Turbulent boundary layer

... School of Engineering Springfield, Massachussetts Drag Reduction and Wake Minimization on Marine Vehicles ,,P. ,3 1991 By: , Craig A. Hunter Pasquale Delore Walter M. Presz, Jr. Final Report Office of Naval Research Grant N0014-89-J-1883 00 July 1991 I I Page 2. Abstract ...

Abstract : This report describes the research effort which was undertaken to extend the capability of numerical techniques developed for computing Magnus effects over right circular cones to artillery projectile shapes of interest to the Army. The changes involved: (1) introduction of longitudinal pressure gradient effects in the boundary layer equations; (2) introduction of turbulent transport properties into the boundary layer equations; (3) modification of the inviscid flow computation for a more general body configuration; and (4) modification of the technique for computing the three dimensional displacement surface. (Author)

The study of sink flow turbulent boundary layers is of particular relevance to the problem of laminarization. The reason lies in the fact that the acceleration parameter which principally determines when a turbulent boundary layer will begin to revert towards laminar is, in these flows, constant from station to station. The paper presents theoretical solutions to this class of boundary layer by making use of the Prandtl mixing-length formula to relate the turbulent shear stress to the mean velocity gradient. Near the wall the Van Driest recommendation for mixing length is adopted and the Van Driest function, A+, is chosen such that the skin friction coefficient does not exceed a certain maximum value.The predicted solutions, which are in good agreement with available experimental data, display a plausible shift from the turbulent towards the laminar solution as the acceleration parameter is increased.

Langmuir circulations are a powerful mechanism of vertical mixing in natural bodies of water, driven by wind and waves. They are important in establishing the mixed layer and pycnocline of the oceanic boundary layer. They affect the atmosphere-ocean exchange of momentum, heat and gases, as well as, indirectly, the global ocean circulation and climate. The generation mechanism of Langmuir circulations is an instability caused by interaction between the Stokes drift transport of surface waves and the wind-induced current, but Langmuir circulations may also be viewed as a distinct form of turbulence, named Langmuir turbulence. These two perspectives are outlined here.

Polymer drag reduction, diffusion and degradation in a high-Reynolds-number turbulent boundary layer (TBL) flow were investigated. The TBL developed on a flat plate at free-stream speeds up to 20m s(-1). Measurements were acquired up to 10.7 m downstream of the leading edge, yielding downstream-distance-based Reynolds numbers up to 220 million. The test model surface was hydraulically smooth or fully rough. Flow diagnostics included local skin friction, near-wall polymer concentration, boundary layer sampling and rheological analysis of polymer solution samples. Skin-friction data revealed that the presence of surface roughness can produce a local increase in drag reduction near the injection location (compared with the flow over a smooth surface) because of enhanced mixing. However, the roughness ultimately led to a significant decrease in drag reduction with increasing speed and downstream distance. At the highest speed tested (20m s(-1)) no drag reduction was discernible at the first measurement location (0.56 m downstream of injection), even at the highest polymer injection flux (10 times the flux of fluid in the near-wall region). Increased polymer degradation rates and polymer mixing were shown to be the contributing factors to the loss of drag reduction. Rheological analysis of liquid drawn from the TBL revealed that flow-induced polymer degradation by chain scission was often substantial. The inferred polymer molecular weight was successfully scaled with the local wall shear rate and residence time in the TBL. This scaling revealed an exponential decay that asymptotes to a finite (steady-state) molecular weight. The importance of the residence time to the scaling indicates that while individual polymer chains are stretched and ruptured on a relatively short time scale (similar to 10-3 s), because of the low percentage of individual chains stretched at any instant in time, a relatively long time period (similar to 0.1 s) is required to observe changes in the mean molecular weight. This scaling also indicates that most previous TBL studies would have observed minimal influence from degradation due to insufficient residence times.

The motion of spanwise vortical elements and large-scale bulges has been tracked in the outer region between wall-normal distance $z/ \delta = 0. 11$ and 0.30 of a turbulent boundary layer at ${\mathit{Re}}_{\theta } = 2460$. The experimental dataset of time-resolved three-dimensional velocity fields used has been obtained by tomographic particle image velocimetry. The tracking of these structures yields their respective average trajectories as well as the variations thereof, quantified by the root mean square of the trajectory coordinates as a function of time. It is demonstrated that the variation in convection can be described by a dispersion model for infinitesimal particles in homogeneous turbulence, which suggests that these vortical structures and bulges are transported passively by the external velocity field without significant changes in their topology, at least over the present observation time of $1. 2\delta / {U}_{e} $. However, this does not mean that the structure’s c...

The use of normal-modes procedures for the study of boundary layers is examined, taking into account aspects of formulation, the parallel-flow assumption, the form of disturbance, and the properties of the disturbance equations. A description is presented of the results of normal-modes calculations. Nonparallel-flow effects are considered along with flat-plate boundary layers in air and water and the effect of surface curvature. An investigation of receptivity is conducted. Receptivity denotes the means by which a particular forced disturbance enters the boundary layer. Attention is given to the prediction of transition and the directions of current and future investigations.

The concept of the boundary layer was developed by [Prandtl] in 1904. It provides an important link between ideal fluid flow and real-fluid flow. Fluids having relatively small viscosity , the effect of internal friction in a fluid is appreciable only in a narrow region surrounding the fluid boundaries. Since the fluid at the boundaries has zero velocity, there is a steep velocity gradient from the boundary into the flow. This velocity gradient in a real fluid sets up shear forces near the boundary that reduce the flow speed to that of the boundary. That fluid layer which has had its velocity affected by the boundary shear is called the boundary layer. For smooth upstream boundaries the boundary layer starts out as a laminar boundary layer in which the fluid particles move in smooth layers. As the laminar boundary layer increases in thickness, it becomes unstable and finally transforms into a turbulent boundary layer in which the fluid particles move in haphazard paths. When the boundary
layer has become turbulent, there is still a very than layer next to the boundary layer that has laminar motion. It is called the laminar sub layer. Various definitions of boundary–layer thickness δ have been suggested. The most basic definition refers to the displacement of the main flow due to slowing down of particles in the boundary zone.

The three dimensional (3D) flight of a golf ball at taking into account the Magnus effect is studied in the paper. For this purpose it is composed a system of six nonlinear differential equations. To determine the 3D orientation of the ball the rotations around all three axes are given by the so-called Cardan angles instead of classical Euler ones. The high nonlinear system differential equations are solved numerically by a special program created in the MatLab-Simulink environment. It is founded the laws of motion, velocities and accelerations on all six coordinates, as well as the projections of trajectory on the three coordinate planes. The presented analytical base and numerical results in the paper increasing and expanding the knowledge in the theory of general motion of spherical solid and leads to new more extensive research in this complicated area.

"This thesis details the development, verification and validation of an unsteady unstructured high order (≥ 3) h/p Discontinuous Galerkin - Fourier solver for the incompressible Navier-Stokes equations on static and rotating meshes in two and three dimensions. This general purpose solver is used to provide insight into cross-flow (wind or tidal) turbine physical phenomena.
Simulation of this type of turbine for renewable energy generation needs to account for the rotational motion of the blades with respect to the fixed environment. This rotational motion implies azimuthal changes in blade aero/hydro-dynamics that result in complex flow phenomena such as stalled flows, vortex shedding and blade-vortex interactions. Simulation of these flow features necessitates the use of a high order code exhibiting low numerical errors. This thesis presents the development of such a high order solver, which has been conceived and implemented from scratch by the author during his doctoral work.

To account for the relative mesh motion, the incompressible Navier-Stokes equations are written in arbitrary Lagrangian-Eulerian form and a non-conformal Discontinuous Galerkin (DG) formulation (i.e. Symmetric Interior Penalty Galerkin) is used for spatial discretisation. The DG method, together with a novel sliding mesh technique, allows direct linking of rotating and static meshes through the numerical fluxes. This technique shows spectral accuracy and no degradation of temporal convergence rates if rotational motion is applied to a region of the mesh. In addition, analytical mappings are introduced to account for curved external boundaries representing circular shapes and NACA foils.

To simulate 3D flows, the 2D DG solver is parallelised and extended using Fourier series. This extension allows for laminar and turbulent regimes to be simulated through Direct Numerical Simulation and Large Eddy Simulation (LES) type approaches. Two LES methodologies are proposed.

Various 2D and 3D cases are presented for laminar and turbulent regimes. Among others, solutions for: Stokes flows, the Taylor vortex problem, flows around square and circular cylinders, flows around static and rotating NACA foils and flows through rotating cross-flow turbines, are presented."

The aim of the methods described is to calculate the properties of turbulent reactive flow fields. At each point in the flow field, a complete statistical description of the state of the fluid is provided by the velocity-composition joint pdf. This is the joint probability density function (pdf) of the three components of velocity and of the composition variables (species mass fractions and enthalpy). The principal method described is to solve a modelled transport equation for the velocity-composition joint pdf. For a variable-density flow with arbitrarily complex and nonlinear reactions, it is remarkable that in this equation the effects of convection, reaction, body forces and the mean pressure gradient appear exactly and so do not have to be modelled. Even though the joint pdf is a function of many independent variables, its transport equation can be solved by a Monte Carlo method for the inhomogeneous flows of practical interest. A second method that is described briefly is to solve a modelled transport equation for the composition joint pdf.The objective of the paper is to provide a comprehensive and understandable of the theoretical foundations of the pdf approach.

We use a direct numerical simulation database of turbulent boundary layers, to identify hairpin packets and their wall signature. We investigate the variation of time scales and length scales associated with coherent structures and the role of hairpin packets on the generation of skin friction, wall-pressure loading and heat transfer. Martin, M.P., JFM, vol. 570, pp. 347- 364, 2006 Martin, M.P., AIAA Paper 2004-2337 Beekman & Martin, APS DFD08 statistical tools, Brown & Thomas, Phys. Fluids, vol. 20, pp243-251, 1977 scientifically-rooted packet-pattern recognition, Ringuette, Wu & Martin, JFM, vol. 594, pp. 59-69, 2008 and validated visualization algorithms O'Farrell, C. Senior Thesis, Princeton University 2008

In this research the experiments were performed in the water tunnel at the Laboratory for Aero and Hydrodynamics to investigate the 3D flow structure over roughness elements as a model for the flow over urban environment. It represents the first phase in an extended study on the dispersion of pollutants in an urban environment, which process is governed by the mentioned flow structure. This is an urgent problem as the air quality in cities is decreasing due to increasing pollution from cars and industrial activity. If we can improve the understanding of the dispersion of these gases, we can possibly improve this situation or at least better predict these problems.
The principal experimental technique that will be employed is Tomographic-PIV , which is a state-of-the-art experimental technique to measure the flow velocity in a 3D volume. So far it has been applied mainly to investigate the flow structures in some classic turbulence cases: a cylinder wake and turbulent boundary layer over a flat plate. Its applicability to more complex geometries, like the rough wall considered here, is unexplored yet and needed to be assessed as a part of this project.

The HIFiRE-5 test article was an elliptic cone with a 2.5-mm nose radius and 2:1 aspect ratio and a 7-degree minor-axis half-angle. The vehicle was flown in April 2012. The upper stage of the sounding rocket failed to ignite, resulting in a peak Mach number of about 3 instead of the target of 7. Flight heat flux and pressure data (reduced from almost 300 thermocouples and 50 pressure transducers) have been compared to α- and β-dependent CFD results for pressure distribution, as well as laminar and turbulent heat-transfer results. Computations were performed at three time points in the ascent trajectory. At each time point, five values each of angle of attack and yaw, ranging from -5.0° to 5.0°, were computed. CFD pressures, normalized with p∞, were interpolated to the flight Mach numbers at specified times throughout the ascent and descent trajectories. At each flight time, α and β were estimated from measured pressure by determining the α-β combination that minimized the RMS difference between the measured and computed pressures. The vehicle attitude, as determined from measured pressure, was compared to the vehicle attitude derived from Inertial Measurement Unit (IMU) results for α and β from the flight. The two methods showed excellent agreement for the entirety of the ascent and reentry portions of the trajectory. A similar normalization of the laminar and turbulent heat transfer CFD results with St was compared to flight heat transfer measurements, and transition locations were inferred. Finally, a computational heat conduction analysis was made to verify assumptions inherent in the calculation of heat flux from temperature.

The uncertainty analysis, design, and qualification of a Turbulent Heat Transfer Test Facility (THTTF) with a smooth wall test surface are presented, and initial results for a test surface roughened with hemispherical elements spaced four base diameters apart are discussed and compared with calculations from a previously developed discrete element prediction method. A description of the facility and discussions of

Concept of boundary layer and definition of boundary layer thickness, displacement, momentum and energy thickness; Growth of boundary layer, laminar and turbulent boundary layers, laminar sub-layer; Von Karman Momentum Integral equation for boundary layers, analysis of laminar and turbulent boundary layers, drag, boundary layer separation and methods to control it, streamlined and bluff bodies

Turbulence is one of the most ubiquitous phenomena in all of fluid mechanics. In the ocean, no less than in the atmosphere, is its influence widespread. For example, the interplay between the ocean stratification and the diffusive turbulent motions is often crucial in determining the structure of each. Again, the response of the ocean to large-scale wind and thermal disturbances and the development of ocean currents is dependent on the transfer of matter, momentum and energy by irregular smaller scale motions of one kind or another.
Not all of the random motions found in the ocean, however, can be described properly as turbulence. The characteristic properties of turbulent motions are that they possess a random distribution of vorticity in which there is no unique relation between the frequency and wave number of the Fourier modes; that they are diffusive and dissipative. A distinction is drawn between turbulence in a stably stratified fluid on the one hand and random field of internal gravity waves on the other. This differentiation is useful, not only conceptually but also observationally since the mechanisms of energy transfer (in both physical and Fourier space) are essentially different.
When the wind blows across the surface of the water, a tangential surface stress is developed both directly from the interfacial stress, and indirectly by the rate of momentum loss from the surface waves by such processes as wave breaking. Below the surface, a turbulent mixed layer develops. If the underlying region is statically stable or neutral, the interface between turbulent and non-turbulent fluid is very sharp, and remains so as the turbulence erodes the lower fluid by entrainment. The temperature and salinity in the mixed layer are both virtually uniform as a result of turbulent diffusion, and the continued erosion results in an increasing contrast between the properties of the water in the mixed layer and that immediately below. In this way, a thermocline develops. If, on the other hand, there is substantial surface cooling, there may be a region below the mixed layer in which the density decreases with depth and which is statically unstable. Convective motions can develop and, particularly in polar waters, may extend to considerable depths.
Turbulence in the oceans can also be generated in more familiar ways, such as in shear zones produced by the confluence of different water messes, particularly in estuaries. Turbulence does not invariably occur, however; the stratification may be sufficiently great that the Richardson number is large enough everywhere to prevent the onset of dynamical instability.
Turbulent mixing, and especially turbulent mixing in a density stratified fluid, is a difficult problem in geophysical fluid mechanics, as well as in environmental and industrial studies. Of particular interest is the mixing in the neighbourhood of relatively sharp density interfaces in the oceans, lakes, reservoirs, and the atmosphere. In environmental fluid mechanics, an understanding of these mixing processes is essential in determining water quality in water bodies containing a sharp density interface. The presence of such an interface, by suppressing fluid turbulence, limits the downward transfer of pollutants and gases such as CO2 and O2 from the upper mixed layer. This has important consequences in the design of wastewater and thermal reservoirs. In the atmosphere serve air pollution problems may result from the presence of thermal inversions that inhibit the vertical transport of pollutants. Her again, a knowledge of the exchange processes across the inversion layer is important in predicting and controlling air quality in the atmosphere.
The information that can be obtained on mixing in a stratified fluid is essential for the development of computer models of geophysical phenomena, because, if better predictions are to be made, the distributions of potential and kinetic energy have to be correctly assessed for each process under study.

A numerical algorithm for the simulation of flow past immersed objects with heat transfer is proposed and validated which conforms with the ideas of the fictitious domain method. A momentum source term is added to account for the presence of the object and a heat source term is proposed to impose the Dirichlet boundary condition on the surface of the objects. The algorithm is an implicit fictitious domain based method where the entire fluid-immersed object domain assumed to be an incompressible fluid. The flow domain is constrained to be divergence free, whereas a rigidity constraint is imposed on the body domain. Heat transfer is similarly considered by assuming that the object domain is filled with a fluid with different thermal properties. The SIMPLE algorithm with a collocated grid arrangement is used for pressure–velocity coupling which is unconditionally stable. The algorithm is validated by considering stationary, forced motion and freely moving objects with both isothermal and freely variable temperature inside the object. Good agreement with previous numerical and experimental studies for all the test cases is observed.

This book is a review of several theoretical and experimental results dealing with boundary layers formed by fluid moving along a wall.  It is not an exhaustive examination of boundary layer theory but instead is a summary of the work the author conducted while working as a civilian researcher at the United States Air Force Research Laboratory.  The work primarily deals with the basic theory and conceptual models for boundary layer flow.  Be forewarned that this is not a simple review of boundary layer theory found in the literature.  Much of the work is a direct challenge to the basic theory and conceptual models existing in the present-day boundary layer literature.  Most of the challenges come in a manner that is relatively easy for the reader to verify themselves.  To further encourage the reader to verify the enclosed work, an Appendix is added to take the reader through the process of setting up and doing their own fluid flow simulations.