# Inbuilt Material Properties

## Fluid Properties

- 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

- 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.
- MW
_{1} - Molecular weight of fluid 1.
- MW
_{2} - 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:

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

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

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

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

## Steam Properties

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.

_{2}, is calculated from the second fluid mass fraction as:

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

All temperatures are in absolute units.

## Incompressible Liquid Properties

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

_{S,F}are in Fahrenheit.

**Jet A**

$Cp=0.162798639+{T}_{s}*0.000576067$

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

$\mu =0.038750078*\left({10}^{{10}^{-4.0265*{\mathrm{log}}_{10}\left(\raisebox{1ex}{${T}_{s}$}\!\left/ \!\raisebox{-1ex}{$1.8$}\right.\right)+9.5660}}-0.7\right)*\rho $

**MIL PRF 23699 Oil**

$Cp=0.38675+{T}_{s}*0.0006155-{T}_{s}^{2}*-4.25*{10}^{-7}$

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

$\mu =0.038750078*\left({10}^{{10}^{-3.454450232*{\mathrm{log}}_{10}\left(\raisebox{1ex}{${T}_{s}$}\!\left/ \!\raisebox{-1ex}{$1.8$}\right.\right)+8.785414669}}-1.153263695\right)*\rho $

**Mil 7808 oil**

$Cp=0.38675+{T}_{s}*0.0006155-{T}_{s}^{2}*-4.25*{10}^{-7}$

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

$\mu =0.038750078*\left({10}^{{10}^{-3.985828904*{\mathrm{log}}_{10}\left(\raisebox{1ex}{${T}_{s}$}\!\left/ \!\raisebox{-1ex}{$1.8$}\right.\right)+9.979718305}}-0.430374380\right)*\rho $

_{S,F}are in Fahrenheit.

**VG32 Oil**

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

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 * T^{2}

κ_{EG} = 0.245110 + 1.75500e-4 * T - 8.52000e-7 * T^{2}

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

_{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}]

_{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/)

- 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 * (T^{2})

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

_{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

## Solid Material Properties

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

- Stainless Steel 321
- ρ = 501.11 ! lbm/ft^3
- Inco 625
- ρ = 523.58 ! lbm/ft^3
- Superwool 607
- ρ = 13.10988 ! lbm/ft^3
- PTFE_PBI
- k = 0.142 ! BTU/hr.ft.F
- Copper
- ρ = 558.0 lbm/ft^3
- Aluminum
- ρ = 169.0 lbm/ft^3

## 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**

“Refutas” method is used for viscosity of liquids

${x}_{i}=massfractionofspeciesi$

$\rho =density,\mu =viscosity,Cp=SpecificHeatatconstantpressure,k=conductivity$

$\nu =kinematicviscosity$

**Liquid/Gas Mixtures**

**Gas Mixtures**

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

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

${y}_{i}=molefractionofspeciesi$

$z=compressibilityfactor$

$\gamma =specificheatratio$

$M{W}_{i}=molecularweightofspeciesi$