This program was initially set up in order to study the influence of erosion in KNO3-sugar motors in comparing thrust measurements with simulations, but it can also be used to predict the functioning of the motor under different limiting conditions like heavy erosion, or no erosion at all.

In this program a number of parameters and different erosion models can be set. Proper simulation should lead to a number of conclusions about the proper functioning of the motor like initial ignition of the burning surface, surfaces which did not burn at all, the magnitude of erosion, but also about the efficiency of the motor.

3 different erosion models are used:

Velocity based model: rb = 1 + erosion (V - Vcr)ⁿ

Mass rate based: rb = 1 + erosion (G - GcR)ⁿ

PVR (or R) based: rb = 1 + erosion (R - Rcr)ⁿ

This means that we start from the assumption that only one critical value exists for V, G and R (in the program called CRV or critical value). In reality this may not be the case. Some models like the Sanderholm model use more than one critical value depending on the Mach number. The erosion formula also uses an exponent "n", of which the value is unknown but usually smaller than 1. In order not to complicate the simulation with too many variables, it was decided to limit the number of critical values to one and to set "n" equal to 1.

Although in the program a large number of variables are calculated many of these variables are not shown in order not to overload the program and keep things practical,.

The total propellant grain (sum of all segments) is divided into 200 equal parts along the axis. At any time during the calculation the following variables are calculated in each of these sections:

- the mean velocity of the gases

- the burning rate

- the pressure

- the inner diameter

- the burning surface

- the slope of the burning surface.

How to use the program:

1. all data are metric (except the erosion data).

2. Under the heading "INPUT" a number of data should be put in. Essentially "Motor Data" and "Erosion Data".

"Motor Data" like the max diameter of the grain, minimal diameter, density of the propellant, diameter of the throat, Ae/At (ratio of nozzle exit area to throat area) , the length of one segment (it is supposed that all segments have the same length). The number of segments limited to 6.

"Erosion Data". The performance of the motor can be calculated with or without erosion. To this end a choice between PVD based (pressure * velocity *diameter) ; velocity based or mass rate based as the basis for the calculation of the erosion, is possible. PVD is default. In any case one type must be selected even if no erosion is to be taken into account. In the letter case the erosion data "<CRV", ">CRV" should be put "0".

If erosion is taken into account than following values have to be filled in:

- "CRV" this the critical value for PVD, velocity or mass rate. Below this value the erosion is "0" or modest. Above CRV erosion is in general much higher.

- "<CRV" is the erosion factor when PVD, Velocity or Mass Rate, is below the critical value

- ">CRV" is the erosion factor when above CRV.

- "MaxErosion" limits the maximum burning rate. The idea behind it is that a burning rate cannot be unlimited. The default is 10

- "rbCorrb" is a correction factor which can be applied to the burning rate. Depending on factors like grain size, grain distribution, quality of the ingredients, temperature,... the burning rate can be faster or smaller (independent of any erosion).

In the PVD mode the CRV value is divided by 10⁶ to avoid the introduction of large numbers. For KNSUSB, CRV is around 8 (actually 8.000.000), while for KNSB it is around 15 (15.000.000). For KNSU the figure is expected to be very low.

In the velocity mode CRV is in the order of 10 to 150 m/s.

5. The propellant of choice should be selected under the subheading "Propellant Data". The Propellant data contains all necessary thermodynamical properties as calculated by PROPEP and the strand burning rates as a function of pressure measured by Nakka ( http://www.nakka-rocketry.net ) with the exception of KNSUSB, which was derived from motor tests.

6. Normally a correction for the calculated Cf and Ccar factors is needed. Values between 0.9 and 0.95 seem appropriate. "etaCcar" deals with the chemical efficiency and heat losses, while "etaCf" deals with the efficiency in the nozzle. It should be noted that lower values for "etaCcar" will lower the calculated pressure and hence the burning rate.

7. The program also allows you to influence the time increment at which the calculation is performed. "InitTimeIncr" holds till t = 0.2 s, while the "SecTimeIncr" can be used post t = 0.2 s. Larger numbers will allow faster calculation. However essentially during the first period the calculation may fail if the time increment is too small (pressure may drop to too low values). In general the default values are a good compromise.

8. It is also possible to set the "Initial Pressure" or diaphragm burst pressure. They may influence the behavior of the motor. Too low pressures may lead to a failing calculation (same problem as explained under pt.7.)

9. When evaluating a measured thrust curve there is a need to recalculate over and over again with changing values. It then becomes difficult to distinguish several curves. To this end the program allows to change the "color" of the graph. Only values between 0 and 16 are allowed (QBcolor)

10. When the thrust window becomes too overloaded it is possible to clean it with "CLS" during the next run.

12. Values of the thrust measured during a test, can be filled in under "Measured Thrust". It is limited to 10 different values. In general this is sufficient to compare simulation with measurement.

13. The second window provides the evolution of the burning surface with time. Max and Min radius are already fixed, "LineDistance" can be changed. It allows to have the burning surface lines closer or more apart. Normally "50" is a good figure for burning times of about 3 to 4 s. These lines are generated after a constant time interval depending on the Line distance setting.

14. Important inputs are dealing with the "Surface Ignition Settings". The Initial burning surface at ignition "InIgn" for on one hand the core (C) and on the other hand for the bottom and top surfaces (BT) of the segments, can be set. It expresses the fraction of the surface that is ignited at t = 0. When IgnFacC or IgnFacB(T) is put 1, then all surface is ignited at t = 0. On the other hand "IngFac" gives the rate at which 100% of the surface will get ignited. It can range from "0" till very high values. 3 or 5 are normal, but also 0.2 is possible. The real time to 100% surface ignition is (1- InIgn) / IgnFac.

15. OUTPUT gives the total propellant mass or "Mb out", the efficiency of the nozzle expansion ratio Ae/At "Ae/At eff" and the "exhaust velocity" realized.

"Mb out is important since due to strong curvature of the burning surface by strong erosion, the calculation yields an error and a deviation from the measured amount of propellant is likely. When no erosion is applied this figure must be equal to the measured one (unless in input wrong like the density of the propellant). "Mb out" can and should be adjusted in changing the propellant density until both (measured and calculated) are equal.

"Ae/At eff" : this figure is that ratio between the results stemming from the simulation based on the actual Ae/At value, compared to an Ae/At which is always perfectly adapted (Pe = Pa or atmospheric pressure). The letter is the maximum that can be reached at atmospheric pressure at sea level conditions. In changing "Ae/At" in the input for the motor data, the best suited Ae/At for that specific simulation (highest efficiency) can be found.

Another output is the "exhaust velocity". This allows comparison with the measured one (any deviation in propellant mass as calculated is taken care of !). If the calculated exhaust velocity is too high it may mean that Ccar or Cf is too high, and that etaCcar and /or etaCf must be adapted.

The program can be downloaded from our Library .