Appendix C
Closures, correlations and sub-models used in the simulations are listed in this
section.
For CFD-DEM simulations, R* is the effective radius between two contacting
particles:
1
R ∗ =
1
R 1
+
1
R 2
(C.1)
E* is the effective Young’s modulus between two contacting particles:
1
E ∗ =
1 − v
2
1
E 1
+
1 − v
2
2
E 2
(C.2)
G* is the effective shear modulus between two contacting particles:
1
G ∗ =
2(2 − v 1 )(1 + v 1 )
E 1
+
2(2 − v 1 )(1 + v 1 )
E 2
(C.3)
For two-fluid models simulations, the bulk viscosity expresses the resistance
against compression, and it is zero for the gas phase if assumed incompressible.
For the solid phase, it follows [3]:
λ s =
4
3
φρ s d s g 0,ss (1 + e)
π
1/2
(C.4)
where e is the restitution coefficient and g 0,ss is the radiation distribution:
g 0,ss =
1 −
φ
φ max
1/3
−1
(C.5)
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to Springer Nature Switzerland AG 2021
K. Wu, Dynamically Structured Flow in Pulsed Fluidised Beds, Springer Theses,
https://doi.org/10.1007/978-3-030-68752-6
153