On pulsatile jets and related flows

  • Daniel Livesey

Student thesis: Phd


An overview of unsteady incompressible jet flows is presented, with the primary interest being radially developing jets in cylindrical polar coordinates. The radial \emph{free} jet emanates from some orifice, being axisymmetric about the transverse ($z$) axis and possessing reflectional symmetry across its $z=0$ centreline. The radial \emph{wall} jet is also axisymmetric about the transverse axis, however in this case impermeability and no-slip conditions are imposed at the wall, which is situated at $z=0$.The numerical solution of a linear perturbation superposed on the free jet, whose temporal form is assumed to be driven by a periodic source pulsation, gives rise to a wave-like disturbance whose amplitude grows downstream as its local wavelength decreases. An asymptotic analysis of this linear perturbation, which applies to the wall jet as well with some minor changes, captures the exact nature of the exponential spatial growth, and also algebraic attenuation of the growth. The linear theory is only valid for a small amplitude pulsation ($|\epsilon|\ll1$, where $\epsilon$ is the perturbation amplitude). When a nonlinear pulsation ($\epsilon = O(1)$) is applied to the radial free jet, any linear theory must be dropped. Solving the full nonlinear system of equations reveals singular behaviour at a critical downstream location, which corresponds to the presence of an infinitely steep downstream gradient.The replacement of molecular diffusivity with a larger-scale eddy viscosity does little to affect the qualitative growth of the linear perturbation. In order for an experimental study to reproduce any of the discussed boundary-layer results, we must consider the behaviour of jet-type flows at finite Reynolds number. This involves solving the full Navier--Stokes equations numerically, to determine the Reynolds number at which we should expect to qualitatively recover boundary-layer behaviour. The steady solution for the radial free jet and its linear pulsation are studied in this way, as is the linear pulsatile planar free jet.We may enhance the streamwise velocity of a radial jet by applying swirl around the $z$ axis. Modulating this swirl is looked at as a possible mechanism to induce the previously discussed pulsation, which then motivates the introduction of a finite spinning disk problem. In this case the system may be completely confined within an enclosed cylinder, making a hypothetical experimental approach somewhat more approachable.
Date of Award1 Aug 2017
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorRichard Hewitt (Supervisor) & Peter Duck (Supervisor)


  • Boundary layers, jets, plumes, wakes, fluid dynamics, asymptotic stability analysis, DNS.

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