Description of a flexible and extendable physical–biogeochemical model system for the water column

A modelling system for coupled physical–biogeochemical simulations in the water column is presented here. The physical model component allows for a number of different statistical turbulence closure schemes, ranging from simple algebraic closures to two-equation turbulence models with algebraic second-moment closures. The biogeochemical module consists of models which are based on a number of state variables represented by their ensemble averaged concentrations. Specific biogeochemical models may range from simple NPZ (nutrient–phytoplankton–zooplankton) to complex ecosystem models. Recently developed modified Patankar solvers for ordinary differential equations allow for stable discretisations of the production and destruction terms guaranteeing conservative and non-negative solutions. The increased stability of these new solvers over explicit solvers is demonstrated for a plankton spring bloom simulation. The model system is applied to marine ecosystem dynamics the Northern North Sea and the Central Gotland Sea. Two different biogeochemical models are applied, a conservative nitrogen-based model to the North Sea, and a more complex model including an oxygen equation to the Baltic Sea, allowing for the reproduction of chemical processes under anoxic conditions. For both applications, earlier model results obtained with slightly different model setups could be basically reproduced. It became however clear that the choice for ecosystem model parameters such as maximum phytoplankton growth rates does strongly depend on the physical model parameters (such as turbulence closure models or external forcing).     

垂直入水空泡内部压强分布数值研究

基于RANS方程,在VOF多相流模型中嵌入水蒸汽和水之间的质量输运模型成功实现了垂直入水空泡流的数值计算。通过与试验结果的对比说明了以上数值方法的可信性,并在此基础之上对带不同锥角头型圆柱体以不同速度垂直撞击自由液面后所生成的空泡内部压强分布进行了深入分析,结果表明:在入水空泡形成阶段,空泡内部压强会出现较大的降低现象,并随着空泡的发展压强值逐渐趋于稳定;空泡形成阶段空泡内部压强随入水物体头部锥角增加而增加;在开空泡阶段空泡内部压强低于环境压强,并随着入水速度增加而呈降低变化趋势,空泡内部压强轴向和径向分布较为稳定,没有较大的压强梯度;在空泡趋于闭合阶段空泡内部压强出现较大的波动,其变化规律与空泡内部空气复杂速度场变化规律相吻合。     

双层Boussinesq水波方程

从Laplace方程出发,推导了一组适应于波浪在非平整地形上传播的双层Boussinesq水波方程,方程以双层水深积分平均速度表达且具有二阶全非线性特征。通过在动量方程中引入高阶色散项和非线性项进一步提高了方程的色散性和非线性性能。常水深情况下,分析了方程的色散关系和二阶波幅传递函数,并与Stokes解析解进行了比较。结果表明,在0.3%误差下方程可适用水深达kh≈6,在此水深范围内二阶波幅传递函数误差在10%以内。在非交错网格下,建立了基于有限差分方法和混合4阶Adams-Bashforth-Moulton时间积分格式的一维数值模型,模拟了波浪在潜堤上的传播变形,并与实验结果进行了对比,吻合程度较好。     

应用分区有限体积法数值计算舵粘性水动力

通过数值求解不可压缩粘性流的RANS方程计算均匀来流中的船舵水动力。采用标准的κ-ε湍流模式封闭方程，并用二阶有限体积法在非交错分区贴体网格上对守恒方程进行离散；采用Rhie和Chow的插值方法确定单元面的质量通量，用SIMPLE法求解压力分布，用壁函数法处理壁面边界条件。对一种NACA冀型舵在两种不同雷诺数下大攻角范围的流动进行了计算，得到的舵水动力与试验结果和他人的计算结果进行比较，在舵未达到失速角前吻合良好，而所确定的舵失速角与最大升力值则均偏小。失速角后舵背流面的流动分离点也能捕捉到。最后分析了雷诺数对舵水动力的影响。     

海底振动管道局部泥沙冲刷数值研究

文章基于迎风有限元方法,对流动方程和泥沙输运方程进行求解,建立起振动管道与泥沙冲刷的耦合运动模型。模型中通过SST k-ω湍流模型对湍流效应进行模拟;管道振动和海床变形引起的不确定边界通过ALE方法进行实时追踪;模型考虑了悬移质输沙率以及推移质输沙率对底床变形的影响作用。数值模型首先与其他已发表的数据进行了比较,表明文章所建立的振动管道局部冲刷程序能够对冲刷深度进行较为准确地预测。文章利用所建数值模型进一步对海底振动管道局部冲刷问题开展了数值研究。相关数值分析结果表明:相对于固定管道的情况,管道振动对局部冲刷有较大的影响作用,管道的振动使管道局部最大冲刷深度增大,管道后方冲刷范围变宽,最大冲刷深度位置后移。     

The influence of different turbulence schemes on modelling primary production in a 1D coupled physical–biological model

A one-dimensional (1D) coupled physical–microbiological model has been applied to a site in the central North Sea. The impact of the choice of the turbulence closure scheme on the modelling the primary production has been investigated.The model was run with four different parameterisations of vertical mixing of heat, momentum and dissolved and suspended matters, using M2 tidal forcing and the hourly mean meteorological forcing of 1989 to reproduce the annual thermal structure and primary production. The four mixing parameterisations are: Level 2 turbulence closure scheme [Mellor, G.L., Yamada, T., 1974. A hierarchy of turbulence closure models for planetary boundary layers. J. Atmos. Sci. 31, 1791–1806; Mellor, G.L., Yamada, T., 1982. Development of a turbulence closure model for geophysical Fluid problems. Rev. Geophys. Space Phys. 20 (4) 851–875] using an explicit numerical scheme [Sharples, J., Tett, P., 1994. Modelling the effect of physical variability on the midwater chlorophyll maximum. J. Mar. Res. 52, 219–238]; a version of the Level 2.5 turbulence closure scheme [Galperin, B., Kantha, L.H., Hassid, S., Rosati, A., 1988. A quasi-equilibrium turbulent energy model for geophysical flows. J. Atmos. Sci. 45, 55–62; Ruddick, K.G., Deleersnijder, E., Luyten, P.J., Ozer, J., 1995. Haline stratification in the rhine/meuse freshwater plume: a 3D model sensitivity analysis. Cont. Shelf Res. 15 (13) 1597–1630] simplified to use an algebraic mixing length by Sharples and Simpson [Sharples, J., Simpson, J.H., 1995. Semidiurnal and longer period stability cycles in the Liverpool Bay region of freshwater influence. Cont. Shelf Res. 15, 295–313], also solved explicitly; the same simplified L2.5 scheme with an implicit numerical solution and modified vertical discretisation scheme [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206]; and another version of the same scheme (but using a different algebraic mixing length) as described by Xing and Davies [Xing, J., Davies, A.M., 1996a. Application of turbulence energy models to the computation of tidal currents and mixing intensities in the shelf edge regions. J. Phys. Oceanogr. 26, 417–447; Xing, J., Davies, A.M., 1996b. Application of a range of turbulence models to the computation of tidal currents and mixing intensities in shelf edge regions. Cont. Shelf. Res. 16, 517–547; Xing, J., Davies, A.M., 1998. Application of a range of turbulence energy models to the computation of the internal tide. Int. J. Numer. Methods Fluids 26, 1055–1084]. Various model outputs at the sea surface and in depth profiles have been compared with data collected in 1989 as part of the North Sea Project [Huthnance, J.M., 1990. Progress on North Sea Project. NERC News, vol. 12, pp. 25–29, UK]. It is shown that the biological results are extremely sensitive to the small changes in the physical conditions, which arise due to the different turbulence schemes tested. The timing of the spring bloom and the maintenance of the midwater chlorophyll maximum all differ greatly between model runs, and the gross primary production varies by a factor of two from the highest to lowest results. The simplified Level 2.5 scheme, implemented using the numerical methods of Annan [Annan, J.D., 1999. Numerical methods for the solution of the turbulence energy equations in the shelf seas. Int. J. Numer. Methods Fluids 29, 193–206], produces results, which give the best agreement with the available data.     

基于BFC-VOF方法的弧形防浪墙水动力数值模拟

文章建立了一种基于适体坐标系(BFC)的计算流体力学模型.采用坐标变换方法实现了任意复杂区域的结构化网格划分,在贴体网格下对二维不可压缩粘性流体的控制方程进行了离散,修正了贴体坐标下的界面跟踪方法(VOF方法).对弧形防浪墙结构附近的压力场,波面历时曲线进行了数值计算.将采用适体坐标的计算结果与在笛卡尔坐标网格下采用部...     

On the role played by turbulence closures in hull shape optimization at model and full scale

 The practical use of automated computational fluid dynamics (CFD)-based design tools in the ship-building industry requires powerful flow solvers which are able to take into account realistic geometries as well as complex physical phenomena, such as turbulence. A shape optimization tool is developed in this framework. A derivative-free optimizer, yielding both flexibility and robustness, is preferred to the classical gradient-based method, which is more difficult to implement and is still limited to only moderately complex problems. The flow solver included in the design procedure solves the incompressible Reynolds-averaged Navier–Stokes equations on unstructured grids using a finite-volume formulation involving several near-wall low-Reynolds-number turbulence models. The design tool is used to optimize the stern of a modern hull shape at model and full scale, with different purposes being considered. More precisely, the drag reduction and the homogenization of the flow in the wake are expected by controlling the longitudinal vortex generated. Our interest is particularly focused on the influence of turbulence modeling in the design process. The effects of a two-equation model based on the eddy-viscosity assumption and a second-order closure relying on the Reynolds stress transport equations are compared. Received: September 24, 2002 / Accepted: April 14, 2003 RID="*" Acknowledgment. The authors thank the scientific committee of CINES (project dmn2050) for the attribution of CPU time.     

水火弯板残余变形预报的数值和量纲分析(英文)

Line heating process is a very complex phenomenon as a variety of factors affects the amount of residual deformations. Numerical thermal and mechanical analysis of line heating for prediction of residual deformation is time consuming. In the present work dimensional analysis has been presented to obtain a new relationship between input parameters and resulting residual deformations during line heating process. The temperature distribution and residual deformations for 6 mm, 8 mm, 10 mm and 12 mm thick steel plates were numerically estimated and compared with experimental and published results. Extensive data generated through a validated FE model were used to find co-relationship between the input parameters and the resulting residual deformation by multiple regression analysis. The results obtained from the deformation equations developed in this work compared well with those of the FE analysis with a drop in the computation time in the order of 100 (computational time required for FE analysis is around 7 200 second to 9 000 seconds and where the time required for getting the residual deformation by developed equations is only 60 to 90 seconds).     

基于Morabito方法的滑行艇喷雾详细研究的计算机程序开发(英文)

Recently, Morabito(2010) has studied the water spray phenomena in planing hulls and presented new analytical equations. However, these equations have not been used for detailed parametric studies of water spray around planing hulls. In this paper, a straight forward analysis is conducted to apply these analytical equations for finding the spray geometry profile by developing a computer program based on presented computational process. The obtained results of the developed computer program are compared against existing data in the literature and favorable accuracy is achieved. Parametric studies have been conducted for different physical parameters. Positions of spray apex are computed and three dimensional profiles of spray are examined. It is concluded that spray height increases by an increase in the speed coefficient or the deadrise angle. Ultimately, a computational process is added to Savitsky's method and variations of spray apex are computed for different velocities. It is shown that vertical, lateral, and longitudinal positions of spray increase as the craft speed increases. On the other hand, two new angles are defined in top view and it is concluded that they have direct relation with the trim angle. However, they show inverse relation with the deadrise angle.     

波浪作用下单体网格式浮架受力的数值模拟

模型试验表明重力式网箱在波浪作用下，单纯浮架的受力贡献比例较大。本文运用波浪理论，通过建立浮架、锚绳及浮子的运动方程，采用五阶龙格-库塔进行数值求解，得到了单体网格式锚碇单纯浮架的数值计算模式。将计算模型简化为四点锚碇，并将计算结果与实验结果进行了比较，二者符合程度较好。在此基础上，比较了单体网格式锚碇与四点锚碇单纯浮架的受力，结果表明网格式锚碇方式浮架受力较小。     

基于增量谐波平衡法的输流管道非线性振动分析

考虑内、外流体的影响,利用Kane方法和拉格朗日应变理论建立了输流管道的二维非线性动力学模型.将动力学模型在平衡位置附近线性化,进行输流管道的线性稳定性分析.采用增量谐波平衡法求解包含三次非线性项动力学模型的稳态周期解.探讨了不同参数影响下输流管道的非线性动力响应以及内流流速的大小对管道动力特性的影响.     

多孔介质中波浪传播的高阶Boussinesq方程*

准确模拟波浪在多孔介质中传播变形对于研究抛石防波堤等结构的消能作用是十分必要的。对Laplace方程、自由表面处的运动学方程和动力学方程以及海底运动学方程进行无因次化,且以自由表面处速度势为切点,进行幂级展开,最终给出4个不同的高阶Boussinesq水波方程。在常水深下对这些方程的一维问题进行了理论研究,并将无因次相速度和无因次虚波数与解析解结果进行对比,方程的相速度与解析解吻合程度较好,虚波数与解析解基本吻合,表明高阶Boussinesq方程可用于模拟波浪在多孔介质中的传播变形。     

带缆遥控水下机器人水动力数学模型及其回转运动分析

提出了一种新型的带缆水下机器人系统三维水动力数学模型。在该模型中脐带缆的控制方程由脐带缆任一微段中的力的平衡条件导出,在此基础上以该脐带缆的控制方程为核心,通过引入脐带缆与水下机器人连接点的边界条件而建立起整个系统的三维水动力学数学模型。数值模拟中作用在机器人主体上的水动力载荷和旋转导管螺旋桨的控制力在考虑了它们之间的相互影响基础上以计算流体力学方法求出。该模型的主要特点是克服了现有的带缆水下机器人系统水动力数学模型将系统各组成部分割裂处理、缺乏从系统整体理论框架中去观察脐带缆、水下机器人主体和螺旋桨推进器水动力特征的缺陷,从一种综合、整体的观点去观察分析带缆遥控水下机器人的动力状态。水下机器人在导管螺旋桨作用下回转运动的数值模拟结果表明,利用所建立的数学模型可以对带缆水下机器人水动力状态进行有效的数值模拟。     

船用大功率柴油机新型燃油系统的数值仿真

本文数值仿真了一种适合劣质燃油（重油）的循环式燃油系统（一泵二嘴四针阀），提出了处理喷油器和燃油分配器边界条件的准维模型以及用于喷油泵边界条件的新模型。该燃油系统已应用于MANB&WL60MC／MCE等大功率柴油机。与常规的数值仿真相比，求解管内流动的二队双曲型偏微分方程的边界条件发生了很大变化，这是燃油系统研究的难点和关键。预测结果与试验结果较为一致。本研究还进行了不同功率点变型方案的模拟研究和结构参数的优化设计分析，以满足不同船舶的需要。     

波浪对箱形船作用的三维耦合计算模型

为获得具有工程实用价值的港口三维船非线性波浪力的时域计算方法,该文建立了波浪对港口中船非线性作用的三维时域计算耦合模型:用欧拉方程计算船底面下的内域,用Boussinesq方程计算船侧面到港口边界的外域,两域在交界面处匹配条件是流量连续和压力相等.并进行了相关模型实验,实验结果和数值计算结果比较表明该耦合计算模型具有满意的精度.此外,该三维耦合模型数学处理简单,计算效率高,可适用于工程计算.     

A numerical model of the long term flow along the Malin-Hebrides shelf

A three dimensional hydrodynamic model of the Malin-Hebrides shelf region is used to investigate the spatial variability of the wind and tidally induced residual flow in the region and the influence of flow from the Irish Sea and along the shelf edge. By this means it is possible to understand the spatial variability in the long term observed flow fields in the region and the range of driving forces producing this flow. The model uses a sigma coordinate grid in the vertical with a finer grid in the near surface and near bed shear layers. The vertical diffusion of momentum in the model is parameterised using an eddy viscosity coefficient which is derived from turbulence energy closure models. Two different turbulence models are used to compute the eddy viscosity, namely a two-equation (itq²−q²ℓ) model which has prognostic equations for both turbulence energy and mixing length and a simpler model in which the mixing length is a specified algebraic function of the water depth.The wind induced response to spatially and temporally constant orthogonal wind stresses, namely westerly and southerly winds of 1 N m⁻², are derived from the model. By using orthogonal winds and assuming linearity, then to first order the response to any wind direction can be derived. Computed flows show a uniform wind driven surface layer of magnitude about 3% of the wind speed and direction 15 ° to the right of the wind, in deep water. Currents at depth particularly in the shelf edge and near coastal region show significant spatial variability which is related to variations in bottom topography and the coastline.Calculations show that tidal residual flows are only significant in the near coastal regions where the tidal current is strong and exhibits spatial variability. Flow into the region from the Irish Sea through the North Channel although having its greatest influence in the near coastal region, does affect currents near the shelf edge region. Again the spatial variability of the flow is influenced by topographic effects.A detailed examination of wind induced current profiles together with turbulence, mixing length and viscosity, at a number of locations in the model from deep ocean to shallow near coastal, shows that both turbulence models yield comparable results, with the mixing length in the two equation model showing a similar dependence to that specified in the simpler turbulence model.Calculations clearly show that flow along the shelf edge area to the west of Ireland and from the Irish Sea entering the region, together with local wind forcing can have a major effect upon currents along the Malin-Hebrides shelf. The flow fields show significant spatial variability in the region, comparable to those deduced from long term tracer measurements. The spatial variability found in the calculations suggests that a very intense measurement programme together with inflow measurements into the area is required to understand the circulation in the region, and provide data sets suitable for a rigorous model validation.     

潜艇流水孔阻力数值计算与回归分析研究

本文研究了压力梯度对于流水孔阻力的影响,采用正交设计与均匀设计方法编排了流水孔阻力系数的计算方案,将计算结果逐步回归,给出了流水孔阻力系数的经验估算公式,并用某型实艇流水孔作算例,验证了回归公式的实用性,发展了预报潜艇流水孔补贴系数的新方法.     

不同时空格式在求解Boussinesq水波模型中的应用

为了解不同时间空间差分格式在常用的二阶或四阶Boussinesq模型中的应用,针对4组近似到0（旷）阶完全非线性的二阶或四阶色散性的高阶Boussinesq水波方程,在非交错网格下,利用Crank-Nicolson格式、蛙跳格式、混合四阶Adams-Bashforth-Moulton格式,建立不同的数学模型。利用这些数值模型模拟波浪在潜堤上的传播变形,通过数值结果与试验结果的比较．考察时间格式及空间格式对模型的影响。结果表明：对同一方程,混合四阶Adams-Bashforth-Mouhon格式和Crank-Nicolson格式均能取得较好模拟效果,蛙跳格式的模拟效果最差;二阶Boussinesq模型采用追赶法求解已能满足要求;对四阶Boussineq模型,二阶空间导数色散项亦采用四阶精度,其数值效果会更好。     

有效应力强度因子幅值计算模型的验证

裂纹闭合效应在金属疲劳中有着十分重要的作用,裂纹闭合概念已经用于解释变幅载荷作用下的裂纹扩展问题,已提出了许多基于裂纹闭合概念的有效应力强度因子计算模型.黄等人在Newman模型的基础上,提出了考虑因素更全面且便于应用的有效应力强度因子幅计算模型以及变幅载荷下工程结构疲劳寿命预测模型.为了验证该模型对不同材料的有效性和适应性,收集了一些相关的试验数据,和该模型的预测结果对比发现该模型的预测结果和试验数据符合得很好.对几种钢、铝合金和钛合金材料在不同应力比下的裂纹扩展速率数据用该模型转换成用有效应力强度因子表示的裂纹扩展速率,结果表明由有效应力强度因子幅表示的扩展速率将不同应力比下较分散的裂纹扩展率数据集中在一个很小的分散带内,同时得到了有参考价值的的一些结论.