Why Do Rockets Have Bells?

hello and welcome back today we're talking about the frequently misused convergent divergent nozzle [Music] the purpose of a nozzle is to accelerate flow that can be air water burnt rocket fuel basically anything most nozzles that you see in your daily life will look like this they start wide and taper down to a smaller area accelerating the fluid even some jet engines use this very simple nozzle and you probably should too but today's video is about the more complicated type of nozzle the de laval nozzle or the convergent divergent nozzle this type of nozzle is typically used for high pressure propulsion systems such as rocket engines or some high performance jet engines unfortunately it's also misused pretty often by makers i'll show some examples now but remember i watch all these guys and i enjoy their videos and i'm not going to hold it against them i have made the exact same mistake so the yaw and pitch thrusters should provide about 3 to 10 newtons of force and the roll thrusters will probably be regulated down to about half that to find the best nozzle design i chose several options none of which had any theoretical calculations behind the design each nozzle has the same throat diameter of four millimeters as well as the same exit diameter of 10 millimeters and a length of 15 millimeters take a guess which nozzle you think will perform the best in the comments down below so here's the lineup did you guess that the straight nozzle would perform the best also the bell-shaped nozzle performed the worst out of all of them using slow motion footage i calculated a rotating speed of 4700 rpm which might seem good for only 2 bars but the thing is i also did the same test without the nozzle and the turbine was reaching almost 12 000 rpm the nozzle is supposed to help increase the speed not the other way around so i 3d printed some more designs including the dual valve nozzle and i tested them out and for my complete surprise the one that worked the best was a straight 2 millimeter circular nozzle the big problem with all these attempts at making a convergent divergent nozzle is that there just isn't enough pressure the inspiration for a de-laval nozzle is actually a venturi tube which has basically the same geometry in a venturi tube the flow is constricted by a nozzle which accelerates it and decreases its pressure then it's re-expanded through a diffuser which is basically a reverse nozzle the pressure and speed are the same before and after the flow goes through the device this is not permanently accelerating your flow like a day level nozzle should in fact if you expand to a larger area than you started with your flow will end up going slower than it was to begin with this is why each of them ended up settling on a straight tube though they may have gotten even better performance if they'd used a convergent nozzle so i made this two millimeter diameter straight through nozzle and it outperformed all the previous contenders in both peak thrust and duration so i'm gonna go with this now it's finally time to talk about the day level nozzle the main difference between a venturi tube in a convergent divergent nozzle is pressure the flow starts out moving relatively slow but with a lot of pressure backing it then the convergent nozzle will accelerate the flow to the speed of sound and finally the divergent nozzle will accelerate it past the speed of sound this nozzle functions because of the strange behavior of fluids when they exceed their own speed of sound at low speeds decreasing area increases speed because the same amount of fluid has to pass through a smaller hole but this has a limit a convergent nozzle cannot exceed the speed of sound continuing to make the hole smaller will actually choke the flow meaning the flow before the nozzle starts to slow down instead of the flow inside the nozzle speeding up it turns out that something about exceeding the speed of sound causes the relationship between area and velocity to be reversed if you have a pipe with full that's already traveling at the speed of sound you actually have to expand the pipe to accelerate it this isn't very intuitive but i'll share the best explanation i've heard at slow speeds flowing gas is considered incompressible it will have more or less constant density anywhere in the flow so it makes sense that smaller areas produce higher velocities but as a flow accelerates its density is less constant and it starts to behave like a compressible fluid what this means is that while the fluid is accelerating closer to the speed of sound the speed will increase and the pressure and density will decrease this finally reaches a turning point at the speed of sound where the nozzle is so small that the density can't decrease anymore without choking your flow but if you expand the gas instead you can continue to decrease that density and it will increase your velocity it's natural to wonder why this happens at the speed of sound but it might be better to think of it in the opposite direction this behavior is kind of what defines the speed of sound more than the other way around but anyway it turns out that in most cases it's just not possible to reach the speed of sound because there simply isn't enough pressure to begin with and this is going to be true for almost any project you might do but if you're still the term to try it out i'll give you some guidance this equation is the exit velocity for a convergent divergent nozzle t is your temperature in kelvin r is the universal gas constant which is just this number using these specific units m is the molecular mass of your gas in grams per mole and gamma is the ratio of specific heats m gamma can be easy to get if you're using a pressure tank with either air or co2 in it but if you're burning rocket fuel you're gonna have to do more digging to find these values and finally p e over p is your exit pressure divided by your starting pressure and you probably want your exit pressure to be equal to your atmospheric pressure because this gives you the fastest possible exit speed now you'll need one more equation before moving on which is the equation for the speed of sound if your exit velocity is somehow bigger than your speed of sound congratulations you can try out a convergent divergent nozzle though if the numbers are pretty similar it's probably not worth the trouble but if you are going to do it you finally get to use this equation this one comes with some new variables a is the area at your point of interest in the nozzle and a star is the area of the throat or the smallest point in the nozzle and in this case m is your mach number not your molecular mass mach number is just your velocity divided by your speed of sound and it's also important to note that a and m must be taken at the same point in the nozzle for example you can't use your starting area and your exit mach number as an example let's assume you know your starting area and your starting speed you can rearrange this to find the throw area by plugging in your initial area and your initial mach number then you can rearrange again and calculate your exit area by plugging in your throw area for a star and your final mach number which you can find using your exit velocity from earlier but you can always go the opposite direction fixing your final area and working your way back to the starting area this equation also ignores the fact that your nozzle will change the mass flow of your system which affects the initial velocities so it will probably take some trial and error to get this perfect so i'll just give you a few last pieces of guidance before you go these equations give you area but they don't give you length i've been told that about a 12 degree angle is pretty efficient for a simple nozzle like this so you can use that in some simple trigonometry to figure out your lengths also when you're testing your nozzle you can judge its performance based on the exhaust if the exhaust expands after leaving the nozzle it has extra pressure meaning you could have gotten extra velocity out of it if it collapses then you over expanded it meaning your nozzle's a little too large and you're losing some efficiency again ideally you want your exhaust to come out in almost a straight line or as close as you can get if you keep making your exit area bigger but your exhaust is still expanding you might not be supersonic yet so you could decrease your throat size and finally be safe especially if you're using a rocket engine if you make your throat too small it will choke your flow and increase the pressure behind the nozzle this will break anything that's not rated for that pressure and if you're using a rocket engine it can make your fuel burn faster which might lead to a rapid unscheduled disassembly but anyway that's all for now i hope you enjoyed the video check the comments see if there's any corrections because this is kind of a complicated topic i'm kon hafi and i'll see you in the next video [Music] you

Channel: The Con Hathy Channel

Views: 14,948

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Id: BXpcariAlVU

Length: 8min 34sec (514 seconds)

Published: Mon Sep 14 2020