I have no knowledge of this subject until this thread, but a quick Google turns up this picture, which shows a fancy swirl pattern as the front, and it could be (just my speculation) that it mixes cold air in from the front so effectively that there's no need for it from the sides. And the TA in TAPS stands for "twin annular," not for the shape of the combustor (which is also annular, inner and outer) but the shape of the swirl pattern.