I was wondering if it is possible for a ramjet to start from 0 velocity.
I know its working principle and all, but is there any missile or aircraft that completely uses ramjet, with no rotating part to compress the air?
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No, a ramjet can't be started at zero speed. Yes, there are missiles that use ramjet propulsion without any rotating parts: they use a rocket to accelerate the missile to high enough speed for the ramjet to operate and develop useful thrust.
More or less by definition, a ramjet requires significant forward velocity to compress the intake air sufficiently to produce useful thrust. Depending on the design, this speed might be as low as about 250 kt (120+ m/s) or somewhat above local Mach 1. That means something has to push the engine (and attached aircraft) to that startup speed.
That "something" can be a turbojet or turbofan engine, a rocket engine, a catapult (I'm not aware of any ramjets that are launched this way, but it's technically possible) -- even a literal gun (ramjet boosted rounds in approximately shotgun sizes were demonstrated as long ago as the 1970s -- NOT the same as a Gyrojet, which was a tiny rocket-only projectile). For missiles launched from a jet warplane, it might be possible to use the plane's forward velocity, or a boost from a gravity drop, to get this initial speed.
No. A ramjet relies on stagnation pressure at the inlet in order to compress air prior to combustion. They are typically not effective until the speeds get quite high, somewhere in the Mach 2+ range.
Ramjet powered missiles which used rocket boosters for launch have been around for decades, possibly the most famous one is the US Navy’s TALOS missile. One of the most ambitious projects from the Cold War was a weapon called Supersonic Low Altitude Missile (SLAM). This would have used a nuclear powered ramjet engine and roamed the skies at supersonic speeds for months on end with a nuclear warhead, waiting for instructions to attack enemy targets.
It is trivially possible to start a ramjet at zero ground speed, since ground speed is completely irrelevant. The only thing that matters is air speed. All you need is high enough winds.
You could put the ramjet into a wind tunnel (hypersonic wind tunnels can generate winds of Mach 5+, there are even wind tunnels which can reach Mach 27 for about a second). A Category 5 Hurricane would also work, as would a strong tornado.
In theory you could have an engine that started in pulsejet operation and switched over to continuous combustion as the speed increased.
In practice, good luck with that. Pulsejets require very specific geometries and a fair bit of black magic; ramjets require very specific geometries and a fair bit of black magic. Trying to build something that works in both modes (much less if you want a transition that isn't "turn off the pulsejet, reconfigure to ramjet mode, dive, and hope the ramjet ignites before you run out of sky")... again, good luck with that.
(...and if you want 'no moving parts', you're asking for a valveless pulsejet, which adds a whole 'nether layer of black magic.)
Try rephrase the question.
A ramjet is basically a continuous explosion in an open pressure valve. No more, no less. Its that explosion that needs both fuel and air.
By asking if it's possible to make it run with either one of those ingredients missing, you might as well ask if it's possible to start a ramjet without actively supplying it with fuel. The answer to that question for obvious reasons is 'nope'. The same goes for the air.
The itty bitty little bit of air that is filling the jet as it is, is not gonna do the job. You have to push in large quantities of air along with the fuel, in order to have something to lite up at all.
By the way, the same thing goes for any jet. That is what the compressor is for. Starting the flame before the compressor is properly running, is not a good idea. The thing that the compressor creates is basically the same as the head wind in a ramjet.
As in airplanes flying ramjet only, I recall seeing a French Dassault jet as a kid, where I could look straight through the jet, front to back, meaning it didn't seem to have any compressor. That should qualify it as a ramjet.