Three-dimensional flow state analysis of microstructures of porous graphite restrictor in aerostatic bearings

Highlights

• A algorithm of the reconstruction method of porous model is proposed with the DCGAN deep learning.

• The microcosmic parameters and flow track in a porous material are obtained. Effects of inlet pressure and gas viscosity are discussed.

• The blocking phenomenon and its influence on the flow rate and pressure distribution are analyzed for providing guidance for the simulation of porous materials in detail.

Abstract

Porous aerostatic bearings as a new type of supporting component used in ultraprecision equipment. The study of porous models is essential as they are a basis for porous aerostatic bearings. However, the effects of micropore structure and flow state inside a material have not been addressed in previous studies. Herein, we propose a high-accuracy and low-cost method using deep learning to reconstruct a three-dimensional (3D) porous model and obtain the 3D flow state inside a porous material. It can reveal richer flow states such as the flow track and movement in three directions, which have not been revealed previously. This new method is effective for studying the properties of porous materials, micro-flow state, and simulation of parameters in detail.

Introduction

Aerostatic bearings are widely used in ultraprecision machine tools, integrated circuit manufacturing equipment, and precise measurement instruments. It offers many advantages, including high accuracy, low friction, and no pollution [1]. A porous aerostatic bearing is a novel bearing that effectively improves the load capacity and dynamic behavior.

A porous restrictor can yield a more even pressure distribution; however, the static and dynamic performances of porous bearings are still being investigated primarily because of their small opening and throat with complex and irregular distributions, which increase the difficulty in constructing three-dimensional (3D) material modeling [2,3]. In a previous study, a porous material was treated as an entire block on a two-dimensional (2D) plane with isotropic permeability. Such approaches, however, have failed to address the flow state inside the porous material as well as the development of the flow state in a 3D space. Therefore, it is essential to reconstruct the 3D porous model and analyze the 3D flow field.

Porous materials have been studied in geological structures, such as porous soil and porous rock. Many equivalent simplified models that do not require destructive measuring instrument have been proposed, such as the pore network model, capillary model, and volume packing model, to accommodate the characteristics of small openings and throat [4]. The solid part of the materials is fitted by simple geometries such as spheres and cylinders, which are stacked together to build a general framework. The throat part is fitted by a simple tube such as circular, square, and capillary tubes [5]. These reconstruction methods are unsatisfactory because they are merely idealized models for qualitative analysis.

In the manufacturing of porous materials, the pore and throat tend to be randomly distributed. Therefore, numerous studies regarding porous material reconstruction based on various stochastic methods have been conducted. In 1975, Joshi [6] proposed the Gaussian analysis. Subsequently, Quiblier [7] used this method in a 3D space and obtained the first 3D porous material model. In 1953, the simulated annealing algorithm was developed by Metropolis et al. to establish a rock structure that is highly similar to a real one [8]. In 1997, Bakke and Oren [9] presented a process simulation analysis for the simulation of the 3D pore network of sandstone. In 2004, Wu Kejian et al. [10] used an efficient Markov chain Mont- Carlo analysis method (MCMC) for simulating soil structure.

The methods above have their own applications, merits, and disadvantages. The Gaussian analysis affords a fast 3D reconstruction but not universal applicability and translatability. The simulated annealing algorithm enables the reconstruction model to contain more information regarding the character of a real sample. However, it cannot realize the structure of a high-connectivity porous framework and requires a significant amount of processing time. The process simulation is complicated and only applied for reconstructing simple porous materials. The MCMC method is a simple and efficient method for building a model; however, it poses challenges when used for 3D heterogeneous materials. In general, stochastic models only contain features that are similar to those of a real sample and do not reflect the actual and individual structure of the porous material.

The only method to obtain the actual structure of a porous material is by experiments. To date, X-ray industrial computed tomography (CT) is the best measuring instrument to reconstruct 3D models in nondestructive testing. Nikles et al. [11] built a 3D porous model using a CT scanning image and introduced Avizo software into the 3D reconstruction. Hu et al. [12] used CT to study the effects of pore microstructures on the anti-clogging performance of porous asphalt concrete. Khormani et al. [13] estimated the mechanical properties of concrete via CT scanning. However, it is costly to obtain micron-scale pore distributions via high-precision CT scanning. Furthermore, it is unrealistic to scan each porous material while constructing a 3D model. Focused ion beam (FIB) or scanning electron microscopy (SEM) is another affordable method for measuring microscopic structures; however, it can only capture the scanning image from the surface. Tomutsa and Radmilovic [14] optimized the accuracy of the slice reconstruction method using FIB. Lu et al. [15] analyzed the fluid lubricating film of a lubricant on the porous composite surface by SEM. Li et al. [16] obtained the composition and microstructure of a composite coatings using SEM. Xin et al. [17] used SEM to detect the microstructure of sandstone and obtained the evolution law of the surrounding rock microstructure of underground coal gasification. Occasionally, ion beams can destroy the microstructure of the porous material. However, SEM does not damage the surface and satisfies the measurement requirements of the pores. However, without the scanning images of internal layers, accuracy will be degraded in 3D reconstruction modeling.

Currently, deep learning is effective for image recognition. The standard convolutional neural network (CNN) contains an input layer, a convolution layer, a pooling layer, a fully connected layer, and an output layer. In 2012, Alex Krizhevsky [18,19] won the first rank of the Image Net competition using the Alex Net network model with an 84% precision rate. Subsequently, the CNN model became popular worldwide and has been widely used in feature extraction and image identification. In 2014, Ian Goodfellow reported the use of the generative adversarial network (GAN) [20,21]. This network comprises two main parts: the discriminant module D and the generating module G. The two modules compete with each other to produce optimized results, i.e., the image produced by G is sufficiently good and cannot be recognized by D. Combining the CNN network with the GAN yields the deep convolutional generative adversarial network (DCGAN), which will automatically obtain features from porous scanning images and then produce high-quality internal layer images that exhibit the features of the real porous material.

The purpose of reconstructing the 3D model is to obtain an accurate 3D flow state in a porous material. Permeability is a critical parameter that depicts the macroscopic reflection of microscopic pore structure characteristics. Wang et al. [22] obtained the permeability of the porous material of aerostatic porous bearing by the experiment. However, discrepancies in permeability exist between theoretically calculated and experimental results. Wang et al. [23] revised the formula for calculating permeability coefficient by including the effect of tortuosity without using an empirical constant. It improved the accuracy of calculations and is easy to popularize.

After obtaining the 3D structure model, the precision of the permeability calculation can be further improved and the anisotropy permeability quantitatively described. By applying flow analysis software such as Fluent and Avizo, the 3D simulation of flow fields in porous materials can be achieved. Sun et al. [24] used Avizo to reconstruct a multiscale and multi-mineral digital core model of low-permeability uranium-bearing sandstone, as well as characterized macroscopic and microscopic pore–throat structures of low-permeability uranium-bearing sandstone. Fan et al. [25] used Avizo to quantitatively identify the pores, coal matrix, and minerals in coal. However, the analysis of flow state inside materials is insufficient. Based on the computational fluid dynamic (CFD) method and dynamic mesh technology, Cui et al. [26,27] quantitatively studied the effects of manufacturing errors on the static characteristics and running accuracy of aerostatic porous bearings. Similar to Cui, most authors only solved the pressure distribution at the outlet and did not divulge the flow state inside porous materials. Hence, it is difficult to accurately predict the performances of bearings without knowing the physics inside the material.

Hence, we herein propose a high-accuracy, low-cost, and a few-sample method to reconstruct 3D porous models and obtain the 3D flow state inside porous materials. Section 2 describes the 3D reconstruction process using the DCGAN deep learning algorithm. In Section 3, the microcosmic parameters of the porous material and the permeability are calculated using a 3D model, which was verified experimentally. The gas flow in a porous material along different directions obtained using CFD software is presented in Section 4. Finally, the flow rate and pressure distribution in 3D flow fields with different inlet pressures are analyzed.