Three-dimensional (3D) unsteady heat flow and molten zone induced by nonlinear bifurcations or imperfect growth conditions are typical in vertical zone-melting crystal growth or refining. Through flow modification, we find that the use of steady ampoule rotation is effective in suppressing these 3D characteristics. Even with only 10 RPM ampoule rotation, numerical simulation indicates that the steady axisymmetric (or nearly) mode can be easily retained for 2-in GaAs under a typical growth condition, in which the 3D unsteady flows prevail for no rotation. A model gallium zone is also examined, and its 3D bifurcations are significantly suppressed by rotation as well. However, if the rotation is not sufficient to suppress the unsteadiness, baroclinic waves may appear. The effects of ampoule rotation for imperfect growth conditions, including asymmetric heating and ampoule tilting, are further illustrated. The ampoule rotation is also found useful.