Conservation relation of generalized growth rate in boundary layers

The elementary task is to calculate the growth rates of disturbances when the e;method in transition prediction is performed. However, there is no unified knowledge to determine the growth rates of disturbances in three-dimensional（3 D） flows. In this paper, we study the relation among the wave parameters of the disturbance in boundary layers in which the imaginary parts of wave parameters are far smaller than the real parts.The generalized growth rate（GGR） in the direction of group velocity is introduced, and the conservation relation of GGR is strictly deduced in theory. This conservation relation manifests that the GGR only depends on the real parts of wave parameters instead of the imaginary parts. Numerical validations for GGR conservation are also provided in the cases of first/second modes and crossflow modes. The application of GGR to the eN method in 3 D flows is discussed, and the puzzle of determining growth rates in 3 D flows is clarified. A convenient method is also proposed to calculate growth rates of disturbances in 3 D flows. Good agreement between this convenient method and existing methods is found except the condition that the angle between the group velocity direction and the x-direction is close to 90?which can be easily avoided in practical application.

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

Receptivity of Mack modes to localized unsteady blowing and suction in a chemical non-equilibrium hypersonic boundary layer

This paper studies the local receptivity of the Mack-mode instability to localized unsteady blowing and suction(UBS)in a chem-ical non-equilibrium(CNE)hypersonic boundary layer.The five-species CNE model is employed,and the receptivity efficiency is formulated by use of the residual theorem.Compared with the results for the calorically perfect gas(CPG)model,we find that the real-gas effect enhances the receptivity efficiency remarkably in the majority of the second-mode frequency band,and the enhancement is mainly attributed to the modification of the base flow due to the CNE effect,which is akin to the cold-wall effect in hypersonic boundary layers.Combined with the destabilizing role of the CNE effect on the Mack second mode,it is concluded that the CNE effect would lead to a greater linearly accumulated perturbation amplitude,implying premature of transition to turbulence in a high-enthalpy hypersonic boundary layer subject to localized perturbations.