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Analyzing and modeling the dynamic thermal behaviors of direct contact condensers packed with PCM spheres

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Abstract

Condensers serve as important components for humidification–dehumidification (HDH) desalination plants. Based on the interpenetration continua approach with volume averaging technique, a mathematical dynamic model for analyzing the heat and mass transfer within direct contact condensers with co-current or countercurrent flow arrangement was developed. It was validated against the experimental data from a small scale HDH desalination system. Comparisons including the productivities and the temperature profiles of gas, liquid, and solid phases show good agreement with the measurements. Phase change material (PCM) melting processes have little effect on water production rate for co-current flow arrangement, but the condenser packed with PCM capsules have higher water production rates than that packed with air capsules packed under given conditions. The relative humidity profile of the bulk gas shows contrary trend with the gas temperature profile. The direct contact condenser with countercurrent flow arrangement can provide much better heat and mass transfer between gas and water and produce about 16.3% more fresh water than the same condenser with co-current flow arrangement in 4 h under given conditions.

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Abbreviations

A crost :

Cross-sectional area of packed bed (m2)

a :

Specific packing area per unit volume of the packed column (m2/m3)

c :

Water vapor concentration in the gas mixture (mol/m3)

c p :

Specific heat at constant pressure (J/(kgK))

D :

Diffusion coefficient (m2/s)

d :

Diameter (m)

G :

Air mass flux (kg/(m2s))

ΔH m :

Latent heat of PCM while melting/solidification (J/kg)

h :

Heat transfer coefficient (W/(m2K))

h fg :

Latent heat of vaporization (J/mol)

k :

Mass transfer coefficient (m/s)

L :

Liquid mass flux (kg/(m2s))

M :

Mass flow rate (kg/s)

m cond :

Condensation mass flow rate (mol/(m3s))

p :

Pressure (kPa)

R :

Universal gas constant (8.314J/(molK))

Re:

Reynolds number, dimensionless

T :

Temperature (K)

t :

Time (s)

U :

Heat transfer coefficient between gas and liquid (W/(m2K))

v :

Mean velocity in the packed bed (m/s)

v sup :

Superficial velocity (m/s)

W :

Molecular weight (kg/mol)

z :

Coordinate of the axial direction

λ :

Thermal conductivity (W/(mK))

β :

Moisture content (kgvapor/kgair)

μ :

Dynamic viscosity (Ns/m2)

\({\varphi}\) :

Relative humidity of the gas mixture, dimensionless

ρ :

Density (kg/m3)

\({\varepsilon}\) :

Porosity or phase fraction, dimensionless

σ :

Surface tension (J/m2)

amb:

Ambient

cw:

Cold fresh water

ball:

The packing sphere or ball

bed:

The packed bed

g :

Gas (air-vapor mixture) phase

inter:

Interfacial

l :

Liquid phase

ref:

Reference conditions

s :

Solid phase

sup:

Superficial

HDH:

Humidification–dehumidification

PCM:

Phase change material/s

CS:

Continuous solid

PDEs:

Partial differential equations

RH:

Relative humidity

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Authors and Affiliations

  1. School of Aeronautics Science and Engineering, Beihang University, Beijing, 100191, China

    Kai Wang

  2. China Aero-Polytechnology Establishment, AVIC, Beijing, 100028, China

    Tao Hu

  3. Faculty of Mechanical Engineering, Technische Universität Müchen, 85748, Garching, Germany

    Abdel H. Hassabou, Markus Spinnler & Wolfgang Polifke

Authors
  1. Kai Wang
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  2. Tao Hu
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  3. Abdel H. Hassabou
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  4. Markus Spinnler
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  5. Wolfgang Polifke
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Corresponding author

Correspondence to Tao Hu.

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Communicated by Andreas Öchsner.

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Wang, K., Hu, T., Hassabou, A.H. et al. Analyzing and modeling the dynamic thermal behaviors of direct contact condensers packed with PCM spheres. Continuum Mech. Thermodyn. 25, 23–41 (2013). https://doi.org/10.1007/s00161-012-0246-9

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  • DOI: https://doi.org/10.1007/s00161-012-0246-9

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