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Analyzing the universality of the dimensionless vibrating number based on the effective moisture diffusivity and its impact on specific energy consumption

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Abstract

Using vibro-fluidized bed dryers (VFB) is an alternative to perform drying with less specific energy consumption compared to fluidized bed dryers (FB). Finding an optimum combination of the dimensionless vibrating number (Γ) with the drying conditions is a key factor to analyze the viability of VFB towards energy efficiency. In the present study, the performance of a VFB was investigated by correlating the drying kinetics of porous particles with the specific energy consumption to obtain an optimum drying condition. Experiments were carried out under different operating conditions and three combinations of vibration amplitude (A) and frequency (F) chosen to yield a constant value of Γ. The impact of the operating parameters was analyzed by effective moisture diffusivity (Deff,G), estimated by fitting the diffusive model to the experimental data. It was found that vibration intensifies Deff,G and is the preponderant effect in the convective mass transfer. Different values of Deff,G were found for the same Γ obtained under the tested combinations of A and F, which indicates that this parameter cannot be used alone as a single descriptor of the vibration energy. Using a high temperature and a gas velocity exceeding the minimum fluidized velocity combined to a higher value of A and a lower value of F enhanced drying, as this combination yielded the highest Deff,G. This same combination of high A and low F associated to low values of temperature and gas velocity enhanced the energy performance. The results also showed that only Γ is not an adequate parameter to perform energy analysis of VFB.

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Abbreviations

a:

Activity [−]

A:

Amplitude of vibration [m]

Bi:

Mass transfer biot number [−]

cpg :

Specific heat of dry air [kJ/kg°C]

C:

Concentration [kg m−3]

Cl :

Liquid concentration [kg m−3]

Cv :

Vapor concentration [kg m−3]

D:

Diffusion coefficient [m2 min−1]

D0 :

Pre-exponential factor [m2 min−1]

Deff,G :

Effective moisture diffusivity (global) [m2 min−1]

Deff,k :

Effective Knudsen diffusivity [m2 min−1]

Deff,l :

Effective liquid diffusivity [m2 min−1]

Deff,s :

Effective surface diffusivity [m2 min−1]

Deff,v :

Effective vapor diffusivity [m2 min−1]

Dl :

Liquid diffusion [m2 min−1]

Dv :

Vapor diffusion [m2 min−1]

Ea :

Activation energy [kJ.mol−1]

f:

Mass flux [kg.m−2.s−1]

F:

Frequency of vibration [Hz]

g:

Gravitational acceleration [m s−2]

\( {\dot{\mathrm{m}}}_{\mathrm{g}} \) :

Air mass flow rate [kg/min]

ms :

Mass of dry solid [kg]

MR:

Moisture ratio [−]

n:

Number of terms of the sum [−]

Qh :

Heat imput to the dryer [kJ.s−1]

r:

Radial coordenate [−]

R:

Particle radius [m]

Rg :

Universal gas constant [J mol−1 K−1]

t:

Drying time [min]

T:

Temperature of the drying air [°C]

Ta :

Ambient temperature [°C]

u:

Gas velocity [m s−1]

umf :

Minimum fluidization velocity [m s−1]

Wev :

Mass of evaporated water [kg]

X:

Moisture content [kg kg−1]

\( \overline{\mathrm{X}} \) :

Average moisture content [kg kg−1]

X0 :

Initial moisture content [kg kg−1]

Xeq :

Dynamic equilibrium moisture content [kg kg−1]

βeff :

Effective mass transfer parameter [m s−1]

Γ:

Dimensionless vibration number [−]

μ:

Chemical potential [J mol−1]

χ:

Dimensionless moisture content [−]

λn :

Roots of the transcendental equation [−]

ϕ:

Parameter of Eq. (17) [−]

ρs :

Solid specific mass [kg m−3]

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Acknowledgments

The authors thank to National Council for Scientific and Technological Development (CNPq/Brazil) and Coordination for the Improvement of Higher Education Personnel (CAPES/Brazil).

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Authors and Affiliations

  1. Laboratory of Processes, Center of Technology, Federal University of Alagoas, Av. Lourival Melo Mota, Tabuleiro dos Martins, zip code, Maceió, AL, 57072-970, Brazil

    L. Meili

  2. Institute of Natural Resources, Federal University of Itajubá—UNIFEI, Itajubá, MG, Brazil

    H. Perazzini

  3. Department of Chemical Engineering, Drying Center, Federal University of São Carlos, São Carlos, SP, Brazil

    M.C. Ferreira & J.T. Freire

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  1. L. Meili
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Correspondence to L. Meili.

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Meili, L., Perazzini, H., Ferreira, M. et al. Analyzing the universality of the dimensionless vibrating number based on the effective moisture diffusivity and its impact on specific energy consumption. Heat Mass Transfer 56, 1659–1672 (2020). https://doi.org/10.1007/s00231-019-02787-8

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