CPFD simulation of a dual fluidized bed cold flow model


The present work was carried out to simulate a cold flow model of a biomass gasification plant. For the simulation, a Eulerian-Lagrangian approach, more specifically the multi-phase particle in cell (MP-PIC) method, was used to simulate particles with a defined particle size distribution. Therefore, Barracuda VR, a software tool with an implemented MP-PIC method specifically designed for computational particle fluid dynamics simulations, was the software of choice. The simulation results were verified with data from previous experiments conducted on a physical cold flow model. The cold flow model was operated with air and bronze particles. The simulations were conducted with different drag laws: an energy-minimization multi-scale (EMMS) approach, a blended Wen-Yu and Ergun drag law, and a drag law of Ganser. The fluid dynamic behavior depends heavily on the particles’ properties like the particle size distribution. Furthermore, a focus was placed on the normal particle stress (PS value variation), which is significant in close-packed regions, and the loop seals’ fluidization rate was varied to influence the particle circulation rate. The settings of the simulation were optimized, flooding behavior did not occur in advanced simulations, and the simulations reached a stable steady state behavior. The Ganser drag law combined with an adjusted PS value with (PS = 30 Pa) or without (PS = 50 Pa) increased loop seal fluidization rates provided the best simulation results.

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Data availability

The data that support the findings of this study are available from the corresponding author, A. Lunzer, upon reasonable request.



air reactor, combustion reactor


bubbling bed


boundary conditions


circulating fluidized bed


computational fluid dynamics


computational particle fluid dynamics


dual fluidized bed


exempli gratia


energy-minimization multi-scale (EMMS drag model)






fuel reactor, gasification reactor


inner loop seal


large eddy simulation


lower loop seal


multi-phase particle in cell


particle size distribution




upper loop seal


Wen-Yu and Ergun (WYE drag model)

a p :

particle acceleration (\( \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right. \))

D :

drag function (\( \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right. \))

F :

interphase momentum transfer function (N/m3)

\( \boldsymbol{g} \) :

gravitational acceleration (\( \raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^2$}\right. \))

p :

pressure (Pa)

P S :

constant to calculate τp (Pa)

t :

time (s)

u f :

fluid velocity (m/s)

u mf :

minimum fluidization velocity (m/s)

u p :

particle velocity


\( {\overline{\boldsymbol{u}}}_{\mathrm{p}} \) :

particle mean velocity (m/s)

x i :

spatial variable (m)

α :

constant to calculate τp

β :

constant to calculate τp

ε cp :

close-pack particle volume fraction

ε f :

fluid volume fraction

ε p :

particle volume fraction

δ ij :

Kronecker delta

m p :

particle mass (kg)

μ :

viscosity (\( \raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}\times \mathrm{s}$}\right. \))


nabla operator (\( \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}$}\right. \))

ρ f :

fluid density (\( \raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^3$}\right. \))

τ D :

damping time due to inelastic particle collisions (s)

τ f :

fluid stress tensor (\( \raisebox{1ex}{$\mathrm{N}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^2$}\right. \))

τ p :

particle normal stress (\( \raisebox{1ex}{$\mathrm{N}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^2$}\right. \))


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Lunzer, A., Kraft, S., Müller, S. et al. CPFD simulation of a dual fluidized bed cold flow model. Biomass Conv. Bioref. 11, 189–203 (2021). https://doi.org/10.1007/s13399-020-01229-4

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  • CFD
  • CPFD simulation
  • Cold flow model
  • Fluidized bed
  • Dual fluidized bed