**7. References**

36 Advanced Fluid Dynamics

(a) (b)

(c) (d)

Fig. 13. Acoustic pressure signals at different observer angles to the flow: 300 (a),(c) and 900

The computational of compressible vortical flows is challenging because of the multi-scale phenomena involved. Computational approaches and numerical methods for the solution of compressible vortical flow problems have been discussed. In particular, the key elements of a successful computational method have been outlined that include low numerical dissipation and low dispersion, as well as the good vortex preservation property. For the sake of illustration, several two-dimensional problems are considered that typically present a challenge for conventional Eulerian numerical schemes. The problems include the preservation of steady vortex in a box domain, acoustic wave scattering by a vortex field and the dynamics and acoustics of counter-rotating vortices pairs. For these problems, several computational solutions are presented and discussed, including those obtained with the CABARET scheme developed by the authors. Analytical and reference solutions are provided where applicable. All test problems considered are promoted as the benchmark problems for new Computational Fluid Dynamics codes that are to be used in application

(b),(d) for Re=5000 (a),(b) and Re=9400 (c),(d).

for hydrodynamics and acoustics of vortex resolving simulations.

**6. Conclusion** 


**3**

*Brazil* 

*State University of Campinas* 

**Fluid Dynamics of Gas – Solid Fluidized Beds** 

Germán González Silva1, Natalia Prieto Jiménez1 and Oscar Fabio Salazar

Fluidization refers to the contact between a bed of solids and a flow of fluid. As a result, the solid particles are transformed into a fluid-like behavior that can be used for different purposes. The fluidized bed reactor is one of the most important technologies for gas-solid heterogeneous operations chemical or petrochemical, considering catalytic or non catalytic processes (Kunii and Levenspiel 1991). The most important industrial applications include catalytic cracking, coal combustion and biomass combustion. One of the most relevant type of fluidized bed reactor is the ascendant flow reactor, which is also known as riser. The riser reactors consist of a tubular column in which both solid and gas flow upwards. The first fluidized bed gas generator was developed in Germany by Fritz Winkler in the 1920s. Later in the 1930s, the american petroleum industry started developing the fluidized bed technology for oil feedstock catalytic cracking, becoming the primary technology for such

Inside the riser reactor, solid particles have a wide range of residence time, which is a disadvantage that reduces the overall conversion and the selectivity of the chemical reactions. For that reason it has recently grown the interest in a new type of gas-solid circulating reactor known as downer. In this reactor the gas and the solid flow cocurrently downward, creating hydrodynamic features comparable to a plug flow reactor and allowing a better control over the conversion, the selectivity and the catalyst deactivation. The concept of downer reactor gas-solid appeared in the 1980s, with the first studies on the fluid dynamics of gas-solid suspensions (Kim and Seader 1983) and with the first downer reactors for patents developed by Texaco for the FCC process (Gross Benjamin and Ramage Michael P 1981; Niccum Phillip K and Bunn Jr Dorrance P 1983). In these studies it is observed that in the downer reactor has a uniform distribution of two-phase flow along the reactor, also observed that the contact time is very low, achieving a 20% decrease in the amounts of coke produced during the FCC process. Applications, differences, advantages and disadvantages to these types of fluidized bed reactors can be found in various publications (Ancheyta 2010; Gonzalez, 2008; Yi Cheng et al. 2008; Crowe 2005; Wen-ching Yang 2003; Grace 1997; Gidaspow 1994; Geldart 1986)

Fluidization occurs when a gas or liquid is forced to flow vertically through a bed of particles at such a rate that the buoyed weight of the particles is completely supported by

**1. Introduction** 

applications (Tavoulareas 1991).

**2. Fluidization regimes and particle classification** 

the drag force imposed by the fluid.

