# High Pressure¶

RocketProps contains saturated liquid data and uses the corresponding states principle (CSP) to extrapolate that data to higher pressure.

## Density¶

For those propellants in REFPROP or CoolProp, high pressure density data is curve fit to those high-quality data.

Those data are curve fit to a modified, polynomial version of the Tait equation

Gas&Liq 5th Ed defines the Tait equation with equation 4-12.2

When no data are available, there are a number of correlations available to approximate the density at high pressure.

### COSTALD¶

The COSTALD model is a CSP model taken from the thermo project which is an open-source project on pypi.org developed by Caleb Bell and Contributors (2016-2020).

In the comparison plots below, it seems to be the most accurate model for all propellants, except for alcohols and parahydrogen.

### Chang-Zhao¶

The Chang-Zhao is taken from Gas&Liq 5th Ed as defined by equation 4-12.3

There is a 2nd version of Chang-Zhao as modified in Journal of Molecular Liquids 160 (2011) 94-102 that is also made available in RocketProps.

### Nasrfar¶

Journal of Molecular Liquids 160 (2011) 94-102 provides another model for compressed density as developed by Nasrfar Moshfeghian.

## Model Comparisons¶

The following charts compare high accuracy density calculations (CoolProp) to the results of RocketProps curve fits and to each of the models mentioned above COSTALD, Chang-Zhao 1, Chang-Zhao 2 and Nasrfar.

Each chart shows the percent standard deviation (%SD) of each model as compared to CoolProp. The error of each model has a 95% chance of being within 2 times %SD, 99.7% chance of being within 3 times %SD.

The charts are shown in order from worst to best in terms of %SD.

Except for the three worst fluids, parahydrogen and the alcohols, the COSTALD, model matches high pressure propellant density better than Chang-Zhao 1, Chang-Zhao 2 or Nasrfar. Usually with less than 1% error; often much less.

For this reason, COSTALD is the default model for propellants without detailed high pressure density data within RocketProps.