Enablers for robust POD models

This paper focuses on improving the stability as well as the approximation properties of reduced order models (ROMs) based on proper orthogonal decomposition (POD). The ROM is obtained by seeking a solution belonging to the POD subspace and that at the same time minimizes the Navier–Stokes residuals. We propose a modified ROM that directly incorporates the pressure term in the model. The ROM is then stabilized making use of a method based on the fine scale equations. An improvement of the POD solution subspace is performed, thanks to a hybrid method that couples direct numerical simulations and reduced order model simulations. The methods proposed are tested on the two-dimensional confined square cylinder wake flow in laminar regime.     

Digital twin of a combustion furnace operating in flameless conditions: reduced-order model development from CFD simulations

The present paper presents the first-of-its-kind digital twin for a furnace operating in flameless combustion conditions. A methodology combining data compression, by means of Proper Orthogonal Decomposition (POD), and interpolation, using Kriging, was developed to design physics-based, reduced-order models (ROMs) for the prediction of combustion data at unexplored operating conditions. Three-dimensional simulations with detailed chemistry were carried out, spanning a wide range of operating conditions in terms of fuel composition (methane-hydrogen mixtures from pure methane to pure hydrogen), equivalence ratio (from 0.7 to 1) and air injector diameter (to adjust the air jet entrainment). Based on the available simulations, a ROM was developed, to predict both spatial fields, local and integral values of thermochemical variables at working conditions not included in the ROM development. Results showed that the developed ROM could reliably predict the temperature and main chemical species distribution in the furnace with an overall error below 10%, proving the effectiveness of the approach for the development of digital twins of combustion systems. A remarkable accuracy was observed for the prediction of specific quantities, including wall temperatures, OH decay length, OH peak value and location and exhaust gas composition, including pollutants, with prediction errors always below 5%, showing the potential of the approach to develop soft sensors.     

近壁湍流的降阶模型及应用

由条带和流向涡的循环再生构成的近壁自维持过程(self-sustaining process, SSP)是壁湍流产生和维持的重要机制. 文章通过对最小槽道的直接数值模拟(direct numerical simulation, DNS)获得近壁自维持过程的流场数据, 采用正规正交分解法(proper orthogonal decomposition, POD)对该数据进行分析, 获得了不同流向和展向尺度的特征模态, 通过将Navier-Stokes方程在这些模态上进行投影, 得到近壁自维持过程的降阶模型, 并采用DNS数据对降阶模型的预测能力进行了评价. 该模型被初步应用于大涡模拟近壁模型的构造.      

On the use of time-resolved particle image velocimetry for the investigation of rod–airfoil aeroacoustics

The present study investigates an experimental methodology to determine aeroacoustic emission from vortex–structure interaction by means of Time-resolved Particle Image Velocimetry (TR-PIV). The aeroacoustic investigation is conducted on a rod–airfoil configuration at Re=6000 based on the rod diameter. The time-resolved velocity field obtained from 2D PIV is employed to evaluate the instantaneous planar pressure field by spatial integration of the Navier–Stokes equations under the assumption of 2D incompressible flow. The instantaneous pressure field computed on a control surface approximating that of the physical airfoil is used as source term of Curle's aeroacoustic analogy in both a distributed and a lumped formulation to obtain the far-field acoustic prediction. The spanwise coherence function of velocity and pressure fluctuations is determined by means of additional experiments, and is applied to weight the contributions at different frequencies. Results are compared with far-field microphone measurements in terms of spectra and directivity pattern. A good agreement is observed for the tonal component corresponding to the periodic interaction of the Kármán vortices with the airfoil leading edge. The contributions at higher frequencies also show an acceptable agreement when the spanwise coherence is taken into account.     

XFEM modeling of hydraulic fracture in porous rocks with natural fractures

Hydraulic fracture (HF) in porous rocks is a complex multi-physics coupling process which involves fluid flow, diffusion and solid deformation. In this paper, the extended finite element method (XFEM) coupling with Biot theory is developed to study the HF in permeable rocks with natural fractures (NFs). In the recent XFEM based computational HF models, the fluid flow in fractures and interstitials of the porous media are mostly solved separately, which brings difficulties in dealing with complex fracture morphology. In our new model the fluid flow is solved in a unified framework by considering the fractures as a kind of special porous media and introducing Poiseuille-type flow inside them instead of Darcy-type flow. The most advantage is that it is very convenient to deal with fluid flow inside the complex fracture network, which is important in shale gas extraction. The weak formulation for the new coupled model is derived based on virtual work principle, which includes the XFEM formulation for multiple fractures and fractures intersection in porous media and finite element formulation for the unified fluid flow. Then the plane strain Kristianovic-Geertsma-de Klerk (KGD) model and the fluid flow inside the fracture network are simulated to validate the accuracy and applicability of this method. The numerical results show that large injection rate, low rock permeability and isotropic in-situ stresses tend to lead to a more uniform and productive fracture network.     

基于POD模态分解的液环泵瞬态气液两相流分析

针对液环泵内气液两相流动的复杂时空规律,采用本征正交分解(POD)方法对其瞬态气液两相流场进行特征分解,分析其相态场、速度场的空间基模态特征及模态系数的时域特征,建立非定常流场降阶模型,并对流场进行预测分析。结果表明POD方法可实现对液环泵内复杂流场的时空解耦分析,相态场及速度场的各阶模态系数在时域内的变化能够反映各阶模态场的能量、频率及相位变化规律,模态场能够反映脉动流场的空间尺度变化规律。POD降阶模型能够对样本空间内的流场进行精确预测,进口压力、相态场及速度场预测结果的最大相对误差分别约为0.2%、4%、8%,在样本空间外POD降阶模型具有一定外延预测精度,当预测目标逐渐远离样本空间时POD预测结果与CFD计算结果之间的误差逐渐增大。     

A moving medium formulation for prediction of propeller noise at incidence

This paper presents a time domain formulation for the sound field radiated by moving bodies in a uniform steady flow with arbitrary orientation. The aim is to provide a formulation for prediction of noise from body so that effects of crossflow on a propeller can be modeled in the time domain. An established theory of noise generation by a moving source is combined with the moving medium Green's function for derivation of the formulation. A formula with Doppler factor is developed because it is more easily interpreted and is more helpful in examining the physic of systems. Based on the technique presented, the source of asymmetry of the sound field can be explained in terms of physics of a moving source. It is shown that the derived formulation can be interpreted as an extension of formulation 1 and 1A of Farassat based on the Ffowcs Williams and Hawkings (FW–H) equation for moving medium problems. Computational results for a stationary monopole and dipole point source in moving medium, a rotating point force in crossflow, a model of helicopter blade at incidence and a propeller case with subsonic tips at incidence verify the formulation.     

HF spectrum activity prediction model based on HMM for cognitive radio applications

Although most of the research on Cognitive Radio is focused on communication bands above the HF upper limit (30 MHz), Cognitive Radio principles can also be applied to HF communications to make use of the extremely scarce spectrum more efficiently. In this work we consider legacy users as primary users since these users transmit without resorting to any smart procedure, and our stations using the HFDVL (HF Data+Voice Link) architecture as secondary users. Our goal is to enhance an efficient use of the HF band by detecting the presence of uncoordinated primary users and avoiding collisions with them while transmitting in different HF channels using our broad-band HF transceiver.A model of the primary user activity dynamics in the HF band is developed in this work to make short-term predictions of the sojourn time of a primary user in the band and avoid collisions. It is based on Hidden Markov Models (HMM) which are a powerful tool for modelling stochastic random processes and are trained with real measurements of the 14 MHz band.By using the proposed HMM based model, the prediction model achieves an average 10.3% prediction error rate with one minute-long channel knowledge but it can be reduced when this knowledge is extended: with the previous 8 min knowledge, an average 5.8% prediction error rate is achieved.These results suggest that the resulting activity model for the HF band could actually be used to predict primary users activity and included in a future HF cognitive radio based station.     

一种数据驱动的翼型流动转捩预测方法

研究翼型绕流的转捩预测方法,对于翼型流动细节的精确模拟和气动力的准确计算以及精细化设计均具有十分重要的意义.采用动模态分解（dynamic mode decomposition,DMD）代替线性稳定性理论（linear stability theory,LST）与eN方法结合,不需要求解稳定性方程,成为一种数据驱动的翼型边界层转捩预测新方法,称为DMD/eN方法.在原有方法的基础上,改进了DMD网格线生成方法和扰动放大N因子的积分策略,并将RANS求解器与改进的DMD/eN方法进行耦合,实现了翼型定常绕流转捩预测自动化.采用该方法对LSC72613跨声速自然层流翼型以及NLF0416低速自然层流翼型在不同攻角下的绕流进行转捩预测,转捩点计算结果均与实验值和LST/eN方法吻合良好.该方法计算得到的N值增长曲线与LST/eN方法的包络线也较为吻合,进一步验证了积分策略的正确性.改进的DMD/eN方法可作为自然层流翼型设计的新的有力工具.      

Predictive flow-field estimation

We are considering the problem of real-time prediction of 3D turbulent velocity fields based on a small number of scalar measurements. The method of proper orthogonal decomposition (POD) allows for the decomposition of an ensemble of velocity fields into a set of spatial basis functions and a set of temporal coefficients. The computation of the temporal coefficients is by no means a trivial matter, especially when one is faced with a large number of modes. In this paper we discuss the use of radial basis function (RBF) models to capture the discrete time evolution and nonlinear dynamics of the POD coefficients. Further, we propose the use of regularized regression techniques to generate models that provide mappings between the POD coefficients and scalar measurements. As a final step towards real-time prediction, the state-space RBF models and regression measurement models are combined using unscented Kalman filters to produce optimal solutions such that a balance between the state models and measurement models is achieved.The proposed methods are tested for two specific cases. The classical Lorenz model is chosen to demonstrate the use and effectiveness of RBF models as a potential candidate for state models. Flow around a wall-mounted cube in a channel at Re=20,000 is considered as the second case. The aim for the second case is to be able to accurately predict the POD coefficients outside the ensemble. It is shown that a large number of POD coefficients is required to approximate the velocity fields with sufficient accuracy. The RBF models are created based on only the temporal information available from the initial ensemble, and it is shown that the RBF model is able to correctly approximate the high-dimensional phase space. Combined with the unscented Kalman filter it is indeed possible to track the evolution of the POD coefficients for a long time. The robustness of the filter is demonstrated by considering the presence of noise in measurements and using measurement information at time steps greater than the evolution time step.     

基于马铃薯叶片光纤光谱信息的晚疫病患病程度预测

针对马铃薯晚疫病害的早期检测和防治问题,利用光谱技术对马铃薯晚疫病叶片过氧化物酶(POD)活性进行预测,并基于POD酶活性实现了马铃薯晚疫病的患病程度预测.采集和测定处于不同温湿度及接菌时间的马铃薯叶片样本的光谱反射率和POD酶活性,选用中心化(MC)预处理方法以消除原始光谱数据的误差.为降低模型复杂程度,利用随机青蛙...     

Tuning of turbulent boundary layer anisotropy for improved surface pressure and trailing-edge noise modeling

The modeling of the surface pressure spectrum beneath a turbulent boundary layer is investigated, focusing on the case of airfoil flows and associated trailing edge noise prediction using the so-called TNO model. This type of flow is characterized by the presence of an adverse pressure gradient along the airfoil chord. It is shown that discrepancies between measurements and results from the TNO model increase as the pressure gradient increases. The original model is modified by introducing anisotropy in the definition of the turbulent vertical velocity spectrum across the boundary layer and by considering a frequency-dependent vertical correlation length. The degree of anisotropy is directly related to the strength of the pressure gradient. It is shown that by appropriately normalizing the pressure gradient and by tuning the degree of anisotropy, experimental results can be closely reproduced by the modified model. The model is validated against Large Eddy Simulation results and additional wind tunnel measurements. It is further validated in the context of trailing edge noise for which the model formulation makes use of the above surface pressure spectrum.     

A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries

The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE.     

Generalized Hartree-Fock theory and the Hubbard model

The familiar unrestricted Hartree-Fock variational principles is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices and these, in turn, provide a convenient formulation of a generalized Hartree-Fock variational principle, which includes the BCS theory as a special case. While this generalization is not new, it is not well known and we begin by elucidating it. The Hubbard model, with its particle-hole symmetry, is well suited to exploring this theory because BCS states for the attractive model turn into usual HF states for the repulsive model. We rigorously determine the true, unrestricted minimizers for zero and for nonzero temperature in several cases, notably the half-filled band. For the cases treated here, we can exactly determine all broken and unbroken spatial and gauge symmetries of the Hamiltonian.Dedicated to Philippe Choquard on his 65th birthday.     

基于桥域理论的Cu单晶纳米切削跨尺度仿真研究

桥域方法是一种典型的跨尺度仿真研究方法.基于桥域理论,本文分析了原子和连续介质耦合区域的处理问题,即在耦合区采用不同的权重计算系统的能量,通过Lagrange乘子法对原子和连续介质位移进行约束.采用桥域方法,建立了单晶Cu米纳切削的跨尺度仿真模型,获得了单晶Cu纳米切削的材料变形机理.同时,研究了不同切削速度对纳米切削过程和原子受力分布的影响,仿真结果表明:随着切削速度的提高,切削区原子所受的力值增大,切屑变形系数减小,已加工表面变质层厚度增加.本文基于桥域理论,实现了Cu单晶纳米切削跨尺度的建模和仿真, 关键词： 桥域法 纳米切削 单晶Cu 切削速度     

快速随机粒子网格法的气动噪声预测方法

耦合随机湍流速度生成模型与线化欧拉方程技术,形成了一套具备模拟噪声在非均匀流场中传播能力的气动噪声混合预测方法。该混合方法的随机湍流速度生成模型采用了快速随机粒子网格法,为声传播模拟提供了可靠的源项。而噪声的传播计算选用线化欧拉方程,其空间离散采用9点5阶的色散保持关系格式,时间推进选用了高精度大时间步长的6级4阶龙格库塔格式,远场边界应用了无分裂形式的理想匹配层边界条件。首先,选用高斯脉冲传播算例对线化欧拉方程的时空离散格式、远场无反射边界条件进行了验证分析。然后,计算分析各向同性湍流的空间相关性验证湍流速度生成模型的可靠性。最后,基于已搭建的气动噪声混合预测方法进行了30P30N三段翼缝翼噪声的计算分析。计算分析可知:监测点处功率谱密度曲线、噪声指向性等计算结果与参考文献结果取得了较好的一致性。数值计算结果表明所建立的气动噪声混合预测方法能有效预测二维复杂构型的气动噪声问题。      

国家气候中心大气环流模式冬季模式误差特征分析

本文利用1982—2010年国家气候中心第二代月动力延伸预测系统中大气环流模式(BCC_AGCM)的回报资料和美国国家环境预测中心和美国国家大气研究中心(NCEP/NCAR)再分析资料,分析了该模式对冬季气温预测的误差特征及其与外强迫的联系.结果表明模式能够在整体上较好地反映出欧亚区域冬季气温的变化趋势,能抓住东亚冬季风区气温年际变化的主要空间模态,对东亚冬季风区冬季气温具有一定的预报能力.预报误差的空间分布和时间演变特征的结果表明,误差在陆地大于海洋,高纬地区大于低纬地区,同时与海拔高度也有密切关系.预报误差的主要模态与一些关键区域的海温和海冰存在显著的相关性,表明模式对外强迫异常的响应能力存在缺陷.这为结合模式对关键区海温和海冰异常的响应能力,有针对性地改进模式对东亚冬季风区冬季气温的预测能力提供了依据.     

Coherence and Reynolds stresses in the turbulent wake behind a curved circular cylinder

The turbulent wake behind a curved circular cylinder is investigated based on data obtained from a direct numerical simulation. Here, emphasis is placed in the assessment of two approaches for simplified modelling: reduced-order modelling (ROM) and Reynolds-averaged Navier–Stokes equations. To this end, the instantaneous vortical structures, the proper orthogonal decomposition (POD) of the flow, and relevant Reynolds stress components have been analysed. The results show that despite the complexity of the instantaneous vortical structures, the wake dynamics are governed by the quasi-periodic shedding of primary vortices. Between 24% and 50% of the kinetic energy in the POD is captured by the two most energetic modes, and about 200 modes are needed to capture 90% of the kinetic energy. These findings suggest that, as long as the large-scale structures of the von Kármán vortex shedding are concerned, the present case can be approached by ROM; but a detailed representation of the flow dynamics without an eddy viscosity model that accounts for the unresolved turbulent fluctuations would require a large amount of degrees of freedom. Concerning the Reynolds stresses, their magnitude varies considerably depending on the depth at which they have been sampled. This dependence is related to the strength of the vortex shedding, and the intensity of the secondary flows induced by the curvature of the cylinder. As a consequence of the combination of these two effects, the correlation between streamwise and vertical velocity fluctuations is highest in the wake behind the midspan of the curved cylinder, and the correlation between cross-flow and vertical velocity fluctuations reaches large values in the lower wake.     

A microscopic,but not self-consistent approach to nuclear binding and deformation energies

Using various versions of the Skyrme force and Negele's interaction, we calculate deformation energies of nuclei by evaluating the expectation value of the many-body Hamiltonian in wave functions taken to be antisymmetrized products of single-particle functions. These single-particle functions are eigenfunctions of a phenomenological potential, here taken to be a deformed Woods-Saxon well. The method can be thought of as an extension of the Strutinsky shell-correction method, to make the connection with the two-body interaction. The method employed here is checked by comparison with Hartree-Fock (HF) results; our method is, however, much faster than the HF method, and, therefore, suitable for a wide range of problems where one tests the sensitivity of results to changes in the two-body interaction. A fairly good agreement with the HF method is obtained for ground-state energies, radii and deformations, as well as for deformations of shape isomers. The main discrepancy is that our energies tend to increase slightly too rapidly with deformation, indicating that we may not have chosen the best phenomenological well. Two-dimensional energy surfaces, which agree quite well with those from the Strutinsky method, are found for ²⁴⁰Pu.