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Journal ArticleDOI

A new model for ejected particle velocity from erupting bubbles in 2-D fluidized beds

TL;DR: In this paper, a new model is proposed for obtaining the velocity profile of the particle ejected from the bubble dome in a freely bubbling 2D fluidized bed, based on the supposition that the initial velocity of the ejected particles, with a direction perpendicular to the dome contour, depends on bubble velocity and bubble growth velocity.
About: This article is published in Chemical Engineering Science.The article was published on 2006-09-01 and is currently open access. It has received 40 citations till now. The article focuses on the topics: Thermal velocity & Shear velocity.

Summary (2 min read)

1. Introduction

  • Fluidized beds are widely used in the industry as, among others, dryers, chemical reactors, biomass and coal combustors/gasifiers.
  • These three models proposed for the particle ejection velocity profile are only valid for verticalascent spherical bubbles (circular bubbles in 2-D fluidized beds) erupting isolated at the bed surface.
  • Therefore, the authors present a new model for the velocity profile of the particles ejected from the bubble dome in these circumstances.
  • The model was contrasted with the experimental results, and showed substantial agreement.

2. Theoretical model

  • Different models appear in the literature for obtaining the velocity profile of the particles ejected from bubble eruption, though all of them are limited to vertical-ascent spherical bubbles.
  • The magnitude of → Up,b decreases linearly with the angle toward the stagnation points, as put forth in Fung and Hamdullahpur (1993).
  • In bubbling fluidized beds, the bubbles grow as they ascend, until they reach a maximum bubble height (Shen et al., 2004).
  • In consequence, the erupting bubble expands preferentially in the horizontal direction, i.e., the growth velocity is maximum at the stagnation points.
  • The profiles of the non-dimensional velocity U∗p = Up/Up,max are plotted in Fig. 2, and they show how Fung’s model underestimates the horizontal component of the particle ejection velocity (Santana et al., 2005), while the differences in the vertical component are negligible, despite the fact that this only occurs for verticalascent circular bubbles.

3. Experiments

  • The compressed air was introduced into the plenum, 30 cm high, through two orifices situated on opposite sides of each other, thus ensuring the correct distribution of the flow.
  • The 2-D fluidized bed was illuminated with two 600-W spotlights situated at its front.
  • The gray scale image was converted into a binary one using a threshold value, hence the bubble phase and the freeboard were transformed into white color and the emulsion phase into black.
  • For the last two frames before bubble eruption, the authors measured the bubble velocity, the bubble area and the bubble area equivalent diameter.
  • These lines intersect the dome contour of the second photograph.

4. Results and discussion

  • Different experiments have been carried out by varying the superficial gas velocity (U/Umf = 2, 3 and 4).
  • In case (b) the greater error appears at both ends of the profile ( 25◦ and 150◦), though in spite of its unusual nature, the error in most of the velocity vectors is under 40%.
  • Fig. 8(a) compares the direction of the erupting bubble ( b) with the angle of the maximum particle velocity vector ( p,max) and Fig. 8(b) compares both velocity magnitudes.
  • The results obtained demonstrate that the model effectively predicts the maximum particle velocity in magnitude and direction—except in isolated cases—like the experiment marked with a square, which corresponds with the picture shown in Fig. 6(d).
  • The experiments show that the bubbles grow more slowly when they approach the bed surface, because they ingest less surrounding air.

5. Conclusions

  • A new model for particle ejection velocity in 2-D fluidized beds is presented, proposing that the particle velocity is the sum of two terms.
  • The model predicts well the velocity profile and takes into account that the velocity of the stagnation points is nonzero.
  • In bubbles that are influenced by the neighboring bubbles (Fig. 6(b)) the result obtained by the model is also acceptable.
  • Max angle formed by the velocity vector at the left stagnation point and the bed surface, deg.
  • Experimental constant in Eq. (9), dimensionless p particle density, kg/m 3 experimental constant in Eqs. (7) and (9), dimensionless.

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Citations
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Journal ArticleDOI
TL;DR: In this paper, the authors compare simulation and experimental results of the hydrodynamics of a two-dimensional, bubbling air-fluidized bed with two different closure models for the gas-particle interaction: the drag models due to Gidaspow and Syamlal & O'Brien, and the simulation results have been obtained by means of Digital Image Analysis (DIA) and Particle Image Velocimetry (PIV) techniques applied on a real bubbling fluidized bed.

111 citations


Cites methods from "A new model for ejected particle ve..."

  • ...With the development of CCD cameras and Particle Image Velocimetry (PIV) or other velocimetry techniques, there are several studies showing experimental information on particle velocity in very thin, fluidized beds, whose behaviour can be considered two or quasi two dimensional (e.g. Bokkers et al., 2004; Liu et al., 2005; Santana et al., 2005; Almendros Ibáñez et al., 2006; Laverman et al., 2008; Sánchez Delgado et al., 2010)....

    [...]

Journal ArticleDOI
TL;DR: In this article, the axial and lateral solids holdup profiles in a 2-D circulating fluidized bed (CFB) were measured with an optical fiber probe under a wide range of operating conditions.

34 citations

Journal ArticleDOI
TL;DR: In this article, a camera-based fuel tracking system for quantification of the motion of individual fuel particles at the surface of bubbling fluidized beds operated under hot conditions is presented and applied.

31 citations

Journal ArticleDOI
TL;DR: In this article, anisotropic magneto resistive (AMR) sensors were used to track a magnetic tracer particle in the form of an NdFeB-based permanent magnet.

30 citations

Journal ArticleDOI
TL;DR: An indirect tracking method for bed material using magnetic separation was applied to a fluid-dynamically down-scaled fluidized bed, to evaluate the influences of different parameters on the lateral dispersion coefficients of the bed material as discussed by the authors.

26 citations

References
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Journal ArticleDOI
TL;DR: The behavior of solids fluidized by gases falls into four clearly recognizable groups, characterized by density difference (ϱs −ϱf) and mean particle size as discussed by the authors, and a numerical criterion which distinguishes between groups A and B has been devised and agrees well with published data.

3,007 citations


"A new model for ejected particle ve..." refers methods in this paper

  • ...For most of the industrial applications, the fluidized inert particles are group B, according with Geldart’s classification (Geldart, 1973)....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a new method of digital image analysis has been developed to study the hydrodynamics of two-dimensional bubbling fluidized beds with a digital video camera, which comprises simultaneous of the size and velocity of gas bubbles, and the axial and radial distribution of bubble voidage.

160 citations


"A new model for ejected particle ve..." refers background or methods or result in this paper

  • ...D fluidized beds, based on the work of Shen et al. (2004), who using an approach similar to the one used by Darton et al. (1977), obtained two expressions: one for bubble diameter and one for bubble velocity, both of which as a function of the height of the bed Db = ( 8(23/4 − 1) )2/3 × [ (U − Umf…...

    [...]

  • ...In all the experiments the height of the bed was below the maximum bubble height (Shen et al., 2004), so the bubbles were in a state of growth when they erupted....

    [...]

  • ...We obtained a value of = 0.80, which concurs with Shen et al. (2004) and =9.86, higher that the one obtained by Shen et al. (2004)....

    [...]

  • ...In bubbling fluidized beds, the bubbles grow as they ascend, until they reach a maximum bubble height (Shen et al., 2004)....

    [...]

  • ...Then, using the results of Shen et al. (2004), we obtained two equations for bubble velocity and bubble growth velocity in a 2-...

    [...]

Journal ArticleDOI
TL;DR: In this article, two alternative ejection mechanisms were proposed, one from the roof of each bursting bubble, and the other from bubble wakes of the bursting bubbles, depending on bed geometry, fluidizing velocity U and particle type.

87 citations


Additional excerpts

  • ...D fluidized beds, this velocity is two times the bubble velocity Ub (Pemberton and Davidson, 1986; Fung and Hamdullahpur, 1993)....

    [...]

  • ...In addition, the effect of the vessel walls is important because they mitigate wake ejection (Pemberton and Davidson, 1986), the result being a greater predominance of the dome mechanism in 2-D fluidized beds....

    [...]

  • ...D beds (Pemberton and Davidson, 1986), while for 3-...

    [...]

  • ...Some other researches (Pemberton and Davidson, 1986; Fung and Hamdullahpur, 1993) have estimated the maximum particle velocity for 3-...

    [...]

  • ...In addition, the effect of the vessel walls is important because they mitigate wake ejection (Pemberton and Davidson, 1986), the result being a greater predominance of the dome mechanism in 2-...

    [...]

Journal ArticleDOI
TL;DR: In this article, the turbulence in the upward gas flow above a gas-fluidised bed was measured by hot wire anemometry and it was shown that the irregularity of the motion is caused by bursting bubbles at the surface of the bed.

64 citations


"A new model for ejected particle ve..." refers background in this paper

  • ...necessary to understand the process being undergone below it, namely, the formation and disintegration of coherent structures like clusters, vortex or ghost bubbles, as well as the interaction between the particles and the gas turbulence (Pemberton and Davidson, 1984; Duursma et al., 2001; Solimene et al., 2004)....

    [...]

  • ...…the process being undergone below it, namely, the formation and disintegration of coherent structures like clusters, vortex or ghost bubbles, as well as the interaction between the particles and the gas turbulence (Pemberton and Davidson, 1984; Duursma et al., 2001; Solimene et al., 2004)....

    [...]

Frequently Asked Questions (1)
Q1. What contributions have the authors mentioned in the paper "A new model for ejected particle velocity from erupting bubbles in 2-d fluidized beds" ?

A new model is proposed for obtaining the velocity profile of the particle ejected from the bubble dome in a freely bubbling 2-D fluidized bed. Its basis is the supposition that the initial velocity of the ejected particles, with a direction perpendicular to the dome contour, depends on bubble velocity and bubble growth velocity. Upon comparing these results with the proposed model, it was established that, excepting some isolated cases, the model properly predicts the magnitude and direction of the maximum particle ejection velocity and the velocity profile. These expressions, together with the proposed model, can be used to calculate the initial velocity of the ejected particles.