The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part of this work focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. Beyond the region of exponential growth, the instability waves evolve into a periodic array of vortices. In the second part of this work, the weakly nonlinear theory is extended to heated (or nonisothermal mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbances is also studied by solving the initial value problem and then examining the behavior of the long-time solution. The excitation produces a wave packet which consists of a few oscillations and is convected downstream by the mean flow. The magnitude of the disturbance in the jet depends on the location of the excitation and there is an optimum position at which little energy input will produce large perturbations. It is found that in order to generate the largest perturbations at any point in the jet, the disturbance should be deposited into the flow at a point where the phase velocity of the most amplified wave equals the fluid velocity (of the base flow).

Unsteady heat transfer by natural convection in a closed square cavity is investigated numerically. A new finite-volume approach is developed and applied to the two-dimensional continuity, vorticity, and energy equations. The variation of the field variables is approximated by bi-quadratic interpolation formulas over the space occupied by the finite volume and the region surrounding it. These are used in the integral conservation laws for energy, vorticity and mass. The convective transport is modelled using a new upstream-weighting approach which uses volume averages for the vorticity and the energy transported across the boundaries of the finite volume. The weighting is dependent on the skewness of the velocity field to the surfaces of the finite volume as well as its strength. It is adaptive to local flow conditions. The velocities are obtained from the application of the velocity induction law. Use is made of an image system for the free vorticity of fluid. In this way, the no-penetration condition is enforced at the cavity boundaries, but at the same time it may allow a slip condition to exist. This is not permitted in a viscous flow analysis, and the slip velocity is reduced to zero by the production of free vorticity at the boundaries. Two test cases are treated which have exact solutions. The first is not new and involves a rotating shaft. The errors are less than.06% for this case. The second case is new and involves convection past a source and sink. The maximum error is 2.3%. For both test cases, the maximum error occurs at moderate values of the cell Peclet number and diminishes at the extreme low and high values. The time-development of the profiles of the vorticity, horizontal velocity, and temperature is examined at different locations within the cavity for Rayleigh numbers equal to 10³, 10⁴, and 10⁵. For these calculations, a 21 x 21 grid was used. The flow is found to approach a steady-state condition. The steady-state results are compared with a benchmark solution. In general, the agreement is excellent. The discrepancy is found to be less than 2% for the vast majority of the results for this relatively coarse grid.

The generation of electricity from tidal currents is an emerging industry with the potential to contribute to the UK energy supply in a predictable and sustainable way. The development of the technology requires the cost effective subsea installation of energy conversion systems in an energetic and challenging marine environment. One concept developed for the fastening of tidal energy converters to the seabed is the Active Gravity Base (AGB), which offers potential reductions in installation cost and time, relative to existing fastening methods. The performance of this concept in response to unsteady flow conditions is explored within this thesis. The dynamic behaviour of a tidal current is driven by a range of factors from gravitational forces of celestial bodies to high-frequency fluctuations of turbulent eddies. The response of the AGB concept to the unsteadiness of tidal currents is herein considered under the two broad time-scales; the directionality of the mean semi-diurnal cycle and the high frequency variations from a given mean flow velocity. The correlation between the direction and velocity of the tidal flow was assessed using hourly averaged data provided by the Admiralty Charts in the northern UK waters. The resulting directionality model was used to predict the performance of the AGB under a range of quasi-steady flow conditions. High frequency velocity measurements of a potential tidal energy site were obtained through collaboration with the University of Washington and the Pacific Northwest National Laboratory. This data was used to estimate the maximum perturbation from the mean velocity that can be expected on an annual basis. An experimental facility was developed within the re-circulating water flume at the University of Edinburgh to examine the dynamic loads generated by controllable two-dimensional flow perturbations. This was successfully achieved using a configuration of twin pitching foils with independent motion control. A relationship between the foil pitch angle and velocity perturbation time series was predicted using a vortex model of the foil wakes. This configuration was shown to be able to generate significant flow fluctuations within the range of reduced frequencies 0:06 ≤ k ≤ 1:9, with a peak gust intensity of Ig = 0:5. The numerical solution was validated against experimental results.

In order to eliminate or reduce vibration problems inturbomachines without a high increase in the complexity of thevibratory behavior, the adjacent airfoils around the wheel areoften mechanically connected together with lacing wires, tip orpart-span shrouds in a number of identical sectors. Although anaerodynamic stabilizing effect of tying airfoils together ingroups on the whole cascade is indicated by numerical andexperimental studies, for some operating conditions suchsectored vane cascade can still remain unstable. The goal of the present work is to investigate thepossibilities of a sectored vane cascade to undergoself-excited vibrations or flutter. The presented method forpredicting the aerodynamic response of a sectored vane cascadeis based on the aerodynamic work influence coefficientrepresentation of freestanding blade cascade. The sectored vaneanalysis assumes that the vibration frequency is the same forall blades in the sectored vane, while the vibration amplitudesand mode shapes can be different for each individual blade inthe sector. Additionally, the vibration frequency as well asthe amplitudes and mode shapes are supposed to be known. The aerodynamic analysis of freestanding blade cascade isperformed with twodimensional inviscid linearized flow model.As far as feasible the study is supported by non-linear flowmodel analysis as well as by performing comparisons againstavailable experimental data in order to minimize theuncertainties of the numerical modeling on the physicalconclusions of the study. As has been shown for the freestanding low-pressure turbineblade, the blade mode shape gives an important contributioninto the aerodynamic stability of the cascade. During thepreliminary design, it has been recommended to take intoaccount the mode shape as well rather than only reducedfrequency. In the present work further investigation using foursignificantly different turbine geometries makes these findingsmore general, independent from the low-pressure turbine bladegeometry. The investigation also continues towards a sectoredvane cascade. A parametrical analysis summarizing the effect ofthe reduced frequency and real sector mode shape is carried outfor a low-pressure sectored vane cascade for differentvibration amplitude distributions between the airfoils in thesector as well as different numbers of the airfoils in thesector. Critical (towards flutter) reduced frequency maps areprovided for torsion- and bending-dominated sectored vane modeshapes. Utilizing such maps at the early design stages helps toimprove the aerodynamic stability of low-pressure sectoredvanes. A special emphasis in the present work is put on theimportance for the chosen unsteady inviscid flow model to bewell-posed during numerical calculations. The necessity for thecorrect simulation of the far-field boundary conditions indefining the stability margin of the blade rows isdemonstrated. Existing and new-developed boundary conditionsare described. It is shown that the result of numerical flowcalculations is dependent more on the quality of boundaryconditions, and less on the physical extension of thecomputational domain. Keywords: Turbomachinery, Aerodynamics,Unsteady CFD, Design, Flutter, Low-Pressure Turbine, Blade ModeShape, Critical Reduced Frequency, Sectored Vane Mode Shape,Vibration Amplitude Distribution, Far-field 2D Non-ReflectingBoundary Conditions. omain. Keywords:Turbomachinery, Aerodynamics, Unsteady CFD,Design, Flutter, Low-Pressure Turbine, Blade Mode Shape,Critical Reduced Frequency, Sectored Vane Mode Shape, VibrationAmplitude Distribution, Far-field 2D Non-Reflecting BoundaryConditions.

Severe stenosis may cause critical flow conditions related to artery collapse, plaque cap rupture which leads directly to stroke and heart attack. In this paper, a nonlinear viscoelastic model and a numerical method are introduced to study dynamic behaviors of the tube wall and viscous flow through a viscoelastic tube with a stenosis simulating blood flow in human carotid arteries. The Mooney-Rivlin material model is used to derive a nonlinear viscoelastic thin-wall model for the stenotic viscoelastic tube wall. The mechanical parameters in the Mooney-Rivlin model are calculated from experimental measurements. Incompressible Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation are used as the governing equation for the fluid flow. Interactions between fluid flow and the viscoelastic axisymmetric tube wall are handled by an incremental boundary iteration method. A Generalized Finite Differences Method (GFD) is used to solve the fluid model. The Fourth-Order Runge-Kutta method is used to deal with the viscoelastic wall model where the viscoelastic parameter is adjusted to match experimental measurements. Our result shows that viscoelasticity of tube wall causes considerable phase lag between the tube radius and input pressure. Severe stenosis causes cyclic pressure changes at the throat of the stenosis, cyclic tube compression and expansions, and shear stress change directions in the region just distal to stenosis under unsteady conditions. Results from our nonlinear viscoelastic wall model are compared with results from previous elastic wall model and experimental data. Clear improvements of our viscoelastic model over previous elastic model were found in simulating the phase lag between the pressure and wall motion as observed in experiments. Numerical solutions are compared with both stationary and dynamic experimental results. Mooney-Rivlin model with proper parameters fits the non-linear experimental stress-strain relationship of wall very well. The phase lags of tube wall motion, flow rate variations with respect to the imposed pulsating pressure are simulated well by choosing the viscoelastic parameter properly. Agreement between numerical results and experimental results is improved over the previous elastic model.

No description available.

Vortices interacting with the solid surface of aerodynamic bodies are prevalent across a broad range of geometries and applications, such as dynamic stall on wind turbine and helicopter rotors, the separated flows over flapping wings of insects, birds, formation of the vortex wakes of bluff bodies, and the lift-producing vortices formed by aircraft leading-edge extensions and delta wings. This study provides fundamental insights into the formation and evolution of such vortices by considering the leading-edge vortices formed in variations of a canonical flapping wing problem. Specifically, the vorticity transport for three distinct maneuvers are examined, a purely rolling wing, a purely pitching wing and a rolling and pitching wing, of aspect-ratio two. Once the maneuvers are characterized, a passive bleed hole will be introduced to a purely rolling wing, to alter flow topology and vorticity transport governing the circulation on the wing. Three-dimensional representations of the velocity and vorticity fields were obtained via plenoptic particle image velocimetry (PPIV) measurements are used to perform a vorticity flux analysis that serves to identify the sources and sinks of vorticity within the flow. Time-resolved pressure measurements were obtained from the surface of the airfoil, and used to characterize the flux of vorticity diffusing from the solid surface. Upon characterizing all of the sources and sinks of vorticity, the circulation budget was found to be fully accounted for. Interpretation of the individual vorticity balance contributions demonstrated the Coriolis acceleration did not contribute to vorticity generation and was a correction term for the apparent vorticity. The transport characteristics varied among the three cases that were investigated. The spanwise convective contribution was signification over various spanwise locations for the pure roll case. For the pure pitch the shear layer contribution and the diffusive contribution. The circulation was dependent the pitch rate, which was evident only at the beginning of the motion, and circulation growth at later times depended only on the pitch angle.The combined pitch roll cases, the transport behavior strongly resembled that of pitch, with little evidence of roll influence, despite that the flow structure and circulation distribution on the inboard part of the wing exhibited roll-like behaviors. In the final case where the wing is pitching and rolling , the shear layer contribution was balanced by the diffusive contribution, similar to that of the pure pitch case. By adding a passive bleed hole to the purely rolling cases, it was found to alter the both the flow topology and vorticity transport.

With the present drive in turbomachine engine developmenttowards thinner and lighter bladings, closer spaced blade rowsand higher aerodynamic loads per blade row and blade, advanceddesign criteria and accurate prediction methods for vibrationalproblems such as forced response become increasingly importantin order to be able to address and avoid fatigue failures ofthe machine early in the design process. The present worksupports both the search for applicable design criteria and thedevelopment of advanced prediction methods for forced responsein transonic turbine stages. It is aimed at a betterunderstanding of the unsteady aerodynamic mechanisms thatgovern forced response in transonic turbine stages and furtherdevelopment of numerical methods for rotor stator interactionpredictions. The investigation of the unsteady aerodynamic excitationmechanisms is based on numerical predictions of thethree-dimensional unsteady flow field in representative testturbine stages. It is conducted in three successive steps. Thefirst step is a documentation of the pressure perturbations onthe blade surface and the distortion sources in the bladepassage. This is performed in a phenomenological manner so thatthe observed pressure perturbations are related to thedistortion phenomena that are present in the blade passage. Thesecond step is the definition of applicable measures toquantify the pressure perturbation strength on the bladesurface. In the third step, the pressure perturbations areintegrated along the blade arc to obtain the dynamic bladeforce. The study comprises an investigation of operationvariations and addresses radial forcing variations. With thehelp of this bottom-up approach the basic forcing mechanisms oftransonic turbine stages are established and potential routesto control the aerodynamic forcing are presented. For the computation of rotor stator interaction aerodynamicsfor stages with arbitrary pitch ratios a new numerical methodhas been developed, validated and demonstrated on a transonicturbine test stage. The method, which solves the unsteadythree-dimensional Euler equations, is formulated in thefour-dimensional time-space domain and the derivation of themethod is general such that both phase lagged boundaryconditions and moving grids are considered. Time-inclination isutilised to account for unequal pitchwise periodicity bydistributing time co-ordinates at grid nodes such that thephase lagged boundary conditions can be employed. The method isdemonstrated in a comparative study on a transonic turbinestage with a nominal non integer blade count ratio and anadjusted blade count ratio with a scaled rotor geometry. Thepredictions show significant differences in the blade pressureperturbation signal of the second vane passing frequency, whichwould motivate the application of the new method for rotorstator predictions with non-integer blade count ratios.

The leading edge flow structure of the NACA 0012 airfoil is experimentally investigated under dynamic stall conditions (M = 0.1; α = 16.7◦, 22.4◦; Rec = 1× 10^6) using planar particle image velocimetry. The airfoil was dynamically pitched about the 1/4 chord at a reduced frequency, k = 0.1. As expected, on the upstroke the flow remains attached in the leading edge region above the static stall angle, whereas during downstroke, the flow remains separated below the static stall angle. A phase averaging procedure involving triple velocity decomposition in combination with the Hilbert transform enables the entire dynamic stall process to be visualized in phase space, with the added benefit of the complete phase space composed of numerous wing oscillations. The formation and complex evolution of the leading edge vortex is observed. This vortex is seen to grow, interact with surrounding vorticity, detach from the surface, and convect downstream. A statistical analysis coupled with instantaneous realizations results in the modification of the classical dynamic stall conceptual model, specifically related to the dynamics of the leading edge vortex.

<p>With the present drive in turbomachine engine developmenttowards thinner and lighter bladings, closer spaced blade rowsand higher aerodynamic loads per blade row and blade, advanceddesign criteria and accurate prediction methods for vibrationalproblems such as forced response become increasingly importantin order to be able to address and avoid fatigue failures ofthe machine early in the design process. The present worksupports both the search for applicable design criteria and thedevelopment of advanced prediction methods for forced responsein transonic turbine stages. It is aimed at a betterunderstanding of the unsteady aerodynamic mechanisms thatgovern forced response in transonic turbine stages and furtherdevelopment of numerical methods for rotor stator interactionpredictions.</p><p>The investigation of the unsteady aerodynamic excitationmechanisms is based on numerical predictions of thethree-dimensional unsteady flow field in representative testturbine stages. It is conducted in three successive steps. Thefirst step is a documentation of the pressure perturbations onthe blade surface and the distortion sources in the bladepassage. This is performed in a phenomenological manner so thatthe observed pressure perturbations are related to thedistortion phenomena that are present in the blade passage. Thesecond step is the definition of applicable measures toquantify the pressure perturbation strength on the bladesurface. In the third step, the pressure perturbations areintegrated along the blade arc to obtain the dynamic bladeforce. The study comprises an investigation of operationvariations and addresses radial forcing variations. With thehelp of this bottom-up approach the basic forcing mechanisms oftransonic turbine stages are established and potential routesto control the aerodynamic forcing are presented.</p><p>For the computation of rotor stator interaction aerodynamicsfor stages with arbitrary pitch ratios a new numerical methodhas been developed, validated and demonstrated on a transonicturbine test stage. The method, which solves the unsteadythree-dimensional Euler equations, is formulated in thefour-dimensional time-space domain and the derivation of themethod is general such that both phase lagged boundaryconditions and moving grids are considered. Time-inclination isutilised to account for unequal pitchwise periodicity bydistributing time co-ordinates at grid nodes such that thephase lagged boundary conditions can be employed. The method isdemonstrated in a comparative study on a transonic turbinestage with a nominal non integer blade count ratio and anadjusted blade count ratio with a scaled rotor geometry. Thepredictions show significant differences in the blade pressureperturbation signal of the second vane passing frequency, whichwould motivate the application of the new method for rotorstator predictions with non-integer blade count ratios.</p>