Application Of E-N Method And Prediction Of Disturbances Propagation In Three-Dimensional Hypersonic Boundary Layers

Technology of hypersonic was developed rapidly in recent years.And hypersonic boundary-layer transition was got more attention than ever.The desire of hypersonic boundary-layer transition prediction calculation was increased.Under those backgrounds,a research of application of e-N method in three-dimensional boundary layers was made in this paper.The propagation of disturbances is the foundation of e-N method for transition prediction.And it's also one of the mean stages in transition process.So it's needed to make clear that how disturbances propagate in general three-dimensional boundary layers.It's a key problem for disturbances propagation calculating that how to determine the wave numbers of disturbances in general three-dimensional boundary layers which vary in both streamwise and spanwise directions.It is a part of main work to get the correct predition of wave number and amplitude of disturnbances during their propagation.So research of e-N method and prediction of disturbances propagation in threedimensional boundary layers are two main parts of this paper.And the main work and conclusions in this paper were showed as follow.1.A conservation relation of imaginary parts of wave parameters was derived according to the dispersion relation of disturbances in three-dimensional boundary layers.The conservation relation could give a theoretical explanation of Mack's simplification treatment for using e-N method in three-dimensional boundary layers.And the simplified e-N method was tested on a backswept wing and a complex aircraft model.2.A code of e-N method for three-dimensional boundary layers transition prediction was finished.And predictions of transition were done on a modelwhich is similar to the Hy Bo LT experiment model and a cone-cylinder-flat platecombined aircraft modelusing this code.The results in different attitudes and attack angles were showed.And some analysis of effects of attitudes and attack angles were made.3.The compatibility relation and the ray-tracing theory,which are theories of wave in fluids,were extended to three-dimensional boundary layers to get the variation of wave numbers for prediction of disturbances propagation.The results of those theories were checked with direct numerical simulation(DNS)results of disturbance equations.The results showed thatthe compatibility relation and the ray-tracing theory both can correctly obtain the wave numbers and amplitudes.4.The results of saddle point method(SPM)which is one of e-N methods and fixed spanwise wave number method were checked.The results showed that both methodscannot get correct amplitudes in general three-dimensional boundary layers.And an explanation of the differencebetween SPM and DNS was given.And the results showed that the SPM is a conservative method.5.The direction of disturbances propagation was analyzed using DNS and linear stability theory(LST).The results showed shat the direction of disturbances propagation is the group velocity direction.And an interesting phenomenon was found that the trace of spanwise wavepackage amplitude position is maybe not the path of wave group velocity,but the downstream boundary line of unstable region of disturbances on the model.6.The stability analysis and transition prediction are both needed to reprocess the grids on general three-dimensional model.Details of grids reprocessing were showed in this paper.And a new three-dimensional interpolation method based on Lagrange interpolation method for three-dimensional structure grid was proposed.7.A relationship between amplitude growth rates in different directions was found that the values of amplitude growth rate projections in group velocity direction,which were obtained by solving the eigenvalue problem of O-S equations with different spanwise growth rates,are the same.The relationship can explain the phenomenon that the two ways,which are calculating amplitudes along group velocity path and the chord,both can obtain the same results on a backswept wing.