Mixture Rules

For each propellant mixture, RocketProps starts with two well-documented propellants and uses the properties of those two propellants to calculate expected properties of the mixture.

Mixtures of N2H4 and MMH, for example, use N2H4 and MHF3 having MMH weight fractions below 86%, and would use MHF3 and MMH for MMH weight fractions above 86%. (Note that MHF3 is a mixture of 86% MMH + 14% N2H4)

The table below shows the reference propellants used to calculate mixtures of base and additive propellants within each weight percent additive range.

Base Propellant	Additive	Additive Wt% Range	1st Ref Propellant	2nd Ref Propellant
N2H4	MMH	0 to 86	N2H4	MHF3
N2H4	MMH	86 to 100	MHF3	MMH
UDMH	N2H4	0 to 50	UDMH	A50
UDMH	N2H4	50 to 100	A50	N2H4
N2O4	NO	0 to 10	N2O4	MON10
N2O4	NO	10 to 25	MON10	MON25
N2O4	NO	25 to 30	MON25	MON30
LF2	LOX	0 to 100	LF2	LOX

Freezing Point

The freezing point of each mixture is determined as outlined in Mixture Freezing Points

Acentric Factor

The value of the mixture Acentric Factor , omega, is calculated using a mole fraction simple mixing rule as recommended by Eqn 5-3.3 of Gas&Liq 5th Ed

\[\text{omega}_{mix} = \sum_i \text{mole_frac}_i \cdot \text{omega}_i\]

Molecular Weight

By definition, the value of the mixture Molecular Weight, MW, is calculated using a mole fraction simple mixing rule.

\[\text{MW}_{mix} = \sum_i \text{mole_frac}_i \cdot \text{MW}_i\]

Reference T & P

In order to create a properties summary such as the M20 Example Mixture Summary the mixture needs to have a reference temperature (\(\text{T}_{mix}\)) and pressure (\(\text{P}_{mix}\)) at which to calculate reference properties.

In case the reference \(\text{T}_i\) and \(\text{P}_i\) for the base propellants are different, the mixture \(\text{T}_{mix}\) and \(\text{P}_{mix}\) are calculated as a mole fraction simple mixing rule of the \(\text{T}_i\) and \(\text{P}_i\) of each base propellant.

\[\text{T}_{mix} = \sum_i \text{mole_frac}_i \cdot \text{T}_i\]

\[\text{P}_{mix} = \sum_i \text{mole_frac}_i \cdot \text{P}_i\]

Reference properties for each base propellant are calculated at \(\text{T}_{mix}\) and \(\text{P}_{mix}\) and are combined with an appropriate mixing rule to compute the mixture reference properties.

Critical Temperature

Calculation of mixture critical temperature (\(\text{T}_{cm}\)) uses the Li correlation from Caleb Bell, Yoel Rene Cortes-Pena, and Contributors (2016-2021). Chemicals: Chemical properties component of Chemical Engineering Design Library (ChEDL) https://chemicals.readthedocs.io/chemicals.critical.html#critical-temperature-of-mixtures.

Although Kay’s rule Eqn 5-3.1 from Gas&Liq 5th Ed (i.e. simple mole fraction mixing rule) is often sufficient. Better accuracy can usually be expected from the Li correlation.

\[\begin{split}T_{cm} = \sum_{i=1}^n \Phi_i T_{ci}\\ \Phi = \frac{x_i V_{ci}}{\sum_{j=1}^n x_j V_{cj}}\end{split}\]

:

Li, C. C. “Critical Temperature Estimation for Simple Mixtures.” The Canadian Journal of Chemical Engineering 49, no. 5 (October 1, 1971): 709-10. doi:10.1002/cjce.5450490529.

Critical Compressibility Factor

Eqn 5-3.2 from Gas&Liq 5th Ed recommends simple mole fraction mixing rule to calculate the mixture critical compressibility factor (\(\text{Z}_{cm}\))

\[\text{Z}_{cm} = \sum_i \text{mole_frac}_i \cdot \text{Z}_i\]

Critical Pressure

The simplest rule which can give acceptable \(\text{P}_{cm}\) values for two-parameter or three-parameter CSP (corresponding states principle) is the modified rule of Prausnitz and Gunn (1958); Eqn 5-3.2 from Gas&Liq 5th Ed.

\[\text{P}_{cm} = \frac{\text{Z}_{cm} \cdot R \cdot \text{T}_{cm}}{\text{V}_{cm}}\]

Vapor Pressure

The mixture vapor pressure \(\text{P}_{vapm}\) is assumed to follow Raoult’s Law for vapor pressure.

\[\text{P}_{vapm} = \sum_i \text{mole_frac}_i \cdot \text{P}_{vapi}\]

Heat Capacity

Mixture heat capacity \(\text{C}_{pm}\) can be estimated with a simple mixing rule as noted in Eqn 2-55 of Perry’s Chemical Engineers’ Handbook 8th Edition by Don Green and Robert Perry

Note that in Perry’s, the Cp has units of energy/mole and therefore uses mole fraction in the simple mixing equation. Since RocketProps uses energy/mass, mass fraction is used in the simple mixing equation.

\[\text{C}_{pm} = \sum_i \text{mass_frac}_i \cdot \text{C}_{pi}\]

Heat of Vaporization

Mixture heat of vaporization \(\text{H}_{vapm}\) is “tricky”. Also note that, like heat capacity \(\text{C}_{pm}\), heat of vaporization, \(\text{H}_{vapm}\) in RocketProps uses energy/mass for \(\text{H}_{vapm}\) and is therefore based on mass fraction, not mole fraction.

The most common use of \(\text{H}_{vapm}\) is in evaluating propellant droplet evaporation in a thrust chamber in order to calculate thrust chamber performance and combustion stability.

When a droplet first begins to evaporate, the instantaneous \(\text{H}_{vapm}\) is based on the mass fraction of vapor given off for each of the mixtures constituents, not the liquid mass fractions. After a droplet has completely evaporated, the net \(\text{H}_{vapm}\) is based on the starting liquid droplet mass fraction.

Calculating the energy release characteristics in a thrust chamber is well beyond the scope of RocketProps. For that reason, RocketProps assumes complete droplet evaporation and calculates mixture heat of vaporization \(\text{H}_{vapm}\) based on initial droplet mass fraction.

\[\text{H}_{vapm} = \sum_i \text{mass_frac}_i \cdot \text{H}_{vapi}\]

Thermal Conductivity

Calculation of mixture thermal conductivity (\(\lambda_m\)) uses the Filippov correlation from Caleb Bell, Yoel Rene Cortes-Pena, and Contributors (2016-2021). Chemicals: Chemical properties component of Chemical Engineering Design Library (ChEDL) https://chemicals.readthedocs.io/chemicals.thermal_conductivity.html#liquid-mixing-rules.

Note that the Filippov correlation applies to binary mixtures only and that RocketProps currently only supports binary mixtures.

\[\lambda_m = w_1 \lambda_1 + w_2\lambda_2 - 0.72 w_1 w_2(\lambda_2-\lambda_1)\]

For future RocketProps mixtures that might move beyond binary mixtures, the DIPPR9H correlation, also from the ChEDL, is included.

\[\lambda_m^{-2} = \frac{\sum_i z_i {MW}_i \lambda_i^{-2}} {\sum_i z_i {MW}_i}\]

Surface Tension

Calculation of mixture surface tension (\(\sigma_m\)) uses the Winterfeld_Scriven_Davis correlation from Caleb Bell, Yoel Rene Cortes-Pena, and Contributors (2016-2021). Chemicals: Chemical properties component of Chemical Engineering Design Library (ChEDL) https://chemicals.readthedocs.io/chemicals.interface.html#mixing-rules.

\[\sigma_m = \sum_i \sum_j \frac{1}{V_L^{L2}}\left(x_i V_i \right) \left( x_jV_j\right)\sqrt{\sigma_i\cdot \sigma_j}\]

Viscosity

The Chemical Engineering Design Library (ChEDL) for liquid mixture viscosity (\(\mu_m\)) recommends logarithmic mixing with weight fractions https://chemicals.readthedocs.io/chemicals.viscosity.html#liquid-mixing-rules is:

With that in mind, mixture viscosity in RocketProps is calculated as:

\[\mu_m = exp(\sum_i \text{massfrac}_i \cdot \ln(\mu_i))\]