Is the two-phase flow pattern by design or are you trying to mitigate consequences of two-phase flow? Also, what are the application and the fluid type?
Although the application is important, generally we have found that well-mixed bubbly flow is the least damaging to a pipe system containing steam-water.
Here are a few thoughts on other flow pattern types based on my experience with steam-water systems.
Plug: if you are refilling an empty pipe you can typically expect the liquid column to move in a plug flow manner (as opposed to stratified flow) if the Froude number is greater than 1. The Froude number is defined as Fr = u/sqrt(g*D), where u is the liquid velocity in the pipe, g is gravity, D is pipe diameter, and sqrt is the mathematical symbol for square root. For Froude numbers less than 1, refill occurs in a stratified flow pattern.
Stratified: In closed pipes, stratified flow is typically observed at low liquid velocities. If the gas is condensable, this flow pattern can lead to flow instabilities as the gas has a large surface area on top of the liquid to condense. In the worst case, this flow pattern can lead to condensation-induced waterhammer events which have a long history of causing equipment damage and worker injury.
Wave: If you start with a stratified flow pattern then increase the gas velocity, waves will begin to form at the liquid surface. As the gas velocity increases, the waves will continue to grow until they touch the top of the pipe at which point you may experience pinging or other, more severe signs of water hammer. Wavy flow is typically not desirable from design standpoint.
Annular: This typically occurs at high gas flow rate and high gas (steam) content. If you have a high liquid content in the pipe, you probably don't have to worry about annular flow. If you have a heat transfer process, annular flow is also not desirable.
Mist: If the flow is primarily gas with a small liquid content and a high gas velocity, then liquid droplets can be entrained in the gas. For many applications involving heat transfer or turbines, this is undesirable.
As far as piping hydraulics, there are several correlations for flow pattern-dependent pressure drop. There are also well established equations for the calculation of flow pattern if the other design parameters are known.
One final thought. If you are planning on a two-phase flow piping system, you should design for waterhammer.
