The Ashtanga practice uses what is known as the Ujjayi breath or "Breath of Victory" during the course of the practice. I have found this also incorporates well into a Vinyasa Flow class, as well as aspects of a Hatha session. New students are always a bit perplexed by this "noisy" breath - I know I was. In my very first yoga class, I was bemused why the instructor was breathing so loud. I was doubly bemused when she kept doing it in subsequent classes. Finally, I said something to my acquaintance about how I was loving the class but didn't know why the instructor kept breathing so loud. She laughed and explained to me that the instructor was using the Ujjayi breath.
Recalling my experience, I now try to make a point of "bringing back the basics" every so often so newer folks aren't perplexed like I was. From Yoga Journal I found this short article:
by: By Aadil Palkhivala
The Ujjayi breath is the breath of victory. In this type of pranayama, the lungs are fully expanded and the chest is puffed out like that of a victorious conqueror.
The sound of Ujjayi pranayama serves two purposes: One, it stimulates the nadis, or energy channels, in the sinuses and at the back of the throat, which, in turn, promotes mental clarity and focus. And two, it provides a sound to latch onto, so that the mind can become more still. When the sound oscillates, the mind too is oscillating, and the student can hear this.
During the inhalation, I teach students to imagine a hole in their throat that they are breathing through, thereby creating the sibilant sound of pranayama. The inhalation should rub against the back of the nasal cavity and throat. During the exhalations, I ask my students to imagine that they are saying "ha" without the "a," and to feel the breath rubbing against the frontal sinuses as it leaves the body. Both inhalation and exhalation must be done with the mouth closed, through the nostrils only.
In my classes, since we live by Lake Superior, I compare the breath to the sound of the waves gently crashing on shore - smooth, rhythmic, calming. I also cite the sound of the wind moving through pine trees.
The loudness of the breath is debatable - I've had instructors encourage a loud breath and other's who've said it should be soft. A louder breath tells the instructor that the student is breathing and not holding their breath or perhaps is working too hard and straining. A softer breath focus's the attention of the practitioner more as they have to closer attention to hear it. Either way is appropriate, the important thing is to continue to bring awareness to the breath and keep the breath smooth and flowing.