Port-to-Throat area ratio and erosive burning question...

[Tad]

I've learned that just because you know the answer to a question doesn't mean you know why that answer is correct or best. So, I know that the Port-to-throat area ratio should be kept around 2.0 to 3.0. I know that less than that can cause "erosive burning". What I don't know is why exactly is erosive burning undesirable and usually avoided in design. Other than having a less efficient burn, are there real dangers to low ratios like 1.3 - 1.5? Can this create an environment for a CATO from things like grain cracking or other spikes in chamber pressure due to increase surface area burning? In summary, why exactly do we avoid low ratios and erosive burning?

Thanks,
Tad

 

[Antares JS]

I've learned that just because you know the answer to a question doesn't mean you know why that answer is correct or best. So, I know that the Port-to-throat area ratio should be kept around 2.0 to 3.0. I know that less than that can cause "erosive burning". What I don't know is why exactly is erosive burning undesirable and usually avoided in design. Other than having a less efficient burn, are there real dangers to low ratios like 1.3 - 1.5? Can this create an environment for a CATO from things like grain cracking or other spikes in chamber pressure due to increase surface area burning? In summary, why exactly do we avoid low ratios and erosive burning?

Thanks,
Tad

I can't speak to low ratios exactly off the top of my head, but erosive burning means that hot gas rushing by the propellant causes the propellant to burn faster than normal, which leads to more combustion gas, which leads to pressure spiking, which leads to CATO's.

 

[AeroTech]

I've learned that just because you know the answer to a question doesn't mean you know why that answer is correct or best. So, I know that the Port-to-throat area ratio should be kept around 2.0 to 3.0. I know that less than that can cause "erosive burning". What I don't know is why exactly is erosive burning undesirable and usually avoided in design. Other than having a less efficient burn, are there real dangers to low ratios like 1.3 - 1.5? Can this create an environment for a CATO from things like grain cracking or other spikes in chamber pressure due to increase surface area burning? In summary, why exactly do we avoid low ratios and erosive burning?

Thanks,
Tad

We like to stay above 1.25:1

 

[prfesser]

Consider a motor casing is rated at a maximum pressure of 900 psi. A motor for this casing is designed to produce 850 psi. If the design for that motor has an area ratio of 3.0, odds are pretty good that the pressure will remain at around 850 psi. If instead the motor was designed with an area ratio of 1.25 there is likely to be a rapid unplanned disassembly. As Antares JS posted, erosive burning will cause a pressure spike.

So how can Aerotech motors use area ratios as low as 1.25? Undoubtedly the erosive burning properties of their propellants have been carefully determined. They can design a motor knowing just how much and how long of a pressure spike will occur. The motor would be designed so that the spike is still below the maximum pressure that the casing can handle.

Personally, I don't characterize my propellants that thoroughly. I just design motors with higher area ratios. If I really want to go to a low area ratio, initial motors are NOT tested on the thrust stand. I've had more experience ruining thrust stands and load cells than I care for...

 

[aerostadt]

Standard calculations for chamber pressure versus time and/or thrust-time curves usually depend on the burn-rate power law. So, if it your propellant is well characterized with a known burn-rate power law, you can make reasonable predictions for the burn-rate and consequently chamber pressure and thrust time-curves, if you don't have erosive burning. If you have the size of the port area close to the throat area, the bore gas velocity is going to be high and the heat transfer to the propellant is going to increase and consequently the burn-rate is going to increase. Conceivably, if you have propellant well characterized for erosive burning, it might be possible to design things to account for the erosive burning. Otherwise, just using the standard burn-rate power law for predictions is going to give wrong pressure predictions that might be disastrously too low.

 

[Tad]

I can't speak to low ratios exactly off the top of my head, but erosive burning means that hot gas rushing by the propellant causes the propellant to burn faster than normal, which leads to more combustion gas, which leads to pressure spiking, which leads to CATO's.

That is exactly my question. Does erosive burning "cause the propellant to burn faster than normal"? You are saying, "yes it does." That would definitely lead to pressure spikes and CATO's.

 

[Tad]

Consider a motor casing is rated at a maximum pressure of 900 psi. A motor for this casing is designed to produce 850 psi. If the design for that motor has an area ratio of 3.0, odds are pretty good that the pressure will remain at around 850 psi. If instead the motor was designed with an area ratio of 1.25 there is likely to be a rapid unplanned disassembly. As Antares JS posted, erosive burning will cause a pressure spike.

So how can Aerotech motors use area ratios as low as 1.25? Undoubtedly the erosive burning properties of their propellants have been carefully determined. They can design a motor knowing just how much and how long of a pressure spike will occur. The motor would be designed so that the spike is still below the maximum pressure that the casing can handle.

Personally, I don't characterize my propellants that thoroughly. I just design motors with higher area ratios. If I really want to go to a low area ratio, initial motors are NOT tested on the thrust stand. I've had more experience ruining thrust stands and load cells than I care for...

Thank you, Prfessor. That really sums it up....and explains the loss of my test stand.
On Burnsim, I paid more attention to keeping my Kn values in check and not so much my area ratio. no bueno. Lesson learned.

 

[Tad]

So, if it your propellant is well characterized with a known burn-rate power law, you can make reasonable predictions for the burn-rate and consequently chamber pressure and thrust time-curves, if you don't have erosive burning.

Yep. I have good data on my propellant but didn't take into account erosive burning. Totally explains it. At least I know what I gotta do....or not do. Thank you very much, Aerostadt

 

[manixFan]

Great thread. It's stuff we know, but sometimes hard to put it all into context. And having just built a new test stand, I'd sure like to not have to replace it right away.

I really think I need to go back and review a lot of the basic principles like this one, it's been a while, and exactly like the OP, I may know the what, but not always the why. I believe knowing the why leads to far better decision making than just relying on a general rule of thumb. I need to refresh a lot of the underlying principles of motor design.


Tony

 

[prfesser]

Thank you, Prfessor. That really sums it up....and explains the loss of my test stand.
On Burnsim, I paid more attention to keeping my Kn values in check and not so much my area ratio. no bueno. Lesson learned.

's'ok, I and my mentor have ruined at least four load cells and completely destroyed one test stand.

The most frustrating occurrence involved a white-smoke propellant. Single 54 mm grain not on the test stand, Kn a bit above 200 if memory serves. Perfect burn. Three grain 29 mm at Kn of about 280. Perfect burn. Repeat of first motor, same case, same nozzle cleaned up, same Kn of course, one grain of the same weight from same batch. Instant blooey. Nozzle went that-a-way---never found it. Case split open. Grain went rolling down a hill, burning merrily with copious white smoke as it tumbled. Found some parts of the load cell, so we had that going for us. <insert wry grin> Sometimes sh..... stuff just happens.

Best -- Terry

 

[aerostadt]

When Thiokol went from the 4-segment SRB to the 5-segment SRB (used on the SLS), they knew that erosive burning would be an issue on the aft segment, because the bore velocity would be getting higher than a regular 4-segment booster (used on the Space Shuttle). They did a CFD computer study and sub-scale testing to find out how erosive burning would change things.

 

[jsdemar]

There are a few deeper discussions of erosive burning in the Research forum.

Also, here's something I wrote up in 2007.
https://thrustgear.com/topics/erosiveburn.htm

 

[Tad]

's'ok, I and my mentor have ruined at least four load cells and completely destroyed one test stand.

Grain went rolling down a hill, burning merrily with copious white smoke as it tumbled.

Best -- Terry

OMG, I hate that I know exactly what that looks like....LMAO!!

Take comfort in knowing it didn't happen on a $250 rocket....

 

[CaptHaywire]

There are a few deeper discussions of erosive burning in the Research forum.

Also, here's something I wrote up in 2007.
https://thrustgear.com/topics/erosiveburn.htm

I found the document very helpful, thanks!

 

[Tad]

There are a few deeper discussions of erosive burning in the Research forum.

Also, here's something I wrote up in 2007.
https://thrustgear.com/topics/erosiveburn.htm

jsdemar,
Yes, I read your write-up. Very useful. I was going for a single 22 inch grain x 3 inch with a 1 inch core and .95 nozzle. It worked on the test stand but failed on the rocket. My port-to-throat ratio was pretty low. Should've known. Great info. Thanks.

 

[aerostadt]

As I recall engineers would become concerned when the Mach number got around M=0.3 to M=0.5 for erosive burning. An estimate of when this occurs can be made by looking 1-D isentropic compressible flow (and perfect gas). The area ratio, i.e., the cross-sectional flow area to the throat, A/A*, is only a function of the specific heat ratio and the Mach number.
https://www.engineering.com/calculators/isentropic-flow-relations-calculator/For M=0.3, A/A*=2.08 and for M=0.5, A/A*=1.35 (use a specific heat ratio for solid propellant of about 1.14 to 1.20 commonly called gamma or k). So, when the cross-sectional bore area (going into the convergent nozzle) is within about twice the throat area, erosive burning is a concern. Ignore angle and use Mach number as input for the calculator.
In contrast M=0.003 gives a area ratio of about A/A*=200. This is what experimental solid rocket people call Kn or the ratio of the burning propellant surface area to the throat area. As can be seen the off-gassing mach number for a typical solid rocket motor is very low.

 

[Chuck Rogers]

I wrote an extensive technical article on this subject, published in High Power Rocketry magazine.

Erosive Burning Design Criteria for High Power and Experimental/Amateur Solid Rocket Motors, by Charles E. Rogers, High Power Rocketry magazine, Vol. 36, No. 1, January 2005, pages 16-37.

It can be downloaded as a pdf file from the RASAero web site ( www.rasaero.com ).

Go to Technical Report Downloads on the left.

Go to the Solid Rocket Motor page.

Go to Erosive Burning Design Criteria for High Power and Experimental/Amateur Solid Rocket Motors

and you can download a pdf of the technical article.


Charles E. (Chuck) Rogers
Rogers Aeroscience

 

[aerostadt]

Wow! A lot of information can be found there.

 

[Chuck Rogers]

Tad said:

<< I've learned that just because you know the answer to a question doesn't mean you know why that answer is correct or best. So, I know that the Port-to-throat area ratio should be kept around 2.0 to 3.0. I know that less than that can cause "erosive burning". What I don't know is why exactly is erosive burning undesirable and usually avoided in design. Other than having a less efficient burn, are there real dangers to low ratios like 1.3 - 1.5? Can this create an environment for a CATO from things like grain cracking or other spikes in chamber pressure due to increase surface area burning? In summary, why exactly do we avoid low ratios and erosive burning?

Thanks,
Tad
>>

We like to stay above 1.25:1

From Figure 8 of the technical article, based on Core Mach Number:




Charles E. (Chuck) Rogers
Rogers Aeroscience

 

[tfish]

From Figure 8 of the technical article, based on Core Mach Number:

View attachment 497643


Charles E. (Chuck) Rogers
Rogers Aeroscience

Tony

 

[AeroTech]

Tad said:

<< I've learned that just because you know the answer to a question doesn't mean you know why that answer is correct or best. So, I know that the Port-to-throat area ratio should be kept around 2.0 to 3.0. I know that less than that can cause "erosive burning". What I don't know is why exactly is erosive burning undesirable and usually avoided in design. Other than having a less efficient burn, are there real dangers to low ratios like 1.3 - 1.5? Can this create an environment for a CATO from things like grain cracking or other spikes in chamber pressure due to increase surface area burning? In summary, why exactly do we avoid low ratios and erosive burning?

Thanks,
Tad
>>



From Figure 8 of the technical article, based on Core Mach Number:

View attachment 497643


Charles E. (Chuck) Rogers
Rogers Aeroscience

Thanks, Chuck.

 

[G_T]

It's late and I apologize I've only skimmed some of the posts. So I'm probably echoing what has already been said.

My standard design port to throat area ratio limit which I don't cross is 1.2, for motors up to baby O. That's with 7 grains plus a tablet with the bottom two tapered for mass flux reasons, for an N. I'd stay a tad bit higher than 1.2 for larger motors, and recommend staying higher for shorter motors. But that's with my formulas, my manufacturing, my geometry, my ignition, etc. YMMV.

Anyway I'd be paying more attention to the mass flux and/or port velocity for erosive burning than worrying overmuch about the port to throat ratio.

The latter mostly has to do with forming a choke point so that the motor will pressurize and the flow will go transonic through the pressure differential in the throat of the nozzle. If the flow doesn't go transonic/supersonic in the throat then the expansion portion of the nozzle will act to decelerate the flow rather than accelerate it. You get a road flare. Ratio too close to 1.0 and there isn't much of a choke so you might not get pressurization the way you want it to happen, until the core opens up during the burn. Startup can be (possibly) made softer that way if you really want to, but you're wasting propellant that isn't making the rocket go anywhere.

Gerald

PS - For those that don't know, a convergent tube acts to accelerate a subsonic flow (with corresponding pressure drop) and decelerate a supersonic flow (with corresponding pressure increase). A divergent tube acts to decelerate a subsonic flow and accelerate a supersonic flow. Hence the shape of the common rocket nozzle. You want to make all that mass of propellant fly out the back as fast as practical!

 

[Chuck Rogers]

Anyway I'd be paying more attention to the mass flux and/or port velocity for erosive burning than worrying overmuch about the port to throat ratio.

Gerald:

Actually, I believe the best approach, which I used in the technical article, is a combined Core Mach Number/Core Mass Flux Erosive Burning Design Criteria, explained in the figure below for motors with constant diameter cores (Figure 8 in it's entirety from the technical article).



Charles E. (Chuck) Rogers
Rogers Aeroscience

 

[Chuck Rogers]

And then for increased propellant loading (increased total impulse for a given motor case size), a Constant Core Mass Flux Design can be used. (Figure 9 from the technical article in it's entirety.)



Charles E. (Chuck) Rogers
Rogers Aeroscience

 

[G_T]

I routinely use the latter.

Gerald

 

[jsdemar]

And then for increased propellant loading (increased total impulse for a given motor case size), a Constant Core Mass Flux Design can be used. (Figure 9 from the technical article in it's entirety.)

Opening the aft grain(s) to reduce mass flux and/or increase the port-to-throat is a simple, workable approach. Good rules-of-thumb to keep from having a bad day. But, it doesn't necessarily optimize the volume loading.

Making the Bates grains longer or inhibited some faces will reduce the burn surface (and therefore mass flux) without losing propellant. The thrust curve will become more progressive, though. This might be ok for a sustainer, but not for a booster.

To increase volume loading while avoiding erosivity requires grain geometries other than Bates grains if you need a high initial thrust. It's a balancing act between maintaining a >1.3 port:throat ratio and not exceeding the max pressure of the hardware.

Some people make use of the initial high mass flux to provide a thrust spike for a strong initial boost. This requires knowing a lot about your propellant and your process. Personally, I avoid that trick.

My approach is to use one or more finocyl grains at the nozzle end along with inhibiting some grain faces. The top grain face is a good candidate because it helps prevent heat transfer into the forward closure. Using Burnsim with several iterations can help tune the shape of the thrust curve while checking throat-to-port and mass flux. Keep in mind that Burnsim doesn't correctly simulate finocyls! It's fairly close but has step transitions in the curve that aren't there in reality.

 

[jderimig]

Making the Bates grains longer or inhibited some faces will reduce the burn surface (and therefore mass flux) without losing propellant. The thrust curve will become more progressive, though. This might be ok for a sustainer, but not for a booster.

I beg to differ. If you mean that a progressive burn MIGHT NOT be ok for a booster, I can agree with that. But generalizing that progressive burning motors are not ok for all boosters I think is wrong. I hope so, because that is what I am planning to do. Back to my Moscow Mule.

 

[jsdemar]

I beg to differ. If you mean that a progressive burn MIGHT NOT be ok for a booster, I can agree with that. But generalizing that progressive burning motors are not ok for all boosters I think is wrong. I hope so, because that is what I am planning to do. Back to my Moscow Mule.

Yes, might not be ok. Thrust-to-weight off the pad, velocity out of the rail, gravity turn on a longer burn, etc.

 

[Chuck Rogers]

My approach is to use one or more finocyl grains at the nozzle end along with inhibiting some grain faces. The top grain face is a good candidate because it helps prevent heat transfer into the forward closure. Using Burnsim with several iterations can help tune the shape of the thrust curve while checking throat-to-port and mass flux. Keep in mind that Burnsim doesn't correctly simulate finocyls! It's fairly close but has step transitions in the curve that aren't there in reality.

John:

The only thing to watch is that a finocyl grain has a higher grain complexity factor than a grain with a cylindrical core.

From the technical article (Pages 19 and 20 of the pdf);

Grain Complexity Factor:



A finocyl grain will have a higher grain complexity factor than a grain with a cylindrical core. Thus a finocyl grain will have higher erosive burning than a grain with a cylindrical core for a given core Mach number and core mass flux. Because of this, if possible, separate erosive burning characterization tests should be performed for finocyl grains.


Charles E. (Chuck) Rogers
Rogers Aeroscience

 

[jsdemar]

A finocyl grain will have a higher grain complexity factor than a grain with a cylindrical core. Thus a finocyl grain will have higher erosive burning than a grain with a cylindrical core for a given core Mach number and core mass flux. Because of this, if possible, separate erosive burning characterization tests should be performed for finocyl grains.

I understand the "complexity factor" as a general principle, but a basic slotted bates grain isn't very complex. There will be some turbulent flow until the burn-back smooths the edges (milliseconds?).



Keeping the grain above this one as a simple Bates with the same core diameter will minimize the initial exposure of the "fins" to erosive flow.

I've made a full 6" O5800 and a "small" 6" Q12000 with this grain design. Initial mass flux for the Q was around 2.7 and the O was 1.8. Only a slight indication of an initial erosive "bump" on the Q.

Often, Burnsim will report that the second from the bottom grain has higher mass flux than the bottom finocyl.

Other factors people should keep in mind are:

• Temperature of the propellant just before flight will increase the burn rate and therefore the initial mass flux.
• Burn rate increases when under acceleration (and spin rate). A static test without significant erosive burning may have a significant amount at liftoff, possibly causing a CATO. Other macro scale failures in the grains (shearing, cracking) may also show up in flight and not on the test stand.