A Second-Order Numerical Model of Protostellar Cloud Collapse and Nebular Formation

1989 ◽  
Vol 101 ◽  
pp. 878
Author(s):  
E. S. Myhill ◽  
W. M. Laula
Keyword(s):  
Numerical Model ◽  
Second Order ◽  
Protostellar Cloud

An Efficient Numerical Model of Pulsating Combustion and Its Experimental Validation

2009 ◽  
Author(s):  
Luca Casarsa ◽  
Pietro Giannattasio ◽  
Diego Micheli
Keyword(s):  
Numerical Model ◽  
Combustion Chamber ◽  
Second Order ◽  
Operating Conditions ◽  
Gas Dynamics Equations ◽  
Time Step ◽  
Flow Equations ◽  
Tail Pipe ◽  
Flux Difference ◽  
Pulse Jet

A simple and efficient numerical model is presented for the simulation of pulse combustors. It is based on the numerical solution of the quasi-1D unsteady flow equations and on phenomenological sub-models of turbulence and combustion. The gas dynamics equations are solved by using the Flux Difference Splitting (FDS) technique, a finite-volume upwind numerical scheme, and ENO reconstructions to obtain second-order accurate non-oscillatory solutions. The numerical fluxes computed at the cell interfaces are used to transport also the reacting species, their formation energy and the turbulent kinetic energy. The combustion progress in each cell is evaluated explicitly at the end of each time step according to a second-order overall reaction kinetics. In this way, the computations of gas dynamic evolution and heat release are decoupled, which makes the model particularly simple and efficient. A comprehensive set of measurements has been performed on a small Helmholtz type pulse-jet in order to validate the model. Air and fuel consumptions, wall temperatures, pressure cycles in both combustion chamber and tail-pipe, and instantaneous thrust have been recorded in different operating conditions of the device. The comparison between numerical and experimental results turns out to be satisfactory in all the working conditions of the pulse-jet. In particular, accurate predictions are obtained of the device operating frequency and of shape, amplitude and phase of the pressure waves in both combustion chamber and tail-pipe.

scholarly journals A semi-implicit, second-order-accurate numerical model for multiphase underexpanded volcanic jets

2013 ◽  
Vol 6 (6) ◽  
pp. 1905-1924 ◽  
Author(s):  
S. Carcano ◽  
L. Bonaventura ◽  
T. Esposti Ongaro ◽  
A. Neri
Keyword(s):  
Relaxation Time ◽  
Numerical Model ◽  
Numerical Simulations ◽  
Solid Phase ◽  
Maximum Velocity ◽  
Second Order ◽  
Three Dimensions ◽  
Lagrangian Model ◽  
Coarse Particles ◽  
Nonequilibrium Effects

Abstract. An improved version of the PDAC (Pyroclastic Dispersal Analysis Code, Esposti Ongaro et al., 2007) numerical model for the simulation of multiphase volcanic flows is presented and validated for the simulation of multiphase volcanic jets in supersonic regimes. The present version of PDAC includes second-order time- and space discretizations and fully multidimensional advection discretizations in order to reduce numerical diffusion and enhance the accuracy of the original model. The model is tested on the problem of jet decompression in both two and three dimensions. For homogeneous jets, numerical results are consistent with experimental results at the laboratory scale (Lewis and Carlson, 1964). For nonequilibrium gas–particle jets, we consider monodisperse and bidisperse mixtures, and we quantify nonequilibrium effects in terms of the ratio between the particle relaxation time and a characteristic jet timescale. For coarse particles and low particle load, numerical simulations well reproduce laboratory experiments and numerical simulations carried out with an Eulerian–Lagrangian model (Sommerfeld, 1993). At the volcanic scale, we consider steady-state conditions associated with the development of Vulcanian and sub-Plinian eruptions. For the finest particles produced in these regimes, we demonstrate that the solid phase is in mechanical and thermal equilibrium with the gas phase and that the jet decompression structure is well described by a pseudogas model (Ogden et al., 2008). Coarse particles, on the other hand, display significant nonequilibrium effects, which associated with their larger relaxation time. Deviations from the equilibrium regime, with maximum velocity and temperature differences on the order of 150 m s−1 and 80 K across shock waves, occur especially during the rapid acceleration phases, and are able to modify substantially the jet dynamics with respect to the homogeneous case.

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