# Control of jets in cross.

2010-07

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Control of jets in cross.

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2010-07

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Thesis or Dissertation

## Abstract

We use direct numerical simulations to study control of jets in cross
ow by axial
pulsing. Our main idea is that pulsing generates vortex rings; the effect of pulsing
on jets in crossflow can therefore be explained by studying the behavior of vortex
rings in crossflow. A method is proposed that allows optimal values of pulsation
frequency, modulation and energy to be estimated a priori. This is accomplished in
the following three stages.
First, direct numerical simulation is used to study the mixing of a passive scalar
by a vortex ring issuing from a nozzle into stationary fluid. The ‘formation number’
(Gharib et al. 1998), is found to be 3.6. Simulations are performed for a range of
stroke ratios encompassing the formation number, and the effect of stroke ratio on
entrainment, and mixing is examined. When the stroke ratio is greater than the
formation number, the resulting vortex ring with trailing column of fluid is shown
to be less effective, at mixing and entrainment. As the ring forms, ambient fluid
is entrained radially into the ring from the region outside the nozzle exit. This
entrainment stops once the ring forms, and is absent in the trailing column. The
rate of change of scalar containing fluid is studied for its dependence on stroke ratio.
This rate varies linearly with stroke ratio until the formation number, and falls below the linear curve for stroke ratios greater than the formation number. This behavior
is explained by considering the entrainment to be a combination of that due to the
leading vortex ring, and that due to the trailing column. For stroke ratios less than
the formation number, the trailing column is absent, and the size of the vortex ring increases with stroke ratio, resulting in increased mixing. For stroke ratios above
the formation number, the leading vortex ring remains the same, and the length of
the trailing column increases with stroke ratio. The overall entrainment decreases
as a result.
Next, direct numerical simulation is used to study the effect of crossflow on
the dynamics, entrainment and mixing characteristics of vortex rings issuing from
a circular nozzle. Three distinct regimes exist, depending on the velocity ratio
and stroke ratio. Coherent vortex rings are not obtained at velocity ratios below
approximately 2. At these low velocity ratios, the vorticity in the crossflow boundary
layer inhibits roll–up of the nozzle boundary layer at the leading edge. As a result,
a hairpin vortex forms instead of a vortex ring. For large stroke ratios and velocity
ratio below 2, a series of hairpin vortices are shed downstream. The shedding is quite
periodic for very low Reynolds numbers. For velocity ratios above 2, two regimes
are obtained depending upon the stroke ratio. Lower stroke ratios yield a coherent
asymmetric vortex ring, while higher stroke ratios yield an asymmetric vortex ring
accompanied by a trailing column of vorticity. These two regimes are separated
by a transition stroke ratio whose value decreases with decreasing velocity ratio.
For very high values of the velocity ratio, the transition stroke ratio approaches
the ‘formation number’ defined by Gharib et al. (1998). In the absence of trailing
vorticity, the vortex ring tilts towards the upstream direction, while the presence of
a trailing column causes it to tilt downstream. This behavior is explained.
Then, we study the mixing behavior of pulsed jets in crossflow using direct
numerical simulations. The pulse is a square wave and the simulations consider
several jet velocity ratios and pulse conditions. We study the effects of pulsing, and
explain the wide range of optimal pulsing conditions found in experimental studies of
the problem. Vortex rings in crossflow exhibit three distinct flow regimes depending
on stroke ratio and ring velocity ratio. The simulations of pulsed transverse jets show
that at high velocity ratios, optimal pulse conditions correspond to the transition of the vortex rings produced by pulsing between the different regimes. At low
velocity ratios, optimal pulsing conditions are related to the natural timescale on
which hairpin vortices form. An optimal curve in the space of stroke ratio and
velocity ratio is developed. Data from various experiments are interpreted in terms
of the properties of the equivalent vortex rings and shown to collapse on the optimal
curve. The proposed regime map allows the effects of experimental parameters such
as pulse frequency, duty cycle, modulation, and pulse energy to all be predicted by
determining their effect on the equivalent stroke and velocity ratios.
The thesis also discusses work towards the development of Large Eddy Sim-
ulation (LES) methodology to predict mixing in very high Reynolds number
turbulent flows. We propose a novel estimation procedure to model the subgrid
velocity for LES. The subgrid stress is obtained directly from the estimated subgrid
velocity. The model coefficients for the subgrid velocity are obtained by imposing
constraints on resulting ensemble-averaged subgrid dissipation and local subgrid kinetic
energy. The subgrid dissipation may be obtained through either eddy–viscosity
models or a new dynamic model for dissipation. The subgrid kinetic energy may be
obtained either from the dynamic Yoshizawa model or a modeled transport equation.
We also extend the estimation procedure to LES of passive scalar transport and propose an estimation model for subgrid scalar concentration. The subgrid
flux is computed directly from the estimated subgrid velocity and estimated subgrid
scalar. The model coefficient for the subgrid scalar is obtained by constraining mean
scalar dissipation which is provided by an eddy–diffusivity approach. The velocity
and scalar estimation models are applied to decaying isotropic turbulence with an
uniform mean scalar gradient and good results are obtained. Realistic backscatter
is also predicted.
A dynamic model for subgrid scale dissipation is proposed. The dissipation is
modeled using invariants of strain–rate tensor. The proposed dynamic approach
uses a second level test filter and the model coefficient is obtained using two scalar and propose an estimation model for subgrid scalar concentration. The subgrid
flux is computed directly from the estimated subgrid velocity and estimated subgrid
scalar. The model coefficient for the subgrid scalar is obtained by constraining mean
scalar dissipation which is provided by an eddy–diffusivity approach. The velocity
and scalar estimation models are applied to decaying isotropic turbulence with an
uniform mean scalar gradient and good results are obtained. Realistic backscatter
is also predicted.
A dynamic model for subgrid scale dissipation is proposed. The dissipation is
modeled using invariants of strain–rate tensor. The proposed dynamic approach
uses a second level test filter and the model coefficient is obtained using two scalar identities. We show that this approach can also be used to obtain the Smagorinsky
model coefficient for subgrid stress. This is an alternative to Germano’s dynamic
procedure where the single model constant is obtained by minimizing the error in a
tensor identity, the Germano identity error

## Description

University of Minnesota Ph.D. dissertation. July 2010. Major: Aerospace Engineering and Mechanics. Advisor: Krishnan Mahesh. 1 computer file (PDF); xv, 129 pages, appendix A pages 94-129. Ill. (some col.)

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Sau, Rajes. (2010). Control of jets in cross.. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/95519.

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