小攻角钝锥高超声速边界层的扰动演化
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摘要
本文采用数值模拟的方法,以小攻角钝锥边界层这一典型的三维高超声速边界层为研究对象,研究了高超声速流动中边界层内扰动的演化。
在基本流计算方面,对传统抛物化N-S方程(PNS方程)求解过程中的流向压力梯度的处理方法进行了改进,用边界层上缘的压力流向梯度代替方程中的压力流向梯度项,使之提供的定常流可以做为基本流用于进行流动稳定性分析。分别对小幅值和有限幅值扰动的演化进行了研究。通过数值计算验证了线性稳定性理论在该类高超声速三维边界层中的适用性;对给定入口两组不同频率分布的扰动,研究了小攻角钝锥的周向非对称转捩的特征;研究了扰动在流场中的非线性演化特征;研究了小攻角钝锥边界层中有限幅值扰动的演化,并与零攻角钝锥、高超声速及不可压缩平板中波包型扰动的演化进行了对比。
通过本文的研究所得结论如下:
1.小攻角钝锥边界层的基本流可以按照三维性的强弱不同分成两个区域。在迎风面及侧面的部分(0-135度的区域),边界层沿周向变化不大,线性稳定性理论可以比较准确的预测扰动的增长;在背风面附近区域,边界层变化比较剧烈,扰动演化呈现明显的三维特征。但在考虑流场三维性的情况下,选取基本流周向变化剧烈区域长度的一半作为三维扰动的等效展向波长,线性稳定性理论也能够比较好的预测扰动的增长。
2.当基本扰动波增长到一定幅值时,原本为衰减的扰动波在非线性的作用下会增长起来;而基本波还将在一段距离内保持线性增长,当基本扰动波的幅值增长到大约0.05-0.1左右时,其演化才明显地呈现非线性特征。这一规律在迎风面、侧面和背风面都存在。
3.通过在计算域入口引入两种频率组分不同的扰动,得到了两种转捩位置的分布。这表明,转捩位置沿周向的分布与入口不稳定波的频率和幅值有很大的关系。某一子午面的转捩位置主要决定于该子午面附近最不稳定波的增长率及该扰动在入口处的幅值。根据这一特点,结合稳定性分析的结果及实验中背景扰动幅值分布的特点,可以解释大多数转捩实验中,背风面先转捩,迎风面后转捩的现象,还可以解释在150度子午面上出现的转捩位置“凹陷”的现象。
4.数值模拟发现,在迎风面和侧面处,入口的等幅值的扰动波会在下游演化成波包型分布,随后在更下游的流场中激发出小尺度三维扰动。这种小尺度扰动的定常部分是一种流向条纹结构,其周向波长都在φ/π≈0.014-0.016之间。而非定常部分的快速增长的机理应该属于二次失稳理论中的基本模态失稳。
5.在零攻角的钝锥边界层中,入口加入波包型扰动,也会在下游激发起与小攻角流动时迎风面类似的小尺度三维结构,其展向波长依然在φ/π≈0.014-0.016之间。入口扰动分布越集中,该结构越靠近上游出现。通过与高超声速及不可压缩平板的波包型扰动演化的对比,发现这种扰动的出现是高超声速边界层中的一种特殊现象。
6.在背风面,基本流的三维性比较强,在其影响下基本扰动是三维的,当基本扰动的幅值增长到足够大时,将会激发起二次谐波及高次谐波,使得流场呈“胞格状”分布,随后将导致流场转捩。背风面三维波的展向尺度与基本流的三维性有关,比迎风面或侧面由于非线性激发的三维扰动展向尺度大的多。
By numerical simulation, the evolutions of the disturbances are investigated in hyersonic boundary layer on a blunt cone at a small angle of attack (AOA).
By using the streamwise pressure gradient on the edge of the boundary layer instead of the one in the boundary layer, traditional technique for the one in parabolized Navier-Stokes (PNS) equation solution was improved, for the use of PNS as basic flows for stability analysis of hypersonic flows.
We investigated the evolutions of the disturbances with small and finite amplitude, respectively. first,the linear stability theory (LST) is verified in the hypersonic 3-dimensional boundary layer; second, inducing two groups of disturbances with different frequencies at inlet, non-symmetrical transiton along the azimuthal direction on blunt cone at small AOA is investigated; third, the nonlinear characters of the second mode disturbances in the flow is studied; then, the evolutions of wave-packet disturbances with finite amplitude in blunt cone at zero-AOA are simulated, and the results are compared with the ones of the same kind disturbances in small AOA blunt cone, hyperconic and incompressible flat bounary layer. And the following conclusions can be drawn:
1. The boundary layer on a blunt cone at small AOA can be seperated into two regions by different 3-dimensional feature. In the windward and side region (φ= 0 ~。-135~。), the boundary layer changes bluntly, and LST predicts the growth well; in the region near the leeward, the bounday layer changes shapely, with the evolution of the disturbance is 3-D, but LST can also provide a good prediction when the 3-D waves are considered which the spanwise wavelength is one half of the length of the region with a sharp variation in the flow field on the leeward.
2. The waves which are linearly decaying can grow by the nonlinear effect when the main disturbance grow to a large enough amplitude, but the main wave can also grow linearly with a distance. When the amplitude of the main wave reached about 0.05-0.1, nonlinear feature can be seen obviously. The rule is in existance on the windray, sideray, and leeray.
3. Transition onset distributions along the azimuthal direction are obtained. It shows that transition onset is relevant to frequencies and amplitudes of the disturbances at the inlet, and is decided by the amplitudes of the most unstable waves at the inlet. According to this, the phenomenon leeside-forward and windside-after over a circular cone at non-zero AOA in most experiments can be explained. Also, it can explain the indentation of transition curve in theφ=150 ? meridian plane.
4. On the windray and sideray, disurbance with equal amplitude along azimuthal direction can become wave-pack distribution in the downstream, and then small scale 3-D disturbances can be excited. The stational parts of the disturbances are stationary streamwise streaky structures, which haveφ/π≈0.014-0.016 spanwise scale. And growth of the non-stational parts should connect with the secondary instability theory.
5. At zero AOA, wave-pack disturbances at inlet also can excite small scale 3-D structures in the downstream and the spanwise wave length is same. The disturbances at inlet are more concentrated, and these structures exited earlier. Compared with the evolutions of the wave-packet waves in hypersonic and incompressible flat, the generation of this kind of disturbance is a special phenomenon in hypersonic boundary layer.
6. The sharp 3-D basic flow leads to 3-D disturbances on the leeray. When the waves grow higher enough, higher harmonic waves will be excited and it makes the flow“cell-like”. Then, it will lead to a transition to turbulence. The scale of 3-D disturbances on the leeray is relevant to the 3-D feature of the basic leeward flow, which is larger than the one on the windray and sideray.
在基本流计算方面,对传统抛物化N-S方程(PNS方程)求解过程中的流向压力梯度的处理方法进行了改进,用边界层上缘的压力流向梯度代替方程中的压力流向梯度项,使之提供的定常流可以做为基本流用于进行流动稳定性分析。分别对小幅值和有限幅值扰动的演化进行了研究。通过数值计算验证了线性稳定性理论在该类高超声速三维边界层中的适用性;对给定入口两组不同频率分布的扰动,研究了小攻角钝锥的周向非对称转捩的特征;研究了扰动在流场中的非线性演化特征;研究了小攻角钝锥边界层中有限幅值扰动的演化,并与零攻角钝锥、高超声速及不可压缩平板中波包型扰动的演化进行了对比。
通过本文的研究所得结论如下:
1.小攻角钝锥边界层的基本流可以按照三维性的强弱不同分成两个区域。在迎风面及侧面的部分(0-135度的区域),边界层沿周向变化不大,线性稳定性理论可以比较准确的预测扰动的增长;在背风面附近区域,边界层变化比较剧烈,扰动演化呈现明显的三维特征。但在考虑流场三维性的情况下,选取基本流周向变化剧烈区域长度的一半作为三维扰动的等效展向波长,线性稳定性理论也能够比较好的预测扰动的增长。
2.当基本扰动波增长到一定幅值时,原本为衰减的扰动波在非线性的作用下会增长起来;而基本波还将在一段距离内保持线性增长,当基本扰动波的幅值增长到大约0.05-0.1左右时,其演化才明显地呈现非线性特征。这一规律在迎风面、侧面和背风面都存在。
3.通过在计算域入口引入两种频率组分不同的扰动,得到了两种转捩位置的分布。这表明,转捩位置沿周向的分布与入口不稳定波的频率和幅值有很大的关系。某一子午面的转捩位置主要决定于该子午面附近最不稳定波的增长率及该扰动在入口处的幅值。根据这一特点,结合稳定性分析的结果及实验中背景扰动幅值分布的特点,可以解释大多数转捩实验中,背风面先转捩,迎风面后转捩的现象,还可以解释在150度子午面上出现的转捩位置“凹陷”的现象。
4.数值模拟发现,在迎风面和侧面处,入口的等幅值的扰动波会在下游演化成波包型分布,随后在更下游的流场中激发出小尺度三维扰动。这种小尺度扰动的定常部分是一种流向条纹结构,其周向波长都在φ/π≈0.014-0.016之间。而非定常部分的快速增长的机理应该属于二次失稳理论中的基本模态失稳。
5.在零攻角的钝锥边界层中,入口加入波包型扰动,也会在下游激发起与小攻角流动时迎风面类似的小尺度三维结构,其展向波长依然在φ/π≈0.014-0.016之间。入口扰动分布越集中,该结构越靠近上游出现。通过与高超声速及不可压缩平板的波包型扰动演化的对比,发现这种扰动的出现是高超声速边界层中的一种特殊现象。
6.在背风面,基本流的三维性比较强,在其影响下基本扰动是三维的,当基本扰动的幅值增长到足够大时,将会激发起二次谐波及高次谐波,使得流场呈“胞格状”分布,随后将导致流场转捩。背风面三维波的展向尺度与基本流的三维性有关,比迎风面或侧面由于非线性激发的三维扰动展向尺度大的多。
By numerical simulation, the evolutions of the disturbances are investigated in hyersonic boundary layer on a blunt cone at a small angle of attack (AOA).
By using the streamwise pressure gradient on the edge of the boundary layer instead of the one in the boundary layer, traditional technique for the one in parabolized Navier-Stokes (PNS) equation solution was improved, for the use of PNS as basic flows for stability analysis of hypersonic flows.
We investigated the evolutions of the disturbances with small and finite amplitude, respectively. first,the linear stability theory (LST) is verified in the hypersonic 3-dimensional boundary layer; second, inducing two groups of disturbances with different frequencies at inlet, non-symmetrical transiton along the azimuthal direction on blunt cone at small AOA is investigated; third, the nonlinear characters of the second mode disturbances in the flow is studied; then, the evolutions of wave-packet disturbances with finite amplitude in blunt cone at zero-AOA are simulated, and the results are compared with the ones of the same kind disturbances in small AOA blunt cone, hyperconic and incompressible flat bounary layer. And the following conclusions can be drawn:
1. The boundary layer on a blunt cone at small AOA can be seperated into two regions by different 3-dimensional feature. In the windward and side region (φ= 0 ~。-135~。), the boundary layer changes bluntly, and LST predicts the growth well; in the region near the leeward, the bounday layer changes shapely, with the evolution of the disturbance is 3-D, but LST can also provide a good prediction when the 3-D waves are considered which the spanwise wavelength is one half of the length of the region with a sharp variation in the flow field on the leeward.
2. The waves which are linearly decaying can grow by the nonlinear effect when the main disturbance grow to a large enough amplitude, but the main wave can also grow linearly with a distance. When the amplitude of the main wave reached about 0.05-0.1, nonlinear feature can be seen obviously. The rule is in existance on the windray, sideray, and leeray.
3. Transition onset distributions along the azimuthal direction are obtained. It shows that transition onset is relevant to frequencies and amplitudes of the disturbances at the inlet, and is decided by the amplitudes of the most unstable waves at the inlet. According to this, the phenomenon leeside-forward and windside-after over a circular cone at non-zero AOA in most experiments can be explained. Also, it can explain the indentation of transition curve in theφ=150 ? meridian plane.
4. On the windray and sideray, disurbance with equal amplitude along azimuthal direction can become wave-pack distribution in the downstream, and then small scale 3-D disturbances can be excited. The stational parts of the disturbances are stationary streamwise streaky structures, which haveφ/π≈0.014-0.016 spanwise scale. And growth of the non-stational parts should connect with the secondary instability theory.
5. At zero AOA, wave-pack disturbances at inlet also can excite small scale 3-D structures in the downstream and the spanwise wave length is same. The disturbances at inlet are more concentrated, and these structures exited earlier. Compared with the evolutions of the wave-packet waves in hypersonic and incompressible flat, the generation of this kind of disturbance is a special phenomenon in hypersonic boundary layer.
6. The sharp 3-D basic flow leads to 3-D disturbances on the leeray. When the waves grow higher enough, higher harmonic waves will be excited and it makes the flow“cell-like”. Then, it will lead to a transition to turbulence. The scale of 3-D disturbances on the leeray is relevant to the 3-D feature of the basic leeward flow, which is larger than the one on the windray and sideray.
引文
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