Experimental evidence of velocity profile inversion in developing laminar flow using magnetic resonance velocimetry. (25th July 2018)

• Record Type: Journal Article
• Authors: Reci, A.; Sederman, A. J.; Gladden, L. F.
• Is Part Of: Journal of fluid mechanics. Volume 851(2018)
• Page Start: 545
• Page End: 557
• Publication Date: 2018-07-25
• Subjects: computational methods, -- low-Reynolds-number flows, -- Navier–Stokes equations; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.512
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : A discrepancy exists between the predictions of analytical solutions of approximate Navier–Stokes equations and numerical finite-difference solutions of the full Navier–Stokes equations regarding the development of laminar flow at the entrance to cylindrical pipes for Newtonian fluids. Starting from a uniform velocity profile at the entrance to the pipe, analytical solutions of approximate Navier–Stokes equations predict the velocity profile to have a maximum at the centre of the pipe at all times. In contrast, numerical finite-difference solutions of the full Navier–Stokes equations have suggested that the location of the velocity maximum moves from the wall towards the centre of the pipe at a short distance from the entrance, after which it remains at the centre of the pipe. This study presents the first experimental evidence of the moving velocity maximum from the wall towards the centre of the pipe. The initial uniform velocity profile was achieved by flowing the fluid through a monolith composed of narrow parallel channels and the flow development was investigated using magnetic resonance velocimetry. The experimentally observed variation of the position and size of the velocity maximum with the Reynolds number and the distance from the entrance to the pipe is shown to be in good agreement with the predictions of numerical finite-difference solutions of the full Navier–Stokes equations.