Inbuilt Material Properties

Fluid Properties

Flow Simulator uses a separate routine to calculate fluid properties. The fluid properties are determined by a perfect gas assumption (properties as a function of temperature only) or interpolation of real gas data. Consider the following mixing conditions:

Air as a perfect gas
Mixture of air as a perfect gas and steam
Mixture of air as a perfect gas and real gas
Mixture of two real gases

When using air as a perfect gas, the properties are returned as a function of the absolute temperature. When using steam or real gas, the properties are returned as a function of absolute temperature, pressure, and the secondary fluid mass fractions. The following fluid properties are returned:

γ: Specific heat ratio.
Cp: Specific heat at constant pressure.
R: Gas constant.
K: Thermal conductivity.
μ: Viscosity.
Pr: Prandtl number.

Nomenclature
T: Fluid temperature.
R_u: Universal gas constant.
X: Secondary fluid mass fraction in pounds of second fluid per pound of mixture.
MW₁: Molecular weight of fluid 1.
MW₂: Molecular weight of fluid 2.

Air Properties

Ideal Gas Assumption

If air is assumed to behave as an ideal gas, its properties are determined by functions dependent on temperature only. The specific heat ratio, taken from NACA 1135, equation 180, is given as:(1)

Thermal conductivity and viscosity are assumed to follow Sutherland’s Law. The following equations, taken from White, are used:(2)

Using a value of 28.96451 for the molecular weight of air, the gas constant becomes:(3)

The specific heat and Prandtl number for air are then calculated from the above using the equations:(4)

The range of validity of these air properties is –300 F to 3500 F.

Steam Properties

The steam properties were derived from ASME steam tables. The thermodynamic properties cover the range where the fluid is a vapor for temperatures between 100 ℉ and 1500 ℉ and pressures between 1.0 psia and 1500 psia. Specific heat ratio and the inverse of specific heat at constant pressure are contained in table form in the program, and linear interpolation by temperature and pressure is used to extract values. The transport properties k and μ are functions of temperature only and are calculated using the equations:

The saturation temperature of steam is contained in tabular form and is checked to ensure that chamber temperature remains in the superheated range in all chambers. The solution is stopped if this error occurs. A warning is displayed and/or printed if the temperature in a chamber gets within 50 ℉ of saturation.

Properties of Mixed Air, Steam, and Real Gases

In Flow Simulator, you can analyze systems with mixtures of steam, air, and real gases (for example, methane and carbon dioxide). The system used to do this is approximate because ideal gas assumptions employ Cp rather than enthalpy for the calculation of the temperature of mixing streams of different fluids.

The mass weighted mixing model is always used for the thermodynamic properties of specific heat at constant pressure. The partial pressure of the fluid is used to obtain properties for steam and real gas. Ideal air properties are not a function of pressure. The mass weighted mixing equations, presented here for specific heat, entropy, enthalpy, and density, are as follows:

The molecular weight and gas constant of the mixture are calculated using:

The viscosity and conductivity of the mixture are calculated using molecular mixing models. For the molecular mixing model, the mole fraction of the second fluid, X₂, is calculated from the second fluid mass fraction as:

Specific equations for the transport properties were obtained from reference [6].

Viscosity for the air-steam mixtures (and viscosity and thermal conductivity for mixtures with real gas) are calculated using the Chapman-Enskog Kinetic Theory from the equation:

All temperatures are in absolute units.

The Prandtl number and the specific heat ratio for the mixture are computed using the mixed properties:

Incompressible Liquid Properties

In Flow Simulator, you can model incompressible liquids. Flow Simulator supports seven liquids:

Water
Jet A
Mil PRF 23699 oil
Mil 7808 oil
VG-32 oil
Ethylene glycol - water solution
Propylene glycol - water solution

Note: In the fluid property calculation equations below, T_S,F are in Fahrenheit.

Jet A

$C p = 0.162798639 + T_{s} * 0.000576067$

$k = 0.101627999 - T_{s} * 5.58261 * 10^{- 5}$

$μ = 0.038750078 * (10^{10^{- 4.0265 * \log_{10} (\frac{T_{s}}{1.8}) + 9.5660}} - 0.7) * ρ$

ρ = 65.00814877 - T_{s} * 0.028173705

MIL PRF 23699 Oil

$C p = 0.38675 + T_{s} * 0.0006155 - T_{s}^{2} * - 4.25 * 10^{- 7}$

$k = 0.080333333 - T_{s} * 3.333333333 * 10^{- 5}$

$μ = 0.038750078 * (10^{10^{- 3.454450232 * \log_{10} (\frac{T_{s}}{1.8}) + 8.785414669}} - 1.153263695) * ρ$

ρ = 62.60095344 * (1.0 - 0.00045 * (T_{s} - 59))

Mil 7808 oil

$C p = 0.38675 + T_{s} * 0.0006155 - T_{s}^{2} * - 4.25 * 10^{- 7}$

$k = 0.088333333 - T_{s} * 1.333333333 * 10^{- 5}$

$μ = 0.038750078 * (10^{10^{- 3.985828904 * \log_{10} (\frac{T_{s}}{1.8}) + 9.979718305}} - 0.430374380) * ρ$

ρ = 60.099410610 * (1.0 - 0.00045 * (T_{s} - 59))

Note: In the fluid property calculation equations above, T_S,F are in Fahrenheit.

VG32 Oil

VG32 Oil properties are implemented as tables in Flow Simulator. The tables for each fluid property are plotted below.

Ethylene Glycol - Water Solution

T: Temperature of the solution in Celsius
x: Mass fraction of Ethylene Glycol

Density Calculation - D. Bohne, S. Fischer, and E. Obermeie: Thermal Conductivity, Density, Viscosity, and Prandtl-Numbers of Ethylene Glycol-Water Mixtures

(5)

Thermal Conductivity Calculation: D. Bohne, S. Fischer, and E. Obermeie: Thermal Conductivity, Density, Viscosity, and Prandtl-Numbers of Ethylene Glycol-Water Mixtures

κ_H20 = 0.570990 + 1.67156e-3 * T - 6.09054e-6 * T²

κ_EG = 0.245110 + 1.75500e-4 * T - 8.52000e-7 * T²

κ_CONST = 0.6635 – 0.3698 * x – 8.85e-4 * T

κ_SOL = (1-x) * k_H20+ x * κ_EG - κ_CONST * (κ_H20- κ_EG ) * (1-x) * x

κ_SOL = κ_SOL * 0.5781759824 (convert from W/m-K to BTU/hr-ft-degR)

Dynamic Viscosity Calculation: Tongfan Sun and Amyn S. Teja: Density, Viscosity, and Thermal Conductivity of Aqueous Ethylene, Diethylene, and Triethylene Glycol Mixtures between 290 K and 450 K

µ_EG = -3.613590 + 986.5190 / (T + 127.8610)

µ_H20 = -3.758023 + 590.9808 / (T + 137.2645)

µ_CONST = -0.165301 -0.287325 * x +1.10978e-3 * T

µ_SOL = EXP [ x * µ_EG + (1-x) * µ_H20 + (µ_EG - µ_H20)* x * (1-x) * µ_CONST]

µ_SOL = µ_SOL * 2.4190883293091 (convert from mPa/s to lbm/hr-ft)

Specific Heat Calculations/Property Tables (source: Engineering Toolbox (https://www.engineeringtoolbox.com/)

Propylene Glycol - Water Solution, Tongfan Sun and Amyn S. Teja: Density, Viscosity and Thermal Conductivity of Aqueous Solutions of Propylene Glycol, Dipropylene Glycol, and Tripropylene Glycol between 290 K and 460 K

T: Temperature of the solution in Celsius
w: Mass fraction of ethylene glycol

Thermal conductivity calculation:

µ_H20 = 0.570990 + 1.67156e-3 * T - 6.09054e-6 * (T²)

µ_PG = 0.191160 + 1.19999e-4 / (T + 9.24590e-7)

µ_CONST = 0.362200 + 9.03450e-2 * FS - 2.0935e-4 * T *

µ_SOL = (1-FS) * µ_H20 + w * µ_PG - µ_CONST * (µ_H20 - µ_PG) * (1-w) * w

µ_SOL = µ_SOL * 0.5781759824 (convert from W/m-K to BTU/hr-ft-degR)

Specific Heat Calculations/property tables - source is Engineering Toolbox (https://www.engineeringtoolbox.com/)

Dynamic Viscosity Calculations/property tables - source is Engineering Toolbox (https://www.engineeringtoolbox.com/)

Water

Water properties are implemented as tables in Flow Simulator. The tables for each fluid property are plotted below:

Solid Material Properties

Flow Simulator supports the following solid materials:

Stainless Steel 321
Inco 625
SuperWool 607
Ceramic Paper
PTFE_PBI
Copper
Aluminum

Stainless Steel 321: ρ = 501.11 ! lbm/ft^3; EMISS = 0.85; Cp = 0.119503 ! BTU/(lb.F); Figure 25.
Inco 625: ρ = 523.58 ! lbm/ft^3; EMISS = 0.71; Cp = 0.098 ! BTU/(lb.F); Figure 26.
Superwool 607: ρ = 13.10988 ! lbm/ft^3; EMISS = 0.79; Cp = 0.1624152097 ! BTU/(lb.F); Figure 27.
PTFE_PBI: k = 0.142 ! BTU/hr.ft.F; ρ = 137.3416 ! lbm/ft^3; EMISS = 0.92; Cp = 0.23168 ! BTU/(lb.F)
Copper: ρ = 558.0 lbm/ft^3; EMISS = 0.55; Cp = 0.0932 BTU/(lb.F); Figure 28.
Aluminum: ρ = 169.0 lbm/ft^3; EMISS = 0.40; Cp = 0.215 BTU/(lb.F); Figure 29.

General Mixing Equations

These mixing laws are used in Flow Simulator for mixtures of two or more built-in fluids or if the Coolprop mixing fails.

Liquid Mixtures

(6)

\frac{1}{ρ_{m i x}} = \sum_{i = 1}^{N s p e c} \frac{x_{i}}{ρ_{i}}

“Refutas” method is used for viscosity of liquids(7)

V B N_{m i x} = \sum_{i = 1}^{N s p e c} x_{i} * (10.975 + 14.534 * ln (ln (ν_{i} + 0.8)))

(8)

ν_{m i x} = e x p (e x p (\frac{V B N_{m i x} - 10.975}{14.534})) - 0.8

(9)

μ_{m i x} = ν_{m i x} * ρ_{m i x}

(10)

k_{m i x} = e x p (\sum_{i = 1}^{N s p e c} x_{i} * ln (k_{i}))

(11)

C p_{m i x} = \sum_{i = 1}^{N s p e c} x_{i} * C p_{i}

$x_{i} = m a s s f r a c t i o n o f s p e c i e s i$

$ρ = d e n s i t y, μ = v i s c o s i t y, C p = S p e c i f i c H e a t a t c o n s t a n t p r e s s u r e, k = c o n d u c t i v i t y$

$ν = k i n e m a t i c v i s c o s i t y$

Liquid/Gas Mixtures

(12)

\frac{1}{ρ_{m i x}} = \sum_{i = 1}^{N s p e c} \frac{x_{i}}{ρ_{i}}

(13)

\frac{1}{μ_{m i x}} = \sum_{i = 1}^{N s p e c} \frac{x_{i}}{μ_{i}}

(14)

k_{m i x} = e x p (\sum_{i = 1}^{N s p e c} x_{i} * ln (k_{i}))

(15)

C p_{m i x} = \sum_{i = 1}^{N s p e c} x_{i} * C p_{i}

Gas Mixtures

The properties of each species in a gas mixture is retrieved using the partial pressure of the gas.

(16)

ρ_{m i x} = \sum_{i = 1}^{N s p e c} ρ_{i}

(17)

z_{m i x} = \sum_{i = 1}^{N s p e c} z_{i}

“Wilke’s” correlation is used for viscosity and conductivity of gases.(18)

ϕ_{i j} = \frac{1}{\sqrt{8} \sqrt{1 + \frac{M W_{i}}{M W_{j}}}} * {(1 + \sqrt{\frac{μ_{i}}{μ_{j}}} \sqrt[4]{\frac{M W_{j}}{M W_{i}}})}^{2}

(19)

μ_{m i x} = \sum_{i = 1}^{N s p e c} \frac{y_{i} * μ_{i}}{\sum_{j = 1}^{N s p e c} y_{i} * ϕ_{i j}}

(20)

k_{m i x} = \sum_{i = 1}^{N s p e c} \frac{y_{i} * k_{i}}{\sum_{j = 1}^{N s p e c} y_{i} * ϕ_{i j}}

(21)

C p_{m i x} = \sum_{i = 1}^{N s p e c} x_{i} * C p_{i}

(22)

γ_{t e r m} = \sum_{i = 1}^{N s p e c} x_{i} * \frac{γ_{i}}{γ_{i} - 1} γ_{m i x} = \frac{γ_{t e r m}}{γ_{t e r m} - 1}

$y_{i} = m o l e f r a c t i o n o f s p e c i e s i$

$z = c o m p r e s s i b i l i t y f a c t o r$

$γ = s p e c i f i c h e a t r a t i o$

$M W_{i} = m o l e c u l a r w e i g h t o f s p e c i e s i$