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Something Interesting!
so this is a little long but, also very good! all about turbos...
Lets get some vocabulary out of the way or you won't be able to follow anything I say....errr...write. Do you know the difference between an inducer and an exducer? Well, take a look at the compressor and turbine on a real turbo. Funny looking fins aren't they? Not the same size all the way down the blade from tip to base. There is a reason for this. Each stage of the blade (small section vs big section) has a special purpose.
First lets look at the compressor wheel and figure out how it works.
The inducer part of of turbine is at the end of the shaft and can be seen by looking into the intake of the turbo compressor housing (looks like a fan). The blades that you see there extend into a larger diameter at the other end of the turbine. This is the exducer stage. The inducer on the compressor turbine is responsible for generating the vacuum at the compressor housing inlet that pulls air into the compressor. The air then "rides" the fins towards the exducer stage, which is a larger diameter, and gets sling-shot towards the outside of the compressor housing. The housing collects this moving air an expels it through the housing's outlet.
The size of the compressor turbine determines the maximum amount of boost that the turbo charger can produce. It also effects the spool-up time of the turbo. The type of compressor wheel is usually designated as its "trim", which is a value that describes the inducer and exducer sizes. Typically, the exducer is significantly larger than the inducer on a compressor turbine.
Next lets look at the exhaust turbine wheel and figure how the inducer and exducer work. And lets learn how the turbine gets moving in the first place. This will be important when we answer your question of making a small turbine and a big compressor.
The exhaust turbine also has an inducer and exducer, but because the exhaust turbine has the opposite function of the compressor turbine, the two are switched. The exhaust gasses are directed towards the outside of turbine through a nozzle. This is the inducer stage because it is the part of the turbine that collects the gasses. As the energy from the gasses is transferred into the turbine, the gasses slow down and exit the turbine through the exducer stage.
Most people think that the exhaust coming out of the engine smacks into the turbine and gets things moving. Like a pinwheel a kid is blowing against. The air smacks the blades and starts it spinning. Well, that is not quite the case in a turbocharger. You need to take into account the gas laws and how a gas behaves under heat, pressure, and volume. We know that a gas that is compressed heats up and a gas that is uncompressed, cools down. That takes care of heat and pressure. The volume of the gas is determined by the cylinders and other hoopla. So when the gas leaves the cylinder, it gets compressed going through the small exhaust manifold outlet. This is by design. You'll see in a minute. As the hot compressed gas exits the exhaust manifold, it enters the turbine inlet - a very small space. At this point, we have very high pressure and very high heat, so our gas has a very high energy level. As it passes through the diffuser and into the turbine housing, it moves from a small space into a large one. Accordingly, it expands, cools, slows down, and dumps all that energy - into the turbine that we've so cleverly positioned in tho housing so that as the gas expands, it pushes against the turbine blades, causing it to rotate.
The exhaust turbine design is a balance between absorbing as much energy from the exhaust gasses as possible and allowing the gasses to flow as easily as possible. This is closely related to the size of the exhaust housing. A larger turbine can absorb more energy from the gasses and spin the shaft with more torque and speed, but too large a turbine will restrict the flow of exhaust such that engine performance is greatly reduced. Typically, the inducer is only slightly larger than the exducer on the exhaust turbine. Generally, you would want to stick with the stock turbine because it's size is not nearly as important as the compressor turbine's size. If you want to reduce restriction through a smaller housing, you can have the turbine "clipped", which reduces the size of the fins and allows more air to flow around the turbine.
Whew. Boil it down. The exhaust turbine and compressor turbine sizes are engaged in a delicate balancing act. The housing used on both sides plays an important role as well. After all, the housings are what make the compression and expansion chambers needed for manipulating the gas state. One reason for a large exhaust is by lowering the outlet pressure, you increased the pressure differential, and now the exhaust gas can expand more, and do more work. That increased work pushes harder on your turbo, and it spools up faster.
Just simply putting in a smaller exhaust turbine and a larger compressor will not reduce spool time. The amount of energy the inducer/exducer needs to get moving may be offset by the weight of the HUGE compressor wheel you are using on the cold side of the turbo.
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