What is the benefit of the spiraled shape? More efficient? If so how come…also why not have an impeller inside a straight tube?
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The shape you are referring to is called a centrifugal compressor / turbine. The spiral shape helps extract energy from the airflow the entire time as it turns towards the center (and the opposite for the compressor). This design is effective for the pressure ratios required by a vehicle, and are very space efficient.
The “impellers in a straight tube” is kind of the idea behind an axial compressor / turbine commonly found in gas turbine engines (like those on aircraft). Axial compressors require a set of rotating blades, followed by a set of stationary blades. The rotor blades extract energy to the flow and send it rotating, and the stator blades turn the flow back to flowing axially. Axial compressors / turbines usually require a few stages of rotors and stators in a row to efficiently function. Therefore, they tend to be a lot longer, and therefore require more space. This space is available in an aircraft engine nacelle, where a long tube is also aerodynamically efficient, but less possible when squeezed in amongst an internal combustion engine. Axial compressors tend to operate more efficiently when higher pressure ratios are required. Cars don’t require the high compression ratios that aircraft do
The spiral shape, and the offset inlet where exhaust gases come into the turbo is the best angle for pushing the turbine. Remember those [toy windmills](https://image.shutterstock.com/image-photo/plastic-windmill-colors-rainbow-on-600w-1970693054.jpg) we had as kids? if you blow on it from the side, it spins much easier/faster than blowing on it from the front. Similar idea here, but more efficient because the air is pushing on the turbine all the way around the spiral, not just from one point.
On the compressor (cold air going into the engine) side, the spinning impeller is going to force air around the spiral and out of the end of it, into the engine
[This image](https://dieselnet.com/tech/images/air/turbo/~turbocharger.jpg) shows quite well how as the exhaust gases flow around the spiral they push the turbine
Clarification: do you mean the duct that goes round and narrows down? That’s a duct to efficiently feed the turbine. The turbo is actually a very tiny “wheel” in the center of it. 1-2 inch diameter. Both the turbine and the the compressor are centrifugal type, and have similar ducts, the duct feeds air all around the circumference of the rotating bit of the turbine. For the compressor, the duct collects compressed air all around the rotating bit.
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