Comments:

1. I can't really speak to cold liquid injection into hot gas, because I've never had access to software that could analyze this. Below comments are for liquid/liquid interaction. Also assume that I refer to cold injection into hot below, so reverse hot/cold as necessary.

2. The best solution to fatigue issues is to try to avoid them to begin with. Ensure injection velocity is in the same neighborhood as the main run velocity. Too little injection, and you'll end up with cold fluid running down the length of the branch side. Too much injection, and you'll end up with cold fluid running down the opposite side. While in the "sweet spot" your fluid will seem to cool down at a uniform rate (with respect to radius) until you accomplish the new thermal uniformity.

3. Don't place a bend too close downstream to the injection point. Even if you do manage to maintain that sweet spot, when the fluid turns the bend, you can end up with a cold spot in and around the centerline of the "pre-bend" line projected onto the extrados of the bend.

4. The operator's / process engineer's desire might be to "thermal shock" the fluid as much as possible to knock off buildup. It's dangerous to thermal shock the pipe itself. Thus, they'll want to ensure that there's sufficient build-up so that you crack the buildup and not the pipe.