超聲速方腔流動(dòng)及控制的數(shù)值模擬
發(fā)布時(shí)間：2018-09-06 12:43
【摘要】：方腔繞流現(xiàn)象普遍存在于航空航天領(lǐng)域中,在一定流動(dòng)條件下會(huì)導(dǎo)致強(qiáng)烈的壓力振蕩,對(duì)環(huán)境及腔內(nèi)裝置產(chǎn)生危害。同時(shí),方腔流動(dòng)本身也涉及到非定常流、渦動(dòng)力學(xué)、剪切層不穩(wěn)定性等諸多流體力學(xué)前沿問(wèn)題。因此,近些年來(lái)一直受到科研工作者與工程師們的關(guān)注。本文采用直接數(shù)值模擬方法對(duì)二維超聲速方腔流動(dòng)及控制進(jìn)行了研究,主要工作包括以下幾個(gè)方面：(1)以長(zhǎng)深比L/D=4的二維方腔為物理模型,通過(guò)直接數(shù)值模擬研究了低雷諾數(shù)下來(lái)流邊界層厚度與馬赫數(shù)對(duì)方腔流動(dòng)的影響。結(jié)果表明：當(dāng)馬赫數(shù)固定為Ma=1.8時(shí),隨著來(lái)流邊界層厚度的減小,方腔流動(dòng)會(huì)經(jīng)歷定常模態(tài)、單—Rossiter Ⅱ模態(tài)、Rossiter Ⅱ模態(tài)為主模態(tài)同時(shí)伴有Rossiter Ⅲ模態(tài)與低頻模態(tài)、Rossiter Ⅲ模態(tài)為主模態(tài)同時(shí)伴有Rossiter Ⅱ模態(tài)與低頻模態(tài)的模態(tài)轉(zhuǎn)變過(guò)程,低頻模態(tài)的產(chǎn)生與剪切層渦結(jié)構(gòu)和方腔后壁拐角不同撞擊形式的切換有關(guān)。剪切模態(tài)下,方腔流動(dòng)主模態(tài)的振蕩頻率及振蕩幅值均會(huì)有所增大,其中振蕩幅值的增大源自剪切層不穩(wěn)定性及其與回流區(qū)相互作用的增強(qiáng)。當(dāng)初始來(lái)流邊界層厚度固定時(shí),隨著來(lái)流馬赫數(shù)的增大,方腔流動(dòng)會(huì)經(jīng)歷尾跡模態(tài)(來(lái)流邊界層厚度足夠小)、剪切模態(tài)、定常模態(tài)的模態(tài)轉(zhuǎn)變過(guò)程；剪切模態(tài)下,方腔流動(dòng)主模態(tài)的振蕩幅值會(huì)逐漸減小,這與剪切層不穩(wěn)定性的減弱有關(guān)。上述模態(tài)轉(zhuǎn)變過(guò)程可通過(guò)流場(chǎng)動(dòng)力學(xué)模態(tài)分解得到的特征模態(tài)空間結(jié)構(gòu)變化直觀體現(xiàn)出來(lái),而且能譜(整體振蕩頻率)與監(jiān)測(cè)點(diǎn)功率譜密度分析得到的振蕩頻率也十分吻合。(2)給定入口處的邊界層速度型(Ma=1.8),研究了方腔后壁拐角倒圓被動(dòng)控制及方腔前壁上游垂直流向亞聲速穩(wěn)定射流主動(dòng)控制對(duì)方腔流動(dòng)的影響。結(jié)果表明：被動(dòng)控制下,隨著倒圓半徑的增大,由于剪切層中渦與方腔后壁撞擊形式的改變,方腔流動(dòng)會(huì)經(jīng)歷Rossiter Ⅱ模態(tài)為主模態(tài)同時(shí)伴有Rossiter Ⅲ模態(tài)與低頻模態(tài)、RossiterⅢ模態(tài)為主模態(tài)同時(shí)伴有Rossiter Ⅱ模態(tài)與低頻模態(tài)、單—Possiter Ⅲ模態(tài)的模態(tài)轉(zhuǎn)變過(guò)程：方腔振蕩幅值會(huì)逐漸減小,這是因?yàn)榧羟袑硬环�(wěn)定性及其與回流區(qū)相互作用的減弱。主動(dòng)控制下,方腔剪切層被抬升以削弱剪切層與方腔后壁的撞擊作用,同時(shí)剪切層會(huì)增厚以降低對(duì)腔內(nèi)壓力擾動(dòng)的感受性,剪切層不穩(wěn)定性及其與回流區(qū)的相互作用也被削弱,從而達(dá)到抑制方腔振蕩的效果。(3)針對(duì)原始變量(ρ,u,,T)形式的二維可壓縮N-S方程,基于加權(quán)內(nèi)積形式的POD與Galerkin映射方法構(gòu)造了新的降階模型(近似全N-S方程模型),理論上可以適用于超聲速方腔流動(dòng)問(wèn)題,并將其與目前常用的適用于中、低馬赫數(shù)方腔繞流問(wèn)題的等熵N-S方程模型進(jìn)行了對(duì)比。結(jié)果表明：對(duì)于來(lái)流邊界層相對(duì)較厚的二維超聲速方腔繞流,近似全N-S方程模型相比于等熵N-S方程模型采用較少的POD模態(tài)就可以準(zhǔn)確預(yù)測(cè)方腔流動(dòng)的主要?jiǎng)恿W(xué)行為,監(jiān)測(cè)點(diǎn)處流向速度功率譜密度給出的振蕩主頻和相應(yīng)幅值以及不同時(shí)刻瞬態(tài)流向速度分布與DNS結(jié)果的對(duì)比很好的驗(yàn)證了這一結(jié)論。對(duì)于來(lái)流邊界層相對(duì)較薄的超聲速方腔繞流,等熵N-S方程模型下POD模態(tài)系數(shù)的Runge-Kutta顯式推進(jìn)最終會(huì)發(fā)散,而在近似全N-S方程模型下卻可以穩(wěn)定進(jìn)行,表明新模型具有更好的魯棒性,但準(zhǔn)確預(yù)測(cè)方腔流動(dòng)的主要?jiǎng)恿W(xué)行為仍需要在降階模型中添加耗散模型。此外,當(dāng)前近似全N-S方程模型的降階處理方法相對(duì)簡(jiǎn)單,可以很方便地推廣應(yīng)用于其它超聲速流動(dòng)問(wèn)題。
[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.
【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：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.
【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：O354.3
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