Similar but not equal. All the losses that subtract from 100% efficiency will work in the opposite direction as a dynamo.
So if the motor is 75% efficient under those conditions, then its 100% efficiency speed (unloaded) might be 4000rpm and it would draw 0A. You can roughly crosscheck by monitoring its stall current at the same voltage : in this case, it may draw 24A at 0 rpm. (The motor regulation would be 1000 rpm for 6A, or 167rpm/A, or 24A for 4000 rpm)
If that's the case, then you have motor constants of 4000/20 = 200RPM/volt, and a winding resistance of 20/24 ohms = 0.8333 ohms.
Given these values - and they are based on my guess of 75% efficiency for your motor - the open circuit voltage would be 3000rpm /(200rpm/v) = 15V.
And if you drew 6A from it, you would drop 5V across the winding resistance, so you would see 15-5 = 10V across your load, instead of 20V.
The bridge rectifier would then drop 2* the diode drop (say 1.4V for silicon diodes) giving 8.6V DC. Schottky diodes or synchronous rectifiers can improve on this, but probably at more cost than is justified for such low power.
Measure the motor regulation by running your motor at different loads and measuring both speed and current, and cross-check by measuring stall current, and you can arrive at the likely dynamo performance for your actual motor.
Can I use a sensorless control of the motor, by sensing the back EMF even if the motor is spinning very low?
Technically, yes you can. However, in practice, it is not possible/difficult. The reason is that because the back emf voltage is so low, you need to amplify it (extra circuits) or work with low resolution data. Since the resolution is lowered, you get cogging because it becomes difficult to identify exact point of zero crossing. Also, back emf can't be lower than the noise in your system, you won't detect it.
How can I energize properly the phases of the BLDC motor, from standstill, if it is sensorless?
You will do an open-loop start-up sequence and hope that the motor catches up. Continue open-loop operation until a critical back emf speed is achieved.
Can I use the IMU for finding out how to spin the BLDC motor properly without counter rotations (meaning that I know when to commutate)?
IMU generally gives information about accelerations. So, you will integrate that to find the rotor positions. This operation will take some time and there will be calculation errors (You'd get cogging in BLDC motors). I'd say, this method would be more difficult than the back-emf method. IMU method is better for stepper motors. (Stepper motors + IMU = nice gimbal system)
How can I hold the motor standstill when reaching the setpoint?
You will switch the mosfets at a constant frequency. The motor will move at a constant speed. Is that what you mean by this question?
Should I implemebt a speed controller or a torque (current) one for such an application (sensorless driving of BLDC motors at low speeds)?
BLDC motors are inefficient and hard to control at low speeds. Why not use a stepper motor? If you really have to use BLDC, though, use both current and back emf method combined. They have their benefits.
Best Answer
You think that the problem is in the motor; that the motor cannot supply more than 33 mA. This isn't correct, the problem is that your 12V fan is not able to function at such a low voltage and thus does not draw much current. Remember: current isn't "pushed" by the source, it's drawn by the load. If you were to short out the rectified output and measure the short circuit current with a multimeter, I guarantee you will see several amps flowing trough (possibly blowing the multimeter fuse, destroying the diodes and/or overheating the motor coils in the process).
A standard silicon rectifier diode will drop 0.7 V when conducting. As a rectifier bridge has two such diodes always in series with the load, the diodes will steal 1.4 V from whatever meager voltage your motor puts out.
You can rectify this by using schottky diodes, which have a much lower voltage drop (about 0.2 V), and using a lower RPM/V (KV in radio control terms) motor. For example, a 140 RPM/V (KV) brushless gimbal motor should put out 21.5 V AC at 3000 RPM, which can then be rectified and dropped down to a nice stable 12V or 5V with a buck converter.
If you want to stick with your motor for whatever reason, and you have the necessary programming skills, you could also write a custom firmware for a commercially produced ESC (RC brushless motor driver) to act as a synchronous rectifier instead. The ESC MOSFETs will drop next to no voltage when conducting and they are already arranged in a full bridge configuration, granting much better efficiency than any diode. You could even boost the motor voltage while rectifying by pulse width modulating the MOSFETs, doing exactly what the ESC normally does but in reverse.