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The problem of wave drag reduction with high-frequency repetitive laser pulse energy depositions is multivariable. Three key non-dimensional parameters, non-dimensional energy, non-dimensional depositing position and Mach number, were constructed from a number of original variables by using Buckingham pi theorem. Influences of these non-dimensional parameters on energy deposition performance, namely drag reduction and energy deposition efficiency, were investigated numerically by solving three-dimensional Navier-Stokes equations with an upwind scheme. Optimizing method of non-dimensional energy and non-dimensional depositing position is proposed. Drag reduction and energy deposition efficiency have exponential relationships with non-dimensional energy; Drag reduction and energy deposition efficiency have quadratic relationships with non-dimensional depositing position. Drag reduction has exponential relationship with freestream Mach number and energy deposition efficiency has quadratic relationship with Mach number. Non-dimensional laser energy and non-dimensional depositing position should be optimized synthetically for a given freestream

Study of Key Non-dimensional Parameters for Wave Drag Reduction with High-Frequency Repetitive Laser Pulse Energy Depositions