Spatially Developing Modes: The Darcy–Bénard Problem Revisited

In this paper, the instability resulting from small perturbations of the Darcy–Bénard system is explored. An analysis based on time–periodic and spatially developing Fourier modes is adopted. The system under examination is a horizontal porous layer saturated by a fluid. The two impermeable and isothermal plane boundaries are considered to have different temperatures, so that the porous layer is heated from below. The spatial instability for the system is defined by taking into account both the spatial growth rate of the perturbation modes and their propagation direction. A comparison with the neutral stability condition determined by using the classical spatially periodic and time–evolving Fourier modes is performed. Finally, the physical meaning of the concept of spatial instability is discussed. In contrast to the classical analysis, based on spatially periodic modes, the spatial instability analysis, involving time–periodic Fourier modes, is found to lead to the conclusion that instability occurs whenever the Rayleigh number is positive.

3D Processing Maps of Cast Mg-9Gd-3Y Alloy and Numerical-Experimental Verification

The hot compression behavior of Mg-9Gd-3Y (GW93) alloy was investigated by carrying out isothermal compression tests at the deformation temperature range of 300–450°C and strain rate range of 0.001–1s−1. Considering the influence of the strain on the formability of the GW93 alloy, three-dimensional (3D) processing maps were established based on the dynamic material model. The 3D processing maps indicate that the formability of the material improved with the decrease of the strain rate and the increase of the heating temperature, and the material at lower heating temperature mostly underwent flow instability. The formable processing region of the hot deformation of the GW93 alloy was concentrated within the temperature range of 380–450°C and the strain rate range of 0.001–0.01 s−1. Subsequently, the 3D processing maps were embedded into the finite element (FE) software DEFORM-3D by means of user subroutines, and the formability of GW93 alloy during the isothermal plane strain forging process was predicted. The FE simulation results revealed that the formability of the material at low strain rate improved compared with that at high strain rate under the same temperature. Finally, an isothermal plane strain forging technological experiment was carried out, and the microstructure of the formed sample was analyzed. The experimental result is in good agreement with that of the numerical simulation. Combined with microstructural observation, the accuracy of the simulation results and the 3D processing maps of the GW93 alloy was verified.

Eigenfunctions of Galactic phase space spirals from dynamic mode decomposition

ABSTRACT We investigate the spatiotemporal structure of simulations of the homogeneous slab and isothermal plane models for the vertical motion in the Galactic disc. We use dynamic mode decomposition (DMD) to compute eigenfunctions of the simulated distribution functions for both models, referred to as DMD modes. In the case of the homogeneous slab, we compare the DMD modes to the analytic normal modes of the system to evaluate the feasibility of DMD in collisionless self-gravitating systems. This is followed by the isothermal plane model, where we focus on the effect of self-gravity on phase mixing. We compute DMD modes of the system for varying relative dominance of mutual interaction and external potential, so as to study the corresponding variance in mode structure and lifetime. We find that there is a regime of relative dominance, at approximately 4 : 1 external potential to mutual interaction where the DMD modes are spirals in the (z, vz) plane, and are nearly un-damped. This leads to the proposition that a system undergoing phase mixing in the presence of weak-to-moderate self-gravity can have persisting spiral structure in the form of such modes. We then conclude with the conjecture that such a mechanism may be at work in the phase space spirals observed in Gaia Data Release 2, and that studying more complex simulations with DMD may aid in understanding both the timing and form of the perturbation that lead to the observed spirals.

Computational Modeling and Simulations of Isothermal Plane (Linear) Air Jet Velocity Profile for Slot Diffusers

In the present work, computational modeling and simulations of isothermal plane (linear) air jet velocity profile for slot diffusers are performed. Plane air jets are formed by linear slots or rectangular openings with a large aspect ratio. Numerical simulations are performed using the commercial computational fluid dynamics (CFD) code ANSYS FLUENT. Three plane air jet flow simulations will be investigated such as free plane (linear) jets, attached jets, and air flow through a slot diffuser in a room setting. The purpose of simulating the free plane jet through a slot diffuser is to study the behavior of jet velocity profile that is not blocked by side walls or ceilings. The jet velocity profile is modified when obstructed by the walls and the air jet desires to attach to the surfaces along its path. For this reason, attached jet simulations through a slot diffuser will be conducted. The CFD study of plane air jet flows will eventually be extended to jet flows through a slot diffuser to a room to investigate the fluid flow behavior that enters a room under a ceiling. In addition, effects of two-equation turbulence models such as standard, renormalization group (RNG), and realizable k-ε on the CFD simulations will be investigated. Predicted velocity profiles and decays of free plane jet through a slot diffuser will be validated with a semi-empirical model [1]. Predicted velocity profiles of attached jet simulations will also be compared with a semi-empirical expression [2]. The slot diffuser air flow simulations will be compared with experimental data by the work of Chen and Srebric [3]. All simulations will be conducted at a specified inlet air velocity. The effects of grid resolution are also examined. It is established that the standard k-ε turbulence model best simulates attached and free jet flows. The standard k-ε turbulence model is applied to a room setting under isothermal conditions. The results are compared with non-isothermal experimental data [3]. It is shown that temperature which is a passive scalar has less influence on the flow pattern at a high air velocity than at a low air velocity in a room setting.

Numerical Investigation of Temperature and Phase Development of (Deformation-) Dilatometer Specimens

The Gleeble 3500 thermo-mechanical testing machine with ISO-Q dilatometer set-up allows the creation of time temperature transformation diagrams at high cooling rates, after deformation and under constant load with a simple experimental set-up. An isothermal plane with temperature gradients perpendicular to this plane arises in the sample which is used for dilatometrical evaluation. The homogeneity and size of this isothermal region has a decisive influence on the measurement results, but cannot be measured with sufficient accuracy. To gain an accurate understanding of the processes in the sample, a coupled thermo-electrical, thermo-metallurgical, thermo-mechanical finite element model of the experiments is set up. To map the temperature control circuit of the machine, a PID controller is implemented, which controls the voltage of the conductive sample heating between the simulation steps. By comparing the temperature and hardness distribution with the experiments, it is shown that in this way the temperature distribution and phase transformation can be mapped. By the findings, the experimental setup was adjusted. This led to an improvement of the measurement results.

Study on Microstructure Evolution of TA1 during Plane Compression and its Similarity to Power Spinning

The hot power spinning process of TA1 has been studied on the base of isothermal plane compression model in this paper. The microstructures of spun workpieces and plane compression specimens are analyzed and the microstructure evolution mechanism has been investigated. The results reveal that the microstructure evolution has similar mechanism between power spinning and plane compression. Plane strain compression can be used to predict and control the microstructure of as-spun TA1 workpiece.

Numerical Study of the Inlet Conditions Influence on Laminar Plane Wall Jets

In this paper, we present a numerical investigation of a laminar isothermal plane two dimensional wall jets. Special attention has been paid to the effect of the inlet conditions at the nozzle exit on the flow thermal characteristics in forced convection regime. Two velocities profiles at the nozzle exit are used: uniform profile and parabolic profile. The system of equations governing the studied configuration is solved with a finite difference scheme and an implicit scheme, for numerical stability we use a staggered non uniform grid. The obtained results show, first, that the inlet conditions affect the flow in the immediate neighbourhood of the nozzle (core region) in which the flow is governed mainly by the inertias forces. At the established region the results become independent of the flow inlet conditions.