Wave packet analysis and breakup length calculations for accelerating planar liquid jets.
Turner, MR, Healey, JJ, Sazhin, SS and Piazzesi, R (2012) Wave packet analysis and breakup length calculations for accelerating planar liquid jets. Fluid Dyn Res, 44. ISSN 01695983

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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 breakup lengths and breakup times for different magnitudes of acceleration and different liquid to air density ratios. This study uses a basic jet velocity profile that has shear layers in both 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 nondimensional velocity of the jet along the jet centreline 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 quasisteady jet to determine when the unsteady effects are significant and whether the jet can be regarded as quasisteady in typical operating conditions for diesel engines. For a heavy fluid injecting into a lighter fluid (density ratio ρair/ρjet = 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 quasisteady jet, whereas for thickening shear layers the unsteady growth rate is larger than that of the quasisteady jet. For large accelerations (large a), the unsteady effect remains at later times but its effect on 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 for which the jet can be considered as quasisteady increases until eventually the whole jet can be considered quasisteady. For a homogeneous jet (q = 1), the range of values of a for which the jet can be considered completely quasisteady increases to larger values of a. Finally, we investigate approximating the wave packet breakup length calculations with a method that 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 typically used in diesel engines.
Item Type:  Article 

Additional Information:  Copyright 2012 Institute of Physics. This is the author's accepted manuscript. 
Divisions:  Faculty of Engineering and Physical Sciences > Mathematics 
Depositing User:  Symplectic Elements 
Date Deposited:  27 Jan 2012 13:15 
Last Modified:  23 Sep 2013 18:58 
URI:  http://epubs.surrey.ac.uk/id/eprint/79619 
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