Reference no: EM131698

In gas-­-solid fluidization, it is frequently common to have a wide size distribution of particles present in the system. During fluidization the smaller particles can be entrained from the fluidization column. Sometimes it is useful to know the maximum particle size that could be elutriated from the system. In order to do this the equation for the terminal velocity will be used as shown below.

u_t is the terminal velocity (m/s)
d_p is the particle diameter (m)
ρ_p is the particle density (kg/m³)
ρ_f is the fluid density (kg/m³)
g is the gravitational constant (9.81 m/s²)
C_D is the drag coefficient.

According to Haider and Levenspiel (1989) a single correlation for the drag coefficient for all flow regimes and non-­-spherical particles is described as follows.

Task

The task for this assignment is to resolve for the particle diameter (dP), in µm, at different terminal gas velocities (ut) between 0 and 1 m/s. The solution should be robust and flexible enough that different parameters (e.g. particle density, sphericity) could be easily modified and a new solution is automatically evaluated. The root finding method could also be able to be easily adapted to handle different nonlinear problems.

For this problem the subsequent parameters will be used.

ρ_p   950 kg/m³
Φ      0.77
ρ_f    1.184
µ     1.85×10-­-5 kg/m³ kg/m•s