This is a screen cap of the HR5 hybrid parameters from the Aestus launch.
I didn't try to make a hybrid burn simulator, I believe there are just too many variables in
hybrid design for across the board accurate burn simulations. Rather, this is a tool designed to make rapid design
changes, or scale a particular design.
A couple of basic design parameters I use is the throat area to injector area ratio. For most amateur designs, that ratio falls between 10 and 20 to 1. The next is oxidizer mass flux. Oxidizer mass flux is the mass of oxidizer flowing through a given port area, in this case it is defined as pounds of oxidizer per square inch of port area. Oxidizer mass flux is an important number since it is possible to literally "blow out" the flame in a hybrid engine. Peak oxidizer mass flux is usually considered to be around .8 pounds, again, that's .8 pounds per second per square inch of port area. Although that number is dependent on other factors such as fuel type, injector design and port design.
The calculator really has two separate functions. On the lower right side of the display is a tank calculator. The first box is tank diameter and should be in inches. The second box is tank length, again in inches. The last box is for N2O pressure in psi. Press the calculate button and the weight of the Nitrous Oxide in pounds and the N2O temperature are displayed. I'd like to thank Anthony Cessaroni for supplying the spread sheet for calculating N2O density versus pressure/temperature used in this calculator. Remember to use the measurements of the tank below the ullage vent if using such.
The main program input variables are in the upper left corner of the form. I'll go through each input separately.
Number of injectors: self explanatory
Injector Diameter: This assumes all injectors are the same diameter, value should be in inches. If using dissimilar injector sizes, you could calculate the total injector area of all injectors, calculate the diameter of a single injector of that area and still use the calculator.
Port Diameter: This is the diameter of the fuel core or port in inches. This assumes a single port configuration.
Fuel Grain Diameter: Again in inches and for a single port design.
Throat Diameter: self explanatory
Injector Cd: This is the discharge coefficient of the injectors. This is an area I've never been able to get a formula to work well with actual data. I've found using .7 for the injector Cd and a pressure drop of 100 psi gets me close. This assumes N2O density at 75 degrees F.
Pressure Drop: This is the drop in pressure in psi across the injector. While a value of 100 psi works with most of my designs, in actual tests the pressure drop is much greater. If you have real data from testing, you can work the Cd and pressure drop to output the flow rate you actually have.
Once all fields have been filled in, you may press the calculate button. I'll go through each of the output values.
Injector Area: is the total surface area of injectors in square inches.
Throat Area: Surface area of the throat in square inches.
Fuel Web: Thickness of a cross section of the fuel grain in inches.
Ox. Mass Flux: This the the weight in pounds of N2O flowing over 1 square inch of port area in one second.
Flow Rate/Fuel Area: This is the pounds of N2O flowing past a square inch of fuel grain area in one second. It neglects the fuel grain ends.
Throat/Injector Ratio: This is the ratio of throat area divided by the total injector area.
Port/Throat Ratio: This is the area of the port divided by the area of the throat.
N2O Flow Rate: This is the flow rate in pounds per second.