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Turbulent impinging jets on rough surfaces 粗糙表面上的湍流撞击射流
Q1 Mathematics Pub Date : 2022-02-02 DOI: 10.1002/gamm.202200005
Francesco Secchi, Thomas Häber, Davide Gatti, Sebastian Schulz, Dimosthenis Trimis, Rainer Suntz, Bettina Frohnapfel

This work presents direct numerical simulations (DNS) of a circular turbulent jet impinging on rough plates. The roughness is once resolved through an immersed boundary method (IBM) and once modeled through a parametric forcing approach (PFA) which accounts for surface roughness effects by applying a forcing term into the Navier–Stokes equations within a thin layer in the near-wall region. The DNS with the IBM setup is validated using optical flow field measurements over a smooth and a rough plate with similar statistical surface properties. In the study, IBM-resolved cases are used to show that the PFA is capable of reproducing mean flow features well at large wall-normal distances, while less accurate predictions are observed in the near-wall region. The demarcation between these two regions is approximately identified with the mean wall height km of the surface roughness distribution. Based on the observed differences in the results between IBM- and PFA-resolved cases, plausible future improvements of the PFA are suggested.

本文提出了圆形湍流射流撞击粗糙板的直接数值模拟。粗糙度通过浸入边界法(IBM)解决,并通过参数强迫方法(PFA)建模,该方法通过在近壁区域的薄层内的Navier-Stokes方程中应用强迫项来解释表面粗糙度效应。使用具有相似统计表面特性的光滑板和粗糙板上的光流场测量来验证具有IBM设置的DNS。在这项研究中,ibm解决的案例表明,PFA能够很好地再现大壁法向距离的平均流动特征,而在近壁区域观察到的预测不太准确。这两个区域之间的分界近似地用表面粗糙度分布的平均壁高k m来确定。基于观察到的IBM和PFA解决案例之间结果的差异,对PFA的未来改进提出了建议。
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引用次数: 3
Data-driven identification of the spatiotemporal structure of turbulent flows by streaming dynamic mode decomposition 基于流动力模态分解的湍流时空结构数据驱动识别
Q1 Mathematics Pub Date : 2022-01-12 DOI: 10.1002/gamm.202200003
Rui Yang, Xuan Zhang, Philipp Reiter, Detlef Lohse, Olga Shishkina, Moritz Linkmann

Streaming Dynamic Mode Decomposition (sDMD) is a low-storage version of dynamic mode decomposition (DMD), a data-driven method to extract spatiotemporal flow patterns. Streaming DMD avoids storing the entire data sequence in memory by approximating the dynamic modes through incremental updates with new available data. In this paper, we use sDMD to identify and extract dominant spatiotemporal structures of different turbulent flows, requiring the analysis of large datasets. First, the efficiency and accuracy of sDMD are compared to the classical DMD, using a publicly available test dataset that consists of velocity field snapshots obtained by direct numerical simulation of a wake flow behind a cylinder. Streaming DMD not only reliably reproduces the most important dynamical features of the flow; our calculations also highlight its advantage in terms of the required computational resources. We subsequently use sDMD to analyse three different turbulent flows that all show some degree of large-scale coherence: rapidly rotating Rayleigh–Bénard convection, horizontal convection and the asymptotic suction boundary layer (ASBL). Structures of different frequencies and spatial extent can be clearly separated, and the prominent features of the dynamics are captured with just a few dynamic modes. In summary, we demonstrate that sDMD is a powerful tool for the identification of spatiotemporal structures in a wide range of turbulent flows.

流动态模式分解(sDMD)是动态模式分解(DMD)的低存储版本,是一种数据驱动的时空流模式提取方法。流式DMD通过使用新的可用数据进行增量更新来近似动态模式,从而避免将整个数据序列存储在内存中。在本文中,我们使用sDMD来识别和提取不同湍流的优势时空结构,这需要对大数据集进行分析。首先,使用公开可用的测试数据集(由直接数值模拟圆柱体后尾流获得的速度场快照组成),将sDMD的效率和精度与经典DMD进行了比较。流式DMD不仅可靠地再现了流的最重要的动态特征;我们的计算还突出了它在所需计算资源方面的优势。随后,我们使用sDMD分析了三种不同的湍流,它们都显示出一定程度的大规模相干性:快速旋转瑞利-巴姆纳德对流、水平对流和渐近吸力边界层(ASBL)。不同频率和空间范围的结构可以清晰地分离,并且仅用几个动态模态就可以捕捉到动力学的突出特征。总之,我们证明了sDMD是识别大范围湍流时空结构的有力工具。
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引用次数: 5
Active control of compressible channel flow up to M a b = 3 using direct numerical simulations with spanwise velocity modulation at the walls 采用直接数值模拟,在壁面沿展向速度调制的情况下,主动控制可压缩通道流动至M a b = 3
Q1 Mathematics Pub Date : 2022-01-11 DOI: 10.1002/gamm.202200004
Marius Ruby, Holger Foysi

Active turbulence control has been pursued continuously for the last decades, striving for an altered, energetically more favorable flow. In this article, our focus is on a promising method inducing a spanwise wall movement in order to reduce turbulence intensity and hence friction drag, investigated by means of direct numerical simulation. This approach transforms a previously time dependent oscillatory wall motion into a static spatial modulation with prescribed wavelength in the streamwise direction [48]. Most procedures related to turbulence control including the present one have been overwhelmingly applied to incompressible flow. This work is different and novel to the effect, that this control method is applied to compressible, supersonic channel flow up to a bulk Mach number of Ma=3. Due to substantial variations of viscosity, density, and temperature within the near-wall region in supersonic flow, the impact of the control method is altered compared to solenoidal flow conditions. By creating a data set of different Mach-/Reynolds numbers and control parameters, knowledge is gained in which way the effectiveness of oscillatory techniques and physical mechanisms change under the influence of compressibility. It is shown that the control method is able to effectively reduce turbulence levels and lead to large drag reduction levels in compressible supersonic flow. Variable property effects even enhance this behavior for the whole set of investigated parameters. Overall, the higher Mach number cases show a larger net power saving compared to the incompressible ones. Furthermore, we observe an increase of the optimum wavelength with increasing Mach number, which helps in guiding optimal implementations of such a control method.

在过去的几十年里,人们一直在追求主动湍流控制,努力获得一种改变的、能量上更有利的流动。在本文中,我们的重点是通过直接数值模拟的方法来研究一种有前途的方法,即通过诱导壁面向展向运动来减少湍流强度,从而减少摩擦阻力。这种方法将先前依赖于时间的振荡壁面运动转换为沿流方向具有规定波长的静态空间调制[48]。大多数与湍流控制有关的程序,包括目前的程序,已经压倒性地应用于不可压缩流动。这项工作的不同和新颖之处在于,这种控制方法适用于可压缩的,超音速通道流动的总体马赫数为Ma = 3。由于超音速流动中近壁面区域内粘度、密度和温度的显著变化,与螺线管流动条件相比,控制方法的影响发生了变化。通过创建不同马赫数/雷诺数和控制参数的数据集,可以了解振荡技术和物理机制在可压缩性影响下的有效性变化方式。结果表明,该控制方法能够有效地降低可压缩超声速流动的湍流度,从而获得较大的减阻量。可变属性效应甚至增强了整个研究参数集的这种行为。总的来说,与不可压缩的情况相比,马赫数较高的情况显示出更大的净功率节省。此外,我们观察到最佳波长随马赫数的增加而增加,这有助于指导这种控制方法的最佳实现。
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引用次数: 2
On the incorporation of a micromechanical material model into the inherent strain method—Application to the modeling of selective laser melting 材料微力学模型与固有应变法的结合——在选择性激光熔化过程建模中的应用
Q1 Mathematics Pub Date : 2021-12-03 DOI: 10.1002/gamm.202200002

In Noll et al.,1 an error was published in the Acknowledgement section. The name “Lena Koppka” was misspelled in the original publication.

The correct Acknowledgement section is presented below:

在Noll et al. 1中,在Acknowledgement部分发布了一个错误。莉娜·科普卡这个名字在最初的出版物中拼写错误。正确的确认部分如下:
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引用次数: 1
Analysis of the sound sources of lean premixed methane–air flames 贫预混甲烷-空气火焰声源分析
Q1 Mathematics Pub Date : 2021-11-23 DOI: 10.1002/gamm.202200001
Sohel Herff, Konrad Pausch, Matthias Meinke, Wolfgang Schröder

Two investigations on the sound generation mechanisms of lean methane–air flames are reviewed and linked. A two-step approach is used for the analysis. First, the compressible conservation equations are solved in a large-eddy simulation formulation to compute the acoustic source terms of the reacting fluid. Second, the acoustic source terms are used in computational aeroacoustics simulations to determine the acoustic field by solving the acoustic perturbation equations. To identify the contributions of the different source terms to the overall sound emission of the flames different source term formulations are considered in the computational aeroacoustics simulations. The results of various flames of increasing complexity are shown: harmonically excited laminar flames, a turbulent jet flame, and an unconfined and a confined swirl flame. The results show that in general the heat release source alone does not determine the acoustic emission of the flame. Only the acoustic emission of the unconfined swirl flame could be computed by the heat release source. To accurately predict the phase and the amplitude of the sound emission of the other flames the acceleration of density gradients occurring at the flame front must be included in the considered set of source terms.

综述了两项关于贫甲烷-空气火焰产生声音机理的研究。分析使用了两步方法。首先,用大涡模拟公式求解可压缩守恒方程,计算反应流体的声源项。其次,将声源项用于计算气动声学模拟,通过求解声扰动方程来确定声场。为了确定不同源项对火焰整体声发射的贡献,在计算气动声学模拟中考虑了不同的源项公式。显示了各种复杂火焰的结果:谐波激发层流火焰,湍流射流火焰,无约束和有约束旋流火焰。结果表明,一般情况下,热源本身不能决定火焰的声发射。只有无约束旋流火焰的声发射可以通过热源计算得到。为了准确地预测其他火焰声发射的相位和振幅,必须在考虑的源项集合中包括发生在火焰前缘的密度梯度加速度。
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引用次数: 2
Simulation-supported characterization of 3D-printed biodegradable structures 模拟支持的3d打印可生物降解结构表征
Q1 Mathematics Pub Date : 2021-11-15 DOI: 10.1002/gamm.202100018
Richard Wolfgang Schirmer, Martin Abendroth, Stephan Roth, Lisa Kühnel, Henning Zeidler, Bjoern Kiefer

In this article, a proof-of-concept study is presented, in which in-situ full-field deformation measurements via digital image correlation, finite element analysis, and nonlinear optimization techniques are combined to characterize the heterogeneous structural behavior of a bio-based material 3D-printed via binder jetting. The special features of this composite material are its biodegradability and its easy manufacturability using conventional 3D printers. The binder-jetting process enables innovative applications such as additively manufactured, highly customized, recyclable, or compostable packaging solutions. Compared to other 3D printing techniques, it is relatively fast and inexpensive and can make use of raw material powders that are by-products of the food or other industries. As an initial step towards gaining a simulation-supported understanding of the complex process-structure-property relations, a first quantitative assessment of the effective behavior of a bio-based binder-jetted material is conducted under the following operating assumptions: (i) Its mechanical response can be described by means of a nonlinear elasto-plastic constitutive law, enriched by a cohesive damage model capturing failure on the structural level, (ii) established mechanical tests on a 3D-printed component, involving standardized sample geometries, and optical measurements, should yield sufficient information to allow the identification of the corresponding material parameters. First, experimental results of optically monitored four-point bending tests, with varying alignments of loading axes and printing directions, are presented in detail. Then the proposed parameter identification strategy is explained and its capabilities and limitations, as made evident from quantitative case studies based on the measured structural response data, are thoroughly discussed.

在本文中,提出了一项概念验证研究,其中结合了通过数字图像相关,有限元分析和非线性优化技术进行现场全场变形测量,以表征通过粘合剂喷射3d打印的生物基材料的非均质结构行为。这种复合材料的特点是它的可生物降解性和使用传统3D打印机易于制造。粘合剂喷射工艺使创新应用成为可能,如增材制造、高度定制、可回收或可堆肥的包装解决方案。与其他3D打印技术相比,它相对快速且便宜,并且可以利用食品或其他行业的副产品原料粉末。作为获得对复杂工艺-结构-性能关系的模拟支持理解的第一步,在以下操作假设下对生物基粘合剂喷射材料的有效行为进行了第一次定量评估:(i)其机械响应可以通过非线性弹塑性本构律来描述,并通过在结构层面上捕获故障的内聚损伤模型来丰富;(ii)对3d打印部件进行的已建立的机械测试,包括标准化的样品几何形状和光学测量,应产生足够的信息,以便确定相应的材料参数。首先,详细介绍了不同加载轴向和打印方向的光学监测四点弯曲试验结果。然后,对所提出的参数识别策略进行了解释,并从基于实测结构响应数据的定量案例研究中,对其能力和局限性进行了深入讨论。
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引用次数: 4
On accurate time integration for temperature evolutions in additive manufacturing 增材制造温度演变的精确时间积分研究
Q1 Mathematics Pub Date : 2021-11-08 DOI: 10.1002/gamm.202100019
Stefan Kollmannsberger, Philipp Kopp

We investigate two numerical challenges in thermal finite element simulations of laser powder bed fusion (LPBF) processes. First, we compare the behavior of first- and second-order implicit time-stepping schemes on a fixed domain. While both methods yield comparable accuracies in the pre-asymptotic regime, the second-order method eventually outperforms the first-order method. However, the oscillations present in the pre-asymptotic range of the second-order method can render it less suitable for simulating LPBF processes. Then, we consider sudden domain extensions resulting from subsequently adding new layers of material with ambient temperature. We model this extension on the continuous level in an energy conservative manner. The discontinuities introduced here reduce the convergence order for both time-stepping schemes to 0.75. First and second order accuracy could only be achieved by strongly grading the time-steps towards the domain expansion.

本文研究了激光粉末床熔合(LPBF)过程热有限元模拟中的两个数值问题。首先,我们比较了一阶和二阶隐式时间步进格式在固定域上的行为。虽然两种方法在前渐近区域产生相当的精度,但二阶方法最终优于一阶方法。然而,二阶方法的前渐近范围内存在振荡,使得它不太适合模拟LPBF过程。然后,我们考虑了由于随后在环境温度下添加新材料层而导致的突然域扩展。我们以能量守恒的方式在连续水平上对这种扩展进行建模。这里引入的不连续将两种时间步进方案的收敛阶降低到0.75。一阶和二阶精度只能通过向域展开方向强烈分级时间步来实现。
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引用次数: 5
Preface on mechanics of additive manufacturing—Part II 增材制造力学前言——第二部分
Q1 Mathematics Pub Date : 2021-11-04 DOI: 10.1002/gamm.202100020
Thorsten Bartel, Markus Kästner, Björn Kiefer, Andreas Menzel
In the first part of this two-part special issue, the focus is on the modeling and simulation of elementary processes within various materials that can be used for additive manufacturing. It comprises selective laser sintering of polymers, topology optimization in the context of additively manufactured structures, a general overview on the challenges related to the modeling and simulation of powder bed fusion additive manufacturing as well as the modeling of phase changes during Selective Laser Melting and the related analysis of process-induced inherent strains. As sophisticated as these models may be, they also require experimental data for verification and validation. The more complex the modeled and simulated processes, as well as the material models themselves, become the more important becomes the sound and comprehensive experimental characterization and experimental investigation of the effective material behavior. Even with accurate and experimentally verified material and process models successfully developed and established the general challenge of their algorithmic implementation remains. In this context, it is essential to establish efficient and robust numerical methods, some of which have to be newly developed due to the high numerical complexity. The contributions of this Part II of the Special Issue of the Surveys for Applied Mathematics and Mechanics (GAMM-Mitteilungen) mainly focus on these above-mentioned aspects: The paper referenced by Kollmannsberger and Kopp [1] elaborates advanced modeling and simulation approaches with emphasis on different time scales. This includes, among other topics, the investigation and comparison of different time-stepping schemes with special focus on robustness, prevention of oscillating solutions and general applicability. In Zhou et al. [2], a multilayer phase-field simulation of selective sintering process and the calculation of effective mechanical properties and residual stresses is proposed. In this regard, quantitative relations between the process parameters and the microstructure and its properties are established. The contribution of Schirmer et al. [3] addresses the additive manufacturing of a novel class of bio-based materials via binder-jetting. The highly customizable printed structures are recyclable and use renewable raw materials that are often industrial by-products. The article presents a proof-of-concept study, in which digital image correlation, finite element analysis and optimization techniques are combined to characterize the heterogeneous structural behavior of such 3D-printed biodegradable materials. The work presented in Raßloff et al. [4] aims at the prediction of structure–property linkages for additively manufactured materials with a particular focus on process-induced imperfections like pores. It uses light microscopy and X-ray computed tomography to determine microstructure characteristics of Ti–6Al–4V in combination with microscale simulations to assess the influe
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引用次数: 0
3D-multilayer simulation of microstructure and mechanical properties of porous materials by selective sintering 选择性烧结多孔材料微观结构和力学性能的三维多层模拟
Q1 Mathematics Pub Date : 2021-10-19 DOI: 10.1002/gamm.202100017
Xiandong Zhou, Yangyiwei Yang, Somnath Bharech, Binbin Lin, Jörg Schröder, Bai-Xiang Xu

This work presents multilayer phase-field simulation of selective sintering process and the calculation of effective mechanical properties and residual stress of the microstructure using the finite element method. The dependence of the effective properties and residual stress on the process parameters, such as beam power and scan speed, are analyzed. Significant partial melting of powders is observed for large beam power and low scan speed, which results in low porosity of the microstructure. Nonlinear relationship between the effective mechanical properties and process parameters is observed. The increasing rate of effective mechanical properties decreases with increasing beam power, while increases with decreasing scan speed. The dependence of effective Young's modulus and Poisson's ratio on porosity are well established using power law models. Stress concentrations are found at the necking region of powders and the intensity increases with the level of partial melting, which results in increasing residual stress in the microstructure. The numerical results reveal quantitatively the process-microstructure-property relation, which implies the feasibility of the subsequent data-driven approach.

本文对选择性烧结过程进行了多层相场模拟,并采用有限元法计算了微观组织的有效力学性能和残余应力。分析了光束功率和扫描速度对有效性能和残余应力的影响。较大的光束功率和较低的扫描速度导致粉末明显的部分熔化,导致微观组织孔隙率低。观察到有效力学性能与工艺参数之间存在非线性关系。有效力学性能的增长速率随光束功率的增大而减小,随扫描速度的减小而增大。利用幂律模型很好地建立了有效杨氏模量和泊松比与孔隙度的关系。应力集中在粉末颈部,应力强度随部分熔化程度的增加而增大,导致显微组织中残余应力增大。数值结果定量地揭示了过程-微观结构-性能之间的关系,为后续数据驱动方法的可行性提供了依据。
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引用次数: 11
Preface on mechanics of additive manufacturing—Part I 增材制造力学前言——第一部分
Q1 Mathematics Pub Date : 2021-09-17 DOI: 10.1002/gamm.202100016
Thorsten Bartel, Markus Kästner, Björn Kiefer, Andreas Menzel
Additive manufacturing processes—often referred to as 3D printing—have developed since the 1980s into a promising and groundbreaking way of producing components and workpieces with geometries of almost any complexity. And the developments continue to advance! In the meantime, various methods that can be divided into different categories have been introduced. To cover just a few of the most common methods, inkjet technologies, material extrusion, powder bed fusion, direct energy deposition, and stereolithography shall be mentioned here. The latter is considered in some sources to be virtually the starting point of additive manufacturing. The category “powder bed fusion” includes processes such as selective laser sintering, selective laser melting, and electron beam melting. Laser cladding is an example of direct energy deposition. In conventional subtractive manufacturing processes, the final contour of the component is achieved by material removal. In contrast, additive manufacturing processes are characterized by the targeted addition of the respective material to the component layer by layer. The great potential of these processes is evident in the aerospace and automotive industries as well as in biomedical technology, and especially in the manufacturing of custom-made products and lightweight constructions. Developments have even gone so far that local material properties can be specifically adjusted by, for example, adapting the material feed. Moreover, no tools or joining processes are in principle required for direct manufacturing. Additive manufacturing processes can thus be initiated and adapted in a much faster and straight-forward way. For applied mathematics and mechanics, additive manufacturing opens up numerous new perspectives and opportunities, but also major challenges. Particularly in the field of topology optimization, additive manufacturing seems to overcome a previously existing and seemingly insurmountable limitation, namely that of realizability. Until recently, the mathematically optimal structure, for example, in the sense of an optimum density distribution within a given design space, was always subjected to the constraint that the structure must also be manufacturable via conventional methods. Among other things, voids were not allowed to become too small and the density distribution had to be binary—either “no material” or “full material”. Nowadays, additive manufacturing processes indeed enable the production of the mathematically/physically optimal structures. With regard to the modeling of the material and structural behavior of additively manufactured components, numerous new challenges arise. In order to be able to perform load-bearing capacity verifications, the constitutive behavior of the material finally obtained must be modeled and predicted as accurately as possible. In this context, the manufacturing process results in specific and spatially highly inhomogeneously distributed residual stresses, which can ha
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引用次数: 0
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