【正文】 t is time。 3)溢洪道頂?shù)膲毫兴煌Ｒ簿褪菍?shù)值模擬液壓平滑 (PR00),k = (PR05)和 k = (PR30)進(jìn)行了調(diào)查研究和對原型粗糙度影響 (PR05)、 1/50模型 (M50)、 1/00模型 (M100)、 1/200模型 (M200)的調(diào)查進(jìn)行的尺度效應(yīng)。 兩方程的 整理總結(jié)的 理論模型（ RNG 模型）用于湍流閉合。 t 是時(shí)間 。 先前 由于 研究水力模型的規(guī)模限制 導(dǎo)致一些誤差 。實(shí)驗(yàn)室在空間 、 施工性模型 、 儀器儀表 、 或測量的限制 ，一般來說，水工結(jié)構(gòu)的明渠流量恒定非均勻流動特性可以解釋為以下關(guān)系（ ASCE， 2020）。最 近，在反弧溢洪道水流進(jìn)行調(diào)查 中發(fā)現(xiàn) ，使用計(jì)算 二維流體力學(xué)，三維流 體學(xué) 。 艾斯 （ 2020）采用 流函數(shù)分析對溢洪道波峰無旋流動。此外，由于規(guī)模效應(yīng)的 誤差 的嚴(yán)重程度增加原型模型的大小比例。最大速度出現(xiàn)在 上游水頭的增加幾乎呈線性增加溢洪道前的距離和位置較低的垂直位置位 上 。但是 我們只是使用長度比例小于 100 或 200在可接受的誤差范圍 的 建筑材料一般粗糙度高度和規(guī)模效應(yīng)的模型，最大速度在垂直的坐標(biāo)堰發(fā)生更嚴(yán)重的粗糙度和規(guī)模效應(yīng)。雖然這是關(guān)于一般反弧的形 狀和其流動特性的理解， 但是 從上游流量條件下的變化 、 修改的波峰形狀或改變航道由于局部幾何性質(zhì) 等的 標(biāo)準(zhǔn)設(shè)計(jì)參數(shù)的偏差 都會 改變的 水流的 流動性 ，影 響的分析 結(jié)果。一個(gè)更好的 解決 卡西迪 的問題的 利用非線性有限元和變分原理方案 被 貝茨（ 1979 年），李等 提 3 出 。宋 和 周（ 1999）開發(fā)了一個(gè)數(shù)值模型可能 被用 來分析隧道或槽溢洪道，特別是進(jìn)口水流條件幾何效應(yīng)的三維流模式。 泄洪流量分析 方法在溢流壩設(shè)計(jì) 領(lǐng)域中被廣泛驗(yàn)證和使用 ， 本研究的目的是調(diào)查 、定量分析的計(jì)算結(jié)果對流動特性的規(guī)模和粗糙度的影響。粗糙高度， K的近似值 明渠流量和水工結(jié)構(gòu)模型 中水是用 來分析縮尺模型的流動特性 。隨著計(jì)算機(jī)技術(shù)和更有效的 CFD 模型 的進(jìn)步，在一個(gè)合理的 時(shí)間和金錢條 件下進(jìn)行 反弧溢洪道的流 態(tài)模型 進(jìn)行 模擬實(shí)驗(yàn) 。 gi是在標(biāo)方向的引力 。彎曲的障礙 、 壁面邊界或其他幾何特征是嵌入在網(wǎng)狀定義分區(qū)和分開流動 的變 量 。 2)建模結(jié)果表明 ,增加的比率引起長度尺度相似現(xiàn)象，是由于日益增長的表面粗糙度造成的。 USBR, 1973).The ogeecrested spillway’s performance attributes are due to its shape being derived from the lower surface of an aerated nappe flowing over a sharpcrested weir. The ogee shape results in nearatmospheric pressure over the crest section for a design head. At heads lower than the design head, the discharge is less because of crest resistance. At higher heads, the discharge is greater than an aerated sharpcrested weir because the negative crest 7 pressure suctions more flow. Although much is understood about the general ogee shape and its flow characteristics, it is also understood that a deviation from the standard design parameters such as a change in upstream flow conditions, modified crest shape, or change in approach channel owing to local geometric properties can change the flow properties. For the analysis of the effects, physical models have been used extensively because a spillway is very important for the safety of dams. The disadvantages with the physical models are high costs and that it can take fairly long time to get the results. Also, errors due to scale effects may increases in severity as the ratio of prototype to model size increases. So, numerical modeling, even if it cannot be used for the final determination of the design, is valuable for obtaining a guide to correct details because putational cost is low relative to physical modeling. In the past few years, several researchers have attempted to solve the flow over spillway with a variety of mathematical models and putational methods. The main difficulty of the problem is the flow transition from subcritical to supercritical flow. In addition, the discharge is unknown and must be solved as part of the solution. This is especially critical when the velocity head upstream from the spillway is a significant part of the total upstream head. An early attempt of modeling spillway flow have used potential flow theory and mapping into the plex potential plane (Cassidy, 1965). A better convergence of Cassidy’s solution was obtained by Ikegawa and Washizu (1973), Betts (1979), and Li et al. (1989) using linear finite elements and the variation principle. They were able to produce answers for the free surface and crest pressures and found agreement with experimental data. Guo et al. (1998) expanded on the potential flow theory by applying the analytical functional boundary value theory with the substitution of variables to derive nonsingular boundary integral equations. This method was applied successfully to spillways with a free drop. Assy (2020) used a stream function to analyze the irrotational flow over spillway crests. The approach is based on the finite diff