**3. Experimental measurement techniques**

For better understanding of these phenomena and to facilitate the solution of mathematical models is necessary to make an analysis of experimental data. This experimental analysis requires specialized measurement techniques are able to explain the flow field must also be automated to minimize human involvement in the process of collecting data.

The measurement techniques, to capture the important fluids dynamic behavior of the twophase flow, can be classified as non-intrusive (**NMT**) and intrusive (**IMT**) techniques. The intrusive techniques are generally probes used to study local basic flow phenomena. Some of these are intended only as research instruments. The most common parameters that are measured with such probes are solids mass flows, radial and axial solids concentration, solids velocities, and distribution.

The particles can be deposited in the measuring device reducing its performance or causing malfunction. Besides this, the flow area reduction makes of the intrusive devices not the best solution. Non-intrusive techniques to characterize the flow within a fluidized bed are more desirable because it does not disturb the flow behavior. In the Table 2 and Table 3 classification techniques are included and recent successes have been achieved.

Fluid Dynamics of Gas – Solid Fluidized Beds 43

Computational Fluid Dynamics (CFD) is a technique which uses conservation principles and rigorous equations of fluid flow (Navier-Stokes) along with specialized turbulence models (k-, k-, SST among others). These models are more accurate and fundamentally more acceptable than empirical ones. The empirical models are approximations that assemble different phenomena to remove a number of unknown parameters. For this

The CFD models can be divided into two groups: the *Eulerian-Eulerian* model in which the gas and solid phases are considered as two interpenetrating continuum flows; and the *Eulerian-Lagrangian* model that consider the gas as a fluid phase and the solids as discrete phase. The *Eulerian-Lagrangian* model calculates the trajectory of each individual particle using Newton's second law. The interaction between particles can be described by the potential energy or the dynamic of collisions. This method has the advantage of knowing exactly the particle trajectory and the system variables. However, this requires high

reason, these models are not reliable and therefore should not be generalized.

computational effort, higher yet when gas and solid velocity fields are coupled.

The gas and solid continuity equations are represented by:

*t* 

Governing equations for *Eulerian-Eulerian* model are here presented in tensor notation.

0 *g g g gg v*

 

(Al-Hasan and Al-Qodah 2007; Bader, R., Findlay, J. and Knowlton, TM 1988; R.-C. Wang and Han 1999)

(Fischer, Peglow, and Tsotsas 2011; Link et al. 2009; Meggitt 2010; Zhengyang Wang et al. 2009; Ye, Qi, and J. Zhu 2009; Zhou et al. 2010; Haiyan Zhu et

(A. Collin, K.-E. Wirth, and Stroeder 2009; Anne Collin, Karl‐Ernst Wirth, and Ströder 2008; Demori et al. 2010; Guo and Werther 2008; Vogt et al. 2005; Wiesendorf 2000)

(1)

al. 2008)

**IMT** References

Mechanical method based on

porosity in fluidized beds.

volume fraction of solids

Table 3. Intrusive measurement techniques.

**4. Computational fluid dynamics (CFD)** 

determination of momentum by means of differential pressure measurements

This technique is commonly used as effective tools to measure the local

This technique is used to measure the local dielectric constant of the gas-solid suspension, which is linked to the local

Pitot Tube

Fiber Optic Probe

Capacitance Probe

**4.1 Governing equations** 

**4.1.1 Continuity equations** 


Table 2. Non-intrusive measurement techniques.

42 Advanced Fluid Dynamics

**NMT** Ref for more details

(C.H. Ibsen, T. Solberg, and B.H. Hjertager 2001; Claus H. Ibsen et al. 2002; Kuan, W. Yang, and Schwarz 2007; Lu, Glass, and Easson 2009; Vidar Mathiesen et al. 1999; Werther, Hage, and Rudnick 1996)

(Franka and Heindel 2009; Newton, Fiorentino, and Smith 2001; Petritsch, Reinecke, and Mewes 2000; Tapp et al. 2003; C. Wu et al. 2008; Heindel, Gray, and Jensen 2008)

(Du, Warsito, and Fan 2005; Kumar, Moslemian, and Milorad P. Dudukovic 1995; Tan et al. 2007; Thatte et al. 2004;

Veluswamy et al. 2011; H. G Wang et al. 2008)

(Muthanna Al-Dahhan et al. 2005; S. Bhusarapu, M.H. Al-Dahhan, and Duduković 2006; Fraguío et al. 2009; Khanna et al. 2008; Larachi et al.; Vaishali et al. 2007)

(van Buijtenen et al. 2011; Fu et al. 2011; He et al. 2009; Hernández-Jiménez et al.; Kashyap and

Gidaspow 2011; Laverman et al. 2008; Sathe et al.

2010)

LDA is a technology used to measure velocities of small particles in flows. The technique is based on the measurement of laser light scattered by particles that pass through a series of interference fringes (a pattern of light and dark surfaces). The scattered laser light oscillates with a specific frequency that is related to the velocity of the

X-ray Radiographic techniques based either based

along the path traversed by the beam

Technique to measure velocity field and turbulent parameters of multiphase flow. This is based on the principle of tracking the motion of a single tracer particle as a marker of the solids phase. The tracer particle contains a radioactive element emitting γrays. This radiation is received by an ensemble of specific detector.

PIV measures whole velocity fields by taking two images shortly after each other and calculating the distance individual particles travelled within this time. The displacement of the particle images is measured in the plane of the image and used to determine the

displacement of the particles

Table 2. Non-intrusive measurement techniques.

on electromagnetic radiation such as X and y rays. The transmission of X-rays or -rays through a heterogeneous medium is accompanied by attenuation of the incident radiation, and the measurement of this attenuation provides a measure of the line integral of the local mass density distribution

Laser Doppler Anemometry (LDA)


Radioactive Particle Tracking (RPT)

Particle Image Velocimetry (PIV)

particles.


Table 3. Intrusive measurement techniques.
