This study investigates the relationship between body-force fields and maximum velocity induced in quiescent air for development of a simple body-force model of a plasma actuator. Numerical simulations are conducted with the body force near a wall. The spatial distribution and temporal variation of the body force are a Gaussian distribution and steady actuation, respectively. The dimensional analysis is performed to derive a reference velocity and Reynolds number based on the body-force distribution. It is found that the derived Reynolds number correlates well with the nondimensional maximum velocity induced in quiescent conditions when the center of the Gaussian distribution is fixed at the wall. Additionally, two flow regimes are identified in terms of the Reynolds number. Considering the variation of the center of gravity of force fields, another Reynolds number is defined by introducing a new reference length. The nondimensional maximum velocity is found to be scaled with the latter Reynolds number, i.e., the maximum induced velocity in quiescent conditions is determined from three key parameters of the force field: the total induced momentum per unit time, the height of the center of gravity, and the standard deviation from it. This scaling turns out to be applicable to existing body-force models of the plasma actuator, despite the force distributions different from the Gaussian distribution. Comparisons of velocity profiles with experimental data validate the results and show that the flow induced by a plasma actuator can be simulated with simple force distributions by adjustment of the key body-force parameters.
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