外文翻譯---明渠中非恒定流和非均勻泥沙輸移的二維數(shù)值模擬（節(jié)選）

1、<p>　　中文2500漢字，1500單詞。8700英文字符</p><p>　　出處： Journal of Hydraulic Engineering, 2004, 130(10):págs. 1013-1024.</p><p><b>　　附錄</b></p><p><b>　　附錄一、英文原文</

2、b></p><p>　　Depth-Averaged Two-Dimensional Numerical Modelingof Unsteady Flow and Nonuniform Sediment Transport in Open Channels</p><p>　　Weiming Wu, M.ASCE1</p><p>　　Abstract: A

3、 depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in openchannels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow w

4、ater equations are solved bythe SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment t

5、ransport. The bed load and suspended load are cal</p><p>　　transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement bet

6、ween the simulated results and measured data.</p><p>　　Introduction</p><p>　　Because of the complexity of the turbulent flows with free water surface and movable channel bed, the numerical simul

7、ation of flow and sediment transport in open channels is very challenging. Its advancement can be attributed to many successful numerical techniques developed in the field of computational fluid dynamics. Among these tec

8、hniques, the staggered grid approach (Harlow andWelsh 1965; Patankar 1980) and Rhie and Chow’s (1983)momentum interpolation method on a nonstaggered grid have been</p><p>　　Sediment transport modeling starte

9、d in the 1950s and has been extensively developed and widely applied to real-life engineering since the 1970s. Several successful 1D models (Han 1980; Chang 1982; Thomas 1982; Holly and Rahuel 1990; Wu and Vieira 2002) h

10、ave been</p><p>　　established to calculate the long-term channel deposition and erosion under quasi-steady and unsteady flow conditions. In recent years, many 2D and 3D sediment transport models (Shimizu et

11、 al. 1990; Spasojevic and Holly 1990; Olsen 1999;Minh Duc 1998; Wu et al. 2000a; and others) have also been established to simulate in more detail the channel evolutionincomplexsituations.Usuallythesemodelssimu

12、late suspendedload transport using the nonequilibrium transport approach, but many of them </p><p>　　Although in a two-phase system flow and sediment always interact with each other, the calculations of flow

13、 and sediment were fully decoupled in early development stages. Recently, several coupled models</p><p>　　have been reported (Holly and Rahuel 1990; and others). A fully coupled model is usually more stable

14、 than a decoupled model. However, establishing a fully coupled model requires solving all the flow and sediment transport equations simultaneously. The nonlinearity of flow problem may reduce the efficiency of sediment t

15、ransport simulation, which can be mathematically simplified to a linear problem. In addition, the time scales of flow and channel morphodynamic processes may be different, especial</p><p>　　Governing Equatio

16、ns and Boundary Conditions Governing Equations of Open-Channel Flow</p><p>　　The depth-integrated continuity and momentum equations of open-channel flow are</p><p>　　where t=time; x and y=horizo

17、ntal Cartesian coordinates; h=flow depth; U</p><p>　　and V=depth-averaged flow velocities in x and y directions;</p><p><b>　　?s =water</b></p><p>　　surface elevati

18、on; g=gravitational acceleration; r=density of flow; Txx,</p><p>　　Txy, Tyx, and Tyy=depth-averaged turbulent stresses;</p><p><b>　　??bx</b></p><p><b>　　an

19、d</b></p><p><b>　　??by =bed</b></p><p>　　shear stresses that are determined byand</p><p>　　; , in which n=Manning’s roughness coefficient and w=bed angl

20、e with the horizontal.</p><p>　　The turbulent shear stresses are determined by the Boussinesq’s assumption</p><p>　　where????=kinematic viscosity of water;</p><p>　　??t =edd

21、y viscosity due to</p><p>　　turbulence; and k=turbulence energy, which is dropped from Eqs. (4a) and (4c) when the zero-equation turbulence models are used.</p><p>　　Several turbulence model

22、s, including the depth-averaged parabolic eddy viscosity model, the mixing length model, the standard ??- ? turbulence model (Rodi 1993), and the renormalization group (RNG)</p><p>　　??- ?turbulence

23、model (Yakhot et al. 1992) have been implemented in</p><p>　　the proposed model to determine the eddy viscosity</p><p>　　??t . In the present</p><p>　　paper,onlythedept

24、h-averagedparabolicmodelandthestandard</p><p>　　??- ???turbulence model are used. In the depth-averaged parabolic model,</p><p>　　the eddy viscosity is calculated by, in which</p>

25、;<p>　　U* =bed shear</p><p>　　velocityand</p><p>　　0.3 and 1.0.</p><p>　　?t =empirical coefficient between</p><p>　　In the standard????- ????turbulence

26、model,??t is calculated with</p><p>　　??t. Here C???=empirical constant. The turbulence energy k and</p><p>　　its dissipation rate ?are determined with</p><p><b>　

27、　where</b></p><p><b>　　and</b></p><p>　　=empirical coefficients. The standard values of these coefficients are</p><p><b>　　and</b></p><p>

28、　　Governing Equations of Sediment Transport</p><p>　　The total load is usually separated as bed load and suspended load regarding sediment transport mode, or divided into bed-material load and wash load acco

29、rding to sediment source. Therefore totalload transport can be modeled with two approaches, either separately as bed load and suspended load, or jointly as bed-material</p><p>　　load (wash load usually is ig

30、nored in the simulation of bed morphological changes).</p><p>　　The advection-diffusion equation of suspended-load transport is</p><p>　　where =depth-averaged concentration of the kt

31、h size class of suspended load; =depth-averaged suspended-load concentration under equilibrium conditions or the suspended-load transport capacity;</p><p>　　=diffusivity coefficient of se

32、diment; ???=nonequilibrium adaptation coefficient of suspended load; and =settling velocity of sediment particles.</p><p>　　The mass balance equation in the bed-load zone is</p><p>　　w

33、here ??=thickness of bed-load zone; =average concentration of bed</p><p>　　load at the bed-load zone;</p><p><b>　　?bx</b></p><p><b>　　and</b></p>

34、<p>　　?by =direction cosines of bed-load</p><p>　　movement, which are usually assumed to be along the direction of bed shear stress, but are adjusted when taking into account the influence of the se

35、condary flow in curved channels and the effect of the gravity over</p><p>　　steep slopes; =actual transport rate of the kth size class of bed load; =porosity of bed material; and =bed change

36、 rate corresponding to the kth size class of sediment.</p><p>　　Forbed-loadtransport,Wellington(1978);Phillipsand</p><p>　　Sutherland(1989); Thuc (1991); and Wu et al. (2000a) adopted

37、 arelation</p><p>　　to determine the bed change. Here, =bed-load transport capacity, and=nonequilibrium adaptation</p><p>　　length of bed load. This relation can be used when bed load is

38、the main transport mode. Similarly, when the suspended load is dominant, the bed</p><p>　　changecanbedeterminedby .</p><p>　　However, in general situations of total-load transport, the be

39、d change should be determined by</p><p>　　where=actual total-load transport rate;=total-load transport capacity; and L=nonequilibrium adaptation length of total load.</p><p>　　Inserting

40、 and in Eq. (9) gives</p><p>　　where, and. Usually we can assume . Therefore, inserting Eq. (10) in Eq. (8) leads to the following</p><p>　　nonequilibrium bed-load transport equatio

41、n:</p><p>　　The governing equation of bed-material load can be derived by summing</p><p>　　Eqs. (7) and (11). As an extreme case, if sediments move mainly as bed load, the diffusion of suspende

42、d load is negligible and the resulting governing equation for bed-material load is similar to Eq. (11), with </p><p>　　and being replaced by the actual transport rate and transport</p>&l

43、t;p>　　capacity of bed-material load. However, if the suspended load is the dominant transport mode, the resulting governing equation for</p><p>　　bed-material load is similar to Eq.

44、 (7), with and being</p><p>　　replaced by the quantities of bed-material load.</p><p>　　Therefore the separation method uses Eqs. (7) and (11) to determine the transport rates of sus

45、pended load and bed load, while the joint method calculates the bed-material load transport rate using only one equation that is similar to Eq. (7) or Eq. (11). The separation method differentiates the characteristics o

46、f bed load and suspended load, and it can provide more information than the joint method, with the additional cost of solving one more equation. To balance the accuracy and the cost of c</p><p><b>　　附錄

47、二、中文翻譯</b></p><p>　　明渠中非恒定流和非均勻泥沙輸移的二維數(shù)值模擬</p><p>　　摘要：明渠中非恒定流和非均勻泥沙輸移的二維(2 d)泥沙數(shù)值模型的建立使用 了有限體積法在nonstaggered，曲線網(wǎng)格。二維淺水方程通過解決簡單的(C)算法 與Rhie and Chow’s的動量插值技術。模擬中的泥沙數(shù)學模型對非均勻泥沙輸移總 負載采用一個不平衡的

48、方法。推移質和懸移質分開計算或共同計算根據(jù)沉積物運 輸模式。泥沙運輸能力是由四個能計算的隱藏和暴露的不同沙粒粒徑公式?jīng)Q定 的。一個經(jīng)驗公式提出了考慮重力渠道和陡峭的斜坡中沉積物運輸能力和河床運 動方向的影響。水流和泥沙運輸方式是模擬在一個解耦，但沉積物模塊采用耦合 計算程序，包括沉積物運輸，河床的演變，和河床材料分類。該模型已經(jīng)在幾個 實驗和現(xiàn)場情況下通過測試并且在模擬結果與測量數(shù)據(jù)方面表現(xiàn)出良好擬合性。</p><

49、p><b>　　介紹</b></p><p>　　由于湍流流動的復雜性與自由表面和可移動的河床條件，數(shù)值模擬開放渠道 中的水流和泥沙輸移是非常具有挑戰(zhàn)性的。它的發(fā)展可以歸因于在計算流體動力 學中許多成功的數(shù)值技術。在這些技術，采用交錯網(wǎng)格方法(HarlowandWelsh 1965; Patankar 1980) and Rhie and Chow’s (1983)動量插值方法在非錯列

50、的網(wǎng)格有被廣 泛用于解決的不可壓縮流體N-S方程(Peric 1985; Majumdar 1988; Zhu 1992; and others)。Wenka(1992)和MingDuc(1998)采用了Rhie and Chow’s方法模擬了明渠恒 定流和非恒定流。在目前的研究中，明the MinhDuc’s的構想被修改了，取而代之 的都是Duc的明渠中二維非恒定流泥沙值模型的建立。</p><p>　　關于沉

51、積物運移的建模從1950年代開始，一直廣泛開發(fā)和廣泛應用于現(xiàn)實生 活中的工程。自 1970年代以來，幾個成功的一維模型 (Han 1980; Chang1982; Thomas 1982; Holly and Rahuel 1990; Wu and Vieira2002)已建立計算長管明渠近 似恒定流和非恒定流條件下的沉積和侵蝕。近年來，許多二維和三維泥沙輸運模 型(Shimizu et al. 1990; Spasojevic and

52、 Holly 1990; Olsen 1999;Minh Duc 1998; Wu et al. 2000a; and others)也一直在建立更詳細地模擬通道演化</p><p>　　復雜的情況。通常這些模型模擬懸移質運輸使用非平衡傳輸?shù)姆椒?，但是當模擬 河道運輸時他們中的許多人采用局部均衡的假設。最近的研究在空間和時間滯后 實測表明，非平衡傳輸運輸模型還需要在許多不同情況下的床沙，例如強大的侵 蝕和強勁的沉

53、積，特別是在非恒定流的條件下。此外，隱藏和暴露現(xiàn)象中存在的 非均勻泥沙運輸在河床材料分揀和河床的構成扮演著重要的角色。本文中描述的 沉積物運輸模型采用非平衡態(tài)運輸方式對象為考慮了隱藏和暴露的床沙質和懸 移質，并且在非均勻泥沙運輸能力計算公式中引入校正因子。</p><p>　　盡管在兩相系統(tǒng)中水流和泥沙質總是相互作用，但是計算流量和泥沙完全解 耦是早期發(fā)展階段。最近，幾個耦合模型已經(jīng)被報道(Holly and R

54、ahuel 1990;and others)。一個完全耦合模型通常是比解耦模型更穩(wěn)定。然而，建立一個完全耦合 模型需要同時解決所有的流量和泥沙輸移方程問題。非線性流問題可能削減泥沙 模擬的效率，可以在數(shù)學上簡化為一個線性問題。此外，流體時間尺度的和形態(tài) 動力學過程可能不同的，尤其是在河床推移質負荷是占主導地位的情況下。因此 完全耦合的流體和泥沙組合可能是性價比不高的。和Wu (1991) and Wu and Vieira (2002)

55、的一樣，本模型采用一個“semicoupling”程序，在這種水流計算解耦從沉積 物的計算，但這三個組件的沉積物模塊(沉積物運輸，河床的演變，和床層物料 分類)是解決一個耦合的方式。這semicoupling過程非常穩(wěn)定而且計算很高效。 明渠流的全流水的連續(xù)性和動量方程是</p><p>　　其中，t 表示時間;</p><p>　　x和y 為水平笛卡兒坐標; h 為水流深度;</

56、p><p>　　U和V 表示泥沙流在x坐標軸和y坐標軸方向的速度; z 為水面高程;</p><p>　　g 表示重力加速度; r 為密度流;</p><p>　　Txx，Txy，Tyx和Tyy 為泥沙湍流應力;</p><p>　　??bx 和??by</p><p><b>　　為河床剪應力，</

57、b></p><p>　　可以通過和; ，n 為曼寧的粗糙度系數(shù)，???為床角水平。 在湍流剪應力取決于布西涅斯克的假設</p><p>　　其中，????為水的運動粘度;</p><p>　　??t 為由于湍流產生的渦流粘度;</p><p>　　k 為湍流能量系數(shù)，方程式(4a)和(4c)在零湍流模型中是適用的。 幾個湍流

58、模型，包括泥沙拋物線渦粘性模型，混合長度模型，標準 ??- ??湍流</p><p>　　模型(Rodi 1993)，和重整化群(RNG) ??- ??湍流模型(Yakhot et al.1992)實現(xiàn)該模型 確定渦流粘度??t 。本文只有泥沙拋物線模型和標準 ??- ??湍流模型是適用的。在泥</p><p>　　沙拋 物線 模型， 計 算 渦 流粘 度通 過 ， U*</p>

59、;<p><b>　　為床剪切速度， </b></p><p>　　，其中?t 經(jīng)驗系數(shù)在0.3和1.0之間。</p><p><b>　　其中，</b></p><p>　　和為 經(jīng) 驗 系 數(shù) ， 這 些 系 數(shù) 的 標 準 值 為</p><p><b>　　控制方程

60、的泥沙</b></p><p>　　總負載通常單獨成為床上負載和懸移質沉積物運輸模式，或根據(jù)沉積物源分 為床材料負載和沖蝕的負載。因此總負荷運輸可以用兩種方法建模，第一種床載 荷和懸移質分開作用，第二種共同作為床材料負載(沖蝕負載通常是忽略了在模 擬中河床形態(tài)的改變)。</p><p>　　懸移質運輸?shù)膶α鲾U散方程是</p><p>　　其中， 為區(qū)

61、有分懸移質顆粒粒徑大小的泥沙濃度;</p><p>　　為根據(jù)平衡條件或懸浮負載運輸能力劃分的泥沙懸移質濃度;</p><p><b>　　為泥沙的擴散系數(shù);</b></p><p>　　??為一個適用于非均勻流中懸移質系數(shù); 為對應泥沙顆粒的沉降速度。 河道區(qū)域中的質量平衡方程為</p><p>　　其中， ??為

62、實測區(qū)的厚度;</p><p>　　為床載荷在河道帶的平均濃度;</p><p>　　?bx 、?by 方向余弦上的實測運動，通常認為是沿河床剪切應力方向上，并考慮二 次流重力在彎曲斷面和陡峭的斜坡通道的影響;</p><p>　　為的區(qū)分泥沙粒徑大小的實際傳輸速率; 為床材料的孔隙度;</p><p>　　為粒徑分類的沉積物的河床變化率

63、。</p><p>　　對于 河道運 輸 ， Wellington (1978); Phillips and Sutherland(1989);Thuc (1991);andWuetal.(2000a)；采用了一個關系式子</p><p>　　來確定河床改變。在這里， 為河道 運輸能力， 為床載荷的非平衡適應長度。這關系可以用在床上負載是主要的 運輸方

64、式。同樣的，當懸浮負載 是主導，河床改變可以由式子 </p><p>　　來確定。 然而，在一般情況下的總負載</p><p>　　運輸，河床改變應該通過來確定</p><p>　　其中，為總負載的實際運輸率;</p><p><b>　　為總負載運輸能力;</b></p><p>　　L 為度

65、總負載的非平衡適應長。</p><p>　　其中， 和 。通常我們可以假定。因此， 將 ?q 插入公式(10)和公式(8)中得出以下非平衡態(tài)實測輸運方程：</p><p>　　控制方程的床材料負載可以獲得求和的方程式(7)、(11)。作為一個極端的例子， 如果沉積物主要是移動床載荷，懸移質擴散可以忽略不計和由此產生的控制方程</p><p>　　為床材料負載類似

66、于。公式(11)， 和表示被取代的床材料負載的實際 的傳輸速率和傳輸容量。然而，如果是模型中是懸移質占主導地位的運輸模式，</p><p>　　由此產生的床材料負載控制方程是與方程(7)類似的，并且 和被取而代 之的是大量的床材料負載。</p><p>　　因此，分離方法使用方程式(7)、(11)來確定運輸率的懸移質和推移質，而 聯(lián)合法計算出床材料負載運輸率只使用一個方程，類似于方程式 (