https://ntrs.nasa.gov/api/citations/20130011028/downloads/20130011028.pdf

High-order entropy stable finite difference schemes for nonlinear conservation laws

Solidification in spray forming takes place in two distinct steps: typically half of the alloy latent heat is removed rapidly from the droplet spray created by gas atomization; the droplets are then constituted into a billet at deposition where the remaining liquid fraction solidifies relatively slowly. However, within the droplet spray, individual droplets have different thermal and solidification histories and depositing droplets may be solid, mushy, or liquid. Despite many studies of solidification behavior in spray forming, uncertainties and some misconceptions remain on how the solidification conditions in the spray and billet interact to give rise to the characteristic spray-formed microstructure comprising refined, polygonal/equiaxed primary grains with low levels of microsegregation. This article presents a simple numerical model for the spray-formed grain size arising from the deposition of the various droplets in the spray and combines insights provided by the model with previous investigations of the phenomena occurring during and immediately after deposition to propose a comprehensive description of the important solidification behavior during spray forming. Remelting, grain multiplication, thermal and elemental equilibration, and microstructural coarsening are proposed to play a critical role in the evolution of the spray-formed microstructure.

Solidification in Spray Forming

The effect of liquid compressibility on the dynamics of a single, spherical cavitating bubble is studied. While it is known that compressibility damps the amplitude of bubble rebounds, the extent to which this effect is accurately captured by weakly compressible versions of the Rayleigh–Plesset equation is unclear. To clarify this issue, partial differential equations governing conservation of mass, momentum, and energy are numerically solved both inside the bubble and in the surrounding compressible liquid. Radiated pressure waves originating at the unsteady bubble interface are directly captured. Results obtained with Rayleigh–Plesset type equations accounting for compressibility effects, proposed by Keller and Miksis [J. Acoust. Soc. Am. 68, 628–633 (1980)], Gilmore, and Tomita and Shima [Bull. JSME 20, 1453–1460 (1977)], are compared with those resulting from the full model. For strong collapses, the solution of the latter reveals that an important part of the energy concentrated during the collapse is used to generate an outgoing pressure wave. For the examples considered in this research, peak pressures are larger than those predicted by Rayleigh–Plesset type equations, whereas the amplitudes of the rebounds are smaller.

/pdf/liquid-compressibility-effects-during-the-collapse-of-a-530rutln5d.pdf

Liquid compressibility effects during the collapse of a single cavitating bubble.

https://hal.inria.fr/hal-00855645/document

An explicit residual based approach for shallow water flows

Variational multiscale method for nonequilibrium plasma flows

An integrated, multiphysics numerical model has been developed through the joint efforts of the University of Oxford (UK), University of Bremen (Germany) and Inasmet (Spain) to simulate the spray forming process. The integrated model consisted of four sub-models: (1) an atomization model simulating the fragmentation of a continuous liquid metal stream into droplet spray during gas atomization; (2) a droplet spray model simulating the droplet spray mass and enthalpy evolution in the gas flow field prior to deposition; (3) a droplet deposition model simulating droplet deposition, splashing and re-deposition behavior and the resulting preform shape and heat flow; and (4) a porosity model simulating the porosity distribution inside a spray formed ring preform. The model has been validated against experiments of the spray forming of large diameter IN718 Ni superalloy rings. The modelled preform shape, surface temperature and final porosity distribution showed good agreement with experimental measurements.

Multiphysics modelling of the spray forming process

Typically, segregated methods have been used for the computation of incompressible flows whereas coupled solvers, for compressible flows. Compared to coupled solvers, segregated methods present the advantage of computational savings in RAM memory and CPU time, although at the cost of an inferior robustness. However, previously published segregated algorithms for general compressible flows are known to present pitfalls, like convergence to wrong solutions, lack of robustness in the presence of strong discontinuities, such as normal and oblique shocks, and complicated boundary condition imposition. Therefore, a segregated method for non-isothermal compressible flows is proposed that preserves the thermodynamic coupling and overcomes the criticisms of existing methods.

A segregated method for compressible flow computation. Part II: general divariant compressible flows

On the thermodynamics, stability and hierarchy of entropy functions in fluid flow

Traditionally, coupled methods have been employed for the computation of compressible flows, whereas segregated methods have been preferred for the computation of incompressible flows. Compared to coupled methods, segregated solvers present the advantage of reduced computer memory and CPU time requirements, although at the cost of an inferior robustness. Therefore, in a series of papers we present unified computational techniques to compute compressible and incompressible flows with segregated stabilized methods. The proposed algorithms have an increased robustness compared to existing techniques, while possessing additional benefits such as employing standard pressure boundary conditions. In this first part, the thermodynamics of isothermal, thermally perfect compressible flows is set up in the framework of symmetric systems and the corresponding segregated algorithms are introduced. Copyright © 2005 John Wiley & Sons, Ltd.

A segregated method for compressible flow computation Part I: isothermal compressible flows

Spanish Ministry of Science and Technology (Project PNE-008/2000-C-01 and 02).
Basque Government, Department of Education, Universities and Research (Project PI-2001-12)

Aitor Landaberea

Papers

Multiphysics modelling of the spray forming process

A segregated method for compressible flow computation. Part II: general divariant compressible flows

On the thermodynamics, stability and hierarchy of entropy functions in fluid flow

A segregated method for compressible flow computation Part I: isothermal compressible flows

The vacuum tribology model (VTM) of TriboLAB