3.7. Gas Species and Properties
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In GASFLOW , the basic thermodynamic properties of all gas species are assumed to be governed by the ideal gas law.
where p is the pressure of the mixture (or partial pressure of a gas component), n is the total number of gram-moles (or number of moles of a gas component), R is the universal gas constant equal to 8.3144 ergs/mole-K, and T is the absolute temperature of the gas mixture.
The above relation can also be written in terms of the mass density, ρ, which is given by nM/V, where M is the molecular weight:
GASFLOW-MPI solves the energy conservation equations in terms of the specific internal energy, I, which is related to the absolute temperature, for an ideal gas, by
Tref is a reference temperature, and is the specific heat capacity at constant volume having units of ergs/g-K. In general, is a function of temperature and one can approximate this function by polynomials of various degrees depending on the accuracy required. GASFLOW-MPI gives the user the following options for the calculation of the internal energies:
ieopt = 1 1st order polynomial
ieopt = 2 2nd order polynomial
The user can select which range of temperature is more appropriate for the application.
trange = 'low' T up to 3000 K
trange = 'high' T up to 5000 K
The user is given the following options for evaluation of the specific heat capacity:
icopt = 0 Derivative of specific internal energy
icopt = 1 Constant value
icopt = 2 2nd order polynomial (T<750 K)
icopt = 3 Gordon & McBride approximation
Note that the conservation equations for mass, energy, and momentum are solved consistently with the user-selected values for ieopt and trange. The recommended selection for icopt is icopt = 0, which ensures that correlations for heat transfer and fluid flow transport properties are evaluated with a consistent specific heat capacity.
The built-in gas component library in GASFLOW-MPI has more than 70 species with properties and the user must choose the species to be calculated from this library.
The input array variable mat in NAMELIST group xput is used to define the species in a calculation. For example, in a problem involving air, steam, and hydrogen, the input will be:
mat = 'air', 'h2o', 'h2',
In this example, air is component 1, water vapor is component 2, and hydrogen is component 3 in the gas mixture. These identification numbers will be used in subsequent input specifications where reference to particular components of the mixture is required.
The concentration, in mole or volume fraction, of each gas component will be specified with the variable gasdef.
In this section, we discuss how to specify the physical transport properties for the gas mixture. These properties determine the rates at which mass, energy, and momentum are transported within the gas by the action of molecular diffusion.
In GASFLOW-MPI, the diffusion process is modeled by Fick’s Law, which states that the diffusive flux is proportional to some gradient quantity that represents a driving potential. The proportionality constant is called the diffusion coefficient.ù
In momentum transfer, the gradient is in the velocity vector, and the diffusion coefficient is the kinematic viscosity ν.
In mass diffusion, the gradient of species density is used, and the diffusion coefficient is called the mass diffusivity, D.
For the diffusion of heat, the heat flux is proportional to the product of the temperature gradient, ∇T, and the thermal diffusivity, α.
For the kinematic viscosity ν, the input variable nu is used, which has units of .
For the mass and thermal diffusivities, we use respectively the nondimensional quantities Sc and Pr (Schmidt and Prandtl numbers) to define them:
The Schmidt and Prandtl numbers are represented by the input variables schmidt and prandtl.
All of these variables are in NAMELIST group xput.
For example, an input line which reads
nu=0.2, prandtl=0.7, schmidt=0.4,
specifies constant values of the kinematic viscosity (ν, nu) as 0.2 , the thermal diffusivity (α ) is 0.286 , and the mass diffusivity (D) is 0.5 . The default value for nu is 0.15 , while those for prandtl and schmidt are both 1 (i. e., α = D = ν = 0.15 ).
If the user requires that the transport properties be functions of the temperature, then the following input options are available:
