Numerical Simulation of Particle-Laden Turbulent Channel Flow
Hans Kuerten
Department of Mechanical Engineering
Eindhoven University of Technology, Eindhoven, the Netherlands
There are various ways to simulate particle-laden turbulent flow. In the most detailed simulation
type, the flow around a particle is solved in all details. Although this method has recently been
applied to particle-laden turbulent channel flow, the computational requirements are huge and
the Reynolds number and number of particles that can be achieved are still limited.
In this presentation a less detailed simulation method is studied, where particles are considered
as point particles, but all length scales of the turbulent fluid flow are resolved. This is a possible
approach if the particle is smaller than the Kolmogorov length scale. This method enables
simulations of turbulent channel flow at relatively high Reynolds numbers and for numbers of
particles on the order of 108. In particular it will be studied whether particle collisions are
important and how the particle collision rate can be described. To that end a deterministic hardsphere collision model has been implemented in a DNS code for turbulent channel flow. The
code is fully parallelized with a combination of MPI and OpenMP.
Although the overall particle volume fraction is less than 10-4, effects of particle collisions are
important due to turbophoresis and preferential concentration, which lead to large local particle
volume fractions, especially near the walls of the channel. This is illustrated in Fig. 1, which
shows the local particle volume fraction close to a wall of the channel.
Figure 2 shows the particle collision rate, i.e. the number of collisions per unit volume and time,
as a function of the wall-normal coordinate for channel flow at Re=950 and 51,200,000 equally
sized particles with a volume fraction of 8.97x10-5. Theoretically, the particle collision rate can be
written as
𝑓𝑐 = 12𝜋𝑑2 𝑛2 𝑔(𝑑)𝑣𝑟 ,
(1)
where d and n are the particle diameter and number density, vr is the magnitude of the relative
velocity of two particles and g(d) is the radial distribution function at contact.
Determination of g(d) from the DNS results is not trivial, since the function g shows singular
behavior at contact in the region away from the walls of the channel. This is caused by the
occurrence of multiple collisions of pairs of particles in short time intervals. However, the product
g(d)vr appears to be regular. In Fig. 2 the result of the theoretical prediction of the collision rate
(1) is included. The agreement is good apart from the central region of the channel, where the
theoretical result underestimates the collision rate.
-3
x 10
2
3
2.5
1.5
z/H
2
1.5
1
1
0.5
0.5
1
2
3
x/H
4
5
6
Fig. 1: Particle volume fraction in a slab close to the wall for particle-laden channel flow at Re=950.
-4
10
-5
fc
+
10
-6
10
-7
10
0
2
10
10
y
+
Fig. 2: Collision rate as a function of the wall-normal coordinate for particle-laden turbulent channel flow at
Re=950; black: DNS; red: theoretical prediction.