This study is an investigation of the film cooling effectiveness and heat transfer coefficient of a two-dimensional turbine rotor blade in a linear transonic cascade. Experiments were performed in Virginia Tech's Transonic Cascade Wind Tunnel with an exit Mach number 0f 1.2 and an exit Reynolds numbers of 5x106 to simulate real engine flow conditions. The freestream and coolant flows were maintained at a total temperature ratio of 2(+,-)0.4 and a total pressure ratio of 1.04. The freestream turbulence was approximately 1%. There are six rows of staggered, discrete cooling holes on and near the leading edge of the blade in a showerhead configuration. Cooled air was used as the coolant. Experiments were performed with and without film cooling on the surface of the blade. The heat transfer coefficient was found to increase with the addition of film cooling an average of 14% overall and to a maximum of 26% at the first gauge location. The average film cooling effectiveness along the chord-wise direction of the blade is 25%. Trends were found in both the uncooled and the film-cooled experiments that suggest either a transition from a laminar to a turbulent film regime or the existence of three-dimensionality in the flow-field over the gauges. / Master of Science

An investigation was conducted in the Langley 8-foot transonic tunnels to determine the aerodynamic loading characteristics of a thin conical cambered low-aspect-ratio delta wing in combination with a basic body and a body indented symmetrically for a Mach number of 1.2 in accordance with the supersonic area rule. The tests were conducted at Mach numbers from 0.60 to 1.12 and at 1.43 and at angles of attack generally from -4° to 20°. The wing vas conically cambered over the outboard 15 percent of each semispan. The wing had an aspect ratio of 2.31, 60° sweepback of the leading edge, and had NACA 65A003 airfoil sections parallel to the model plane of symmetry over the uncambered portion. The results of this investigation indicate that a leading-edge separation vortex forms at moderate angles of attack and causes the shape of the span load distribution to change markedly. Significant center of pressure movements are noted at transonic speeds. Indenting the body in accordance with the supersonic area rule had little effect on the aerodynamic loading characteristics. Comparisons with expert mental data for a similar plane wing indicates that the cambered wing is considerably more effective than the plane wing in utilizing the leading edge suction forces to produce thrust. A comparison between experimental and theoretical results indicates fair agreement around sonic speeds. / Master of Science

This experiment investigated the effects of a non-axisymmetric endwall contour and upstream purge flow on the secondary flow of an inlet guide vane. Three cases were tested in a transonic wind tunnel with an exit Mach number of 0.93-a flat endwall with no upstream purge flow, the same flat endwall with upstream purge flow, and a 3D contoured endwall with upstream purge flow. All cases had a backward-facing step upstream of the vanes. Five-hole probe measurements were taken 0.2, 0.4, and 0.6 Cx downstream of the vane row trailing edge, and were used to calculate loss coefficient, secondary velocity, and secondary kinetic energy. Additionally, surface static pressure measurements were taken to determine the vane loading at 4% spanwise position. Surface oil flow visualizations were performed to analyze the flow qualitatively. No statistically significant differences were found between the three cases in mass averaged downstream measurements. The contoured endwall redistributed losses, rather than making an improvement distinguishable beyond experimental uncertainty. Flow visualization found that the passage vortex penetrated further in the spanwise direction into the passage for the contoured endwall (compared to the flat endwall), and stayed closer to the endwall with a blowing ratio of 1.5 with a flat endwall (compared to no blowing with flat endwall). This was corroborated by the five hole probe results. / Master of Science

Various sources of error can cause discrepancies among flight test results, experimental measurements and numerical predictions in the transonic regime. For unsteady flow, the effects of wind tunnel walls or a finite computational domain are the least understood and perhaps the most important. Although various techniques can be used in steady wind tunnel testing to minimize wall reflections, e.g., using slotted walls with ventilation, wind tunnel wall effects remain in unsteady wind tunnel testing even when they have been essentially eliminated from the steady flow. Even when the walls are ten chord lengths or more from the airfoil being tested, they can have a substantial effect on the unsteady aerodynamic response of the airfoil. In this study we compare numerical computations of two- and three-dimensional unsteady transonic flow with one another, and with experimental measurements, to isolate and examine the effects of tunnel walls. An extension of the time-linearized code developed by Fung, Yu and Seebass (1978) is used to obtain numerical results in two dimensions for comparison with one another and with the experimental measurments of Davis and Malcolm (1980). The steady flow which is perturbed by small unsteady airfoil motions is found numerically by specifying the pressure distribution rather than the airfoil coordinates using the procedure provided by Fung and Chung (1982). This provides results that are nearly free from effects caused by the small perturbation approximation; it also simulates the viscous effects present in the experimental measurements. A similar algorithm, developed especially for this study, is used for the related investigations in three dimensions. Different wall conditions are simulated numerically. Aside from a shift of frequency due to nonlinear effects, our numerical predictions of resonance conditions in two dimensions agree very well with those of linear acoustic theory. A substantial discrepancy between unconfined computations and wind tunnel experiments is observed in the low frequency range. This discrepancy highlights the importance of wall interference and wind tunnel measurements of unsteady transonic flows and delineates the conditions required to suppress them satisfactorily.

No description available.

Aeromechanics is one of the main limitations for more efficient, lighter, cheaper and reliable turbomachines, such as steam or gas turbines, as well as compressors and fans. In fact, aircraft engines designed in the last few years feature more slender, thinner and more highly loaded blades, but this trend gives rise to increased sensitivity for vibrations induced by the fluid and result in increasing challenges regarding structural integrity of the engine. Forced vibration as well as flutter failures need to be carefully avoided and an important parameter predicting instabilities in both cases is the aerodynamic damping. The aim of the present project is to numerically investigate aerodynamic damping in the first rotor of a transonic compressor (VINK6). The transonic flow field leads to a bow shock at each blade leading edge, which propagates to the suction side of the adjacent blade. This, along with the fact that the rotating blade row vibrates in different mode shapes and this induces unsteady pressure fluctuations, suggests to evaluate unsteady flow field solutions for different cases. In particular, the work focuses on the unsteady aerodynamic damping prediction for the first six mode shapes. The aerodynamic coupling between the blades of this rotor is estimated by employing a transient blade row model set in blade flutter case. The commercial CFD code used for these investigations is ANSYS CFX. Aerodynamic damping is evaluated on the basis of the Energy Method, which allows to calculate the logarithmic decrement employed as a stability parameter in this study. The least logarithmic decrement values for each mode shape are better investigated by finding the unsteady pressure distribution at different span locations, indication of the generalized force of the blade surface and the local work distribution, useful to get insights into the coupling between displacements and consequent generated unsteady pressure. Two different transient methods (Time Integration and Harmonic Balance) are employed showing the same trend of the quantities under consideration with similar computational effort. The first mode is the only one with a flutter risk, while the higher modes feature higher reduced frequencies, out from the critical range found in literature. Unsteady pressure for all the modes is quite comparable at higher span locations, where the largest displacements are prescribed, while at mid-span less comparable values are found due to different amplitude and direction of the mode shape. SST turbulence model is analyzed, which does not influence in significant manner the predictions in this case, with respect to the k-epsilon model employed for the whole work. Unsteady pressure predictions based on the Fourier transformation are validated with MATLAB codes making use of Fast Fourier Transform in order to ensure the goodness of CFX computations. Convergence level and discrepancy in aerodamping values are stated for each result and this allows to estimate the computational effort for every simulation and the permanent presence of numerical propagation errors. / Aeromekanik är en av huvudbegränsningarna för mer effektiva, lättare, billigare och mer pålitliga turbomaskiner, som ångturbiner, gasturbiner, samt kompressorer och fläktar. I själva verket har flygplansmotorer som designats under de senaste åren har fått tunnare och mer belastade skovlar, men denna trend ger upphov till ökad känslighet för aeromekaniska vibrationer och resulterar i ökande utmaningar när det gäller motorns strukturella integritet. Aerodynamiskt påtvingade vibrationer såväl som fladder måste predikteras noggrant för att kunna undvikas och en viktig parameter som förutsäger instabilitet i båda fallen är den aerodynamiska dämpningen. Syftet med det aktuella projektet är att numeriskt undersöka aerodynamisk dämpning i den första rotorn hos en transonisk kompressor (VINK6). Det transoniska flödesfältet leder till en bågformad stötvåg vid bladets främre kant, som sprider sig till sugsidan på det intilliggande bladet. I och med detta, tillsammans med det faktum att den roterande bladraden vibrerar i olika modformer och detta inducerar instationära tryckfluktuationer, syftar detta arbete på att utvärdera flödesfältslösningar för olika fal. I synnerhet fokuserar arbetet på prediktering av den instationära aerodynamiska dämpningen för de första sex modformen. Den aerodynamiska kopplingen mellan bladen hos denna rotor uppskattas genom att använda en transient bladradmodell uppsatt för fladderberäkningen. Den kommersiella CFD-koden som används för denna utredning är ANSYS CFX. Aerodynamisk dämpning utvärderas med hjälp av energimetoden, som gör det möjligt att beräkna den logaritmiska minskningen som används som en stabilitetsparameter i denna studie. De minsta logaritmiska dekrementvärdena för varje modform undersöks bättre genom att hitta den ostadiga tryckfördelningen på olika spannpositioner, som är en indikering av den lokala arbetsfördelningen, användbar för att få insikt i kopplingen mellan förskjutningar och därmed genererat ostabilt tryck. Två olika transienta metoder används som visar samma trend för de kvantiteter som beaktas med liknande beräkningsinsatser. Den första modformen är den enda med en fladderrisk, medan de högre modformerna har högre reducerade frekvenser, och ligger utanför det kritiska intervallet som finns i litteraturen. Instationärt tryck för alla moder är ganska jämförbart på de högre spannpositioner, där de största förskjutningarna föreskrivs, medan runt midspannet finns mindre jämförbara värden på grund av olika amplitud och riktning för modformen. SSTturbulensmodellen analyseras, som i detta fall inte påverkar predikteringen på ett betydande sätt. Det predikterade instationära trycket baserad på Fourier-transformationen valideras med MATLAB-koder som använder sig av Fast Fourier Transform för att säkerställa noggrannheten hos CFX-beräkningar. Konvergensnivå och skillnader i aerodämpningsvärden anges för varje resultat och detta gör det möjligt att uppskatta beräkningsinsatsen för varje simulering och uppskatta utbredningen av det numeriska felet.

A numerical procedure is presented which uses the truncation error injection methodology to efficiently achieve accurate approximations to complex problems having disparate length scales in the context of solving viscous, transonic flow over an airfoil. The truncation error distribution is estimated using the solution on a coarse grid. Local fine grids are formed which improve the resolution in regions of large truncation error. A fast fourth-order accurate scheme is presented for interpolating and relating the solutions between the generalized curvilinear coordinate systems of the local and global grids. It is shown that accurate solutions can be obtained on a global coarse grid with correction information obtained on local fine grids, which may or may not be topologically similar to the global grid as long as they are capable of resolving the local length scale. Dirichlet boundary conditions for the local grid yield the best results. The scheme also serves as the basis of a local refinement technique wherein a grid local to the nose of an airfoil is used to resolve a supersonic zone terminated by a shock and its interaction with a turbulent boundary layer. The solution on the local grid reveals details of the shock structure and a jet-like flow emanating from the root of the normal shock in the shock boundary layer interaction zone.

This dissertation deals with the instability, known as flutter, of the lifting and control surfaces of aircraft of advanced design at high altitudes and speeds. A simple model is used to represent the aerodynamics for flutter analysis of a two-degree-of-freedom airfoil system. Flutter solutions of this airfoil system are shown to be algebraically homomorphic in that solutions about different elastic axes can be found by mapping them to those about the mid-chord. Algebraic expressions for the flutter speed and frequency are thus obtained. For the prediction of flutter of a wing at transonic speeds, an accurate and efficient computer code is developed. The unique features of this code are the capability of accepting a steady mean flow regardless of its origin, a time dependent perturbation boundary condition for describing wing deformations on the mean surface, and a locally applied three-dimensional far-field boundary condition for minimizing wave reflections from numerical boundaries. Results for various test cases obtained using this code show good agreement with the experiments and other theories.

An adaptive refinement procedure combining the ideas of solving a modified difference equation and of adaptive mesh refinement is introduced. The numerical solution on a fixed grid is improved by inclusion of approximated truncation error computed from local subgrid refinement. Following this procedure, a reliable scheme has been developed for refined computations of the flow past a wedge at transonic speeds. Effects of the truncation error on the pressure, wave drag, sonic line, and shock position are investigated. By comparing the pressure drag on the wedge and the wave drag due to the shocks, the existence of a supersonic-to-supersonic shock originating from the wedge shoulder is confirmed.

This investigation studies the leakage flows over the high pressure turbine blade tip at high speed flow conditions. There is an unavoidable gap between the un-shrouded blade tip and the engine casing in a turbine stage, where the pressure difference between the pressure and the suction surfaces of the blade gives rise to the development of leakage flows through this gap. These flows contribute to about one third of the aerodynamic losses in a turbine stage. In addition they expose the blade tip to a very high temperature and result in thermal damages which reduce the blade‟s operational life. Therefore any improvement on the tip design to reduce these flows has a significant impact on the engine‟s efficiency and turbine blade‟s operational life. At the engine operational condition, the leakage flows over the high pressure turbine blade tip are mostly transonic. On the other hand literature survey has shown that most of the studies on the tip leakage flows have been performed at low speed conditions and there are only a few experimental works on the transonic tip flows. This project aims to explore the tip leakage flows at high speed condition which is the real engine condition, both experimentally and computationally and establish a comprehensive understanding of these flows on different tip geometries. The effect of tip geometry was studied using the flat tip and the cavity tip models and the effect of in-service burnout on these two tip models was established using the radius-edge flat tip and the radius-edge cavity tip models. The experimental work was carried out in the transonic wind tunnel of Queen Mary University of London and the computational simulations were performed using RANS and URANS. As the flow approached each tip model it turned and accelerated around its leading edge in the same way as the flow turns around the leading edge of an aerofoil. In the case of the tip models with sharp edges the tip flow separated at the inlet to the tip gap. For the flat tip model the flow reattachment occurred further downstream whereas in the case of the cavity tip model the length of the pressure side rim was not sufficient for the reattachment to occur and the separated flow left the rim as a free shear layer. The cavity tip model was found to have a smaller effective tip gap and hence smaller discharge coefficient in comparison to the flat tip model. For the radius-edge tip models, no separation occurred at the inlet to the tip gap and the effective tip gap was found to be the same as the geometrical tip gap. Therefore it was concluded that the tip model with radius-edges had a larger effective tip gap and hence a greater discharge coefficient than the tip geometry with sharp edges. It was observed that in the case of the supersonic tip leakage flows, decreasing the pressure ratio PR (i.e. the ratio of the static pressure at the tip gap exit to the stagnation pressure at the inlet to the tip gap) increased the discharge coefficient Cd for the tip models with sharp edges but it decreased the Cd value in the case of the tip models with radius edges. The cavity tip model with sharp edges was found to have the smallest discharge coefficient and thus the best performance in reducing the tip leakage flows as compared to all the other tip models studied in this investigation.