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Experimental and Numerical Study of Multiphase, Multicomponent Flow in Porous Media with a Multiphase Mixture Model

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Abstract

This article describes experimental results and the numerical validation for multiphase, multicomponent evaporation in porous media 1d flow. We apply the model of Lindner et al. (Transp. Porous Media 112(2):313–332, 2016. doi:10.1007/s11242-016-0646-6). The permeability of the porous medium is measured in an additional setup with a constant head permeameter to verify the validity of Darcy flow. The heat losses are considered in an analytical approach of correlating measured temperatures and heat inputs with enthalpies. A method of interpreting the experimental results is discussed to determine the phase state. We can show good qualitative agreement of the shift and position of the evaporation region when varying boundary conditions such as mass flux, concentration and heat input.

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Abbreviations

\(A^\alpha , B^\alpha , C^\alpha \) :

Coefficients of Antoine equation of component \(\alpha \) \((-)\)

\(A_{12}, A_{21}\) :

Coefficients for Margules equation \((-)\)

\(a_{s}\) :

Specific surface of pores (1/m)

\(b_{sf}\) :

Material-fluid parameter for boiling heat flux \((-)\)

\(c_{p,k}\) :

Isobaric specific heat capacity of k phase (J/kg K)

\(c_{p,k}^\alpha \) :

Isobaric specific heat capacity of component \(\alpha \) in phase k (J/kg K)

\(c_i\) :

Constants \((-)\)

f :

Friction factor \((-)\)

\(f^*\) :

Modified friction factor \((-)\)

\(\mathbf {g}\) :

Gravity vector (\(\hbox {m/s}^\mathrm{2}\))

h :

Specific enthalpy (J/kg)

\(h_k\) :

Specific enthalpy of phase k (J/kg)

\(h_k^\alpha \) :

Specific enthalpy of component \(\alpha \) in phase k (J/kg)

\(\Delta h_k^\alpha \) :

Excess enthalpy of mixing of component \(\alpha \) in phase k (J/kg)

H :

Volumetric enthalpy (\(\hbox {J/m}^\mathrm{3}\))

\(h_\text {hydr}\) :

Hydraulic head (m)

\(h_{fg}^\alpha \) :

Enthalpy of vaporization of component \(\alpha \) (J/kg)

\(\bar{h}_{sk}^\alpha \) :

Mean heat transfer coefficient of solid phase and k phase \((\hbox {W/m}^\mathrm{2}\)  K)

\(\mathbf {j}_l\) :

Diffusive mass flux of the liquid phase in the mixture \((\hbox {kg/s} \,m^2)\)

\(k_k\) :

Heat conductivity of phase k (W/m  K)

\(K \) :

Permeability \((\hbox {m}^2)\)

\(k_r \) :

Relative permeability \((-)\)

\(\dot{m} \) :

Mass flux (kg/s m\(^2\))

p :

Pressure (Pa)

\(p^{\alpha ,0}\) :

Equilibrium vapor pressure of component \(\alpha \) (Pa)

\(P_\text {el}\) :

Electrical input power (W)

\(p_c\) :

Capillary pressure (phase pressure difference) (Pa)

\(\dot{q}\) :

Heat source \((\hbox {W/m}^3)\)

\(\dot{q}_{sf}\) :

Heat exchange between solid and fluid phase \((\hbox {W/m}^3)\)

\(\dot{q}_ \text {boil,multicomponent} \) :

Additional heat exchange during boiling \((\hbox {W/m}^3)\)

\(\dot{Q}_\text {tot,corr.}\) :

Corrected total heat flow (W)

\(R_\text {cap}\) :

Capillary radius (m)

\(R_\text {fiber}\) :

Fiber radius (m)

s :

Saturation of the liquid phase \((-)\)

T :

Temperature (K)

\(T_f\) :

Average temperature of fluid phases (K)

\(T_H\) :

Measured temperature at heating foil (K)

\(T_s\) :

Solid temperature (K)

\(T_V\) :

Measured temperature at porous medium (K)

\(\mathbf {u}\) :

Velocity vector (m/s)

\(u_\text {Darcy}\) :

Darcy velocity (m/s)

\(\dot{V} \) :

Volume flow \((\hbox {m}^3/s)\)

\(w_k^\alpha \) :

Mass fraction of component \(\alpha \) in phase k \((-)\)

\(x^\alpha \) :

Mole fraction of component \(\alpha \) in the liquid phase \((-)\)

\(y^\alpha \) :

Mole fraction of component \(\alpha \) in the gas phase \((-)\)

z :

Coordinate (m)

Nu :

Nusselt number \((-)\)

Pr :

Prandtl number \((-)\)

Re :

Reynolds number \((-)\)

Re \({_K}\) :

Reynolds number with square root of permeability as characteristic length \((-)\)

St \(_v\) :

Stanton number of evaporation \((-)\)

\(\mathscr {L}\) :

Characteristic length (m)

\(\gamma ^\alpha \) :

Activity coefficient for component \(\alpha \) \((-)\)

\(\gamma _h\) :

Advection correction coefficient \((-)\)

\(\gamma _\rho \) :

Density correction coefficient \((-)\)

\(\mu \) :

Dynamic viscosity (Pa   s)

\(\nu \) :

Kinematic viscosity \((\hbox {m}^2/s)\)

\(\phi \) :

Porosity \((-)\)

\(\varrho \) :

Density \((\hbox {kg/m}^3)\)

\(\sigma \) :

Surface tension (N/m)

\(\alpha \) :

General component

\(\text {amb}\) :

At ambient state

\( \text {boil} \) :

Boiling

\( \text {bubble} \) :

At bubble point

\( \text {dew} \) :

At dew point

\( \text {dryout} \) :

At dryout state

\( \text {eff} \) :

Effective

f :

Fluid

i :

Discrete value

\( \text {in} \) :

Inflow

k :

General phase

l :

Liquid phase

\( \text {ref} \) :

At reference state

s :

Solid

\( \text {sat} \) :

At saturation state

v :

Superheated phase (vapor)

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Acknowledgments

This work was developed during a research project with Institut für Technik Intelligenter Systeme (ITIS GmbH) and Institute for Thermodynamics at University of the Federal Armed Forces Munich.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Institute for Thermodynamics, University of the Federal Armed Forces Munich, Neubiberg, Germany

    F. Lindner, M. Pfitzner & Ch. Mundt

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  1. F. Lindner
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  2. M. Pfitzner
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  3. Ch. Mundt
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Correspondence to F. Lindner.

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Lindner, F., Pfitzner, M. & Mundt, C. Experimental and Numerical Study of Multiphase, Multicomponent Flow in Porous Media with a Multiphase Mixture Model. Transp Porous Med 116, 143–161 (2017). https://doi.org/10.1007/s11242-016-0768-x

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