Turbulence modeling in the wide energy spectrum: Explicit formulas for Reynolds number dependent energy spectrum parameters

The energy spectrum function is an important turbulence quantity in the breakage and coalescence models. An energy spectrum model valid in the entire spectrum of turbulence has been proposed by Pope (2000). However, the use of this energy spectrum model requires re-fitting of model parameters when the turbulent flow; characterized by Reynolds numbers, is changed. This re-fitting results in the need for an optimization routine which may be time consuming to implement and also increases the computational cost of solving the breakage and coalescence models. For this reason, in the present study, novel approximate explicit formulas are proposed that allow the calculation of model parameters in the Pope model energy spectrum without the need for optimization techniques.