Wave packet analysis and break-up length calculations for an accelerating planar liquid jet

Abstract

This paper examines the process of transition to turbulence within an accelerating planar liquid jet. By calculating the propagation and spatial evolution of disturbance wave packets generated at a nozzle where the jet emerges, we are able to estimate break-up lengths and break-up times for different magnitudes of acceleration and different liquid to air density ratios. This study uses a basic jet velocity profile which has shear layers in both the air and the liquid either side of the fluid interface. The shear layers are constructed as functions of velocity which behave in line with our CFD simulations of injecting Diesel jets. The non-dimensional velocity of the jet along the jet centre-line axis is assumed to take the form V (t) = tanh(at) where the parameter a determines the magnitude of the acceleration. We compare the fully unsteady results obtained by solving the unsteady Rayleigh equation, to those of a quasi-steady jet to determine when the unsteady effects are significant, and if the jet can be regarded as quasi-steady in typical operating conditions for Diesel engines.For a heavy fluid injecting into a lighter fluid (density ratio ρ air /ρ jet = q < 1) it is found that unsteady effects are mainly significant at early injection times where the jet velocity profile is changing fastest. When the shear layers in the jet thin with time, the unsteady effects cause the growth rate of the wave packet to be smaller than the corresponding quasi-steady jet, while for thickening shear layers the unsteady growth rate is larger than that of the quasi-steady jet. For large accelerations (large a) the unsteady effect remains at later times but its effect on 1 Corresponding author: M.Turner@surrey.ac.uk 2 Present address: Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH UK 3 Present address: ANSYS UK, Ltd., 97 Milton Park, Abingdon, Oxfordshire OX14 4RY UK 21 November 2011 the growth rate of the wave packet decreases as the time after injection increases. As the rate of acceleration is reduced, the range of velocity values that the jet can be considered as quasi-steady increases until eventually the whole jet can be considered quasi-steady. For a homogeneous jet (q = 1) the range of values of a for which the jet can be considered completely quasi-steady increases to larger values of a.Finally we investigate approximating the wave packet break-up length calculations with a method which follows the most unstable disturbance wave as the jet accelerates. This approach is similar to that used in CFD simulations as it greatly reduces computational time. We investigate whether or not this is a good approximation for the parameter values typical used Diesel engines.

Vorticity dynamics for transient high-pressure liquid injection

“…This is consistent with the previous studies that showed acceleration did not have a noticeable effect on the break-up length or the overall characteristics of the transient liquid jet. 20 However, the liquid acceleration caused by the instability can be responsible for producing small-scale instabilities at the interface. …”

“…Abani and Reitz 22 formulated a new break-up model for unsteady axisymmetric turbulent jets based on an extension of steady-state. Turner et al 20 studied the effects of acceleration on the break-up lengths and time for planar liquid jets by implementing a wave-packet analysis on the disturbances initiated from the orifice. They showed that the unsteady effects of the jet is noticeable for high accelerations and high liquid-to-air density ratios, especially at early stages of the injection.…”

Non-modal stability of round viscous jets

“…in internal combustion engines the fuel jet is accelerated during a limited interval of time before the volumetric flux of the fuel levels off). Linear stability analysis of unsteady flows is significantly more complex compared with that of stationary flows (Schmid & Henningson 2001;Turner et al 2012a). The time scale of the disturbance growth and propagation should be small compared with the time scale of acceleration/deceleration of the main flow.…”