The emergence of a submerged vortex upstream of a pump can reduce pump intake efficiency and cause structural damage. In this study, we consider the use of active flow control with steady blowing to increase the pressure distribution within a single-phase pump-induced wall-normal vortex model, which is based on the Burgers vortex with a no-slip boundary condition prescribed along its symmetry plane. The goal of our control is to modify the vortex core velocity profile. These changes are sought to increase the core pressure such that detrimental effects on the pump are alleviated. Three-dimensional direct numerical simulations (DNS) are performed to examine the dynamics of the vortex with the application of wall-normal momentum injection at and around the root of the vortex. We find that the active flow control approach can effectively modify the wall-normal vortical structure and significantly increase the low-core pressure by up to 81% compared to that of the uncontrolled case. The result shows that the control setup is also effective when it is introduced in an off-centered manner. Compared to the unsteady blowing and suction based actuation from our previous work, the current steady control technique offers an effective and simple flow control setup that can support robust operations of pumps.