超声速方腔流动及控制的数值模拟
发布时间：2018-09-06 12:43
【摘要】：方腔绕流现象普遍存在于航空航天领域中,在一定流动条件下会导致强烈的压力振荡,对环境及腔内装置产生危害。同时,方腔流动本身也涉及到非定常流、涡动力学、剪切层不稳定性等诸多流体力学前沿问题。因此,近些年来一直受到科研工作者与工程师们的关注。本文采用直接数值模拟方法对二维超声速方腔流动及控制进行了研究,主要工作包括以下几个方面：(1)以长深比L/D=4的二维方腔为物理模型,通过直接数值模拟研究了低雷诺数下来流边界层厚度与马赫数对方腔流动的影响。结果表明：当马赫数固定为Ma=1.8时,随着来流边界层厚度的减小,方腔流动会经历定常模态、单—Rossiter Ⅱ模态、Rossiter Ⅱ模态为主模态同时伴有Rossiter Ⅲ模态与低频模态、Rossiter Ⅲ模态为主模态同时伴有Rossiter Ⅱ模态与低频模态的模态转变过程,低频模态的产生与剪切层涡结构和方腔后壁拐角不同撞击形式的切换有关。剪切模态下,方腔流动主模态的振荡频率及振荡幅值均会有所增大,其中振荡幅值的增大源自剪切层不稳定性及其与回流区相互作用的增强。当初始来流边界层厚度固定时,随着来流马赫数的增大,方腔流动会经历尾迹模态(来流边界层厚度足够小)、剪切模态、定常模态的模态转变过程；剪切模态下,方腔流动主模态的振荡幅值会逐渐减小,这与剪切层不稳定性的减弱有关。上述模态转变过程可通过流场动力学模态分解得到的特征模态空间结构变化直观体现出来,而且能谱(整体振荡频率)与监测点功率谱密度分析得到的振荡频率也十分吻合。(2)给定入口处的边界层速度型(Ma=1.8),研究了方腔后壁拐角倒圆被动控制及方腔前壁上游垂直流向亚声速稳定射流主动控制对方腔流动的影响。结果表明：被动控制下,随着倒圆半径的增大,由于剪切层中涡与方腔后壁撞击形式的改变,方腔流动会经历Rossiter Ⅱ模态为主模态同时伴有Rossiter Ⅲ模态与低频模态、RossiterⅢ模态为主模态同时伴有Rossiter Ⅱ模态与低频模态、单—Possiter Ⅲ模态的模态转变过程：方腔振荡幅值会逐渐减小,这是因为剪切层不稳定性及其与回流区相互作用的减弱。主动控制下,方腔剪切层被抬升以削弱剪切层与方腔后壁的撞击作用,同时剪切层会增厚以降低对腔内压力扰动的感受性,剪切层不稳定性及其与回流区的相互作用也被削弱,从而达到抑制方腔振荡的效果。(3)针对原始变量(ρ,u,,T)形式的二维可压缩N-S方程,基于加权内积形式的POD与Galerkin映射方法构造了新的降阶模型(近似全N-S方程模型),理论上可以适用于超声速方腔流动问题,并将其与目前常用的适用于中、低马赫数方腔绕流问题的等熵N-S方程模型进行了对比。结果表明：对于来流边界层相对较厚的二维超声速方腔绕流,近似全N-S方程模型相比于等熵N-S方程模型采用较少的POD模态就可以准确预测方腔流动的主要动力学行为,监测点处流向速度功率谱密度给出的振荡主频和相应幅值以及不同时刻瞬态流向速度分布与DNS结果的对比很好的验证了这一结论。对于来流边界层相对较薄的超声速方腔绕流,等熵N-S方程模型下POD模态系数的Runge-Kutta显式推进最终会发散,而在近似全N-S方程模型下却可以稳定进行,表明新模型具有更好的鲁棒性,但准确预测方腔流动的主要动力学行为仍需要在降阶模型中添加耗散模型。此外,当前近似全N-S方程模型的降阶处理方法相对简单,可以很方便地推广应用于其它超声速流动问题。
[Abstract]:The flow around a square cavity is ubiquitous in the aerospace field, which can cause strong pressure oscillation under certain flow conditions, which is harmful to the environment and the devices in the cavity. In this paper, direct numerical simulation method is used to study the flow and control of two-dimensional supersonic square cavity. The main work includes the following aspects: (1) The thickness and Mach number of the low Reynolds number downstream boundary layer are studied by direct numerical simulation using the two-dimensional square cavity with L/D=4 as the physical model. The results show that when the Mach number is fixed at Ma=1.8, with the decrease of the thickness of the boundary layer, the flow in the square cavity will undergo a steady mode. The single-Rossiter II mode, the Rossiter II mode are the dominant mode, accompanied by the Rossiter III mode and the low-frequency mode. The Rossiter III mode is the dominant mode and accompanied by the Rossiter II mode. In shear mode, the oscillation frequency and amplitude of the main mode of the square cavity flow will increase, and the amplitude of the oscillation will increase due to the instability of the shear layer and its relationship with the recirculation region. When the initial inflow boundary layer thickness is fixed, the flow in a square cavity will undergo a wake mode (the inflow boundary layer thickness is small enough), a shear mode, and a steady mode transition process. Under the shear mode, the oscillation amplitude of the main mode of the square cavity flow will gradually decrease, which is related to the instability of the shear layer. The above-mentioned mode transition process can be visually reflected by the change of the spatial structure of the characteristic modes obtained from the dynamic mode decomposition of the flow field, and the energy spectrum (overall oscillation frequency) is in good agreement with the oscillation frequency obtained from the power spectral density analysis of the monitoring point. (2) The boundary layer velocity pattern (Ma = 1.8) at a given entrance is studied. The results show that under the passive control, with the increase of the radius of the circle, the flow in the square cavity will undergo Rossiter II mode dominance due to the change of the collision form between the vortex in the shear layer and the rear wall of the square cavity. There are Rossiter III modes and low frequency modes, Rossiter III modes are dominant modes and Rossiter II modes and low frequency modes. The mode transition process of single-Possiter III modes: the amplitude of the square cavity oscillation decreases gradually because of the shear layer instability and the weakening of its interaction with the recirculation region. The shear layer is lifted to weaken the impact between the shear layer and the back wall of the square cavity, and the shear layer is thickened to reduce the sensitivity to the pressure disturbance in the cavity. The instability of the shear layer and its interaction with the recirculation region are also weakened to suppress the oscillation of the square cavity. (3) Two-dimensional compressible N-S square in the form of the original variable (p, u, T) Based on the weighted inner product POD and Galerkin mapping method, a new reduced-order model (approximate full N-S equation model) is constructed, which can be applied to the supersonic flow in a square cavity theoretically. The model is compared with the isentropic N-S equation model commonly used to solve the flow around a square cavity with medium and low Mach numbers. The approximate full N-S equation model can accurately predict the main dynamic behavior of a two-dimensional supersonic square cavity with relatively thick flow boundary layer by using fewer POD modes than the isentropic N-S equation model. The oscillatory dominant frequency and corresponding amplitude given by the power spectral density of the flow direction at the monitoring point and the transient flow direction velocity at different times can be predicted by using the approximate full N-S equation model. The comparison between the degree distribution and DNS results shows that the Runge-Kutta explicit propulsion of POD modal coefficients in the isentropic N-S equation model will eventually diverge for the supersonic square cavity with relatively thin incoming boundary layer, but it can be carried out stably in the approximate full N-S equation model. The results show that the new model has better robustness, but the new model has better robustness. It is still necessary to add a dissipation model to the reduced-order model to accurately predict the main dynamic behavior of the cavity flow. In addition, the current reduced-order method of approximate full N-S equation model is relatively simple and can be easily extended to other supersonic flow problems.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O354.3
[Abstract]:The flow around a square cavity is ubiquitous in the aerospace field, which can cause strong pressure oscillation under certain flow conditions, which is harmful to the environment and the devices in the cavity. In this paper, direct numerical simulation method is used to study the flow and control of two-dimensional supersonic square cavity. The main work includes the following aspects: (1) The thickness and Mach number of the low Reynolds number downstream boundary layer are studied by direct numerical simulation using the two-dimensional square cavity with L/D=4 as the physical model. The results show that when the Mach number is fixed at Ma=1.8, with the decrease of the thickness of the boundary layer, the flow in the square cavity will undergo a steady mode. The single-Rossiter II mode, the Rossiter II mode are the dominant mode, accompanied by the Rossiter III mode and the low-frequency mode. The Rossiter III mode is the dominant mode and accompanied by the Rossiter II mode. In shear mode, the oscillation frequency and amplitude of the main mode of the square cavity flow will increase, and the amplitude of the oscillation will increase due to the instability of the shear layer and its relationship with the recirculation region. When the initial inflow boundary layer thickness is fixed, the flow in a square cavity will undergo a wake mode (the inflow boundary layer thickness is small enough), a shear mode, and a steady mode transition process. Under the shear mode, the oscillation amplitude of the main mode of the square cavity flow will gradually decrease, which is related to the instability of the shear layer. The above-mentioned mode transition process can be visually reflected by the change of the spatial structure of the characteristic modes obtained from the dynamic mode decomposition of the flow field, and the energy spectrum (overall oscillation frequency) is in good agreement with the oscillation frequency obtained from the power spectral density analysis of the monitoring point. (2) The boundary layer velocity pattern (Ma = 1.8) at a given entrance is studied. The results show that under the passive control, with the increase of the radius of the circle, the flow in the square cavity will undergo Rossiter II mode dominance due to the change of the collision form between the vortex in the shear layer and the rear wall of the square cavity. There are Rossiter III modes and low frequency modes, Rossiter III modes are dominant modes and Rossiter II modes and low frequency modes. The mode transition process of single-Possiter III modes: the amplitude of the square cavity oscillation decreases gradually because of the shear layer instability and the weakening of its interaction with the recirculation region. The shear layer is lifted to weaken the impact between the shear layer and the back wall of the square cavity, and the shear layer is thickened to reduce the sensitivity to the pressure disturbance in the cavity. The instability of the shear layer and its interaction with the recirculation region are also weakened to suppress the oscillation of the square cavity. (3) Two-dimensional compressible N-S square in the form of the original variable (p, u, T) Based on the weighted inner product POD and Galerkin mapping method, a new reduced-order model (approximate full N-S equation model) is constructed, which can be applied to the supersonic flow in a square cavity theoretically. The model is compared with the isentropic N-S equation model commonly used to solve the flow around a square cavity with medium and low Mach numbers. The approximate full N-S equation model can accurately predict the main dynamic behavior of a two-dimensional supersonic square cavity with relatively thick flow boundary layer by using fewer POD modes than the isentropic N-S equation model. The oscillatory dominant frequency and corresponding amplitude given by the power spectral density of the flow direction at the monitoring point and the transient flow direction velocity at different times can be predicted by using the approximate full N-S equation model. The comparison between the degree distribution and DNS results shows that the Runge-Kutta explicit propulsion of POD modal coefficients in the isentropic N-S equation model will eventually diverge for the supersonic square cavity with relatively thin incoming boundary layer, but it can be carried out stably in the approximate full N-S equation model. The results show that the new model has better robustness, but the new model has better robustness. It is still necessary to add a dissipation model to the reduced-order model to accurately predict the main dynamic behavior of the cavity flow. In addition, the current reduced-order method of approximate full N-S equation model is relatively simple and can be easily extended to other supersonic flow problems.
【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O354.3
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