A general framework for verification and validation of large eddy simulations

A general framework（methodology and procedures） for verification and validation（V＆V） of large eddy simulations in computational fluid dynamics（CFD） is derived based on two hypotheses. The framework allows for quantitative estimations of numerical error, modeling error, their coupling, and the associated uncertainties. To meet different needs of users based on their affordable computational cost, various large eddy simulation（LES） V＆V methods are proposed. These methods range from the most sophisticated seven equation estimator to the simplest one-grid estimator, which will be calibrated using factors of safety to achieve the objective reliability and confidence level. Evaluation, calibration and validation of various LES V＆V methods in this study will be performed using rigorous statistical analysis based on an extensive database. Identification of the error sources and magnitudes has the potential to improve existing or derive new LES models. Based on extensive parametric studies in the database, it is expected that guidelines for performing large eddy simulations that meet pre-specified quality and credibility criteria can be obtained. Extension of this framework to bubbly flow is also discussed.

A new method of LES verification and validation for attached turbulent cavitating flow

The large eddy simulation(LES)is used to resolve the flow structure in the cavitating turbulent flow around the Clark-Y hydrofoil coupled with a homogeneous cavitation model.A new method is proposed in this paper to calculate the LES error of the time-averaged streamwise velocity for the LES verification and validation(V&V).From the instantaneous cavity patterns,it is demonstrated that the predicted results agree fairly well with the experimental data.With this new proposed method,the LES errors can be easily and effectively calculated with a limited mesh number,and the method might be used in the other applications of the LES V&V.Results of the LES errors obtained by the new method show that the relatively steady flow can be simulated with small errors,while the complex flow structures at the cavity shedding region might lead to an increase of errors in the LES modeling.In addition,the distributions of the resolved Reynolds stresses are used to estimate the influences of the cavitation on the turbulent fluctuations.Results indicate that the turbulent fluctuations for the cavitating flow are much larger in magnitude as compared to the cases without cavitation.

Five-equation and robust three-equation methods for solution verification of large eddy simulation

This study evaluates the recently developed general framework for solution verification methods for large eddy simulation（LES） using implicitly filtered LES of periodic channel flows at friction Reynolds number of 395 on eight systematically refined grids.The seven-equation method shows that the coupling error based on Hypothesis I is much smaller as compared with the numerical and modeling errors and therefore can be neglected. The authors recommend five-equation method based on Hypothesis II, which shows a monotonic convergence behavior of the predicted numerical benchmark（S_C）, and provides realistic error estimates without the need of fixing the orders of accuracy for either numerical or modeling errors. Based on the results from seven-equation and five-equation methods, less expensive three and four-equation methods for practical LES applications were derived. It was found that the new three-equation method is robust as it can be applied to any convergence types and reasonably predict the error trends. It was also observed that the numerical and modeling errors usually have opposite signs, which suggests error cancellation play an essential role in LES. When Reynolds averaged Navier-Stokes（RANS） based error estimation method is applied, it shows significant error in the prediction of S_C on coarse meshes. However, it predicts reasonable S_C when the grids resolve at least 80% of the total turbulent kinetic energy.

Some notes on numerical simulation and error analyses of the attached turbulent cavitating flow by LES

In this letter, the attached turbulent cavitating flow around the Clark-Y hydrofoil is investigated by the numerical simulation with special emphasis on error analysis of large eddy simulation（LES） for the unsteady cavitation simulation. The numerical results indicate that the present simulation can capture the periodic cavity shedding behavior and show a fairly good agreement with the available experimental data. Further analysis demonstrates that the cavitation has a great influence on LES numerical error and modeling error. The modeling error and numerical error are almost on the same order of magnitude, while the modeling error often shows a little bit larger magnitude than numerical error. The numerical error and modeling error sometimes can partially offset each other if they have the opposite sign. Besides, our results show that cavitation can extend the magnitudes and oscillation levels of numerical error and modeling error.

文丘里管内空化流动大涡模拟的验证与确认

[目的]旨在定量分析验证与确认(V&V)方法对有限空间内部空化流动求解的准确度描述的适应性,对文丘里管内不同空化数下的流动进行大涡模拟(LES),用以实施V&V方法,并扩展该方法的应用范围。[方法]首先,采用大涡模拟结合Zwart-Gerber-Belamri (ZGB)空化模型对不同空化数下文丘里管内部的流动进行数值模拟;然后,采用基于五方程的V&V方法,计算不同工况下进出口压力比和各监测点压力系数的准确度阶数及数值基准值;最后,计算大涡模拟的验证不确定度,以及与模拟值和试验结果的对比误差进行比较,完成确认过程。[结果]结果表明,在3种空化数下,进出口压力比这一全局量的验证不确定度均较低,且均实现了对应不确定度水平下的确认。除空化数σ=0.263时x/D_(th)=9及x/D_(th)=13监测点处压力系数的验证不确定度较高且未实现确认外,其余监测点各工况下压力系数验证不确定度均较低,均实现了对应不确定度水平下的确认。[结论]基于五方程的V&V方法能很好地反映文丘里管内部流动大涡模拟的误差,但计算资源消耗偏大,需进一步改进有限空间内部空化流动大涡模拟的V&V方法。