Numerical simulation of pressure-driven startup laminar flows through a planar T-junction channel N.P. Moshkin a,b,⇑ , D. Yambangwai a,c a CHE, Si Ayutthaya Rd., Bangkok 10400, Thailand b School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand c Department of Mathematics, School of Science, University of Phayao, Phayao 56000, Thailand article info Article history: Received 18 January 2011 Received in revised form 23 July 2011 Accepted 23 July 2011 Available online 3 August 2011 Keywords: Start-up laminar flow Viscous incompressible fluid Planar T-junction channel Finite volume method Navier–Stokes equations abstract A start-up flow of a viscous incompressible fluid in a T-junction channel is studied numer- ically. The flow starting from rest is driven by a constant pressure drops suddenly applied between the entries and exits of a planar T-junction channel. The Navier–Stokes equations in primitive variables are solved numerically using finite-volume techniques. Predicted variations with time of the volume flow rates and the flow patterns are presented for sev- eral values of pressure drops. It has been shown that a start-up flow can pass through dif- ferent regimes (or different flow direction) before asymptotically reaching steady state distribution. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Even though someone may not realize it, proper system startup is critical to mass and heat transfer in a fluid flow. Sig- nificant damage to fluids – an equipment – can occur if the system is not started up properly. Just as a proper system start-up is important, it is as critical to shut your system down properly. The beginning of motion in a straight, one enter and one exit, channel is a classical problem in fluid dynamics. The response of incompressible fluid in a parallel-plate channel or circular pipe to a suddenly imposed time-independent pressure drop is well known. The unsteady velocity profiles in a channel or pipe are presented through infinite series solutions. As expected, the flow asymptotically attains the fully developed velocity distribution. The relationship between pressure drop and flow rate becomes much more complex in case a flow of a viscous incompressible fluid through a given domain with several ‘through-flow’ boundaries (inflow and outflow). Flow through branching channels has been widely used in engineering construction, such as piping systems and venti- lation systems, and is encountered in human bodies (blood flows in veins and arteries). The mechanics of such flow are com- plex and not well understood exhibiting nontrivial flow patterns which include zones of recirculation and stream wise vortices. The distribution of the flow into various branches depends on the flow resistances of these branches and in general, it is even impossible to predict the direction of flow through branches under given pressure drops. For example, the T-junc- tion geometric model has been serving as an ideal simplified model to study hemodynamics phenomena both experimen- tally and theoretically. It has been a geometrical model of choice because in addition to its simplicity, its flow features demonstrate the most common flow behavior at arterial bifurcations [1]. 1007-5704/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2011.07.030 ⇑ Corresponding author at: School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand. E-mail addresses: nikolay.moshkin@gmail.com, moshkin@math.sut.ac.th (N.P. Moshkin). Commun Nonlinear Sci Numer Simulat 17 (2012) 1241–1250 Contents lists available at SciVerse ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns