Spin-Up from Rest of a Liquid Metal with Deformable Free Surface in a Cylinder under the Influence of a Uniform Axial Magnetic Field

Spin-up from rest of a liquid metal having deformable free surface in the presence of a uniform axial magnetic field is numerically studied. Both liquid and gas phases in a vertically mounted cylinder are assumed to be an incompressible, immiscible, Newtonian fluid. Since the viscous dissipation and the Joule heating are neglected, thermal convection due to buoyancy and thermocapillary effects is not taken into account. The effects of Ekman number and Hartmann number were computed with fixing the Froude number of 1.5, the density ratio of 800, and the viscosity ratio of 50. The evolutions of the free surface, three-component velocity field, and electric current density are portrayed using the level-set method and HSMAC method. When a uniform axial magnetic field is imposed, the azimuthal momentum is transferred from the rotating bottom wall to the core region directly through the Hartmann layer. This is the most striking difference from spin-up of the nonmagnetic case.

Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential

As it was shown earlier, a wide class of nonlinear 3-dimensional (3D) fluid flows of incompressible viscous fluid can be described by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by a three-component velocity field having a two-component vorticity field. Both these fields may, in general, depend on all three spatial variables and time. In this paper, the governing equations for the quasi-potential are derived and simple illustrative examples of 3D flows in the Cartesian coordinates are presented. The generalisation of the developed approach to the fluid flows in the cylindrical and spherical coordinate frames represents a nontrivial problem that has not been solved yet. In this paper, this gap is filled and the concept of a quasi-potential to the cylindrical and spherical coordinate frames is further developed. A few illustrative examples are presented which can be of interest for practical applications.

Effects of Particle Properties on Visualizing Flows in a Two- Stage Electrostatic Precipitator Using Particle Image Velocimetry

The amount of particulate matter (PM) in the environment has been confirmed to be health risks on human bodies[1, 2], and therefore removing suspended particles has become the research goal of many studies. Electrostatic precipitator (ESP) is one of the high-efficiency particle collection technologies[3-7]. Particle Image Velocimetry (PIV) has been an effective tool for visualizing the flow patterns in experimental fluid mechanics, and many studies adopted this technique to study flows in ESP[8-10]. However, particles charged by the electric field can cause deviation in measurement results since it does not follow the ionized air flow which can be charged differently from the tracer particles. In this study, the observation of the effects of different particle properties on flow field in a two-stage ESP is the objectives of this study. A two-stage ESP was built and four different seeding particles, aluminum oxide (Al2O3) particle, oil droplet particle, sodium chloride (NaCl) particle, and titanium dioxide (TiO2) particle, are tested in the current study. In this study, the streamwise velocity of the flows ranges from 2.36 m/s to 4.18 m/s, the voltage of the corona electrode varies from 8 kV to 12 kV with a positive polarity, and the voltage of the collector electrode is fixed at 16 kV. To investigate the 3-D flow patterns inside the channel, data at different planes were taken for comparison. The results show that by increasing charge voltage from 8 kV to 12 kV with a streamwise flow velocity the 2.36 m/s, the y-component velocity for Al2O3 particle, oil droplet particle, NaCl particle and TiO2 particle increased by 50.6%, 76.0%, 33.5% and 51.9%, respectively. Moreover, for the case of the 4.18 m/s primary flow, the y-component velocity for Al2O3 particle, oil droplet particle, NaCl particle and TiO2 particle increase by 52.7%, 59.2%, 59.4% and 65.9% after the voltages increase from 8 kV to 12 kV. PIV results for oil droplet particle shows slower y-component velocities, which can be due to the lower Archimedes number of 3.12E-06 and the mobility number that is larger than 3. On the contrary, in most of results from TiO2 particles show high y-component velocity, which is due to the highest Archimedes number of 1.15E-03 of the seeding particles tested in this study. This result shows that the particle is less affected by buoyancy effect. The PIV results of the middle plane also shows that the ycomponent of velocity from -2.6 m/s to -0.5 m/s, in contrast to -1.0 m/s to 1.0 m/s from the near wall observation plane. These results are consistent to simulation results of the electric field distribution, whichshows unequal electric field strengths between the middle and near wall regions of the test section. Only half of the cage shape distribution of the electric field can be observed, and primary flow influences the ionic wind to move to the downstream area. Based on the results, the oil droplet and TiO2 particles are more suitable for the role of tracer particles compared to aluminum oxide and sodium chloride particles.

Turbulence Anisotropy Investigations in an Internal Combustion Engine

The assumption of isotropic turbulence is commonly incorporated into models of internal combustion engine (ICE) in-cylinder flows. While preliminary analysis with two-dimensional velocity data indicates that the turbulence may tend to isotropy as the piston approaches TDC, the validity of this assumption has not been fully investigated, partially due to lack of three-component velocity data in ICEs. In this work, the velocity was measured using two-dimensional, three-component (2D-3C) particle image velocimetry in a single-cylinder, motored, research engine to investigate the evolution of turbulence anisotropy throughout the compression stroke. Invariants of the Reynolds stress anisotropy tensor were calculated and visualized, through the Lumley triangle, to investigate turbulence states. Results showed the turbulence to be mostly anisotropic, with preferential tendency toward 2D axisymmetry at the beginning of the compression stroke and approaching isotropy near top-dead-center. Findings provide new insights into turbulence in dynamic, bounded flows to assist with the development of physics-based, quantitative models.

Multifractal Model of Atmospheric Turbulence Applied to Elastic Lidar Data

This paper shall present a multifractal interpretation of turbulent atmospheric entities, considering them a complex system whose dynamics are manifested on continuous yet non-differentiable multifractal curves. By bringing forth theoretical considerations regarding multifractal structures through non-differentiable functions in the form of an adaptation of scale relativity theory, the minimal vortex of an instance of turbulent flow is considered. In this manner, the spontaneous breaking of scale invariance becomes a mechanism for atmospheric turbulence generation. This then leads to a general equation for the non-differentiable vortex itself, with its component velocity fields, and to a vortex turbulent energy dissipation—all of which are plotted and studied. Once the structure of the non-differentiable multifractal structure is mathematically described, an improved phenomenological turbulence model and relations between turbulent energy dissipation and the minimal vortex are employed together, exemplifying the codependency of such models. Using turbulent medium wave propagation theory, certain relations are then extrapolated which allow the obtaining of the inner and outer length scales of the turbulent flow using lidar data. Finally, these altitude profiles are compiled and assembled into timeseries to exemplify the theory and to compare the results with known literature. This model is a generalization of our recent results published under the title “On a Multifractal Approach of Turbulent Atmosphere Dynamics”.

Colour-Doppler echocardiography flow field velocity reconstruction using a streamfunction–vorticity formulation

We introduce a new method ( Do ppler Ve locity R econstruction or DoVeR), for reconstructing two-component velocity fields from colour Doppler scans. DoVeR employs the streamfunction–vorticity equation, which satisfies mass conservation while accurately approximating the flow rate of rotation. We validated DoVeR using artificial colour Doppler images generated from computational fluid dynamics models of left ventricle (LV) flow. We compare DoVeR against the conventional intraventricular vector flow mapping (iVFM 1D ) and reformulated iVFM (iVFM 2D ). LV model error analysis showed that DoVeR is more robust to noise and probe placement, with noise RMS errors ( nRMSE ) between 3.81% and 6.67%, while the iVFM methods delivered 4.16–24.17% for iVFM 1D and 4.06–400.21% for iVFM 2D . We test the DoVeR and iVFM methods using in vivo mouse LV ultrasound scans. DoVeR yielded more haemodynamically accurate reconstructions, suggesting that it can provide a more reliable approach for robust quantification of cardiac flow.

Turbulence Anisotropy Investigations in an Internal Combustion Engine

The assumption of isotropic turbulence is commonly incorporated into models of internal combustion engine (ICE) in-cylinder flows. While preliminary analysis with two-dimensional velocity data indicates that the turbulence may tend to isotropy as the piston approaches TDC, the validity of this assumption has not been fully investigated, partially due to lack of three-component velocity data in ICEs. In this work, the velocity was measured using two-dimensional, three-component (2D-3C) particle image velocimetry in a single-cylinder, motored, research engine to investigate the evolution of turbulence anisotropy throughout the compression stroke. Invariants of the Reynolds stress anisotropy tensor were calculated and visualized, through the Lumley triangle, to investigate turbulence states. Results showed the turbulence to be mostly anisotropic, with preferential tendency toward 2D axisymmetry at the beginning of the compression stroke and approaching isotropy near top-dead-center. Findings provide new insights into turbulence in dynamic, bounded flows to assist with the development of physics-based, quantitative models.

QUESTIONS AND PROBLEMS OF MATHEMATICAL MODELING QUA NONEQUILIBRIUM OF COMBUSTION PROCESSES

On the basis of thermodynamic analysis, new mathematical models of the combus- tion process (thermal theory) and vibrational combustion are constructed. A global inhomo- geneity of the system can be described as an inhomogeneous distribution of the enthalpy over a two-component mixture. In this case, for the combustion process in the phase space of the variables (%, P, T, n, S, E), an increase in the enthalpy is not a total differential. An increase in the enthalpy is a total differential on the local equilibrium manifold (a laminar combustion process). These two assertions, which allow one to single out in the phase space the corre- sponding adiabatic of the combustion process (the Hugoniot adiabatic) and the equation for the entropy, close the classical mathematical model of the combustion process. The above numerical experiments show that two regimes of the combustion process (deflagration and detonation) depend on the structure of the standard chemical potential Moreover, a control of the passive component velocity at the inlet results in (depending on the structure of the standard chemical potential) high-frequency oscillations, which are responsible for a blow-up.

LDV Characterization of Unsteady Vaned Diffuser Flow in a Centrifugal Compressor

Modern turbomachinery faces increased performance demands in terms of efficiency, compactness, and pressure-rise. Advancements in computational technology have allowed numerical methods to become the backbone of design development efforts. However, the unique complexities of centrifugal compressor flow-fields pose difficult computational problems. As such, advanced experimental methods must be used to obtain high-quality datasets to further inform, improve, and validate computational methods in complex flow regimes. Recent experimental work on a high-speed centrifugal compressor has provided detailed, unsteady, three-component velocity data using Laser Doppler Velocimetry. A passage vortex is present and its nascent tied to the increased incidence at mid-span associated with impeller wake flow. This vortex begins in the hub-pressure side corner and grows to fill the passage and become temporally stable. The vortex development is unsteady in nature and the unsteady effects persist 40% downstream of the throat. Distinct jet and wake flow patterns from the impeller also do not agglomerate until 40% downstream of the throat. Additionally, the critical impact of the unsteady flow development on the time-averaged flow-field is explained.