Entry Lengths of Laminar Pipe and Channel Flows

Abstract

Numerical simulations of laminar pipe and channel flows were carried out: (i) to understand the effect of inlet conditions, viz., flat inlet and streamtube inlet, on entry lengths, and (ii) to investigate the flow development in radial/transverse locations. Results show that hydrodynamic entry lengths from the streamtube inlet simulations are significantly lower compared to the entry lengths from the flat inlet simulations for low Reynolds numbers. Moreover, results from the current study (Newtonian flow with no-slip) as well as the results from the literature (non-Newtonian flow with no-slip) showed that for many flow situations, the slowest development of axial velocity in the transverse location happens to be very near to the wall. For the above cases, the existing entry length criteria (centerline as well as global entry length) are not appropriate to define the entry length. We have proposed a new entry length criterion based on the displacement thickness which is an integral measure of the velocity profile. A new entry length correlation using the displacement thickness criterion is proposed for Newtonian flows in pipe and channel based on simulations with the streamtube inlet condition.

Global oscillations in low-density round jets with parabolic velocity profiles

“…So, computing the accurately from the experimental nozzle exit velocity profiles is essential for understanding and comparing the results with stability and numerical simulations. In order to compute the accurately in the present study, the experimental nozzle exit velocity profiles are fitted from the collection of profiles obtained from solving the boundary layer equations inside the axisymmetric pipe (Joshi & Vinoth 2018). The dashed lines in figure 2( a ) represent the fitted velocity profiles.…”

“…The velocity profile with a given and a constant mass fraction profile of helium corresponding to the density of the helium–air mixture are imposed at the inlet. The velocity profile for the inlet is selected from the axisymmetric pipe profiles, which are obtained from solving the laminar incompressible boundary layer equations inside an axisymmetric pipe (Joshi & Vinoth 2018). The pressure outlet condition, which extrapolates the interior's flow variables, is specified at far-field boundaries and the domain exit.…”

“…Even in isothermal jets, limited experimental studies are available on jets with parabolic profiles in the literature (Ito & Seno 1979; Tucker & Islam 1986; Lai 1991; Kozlov et al. 2008) due to the requirement of a long nozzle length for generating the parabolic velocity profile at the nozzle exit (Joshi & Vinoth 2018). In most practical applications, the injector length is long enough for the velocity profile at the injector/nozzle exit to approach the fully developed parabolic profile ().…”

3D‐printed, patient‐specific intracranial aneurysm models: From clinical data to flow experiments with endovascular devices

“…The vascular lumen of an aneurysm before (top) and after (bottom) manually reducing artifacts: holes and rudiments, for example, from surrounding tissues, vessels, and noise (a), artificial narrowing of the vessel (b), the artificial blending of aneurysm and vessel (c). The vasculature shown was used for the Multiple Aneurysms AnaTomy Challenge (MATCH) 2018, 22 but not for flow experiments in this study.…”

“… is the distance needed for flow to fully develop after entering a pipe. The minimal can be estimated as (where is the Reynold’s number and ID is the inner diameter of the vessel) 22 . The was estimated as using the following assumptions: the mean velocity () and diameter ( ID ) of internal carotid artery was approximately 20 cm/s and 0.5 cm 23 , respectively; the blood viscosity () in the assumption of the infinite shear rate limit was 3.5 cP 24 ; and the blood density () was assumed to be 1060 kg/m 3 .…”