Computational fluid dynamics (CFD) software tools for microfluidic applications – A case study
Introduction
Today CFD methods are well described in many textbooks [1], [2] and applied routinely in engineering science. They serve as valuable tools for design and engineering of components and systems in turbo machinery, aerospace and many other fields [1]. In this paper we focus on the application of CFD as engineering tool for microfluidic devices and the particularities associated with it [3]. In micro dimensions, for example, surface forces dominate over body forces requiring special attention for problems involving two phase flows with free surfaces which are often driven by capillary forces. Typical flow situations are capillary wicking or formation of droplets which are characterised by low Weber and Reynolds numbers [4], [5], [6]. To model free surface flows including surface tension effects – amongst others – the so called volume-of-fluid method (VOF) has been established [7] and is still being refined [8], [9], [10], [11]. Another particularity in microfluidics is the increased importance of diffusion for mixing phenomena. Since in microfluidic flow problems the Reynolds numbers are typically very small, turbulence is hardly ever observed and mixing is driven by diffusion only at low Peclet numbers [12]. Effective mixing within short times can thus only be achieved by decreasing the diffusion length of the fluids which can technically be realized by multi lamination or chaotic advection [13], [14], [15], [16], [17], [18]. On the one hand the absence of turbulence in microfluidics simplifies the CFD treatment substantially but on the other hand diffusion is difficult to account for with the required accuracy in practical cases. High order discretisation schemes are required to suppress the so called “numerical diffusion” which is nothing else than numerical errors being accumulated by the algorithm.
Both of the described particularities, free surfaces as well as diffusion have been dealt with in length in the CFD-literature from a numerical point of view. In principle there are many approaches known to simulate these types of problems in more or less specific situations at various degrees of accuracy (see for example [11], [13], [19], [20]). In this paper however, we want to assess the topic from an engineering perspective and ask the question: How helpful are the software tools being available for the micro engineer to address these problems in practice? As it is the nature of the selected engineering problems, they can not be solved analytically and thus have to be considered numerically with CFD. The crucial points in this context are the availability and the applicability of CFD-tools for engineering purposes in the considered cases. To do so a case study of various commercial CFD codes has been performed with respect to experimental results, where available. Due to the variety of commercial software tools and the limited resources for performing such case studies the authors restricted their choice to the four previously mentioned Finite Volume codes. A comparison to well established Finite Element codes like COVENTOR [21] or COMSOL [22] was not possible in the framework of this work.
Benchmarking in general is an essential part of CFD research and code validation [23], [24], [25], [26], [27], [28]. However, due to the commercial nature of the software applied for the presented study, the algorithms are not in the public domain and are not know in detail. Therefore the presented case study can only be descriptive instead of analytic i.e. the outcome of the simulations can be documented and discussed but not be analysed in detail. Nevertheless, the state of the art of CFD simulation in microfluidics is presented by this approach and the question is addressed which tools are available and well suited for a specific purpose, if any. The devices studied in this paper were not selected for the purpose of driving certain numerical codes into problems, but are a representative selection of the problems encountered by the authors over the years in microfluidic research. Indeed, the major part of the paper deals with the application of simulation methods to these microfluidic devices that have not been published before. The results hopefully will provide guidance to micro engineers applying CFD as engineering tool as well as support for developers of CFD code in search of even faster and more accurate algorithms.
Section snippets
Approach
The approach followed in this paper is based on the assessment of selected simulation problems or cases which are considered to be typical and representative for microfluidic applications. Especially the diffusion at low Reynolds numbers and the aspects of surface tension dominated free surface flows have been considered for selection of the cases. Each of the four chosen problems presented in Section 4 in detail is simulated with each of the four selected CFD codes introduced in Section 3. The
Description of the applied hard- and software
In the present case study the software codes CFD-ACE+ [30], CFX [31], FLOW-3D [32] and FLUENT [33] have been investigated. All of the codes are based on the finite-volume method (FVM) [1] to solve the Navier–Stokes equations, except Flow-3D. Flow-3D is based on a combination of finite difference and finite volume perspectives and it uses a control volume approach to solve the conservation equations [23], [24], [34]. The velocity pressure coupling is generally accomplished by the SimpleC
Simulations and results
All simulation problems discussed in the following were simulated on a structured grid as motivated in the beginning. Transient simulations were performed in an explicit formulation using a first order Euler scheme with fixed time steps, except for Flow-3D were an automatic time step had to be used as described in the previous section. The VOF method is treated by all tools in an explicit way except for CFX which uses a so called high-resolution scheme with an implicit second order Euler scheme.
Computational speed
The assessment of computational speed provided in the following is only reflecting the performance of the studied software tools with respect to the closely defined benchmark problems presented in this work. It should be mentioned, that either software would most likely be able to simulate any of the problems faster. For most of the software tools the setup of the presented problems enforcing a structured grid and fixed times step are not the ideal settings to achieve maximum computational
Conclusions
The presented results show that qualitatively all tools can perform well in calculating convection diffusion problems with a second order algorithm for the tracer scalar. The numerical diffusion is comparable and small for all tools and should allow for quantitative statements on flow patterning and lamination in mixing devices. Due to lack of experimental data a real quantitative assessment was not possible in this work.
In contrast to the case of mixing and flow patterning by convection and
Acknowledgements
The authors want to thank all of the mentioned companies for supplying their software products for this case study, partly free of costs. Without their help and excellent support it would have been very difficult for the authors to introduce themselves quickly to the various software packages and to set up the simulation problems. Part of this work was supported by the German Federal Ministry of Education and Research (BMBF) within the MicroDMFC-Project (no. 03SF0311B) which is gratefully
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