244 Computational Modelling in Hydraulic and Coastal Engineering
xlabel('Time x 12 [s]')
ylabel('Water depth over the sandbar [m]')
PROBLEM 8.8
Solve the same problem by making the suggested modifications while keeping the rest of the data constant:
1. Change the wave height from 2.0 m to 1.0, 1.5 and 2.5 m.
2. Change the wave period from 6 s to 3, 8 and 9 s.
3. Change the bed slope from 0.02 to 0.018 and 0.022.
4. Change the bed roughness from 0.001 m to 0.0005, 0.0015 and
0.005 m.
5. Change the mean particle diameter from 0.001 m to 0.00075, 0.0015
and 0.005 m.
Run the simulations, analyse the data and comment on the sensitivity of the
model to the various parameters involved.
8.5 TRACER METHOD APPLIED
TO ACTIVE PARTICLES
8.5.1 Qualitative description
In Section 8.3, it was presented how the numerical diffusion error was
eliminated from the simulation of advection–diffusion transport of a substance by using the Lagrangian particle-tracking method. In that case the
pre-existing hydrodynamics remained unaffected, a fact characteristic of
‘passive’ particles, and the movement of the dissolved or suspended matter
was described by a large number of such particles.
However, whenever dealing with ‘active’ particles, the particles drive
and interact with the hydrodynamics of the flow domain and the problem
becomes a two-phase flow. Typical examples of two-phase flows are hyperconcentrated sediment and debris flows, and flow driven by air bubbles.
In the following, the problem of air-bubble flow will be addressed.
Understanding of the air-bubble flow mechanics is of direct interest to
a variety of engineering applications such as circulation and aeration in
sewage treatment plants, a bubble curtain for salinity control in waterway gate locks and water quality enhancement in small enclosed water
bodies.
The two basic parameters for air-bubble flow are the driving air–gas
discharge, q s , and the bubble diameter, D b (or radius, R b ). It is assumed that
the air bubbles soon reach an equilibrium state with the ambient fluid and
maintain a vertical velocity relative to the fluid, U b , which depends on their
diameter. The flow is generated by the distributed load of the local drag
xlabel('Time x 12 [s]')
ylabel('Water depth over the sandbar [m]')
PROBLEM 8.8
Solve the same problem by making the suggested modifications while keeping the rest of the data constant:
1. Change the wave height from 2.0 m to 1.0, 1.5 and 2.5 m.
2. Change the wave period from 6 s to 3, 8 and 9 s.
3. Change the bed slope from 0.02 to 0.018 and 0.022.
4. Change the bed roughness from 0.001 m to 0.0005, 0.0015 and
0.005 m.
5. Change the mean particle diameter from 0.001 m to 0.00075, 0.0015
and 0.005 m.
Run the simulations, analyse the data and comment on the sensitivity of the
model to the various parameters involved.
8.5 TRACER METHOD APPLIED
TO ACTIVE PARTICLES
8.5.1 Qualitative description
In Section 8.3, it was presented how the numerical diffusion error was
eliminated from the simulation of advection–diffusion transport of a substance by using the Lagrangian particle-tracking method. In that case the
pre-existing hydrodynamics remained unaffected, a fact characteristic of
‘passive’ particles, and the movement of the dissolved or suspended matter
was described by a large number of such particles.
However, whenever dealing with ‘active’ particles, the particles drive
and interact with the hydrodynamics of the flow domain and the problem
becomes a two-phase flow. Typical examples of two-phase flows are hyperconcentrated sediment and debris flows, and flow driven by air bubbles.
In the following, the problem of air-bubble flow will be addressed.
Understanding of the air-bubble flow mechanics is of direct interest to
a variety of engineering applications such as circulation and aeration in
sewage treatment plants, a bubble curtain for salinity control in waterway gate locks and water quality enhancement in small enclosed water
bodies.
The two basic parameters for air-bubble flow are the driving air–gas
discharge, q s , and the bubble diameter, D b (or radius, R b ). It is assumed that
the air bubbles soon reach an equilibrium state with the ambient fluid and
maintain a vertical velocity relative to the fluid, U b , which depends on their
diameter. The flow is generated by the distributed load of the local drag