Self-similar properties of decelerating turbulent jets

Abstract

The flow in a decelerating turbulent round jet is investigated using direct numerical simulation. The simulations are initialised with a flow field from a statistically stationary turbulent jet. Upon stopping the inflow, a deceleration wave passes through the jet, behind which the velocity field evolves towards a new statistically unsteady self-similar state. Assumption of unsteady self-similar behaviour leads to analytical relations concerning the evolution of the centreline mean axial velocity and the shapes of the radial profiles of the velocity statistics. Consistency between these predictions and the simulation data supports the use of the assumption of self-similarity. The mean radial velocity is predicted to reverse in direction near to the jet centreline as the deceleration wave passes, contributing to an approximately threefold increase in the normalised mass entrainment rate. The shape of the mean axial velocity profile undergoes a relatively small change across the deceleration transient, and this observation provides direct evidence in support of previous models that have assumed that the mean axial velocity profile, and in some cases also the jet spreading angle, remain approximately constant within unsteady jets.

Vortex rings produced by non-parallel planar starting jets

“…They also note distinct deviations when analysing characteristic turbulent quantities in separate regions of the pulsed jet as the vortex ring appears to boast greater shearing stresses than the trailing jet. A recent direct numerical simulation study by Shin, Aspden & Richardson (2017) is concerned with a suddenly stopped, hence decelerating axisymmetric jet. The authors suggest that behind the deceleration wave, a statistically unsteady self-similar state can be noted, building on the experimental work by Witze (1983) who studied the velocity field of an impulsively started axisymmetric jet and a simplified analytical approach by Musculus (2009) addressing the entrainment rate during the deceleration phase of a single-pulsed jet.…”

A Novel One- and Zero-Dimensional Model for Turbulent Jet Ignition

“…Fig. 9 compares the centerline profile of the axial velocity as predicted by the 1-D model against the DNS of Shin et al (2017) at various time-instances after the nozzle velocity drops to zero. The steady-state jet profile predicted by the 1-D model agrees well with the one from the DNS.…”

“…For the first four validation cases, the combustion products are fully burnt and their composition is the same as of the main chamber (Ghorbani et al 2014); Fig. 9 centerline profiles of the axial velocity from the 1-D model (dashed lines) versus the DNS (symbols) of Shin et al (2017) at several instants in the range t = 0-69 (in jet time) after the inflow was stopped therefore A = B = 0 in Eq. (45).…”

Modeling aerial transmission of pathogens (including the SARS-CoV-2 virus) through aerosol emissions from e-cigarettes

“…GMean N p = 7.4/L LE 19 subjects 4 HE 2011 [90] GMean N p = 3500/L HE (7 asthmatic) [98] up tp N p ≈ 1000/exh HE (13 smokers) Close [92] d p = 0.75 − 1.0 µm age 18-45 much larger in speech n p < 0.1/cm 3 than in breathing 10 asthmatic APS For such values and scales the starting jet can be regarded as isothermal with thermal buoyancy becoming relevant only in the puff stage [108,109]. It is well known that steady and unsteady jet/puff systems can be well approximated by analytic models that assume axial symmetry and a self similar profile for the average centerline and radial components of the velocity field in cylindrical coordinates U = [U z , U r , U φ ] [104,105,113,114] (see figure 3)…”

“…It is well known that steady and unsteady jet/puff systems can be well approximated by analytic models that assume axial symmetry and a self similar profile for the average centerline and radial components of the velocity field in cylindrical coordinates [94, 95, 103, 104] (see figure 4) where f, g are empiric Gaussian or polynomial functions of the self similar variable η = r/z and the centerline velocity is U c = U z for r = 0 along the z axis, hence f ( η ), g ( η ) must satisfy U z = U c and U r = 0 at r = 0 (see examples in [77, 94, 95, 96, 97, 98, 99, 100, 101]). An axially symmetric self similar jet/puff system fulfills the conservation of linear specific momentum Q = V U c (puff) and force where V is the penetration volume [94, 100, 101], hence for an initial time t = t 0 .…”