Why does a turbocharged car only produce significant boost whilst the engine is under load? Is is something to do with how much exhaust is being produced or is there some kind of valve mechanism that controls this?
i.e. running the engine at 3000 RPM in neutral would not produce as much boost as the engine running at 3000 RPM whilst pulling the car uphill in gear.
Let me lead off with an excellent book on the topic: Corky Bell's Maximum Boost. There is a sound treatment of the basics of turbocharger operation in addition to some dated and esoteric applications that are still interesting. For example, I find the discussion of turbocharging different types of carburetor to be of intellectual if not practical interest.
To summarize the points called out in your question, here are some of the major aspects of the turbocharged engine that are of interest:
The air flow: remember that an internal combustion engine is effectively an air pump. If we're talking about an engine that is operating "under load", we can assume that you've opened the throttle. For example, when rolling down hill, you don't need to hit the throttle so the entire intake to exhaust path is pumping a smaller air mass. However, driving uphill will require you to open the throttle (give it gas), adding air to the intake. This causes the engine computer to add fuel to the mixture. The fuel-air mixture is burned to produce energy. The exhaust from this combustion then proceeds to ...
The turbine: this is part that looks like the front of a jet engine sitting in the exhaust gas path. The turbine sits on one end of a spinning shaft. On the other side is the compressor. That is the part that actually makes the boost on the intake side of the engine. The more exhaust gas pushes past the turbine, the more it wants to spin and make boost on the compressor side. However, there is also ...
The wastegate: this is a valve that also sits in the exhaust gas path. It provides a short cut for the exhaust if the engine does not really need boost at this time. This can be used for peak boost control (too much boost can physically destroy your engine). This can be a purely mechanical sprung valve that stays closed up to a certain positive pressure in the intake path and then progressively opens as boost increases. It could also be under the direct control of the engine computer. For example, my car (in stock tune) was very annoying in its refusal to stay at peak boost in third gear. It also would refuse to boost past a certain point with partial throttle. The engine computer was effectively saying "no, that's enough fun for now."
For example, if I am rolling downhill in gear with my foot off the gas, the throttle is closed. There isn't enough air mass passing through the intake to exhaust path to make the turbo spin, wastegate or not.
However, the scene changes at the bottom of the hill as we climb the next rise. I have to open the throttle to get up the hill. If I'm in low gear, the RPMs will be higher, the exhaust gas energy will be higher and the turbine will spin right up. However, since I'd require partial throttle at lower gear for the same acceleration, my engine computer might veto boost past a certain point, opening the wastegate.
If I'm in high gear, the RPMs will be lower and I'll have to open the throttle wide open to get up the hill. However, the exhaust gas volume and velocity will be low and it's possible that I won't have enough energy for the turbo to make any significant positive pressure (e.g., around 40 mph in fifth in my car). Even though I'd really like to make boost in this situation, I won't be able to.
You pretty much guessed it, and if you didn't wikipedia is your friend.
In summary, turbocharger operates by having two turbines connected to the same rotating axis. One turbine is spun by the exhaust gases, which cause the other turbine to spin. The second one is what forces the air into the intake of the engine.
At idle rpm, there's barely any exhaust to produce boost. Open throttle => more air moved through the engine => more exhaust => more boost.
Not exactly... Remember, not all turbocharged engines use wastegate's.
What happens is say your engine is turning at 2000 RPM's with no load, now you put on a load, the RPM's drop and to bring it back up to 2000 RPM's you have to add throttle which is dumping fuel in to the engine. As you dump fuel, your increasing the combustion pressure, and ultimately the higher exhaust pressure's are going to spin the turbine fast, and produce more boost which will increase the combustion pressure even more (more O2 now available). See, on a engine with no load, even without a wastegate the turbo is not doing much.
and to make things a bit more complicated here, on a diesel engine it works similar but different. There is no intake air regulation on a diesel, the intake is always unrestricted and output is determined by the amount of fuel injected. This is why when diesel's rev they put out a lot of smoke until the engine catches up. Turbo charged diesel's rely on the turbocharger itself as a form of intake air regulation.
Your car's engine uses more fuel to spin the engine to 3000RPM when it is under load as opposed to being revved in neutral. That's the short answer.
More fuel means more exhaust gas, which means more boost. Conversely, when you are revving in neutral, much less fuel is used, and therefore much less exhaust gas to spin the turbo. This is also why your car is heavier on gas going uphill than downhill.
Also, your car's management system would probably disengage your wastegate/blow-ff valve when your throttle is disengaged. It's a safety feature.
