Propellant Characterization
In order to simulate a motor in BurnSim you need your propellant's characterization numbers. This consists of 4 things. Propellant density, C* / ISP*, Burn Rate Exponent (n) and Burn Rate Coefficient (a). Propellant density and C* / ISP* can be determined through ProPep software.
Using ProPep3
ProPep3 is a free Windows program (XP through Windows 7, 32- and 64-bit, and it runs fine on modern Windows too) that computes a propellant's theoretical thermochemical performance from its ingredient formulation - the modern replacement for the original 1980s DOS ProPep. Download the installer (ProPEP3.msi) from that page and run it; a PDF manual is linked from the same page for the full reference. If you're upgrading from an older ProPep3 install, back up your existing database file first - installing the new version overwrites it.
Running an analysis
Enter your propellant as a formulation: each ingredient (oxidizer, fuel, binder, and any additives such as a burn-rate catalyst or opacifier) by weight percentage, along with the chamber pressure you're characterizing at - typically your expected working pressure, since these numbers do shift somewhat with pressure. ProPep3 runs a thermochemical equilibrium calculation on that formulation and reports theoretical performance for it.
Mapping the output to BurnSim
ProPep3's output covers everything BurnSim needs except a and n - those still require real test data (see below), since they describe how fast your particular propellant actually burns, not just the theoretical energy content of the formulation. From the ProPep3 report:
- Density - the formulation's theoretical density. Enter it in BurnSim's Density field (lb/in^3) - convert if ProPep3 reports it in g/cc (1 g/cc = 0.036127 lb/in^3).
- C* (characteristic velocity) - goes straight into BurnSim's C* field (ft/sec).
- Specific heat ratio (gamma, sometimes labeled k) - goes into BurnSim's Specific heat ratio field.
- Molar mass (molecular weight of the combustion products) - goes into BurnSim's Molar mass field (g/mol).
These four numbers - density, C*, specific heat ratio, molar mass - are BurnSim's ordinary characterization fields, and the last three are also everything Lenoir-Robillard erosive burning needs to derive its flame temperature. There's nothing extra to look up for erosive burning to work with its defaults.
Optional: erosive burning overrides
The erosive burning override fields on the Propellant panel (beta, viscosity, Prandtl, surface temp, solid heat capacity, combustion temp) are meant to stay blank for most users - BurnSim derives reasonable defaults from the four numbers above. If your ProPep3 report includes a chamber/flame temperature and you'd rather pin BurnSim's Combustion temp override to that reported value instead of the derived one, you can, but it isn't required to get erosive burning working. Mukunda-Paul needs even less: it doesn't use C*, specific heat ratio or molar mass at all, and its only optional override, combustion-gas viscosity, isn't part of a standard ProPep3 report - leave it blank and BurnSim uses its nominal default.
Determining Burn Rate (a and n) from Test Data
To get the burn rate exponent (n) and burn rate coefficient (a) you need test data. Specifically, several burn rate / pressure data points. IE, at what rate does the propellant burn at various chamber pressures. A minimum of 3 data points must be used, more is better. The test data can be acquired through the use of a test motor. The design I use is a simple motor that uses 4" diameter end burning grains with interchangeable nozzles and a pressure transducer.
For a much more in-depth treatment of this whole topic - test motor design, strand burners, and the math behind fitting a and n - see Richard Nakka's Solid Propellant Burn Rate page.
You can also use a simple bates grain motor that is designed to keep the Kn as constant as possible, a strand burner, or other techniques. What is important is to get as accurate as possible data points.
Once you have those data points there are several options for getting your Burn Rate Exponent and Coefficent. I use a spreadsheet in Microsoft Excel. The spreadsheet uses some advanced features in Excel to match the data points to a curve and provided the necessary values. Some versions of ProPep will also do this data crunching for you.
In BurnSim 4
BurnSim 4 doesn't yet have an automated characterization tool that fits a/n directly from imported test data - you still need the spreadsheet or ProPep approach above. Once you have candidate values, the Test Data tab lets you import your test points and overlay them against a simulation using those values, so you can visually check the fit (or refine by eye) without leaving BurnSim.