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This describes mass transfer of dissolved species by diffusion across a phase interface. Examples are:
Evaporation of a liquid into a gaseous mixture containing its vapor, e.g., evaporation of water droplets into air + water vapor.
Absorption/Dissolution of a dissolved gas in a liquid from a gaseous mixture, e.g., absorption of ammonia by water from a mixture of air+ammonia.
Additional theoretical information is available. For details, see General Species Mass Transfer.
Species transfer requires a number of related items of information to be provided.
In ANSYS CFX, interphase species transfer may be specified between any two components A and B in fluids and respectively, subject to the following conditions:
The mass fractions A and B must both be determined from transport equations.
It is not possible to specify species transfer of a component whose mass fraction is determined algebraically, or from the constraint equation.
Unless the Mass Transfer option Sum Species Mass Transfers is selected, the resulting interphase mass flow rate is sufficiently small that continuity equation sources may be neglected, and latent heat effects in the energy equation are negligible.
This will be generalized in future releases.
The coupled components | constitute a Component Pair associated with the fluid pair | Component pairs are analogous to Additional Variables Pairs. For details, see Additional Variables in Multiphase Flow.
The species transfer model assumes:
That dynamic equilibrium prevails at the interface between the two phases.
That mass transfer either side of the phase interface may be modeled by two independent mass transfer coefficients.
Hence, species transfer is implemented as a Two Resistance Model, analogous to the Two Resistance Model for heat transfer.
The Single Resistance options Ranz Marshall, Sherwood Number, Hughmark and Mass Transfer Coefficient apply the corresponding correlation on the continuous fluid side and a zero resistance on the dispersed phase side of the interphase. The correlations are analogous to additional variable mass transfer. For details, see Particle Model Correlations.
A number of interfacial equilibrium models are available. Different ones are recommended for different physical situations. Additional theoretical information is available. For details, see Equilibrium Models.
For evaporation of an ideal liquid into a gas containing its vapor, Raoult's Law should be employed to describe the equilibrium condition. This requires the following additional information:
The Thermodynamic Phase (liquid or gas) must be declared on the Materials Properties form for each fluid and .
The Saturation Pressure must be declared for the vapor component. This may be a constant or an expression. In the latter case, it should be a function of absolute temperature. There are two possible ways of defining the saturation pressure:
Using the optional parameter Saturation Pressure under the option for Raoult's Law on the Component Pairs form. It may be set as a constant or an expression. If the latter, be defined as a function of temperature.
Alternatively, you may define a Homogeneous Binary Material (HBM) under the Material details view. The HBM should consist of the two components in the component pair and the saturation conditions should be defined as material properties of the HBM.
You must use one of these methods to define the Saturation Pressure; otherwise, a error will be generated. If you use both methods, then the Saturation Pressure parameter of Raoults Law takes precedence.
For absorption/dissolution of a dissolved gas from a liquid into a gaseous mixture, Henry's Law should be employed to describe the equilibrium condition. This requires the following additional information:
The Thermodynamic Phase (liquid or gas) must be declared on the Materials Properties form for each fluid and .
Henry's Coefficient must be declared for the vapor component.
Care should be exercised in defining the Henry coefficient. There is no agreed convention as to its correct definition, so a units conversion may be necessary. ANSYS CFX has a choice of two conventions:
Molar Fraction Henry Coefficient, H^{ x}, with units of pressure, or
Molar Concentration Henry Coefficient, H^{ c}, with units of pressure per molar concentration.
In situations where the above two simple laws do not apply, such as liquid-liquid extraction, or multicomponent transfer, you may specify empirical data for the equilibrium condition, if available. For this purpose, you have a choice of three dimensionless quantities:
Molar Concentration Equilibrium Ratio,
Molar Fraction Equilibrium Ratio, or
Mass Fraction Equilibrium Ratio.
These specify the equilibrium ratios of the indicated concentration variables, for the first fluid divided by the second fluid.
The Two Resistance model applies to both the Particle and Mixture models, which determine the interfacial area density. It remains to specify the two mass transfer coefficients on each side of the phase interface.
The available correlations for mass transfer coefficients are analogous to those for heat transfer and additional variables.
A fluid specific Mass Transfer Coefficient may be specified directly for each fluid.
A fluid specific Sherwood Number may be specified directly for each fluid. The Sherwood number is always defined relative to the physical properties of the fluid to which it pertains:
Equation 10. |
is the mass transfer coefficient and is the interfacial length scale (the mean particle diameter for the Particle Model and the mixture length scale for the Mixture Model.
Ranz Marshall and Hughmark correlations are available on the continuous phase side only of a continuous-dispersed phase pair, using the Particle Model.
It is possible to specify a Zero Resistance condition on one side of the phase interface. This is equivalent to an infinite fluid specific mass transfer coefficient . Its effect is to force the interfacial concentration to be the same as the bulk concentration of that phase.
The selection of physically correct mass transfer correlations is highly problem dependent. In the case of mass transfer between a continuous phase and a dispersed phase of approximately spherical particles, the following should be adequate for most problems of interest:
Ranz Marshall or Hughmark in the continuous phase.
Zero Resistance in the dispersed phase.
The latter assumption implies that mass transfer occurs very quickly between the dispersed phase and the interface. Consequently, interfacial concentrations on the dispersed phase side are assumed equal to the bulk dispersed phase concentrations. This will usually be valid for droplet evaporation, or gas absorption / dissolution in bubbles.
In cases where there is significant resistance to mass transfer on the dispersed phase side, the Zero Resistance model should be replaced by a user-specified correlation for dispersed phase Mass Transfer Coefficient or Sherwood Number.
For evaporation of a pure liquid into its vapor, use Raoults Law for the interfacial equilibrium model. For most cases of droplet evaporation, the resistance mass transfer on the droplet side is negligible. If that is the case, use Zero Resistance on the dispersed phase side, and Ranz-Marshall or Hughmark on the continuous phase side.
If the liquid consists of just one component, you should define it as a two component mixture with a dummy material as the Constraint material, and the pure liquid as the Transported material. You will then be able to define a component pair consisting of the pure liquid coupled to its vapor component in the gaseous phase.
Use Henrys Law for the interfacial equilibrium model. If the resistance to mass transfer on the dispersed phase side is negligible, then use Zero Resistance on the dispersed phase side, and Ranz-Marshall or Hughmark on the continuous phase side.
By default, ANSYS CFX computes thermodynamic properties of mixtures assuming that they are ideal mixtures. This is not appropriate, for example, for gases dissolved in a liquid. If the effect of the gas phase properties (e.g., density) on the liquid phase properties is negligible, then you explicitly specify mixture properties in ANSYS CFX-Pre to override the solver calculated mixture properties with appropriate values. The most important mixture property to override is density, but molar mass, dynamic viscosity and specific heat capacity should also be defined if you believe the solver calculated values will be inappropriate. Information on how the solver calculates mixture properties is available. For details, see Radiation Properties.
The ANSYS CFX implementation of component mass transfer is a preliminary implementation, with some limitations which are repeated here.
The resulting interphase mass flow rate is assumed to be sufficiently small that continuity equation sources may be neglected.
Consequently, latent heat effects in the energy equation are neglected.
Thus, component mass transfer is assumed to transfer very small amounts of material between phases, and the driving force is assumed to be governed solely by concentration differences. Component mass transfer due to heat transfer is not yet modeled.