Computational fluid dynamics (CFD) software tools for microfluidic applications - A case study

This paper reports on an exemplary study of the performance of commercial computational fluid dynamic (CFD) software programs when applied as engineering tool for microfluidic applications. Four commercial finite volume codes (CFD-ACE+, CFX, Flow-3D and Fluent) have been evaluated by performing CFD-simulations of typical microfluidic engineering problems being relevant for a large variety of lab-on-a-chip (LOAC) applications. Following problems are considered as examples: multi lamination by a split and recombine mixer, flow patterning on a rotating platform (sometimes termed “lab-on-a-disk”), bubble dynamics in micro channels and the so called TopSpot^® droplet generator for micro array printing. Hereby mainly the capability of the software programs to deal with free surface flows including surface tension and flow patterning of two fluids has been studied. In all investigated programs the free surfaces are treated by the volume-of-fluid (VOF) method and flow patterning is visualised with a scalar marker method. The study assesses the simulation results obtained by the different programs for the mentioned application cases in terms of consistency of results, computational speed and comparison with experimental data if available.     

The flow induced in a three layer stratified fluid by a submerged sink or source with stagnation points on the free surfaces

A boundary integral technique is developed to study the free surface flow of a steady, two-dimensional, incompressible, irrotational and inviscid fluid which is induced in both two and three layer stratified fluids in the presence of gravity by a submerged sink or source with stagnation points on the free surfaces. A special form of the Riemann–Hilbert problem, namely the Dirichlet boundary problem, is applied in the derivation of the governing non-linear boundary integral–differential equations which have been solved for the fluid velocity on the free surfaces and this involves the use of an interpolative technique and an iterative process. Results have been obtained for the free surface flow for various Froude numbers and sink heights in both two and three layer fluids. Further, we have also studied the critical Froude numbers for which no convergent solutions are possible for any larger values of the Froude number. We have found that the free surfaces are dependent on two parameters, namely the Froude number and the ratio of sink height to the thickness of either the middle layer in a three layer system and the bottom layer in a two layer system.     

A fixed-grid model for simulation of a moving body in free surface flows

A two-dimensional computer model is developed to simulate free surface flow interaction with a moving body. The model is based on the cut-cell technique in a fixed-grid system. In this model, a body is approximated by the partial cell treatment (PCT), in which an irregular body is represented by the volumetric fraction of solid in Cartesian cells. The body motion is tracked by Lagrangian method whereas the fluid motion around the body is solved by Eulerian method. The concept of “locally relative stationary (LRS)” is introduced in this study. In the LRS method, a source term is added locally to the conventional continuity equation on body surfaces to take account of body motions, which subsequently affects the computational results of fluid pressure and flow velocity around the body. The LRS method is incorporated into an earlier Reynolds averaged Navier-Stokes (RANS) equations model developed by Lin and Liu [A numerical study of breaking waves in the surf zone. J Fluid Mech 1998;359:239-64]. The new model is capable of simulating generic turbulent free surface flows and their interaction with a moving body or multiple moving bodies. A series of numerical experiments have been conducted to verify the accuracy of the model for simulation of moving body interaction with a free surface flow. These tests include the generation of a solitary wave with the prescribed wave paddle movements, water exit and water impact and entry of a horizontal circular cylinder, fluid sloshing in a horizontally excited tank, and the acceleration/deceleration of an elliptical cylinder near a water surface. Excellent agreements are obtained when numerical results are compared to available analytical, experimental, and other numerical results. The model is a simple-to-implement computational tool for simulating a moving body in turbulent free surface flows.     

Gravity capillary waves generated by a moving pressure distribution in the presence of constant vorticity and dissipation

Two-dimensional nonlinear free-surface flows due to a pressure distribution moving at a constant velocity at the surface of a fluid of infinite depth are considered. The effects of the gravity and of the surface tension are included in the dynamic boundary condition. The vorticity in the fluid is assumed to be constant. The dissipation is modelled by a quasi potential approximation. The problem is solved numerically by a boundary integral equation method and numerical solutions are presented. The results unify previous findings for irrotational gravity capillary waves, waves in the presence of constant vorticity and free surface flows with dissipation.     

Flow pattern around an appended tanker hull form in simple maneuvering conditions

A detailed computational study is presented of the flow pattern around the Esso Osaka with rudder in simple maneuvering conditions: “static rudder” and “pure drift”. The objectives are: (1) apply RANS for maneuvering simulation; (2) perform verification and validation on field quantities; (3) characterize flow pattern; and (4) correlate behavior of the integral quantities with the flow field. The general-purpose code CFDSHIP-IOWA is used. The free surface is neglected and the two-equation k-ω turbulence model is used. The levels of verification of the velocity components for the “straight-ahead”, “static rudder” and “pure drift” conditions show ranges from 5.5% to 28.3% of free stream, U₀, for the axial velocity U and 2.5-29.1%U₀ for the cross flow (V, W). Qualitative validation against limited experimental data shows encouraging results with respect to trends and levels. The flow pattern is characterized by fore and aft body bilge and side vortices, which are similar for “straight-ahead” and “static rudder” conditions, except in close vicinity of the rudder. The “pure drift” condition shows strong asymmetry on windward vs. leeward sides and a more complex vortex system with additional bilge vortices. Similarities and differences with data for other tanker, container, and surface combatant hulls and relation between flow pattern and forces and moments are discussed. Future work focuses on influence of propeller.     

Fast animation of debris flow with mixed adaptive grid refinement

Animating debris flow is one of the most challenging tasks in computer graphics, because of its complex dynamic mechanism and the interaction between flows and solids in so large scale region. The difficulty focuses on how to resolve the contradiction between lower computational load and higher request of animating quality. A highly effective method of modeling and animating of debris flow with adaptive grid is presented. First, the debris flow is modeled as Bingham plastic fluid with view‐dependent adaptive grid that is adopted to model the flow volume, and the boundless grids can cover the large scale region of debris flow. Then the mixed grids are built for confluent flows, and the two‐way coupling interaction between flows and environment is considered. After extracting the debris flow surface, adaptive surface tension combining wave particles equation is used to enhance the details and sprays are generated by particles considering the interaction between two fluid volumes. Finally, different dynamic realistic scenes with debris flow are successfully animating at interactive rates. Copyright © 2013 John Wiley & Sons, Ltd.     

OFF,Open source Finite volume Fluid dynamics code: A free,high-order solver based on parallel,modular, object-oriented Fortran API

OFF, an open source (free software) code for performing fluid dynamics simulations, is presented. The aim of OFF is to solve, numerically, the unsteady (and steady) compressible Navier–Stokes equations of fluid dynamics by means of finite volume techniques: the research background is mainly focused on high-order (WENO) schemes for multi-fluids, multi-phase flows over complex geometries. To this purpose a highly modular, object-oriented application program interface (API) has been developed. In particular, the concepts of data encapsulation and inheritance available within Fortran language (from standard 2003) have been stressed in order to represent each fluid dynamics “entity” (e.g. the conservative variables of a finite volume, its geometry, etc…) by a single object so that a large variety of computational libraries can be easily (and efficiently) developed upon these objects. The main features of OFF can be summarized as follows:     

A numerical study of a particular non-conservative hyperbolic problem

We study the ability of several numerical schemes to solve a non-conservative hyperbolic system arising from a flow simulation of solid-liquid-gas slurries with the so-called virtual mass effect. Two classes of numerical schemes are used: some Roe-type finite volume schemes, which are based on the resolution of linearized Riemann problems, and some (centered or upwind) schemes with an additional artificial diffusion, such as the classical Rusanov scheme. For flow regimes of interest (steady as well as unsteady flows), the computational process breaks down for some schemes. Indeed, for such flows, the system has at least one eigenvalue having a small magnitude in the interior of the computational domain and this is a possible reason for the failure of some upwind schemes using the resolution of a linearized Riemann problem. Such a failure does not appear with, for instance, the Rusanov scheme which is well known for its robustness. Furthermore, since the system is non-conservative, it is not clear what a weak solution is, when the solution is discontinuous (at least, one needs to have the non-conservative equivalent of the Rankine-Hugoniot jump conditions) and we show that the approximate solution given by different numerical schemes converges towards different “weak solutions”.     

A numerical solution of the leveling problem

The present paper provides a numerical solution to the leveling problem. The solution treats a free surface flow of a viscous fluid of finite depth with surface tension effects. The Navier-Stokes equations were solved using a modified MAC method, adapted to high viscosities (low Re), and surface tension. Leveling experiments performed with Newtonian fluids fit the numerical solution quite well.     

Exact control of genetic networks in a qualitative framework: The bistable switch example

A qualitative method to control piecewise affine differential systems is proposed and explored for application to genetic regulatory networks. This study considers systems whose outputs and inputs are of a qualitative form, well suited to experimental devices: the measurements indicate whether the variables are “strongly” or “weakly” expressed, that is, only the region of the state space where trajectories evolve at each instant can be known. The control laws are piecewise constant functions in each region and in time, and are only allowed to take three qualitative values corresponding to no control (u=1), high synthesis rates () or low synthesis rates (). The problems of controlling the bistable switch to each of its steady states is considered. Exact solutions are given to asymptotically control the system to either of its two stable steady states. Two approximate solutions are suggested to the problem of controlling the system to the unstable steady state: either control to a neighborhood of the state, or in the form of a periodic cycle that passes through the state.     

Simulating flows with moving rigid boundary using immersed-boundary method

The present study is to apply the immersed-boundary method to simulate 2- and 3-D viscous incompressible flows interacting with moving solid boundaries. Previous studies indicated that for stationary-boundary problems, different treatments inside the solid body did not affect the external flow. However, the relationship between internal treatment of the solid body and external flow for moving-boundary problems was not studied extensively and is investigated here. This is achieved via direct-momentum forcing on a Cartesian grid by combining “solid-body forcing” at solid nodes and interpolation on neighboring fluid nodes. The influence of the solid body forcing within the solid nodes is first examined by computing flow induced by an oscillating cylinder in a stationary square domain, where significantly lower amplitude oscillations in computed lift and drag coefficients are obtained compared with those without solid-body-forcing strategy. Grid-function convergence tests also indicate second-order accuracy of this implementation with respect to the L¹ norm in time and the L² norm in space. Further test problems are simulated to examine the validity of the present technique: 2-D flows over an asymmetrically-placed cylinder in a channel, in-line oscillating cylinder in a fluid at rest, in-line oscillating cylinder in a free stream, two cylinders moving with respect to one another, and 3-D simulation of a sphere settling under gravity in a static fluid. All computed results are in generally good agreement with various experimental measurements and with previous numerical simulations. This indicates the capability of the present simple implementation in solving complex-geometry flow problems and the importance of solid body forcing in computing flows with moving solid objects.     

Analytical solution for suction and injection flow of a viscoplastic Casson fluid past a stretching surface in the presence of viscous dissipation

In this study, steady two-dimensional flow of a viscoplastic Casson fluid past a stretching surface is considered under the effects of thermal radiation and viscous dissipation. Both suction and injection flows situations are considered. The partial differential governing equations are transformed into ordinary differential equations and solved analytical. Analytical solutions for velocity and temperature are obtained in terms of hypergeometric function and discussed graphically. Moreover, numerical results are also obtained by Runge–Kutta–Fehlberg fourth–fifth-order (RKF45) method and compared with the analytical results. The results showed that the injection and suction parameter can be used to control the direction and strength of flow. The effects of Casson parameter on the temperature and velocity are quite opposite. The effects of thermal radiation on the temperature are much more stronger in case of injection. The heat transfer coefficient shows higher value for Casson fluid while for Newtonian fluid is the lowest.

     

Magnetohydrodynamic (MHD) flow of a micropolar fluid towards a stagnation point on a vertical surface

The steady MHD mixed convection stagnation point flow towards a vertical surface immersed in an incompressible micropolar fluid is investigated. The external velocity impinges normal to the wall and the wall temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides that usually reported in the literature for the opposing flow.     

Monte Carlo simulations of the HP model (the "Ising model" of protein folding)

Using Wang–Landau sampling with suitable Monte Carlo trial moves (pull moves and bond-rebridging moves combined) we have determined the density of states and thermodynamic properties for a short sequence of the HP protein model. For free chains these proteins are known to first undergo a collapse “transition” to a globule state followed by a second “transition” into a native state. When placed in the proximity of an attractive surface, there is a competition between surface adsorption and folding that leads to an intriguing sequence of “transitions”. These transitions depend upon the relative interaction strengths and are largely inaccessible to “standard” Monte Carlo methods.     

Direction-based adaptive data propagation for heterogeneous sensor mobility

We consider sensor networks where the sensor nodes are attached on entities that move in a highly dynamic, heterogeneous manner. To capture this mobility diversity we introduce a new network parameter, the direction-aware mobility level, which measures how fast and close each mobile node is expected to get to the data destination (the sink). We then provide local, distributed data dissemination protocols that adaptively exploit the node mobility to improve performance. In particular, “high” mobility is used as a low cost replacement for data dissemination (due to the ferrying of data), while in the case of “low” mobility either (a) data propagation redundancy is increased (when highly mobile neighbors exist) or (b) long-distance data transmissions are used (when the entire neighborhood is of low mobility) to accelerate data dissemination toward the sink. An extensive performance comparison to relevant methods from the state of the art demonstrates significant improvements, i.e. latency is reduced by even four times while keeping energy dissipation and delivery success at very satisfactory levels.     

Generalized boundary conditions on the basis of a deformable-cell method: Free surfaces, density interfaces and open boundaries

In the numerical analysis of flows, we need to treat various types of boundary conditions; in particular, in the fields of oceanophysics or hydraulics, “free surface”, “density interface” and “open boundary” have been considered difficult to treat. On the basis of a deformable-cell method, the cells dividing the fluid can be deformed in accordance with the moving boundaries, as in the arbitrary-Lagrangian-Eulerian method, and these boundary conditions are systematically treated with a “generalized boundary equation”. The validity of this method is shown by a flow with a free surface, a density interface and an open boundary.     

Monte Carlo simulations of the 2d-Ising model in the geometry of a long stripe

The two-dimensional Ising model in the geometry of a long stripe can be regarded as a model system for the study of nanopores. As a quasi-one-dimensional system, it also exhibits a rather interesting “phase behavior”: At low temperatures the stripe is either filled with “liquid” or “gas” and “densities” are similar to those in the bulk. When we approach a “pseudo-critical point” (below the critical point of the bulk) at which the correlation length becomes comparable to the length of the stripe, several interfaces emerge and the systems contains multiple “liquid” and “gas” domains. The transition depends on the size of the stripe and occurs at lower temperatures for larger stripes. Our results are corroborated by simulations of the three-dimensional Asakura–Oosawa model in cylindrical geometry, which displays qualitatively similar behavior. Thus our simulations explain the physical basis for the occurrence of “hysteresis critical points” in corresponding experiments.     

Investigation of wall bounded flows using SPH and the unified semi-analytical wall boundary conditions

Semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in smoothed particle hydrodynamics (SPH) for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which implies exact energy conservation. It will be shown that this property holds only in the limit of the continuous SPH approximation, whereas in the discrete SPH formulation it is only approximately true, leading to numerical noise. This noise, interpreted as a form of “turbulence”, is treated using an additional volume diffusion term in the continuity equation which we show is equivalent to an approximate Riemann solver. Subsequently two extensions to the boundary conditions are presented. The first dealing with a variable driving force when imposing a volume flux in a periodic flow and the second showing a generalization of the wall boundary condition to Robin type and arbitrary-order interpolation. Two modifications for free-surface flows are presented for the volume diffusion term as well as the wall boundary condition. In order to validate the theoretical constructs numerical experiments are performed showing that the present volume flux term yields results with an error 5 orders of magnitude smaller then previous methods while the Robin boundary conditions are imposed correctly with an error depending on the order of the approximation. Furthermore, the proposed modifications for free-surface flows improve the behavior at the intersection of free surface and wall as well as prevent free-surface detachment when using the volume diffusion term. Finally, this paper is concluded by a simulation of a dam break over a wedge demonstrating the improvements proposed in this paper.     

Flow-induced waterway in a heterogeneous granular material

In a heterogeneous granular material, viscous flow concentrates to regions with lower particle number density, or higher permeability region, denoted here by “macroscopic cavity”. This in turn enhances the normal stress toward the fluid region on the upstream boundary, which destroys the boundary if the local stress exceeds a certain magnitude. The latter may further enhance the concentration of flow into the cavity region, which is repeated to form a large scale fluidized region toward upstream direction. These processes have been elucidated in our previous experiment using glass beads layer confined between two parallel plane walls. In this paper, a numerical simulation taking into account of the global flow field on the basis of the generalized Darcy?s equation as well as the local stick-slip equation on the basis of the Newton?s equation of motion is performed. Our numerical simulation can successfully reproduce our experimental findings by imposing a suitable pressure gradient and frictional coefficient. The present numerical method can be applied to more general distribution of cavities, including three-dimensional ones, which may predict the formation of long underground waterways or creation of the passage of blood flows (angiogenesis).     

Reduced order modeling of a two-dimensional flow with moving shocks

The objective of this paper is to demonstrate the ability of proper orthogonal decomposition, in combination with domain decomposition, to produce accurate reduced order models (ROMs) for two-dimensional high-speed flows with moving shock waves. To demonstrate this ability, a blunt body flow with quasi-steady shock motion is considered. The blunt body flow contains a strong bow shock that is moved via a change in inlet Mach number and angle of attack. Accuracy is quantified by comparing surface pressures obtained from the ROMs with those from the full order simulation under the same free stream conditions. The order reduction, and computational performance of the ROM is also quantified relative to the full order simulation. The robustness of the ROM to varying flow parameters is explored. A non-Galerkin quasi-implicit steady state implementation is considered.