Hey Josh, very nice video! I am doing my masters in Mechanical Engineering, and I've been struggling with the course of turbomachinery, since I did not have a very solid base in aerodynamics. However, following your channel I've been able to understand many things, and has allowed me to pass the course recently. Just wanted to thank you for your altruism in sharing your knowledge with us, and encourage you to never give up on that, it is highly appreciated. Cheers man!
I couldn't get Science subject due to no vaccancy. But I've always been enthusiastic for Science. And Rocket Science is something that I wanted to study for a long time and eventually I got u as a Fantastic teacher of Rocket Science
Thanks for the video! I'm writing code for a college project that finds mach numbers before and after the throat based on different area ratios, and this video really helped. It makes much more sense now!
thank you Sir , all my respect , you are the best instructor ever seen on youtube A question please : in all the video , you have considered inlet flow as subsonic , but what happen if the inlet flow is supersonic ?
then the converging part is a supersonic diffuser: P increases and V (and M) decreases until a normal shock in the throat, then the diverging part is a subsonic differ: P further increases and V decreases until the compressor face. That is, if all the ratios etc. are good. If not then it unstarts, the normal shock goes out the left side, and the whole thing is subsonic.
Hi Josh.. Can you please explain the relation between under expansion, over expansion to Pressure thrust. Like pressure thrust is zero when pe equals pb but there are two conditions when these are not equal over expansion and under expansion. Please elaborate this concept.
Great video! I just had one question. How is it that we control the Back Pressure? For example, a rocket has its combustion chamber that goes into the converging side of the nozzle with a certain pressure that then is choked and then shot out into the air... so when you say controlling the back pressure how is it that you are controlling the air. Sorry if its a dumb question but I think its critical to me understanding how rocket propulsion works with CD nozzles.
Thank you! If you are making a model rocket, for instance, then the back pressure is determined by the atmospheric pressure, and will decrease as you increase in altitude. If you are testing in a wind tunnel, then you can use a pump to decrease the ambient pressure in the tunnel. I just said that we controlled it because it helps simplify the explanation, but in reality, the back pressure is whatever the atmospheric pressure is.
If you are actually trying to machine one of these things a pair of straight tapered cones can closely approximate the smooth curves. Start with a 60 deg half angle (120 deg total) to from the combustion chamber diameter to the throat diameter. The expansion angle should be 7.5 Dec. (15 dag total) to half the diameter of the combustion chamber. Smooth the transitions between the converging and diverging sections of the nozzle. Of course this engineer has provided a method of actually calculating the diameter of the throat.
In most cases, that's dictated by the atmospheric pressure where the nozzle is operating. If you're on the ground, it's the air pressure at the ground. If you're at 10 kilometers, it's the pressure at 10 kilometers. You can also operate an engine in a vacuum chamber during testing, for instance, where the back pressure would be the pressure you can achieve in the chamber after pumping down.
How the normal shock which spike's up the pressure instantly .... affects Pe of the nozzle... will it overpower Pe and be a criteria to compare with Pb subsequently
Great video, When you say 'pull the back pressure down' what real world mechanic is doing this? does the pressure drop just because the rocket is increasing in altitude? or is the pressure dropped by increasing the exit area?
Right, the back pressure is dropping because the rocket is increasing in altitude. When I need a quick pressure for a calculation I'll use the Standard Atmosphere table on Engineering Toolbox. A lot of fluids books also have these tables. You can also drop the back pressure in a wind tunnel test by pumping the tunnel down closer to a vacuum to simulate higher altitudes.
Sir , we overexpand pressure in the order to decrease pressure caused by normal chock . You have said that we decrease Pb . But do you think that we can control Pb ? I think that we can only control Pe , because Pb is the atmospheric exterior pressure
Thank you Josh for your clear explanation videos about the topic👍 I still have a question though, about the thrust formula : F = m_dot*Ve + (Pe-Pb)*Ae What is the Exit velocity (Ve), the Exit Pressure (Pe) and the Exit Area (Ae)? Is it at the end of the nozzle in all 7 cases ? Just before the normal shock ? Or just after the normal shock ?
Also works with magnetically confined plasma initiated with Townsend avalanche ionization of gasses and even Directed solar wind plasma. Although conventional rocket exhaust is technically plasma but humans still using mechanical constriction that require cooling system without gigavolt plasma accelerators to boost thrust.
Yes, divergent area depends on pressure at a range of altitudes. Pe is a know value for each stage of the rocket, since it's the atmospheric pressure at different altitudes.
Thank you! If the flow is supersonic in the converging section, then the gas will actually slow down as it reaches the throat. I go through this in more detail in my 'Area-Mach Number Relation' video.
so another way to say P sub b ... is the air pressure not modified by the engine ... . Question - assuming it is a jet engine ... and they are mounted so that P sub e is under the flow from the wings does the air flow from the top of the wing and the bottom of the wing have a minimal effect, marginal effect or considerable effect ... how would one go about relating these 3 options to determine if any effect from the wing airflow is additive subtractive or negligible ... because ambient air at the exit of the nozzle isnt exactly ambient due to air flow and turbulence around the body being looked at ... there will be some effect and we cannot be certain it isnt adding subtracting or not worrisome ... also if one modifies the flow of air through the engine into a hyperbolic flow (larger volume output for a given unit of time Viktor Schauberger hyperbolic flows cone ideas) how might that change the output overall of the engine
still I strongly suggest slow your speech down a tad ... playing the video at 75% helps but speaking slower and not racing through the material would be better ... listen to the video real time and then relisten at 75% ... and see what I mean ... after all you have 4 hours of stream time to get it in
Hey Josh its like i have found something BRILLIANT thanks for foing such a great Social Work Just started my BS Space Sc One Childish Qustions if u have time ( i am an amature) I have been studying till now that when we decrease area presure Increases where as i found you explaining it decrease when leaving A* ?
My pleasure, and good luck with your studies! The simple answer to your question is that it depends. Now let's get into the longer answer. Ignore the variable A* for now. Whether the pressure decreases or increases with a certain change in area depends on whether the flow is subsonic or supersonic. If you go to about 5:11 in this video (goo.gl/RdW3nE), I talk about the area-Mach number relation, and how the results from the equation change from subsonic to supersonic flow. For subsonic flow, as we decrease the area, the flow speeds up and the pressure decreases. This is the normal result that you will see or have seen in fluid dynamics courses that don't cover compressible flow. This is why you always see the pressure decrease in the converging section on the plot I've drawn. The converging section is always subsonic. Now if the flow in the diverging section is subsonic, then as the area increases, the flow slows down and the static pressure increases. This is what you see on the plots for case 1 in the diverging section. For supersonic flow in the diverging section, as the area increases, the flow actually speeds up further, and the static pressure decreases. This is the opposite of what happened with subsonic flow. When it comes to how area change affects velocity, and thus pressure, subsonic and supersonic flow are basically opposites. The concept of A* is not needed to understand what happens to static pressure in a subsonic or supersonic flow where the area is changing. All you need to understand is the area-Mach number relation (again, see the video I linked to before). I'll probably make a video going into more depth on A* because it can be confusing, especially for flows that are non-isentropic. But for now, I hope that helped answer your question.
What happens if we reduce further the throat area once the gas is choked, considering a low pressure at the exit ? Does it remain at M=1 while increasing its pressure ? Why do rockets never have throats area below the strict necessary to choke the flow ? BTW, awsome job.
Thanks! The quick answer is that the flow will still be choked, and all you will get is a reduced mass flow rate which will effectively decrease your thrust. Let's say that we're at a condition that is choked, and we keep the reservoir and back pressure fixed from now on. All we will do is change the throat area. We know from the area-Mach number relation that the only location we can have sonic flow is at the throat. If we decrease the throat area, the flow is still choked, and the location where the flow is sonic still has to be at the throat. This is important because while the throat area (A* = At for choked flow) has decreased, the throat pressure, throat temperature, etc. are still the same values they were before (P*, T*, etc.). The mass flow rate can be computed by taking the product of the throat density (rho*), throat gas velocity (u*), and the throat area (A*). The density is a function of the pressure and temperature, which haven't changed. The velocity is a function of the temperature, which hasn't changed. The only thing that has changed is the throat area, which we have decreased. This shows that the mass flow rate will decrease with a decrease in throat area. From my Nozzle Mass Flow Rate video (ruclips.net/video/aMTmRCdmvVQ/видео.html), we can see this result in a slightly more useful form for rockets, which gives the mass flow rate as a function of reservoir pressure, reservoir temperature, throat area, specific heat ratio, and specific gas constant (P_0, T_0, A*, gamma, and R). The trend is the same (as it should be since it's derived from the same equations we talked about before), where since we are keeping the reservoir conditions constant and just decreasing the throat area, we get a decrease in the mass flow rate. From my Turbojet Thrust Equation video (ruclips.net/video/aNyYxVHBSWQ/видео.html), you can see that the mass flow rate is a really important part of the total thrust of an engine (neglect u_a for a rocket), so we don't want to decrease it if we're interested in increasing thrust. For a similar computation, see my Afterburner Nozzle video (ruclips.net/video/YKCqyaYMSs8/видео.html). Hope that answers your question!
I think it totally does, the result is very clear based on the equations. From a physical point of view, I didn't have in mind the sonic flow could only be reached before the throat. If I understand correctly, in a continuously decreasing area section (a cone with a small hole at the end), whatever the static conditions at both ends, you will never reach M=1 before the moment the section diverges (here the end of the cone) ? Your flow cannot reach and remain at M=1 in a decreasing area tube ?
Right. This is why it's normally easier to think about nozzle choking using only a converging nozzle, which is what I do in my afterburner example video. If you want to dive a little deeper into this subject, you'll actually find that when you relax some of the assumptions used to derive the conservation equations, the M = 1 condition (also sometimes called the sonic line in the throat) will not be exactly at the minimum area location. It will be slightly curved out into the diverging section. But, this can't happen if you're assuming the flow is quasi-1D when deriving the conservation equations. If you want to look into this further, Google something like Sauer's method/solution for the sonic line. There's a good derivation in Zucrow and Hoffman's Gas Dynamics Volume 2, I believe.
The two main things you can do to get supersonic flow are (1) increase chamber (reservoir) pressure or (2) decrease the back pressure. The chamber pressure is based on the design of the engine, and the back pressure is basically set by the altitude your engine is currently at. That is, the back pressure will decrease as you increase in altitude.
The back pressure in most practical cases is just determined by the ambient pressure of the air. So as you fly higher in the atmosphere, the back pressure decreases. If you see rockets being tested on test stands (lots of videos on RUclips), they're probably just operating at about 1 atm, which means the flow will be overexpanded (in general). This is because a fixed nozzle design is only optimal (supersonic isentropic) at one back pressure (i.e. one altitude). Optimizing the nozzle design for 1 atm doesn't make sense, since presumably the goal of your rocket is to fly something to a higher altitude. If you want to test your engine at the design-point altitude without flying it, you can always put your engine inside a vacuum chamber that is capable of pumping down to whatever ambient pressure you want. This is harder than it sounds though, since right when you start the engine, it changes the pressure of the chamber due to the high mass flow through the nozzle.
@@adhithasimhanraghavan7516 Every nozzle has its own Po and Ae/At, so the Pe is fixed by design (in liquid rocket engines you can change Po by throttling up or down, in solid rocket motors the Po profile over time is predefined by the grain shape and isn't adjustable). Each nozzle is designed to work between Pbmax (ignition) and Pbmin (cutoff) since the atmospheric pressure drops exponentially with the altitude. So one wants to have a Pe that is between Pbmin and Pbmax, in order to avoid the normal shock and let the nozzle operate just in overexpanded (initially) and underexpanded (at the end) conditions. In fact the Pe is always chosen closer to Pbmax than to Pbmin, since the rocket accelerates and it spends more time at the lower altitude. The other reason for that choice is something that he didn't talk about: in real viscous flows the boundary layer can cause the flow to separate from the nozzle wall generating both major instability and loss of thrust. This problem usually happens when Pe is lower than ~0.3Pb, so you must avoid it. So the answer to your question is yes, the Po/Pb is predefined for each nozzle, but it's not a fixed value, it's a range (Po/Pbmax - Po/Pbmin) that must fulfil the conditions above in order for the nozzle to operate correctly.
I've never seen a person explaining the delaval nozzle this far. Genius man!
Thanks! Glad you like it.
I wish this channel existed when I was studying engineering
Well it's never too late to brush up on some of the really cool stuff!
JoshTheEngineer That’s why I’m here!
Well I'm glad to have you!
The first RUclips video that I don't have to play at 1.5 speed. Great work man
jaja
Ha, thank you!
Josh, thanks again, you way of doing this is way better than my grad lectures...
No problem! Best way to learn a topic is to get information from a bunch of different sources.
The way you organise the tutorial and the board is so fascinating
Thanks alot
Hey Josh, very nice video!
I am doing my masters in Mechanical Engineering, and I've been struggling with the course of turbomachinery, since I did not have a very solid base in aerodynamics. However, following your channel I've been able to understand many things, and has allowed me to pass the course recently. Just wanted to thank you for your altruism in sharing your knowledge with us, and encourage you to never give up on that, it is highly appreciated.
Cheers man!
Thanks for the kind words Juan! I'm doing my best to continue putting out videos!
Was uploaded 5 yr ago! Still helping people out, beauty of internet.
The whole explanation was clear and you made it so simple, thank you teach.
This is the best RUclips video I’ve ever seen. Been looking for a channel like this for a long time. Thanks man, keep putting out great content.
by far the best theoretical explanation of CD nozzles. Brilliant
I couldn't get Science subject due to no vaccancy. But I've always been enthusiastic for Science. And Rocket Science is something that I wanted to study for a long time and eventually I got u as a Fantastic teacher of Rocket Science
I'm glad to hear that, thank you!
Everything makes sense now! Thanks for the upload. Appreciate it.
Glad it clicked!
GOLD! I’ve struck GOLD! Thanks for the awesome video. Will certainly watch more.
Hey thanks!
I'm so happy that I found this channel. Thank you so much Josh
You're welcome!
Very detailed and accurate. A solid explanation!
Your channel has a bright future! Love it!
I certainly hope so! Thanks!
Thanks for the video! I'm writing code for a college project that finds mach numbers before and after the throat based on different area ratios, and this video really helped. It makes much more sense now!
No problem! I'm glad you found it helpful!
The best explanation I found for this topic. Thank you!
Thanks, I appreciate it!
I am learning Rocket Propulsion Elements now, and your video is really good to me. Thanks a lot!
I think I am pretty lucky XD.
Everything spoken fluently, straightforward yet detailed. Brilliant
Thank you!
You explain with security, that's very good. Thanks for the video.
Thank you for this excellent explanation!
Thank you so Much Josh! Sending you lots of love from Milan, Italy!
Brilliant explanation. Will be pointing my students in this direction, for sure.
Thanks Dan, appreciate it!
Consider thousands of likes from my side...
Damn youtube, it only permits one like, but you explained it excellently
I appreciate it!
Thank you so much for this video!! Loved it. Really helpful for my exams :)
Glad to hear it helped!
Amazing work.
I'm currently developing a Hybrid rocket engine and this video helped to bring clarity to my understanding thank you!
That's great!
Your tutorials are way better than those of my professors here. All the very best for your channel!! Love from Hong Kong
Thank you!
Good lord this was insightful. Gas Dynamics final at 8:00 am tomorrow.
Thanks! Hope it went well.
Simply, thanks.
you did help me understand this topic clearly, thank you for that.
You're welcome!
This is a brilliant video. Thank you so much.
You're welcome!
Thank you, brother. Many doubts cleared.
Awesome!
This is very helpful! Thank you
You're welcome!
Excellent video, massive help
Thank you!
This really helped me!
Keep up the great work! Cheers man :)
Thank you, I'll try!
Definitely it was an awesome lecture for me. Thanks for your teaching and also your charming eyes.
You're welcome!
Excellent video, greetings from Mexico.
Thanks! Good to see other countries here.
I really en joyed that. Thanks!
Thank you!
have been watching your video just for a few minutes and i already love you, uff... love from italy
Thanks!
Thanks. Your explain is very good.
Thank you!
Thank you for the video
Far superior to my lectures, this was amazing
Thanks!
Great explanation!
Thank you!
Sir, your channel is astonishing. Thanks for your hard effort to explain aeronautical-related topics!
Thanks, that means a lot!
Normally I never give up-vote, but here I also have to subscribe
Thanks, I appreciate it!
think you very much, I need this lecturer in PDF
thank you josh the engineer you are my hero
Glad I could help!
thank you. very helpful !!
You're welcome!
Very 'very' cool man!!!!
Thanks a lot .. you explained very well
Thanks
You're welcome!
thank you Sir , all my respect , you are the best instructor ever seen on youtube
A question please : in all the video , you have considered inlet flow as subsonic , but what happen if the inlet flow is supersonic ?
scramjet
then the converging part is a supersonic diffuser: P increases and V (and M) decreases until a normal shock in the throat, then the diverging part is a subsonic differ: P further increases and V decreases until the compressor face. That is, if all the ratios etc. are good. If not then it unstarts, the normal shock goes out the left side, and the whole thing is subsonic.
Hi Josh..
Can you please explain the relation between under expansion, over expansion to Pressure thrust.
Like pressure thrust is zero when pe equals pb but there are two conditions when these are not equal over expansion and under expansion. Please elaborate this concept.
Wonderful.
Thanks!
Great video! I just had one question. How is it that we control the Back Pressure? For example, a rocket has its combustion chamber that goes into the converging side of the nozzle with a certain pressure that then is choked and then shot out into the air... so when you say controlling the back pressure how is it that you are controlling the air. Sorry if its a dumb question but I think its critical to me understanding how rocket propulsion works with CD nozzles.
Thank you! If you are making a model rocket, for instance, then the back pressure is determined by the atmospheric pressure, and will decrease as you increase in altitude. If you are testing in a wind tunnel, then you can use a pump to decrease the ambient pressure in the tunnel. I just said that we controlled it because it helps simplify the explanation, but in reality, the back pressure is whatever the atmospheric pressure is.
Awesome this is!
Thanks!
great series of videos... just a question: which is the "choked flow video" you mention at 6.30 ?
Thanks! That should be in my Sonic State video: ruclips.net/video/jnRudznUqDM/видео.html
Hello Josh, Please does the gamma change along the nozzle as temperature varies which affect the gas Cp?
Hi Josh. Do you have a good reference for pulsed supersonic valve?
Hi Josh. If we reserve the direction of the flow from diverging to converging. Will it able to produce high pressure low velocity fluid?
Do you get flow separation at the shock in the divergent nozzle.?
If you are actually trying to machine one of these things a pair of straight tapered cones can closely approximate the smooth curves. Start with a 60 deg half angle (120 deg total) to from the combustion chamber diameter to the throat diameter. The expansion angle should be 7.5 Dec. (15 dag total) to half the diameter of the combustion chamber. Smooth the transitions between the converging and diverging sections of the nozzle.
Of course this engineer has provided a method of actually calculating the diameter of the throat.
Awesome.
Thanks!
Thanks bro such a nice explanation
. Just want to say add pictures in your videos so that content would be more relatable. BTW nice👍 video🎥📹📹📹.
You're welcome, and thank you! I'll definitely consider including pictures in the future.
@@JoshTheEngineer I'll further this. An animation show Pb/P0 relationship going from 1 to smalled Pb and seeing the differences would be amazing.
Do nozzles designed using the Method of Characteristics experience shock waves if, for example, the flow through the nozzle was caused by Pb/P0 | NS?
Hello Josh, great video !! But how are we actually pulling down the back pressure and the exit pressure ? How can we manipulate these factors ?
In most cases, that's dictated by the atmospheric pressure where the nozzle is operating. If you're on the ground, it's the air pressure at the ground. If you're at 10 kilometers, it's the pressure at 10 kilometers. You can also operate an engine in a vacuum chamber during testing, for instance, where the back pressure would be the pressure you can achieve in the chamber after pumping down.
Are we considering Pe=Pb= atmospheric pressure at exit?
Taking Mechanical course and studying Fluid Mechanics now.
Hopefully I can make it in the final exam.
Good luck!
can you explain how this relates to aerospikes?
thank you from Interfluo
You're welcome!
How the normal shock which spike's up the pressure instantly .... affects Pe of the nozzle... will it overpower Pe and be a criteria to compare with Pb subsequently
Do we require a de Laval nozzle for model rockets? Is the exhaust flow in a model rockets supersonic?
Soham Prajapati for perchlorate motors it sure is
Great video, When you say 'pull the back pressure down' what real world mechanic is doing this? does the pressure drop just because the rocket is increasing in altitude? or is the pressure dropped by increasing the exit area?
Right, the back pressure is dropping because the rocket is increasing in altitude. When I need a quick pressure for a calculation I'll use the Standard Atmosphere table on Engineering Toolbox. A lot of fluids books also have these tables. You can also drop the back pressure in a wind tunnel test by pumping the tunnel down closer to a vacuum to simulate higher altitudes.
If I assume chamber pressure and Based on this assumption i design the nozzle , how can I be sure i can achieve this pressure inside the chamber ?
Sir , we overexpand pressure in the order to decrease pressure caused by normal chock . You have said that we decrease Pb . But do you think that we can control Pb ? I think that we can only control Pe , because Pb is the atmospheric exterior pressure
Thanks
No problem!
Thank you Josh for your clear explanation videos about the topic👍
I still have a question though, about the thrust formula :
F = m_dot*Ve + (Pe-Pb)*Ae
What is the Exit velocity (Ve), the Exit Pressure (Pe) and the Exit Area (Ae)?
Is it at the end of the nozzle in all 7 cases ?
Just before the normal shock ? Or just after the normal shock ?
The Exit velocity is the velocity after the oblique shock in the case if an over expanded nozzle.
I mean normal shock*
Also works with magnetically confined plasma initiated with Townsend avalanche ionization of gasses and even Directed solar wind plasma.
Although conventional rocket exhaust is technically plasma but humans still using mechanical constriction that require cooling system without gigavolt plasma accelerators to boost thrust.
How will the flow is underexpanding and overexpanded?? Using the same fluid and same nozzle
Is this channel like the aerospace version of engineering explained?
I guess you could sort of call it that.
what does this p/p0 represent?
Is Pe predefined while designing the divergent part or will it alter as the flow accelerates.... i want to know what is actually controlling Pe
Yes, divergent area depends on pressure at a range of altitudes. Pe is a know value for each stage of the rocket, since it's the atmospheric pressure at different altitudes.
You're a beast! What is your background?
Thanks! Background is in aerospace and mechanical engineering.
Converging-Diverging Nozzle and it regime flow representation: stagnant background pressure, p0, pb
will the flow still choked in the throat for case 5,6,7?
Yep, the flow is choked for every case that is not fully subsonic. This includes states 3, 4, 5, 6, and 7.
and what will happen if the initial speed of the gas,in the converging section,is above mach 1?
by the way....nice video
Thank you! If the flow is supersonic in the converging section, then the gas will actually slow down as it reaches the throat. I go through this in more detail in my 'Area-Mach Number Relation' video.
JoshTheEngineer i went lost in the first minute of that video..sorry..so the speed at the exit will not be greater than the speed at the entry?
so another way to say P sub b ... is the air pressure not modified by the engine ...
.
Question - assuming it is a jet engine ... and they are mounted so that P sub e is under the flow from the wings does the air flow from the top of the wing and the bottom of the wing have a minimal effect, marginal effect or considerable effect ... how would one go about relating these 3 options to determine if any effect from the wing airflow is additive subtractive or negligible ...
because ambient air at the exit of the nozzle isnt exactly ambient due to air flow and turbulence around the body being looked at ... there will be some effect and we cannot be certain it isnt adding subtracting or not worrisome ... also if one modifies the flow of air through the engine into a hyperbolic flow (larger volume output for a given unit of time Viktor Schauberger hyperbolic flows cone ideas) how might that change the output overall of the engine
still I strongly suggest slow your speech down a tad ... playing the video at 75% helps but speaking slower and not racing through the material would be better ... listen to the video real time and then relisten at 75% ... and see what I mean ... after all you have 4 hours of stream time to get it in
Hey Josh its like i have found something BRILLIANT thanks for foing such a great Social Work
Just started my BS Space Sc
One Childish Qustions if u have time ( i am an amature)
I have been studying till now that when we decrease area presure Increases where as i found you explaining it decrease when leaving A* ?
I guess its due to we are discusing "Gas Dynamics"
maybe
My pleasure, and good luck with your studies!
The simple answer to your question is that it depends. Now let's get into the longer answer. Ignore the variable A* for now. Whether the pressure decreases or increases with a certain change in area depends on whether the flow is subsonic or supersonic. If you go to about 5:11 in this video (goo.gl/RdW3nE), I talk about the area-Mach number relation, and how the results from the equation change from subsonic to supersonic flow.
For subsonic flow, as we decrease the area, the flow speeds up and the pressure decreases. This is the normal result that you will see or have seen in fluid dynamics courses that don't cover compressible flow. This is why you always see the pressure decrease in the converging section on the plot I've drawn. The converging section is always subsonic. Now if the flow in the diverging section is subsonic, then as the area increases, the flow slows down and the static pressure increases. This is what you see on the plots for case 1 in the diverging section.
For supersonic flow in the diverging section, as the area increases, the flow actually speeds up further, and the static pressure decreases. This is the opposite of what happened with subsonic flow. When it comes to how area change affects velocity, and thus pressure, subsonic and supersonic flow are basically opposites.
The concept of A* is not needed to understand what happens to static pressure in a subsonic or supersonic flow where the area is changing. All you need to understand is the area-Mach number relation (again, see the video I linked to before). I'll probably make a video going into more depth on A* because it can be confusing, especially for flows that are non-isentropic. But for now, I hope that helped answer your question.
What happens if we reduce further the throat area once the gas is choked, considering a low pressure at the exit ? Does it remain at M=1 while increasing its pressure ? Why do rockets never have throats area below the strict necessary to choke the flow ?
BTW, awsome job.
Thanks! The quick answer is that the flow will still be choked, and all you will get is a reduced mass flow rate which will effectively decrease your thrust.
Let's say that we're at a condition that is choked, and we keep the reservoir and back pressure fixed from now on. All we will do is change the throat area. We know from the area-Mach number relation that the only location we can have sonic flow is at the throat. If we decrease the throat area, the flow is still choked, and the location where the flow is sonic still has to be at the throat. This is important because while the throat area (A* = At for choked flow) has decreased, the throat pressure, throat temperature, etc. are still the same values they were before (P*, T*, etc.). The mass flow rate can be computed by taking the product of the throat density (rho*), throat gas velocity (u*), and the throat area (A*). The density is a function of the pressure and temperature, which haven't changed. The velocity is a function of the temperature, which hasn't changed. The only thing that has changed is the throat area, which we have decreased. This shows that the mass flow rate will decrease with a decrease in throat area.
From my Nozzle Mass Flow Rate video (ruclips.net/video/aMTmRCdmvVQ/видео.html), we can see this result in a slightly more useful form for rockets, which gives the mass flow rate as a function of reservoir pressure, reservoir temperature, throat area, specific heat ratio, and specific gas constant (P_0, T_0, A*, gamma, and R). The trend is the same (as it should be since it's derived from the same equations we talked about before), where since we are keeping the reservoir conditions constant and just decreasing the throat area, we get a decrease in the mass flow rate.
From my Turbojet Thrust Equation video (ruclips.net/video/aNyYxVHBSWQ/видео.html), you can see that the mass flow rate is a really important part of the total thrust of an engine (neglect u_a for a rocket), so we don't want to decrease it if we're interested in increasing thrust. For a similar computation, see my Afterburner Nozzle video (ruclips.net/video/YKCqyaYMSs8/видео.html).
Hope that answers your question!
I think it totally does, the result is very clear based on the equations. From a physical point of view, I didn't have in mind the sonic flow could only be reached before the throat. If I understand correctly, in a continuously decreasing area section (a cone with a small hole at the end), whatever the static conditions at both ends, you will never reach M=1 before the moment the section diverges (here the end of the cone) ? Your flow cannot reach and remain at M=1 in a decreasing area tube ?
Right. This is why it's normally easier to think about nozzle choking using only a converging nozzle, which is what I do in my afterburner example video. If you want to dive a little deeper into this subject, you'll actually find that when you relax some of the assumptions used to derive the conservation equations, the M = 1 condition (also sometimes called the sonic line in the throat) will not be exactly at the minimum area location. It will be slightly curved out into the diverging section. But, this can't happen if you're assuming the flow is quasi-1D when deriving the conservation equations. If you want to look into this further, Google something like Sauer's method/solution for the sonic line. There's a good derivation in Zucrow and Hoffman's Gas Dynamics Volume 2, I believe.
I will check this out. Thanks a lot.
Thank you, but how we do increase the Back Pressure needed to create supersonic flow? That is not very clear?
The two main things you can do to get supersonic flow are (1) increase chamber (reservoir) pressure or (2) decrease the back pressure. The chamber pressure is based on the design of the engine, and the back pressure is basically set by the altitude your engine is currently at. That is, the back pressure will decrease as you increase in altitude.
@@JoshTheEngineer thank you!
Why do we study the effect of lowering the back pressure and not the increase of the inlet/stagnation pressure? Isn't that a bit counterintuitive?
In the first case... did u meant to say that the combustion chamber is not at all firing so that Pb=Po....
Amazing explanation, but thank God playback speed exists, too fast for me haha
when are all the cases when back pressure is equal to exit pressure? so confused
What happens between p*/p0 and pb/p0|NSE
Why Pe = Pb for isentropic flow?
Check out his isentropic relations video, he might explain it there.
How does one decrease the back pressure practically?
The back pressure in most practical cases is just determined by the ambient pressure of the air. So as you fly higher in the atmosphere, the back pressure decreases. If you see rockets being tested on test stands (lots of videos on RUclips), they're probably just operating at about 1 atm, which means the flow will be overexpanded (in general). This is because a fixed nozzle design is only optimal (supersonic isentropic) at one back pressure (i.e. one altitude). Optimizing the nozzle design for 1 atm doesn't make sense, since presumably the goal of your rocket is to fly something to a higher altitude. If you want to test your engine at the design-point altitude without flying it, you can always put your engine inside a vacuum chamber that is capable of pumping down to whatever ambient pressure you want. This is harder than it sounds though, since right when you start the engine, it changes the pressure of the chamber due to the high mass flow through the nozzle.
@@JoshTheEngineer So, rocket nozzle at each stage of separation will have its unique Po/Pb, isn't it?.
@@adhithasimhanraghavan7516 Every nozzle has its own Po and Ae/At, so the Pe is fixed by design (in liquid rocket engines you can change Po by throttling up or down, in solid rocket motors the Po profile over time is predefined by the grain shape and isn't adjustable). Each nozzle is designed to work between Pbmax (ignition) and Pbmin (cutoff) since the atmospheric pressure drops exponentially with the altitude. So one wants to have a Pe that is between Pbmin and Pbmax, in order to avoid the normal shock and let the nozzle operate just in overexpanded (initially) and underexpanded (at the end) conditions. In fact the Pe is always chosen closer to Pbmax than to Pbmin, since the rocket accelerates and it spends more time at the lower altitude. The other reason for that choice is something that he didn't talk about: in real viscous flows the boundary layer can cause the flow to separate from the nozzle wall generating both major instability and loss of thrust. This problem usually happens when Pe is lower than ~0.3Pb, so you must avoid it.
So the answer to your question is yes, the Po/Pb is predefined for each nozzle, but it's not a fixed value, it's a range (Po/Pbmax - Po/Pbmin) that must fulfil the conditions above in order for the nozzle to operate correctly.
18:00 Mach Diamonds
Perfect at 0.75x speed. Slow down man, what's the rush?
I'm looking forward for the aerospike engineering video if there will ever be one. Cheers!
That's what I literally call myself, "JoshTheEngineer"
Dude, this video is super concise, clean, sharp! I'm impressed! Dude, you need to be a professor!
Always nice to meet another Josh! And thanks!