边界层中展向波包型扰动转捩的数值模拟及用PSE方法的预测
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摘要
本文基于空间模式，研究了不可压缩平板边界层和曲面边界层中扰动的演化和转捩问题首先针对平板边界层，研究了展向等幅值型和展向波包型两类扰动的演化全过程，分析了这两类扰动的转捩机理；使用改进的PSE研究了平板边界层扰动的演化并预测了转捩位置，和数值模拟结果进行比较；最后研究了典型曲面边界层中扰动演化及PSE的应用共得到以下结果：
(1)展向等幅值扰动的演化特征：在上游，二维基本波占据主要地位，随着演化，二维基本波的幅值先增大后减小，减小的原因是三维基本波的快速增长，三维基本波的幅值将超过二维基本波占据主导地位三维基本的快速增长，使更多的高次谐波被激发出来，转捩因此发生
(2)展向波包型扰动的演化特征：随着扰动的演化，波包型扰动从展向一个峰值分裂为两个峰值，波峰中间出现展向高波数的三维扰动，然后两个峰值会逐步消失；波包展向所占的范围也逐步展向拓宽；展向大尺度结构逐步破碎成小尺度结构；初期的低波数波演化出越来越多的高波数三维波；流动结构依次出现月牙形结构涡结构流向条纹结构，到最终无序的湍流结构
(3)展向等幅值和展向波包型扰动的转捩机理为：在扰动演化的初期，不稳定区域较小，只有某些波能增长起来，随着演化，非线性作用将使平均流速度剖面快速变化，导致不稳定区域的扩大，这将使更多的高波数谐波快速增长针对不同的展向位置，一定幅值的展向波包型扰动都将引发转捩，不同的展向位置转捩位置不同，但转捩过程和特征是类似的
(4)对于研究的各类边界层，在转捩开始之前PSE方法预测扰动演化的结果与数值模拟一致，PSE方法失效的位置与数值模拟得到的转捩开始发生的位置基本一致因此，可以用PSE方法的失效位置来预测转捩位置
(5)用PSE方法研究了展向等幅值扰动的展向波数和幅值对转捩位置的影响存在使转捩位置最靠前的展向波数，当大于这个波数时转捩位置随波数的增大而靠后扰动幅值越大转捩位置越靠上游
(6)对于等曲率的圆环管道流动，曲率的存在将抑制转捩的发生，曲率越大转捩位置越靠后；对于NACA0012翼型曲面边界层，给出了转捩位置和二维扰动波幅值频率的关系，并预测了转捩的位置
In this paper, the evolutions of disturbances in incompressible boundary layers onflat plates and curved surfaces were investigated based on the spatial model. Firstly,the evolutions of two types of disturbances were studied. The two types were identicalamplitude and wavepacket along the spanwise in flat plate boundary layers. Thetransition mechanisms of two types of disturances were studied too. Secondly, withthe improved PSE method, the evolution of disturbances and prediction of thetransition position were studied in flat plate boundary layers. The results werecompared with the numerical simulation. Lastly, the disturbances evolution and theapplication of PSE in curved boundary layers were researched. We obtained thefollowing conclusions:
(1) The evolution characteristics of identical amplitude disturbances alongspanwise were showed. In the upstream, the two-dimensional basic wavedominated. With the disturbance evolution, the amplitude of the2-D basicwave increased firstly and then decreased. The decrease was induced by therapid growth of3-D basic waves. Then3-D basic waves would dominantwhen the amplitudes exceeded2-D wave. Because of the rapid growth of3-D waves, the high harmonic waves were stimulated and the spanwise sizebecame smaller, then the transition occurred.
(2) The evolution characteristics of spanwise wavepacket disturbances wereshowed. With the evolution of disturbances, one peak splited to two peaks.Between peaks, the high wavenumber3-D waves appeared and then thepeaks would gradually vanish. The spanwise of wavepacket would expand.The large scale structures broken into small scale structures. The higherwavenumber3-D waves were simulated by low wavenumber waves. Theflow structures would be crescent,-vortex, streamwise streak andunordered turbulence structure successively.
(3) For identical amplitude and wavepacket disturbances, the stabilities of localmean flow were analysed. The transition mechanism was obtained. In initialstage of evolution, the stable zone was small and only a few waves couldgrow. With the evolution, the mean flow velocity profile changed quickly due to the nonlinear effect. The instability zone enlarged and more andmore high harmonic waves were simulated rapidly and the transitionhappened. The analysis of different spanwise positions indicated that thetransiton was triggered by definite amplitude of spanwise wavepacketdisturbance. In different spanwise positions, the transition positions weredifferent, but the transition processes and characteristics were similar.
(4) For all kinds of boundary layers that were discussed, the evolution ofdisturbances was consistent by PSE and numerical simulation beforetransition. The position of the PSE invalid and the beginning of transitionby numerical simulation were the same basically. Therefore, the PSEinvalid position could predict the transition position.
(5) With PSE method, the influence of spanwise wavenumber and amplitude onthe transition position was studied for identical amplitude disturbances. Thespanwise wavenumber which made the transition position forefront existed.When the wavenumbers were larger than critical wavenumber, thetransition position would delay with the wavenumber increase. The largerwere the initial amplitudes, the fronter were the transition positions.
(6) For the identical curvature circle pipeline, the transitions were restrainedbecause of the curvature. The transition positions would be delay with thelarger curvature. For the NACA0012wing boundary layer, the relations ofthe transition position and the amplitude and frequency of2-D wave weredisscussed. Besides, the transition positions were predicted.
(1)展向等幅值扰动的演化特征：在上游，二维基本波占据主要地位，随着演化，二维基本波的幅值先增大后减小，减小的原因是三维基本波的快速增长，三维基本波的幅值将超过二维基本波占据主导地位三维基本的快速增长，使更多的高次谐波被激发出来，转捩因此发生
(2)展向波包型扰动的演化特征：随着扰动的演化，波包型扰动从展向一个峰值分裂为两个峰值，波峰中间出现展向高波数的三维扰动，然后两个峰值会逐步消失；波包展向所占的范围也逐步展向拓宽；展向大尺度结构逐步破碎成小尺度结构；初期的低波数波演化出越来越多的高波数三维波；流动结构依次出现月牙形结构涡结构流向条纹结构，到最终无序的湍流结构
(3)展向等幅值和展向波包型扰动的转捩机理为：在扰动演化的初期，不稳定区域较小，只有某些波能增长起来，随着演化，非线性作用将使平均流速度剖面快速变化，导致不稳定区域的扩大，这将使更多的高波数谐波快速增长针对不同的展向位置，一定幅值的展向波包型扰动都将引发转捩，不同的展向位置转捩位置不同，但转捩过程和特征是类似的
(4)对于研究的各类边界层，在转捩开始之前PSE方法预测扰动演化的结果与数值模拟一致，PSE方法失效的位置与数值模拟得到的转捩开始发生的位置基本一致因此，可以用PSE方法的失效位置来预测转捩位置
(5)用PSE方法研究了展向等幅值扰动的展向波数和幅值对转捩位置的影响存在使转捩位置最靠前的展向波数，当大于这个波数时转捩位置随波数的增大而靠后扰动幅值越大转捩位置越靠上游
(6)对于等曲率的圆环管道流动，曲率的存在将抑制转捩的发生，曲率越大转捩位置越靠后；对于NACA0012翼型曲面边界层，给出了转捩位置和二维扰动波幅值频率的关系，并预测了转捩的位置
In this paper, the evolutions of disturbances in incompressible boundary layers onflat plates and curved surfaces were investigated based on the spatial model. Firstly,the evolutions of two types of disturbances were studied. The two types were identicalamplitude and wavepacket along the spanwise in flat plate boundary layers. Thetransition mechanisms of two types of disturances were studied too. Secondly, withthe improved PSE method, the evolution of disturbances and prediction of thetransition position were studied in flat plate boundary layers. The results werecompared with the numerical simulation. Lastly, the disturbances evolution and theapplication of PSE in curved boundary layers were researched. We obtained thefollowing conclusions:
(1) The evolution characteristics of identical amplitude disturbances alongspanwise were showed. In the upstream, the two-dimensional basic wavedominated. With the disturbance evolution, the amplitude of the2-D basicwave increased firstly and then decreased. The decrease was induced by therapid growth of3-D basic waves. Then3-D basic waves would dominantwhen the amplitudes exceeded2-D wave. Because of the rapid growth of3-D waves, the high harmonic waves were stimulated and the spanwise sizebecame smaller, then the transition occurred.
(2) The evolution characteristics of spanwise wavepacket disturbances wereshowed. With the evolution of disturbances, one peak splited to two peaks.Between peaks, the high wavenumber3-D waves appeared and then thepeaks would gradually vanish. The spanwise of wavepacket would expand.The large scale structures broken into small scale structures. The higherwavenumber3-D waves were simulated by low wavenumber waves. Theflow structures would be crescent,-vortex, streamwise streak andunordered turbulence structure successively.
(3) For identical amplitude and wavepacket disturbances, the stabilities of localmean flow were analysed. The transition mechanism was obtained. In initialstage of evolution, the stable zone was small and only a few waves couldgrow. With the evolution, the mean flow velocity profile changed quickly due to the nonlinear effect. The instability zone enlarged and more andmore high harmonic waves were simulated rapidly and the transitionhappened. The analysis of different spanwise positions indicated that thetransiton was triggered by definite amplitude of spanwise wavepacketdisturbance. In different spanwise positions, the transition positions weredifferent, but the transition processes and characteristics were similar.
(4) For all kinds of boundary layers that were discussed, the evolution ofdisturbances was consistent by PSE and numerical simulation beforetransition. The position of the PSE invalid and the beginning of transitionby numerical simulation were the same basically. Therefore, the PSEinvalid position could predict the transition position.
(5) With PSE method, the influence of spanwise wavenumber and amplitude onthe transition position was studied for identical amplitude disturbances. Thespanwise wavenumber which made the transition position forefront existed.When the wavenumbers were larger than critical wavenumber, thetransition position would delay with the wavenumber increase. The largerwere the initial amplitudes, the fronter were the transition positions.
(6) For the identical curvature circle pipeline, the transitions were restrainedbecause of the curvature. The transition positions would be delay with thelarger curvature. For the NACA0012wing boundary layer, the relations ofthe transition position and the amplitude and frequency of2-D wave weredisscussed. Besides, the transition positions were predicted.
引文
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