Skip to main content
SpringerLink
Log in

Experimental and numerical investigations of a fixed-bed distributor for obtaining the outlet fluid velocity profile

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

In this study, computational fluid dynamics (CFD) was used to simulate a fixed-bed distributor, investigating spherical particles in body-centered cubic (BCC) and hexagonally close-packed (HCP) structures. The bed-to-particle diameter ratio (D/dp) varied in the range of 4.158–16.65, while the range for the ratio of bed height to particle diameter (h/dp) was 5–13. The simulations were carried out for Reynolds number (Rep) in the range of 4–589, including laminar and turbulent flow regimes. To conduct validation, the numerical results were compared with our experimental data as well as seven empirical equations, where perfect match was found for both laminar and turbulent flows. Then simulations were conducted to generate the required data for an artificial neural network (ANN) to predict the velocity profile at the distributor outlet in order to save the computational CPU time. The R2, MAE and RMSE values of the neural network for predicting the fluid outlet velocity were 0.972, 0.0274 and 0.0512, respectively. The function obtained from the neural network is an efficient tool for the optimum design of fixed-bed distributors. This function could be directly used in three-dimensional fixed-bed distributor models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

\(C_{1\varepsilon }\) :

Model parameter in the ε equation

\(C_{2\varepsilon }\) :

Model parameter in the ε equation

\(C_{3\varepsilon }\) :

Model parameter in the ε equation

\(C_{\mu }\) :

Model parameter in the k–ε model

\(d_{{\text{p}}}\) :

Particle diameter (m)

\(D\) :

Bed diameter (m)

\(G_{b}\) :

Turbulence kinetic energy generated by buoyancy (m2 s−2)

\(G_{K}\) :

Turbulence kinetic energy generated by mean velocity gradients (m2 s−2)

\(h\) :

Height of the packed bed (m)

K :

Permeability (m2)

K :

Turbulent kinetic energy (m2 s−2)

\(n\) :

Number of data

P :

Pressure (Pa)

\({\text{Re}}_{{\text{p}}}\) :

Particle Reynolds number

RH:

Relative humidity

T :

Temperature (°C)

W :

Distance from the reactor wall (m)

X :

CFD coordinate direction (m)

Y :

CFD coordinate direction (m)

\(Y_{M}\) :

Share of noise expansion

\(y_{m}\) :

Mean value of CFD results

\(y_{{i,{\text{pred}}}}\) :

Predicted value

\(y_{{i,{\text{simulate}}}}\) :

Simulated value

Z :

CFD coordinate direction (m)

z c :

Air compressibility factor

\(\Delta P\) :

Pressure drop (Pa)

\(\varepsilon\) :

Turbulent dispersion rate (m2 s−3)

\(\epsilon_{m}\) :

Void fraction

\(\mu_{{\text{t}}}\) :

Turbulent viscosity (m2 s−1)

\(\vartheta\) :

Dynamic viscosity (Pa s)

\(\rho\) :

Density (kg m−3)

\(\sigma_{k}\) :

Model parameter

\(\sigma_{\varepsilon }\) :

Model parameter

References

  1. Y.S. Choi, S.J. Kim, D. Kim, A semi-empirical correlation for pressure drop in packed beds of spherical particles. Transp. Porous Media 75, 133–149 (2008). https://doi.org/10.1007/s11242-008-9215-y

    Article  Google Scholar 

  2. A. Montillet, Flow through a finite packed bed of spheres: a note on the limit of applicability of the forchheimer-type equation. J. Fluids Eng. 126, 139 (2004). https://doi.org/10.1115/1.1637928

    Article  Google Scholar 

  3. F. Depypere, J.G. Pieters, K. Dewettinck, CFD analysis of air distribution in fluidised bed equipment. Powder Technol. 145, 176–189 (2004). https://doi.org/10.1016/j.powtec.2004.06.005

    Article  Google Scholar 

  4. P.M.G. Nejad, M.S. Hatamipour, Investigation on the removal of carbon dioxide exhausted from industrial units in a lab-scale fluidized bed reactor. Bull. Chem. React. Eng. Catal. 15, 579–590 (2020). https://doi.org/10.9767/bcrec.15.2.7882.579-590

    Article  Google Scholar 

  5. R.A. Corrêa, L.A. Calçada, R.P. Peçanha, Development of a fluidized bed system for adsorption of phenol from aqueous solutions with commercial macroporous resins. Braz. J. Chem. Eng. 24, 15–28 (2007). https://doi.org/10.1590/S0104-66322007000100002

    Article  Google Scholar 

  6. D.C. Sau, K.C. Biswal, Computational fluid dynamics and experimental study of the hydrodynamics of a gas–solid tapered fluidized bed. Appl. Math. Model. 35, 2265–2278 (2011). https://doi.org/10.1016/j.apm.2010.11.037

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Kumar, G.K. Roy, Effect of different types of promoters on bed expansion in a gas–solid fluidized bed with varying distributor open areas. J. Chem. Eng. Jpn. 35, 681–686 (2002). https://doi.org/10.1252/jcej.35.681

    Article  Google Scholar 

  8. N. Hilal, M.T. Ghannam, M.Z. Anabtawi, Effect of bed diameter, distributor and inserts on minimum fluidization velocity. Chem. Eng. Technol. 24, 161–165 (2001). https://doi.org/10.1002/1521-4125(200102)24:2%3c161::AID-CEAT161%3e3.0.CO;2-S

    Article  Google Scholar 

  9. M. Jovanovic, Z. Grbavcic, N. Rajic, B. Obradovic, Removal of Cu(II) from aqueous solutions by using fluidized zeolite A beads: hydrodynamic and sorption studies. Chem. Eng. Sci. 117, 85–92 (2014). https://doi.org/10.1016/j.ces.2014.06.017

    Article  Google Scholar 

  10. D.V. Kalaga, A. Dhar, S.V. Dalvi, J.B. Joshi, Particle-liquid mass transfer in solid–liquid fluidized beds. Chem. Eng. J. 245, 323–341 (2014). https://doi.org/10.1016/j.cej.2014.02.038

    Article  Google Scholar 

  11. D. Mandal, D. Sathiyamoorthy, M. Vinjamur, Experimental investigation of heat transfer in gas–solid packed fluidized bed. Powder Technol. 246, 252–268 (2013). https://doi.org/10.1016/j.powtec.2013.04.054

    Article  Google Scholar 

  12. M.A. Stylianou, V.J. Inglezakis, M. Loizidou, Comparison of Mn, Zn, and Cr removal in fluidized- and fixed-bed reactors by using clinoptilolite. Desalin. Water Treat. 53, 3355–3362 (2015). https://doi.org/10.1080/19443994.2014.934103

    Article  Google Scholar 

  13. U. Vengateson, R. Mohan, Experimental and modeling study of fluidized bed granulation: effect of binder flow rate and fluidizing air velocity. Resour. Technol. 2, S124–S135 (2016). https://doi.org/10.1016/j.reffit.2016.10.003

    Article  Google Scholar 

  14. J. Kruger, C. Toit, W. Merwe, Numerical validation of the Eisfeld and Schnitzlein pressure drop correlation for small aspect ratio packed beds, in 11th International Conference on CFD in the Minerals and Process Industries (2015), pp. 1–7

  15. R.K. Reddy, J.B. Joshi, CFD modeling of pressure drop and drag coefficient in fixed beds: wall effects. Particuology 8, 37–43 (2010). https://doi.org/10.1016/j.partic.2009.04.010

    Article  Google Scholar 

  16. T. Atmakidis, E.Y. Kenig, CFD-based analysis of the wall effect on the pressure drop in packed beds with moderate tube/particle diameter ratios in the laminar flow regime. Chem. Eng. J. 155, 404–410 (2009). https://doi.org/10.1016/j.cej.2009.07.057

    Article  Google Scholar 

  17. O. Bey, G. Eigenberger, Fluid flow through catalyst filled tubes. Chem. Eng. Sci. 52, 1365–1376 (1997). https://doi.org/10.1016/S0009-2509(96)00509-X

    Article  Google Scholar 

  18. G.T. Bolton, C.W. Hooper, R. Mann, E.H. Stitt, Flow distribution and velocity measurement in a radial flow fixed bed reactor using electrical resistance tomography. Chem. Eng. Sci. 59, 1989–1997 (2004). https://doi.org/10.1016/j.ces.2004.01.049

    Article  Google Scholar 

  19. C. Boyer, B. Fanget, Measurement of liquid flow distribution in trickle bed reactor of large diameter with a new gamma-ray tomographic system. Chem. Eng. Sci. 57, 1079–1089 (2002). https://doi.org/10.1016/S0009-2509(01)00361-X

    Article  Google Scholar 

  20. A.G. Dixon, Correlations for wall and particle shape effects on fixed bed bulk voidage. Can. J. Chem. Eng. 66, 705–708 (1988). https://doi.org/10.1002/cjce.5450660501

    Article  Google Scholar 

  21. A.G. Dixon, M. Nijemeisland, CFD as a design tool for fixed-bed reactors, in Industrial and Engineering Chemistry Research (2001), pp. 5246–5254

  22. B. Eisfeld, K. Schnitzlein, The influence of confining walls on the pressure drop in packed beds. Chem. Eng. Sci. 56, 4321–4329 (2001). https://doi.org/10.1016/S0009-2509(00)00533-9

    Article  Google Scholar 

  23. H. Susskind, W. Becker, Pressure drop in geometrically ordered packed beds of spheres. AIChE J. 13, 1155–1159 (1967). https://doi.org/10.1002/aic.690130622

    Article  Google Scholar 

  24. P. Sahoo, A. Sahoo, CFD simulation for hydrodynamic behaviour of fine particles in a fluidized bed. Indian J. Chem. Technol. 23, 253–261 (2016)

    Google Scholar 

  25. E.A. Foumeny, F. Benyahia, J.A.A. Castro et al., Correlations of pressure drop in packed beds taking into account the effect of confining wall. Int. J. Heat Mass Transf. 36, 536–540 (1993). https://doi.org/10.1016/0017-9310(93)80028-S

    Article  Google Scholar 

  26. S. Damiaa, Artificial Neural Network Prediction of Hydrodynamics Characteristics of Inclined Fluidized Bed with Ring-Promoted. In: International Conference For Engineering Sciences (At Al-Mustansiriyah University/College of Engineering, Baghdad, 2014)

  27. B. Guo, D. Li, C. Cheng et al., Simulation of biomass gasification with a hybrid neural network model. Bioresour. Technol. 76, 77–83 (2001). https://doi.org/10.1016/S0960-8524(00)00106-1

    Article  Google Scholar 

  28. L. Cavas, Z. Karabay, H. Alyuruk et al., Thomas and artificial neural network models for the fixed-bed adsorption of methylene blue by a beach waste Posidonia oceanica (L.) dead leaves. Chem. Eng. J. 171, 557–562 (2011). https://doi.org/10.1016/j.cej.2011.04.030

    Article  Google Scholar 

  29. S. Chowdhury, S.P. Das, Artificial neural network (ANN) modeling of adsorption of methylene blue by NaOH-modified rice husk in a fixed-bed column system. Environ. Sci. Pollut. Res. 20, 1050–1058 (2013). https://doi.org/10.1007/s11356-012-0912-2

    Article  Google Scholar 

  30. M. Yusuf, K. Song, L. Li, Fixed bed column and artificial neural network model to predict heavy metals adsorption dynamic on surfactant decorated graphene. Colloids Surf. A Physicochem. Eng. Asp. (2020). https://doi.org/10.1016/j.colsurfa.2019.124076

    Article  Google Scholar 

  31. D. Saha, A. Bhowal, S. Datta, Artificial neural network modeling of fixed bed biosorption using radial basis approach. Heat Mass Transf. Stoffuebertragung 46, 431–436 (2010). https://doi.org/10.1007/s00231-010-0584-8

    Article  ADS  Google Scholar 

  32. F.E. Jones, Calculation of compressibility factor for air over the range of pressure, temperature, and relative humidity of interest in flowmeter calibration [Final Report] (1983)

  33. M. Mourabet, A. El-Rhilassi, M. Bennani-Ziatni, A. Taitai, Comparative study of artificial neural network and response surface methodology for modelling and optimization the adsorption capacity of fluoride onto apatitic tricalcium phosphate. Univers. J. Appl. Math. 2, 84–91 (2014). https://doi.org/10.13189/ujam.2014.020202

    Article  Google Scholar 

  34. M. Saeedan, M. Bahiraei, Effects of geometrical parameters on hydrothermal characteristics of shell-and-tube heat exchanger with helical baffles: numerical investigation, modeling and optimization. Chem. Eng. Res. Des. 96, 43–53 (2015). https://doi.org/10.1016/j.cherd.2015.02.004

    Article  Google Scholar 

  35. G.S. Beavers, E.M. Sparrow, S.E. Rodenz, Influence of bed size on the flow characteristics and porosity of randomly packed beds of spheres. J. Appl. Mech. 40, 655–660 (1973). https://doi.org/10.1115/1.3423067

    Article  ADS  Google Scholar 

  36. A. De Klerk, Voidage variation in packed beds at small column to particle diameter ratio. AIChE J. 49, 2022–2029 (2003)

    Article  Google Scholar 

  37. R. Jeschar, Druckverlust in mehrkornschüttungen aus kugeln. Arch. Eisenhüttenwes 35, 91–108 (1964)

    Article  Google Scholar 

  38. D. Handley, Momentum and heat transfer mechanism in regular shaped packing. Trans. Inst. Chem. Eng. 46, T251–T264 (1968)

    Google Scholar 

  39. D. Mehta, M.C. Hawley, Wall effect in packed columns. Ind. Eng. Chem. Process. Des. Dev. 8, 280–282 (1969). https://doi.org/10.1021/i260030a021

    Article  Google Scholar 

  40. S. Ergun, Fluid flow through packed columns. Chem. Eng. Prog. 48, 89–94 (1952)

    Google Scholar 

  41. P.C. Carman, Fluid flow through granular beds. Trans. Inst. Chem. Eng. 15, 150–166 (1937)

    Google Scholar 

  42. N.M. Zhavoronkov, M.E. Aerov, N.N. Umnik, Hydraulic resistance and density of packing of a granular bed. J. Phys. Chem. 23, 342–361 (1949)

    Google Scholar 

  43. W. Reichelt, Zur Berechnung des Druckverlustes einphasig durchströmter Kugel- und Zylinderschüttungen. Chem. Ing. Tech. 44, 1068–1071 (1972). https://doi.org/10.1002/cite.330441806

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by vice chancellor of research of University of Isfahan under grant No. 933411137003. The sincere help of Dr. M. Mastani in language editing of this article is acknowledged.

Author information

Authors and Affiliations

  1. Chemical Engineering Department, Faculty of Engineering, University of Isfahan, Isfahan, Iran

    Puriya Mohamad-Gholy-Nejad & Mohammad Sadegh Hatamipour

Authors
  1. Puriya Mohamad-Gholy-Nejad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Sadegh Hatamipour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Sadegh Hatamipour.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mohamad-Gholy-Nejad, P., Hatamipour, M.S. Experimental and numerical investigations of a fixed-bed distributor for obtaining the outlet fluid velocity profile. Eur. Phys. J. Plus 136, 599 (2021). https://doi.org/10.1140/epjp/s13360-021-01612-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-01612-8

Search

Navigation