### Abstract

It is well known that most gas fluidized beds of particles bubble, while most liquid fluidized beds do not. It was shown by Anderson, Sundaresan & Jackson (1995), through direct numerical integration of the volume-averaged equations of motion for the fluid and particles, that this distinction is indeed accounted for by these equations, coupled with simple, physically credible closure relations for the stresses and interphase drag. The aim of the present study is to investigate how the model equations afford this distinction and deduce an approximate criterion for separating bubbling and non-bubbling systems. To this end, we have computed, making use of numerical continuation techniques as well as bifurcation theory, the one- and two-dimensional travelling wave solutions of the volume-averaged equations for a wide range of parameter values, and examined the evolution of these travelling wave solutions through direct numerical integration. It is demonstrated that whether bubbles form or not is dictated by the value of Ω = (ρ_{s} v^{3}_{t})^{1/2}, where ρ_{s} is the density of particles, v_{t} is the terminal settling velocity of an isolated particle, g is acceleration due to gravity and A is a measure of the particle phase viscosity. When Ω is large (> ∼ 30), bubbles develop easily. It is then suggested that a natural scale for A is ρ_{s} v_{t} d_{p}, so that Ω^{2} is simply a Froude number.

Original language | English (US) |
---|---|

Pages (from-to) | 157-188 |

Number of pages | 32 |

Journal | Journal of Fluid Mechanics |

Volume | 334 |

DOIs | |

State | Published - Mar 10 1997 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Journal of Fluid Mechanics*,

*334*, 157-188. https://doi.org/10.1017/S0022112096004351

}

*Journal of Fluid Mechanics*, vol. 334, pp. 157-188. https://doi.org/10.1017/S0022112096004351

**Fully developed travelling wave solutions and bubble formation in fluidized beds.** / Glasser, Benjamin; Kevrekidis, I. G.; Sundaresan, S.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Fully developed travelling wave solutions and bubble formation in fluidized beds

AU - Glasser, Benjamin

AU - Kevrekidis, I. G.

AU - Sundaresan, S.

PY - 1997/3/10

Y1 - 1997/3/10

N2 - It is well known that most gas fluidized beds of particles bubble, while most liquid fluidized beds do not. It was shown by Anderson, Sundaresan & Jackson (1995), through direct numerical integration of the volume-averaged equations of motion for the fluid and particles, that this distinction is indeed accounted for by these equations, coupled with simple, physically credible closure relations for the stresses and interphase drag. The aim of the present study is to investigate how the model equations afford this distinction and deduce an approximate criterion for separating bubbling and non-bubbling systems. To this end, we have computed, making use of numerical continuation techniques as well as bifurcation theory, the one- and two-dimensional travelling wave solutions of the volume-averaged equations for a wide range of parameter values, and examined the evolution of these travelling wave solutions through direct numerical integration. It is demonstrated that whether bubbles form or not is dictated by the value of Ω = (ρs v3t)1/2, where ρs is the density of particles, vt is the terminal settling velocity of an isolated particle, g is acceleration due to gravity and A is a measure of the particle phase viscosity. When Ω is large (> ∼ 30), bubbles develop easily. It is then suggested that a natural scale for A is ρs vt dp, so that Ω2 is simply a Froude number.

AB - It is well known that most gas fluidized beds of particles bubble, while most liquid fluidized beds do not. It was shown by Anderson, Sundaresan & Jackson (1995), through direct numerical integration of the volume-averaged equations of motion for the fluid and particles, that this distinction is indeed accounted for by these equations, coupled with simple, physically credible closure relations for the stresses and interphase drag. The aim of the present study is to investigate how the model equations afford this distinction and deduce an approximate criterion for separating bubbling and non-bubbling systems. To this end, we have computed, making use of numerical continuation techniques as well as bifurcation theory, the one- and two-dimensional travelling wave solutions of the volume-averaged equations for a wide range of parameter values, and examined the evolution of these travelling wave solutions through direct numerical integration. It is demonstrated that whether bubbles form or not is dictated by the value of Ω = (ρs v3t)1/2, where ρs is the density of particles, vt is the terminal settling velocity of an isolated particle, g is acceleration due to gravity and A is a measure of the particle phase viscosity. When Ω is large (> ∼ 30), bubbles develop easily. It is then suggested that a natural scale for A is ρs vt dp, so that Ω2 is simply a Froude number.

UR - http://www.scopus.com/inward/record.url?scp=0031103388&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031103388&partnerID=8YFLogxK

U2 - 10.1017/S0022112096004351

DO - 10.1017/S0022112096004351

M3 - Article

VL - 334

SP - 157

EP - 188

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -