Large Eddy Simulation of Propellers

Version	Summary	Created by	Modification	Content Size	Created at	Operation
1		Min Shan	--	1644	2023-12-13 07:54:56	\|
2	Reference format revised.	Lindsay Dong	Meta information modification	1644	2023-12-18 03:17:43	\|

This entry is adapted from the peer-reviewed paper 10.3390/app132111716

turbulence model deep learning large eddy simulation

1. Introduction

The turbulence problem encompasses various engineering fields, so that finding a solution for this problem is of great significance in these fields. During the past decades, researchers have continuously conducted exploration and research of turbulence. The concept of rapid distortion of a fluid ^[1]^[2] and the proposition of different scaling rates and the demonstration of turbulent boundary layers ^[3] have given us a better understanding of turbulent flow. With the advancement of computer technologies and the implementation of particle image velocimetry (PIV), research on turbulence has become increasingly profound and detailed. While previous efforts have deepened the comprehension of turbulent flow, the fundamental issues related to turbulent flow ^[4], and its effective application in engineering remain unaddressed. Turbulent flow is still a significant hurdle for success in the engineering of aviation, aerospace and navigation. The essence of turbulent flow, the physical laws governing its evolution, and optimal utilization in engineering have always been important research topics attracting the attention of researchers.

Numerical computation methods for turbulence flow can be categorized into direct numerical simulation (DNS), large eddy simulation (LES), and Reynolds-averaged Navier–Stokes (RANS) based on grid resolution scales. With improvement in computer performance and the development of parallel computing, DNS and LES have been increasingly utilized both in research and engineering. However, for complex geometries and flows with a high Reynolds number, the substantial increase in grid size severely limits the applicability of these methods. In contrast, although the accuracy of the RANS model is inferior to the former two methods, its user-friendly nature and high efficiency have made it widely adopted in engineering practice ^[5]. Particularly in the aerospace domain, where the Reynolds numbers of flows are generally high, turbulence computation mainly depends on existing RANS models.

Reynolds-averaged numerical simulation (RANS) is the most extensively employed turbulence numerical simulation method in engineering. Most of the RANS models are based on the assumption of eddy viscosity, which yields satisfactory results for attached flows. However, in the case of complex flows such as separated flow, the relationship between Reynolds stress and strain is no longer that of a simple linear correlation. The anisotropy of turbulent flow makes turbulence modeling significantly challenging ^[6], and consequently, the calculation results of the RANS model often exhibit significant deviations from the actual flows. In addition, empirical parameters in the model are often determined based on some specific flows, which increases the model’s uncertainty and subsequently affects its applicability.

Large eddy simulation (LES) is a turbulence numerical simulation method that lies between direct numerical simulation (DNS) and Reynolds-averaged numerical simulation (RANS). It filters the Navier–Stokes equations, dividing the flow field into large-scale and small-scale components. LES directly simulates the large-scale eddies, while a sub-grid-scale model is used to model and solve the small-scale components. However, on the near-wall surface, since there is no inertial sub-region, the number of grids for LES near the wall surface is always required to reach the fineness of DNS. This also leads to a large consumption of computing resources for LES simulation, which limits its application in engineering applications, especially engineering computation for flows with complex shapes. Therefore, many researchers have attempted to integrate RANS and LES models to establish complex system models to reduce computational costs while achieving accurate simulation results.

In fact, there are two main types of approaches to establishing complex system models. The first one is based on the framework of theoretical models, where an ideal system description is made according to the governing equations of the physical problem. This type of model typically requires researchers to have a deep understanding of the physical processes and be able to translate them into mathematical models. Most of the current turbulence models, such as the k-ω model ^[7] and the Spalart-Allmaras (SA) model ^[8], are developed by using this approach. The second type is based on data-driven approaches, which involve direct construction of black-box or grey-box models based on sample data obtained from system simulations or experiments. How to effectively utilize large datasets, extract key information from them, and guide the development of fluid mechanics have become focuses of researchers’ attention.

Machine learning techniques, such as radial basis function neural networks (BRFNN), random forests (RF), support vector machines (SVM), and neural networks (NNS), have been widely applied in many areas such as speech and image recognition ^[9]^[10], signal processing ^[11], and model reduction ^[12]. The combination of machine learning and turbulence modeling has become an emerging research direction in the field of fluid mechanics. Existing research findings have strongly validated its feasibility and indicate the positive prospects of machine learning in future applications of turbulence modeling ^[13]. However, there are still many challenges and unsolved problems in this field. For instance, how to improve the generalization ability, robustness, and stability of the models is the main concern of researchers. Existing studies showed that the model performance tends to degrade to varying degrees when there are significant differences between the predicted data and the training data or when there are changes in the geometric shape. This is to some extent an inherent limitation of data-driven methods. Additionally, some aspects in the model construction, such as data processing and feature engineering, selection of model objects, and constraint conditions, can also influence the final performance of the models.

2. Large Eddy Simulation of Propellers

2.1. RANS Simulation

Reynolds-averaged Navier–Stokes (RANS) simulation is a classical numerical simulation method widely used in the field of fluid mechanics. Instead of directly solving the Navier–Stokes equation (NS equation) for turbulent flow, the RANS method applies time-averaging to the Reynolds equation ^[14]. It utilizes assumed Reynolds stress to establish a connection between turbulent fluctuation values and time-averaged values. In addition, it introduces a turbulent flow model to close the Reynolds time mean equations. The RANS time-averaging approach avoids directly solving turbulent flow, thus significantly improving computational speed and efficiency. Consequently, it has become the most commonly employed numerical simulation method in engineering. The RANS turbulence models includes the SA one-equation model and two-equation models. For example, k-ε and k-ω models are widely used two-equation models. Some studies, including those conducted by GonzàLez ^[15] and Chea ^[16], utilized the RANS method for unsteady numerical simulation of flow fields. Ahmed ^[17] applied the RANS method to investigate the hydraulic performance of axial flow pumps. Xiang et al. ^[18] conducted numerical simulations on wind turbines, exploring the wind field and wind-sand erosion issues. The RANS method has been applied in practical engineering problems due to its low computational time and the requirement of low grid resolution. When the accuracy of the results is not critical, the RANS method can save computational costs and expedite the simulation process.

2.2. LES Simulation

Large eddy simulation (LES) is a numerical method used to investigate turbulent flows and is particularly suitable for resolving flow phenomena. In LES, small eddies in the flow field are filtered through a filter function, while the large eddies and smaller eddies are directly solved using the NS equation. The additional impact of the small eddies on the large eddies is considered through sub-grid scale (SGS) models. For instance, Lu ^[19] carried out LES simulations to analyze lift and drag around a cylinder and used SGS models to capture the detailed characteristics of the flow field. Researchers have also attempted to apply LES to practical engineering. Kye et at. ^[20]^[21] employed LES to study the diffuser of a centrifugal pump and analyzed the flow behavior and the interaction between guide vanes. They found that LES can improve the accuracy of numerical simulations when the working conditions deviate from the design. Scholars have also investigated two-dimensional and three-dimensional LES, highlighting the limitation of simplifying three-dimensional flows to two-dimensional, since it ignores spanwise fluctuations of large eddies and leads to inaccurate calculations. Bouri ^[22] investigated flows around a square column and found that the two-dimensional LES fails to reflect actual flow behavior. The above-mentioned research indicates that LES and detached eddy simulation (DES) methods have been gradually transitioned to engineering applications. With the computational requirements taken into account, direct application of high-precision numerical simulation methods in engineering is challenging. However, with continuous advancements in computer technology and simulation methods, LES simulations have played a significant role in exploring turbulent flows and solving practical engineering problems.

2.3. Application of Deep Learning in Turbulence Modelling

In recent years, machine learning and deep learning methods have been used in the field of fluid mechanics, demonstrating immense potential in applications such as turbulence modeling.

Various machine learning techniques have been applied to modify traditional RANS models to enhance the flow prediction, including modifying model parameters with Bayesian methods ^[23], introducing a correction factor for the turbulence production term using neural networks ^[24], adding a spatially distributed correction field via field inversion and Gaussian process ^[25], etc. However, the various types of corrections trained for traditional RANS models are usually not physically interpretable.

Other than simply adding corrections to existing model parameters, more comprehensive efforts have been made to construct new Reynolds stress closures via physics-informed machine learning. A random forest method was used in Wang ^[26] to train Reynolds stress discrepancy functions, but the performance of mean quantities needs to be further validated. At the same time, the gene expression programming (GEP) method has been introduced ^[27] to develop explicit algebraic (Reynolds) stress models (EASM) based on the stress tensor decomposition proposed by Pope ^[28].

Although machine learning for turbulence model development is becoming a growing trend, obstacles and problems still exist in training and implementing the models to engineering applications. Using machine learning to enhance traditional turbulence models for improved accuracy in flow predictions remains an area that requires continuous and thorough exploration.

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Yuhuang Ye

Liang Li

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Update Date: 18 Dec 2023

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