The Transition to Superrotation in Terrestrial Atmospheres

We show that by changing a single non-dimensional number, the thermal Rossby number, global atmospheric simulations with only axisymmetric forcing pass from an Earth-like atmosphere to a superrotating atmosphere that more resembles the atmospheres of Venus or Titan. The transition to superrotation occurs under conditions in which equatorward-propagating Rossby waves generated by baroclinic instability at intermediate and high latitudes are suppressed, which will occur when the deformation radius exceeds the planetary radius. At large thermal Rossby numbers following an initial, nearly axisymmetric phase, a global baroclinic wave of zonal wavenumber one generated by mixed barotropic-baroclinic instability dominates the eddy flux of zonal momentum. The global wave converges eastward zonal momentum to the equator and deposits westward momentum at intermediate latitudes during spinup and before superrotation emerges, and the baroclinic instability ceases once superrotation is established. A global barotropic mode of zonal wavenumber one generated by a mix of high- and low-latitude barotropic instability is responsible for maintaining superrotation in the statistically steady state. At intermediate thermal Rossby numbers, momentum flux by the global baroclinic mode is subdominant relative to smaller baroclinic modes, and thus strong superrotation does not develop.Comment: accepted for publication in JGR-Planet

The Impacts of Three Flamelet Burning Regimes in Nonlinear Combustion Dynamics

Axisymmetric simulations of a liquid rocket engine are performed using a delayed detached-eddy-simulation (DDES) turbulence model with the Compressible Flamelet Progress Variable (CFPV) combustion model. Three different pressure instability domains are simulated: completely unstable, semi-stable, and fully stable. The different instability domains are found by varying the combustion chamber and oxidizer post length. Laminar flamelet solutions with a detailed chemical mechanism are examined. The $\beta$ Probability Density Function (PDF) for the mixture fraction and Dirac $\delta$ PDF for both the pressure and the progress variable are used. A coupling mechanism between the Heat Release Rate (HRR) and the pressure in an unstable cycle is demonstrated. Local extinction and reignition is investigated for all the instability domains using the full S-curve approach. A monotonic decrease in the amount of local extinctions and reignitions occurs when pressure oscillation amplitude becomes smaller. The flame index is used to distinguish between the premixed and non-premixed burning mode in different stability domains. An additional simulation of the unstable pressure oscillation case using only the stable flamelet burning branch of the S-curve is performed. Better agreement with experiments in terms of pressure oscillation amplitude is found when the full S-curve is used.Comment: 25 pages, 12 figures. Submitted to Combustion and Flame for a Special Issu

Direct numerical simulation of a turbulent flow over an axisymmetric hill

Direct numerical simulation (DNS) of a turbulent flow over an axisymmetric hill has been carried out to study the three-dimensional flow separation and reattachment that occur on the lee-side of the geometry. The flow Reynolds number is ReH = 6500, based on free-stream quantities and hill height (H). A synthetic inflow boundary condition, combined with a data feed-in method, has been used to generate the turbulent boundary layer approaching to the hill. The simulation has been run using a typical DNS resolution of Dxþ ¼ 12:5; Dzþ ¼ 6:5, and Dyþ1 ¼ 1:0 and about 10 points in the viscous sublayer. It was found that a separation bubble exists at the foot of the wind-side of the hill and the incoming turbulent boundary layer flow undergoes re-laminarization process around the crest of the hill. These lead to a significant flow separation at the lee-side of the hill, where a very large primary separation bubble embedded with a smaller secondary separations have been captured. The present low-Re simulation reveals some flow features that are not observed by high-Re experiments, thus is useful for future experimental studies

Dynamic analysis of fast-acting solenoid actuators

There has been a recent revival of interest in the design of fast-acting solenoid actuators. This is due to the emergence of new control applications in the automotive industry constrained by tighter emission and noise regulations. In the context of developing a rapid computer-aided design tool for such applications, the thesis proposes several methods for computing the static and dynamic electromagnetic performance of solenoid actuators with a particular attention given to two actuator types : an axisymmetric and a rectangular solenoid actuator with a flat-faced armature. The magnetostatic performance of both actuator types is first evaluated by developing a detailed magnetic equivalent circuit in which the actuator geometry, saturation and end-effects are all taken into account. A comparison of the analytical model, based on the computation of the magnetisation characteristics and static forces for several airgap lengths, is given with finite-elements and measurements. In order to increase the computational speed of the static performance, the concept of magnetic gauge curve is presented. It is shown that this approach is in principle valid for any type of variable reluctance machine. Although the complexity of the gauge curve expression varies significantly from one device to another, it is shown that this method is an efficient way to store the magnetic data for a rapid computer aided-design or a real time application. When applied to the two previous types of solenoid actuator, it also leads to a very fast and accurate static force computation. The dynamic performance of the solid iron actuators requires the evaluation of the magnetic damping due to eddy currents. Based on a ID model of the flux and eddy current diffusion within an iron bar, an electromagnetic equivalent circuit of the axisymmetric is derived, in which the material nonlinearity, armature movement and eddy currents, a function of the previous parameters, actuator geometry and driving conditions, are modelled. A dynamic model of the partly solid iron rectangular actuator is also proposed and evaluated. In both cases a comparison of the transient current and force waveforms with 2D or 3D finite elements and measurements is given under various driving conditions

Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets

Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin–Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211–237) at low Strouhal number ( St ) and non-zero azimuthal wavenumbers ( m ). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency–wavenumber space where each dominates, finding lift-up to be dominant as St/m→0 . Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core

Application of state-of-the-art FEM techniques to magnetostatic NDE

A typical example of the complexities involved in the numerical modeling of electromagnetic phenomena is that of modeling the magnetic flux leakage inspection of gas transmission pipelines. The problem calls for three-dimensional modeling of motionally induced currents (using transient analysis), modeling nonlinearity of the ferromagnetic parts, and accurate modeling of the permanent magnet used in the magnetizer. Researchers, have thus far simplified the problem using several assumptions, including that of axisymmetry, and modeling velocity effects using steady-state analysis. However, there has been no attempt to quantify the errors introduced by these assumptions. Also, due to the unavailability of commercial codes to solve three-dimensional motion-related problems using transient analysis, a detailed study of the true nature of velocity effects has not been possible;This dissertation implements and evaluates state-of-the-art finite element modeling techniques applied to the specific problem of modeling magnetic flux leakage inspection of gas pipelines. This provides the basis from which conclusions can be drawn on the general problem of modeling magnetostatic phenomena. Axisymmetric and three-dimensional models are developed capable of modeling velocity effects. A detailed analysis of the differences between axisymmetric and three-dimensional geometries, based on a study of permeability variations in the vicinity of defects is presented. Also, the need for transient analysis is argued based on results generated. As part of this study, serious problems (including spurious solutions and corner singularities) associated with the traditional node-based finite-element techniques, when applied to the three-dimensional modeling, are discussed. In this work, new and efficient numerical modeling concepts, using the edge-based finite-element technique are employed to overcome these problems;This study demonstrates the need for accurate modeling of the full three-dimensional geometry, incorporating velocity effects and nonlinear permeability, for realistic predictions of flux leakage inspection tools. Major contributions of this work include: (1) detailed analysis of the physical processes associated with the magnetic flux leakage tool, (2) design ideas to improve the performance of the tool, and (3) development of an edge-based finite element code for modeling magnetostatic nondestructive testing applications in three-dimensions incorporating velocity effects. This is the first study of this nature, applied to pipeline inspection, and, many of the conclusions presented can be applied to nondestructive testing techniques in general

Numerical Solution of an Axisymmetric Eddy Current Model with Current and Voltage Excitations

This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10915-022-01780-4The aim of this paper is to study the numerical approximation of an axisymmetric time-harmonic eddy current problem involving an in-plane current. The analysis of the problem restricts to the conductor. The source of the problem is given in terms of boundary data currents and/or voltage drops defined in the so-called electric ports, which are parts of the boundary connected to exterior sources. This leads to an elliptic problem written in terms of the magnetic field with nonlocal boundary conditions. First, we prove the existence and uniqueness of the solution for a weak formulation written in terms of Sobolev spaces with appropriate weights. We show that the magnetic field is not the most appropriate variable to impose the boundary conditions when Lagrangian finite elements are used to discretize the problem. We propose an alternative weak formulation of the problem which allows us to avoid this drawback. We compute the numerical solution of the problem by using Lagrangian finite elements ad hoc modified on the vicinity of the symmetry axis. We provide a convergence result under rather general conditions. Moreover, we prove quasi-optimal order error estimates under additional regularity assumptions. Finally, we report numerical results which allow us to confirm the theoretical estimates and to assess the performance of the proposed method in a physical application which is the motivation of this paper: the computation of the current density distribution in a steel cylindrical bar submitted to electric-upsetting.R. Rodríguez was partially supported by CONICYT-Chile through project AFB170001. P. Venegas was partially supported by FONDECYT-Chile project 1211030 and by Centro de Modelamiento Matemático (CMM), FB210005, BASAL funds for centers of excellence from ANID-Chile. B. López-Rodríguez was partially supported by Universidad Nacional de Colombia through Hermes project 52759.S

A linearised hp-finite element framework for acousto-magneto-mechanical coupling in axisymmetric MRI scanners

We propose a new computational framework for the treatment of acousto-magneto-mechanical coupling that arises in low-frequency electro-magneto-mechanical systems such as MRI scanners. Our transient Newton-Raphson strategy involves the solution of a monolithic system obtained from the linearisation of the coupled system of equations. Moreover, this framework, in the case of excitation from static and harmonic current sources, allows us to propose a simple linearised system and rigorously motivate a single-step strategy for understanding the response of systems under different frequencies of excitation. Motivated by the need to solve industrial problems rapidly, we restrict ourselves to solving problems consisting of axisymmetric geometries and current sources. Our treatment also discusses in detail the computational requirements for the solution of these coupled problems on unbounded domains and the accurate discretisation of the fields using hp-finite elements. We include a set of academic and industrially relevant examples to benchmark and illustrate our approach

Recent progress in numerical analysis for electromagnetic devices

Over the past ten years, the ability of computers has progressed rapidly, and techniques of numerical analysis have improved vastly. The 3D analysis of electrostatic and magnetostatic fields can easily be carried out on a workstation, and results obtained contribute to the design and development of new products. The main factors of progress in numerical analysis using the finite-element method are reviewed.</p