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Lattice Boltzmann simulation on liquid flow and mass transport in a bioreactor with cylinder bundle for hydrogen production

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Abstract

The lattice Boltzmann method is adopted to simulate hydrodynamics and mass transfer accompanying with biochemical reaction in a channel with cylinder bundle, which is the scenario of biohydrogen production by photosynthetic bacteria in the biofilm attached on the surface of cylinder bundle in photobioreactor. The effects of cylinder spacing, Reynolds number and cylinder arrangement are investigated. The numerical results reveal that highest glucose concentration and the lowest hydrogen concentration are obtained at the front of the first row cylinders for all cases. The staggered arrangement leads to an increment in average drag coefficient, Sherwood number and consumption efficiency of substrate under a given condition, and the increment in Sherwood number reaches up to 30 %, while that in drag coefficient is around 1 %, moreover, the increment in consumption efficiency reaches the maximum value of 12 %. The results indicate that the staggered arrangement is beneficial to the mass transfer and biochemical reaction.

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Abbreviations

c :

Lattice speed (m s−1)

C x :

Cell density (kg m−3)

D :

Cylinder diameter (m)

D σ :

Diffusivity coefficient of σ-species (m2 s−1)

C D :

Drag coefficient

e i :

Discrete particle velocity in LBE model (m s−1)

\(f_{i} , { }f_{i}^{eq}\) :

Density distribution function and corresponding equilibrium distribution function of the ith discrete velocity

\(f_{i}^{ + } ({\mathbf{x}}_{w} ,t)\) :

Post-collision distribution function at the node x w

\(\overline{{f_{i}^{eq} }} \left( {{\mathbf{x}}_{w} } \right)\) :

Approximated equilibrium part at the node x w

F :

The total force acted on the fluid by the solid body (J m−1)

\(g_{i,\sigma } , { }g_{i,\sigma }^{{^{eq} }}\) :

Concentration distribution function and corresponding equilibrium distribution function of σ-species

J 0 :

Rest fraction

J i,σ , K i :

Specially chosen constants

k s :

Monod constant (kg m−3)

Ma:

Mach number

p :

Fluid pressure (Pa)

Pe:

Peclet number

Re:

Reynolds number

r σ :

React rate of σ-species (kg m−3 s−1)

R σ :

Dimensionless react source term of σ-species

Sc:

Schmidt number

Sh:

Sherwood number

t :

Time (s)

u :

Flow velocity (m s−1)

\(\overline{{{\mathbf{u}}_{w} }}\) :

Approximation of velocity at node x w (m s−1)

s 1, s 2 :

Horizontal and vertical cylinder spacings (m)

S 1, S 2 :

Dimensionless horizontal and vertical cylinder spacings

x :

Cartesian position vector (m)

Y x/s :

Cell yield

α :

Specific area (m−1)

Δ:

Fraction of the intersected link in the fluid region, \(\Delta = | {{\mathbf{x}}_{f} - {\mathbf{x}}_{b} } |/| {{\mathbf{x}}_{f} - {\mathbf{x}}_{w} } |\)

δ t :

Time space (s)

δ x :

Lattice space (m)

ν :

Kinematical viscosity (m2 s−1)

ρ :

Flow density (kg m−3)

\(\overline{{\rho_{w} }}\) :

Approximation of density at the node x w (kg m−3)

τ ν :

Dimensionless relaxation time

τ σ :

Dimensionless relaxation time related to the diffusion coefficient

w i :

Weight coefficient

μ max :

Maximum specific growth rate (s−1)

η :

Substrate consumption efficiency per cylinder’s surface

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Acknowledgments

The authors would like to acknowledge the joint support of National Science Fund for Distinguished Young Scholars (No. 50825602), National Natural Science Foundation of China (No. 51136007, 20876183), the Fundamental Research Funds for the Central Universities (No. CDJXS 10142223).

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Authors and Affiliations

  1. Key Laboratory of Low-Grade Energy Utilization Technologies and Systems, Chongqing University, Chongqing, 400030, China

    Qiang Liao, Yan-Xia Yang, Xun Zhu, Hong Wang & Yu-Dong Ding

  2. Institute of Engineering Thermophysics, Chongqing University, Chongqing, 400030, China

    Qiang Liao, Yan-Xia Yang, Xun Zhu, Hong Wang & Yu-Dong Ding

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  1. Qiang Liao
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  2. Yan-Xia Yang
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Correspondence to Qiang Liao.

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Liao, Q., Yang, YX., Zhu, X. et al. Lattice Boltzmann simulation on liquid flow and mass transport in a bioreactor with cylinder bundle for hydrogen production. Heat Mass Transfer 51, 859–873 (2015). https://doi.org/10.1007/s00231-014-1458-2

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  • DOI: https://doi.org/10.1007/s00231-014-1458-2

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