A 2D Simulation Method for Computing Droplet Size Spectrum During the Atomization of High-Speed Liquid Jets

2004 ◽  
Author(s):  
Gian Marco Bianchi ◽  
Piero Pelloni ◽  
Stefano Toninel ◽  
Davide Paganelli ◽  
Daniele Suzzi
Keyword(s):  
Sensitivity Analysis ◽  
Stability Analysis ◽  
Linear Stability ◽  
Droplet Size ◽  
Linear Stability Analysis ◽  
High Speed ◽  
Simulation Method ◽  
Droplet Formation ◽  
Size Spectrum ◽  
Computational Domain

Based on both experimental observations and available numerical methods, an innovative 2D approach for determining droplet size during the atomization process has been developed. Based on experimental evidences (see [1] and [2]) atomization of turbulent high speed jets is assumed to occur in a two stage process: ligaments detachment and droplets formation. The simulation method here proposed wants to take the advantages typical of the two most effective methods in spray investigation. It joins LES (i.e Large Eddy Simulations) approach and Linear Stability Analysis: the first one is used to solve the liquid-air fluid dynamics interaction and in particular the instabilities leading to ligament formation. The second one is finally adopted to compute the droplet size spectrum from ligament break-up. Therefore dynamics of ligament formation is directly computed while droplet formation is modelled by using a Linear Stability Analysis. The numerical simulation adopts a VOF (i.e. Volume of Fluid) method to track liquid-gas interface. Turbulence effects on liquid surface are accounted for by adding a turbulent flow field at the nozzle exit which represents a part of the boundary condition of the computational domain. A physical criterion is then applied to detach ligaments from liquid jet surface which will reduce in diameter during simulation. The droplet formation is then computed by applying the linear stability analysis to the ligaments, assumed being circular and subject to circulation. An extensive validation and sensitivity analysis has been carried out in order to assess method advantages and limits. The experimental results of Wu et al. [3] and Horoyasu et al. [4] were used as test cases. A sensitivity analysis has been performed under typical HSDI Diesel engine injection conditions. The method proved to exhibit promising attitude in the reconstruction of the droplet size spectrum depending on injection parameter or conditions.

scholarly journals Linear Stability Analysis and Validation of a Unified Solution Method for Fluid-Structure-Interaction on Structural Dynamic Problems

2005 ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Structural Dynamic ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: Partitioned methods and monolithic methods. Both methods use two separate sets of equations for fluid and solid. A unified solution method has been presented [1], which is different from these methods. The new method treats both fluid and solid as a single continuum, thus the whole computational domain is treated as one entity discretised on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, 2 time marching and one spatial discretisation scheme, widely used for fluids’ equations, are applied for the solution of the equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps and beam sizes is also presented. For all cases examined the numerical solution was stable and robust and proved to be suitable for the next stage of application to full fluid-structure interaction problems.

Linear Stability Analysis and Application of a New Solution Method of the Elastodynamic Equations Suitable for a Unified Fluid-Structure-Interaction Approach

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure-interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: partitioned methods and monolithic methods. Both methods use separate sets of equations for fluid and solid that have different unknown variables. A unified solution method has been presented in the previous work of Giannopapa and Papadakis (2004, “A New Formulation for Solids Suitable for a Unified Solution Method for Fluid-Structure Interaction Problems,” ASME PVP 2004, San Diego, CA, July, PVP Vol. 491–1, pp. 111–117), which is different from these methods. The new approach treats both fluid and solid as a single continuum; thus, the whole computational domain is treated as one entity discretized on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, the elastodynamic equations are reformulated so that they contain the same unknowns as the Navier–Stokes equations, namely, velocities and pressure. Two time marching and one spatial discretization scheme, widely used for fluid equations, are applied for the solution of the reformulated equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps, and beam dimensions is also presented. For all cases examined, the numerical solution was stable and robust and therefore is suitable for the next stage of application to full fluid-structure-interaction problems.

scholarly journals The Growth and Saturation of Submesoscale Instabilities in the Presence of a Barotropic Jet

2018 ◽  
Vol 48 (11) ◽  
pp. 2779-2797 ◽  
Author(s):  
Megan A. Stamper ◽  
John R. Taylor ◽  
Baylor Fox-Kemper
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Initial Conditions ◽  
Boussinesq Equations ◽  
Small Region ◽  
Computational Domain ◽  
Mean Flow ◽  
The Mean

AbstractMotivated by recent observations of submesoscales in the Southern Ocean, we use nonlinear numerical simulations and a linear stability analysis to examine the influence of a barotropic jet on submesoscale instabilities at an isolated front. Simulations of the nonhydrostatic Boussinesq equations with a strong barotropic jet (approximately matching the observed conditions) show that submesoscale disturbances and strong vertical velocities are confined to a small region near the initial frontal location. In contrast, without a barotropic jet, submesoscale eddies propagate to the edges of the computational domain and smear the mean frontal structure. Several intermediate jet strengths are also considered. A linear stability analysis reveals that the barotropic jet has a modest influence on the growth rate of linear disturbances to the initial conditions, with at most a ~20% reduction in the growth rate of the most unstable mode. On the other hand, a basic state formed by averaging the flow at the end of the simulation with a strong barotropic jet is linearly stable, suggesting that nonlinear processes modify the mean flow and stabilize the front.

Effects of three-dimensionality on instability and turbulence in a frontal zone

2015 ◽  
Vol 784 ◽  
pp. 252-273 ◽  
Author(s):  
Eric Arobone ◽  
Sutanu Sarkar
Keyword(s):  
Stability Analysis ◽  
Potential Energy ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Frontal Zone ◽  
Gravitational Instability ◽  
Three Dimensional ◽  
Computational Domain ◽  
Coriolis Parameter ◽  
Symmetric Instability

Linear stability analysis and direct numerical simulation are used to investigate the evolution of a symmetrically unstable uniform frontal zone. Simulations in a three-dimensional computational domain capable of resolving near-symmetric currents develop strong nonlinearities without the emergence of pure symmetric instability. Linear stability analysis demonstrates that for $ft>1$ ( $f$ is the Coriolis parameter and $t$ denotes time) the flow generates strongly asymmetric structures which become nearly symmetric when $ft\gg 1$. Unlike the currents generated during pure symmetric instability, near-symmetric instability generates currents that do not align with isopycnals. This greatly modifies their energetics and evolution, leading to regions of the flow that are unstable to gravitational instability and energized by the reservoir of available potential energy. A high-resolution simulation demonstrates the flow evolution from near-symmetric currents to secondary shear-convective instabilities and finally, through tertiary instabilities, to fully three-dimensional turbulence. The effect of this sequence of instabilities is quantified through velocity and vorticity statistics as well as budgets for turbulent kinetic and potential energy. It is not until $ft\sim 10$ that the energy source for fluctuations is primarily shear, in contrast to the purely symmetric instability which draws its energy exclusively from shear production.

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