本文選題：植被水流 + 流速解析解��； 參考：《武漢大學(xué)》2016年博士論文

【摘要】：本文主要研究在植被存在情況下明渠水流的運(yùn)動特性,即明渠植被水流的水動力學(xué)特性。研究的主要內(nèi)容包括不同類型植被水流的流速分布解析解以及植被對水流的阻力特性。分別對柔性植被,雙層剛性植被存在情況下的明渠恒定均勻流推導(dǎo)出縱向流速垂向分布的解析解模型。對非淹沒剛性植被存在情況下,恒定非均勻流中的植被阻力特性進(jìn)行研究,推導(dǎo)出植被拖曳力系數(shù)與雷諾數(shù)的變化關(guān)系。本文采用數(shù)學(xué)模型推導(dǎo)和實驗室試驗的相結(jié)合的方法對植被水流的水動力學(xué)特性進(jìn)行了詳細(xì)的研究,可以分為以下幾個方面。柔性植被受到水流的作用會發(fā)生彎曲變形,本文針對這種情況研究并推導(dǎo)出柔性植被的彎曲特性以及在小彎曲情況下水流縱向流速的垂向分布解析解。將淹沒柔性植被水流在垂向上分為植被層和自由水層分別來研究。首先,在植被層中對柔性植被應(yīng)用懸臂梁理論推導(dǎo)出植被彎曲后各點的角度以及彎曲后的高度。然后,將植被阻力和雷諾應(yīng)力的表達(dá)式代入水流控制方程中求解得到流速的解析解。其中,與剛性植被阻力不同,彎曲柔性植被在水流方向上的阻力為拖曳力與摩擦力的合力。當(dāng)植被彎曲程度較小時,植被層中雷諾應(yīng)力符合指數(shù)分布的形式,所以由此求解控制方程得到的流速解析解適用于植被發(fā)生小彎曲的情況。在自由水層中,為滿足流速梯度在水面為零的條件,推導(dǎo)求解出流速分布的多項式表達(dá)式,與傳統(tǒng)的對數(shù)流速表達(dá)式相比,該多項式表達(dá)式可以更好地符合實際情況。當(dāng)水流流速較大或者植被柔性較高時,植被會發(fā)生大撓度的彎曲變形,在這種情況下,植被層中的雷諾應(yīng)力不再符合指數(shù)分布形式,所以在植被小彎曲情況下得到的水流流速解析解在這里不適用。并且試驗結(jié)果表明,植被彎曲程度較大時,其對水流的阻力會大幅減小,并與水流的流速近似為線性關(guān)系�；谶@個現(xiàn)象,本文提出了新的植被阻力公式,并通過引入植被層和自由水層的卡門系數(shù),求解得出植被發(fā)生大彎曲變形情況下,水流的縱向流速垂向分布的解析解。并且該模型能夠很好地吻合試驗所得的流速數(shù)據(jù)。在天然環(huán)境下,河道中的植被高度往往是不一樣的,并且是高低交錯排列的,在這種情況下,水流的流速特性更為復(fù)雜。本文以雙層剛性植被為例,采用冪級數(shù)等方法求解水流控制方程,研究并得到雙層剛性植被存在時,各層水流縱向流速的垂向分布解析解。與此同時,在實驗室進(jìn)行了雙層植被水流的試驗,并通過PIV粒子圖像測速系統(tǒng)測量得到水流的流速特性,試驗結(jié)果顯示出流速在植被層下部近似恒定,而在植被層上部逐漸增大。通過與試驗數(shù)據(jù)的對比,該流速解析解模型可以很好地預(yù)測雙層植被水流的流速特性,同時本文給出了雙層植被水流的剪切渦入侵深度的經(jīng)驗公式。上面所敘述的植被水流特性研究都是針對恒定均勻流情況,然而在實際河道中,水流往往是非均勻的。前人的研究成果已經(jīng)得出在恒定均勻流情況下,拖曳力系數(shù)與雷諾數(shù)的關(guān)系,當(dāng)采用前人所得到的拖曳力系數(shù)關(guān)系代入圣維南方程中求解恒定非均勻流的水面線時,計算結(jié)果與實際情況相差較大。說明在非均勻流情況下,植被的拖曳力系數(shù)不僅與雷諾數(shù)有關(guān),還與水流的非均勻性有關(guān)。針對這種情況,本文研究并得出在恒定非均勻流情況下,植被拖曳力系數(shù)與雷諾數(shù)的關(guān)系是近似拋物線分布的,且拋物線的形狀與水流的非均勻性和植被屬性有關(guān)。同時,本文給出了在恒定非均勻流情況下,植被拖曳力系數(shù)的經(jīng)驗公式。在天然環(huán)境中,由于降雨的影響,河道中水面線也會發(fā)生變化。本文在上述恒定非均勻流的基礎(chǔ)上加入降雨因素,繼續(xù)研究在這些因素的綜合影響下植被對水流的阻力特性。首先,在圣維南方程組中加入降雨項,推導(dǎo)出該情況下植被拖曳力系數(shù)的表達(dá)式。然后,通過實驗室試驗得到不同植被密度下、不同降雨強(qiáng)度下的水面線,并采用對數(shù)形式的水面線模型進(jìn)行擬合,最終得到不同植被密度下、不同降雨強(qiáng)度時的拖曳力系數(shù)與雷諾數(shù)的關(guān)系。研究表明降雨對植被阻力特性有著較大的影響,并且隨著降雨強(qiáng)度的增大,這種影響也在隨之增大。在降雨強(qiáng)度很大的情況下,植被拖曳力系數(shù)隨著雷諾數(shù)的增加而減小,呈現(xiàn)單調(diào)遞減特性,這與沒有降雨情況下的植被拖曳力系數(shù)特性完全不同。
[Abstract]:This paper mainly studies the motion characteristics of open channel flow under the presence of vegetation, that is the hydrodynamic characteristics of the vegetation flow of the open channel. The main contents of the study include the analytical solution of the flow velocity distribution of different types of vegetation flow and the resistance characteristics of the vegetation to the flow of water. The analytical solution model of vertical distribution of longitudinal velocity is derived. Under the presence of non submerged rigid vegetation, the characteristics of vegetation resistance in constant inhomogeneous flow are studied, and the relationship between the change of the drag coefficient of vegetation and the Reynolds number is derived. The hydrodynamic characteristics are studied in detail, which can be divided into the following aspects. The flexural deformation of the flexible vegetation will occur under the action of water flow. In this case, the bending characteristics of the flexible vegetation and the vertical distribution of the longitudinal flow velocity under the small bending condition are derived. Vertically, the vegetation layer and the free water layer are separately studied. First, the angle of each point and the height after the bending of the vegetation are derived from the cantilever beam theory in the vegetation layer. Then, the analytic solution of the velocity is obtained by replacing the expression of the vegetation resistance and Reynolds stress into the flow control equation. The resistance of the vegetative vegetation is different. The resistance of the flexural flexible vegetation in the direction of the flow is the resultant force of the drag force and the friction force. The Reynolds stress in the vegetation layer is in the form of exponential distribution when the degree of vegetation bending is small, so the analytical solution obtained by the solution of the control equation is suitable for the small bending of the vegetation. In order to satisfy the condition that the velocity gradient is zero on the surface of the water, the polynomial expression of the velocity distribution is derived. Compared with the traditional logarithmic velocity expression, the polynomial expression can better conform to the actual situation. When the flow velocity is larger or the vegetation flexibility is higher, the vegetation will bend the deflection of large deflection, in this case, The Reynolds stress in the vegetation layer is no longer in the form of exponential distribution, so the analytical solution of the flow velocity obtained under the small vegetation bending is not applicable here. And the experimental results show that the resistance of the flow to the flow will be greatly reduced when the degree of vegetation bending is large and the flow velocity is approximately linear. Based on this phenomenon, this paper A new formula of vegetation resistance is proposed. By introducing the Carmen coefficient of the vegetation layer and the free water layer, the analytical solution of vertical velocity distribution of the longitudinal velocity of the flow is obtained under the condition of large bending deformation of the vegetation, and the model can well accord with the flow velocity data obtained by the experiment. In natural environment, the height of vegetation in the river is often the same. In this case, the flow velocity characteristics are more complex. In this case, the flow velocity characteristics are more complex. In this paper, a two layer rigid vegetation is taken as an example to solve the flow control equation by means of power series and so on. The experiments of the double layer vegetation flow were carried out and the flow velocity characteristics were measured by the PIV particle image velocimetry system. The experimental results showed that the velocity of flow was approximately constant at the lower part of the vegetation layer and increased gradually in the upper part of the vegetation layer. By comparing with the experimental data, the flow velocity solution model could predict the flow of double layer vegetation well. At the same time, the empirical formula of the invasion depth of the shear vorticity of the two-layer vegetation flow is given. The study on the characteristics of the vegetation flow described above is aimed at the constant uniform flow. However, in the actual River, the flow is often inhomogeneous. The results of previous studies have already obtained the drag coefficient under the condition of constant uniform flow. The relationship between the Reynolds number and the drag force coefficient obtained by the predecessors is replaced by the Saint Venant equation to solve the water surface line of the constant nonuniform flow. The calculation results are quite different from the actual conditions. It shows that the drag coefficient of the vegetation is not only related to the Reynolds number, but also related to the inhomogeneity of the flow in the case of inhomogeneous flow. The relationship between the drag coefficient of the vegetation and the Reynolds number is approximately parabolic, and the shape of the parabola is related to the inhomogeneity of the flow and the vegetation properties. At the same time, this paper gives an empirical formula for the drag coefficient of the vegetation under the condition of constant inhomogeneous flow. In the environment, the water surface line in the river will also change because of the influence of rainfall. In this paper, we add rainfall factors on the basis of the constant non-uniform flow, and continue to study the resistance characteristics of the vegetation to the flow under the comprehensive influence of these factors. First, the rainfall item is added to the Saint Venant equation, and the drag coefficient of the vegetation is derived. Then, the water surface lines under different vegetation density and different rainfall intensity are obtained through laboratory experiments, and the logarithmic surface line model is used to fit the relationship between the drag force coefficient and the Reynolds number under different vegetation density and different rainfall intensity. The study shows that rainfall has a better characteristic of vegetation resistance than the Reynolds number. With the increase of rainfall intensity, the drag coefficient of vegetation decreases with the increase of Reynolds number, and presents a monotonous decreasing characteristic, which is completely different from the characteristics of the drag coefficient of the vegetation without rainfall.
【學(xué)位授予單位】：武漢大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：TV133

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