Turbulence

Wall-bounded turbulent flows are pervasive in numerous physics and engineering applications. Such flows tend to have a strong impact on the design of ships, airplanes and rockets, industrial chemical mixing, wind and hydrokinetic energy, utility infrastructure and innumerable other fields. Understanding and controlling wall bounded turbulence has been a long-pursued endeavor yielding plentiful scientific and engineering discoveries, but there is much that remains unexplained from a fundamental viewpoint. One unexplained phenomenon is the formation and impact of coherent structures like the ejections of slow near-wall fluid into faster moving ow which have been shown to correlate with increases in friction drag. This thesis focuses on recognizing and regulating organized structures within wall-bounded turbulent flows using a variety of machine learning techniques to overcome the nonlinear nature of this phenomenon.
Deep Learning has provided new avenues of analyzing large amounts of data by applying techniques modeled after biological neurons. These techniques allow for the discovery of nonlinear relationships in massive, complex systems like the data found frequently in fluid dynamics simulation. Using a neural network architecture called Convolutional Neural Networks that specializes in uncovering spatial relationships, a network was trained to estimate the relative intensity of ejection structures within turbulent flow simulation without any a priori knowledge of the underlying flow dynamics. To explore the underlying physics that the trained network might reveal, an interpretation technique called Gradient-based Class Activation Mapping was modified to identify salient regions in the flow field which most influenced the trained network to make an accurate estimation of these organized structures. Using various statistical techniques, these salient regions were found to have a high correlation to ejection structures, and to high positive kinetic energy production, low negative production, and low energy dissipation regions within the flow. Additionally, these techniques present a general framework for identifying nonlinear causal structures in general three-dimensional data in any scientific domain where the underlying physics may be unknown.

Turbulent flow is a complex three dimensional system of velocity and pressure fluctuations in a fluid that creates vorticity, eddies and other flow structures. In this study we are specifically concerned with the surface pressure fluctuations below a turbulent boundary layer which is one of the primary sources of panel vibration on aircraft fuselages and ship hulls as well a major issue in ship hydrodynamics. The most accepted analytical approaches to describe the surface pressure fluctuations are the Chase model [1] for the surface pressure wavenumber spectrum and Goody’s model [2] for the pressure spectrum at a point. The most accurate numerical approach to use is Direct Numerical Simulations (DNS) [3]. In this study we compared Chase and Goody’s models against DNS of a turbulent channel flow in the space–time and wavenumber-frequency domains and estimated regions of convergence between the analytical models and the DNS data.

The objective of this thesis is to review recently developed empirical and analytical models for the surface pressure and wavenumber spectra for fully developed boundary layers to highlight the effect of assumptions about the turbulence length scales and show how the effects of mean flow Reynolds number has on the spectra shape. The Goody model is used as a reference model to compare the spectra shape as it characterizes the basic physical features of the wall-pressure spectrum under a zero-pressure gradient turbulent boundary layer and scales as a function of Reynolds number. The turbulence length scales of the comparison models are modified to observe the effects on the shape of the spectra. A new model is also considered that also scales as a function of Reynolds number and is compared to the Goody model.

A motion compensated ADV system was evaluated to determine its ability to
make measurements necessary for characterizing the variability of the ambient current in
the Gulf Stream. The impact of IMU error relative to predicted turbulence spectra was
quantified, as well as and the ability of the motion compensation approach to remove
sensor motion from the ADV measurements. The presented data processing techniques
are shown to allow the evaluated ADV to be effectively utilized for quantifying ambient
current fluctuations from 0.02 to 1 Hz (50 to 1 seconds) for dissipation rates as low as
3x10-7. This measurement range is limited on the low frequency end by IMU error,
primarily by the calculated transformation matrix, and on the high end by Doppler noise.
Inshore testing has revealed a 0.37 Hz oscillation inherent in the towfish designed and
manufactured as part of this project, which can nearly be removed using the IMU.

Future helicopters will require all-weather capability for stabilized flight through severe atmospheric turbulence. This requirement has brought into focus the effect of turbulence on handling qualities. Accordingly, there is renewed interest in modeling and simulating turbulence and predicting turbulence-induced rotor oscillations. This thesis addresses three fundamental aspects of the problem: (1) modeling and simulation of turbulence including cross-correlation; (2) three-dimensional dynamic-wake effects on rotor response to turbulence and (3) prediction of turbulence and response statistics. The analysis is based on the theory of isotropic and homogeneous turbulence and Taylor's frozen-field approximation. Quasisteady airfoil aerodynamics and a three-dimensional wake are used. Both the isolated blades and isolated rotors are treated. The parallelization is carried out on a massively parallel MasPar SIMD computer. Major conclusions include: (i) The effects of cross-correlation are negligible when two stations lie on the same blade and appreciable when two stations lie on different blades. (ii) In modeling the three-dimensional wake, 3 harmonics are required and dynamic wake has dominant influence on response statistics. (iii) With increasing comprehensiveness of helicopter-turbulence modeling, the sequential execution times increase dramatically; by comparison, the parallel execution times are far lower and, more significantly, remain nearly constant.

The rollup of a vortex sheet of elliptic span loading in the presence of a vortex of finite core size is studied in the Trefftz plane. The vorticity in the finite vortex is taken to be uniform and sign opposite to that of the sheet and the flow is assumed to be inviscid and incompressible. A numerical scheme is developed to determine the evolution of (a) the finite vortex using the Contour Dynamics technique, (b) the vortex sheet using an algorithm developed by Krasny. The interaction is shown to substantially affect the development of the vortex sheet rollup. The vortex sheet undergoes significant deformation at the rolling up tip region due to its devouring the vortex patch as well as due to the formation of secondary rollup features on the sheet. These features are believed to be important in inhibiting rollup considerably. The interaction is quantified by using a criterion developed to measure the extent of the tip vortex rollup and its characteristics are studied for a range of flow parameters. The strength of the rolling up tip region of the vortex sheet is found to be highly dependent on the location and the vorticity in the finite vortex.

In this thesis, a two-dimensional in the vertical plane numerical model has been developed for simulation of the free surface and density interface profiles due to a wind shear stress applied on a stratified water body, such as lake or reservoir. The results agreed qualitatively and quantitatively with our experimental results, as well as with the work of other researchers. A computer algorithm is established that can be used to estimate the shear stress along the interface and the velocity field throughout the water body. The model can be applied for prediction of wind-induced mixing processes in elongated lakes or reservoirs.

The atmospheric turbulence that a blade station experiences is called blade-fixed
turbulence. It can qualitatively differ from the conventional body-fixed turbulence
such as experienced by an element of the body or fuselage. This difference is due
to the rotational ,-elocity, which causes fore-and-aft motions of the blade station
through the turbulence waves. A closed-form solution of a frequency-time spectrum
for the dominant vertical turbulence velocity at an arbitrary blade station is
dc,·eloped. This solution makes it possible to explain qualitatively the turbulence
cllcrgy transfer due to rotational velocity from the low-frequency region (< 1P or
1/ rcv.) to the high-frequency(> 1P) region with the occurrence of spectral peaks
and split peaks at 1P /2, 1P, 3P /2, 2P etc. Comparison of blade responses to bladeand
body-fixed turbulence is also presented over a comprehensive range of turbulcuce
scale length and advance ratio; the comparison covers frequency-time spectra,
correlations including standard deviations, and average threshold-crossing rates of
a flapping blade. A major contribution is to formulate both the cyclostationary
turbulence and blade response by the frequency-time spectra, which predict simultaneously
the time- ancl frequency-dependent characteristics such as the energy
culltained in the frequency and time intervals. For low-altitude and low-advanceratio
flights, such as nap-of-the earth or NOE flights, rotational velocity effects on
turbulence modeling qualitatively affect the prediction of turbulence ancl response
statistics.

The phenomenon of flow-induced vibration is found in many
engineering systems. The fluid flow generates forces on the
structure that cause motion of the structure. In turn, the
structural motion changes the angle of attack between the flow and
the structure, hence the forces on the structure. Furthermore,
turbulence generally exists in a natural fluid flow; namely, the fluid
velocity contains a random part. Thus, the problem is formulated as
a nonlinear system under random excitations.
This thesis is focused on one type of motion known as
galloping. A mathematical model for the motion of an elastically
supported square cylinder in turbulent flow is developed. The
physical nonlinear equation is converted to ideal stochastic
differential equations of the Ito type using the stochastic averaging
method. The probability density for the motion amplitude and the
values for the most probable amplitudes are obtained for various
mean flow velocities and turbulence levels.

The aim of this thesis is to develop a theory for non stationary propulsor flow noise. The model which is proposed is based on Amiet's paper "Acoustic Radiation from an Airfoil in a Turbulent Stream" [1], which describes broad band noise when a simple model of airfoil interacts with a turbulent flow, under the assumption of stationarity. The Karhunen-Loeve method provides a set of modes which describe the turbulent flow without the assumption of stationarity. A method is described to obtain broad band noise calculations when the mean turbulent flow varies with time and produces non stationary turbulence. A comparison of the numerical results obtained with the results from the paper of reference [1] shows the characteristics of time varying sound radiation. The various mathematical formulae will give a starting point to the analysis of real time varying flows, which are not considered in this thesis.