The motions of the airflow induced by the movement of an automatic guided vehicle (AGV) in a cleanroom are numerically studied by large-scale simulation. For this purpose, numerical experiments scheme based on domain decomposition method is designed. Compared with the related past research, the high Reynolds number is treated by large-scale computation in this work. A domain decomposition Lagrange-Galerkin method is employed to approximate the Navier-Stokes equations and the convection diffusion equation; the stiffness matrix is symmetric and an incomplete balancing preconditioned conjugate gradient (PCG) method is employed to solve the linear algebra system iteratively. The end wall effects are readily viewed, and the necessity of the extension to 3 dimensions is confirmed. The effect of the high efficiency particular air (HEPA) filter on contamination control is studied and the proper setting of the speed of the clean air flow is also investigated. More details of the recirculation zones are revealed by the 3D large-scale simulation.

Automatic guided vehicles (AGVs) play a more and more important role in the material handling system of modern computer integrated manufacturing systems (CIMS). Based on the demands of just-in-time delivery, AGVs are now used more and more widely in modern hospitals, medical centers, port logistics, airports, and semiconductor industry. With the increase in both size and weight of the wafers, AGVs are used to carry the wafers instead of operators to save labor and to decrease wafer damage and contamination.

Cleanrooms are commonly used to provide a contamination control environment to produce high quality and precision products in modern semiconductor industry. The external clean airflow in the cleanroom plays a role of removing microcontaminants and hazardous gas, which are usually generated in manufacturing and transportation process. A vertical external airflow is usually necessary and efficient to keep the cleanness of the cleanroom; however, some microcontaminants that circulate within recirculation zones and deposit on the products and equipment are extremely difficult to be removed. Therefore, simulation of the motion of the airflow in the cleanroom shows its importance.

However, existing techniques available in the literature show a variety of concerns about the characteristics [

The current study is to improve the simulation of airflow in the cleanroom and to investigate the contaminant control inside. It is expected to have a better view about the recirculation zones by using large-scale computation based on a domain decomposition method. To handle the problem caused by the nonlinear convective terms of flow problems, which result in the nonsymmetry of the stiffness matrix, an adapted Lagrange-Galerkin method for the domain decomposition method is used. Compared with the classical methods, which employ product-type methods such as GPBiCG or BiCGSTAB as the iteration solver [

The remaining sections are arranged as follows. Section

To maintain the cleanliness of the cleanroom, the external airflow entering the cleanroom should be filtered by the

A moving AGV in a cleanroom.

The height and width of the cleanroom are set to 2.1 m and 9.2 m, respectively, and a wafer cassette is above the top surface of the AGV, which is consistent with the experiment in [

In order to investigate the distribution of micro contaminant, the tyres are assumed to be the source of the micro containments and the concentration at the bottom of AGV is set as constant.

Let^{2}]; ^{3}]; ^{3}]; ^{2}] defined by

Let ^{2}/s], and

An adapted Lagrange-Galerkin method is applied to the nonlinear terms in (

With definition in (

Here, the notation

Let the subscript

The finite element spaces used in this work are as follows:

The weak form of the Navier-Stokes equations (

As is shown in (

The scheme is as follows:

for

STEP 1:

STEP 2:

It should be noted that the element information term

The model is extended to three dimensions in this work and the width in

A 3D AGV.

To compare the numerical results with numerical results and experimental results obtained by Kanayama et al. [

In order to investigate the end wall effects produced by the three-dimensional model, the restriction in

In this simulation, the tyres are assumed to be the source of the micro containments and the concentration is set to be 0.01 mg/L at the bottom of AGV.

In the domain decomposition system used in this work, computation models are firstly divided into several parts before the domain decomposition computation; parts are further decomposed into subdomains, and for each parts, domain decomposition is performed by the current processor element (PE), see Figure

A domain decomposition system.

During the computation of PCG loop, PEs work independently almost all the time and only the information of the elements that belong to the current parts is available; however, when computing the residual, the PEs need to work synchronously and the collection of local residuals from all the PEs is performed.

As a hybrid Schwarz type preconditioner, the classical balancing domain decomposition (BDD) preconditioner [

A strategy to neglect the

The criteria of the stationary stage is set by an element based

The solver is tested by a 3D lid-driven cavity problem. The current results of Re = 400 (Figure

Comparison of

The efficiency of the incomplete balancing domain decomposition preconditioner is also tested by comparing it with other preconditioners and results are shown in Figure

IBDD versus BDD.

Figure

The ADVENTURE_CAD and ADVENTURE_Metis [

The meshing of the 3D AGV model.

As is mentioned in Section 3.1, the three-dimensional model is decomposed in several parts by domain decomposition method. By using 9 single-core CPUs (9 PEs in total), a nonoverlapped domain decomposition result of the three-dimensional AGV model is demonstrated by Figure

The domain decomposed 3D AGV model.

A finer mesh of

Velocity vectors around the AGV (a) current 3D results; (b) Kanayama et al.’s 2D results.

Aiming at getting a stationary stage of the ADV at a constant speed,

The experiment in [

Kanayama et al.’s experimental visualization.

Velocity vectors around 3D AGV model.

Compared with the pseudo 2D results in Figure

The eddy behind the AGV and the wafer cassette becomes smaller, which reflects the end-wall effects of

Similarly, the eddy in the plane

It is worth pointing out that in spite of the fact that the computation domain is not simply-connected, the Lagrange-Galerkin does not encounter any difficulties at these “holes”; both Figures

To compare the numerical results of Kanayama et al., the space between the grating zone and the bottom of the AGV is supposed to be the source of pollution first, which generates 1 contaminant per second. The comparison of the amount concentration on the upper face of AGV is illustrated in Figure

Contaminants distribution.

The necessity of the vertical external airflow was further proved by numerical experiments with boundaries described in Section

Isolines of contaminants concentration. (a) Without vertical external air; (b) with vertical external air.

In this work, the concern about the proper setting of the speed of external vertical clean air under boundary conditions described in Section

The effects of

From Figure

The Raynolds number in this model is about 33,000. In this work, by using domain decomposition, an AGV model of over 30 million DOF is solved. Isolines of the vorticity are illustrated in Figure

Isolines of vorticity.

The model was divided into

CPU: Intel(R) Core(TM) i7 920@2.67 GHz,

Memory: 12 [GB].

Due to the unconditional stability of the adapted Lagrange-Galerkin method,

A moving AGV in a cleanroom is numerically simulated in three dimensions by large-scale computation in this work. The main conclusions can be summarized as follows.

By using large-scale simulation, the results are consistent with the conventional simulations; moreover, more details of the computational models are revealed, which is important for contaminant control in practice.

To use three-dimensional modeling is necessary to improve the numerical simulation of moving AGVs in cleanrooms.

The proper setting of the speed of external vertical clean air is found, which can be applied to the design and optimization of cleaning room.

The adapted Lagrange-Galerkin method shows good computation accuracy in solving complex problems.

By using incomplete balanced domain decomposition preconditioner, the scheme has the solvability for large-scale problems with up to 30 million of DOF.

The information of recirculation zones is extremely valuable for modern health centers and semiconductor industry to optimize and improve the facilities and to make a clearer cleanroom. In spite of the pervasive applications of AGV systems, the simulation of airflows induced by AGVs still calls for much attention in the future.

This work was supported by the National Science Foundation of China (NSFC), Grant 11202248, 91230114, and 11072272; the China Postdoctoral Science Foundation, Grant 2012M521646; and the Guangdong National Science Foundation, Grant S2012040007687.