This thesis is focused on solving hydraulic losses during unsteady flow of liquid in pipe for both laminar and turbulent flow in smooth pipes. Radial viscosity distribution is assumed to be the same as for steady flow. Viscosity distribution is derived from velocity profile, which is mathematically described with suitably chosen function. Laplace images of unsteady velocity profile and mean velocity in cross-section are derived depending on pressure difference. Loss coefficient is derived and on base of transfer matrix method, self-numbers are calculated. Self-numbers represent attenuation and own frequency. Self-numbers are compared to values from software called “F-ACHAR” and loss coefficient is compared to the one for quasi-steady method.

Pulse detonation engines show potential to increase the efficiency of conventional gas turbine engines if used in place of the steady combustor. However, since the interaction of pressure pulses with the turbine is not yet well understood, a rig was built to compare steady flow with pulsing flow. Compressed air is used in place of combustion gases and pressure pulses are created by rotating a ball valve with a motor. This work accomplishes two main objectives that are different from previous research in this area. First, steady flow through an axial turbine is compared with full annular pulsed flow closely coupled with the turbine. Second, the error in turbine efficiency is approximately half the error of previous research comparing steady and pulsed flow through an axial turbine. The data shows that a turbine driven by full annular pressure pulses has operation curves that are similar in shape to steady state operation curves, but with a decrease in turbine performance that is dependent on pulsing frequency. It is demonstrated that the turbine pressure ratio increases with pulsed flow through the turbine and that this increase is less for higher pulsing frequencies. For 10 Hz operation the turbine pressure ratio increases by 0.14, for 20 Hz it increases by 0.12, and for 40 Hz it increases by 0.06. It is demonstrated that the peak turbine efficiency is lower for pulsed flow when compared with steady flow. The difference between steady and pulsed flow peak efficiency is less severe at higher pulsing frequencies. For 40 Hz operation the turbine efficiency decreases by 5 efficiency points, for 20 Hz it decreases by 9 points, and for 10 Hz it decreases by 11 points. It is demonstrated that the specific power at a given pressure ratio for pulsed flow is lower than that of steady flow and that the decrease in specific power is lower for higher pulsing frequencies. On average, the difference in specific power between steady and pulsed flow is 0.43 kJ/kg for 40 Hz, 1.40 kJ/kg for 20 Hz, and 1.91 kJ/kg for 10 Hz.

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Unsteady flow fields over a NACA 0012 at an angle of attack are investigated. The first is the classical pitching motion about the airfoil's quarter chord. The second is the flow over a fixed airfoil immersed in the wake of the pitching airfoil. Large reduced frequencies are considered. Measurements were obtained in a water tunnel by Laser-Doppler velocimetry. Ensemble-averaged velocity measurements were obtained in the vicinity of the trailing edges of both the pitching and the fixed airfoils. The flowfields in the wake and at the trailing edges of both airfoils were studied visually. The validity of the quasi-steady and an extension to an unsteady Kutta condition are examined. A new dynamic similarity parameter is proposed. An analytical method based on the dynamics of discrete vortices is employed. Numerical calculations of the flow over the fixed airfoil are compared with experimental results. / Ph. D.

The influence of tip clearance and angle of attack upon the mid-span unsteady pressure response of a vibrating flat plate was investigated experimentally. Unsteady pressure measurements were taken for a variety of incidence angles, vibration frequencies and tip clearances over a Mach number range of 0.2 to 0.6. It was found that changes in tip clearance had an effect on measured pressure fluctuations at higher angles of attack and larger Mach numbers. It was also observed that the amplitude of the unsteady pressure increased as the incidence angle was increased. The plate was mechanically induced to oscillate in translation, simulating the flISt bending mode. Averaged Fast Fourier Transforms were used to determine pressure oscillation amplitudes and phase lags with respect to the plate motion. / Master of Science

Strong interactions between flow about an aircraft wing and the wing structure can result in aeroelastic phenomena which significantly impact aircraft performance. Time-accurate methods for solving the unsteady Navier-Stokes equations have matured to the point where reliable results can be obtained with reasonable computational costs for complex non-linear flows with shock waves, vortices and separations. The ability to combine such a flow solver with a general finite element structural model is key to an aeroelastic analysis in these flows. Earlier work involved time-accurate integration of modal structural models based on plate elements. A finite element model was developed to handle three-dimensional wing boxes, and incorporated into the flow solver without the need for modal analysis. Static condensation is performed on the structural model to reduce the structural degrees of freedom for the aeroelastic analysis. Direct incorporation of the finite element wing-box structural model with the flow solver requires finding adequate methods for transferring aerodynamic pressures to the structural grid and returning deflections to the aerodynamic grid. Several schemes were explored for handling the grid-to-grid transfer of information. The complex, built-up nature of the wing-box complicated this transfer. Aeroelastic calculations for a sample wing in transonic flow comparing various simple transfer schemes are presented and discussed. / M.S.

These thesis review some recent results on the construction of very high order multidimensional upwind schemes for the solution of steady and unsteady conservation laws on unstructured triangular grids.<p>We also consider the extension to the approximation of solutions to conservation laws containing second order dissipative terms. To build this high order schemes we use a subtriangulation of the triangular Pk elements where we apply the distribution used for a P1 element.<p>This manuscript is divided in two parts. The first part is dedicated to the design of the high order schemes for scalar equations and focus more on the theoretical design of the schemes. The second part deals with the extension to system of equations, in particular we will compare the performances of 2nd, 3rd and 4th order schemes.<p><p>The first part is subdivided in four chapters:<p>The aim of the second chapter is to present the multidimensional upwind residual distributive schemes and to explain what was the status of their development at the beginning of this work.<p>The third chapter is dedicated to the first contribution: the design of 3rd and 4th order quasi non-oscillatory schemes.<p>The fourth chapter is composed of two parts: we start by understanding the non-uniformity of the accuracy of the 2nd order schemes for advection-diffusion problem. To solve this issue we use a Finite Element hybridisation.<p>This deep study of the 2nd order scheme is used as a basis to design a 3rd order scheme for advection-diffusion.<p>Finally, in the fifth chapter we extend the high order quasi non-oscillatory schemes to unsteady problems.<p>In the second part, we extend the schemes of the first part to systems of equations as follows:<p>The sixth chapter deals with the extension to steady systems of hyperbolic equations. In particular, we discuss how to solve some issues such as boundary conditions and the discretisation of curved geometries.<p>Then, we look at the performance of 2nd and 3rd order schemes on viscous flow.<p>Finally, we test the space-time schemes on several test cases. In particular, we will test the monotonicity of the space-time non-oscillatory schemes and we apply residual distributive schemes to acoustic problems. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Indiana University-Purdue University Indianapolis (IUPUI) / A wave rotor constant volume combustor (WRCVC) was designed and built as a collaborative work of Rolls Royce LibertyWorks, Indiana University-Purdue University at Indianapolis (IUPUI), and Purdue University, and ran experimental tests at Purdue's Zucrow Laboratories in 2009. Instrumentation of the WRCVC rig inlet flow included temperature and pressure transducers upstream of the venturi and at the fuel delivery plane. Other instrumentation included exhaust pressures and temperatures. In addition, ion sensors, dynamic pressure sensors, and accelerometers were used to instrument the rotating hardware. The rig hardware included inlet guide vanes directly in front of the rotating hardware, which together with concern for damage potential, prevented use of any pressure transducers at the entrance to the rotor. For this reason, a complete understanding of the conditions at the WRCVC inlet is unavailable, requiring simulations of the WRCVC to estimate the inlet pressure at a specific operating condition based on airflow. The operation of a WRCVC rig test is a sequence of events over a short time span. These events include introduction of the main air flow followed by time-sequenced delivery of fuel, lighting of the ignition source, and the combustion sequence. The fast changing conditions in the rig inlet hardware make necessary a time-dependent computation of the rig inlet section in order to simulate the overall rig operation. The chosen method for computing inlet section temperature and pressure was a time-dependent lumped volume model of the inlet section hardware, using a finite difference modified Euler predictor-corrector method for computing the continuity and energy equations. This is coupled with perfect gas prediction of venturi air and fuel flow rates, pressure drag losses at the fuel nozzles, pressure losses by mass addition of the fuel or nitrogen purge, friction losses at the inlet guide vanes, and a correlation of the non-dimensional flow characteristics of the WRCVC. The flow characteristics of the WRCVC are computed by varying the non-dimensional inlet stagnation pressure and the WRCVC's operational conditions, assuming constant rotational speed and inlet stagnation temperature. This thesis documents the creation of a computer simulation of the entire WRCVC rig, to understand the pressure losses in the inlet system and the dynamic coupling of the inlet section and the WRCVC, so that an accurate prediction of the WRCVC rotor inlet conditions can be computed. This includes the computational development of the WRCVC upstream rig dynamic model, the background behind supporting computations, and results for one test sequence. The computations provide a clear explanation of why the pressures at the rotor inlet differ so much from the upstream measured values. The pressure losses correlate very well with the computer predictions and the dynamic response tracks well with the estimation of measured airflow. A simple Fortran language computer program listing is included, which students can use to simulate charging or discharging of a container.

<p>Severe floods caused by heavy autumn rains in year 2000 raised the question whether measures to reduce the damage from high water levels, in the area surrounding lake Glafsfjorden and along the river Byälven down to lake Vänern, are possible. One option is to reduce flow resistance along the river and thereby lower the maximum water level a given inflow would cause. Good knowledge of hydraulic and hydrological conditions is necessary in order to estimate the effect of such flow-reducing measures. In order to quantify such effect a 1-dimensional hydraulic flow model has been set up for the river Byälven using the software package MIKE 11. The model is more detailed, especially concerning topography and bathymetry, than earlier models used for studies of the river. Boundary conditions consist of measured inflows, the level of the lake Vänern and runoff calculated using the HBV-model. The model was calibrated for two different floods and a good fit to measured water levels was obtained for both these periods. Using the calibrated model critical sections, causing much flow resistance during high floods, were identified. With that knowledge different measures to reduce high water levels was adopted to the model both individually and combined with each other and the model was run with boundary conditions mainly from the flood in year 2000. The most radical measures simulated resulted in a lowering of the maximum water in the two largest reservoirs Glafsfjorden and Harefjorden with 78 and 97 cm respectively. A more modest combination of measures gave water levels 48 and 84 cm lower than a model run without changes. Some combinations of relatively small measures lowered the maximum water level by a few decimeters. The simulation results give good guidance to further investigations and decisions of actual changes. The model constitutes a useful tool when making flood maps of the area and if water level forecasts would be needed during future floods.</p> / <p>Allvarliga översvämningar i samband med höstregn år 2000 väckte frågan om det går att vidta åtgärder för att minska skadorna vid höga flöden i området runt Glafsfjorden och längs Byälvens sträckning ner till Vänern. Ett alternativ är att med åtgärder längs älven underlätta vattnets utflöde och på så sätt minska den högsta vattennivå ett givet flöde orsakar. God kunskap om hydrauliska och hydrologiska förhållanden behövs för att bedöma nyttan av olika åtgärdsalternativ. För att kunna avgöra effekterna av olika åtgärdsalternativ har en 1-dimensionell strömningsmodell satts upp för Byälven i programverktyget MIKE 11. Modellen är mer detaljerad, framförallt beträffande höjdinformationen, än tidigare modeller som använts för studier av Byälven varit. Randvillkor till modellen utgörs av registrerade inflöden, Vänerns vattenstånd och avrinning modellerad med HBV-modellen. Modellen har kalibrerats för två översvämningsperioder och god anpassning uppnåddes för de vattenstånd som dessa situationer representerar och med dess hjälp har sedan älven studerats och områden som bromsar flödet har kunnat identifieras. Med kunskap om vilka områden som begränsar flödet mest har ett antal olika åtgärder simulerats i modellen, både var för sig och kombinerade med varandra. Randvillkoren för översvämningen år 2000 behölls och förändringarna lades in i modellen. De extremaste åtgärderna som simulerats resulterade i minskningar av de högsta vattennivåerna i de två största vattenmagasinen Glafsfjorden och Harefjorden med 78 respektive 97 cm. Mer realistiska åtgärdspaket gav minskningar med i storleksordningen 48 respektive 84 cm och även relativt små ingrepp gav minskningar på några decimeter. Simuleringsresultaten ger god vägledning för vidare undersökningar av och beslut om konkreta åtgärder i Byälven. Dessutom utgör modellen ett bra verktyg för att ta fram översvämningskartor och för att prognostisera vattennivåer vid nya översvämningssituationer.</p>