating the free surface. The geometry of the simulation is set up according to the wave tank of physical experiments (i.e. 0.26 m wide, 0.50 m deep and 4.0 m). In order to calibrate the simulation model based on the laboratory measurements, the friction coefficient between solid block and incline is changed to 0.41; likewise, the terminal velocity of the landslide is set to 0.87 m/s. Good agreement between the numerical solutions and the experimental results is found. Sensitivity analyses of landslide parameters (e.g. slide volume, water depth, etc.) on <em>η<sub>max </sub></em>are performed. Dimensionless parameters are employed to study the sensitivity of the initial landslide waves to various landslide parameters.</p>

On the weakly nonlinear development of Tollmien-Schlichting wavetrains in boundary layers

1996 ◽  
Vol 323 ◽  
pp. 133-171 ◽  
Author(s):  
Xuesong Wu ◽  
Philip A. Stewart ◽  
Stephen J. Cowley
Keyword(s):  
Numerical Solutions ◽  
Asymptotic Methods ◽  
Nonlinear Effects ◽  
Mean Flow ◽  
Flow Distortion ◽  
Weakly Nonlinear ◽  
Nonlinear Development ◽  
Finite Distance ◽  
Tollmien Schlichting ◽  
High Reynolds

The nonlinear development of a weakly modulated Tollmien-Schlichting wavetrain in a boundary layer is studied theoretically using high-Reynolds-number asymptotic methods. The ‘carrier’ wave is taken to be two-dimensional, and the envelope is assumed to be a slowly varying function of time and of the streamwise and spanwise variables. Attention is focused on the scalings appropriate to the so-called ‘upper branch’ and ‘high-frequency lower branch’. The dominant nonlinear effects are found to arise in the critical layer and the surrounding ‘diffusion layer’: nonlinear interactions in these regions can influence the development of the wavetrain by producing a spanwise-dependent mean-flow distortion. The amplitude evolution is governed by an integro-partial-differential equation, whose nonlinear term is history-dependent and involves the highest derivative with respect to the spanwise variable. Numerical solutions show that a localized singularity can develop at a finite distance downstream. This singularity seems consistent with the experimentally observed focusing of vorticity at certain spanwise locations, although quantitative comparisons have not been attempted.

scholarly journals The NANOFLUID FLOW BETWEEN PARALLEL PLATES AND HEAT TRANSFER IN PRESENCE OF CHEMICAL REACTION AND POROUS MATRIX

2020 ◽  
Vol 50 (4) ◽  
pp. 283-289
Author(s):  
S. Jena ◽  
S. R. Mishra ◽  
P.K. Pattnaik ◽  
Ram Prakash Sharma
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Chemical Reaction ◽  
Numerical Solutions ◽  
Porous Matrix ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Similarity Transformations ◽  
Fourth Order Method ◽  
Source Sink

This paper deals with nanofluid flow between parallel plates and heat transfer through porous media with heat source /sink. The governing equations are transformed into self-similar ordinary differential equations by adopting similarity transformations and then the converted equations are solved numerically by Runge-Kutta fourth order method. Special emphasis has been given to the parameters of physical interest which include Prandtl number, magnetic parameter, porous matrix, chemical reaction parameter and heat source parameter. The results obtained for velocity, temperature and concentration are shown in graphs. The comparison of the special case of this present results with the existing numerical solutions in the literature shows excellent agreement.

scholarly journals A single-beam photothermal interferometer for in situ measurements of aerosol light absorption

2020 ◽  
Vol 13 (12) ◽  
pp. 7097-7111
Author(s):  
Bradley Visser ◽  
Jannis Röhrbein ◽  
Peter Steigmeier ◽  
Luka Drinovec ◽  
Griša Močnik ◽  
...  
Keyword(s):  
Detection Limit ◽  
Cross Section ◽  
Light Absorption ◽  
Detection Limits ◽  
Field Measurements ◽  
Absorption Cross ◽  
Single Beam ◽  
Dual Beam ◽  
Set Up

Abstract. We have developed a novel single-beam photothermal interferometer and present here its application for the measurement of aerosol light absorption. The use of only a single laser beam allows for a compact optical set-up and significantly easier alignment compared to standard dual-beam photothermal interferometers, making it ideal for field measurements. Due to a unique configuration of the reference interferometer arm, light absorption by aerosols can be determined directly – even in the presence of light-absorbing gases. The instrument can be calibrated directly with light-absorbing gases, such as NO2, and can be used to calibrate other light absorption instruments. The detection limits (1σ) for absorption for 10 and 60 s averaging times were determined to be 14.6 and 7.4 Mm−1, respectively, which for a mass absorption cross section of 10 m2 g−1 leads to equivalent black carbon concentration detection limits of 1460 and 740 ng m−3, respectively. The detection limit could be reduced further by improvements to the isolation of the instrument and the signal detection and processing schemes employed.

scholarly journals Transportation of Al2O3-SiO2-TiO2 modified nanofluid over an exponentially stretching surface with inclined magnetohydrodynamic

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 279-285
Author(s):  
Prvaeen Dadheech ◽  
Priyanka Agrawal ◽  
Anil Sharma ◽  
Kottakkaran Nisar ◽  
Sunil Purohit
Keyword(s):  
Magnetic Field ◽  
Base Fluid ◽  
Numerical Solutions ◽  
Graphical Representation ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Similarity Transformations ◽  
Exponentially Stretching ◽  
Inclined Angle ◽  
Fourth Order Method

In the present study Al2O3-SiO2-TiO2/C2H6O2 modified nanofluid flow over a stretching surface is considered with imposed inclined magnetic field. Three different suspended nanoparticles in a base fluid are considered in this next generation of hybrid nanofluid called as modified nanofluid. Ethanol glycol is taken as a base fluid with suspension of three nanoparticles of Al2O3, SiO2, and TiO2. The mathematical model of the flow is encountered by Runga-Kutta fourth order method using appropriate similarity transformations. As a key result it is observed that the capacity of heat transportation of modified nanofluid is higher as compared with nanofluids and hybrid nanofluids. Numerical solutions with graphical representation are presented. With increased inclined angle, parameter of magnetic field, and volume friction parameter a decrement in velocity field has been noticed for modified nanofluid.

scholarly journals Heat Transfer in Hydromagnetic Flow over an Unsteady Stretching Permeable Sheet

2019 ◽  
Vol 4 (4) ◽  
pp. 1018-1030
Author(s):  
Susheela Chaudhary ◽  
Santosh Chaudhary ◽  
Sawai Singh
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Research Work ◽  
Magnetic Field Effect ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Layer Flow ◽  
Fourth Order Method

Unsteady laminar boundary layer flow of viscous incompressible electrically conducting fluid along a continuous stretched permeable surface with the magnetic field effect is investigated. The defining characteristics of unsteady laminar boundary layer flow are governed a more than one independent variables, stretching velocity and surface temperature of the field. Governing equations are obtained for influencing parameters and transformed into ordinary differential equations by taking convenient similarity variables. Runge-Kutta fourth order method in corporation by the shooting technique is introduced to carry out numerical computations of the investigation. Velocity and temperature profiles are computed and represented graphically for the influences of suction/injection parameter, unsteadiness parameter, magnetic parameter and Prandtl number, while numerical solutions of local skin friction coefficient and local Nusselt number are discussed through tables. For non-magnetic condition, results are found in concordance with earlier research work.

On the formation of Moore curvature singularities in vortex sheets

1999 ◽  
Vol 378 ◽  
pp. 233-267 ◽  
Author(s):  
STEPHEN J. COWLEY ◽  
GREG R. BAKER ◽  
SALEH TANVEER
Keyword(s):  
Complex Plane ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Nonlinear Effects ◽  
Vortex Sheet ◽  
Finite Amplitude ◽  
Analytical Continuation ◽  
Curvature Singularity ◽  
Singularity Formation ◽  
Vortex Sheets

Moore (1979) demonstrated that the cumulative influence of small nonlinear effects on the evolution of a slightly perturbed vortex sheet is such that a curvature singularity can develop at a large, but finite, time. By means of an analytical continuation of the problem into the complex spatial plane, we find a consistent asymptotic solution to the problem posed by Moore. Our solution includes the shape of the vortex sheet as the curvature singularity forms. Analytic results are confirmed by comparison with numerical solutions. Further, for a wide class of initial conditions (including perturbations of finite amplitude), we demonstrate that 3/2-power singularities can spontaneously form at t=0+ in the complex plane. We show that these singularities propagate around the complex plane. If two singularities collide on the real axis, then a point of infinite curvature develops on the vortex sheet. For such an occurrence we give an asymptotic description of the vortex-sheet shape at times close to singularity formation.

Axisymmetric compressible flow in a rotating cylinder with axial convection

1985 ◽  
Vol 154 ◽  
pp. 121-144 ◽  
Author(s):  
Marius Ungarish ◽  
Moshe Israeli
Keyword(s):  
Compressible Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Nonlinear Effects ◽  
Ideal Gas ◽  
Navier Stokes ◽  
Linear Perturbation ◽  
Linear Extensions ◽  
Navier Stokes Equations ◽  
Thermally Conducting

The steady compressible flow of an ideal gas in a rotating annulus with thermally conducting walls is considered for small Rossby number ε and Ekman number E and moderate rotational Mach numbers M. Attention is focused on nonlinear effects which show up when σ and εM2 are not small (σ = ε/HE½, H is the dimensionless height of the container). These effects are not properly predicted by the classical linear perturbation analysis, and are treated here by quasi-linear extensions.The extra work required by these extensions is only the numerical solution of one ordinary differential equation for the pressure.Numerical solutions of the full Navier–Stokes equations in the nonlinear range are presented, and the validity of the present approach is confirmed.

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