IMECH-IR  > 非线性力学国家重点实验室
基于浸入边界方法的复杂几何边界湍流壁面模化的大涡模拟
Alternative TitleWall-modeled Large-eddy Simulation in Combination with the Immersed Boundary Method for Turbulent Flows with Complex Geometric Boundaries
时北极
Thesis Advisor何国威
2019-05-28
Degree Grantor中国科学院大学
Place of Conferral北京
Subtype博士
Degree Discipline流体力学
Keyword大涡模拟 浸入边界方法 壁模型 近壁速度重构模型 壁面滑移速度模型 体积力重构模型
Abstract

复杂边界高雷诺数壁湍流是自然界以及工程流动的重要特征,也是计算流体力学的主要挑战。数值模拟研究该流动两个主要困难是:(1) 解析近壁湍流所需求的计算量超出了目前计算机的能力;(2) 处理复杂几何及运动边界问题是传统计算流体力学方法和程序的瓶颈。壁面模化大涡模拟采用壁模型来模化近壁流动,避免了直接解析湍流边界层从而显著的降低计算量。该方法是工业应用的主要方案。浸入边界方法将边界的影响等效为流动方程中的体积力,并对流场和边界分别进行描述。该方法有效的克服了复杂边界问题中方程求解的困难,近年来已被成功的应用于层流及中等雷诺数的湍流数值模拟中。将壁面模化大涡模拟与浸入边界方法相结合是模拟复杂边界湍流的可能途径,具有广阔的应用前景。

本文主要研究将光滑界面浸入边界方法与大涡模拟壁模型相结合来模拟复杂边界湍流。相比于贴体网格方法,它需要处理三个额外的问题:(1) 流场的欧拉网格与边界不重合,难以直接修正壁面上的动量通量;(2) 边界对流动的影响以等效体积力的形式出现;(3) 欧拉与拉格朗日网格间需要通过插值进行物理量的传递。针对上述问题,本文的主要思路是:首先在近壁欧拉网格内嵌入辅助的拉格朗日网格,并采用壁模型来模化壁面层内流动。其次,通过壁模型构造等效体积力来反映壁面层内流动对外区的影响。最后,将体积力施加在远离壁面的代理层上或者维持壁面层内切向速度的线性剖面来抑制插值误差。

本文从构造等效体积力以及抑制插值误差的方式入手,提出三种不同的思路将光滑界面浸入边界方法与大涡模拟壁模型相结合,并通过标准算例的数值模拟评估不同方式及壁面层流动模型的有效性及优缺点。

本文的主要创新性工作包含如下三个部分:

(一)、近壁速度重构模型

近壁速度重构模型的特点是在浸没边界外建立一层拉格朗日代理层来引入显式的速度重构,然后在代理边界上计算并施加等效体积力从而代替几何边界的影响。计算等效体积力时所需的代理层速度通过壁模型来重构以满足模型所确定的速度剖面。本文在一系列标准算例中验证了近壁速度重构模型的有效性。层流状态的数值结果表明,在代理层上施加等效体积力可以减小对近壁流场的扰动,并且可以准确预测流动的速度剖面。在此基础上,本文进一步验证了近壁速度重构模型模拟湍流运动的准确性以及不同壁模型的影响。结果表明Werner-Wengle (WW)模型可以准确预测槽道湍流的平均速度剖面,而后台阶绕流以及周期山状流的结果发现,WW模型可以较好地预测流动再附后的平均速度剖面,但是难以准确地计算壁面摩擦力以及回流区内的流场。近壁边界层模型则可以改善壁面摩擦力的计算结果,但是不能准确地模拟流场。本文对这一现象进行了初步的分析,并提出了可能的解决方案。

(二)、壁面滑移速度模型

壁面滑移速度模型在浸没边界上重构滑移速度来代替无滑移边界条件,从而构建浸没边界上的等效体积力。该方法首先由壁模型计算壁面摩擦力,然后根据近壁区流动的动量守恒重构壁面滑移速度,根据无穿透条件确定壁面法向速度。在此过程中,近壁流动的切向速度剖面仍然保持为线性以降低插值误差并同时修正匹配面上的速度梯度。壁模型方程中考虑了切向压力梯度所引起的非平衡效应,并将其同时用于计算壁面摩擦力以及重构壁面滑移速度。槽道湍流的数值模拟结果表明该方法可以准确地预测流动的平均统计特性。在此基础上,本文进一步评估该方法用于模拟具有复杂几何边界的湍流分离流动的能力并考查壁模型中考虑压力梯度的影响。结果表明,平衡层模型会显著低估壁面摩擦力,同时无法准确预测分离区内的平均速度剖面。而考虑切向压力梯度的非平衡模型可以显著改进壁面摩擦力的计算结果,并且即使在较粗网格上依然能够准确地预测强压力梯度区以及分离区内流动的平均统计特性。本文进一步分析了近壁区涡粘系数的影响,结果表明在壁模型方程中若仅考虑压力梯度项,那么应同时考虑其对壁面层内涡粘系数的影响,否则会高估壁面摩擦力。

(三)、体积力重构模型

体积力重构模型对局部的切向和法向等效体积力分别进行计算。该模型首先从近壁流动的积分动量守恒方程出发,建立了切向等效体积力与壁面切应力的关系。据此可以通过壁模型计算壁面摩擦力来直接重构切向体积力,从而避免了显式的切向速度重构。法向等效体积力则依然通过引入辅助的代理层,并重构其法向速度来计算。当网格可以解析壁面层流动时,体积力重构模型将退化为经典的直接力方法,而当网格较粗时,该模型等价于致动面模型。本文基于体积力重构模型,实现了高雷诺数回转体绕流的大涡模拟。该方法与非平衡壁模型模型相结合可以准确地模拟流动的特征结构以及尾迹演化特性,并且可以准确地预测中间尾迹的自相似性。不同壁模型的计算结果表明,考虑压力梯度时可以改善对摩擦力峰值的预测结果。本文进一步考虑了模型参数的影响,结果表明当网格较粗时匹配面应适当地靠近壁面否则会高估壁面摩擦力的分布,然而在近壁代理层的位置并显著不影响结果的准确性。

Other Abstract

High Reynolds number wall-bounded turbulent flows with complex geometries are very common in nature and industry, and they are still the main challenges to the wall-resolved large-eddy simulation (LES) because of the prohibitive computational cost. Wall-model LES, in which the near-wall flow structures are described by a wall-layer model instead of resolving them directly, can reduce the computational cost significantly and becomes the main stratrgy in industrical applications. In the immersed boundary method (IB), the flow and boundary are treated separately and the boundary effects on the flow are transmitted into the momentum equations as body forcing terms. For its automatic advantage in dealing with complex geometrical and moving boundaries, the IB method has been sucessfully used in simulating different types of laminar flows and turbulent flows at the moderate Reynodsl number. In recent years, the immersed boundary method in combination with the wall-modeled large-eddy simulation have become an effective and promising approach to deal with the high Reynolds number turbulent flows which have complex geometries.

The main objective of the present dissertation is to develop the method of coupling the immersed boundary method with the wall-modeled large-eddy simulation. Compared with the body-fitted methods, when combine wall model with the IB method, three additional problems need to be addressed: (1) the immersed surface generally does not coincide with the Eulerian grids thus it’s not straightfoward to correct the momentum flux on the wall; (2) the effects of the boundary are represented by the effective body forces which are often computed through an objective velocity; (3) the transmission of flow variables between the Euerlian and Lagrangian grids are realized through interpolations. To overcome these difficulties, an embedded body-confromal Lagrangian mesh is firstly constructed to discrete the inner-layer flow, and then the influence to the outer flow is reflected through an equivalent body force which can be reconstructed through a wall-layer model in different manners. To suppress the interpolation error, the body force is constructed and distributed on a layer located away from the wall or by maintaining a linear profile of the tangential velocity in the near wall.

In the present paper, three coupling strategies are put forward from the manners of computing the effective body forces and reducing the interpolation error. The main innovative works of this dissertation are as follows:

1.    Near-wall velocity reconstruction model

The main features of the near-wall velocity reconstruction model is to impose the IB method on the surrogate layer instead of the wall. In the current method, two layers of auxiliary Lagrangian mesh are constructed near the wall to introduce explicit rexonstructions of velocities. The body forces are computed by using the direct-foricng method in which the velocities on the surrogate wall are reconstructed through the profiles specified by wall models.

The effects of implementing the IB method on the surrogate wall is firstly validated by simulation of laminar flows. The results show that the construction and distribution of the effective body forces on the surrogate layer help to reduce the unphysical contaminations near the surrogate position and have limited effects on the flow outside the matching surface. The coupling effects of the surrogate wall model are validated by the simulation of different benchmark turbulent flows and the influence of the wall-layer models are also assessed. The results show that, the current method in combination with the equilibrium wall-layer model compute the mean velocity profiles well, but can not predict the flow separation accurately and the the wall-shear stress is also heavily under-predicted. The non-equilibrium wall-layer model which takes into account the pressure gradient predicts the wall-shear stress with great improvement but conversely, it can’t simulate the mean flow characteristics accurately. A preliminary analysis of this phenomenon is discussed and the possible solutions are also proposed.

2.    The slip-wall model

The imposition of the slip-wall model is perfromed as a prescribed slip-velocity instead of the no-slip condition on the wall. Firstly, the wall-shear stresses is computed on a body-confromal Lagrangian mesh embedded in the inner-layer. Then the tangential slip-velocity on the immersed wall is reconstructed to preserve the momentum conservation of the flow near-wall, and the normal component is specified through the impenetrable boundary condition. In this procedure, a linear velocity profile in the inner-layer is retained to alleviate the interpolation error and modify the momentum flux on the matching surface. To account for the non-equilibrium effects, the tangential pressure gradient blend into the model equation to compute the wall-shear stress and reconstruct the slip-velocity.

The coupling strategy is firstly validated in channel flow, and the mean velocity profile is well predicted. The backward-facing step flow and flow over periodic hills are also successively considered to assess the perfromance of the current method for flows with complex geometries and separation. Both the equilibrium stress balance model and the non-equilibrium wall model are utilized for comparison. It shows that the wall-shear stress is heavily under-predicted by the equilibrium stress balance model and remarkable discrepancies of the mean velocity profiles can also be seen in the recirculation region. However, when taking into account the tangential pressure gradient, the non-equilibrium wall model is superior to the equilibrium one for its ability to predict the wall-shear stress and flow separation with great improvements. The hydrodynamic coefficients and the mean flow statistics are all in good agreement with the references even on very coarse grids. The influence of the near-wall eddy viscosity is also investigated and the result shows that when account for the pressure gradient only, the eddy viscosity have to be corrected at the same time to account for the non-equilibrium effects. Otherwise, the wall-shear stress will be over-pedicted.

3.    The body force reconstruction model

The body force reconstruction model is a more direct approach, in which the tangential and normal component of the effective body forces are computed separately. Firstly, the momentum equation is integrated along the wall-normal direction to link the tangential component of the effective body force for the IB method to the wall-shear stress predicted by the wall model. Then, a set of Lagrangian points near the wall are introduced to compute the normal component of the body force by reconstructing the normal velocity on the surrogate wall. This method will be a classical direct-forcing IB method if the grid is fine enough to resolve the flow near wall. If the grid is far from resolving the inner-layer, the proposed method can be reduced to the actuator type models.

The proposed method has been validated by the benchmark simulation of flows around an axisymmetric body at high Reynolds number by using the wall-modeled LES with three different wall models, i.e., the equilibrium stress balance model, the non-equilibrium stress balance model with the pressure gradient, and the WW model. The distribution of the streamwise velocity in the wake, the pressure coefficient, and the skin-friction coefficients on the wall predicted by non-equilibrium model agree well with the reference data. An acceptable agreement is obtained for all the three models, while the non-equilibrium stress balance model with the pressure gradient term gives better predictions on the peaks of pressure and skin-friction coefficients. The influence of the positions of the matching surface and the surrogate layer are also investigated. It is found that, if the mesh is too coarse and the matching surface located further away from the wall, then the wall-shear stress will be over-estimated. While the position of the surrogate layer plays an insignificant role to the final results as long as it was located near the wall.

Language中文
Document Type学位论文
Identifierhttp://dspace.imech.ac.cn/handle/311007/79090
Collection非线性力学国家重点实验室
Corresponding Author时北极
Recommended Citation
GB/T 7714
时北极. 基于浸入边界方法的复杂几何边界湍流壁面模化的大涡模拟[D]. 北京. 中国科学院大学,2019.
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