In fluid flow piping systems, tee and wye junctions are commonly encountered and the study of flow through them has been well documented. Most of these studies have focused on flow characterized as turbulent for which there are nearly constant losses in pressure and kinetic energy in the junctions. Laminar flow has received much less attention since it is not frequently observed in macro scale piping systems where pipe diameters are measured in centimeters. The recent increase in use of micro scale flow devices calls for more research into laminar flow behavior that dictates the design and operation of these devices. This paper documents results from computational fluid dynamics (CFD) simulations of flow in planar tee and wye junctions. The junctions studied consisted of circular pipes with two outlets and one inlet. The angles between the tee and wye junctions were fixed to 180 and 60 degrees, respectively. The inlet pipe diameter was fixed at 50 microns and the outlet pipe diameters were chosen to satisfy the continuity equation constrained to have equal velocities in all pipes. The lengths of the inlet and outlet pipes were varied to achieve fully developed flow within the junction. Following a grid resolution study performed on a sample tee junction, a generalized algorithm was designed and implemented to create three-dimensional models of these junctions subject to the former conditions. In the CFD simulations, Reynolds number was varied in the laminar characterized region between 1 and 2000. The simulations calculated static pressure and velocity magnitude values for a number of planes intersecting the junctions along the inlet and outlet pipes. From these values, pressure and kinetic energy gradients were calculated to estimate the static pressure and kinetic energy at the inlet and outlet pipes of each junction. Finally, these inlet and outlet values were used to calculate the stagnation pressure loss coefficient, which reflects dimensionless losses of pressure and kinetic energy for the junction. These coefficients ranged from 1 to 300 for the tee junction and 1 to 400 for the wye junction over the specified range of Reynolds number. The values were inversely proportional to Reynolds number and curve fits were provided for valid ranges.
The goal of this study was to determine the entrance length — the distance from a microtube entrance to the point where flow is fully developed — for laminar liquid flow in smooth, straight, circular-microtubes and trapezoidal microchannels. Knowledge of the entrance length and pressure losses in this region for microtubes are of interest in microfluidic devices, in porous media, and in other networks of small ducts or pores. Although laminar entrance length has been studied extensively in macroscale tubes, only recently has attention been paid problem of entrance length in microtubes. Some differences do exist in macro versus micro flow, sometimes attributed to the relatively small volume to surface area ratio at the microscale. The entrance length determined in this study is intended to provide a means to analyze and design microtubes or networks of microtubes. The inlet velocity was varied to provide a Reynolds number of 10 to 2000 and the length was varied based on Reynolds number to ensure the length captured the entire entrance region. Simulations of water at standard conditions were performed using FLUENT and a custom written computer code, which automated the process of creating the flow geometries, extracting results, and determining the entrance length for each run. A grid resolution study was performed to ensure grid size was not a factor. Pressure and velocity distributions as a function of position were extracted to determine flow characteristics. Fluid velocity magnitudes from the tube centerline to 95% of the distance to the tube wall were used to determine when fully developed flow was reached by finding the point at which all velocity magnitudes did not change by more than 1% for additional distance along the tube. Results were compared to results from the literature for entrance length in macro-scale tubes and found to be qualitatively the same. The entrance length (in units of the number of diameters) for circular tubes is often expressed as C times the Reynolds number. For Reynolds numbers greater than 100, this study found C to be 0.0505, which is in general agreement with macroscale experiments and simulations, where C is reported to be between 0.05 and 0.2. For trapezoidal microchannels we found a relationship for entrance length over hydraulic diameter that is proportional (slope of 0.674) to Reynolds number for Reynolds number over 100. As Reynolds numbers get small the value of entrance length over hydraulic diameter goes to 0.674.
The goal of this study was to determine laminar stagnation pressure loss coefficients for circular ducts in which flow encounters a planar bifurcation. Flow conditions and pressure losses in these laminar bifurcations are of interest in microfluidic devices, in porous media, and in other networks of small ducts or pores. Until recently, bifurcation geometries had been studied almost exclusively for turbulent flow, which is often found in fluid supply and drain systems. Recently, pressure loss coefficients from simulations of a few arbitrary bifurcation geometries in two-dimensions have been published — the present study describes the extension of these two-dimensional simulations to three-dimensional circular ducts. The pressure loss coefficients determined in this study are intended to allow realistic simulation of existing laminar flow networks or the design of these networks. This study focused on a single inlet duct with two outlet ducts, which were allowed to vary in diameter, flow fraction, and angle — all relative to the inlet duct. All ducts considered in this study were circular with their axes in a common plane. Laminar stagnation pressure loss coefficients were determined by simulating incompressible flow through 475 different geometries and flow condition combinations. In all cases, the flow was laminar in the inlet and outlet ducts with a Reynolds number of 15 in the inlet duct. Simulations of the dividing flow geometries were done using FLUENT and a custom written computer code, which automated the process of creating the three-dimensional flow geometries. The outputs, pressure and velocity distributions at the inlet and outlets, were averaged over the circular ducts and then used to calculate pressure loss coefficients for each of the geometries and flow fraction scenarios simulated. The results for loss coefficient for the geometries considered ranged from 2.0 to 70. The loss coefficient for any geometry increased significantly as the outlet flow fraction increased. A consistent increase in loss coefficient was also observed as a function of decreasing outlet duct diameter. Less significant variation of the loss coefficient was observed as a function of the angles of the outlet ducts.
The goal of this study was to determine laminar pressure loss coefficients for flow in microelbows with circular and trapezoidal cross-sections. Flow conditions and pressure losses in these elbows are of interest in microfluidic devices, in porous media, and in other types of microfluidic networks. The literature focuses almost exclusively on loss coefficients due to turbulent flow in macroelbows with very little data on laminar flow in macroelbows. The pressure loss coefficients determined in this study are intended to aid in realistic simulation of existing laminar flow networks or the design of these networks. This study focused on an elbow of constant cross-section with inlet and outlet tubes of sufficient length so as to allow fully developed laminar flow at the entrance to the elbow and at the outlet tube exit. For the circular elbow, both the ratio of elbow radius to inner diameter and inlet Reynolds number were allowed to vary over the ranges of 0.5—10.5 and 1—2500, respectively. The laminar pressure loss coefficients were determined by simulating incompressible flow over the range of geometries and Reynolds numbers in the commercial CFD software FLUENT. The pressure and velocity distributions in the inlet and outlet tubes were averaged at multiple upstream and downstream positions, and were then used to extrapolate the loss coefficient due to the elbow. The results showed that the loss coefficient for larger ratios tended to be higher, in some cases in excess of 100, at low Reynolds number flows, but as the flow approached the transitional regime, the loss coefficients leveled out to roughly their accepted turbulent values of between 0.4 and 1.0. These results show good qualitative and quantitative agreement with limited laminar elbow experimental data available for macroelbows. For the trapezoidal elbows the loss coefficient levels off to about two for Reynolds numbers greater than 100.
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