Would the 2 orbiting black holes emit gravitational waves? Would the 2 orbiting black holes emit gravitational waves even if they are moving at a constant speed in orbits? Here, can we consider the changing direction of black holes in their orbits as acceleration that can be a cause of gravitational waves?
 A: The basic answer is yes, the changing velocity vector is an acceleration which in turn leads to an accelerating mass quadrupole moment and the emission of gravitational waves.
However, the scenario you propose is physically inconsistent. If the speed of the black holes were to remain absolutely constant, then their separation and orbital energy couldn't change, which is inconsistent with gravitational wave emission, since these must remove energy from the system.
However, as a thought experiment, we could arrange for some mechanism to keep the black hole speed constant by supplying energy to the system. We would find that this energy supply would be that needed to balance the gravitational wave losses.
The physically consistent solution is that gravitational waves take away energy, the orbit shrinks and the speed of the black holes increases. This leads to a greater gravitational wave loss, the inspiral and ultimately the merger of the black holes.
A: Gravitational waves behave, at least superficially, in a similar manner to "classical" electromagnetic waves: meaning that if you have a charged particle (so in the case of gravitation: a particle with mass) and that particle is performing an accelerated, undulatory motion, then you can rest assure that waves would be emitted, no matter the value or constancy of the angular velocity.
Note also that it's not strictly necessary to have two bodies orbiting each other to get gravitational waves, as we were saying: it's sufficient to have a single body under accelerated, let's say circular, motion. But of course since gravity is so weak compared to the other interactions it's necessary to deal with really massive bodies (black holes, neutron stars) to get observable gravitational waves; and in practice the only way to get a body as massive as a black hole to move into a circular motion is to have it orbiting another one of its kind.
