A three-dimensional unstructured incompressible RANS code has been developed using artificial compressibility and Spalart-Allmaras eddy viscosity model. A node-based finite volume method is used in which all flow variables are defined at the vertices of tetrahedrons in an unstructured grid. The inviscid fluxes are computed by using the Roe's flux difference splitting method, and higher order accuracy is attained by data reconstruction based on Taylor series expansion. Gauss theorem is used to formulate necessary gradients. For time integration, an implicit scheme based on linearized Euler backward method is used. A tetrahedral unstructured grid generation code has been also developed and applied to the tip clearance flow in a highly staggered cascade. Surface grids are first generated in the flow passage and blade tip by using several triangulation methods including Delaunay triangulation, advancing front method and advancing layer method. Then the whole computational domain including tip gap region is filled with prisms using the surface grids. Each prism is divided into three tetrahedrons. To accomplish this division in a consistent manner, connectivity pattern is assigned to each triangle in the surface grids. A new algorithm is devised to assign the connectivity pattern without reference to the particular method of triangulation. This technique offers great flexibility in surface grid generation. The code has been validated by comparisons with available computational and experimental results for several test cases: invisicd flow around NACA section, laminar and turbulent flow over a flat plate, turbulent flow through double-circular arc cascade and laminar flow through a square duct with 90° bend. For the laminar flat plate case, the velocity profile and skin friction coefficient are in excellent agreement with Blasius solution. For the turbulent flat plate case, velocity profiles are in full agreement with the law of the wall up to Reynolds number of 1.0E8, however, the skin friction coefficient is under-predicted by about 10% in comparison with empirical formula. Blade loading for the two-dimensional circular arc cascade is also compared with experiments. The results obtained with the experimental inflow angle (51.5° ) show some discrepancies at the trailing edge and severely under-predict the suction peak at the leading edge. These discrepancies are completely remedied if the inflow angle is increased to 53.5° . The code is also capable of predicting the secondary flow in the square duct with 90° bend, and the velocity profiles are in good agreement with measurements and published Navier-Stokes computations. Finally the code is applied to a linear cascade that has GE rotor B section with tip clearance and a high stagger angle of 56.9° . The overall structure of the tip clearance flow is well predicted. Loss of loading due to tip leakage flow and reloading due to tip leakage vortex are presented. On the end wall, separation line of the tip leakage vortex and reattachment line of passage vortex are identified. The location of the tip leakage vortex in the passage agrees very well with oil flow visualization. Separation bubble on the blade tip is also predicted. Mean streamwise velocity contours and cross sectional velocity vectors are compared with experimental results in the near wake, and good agreements are observed. It is concluded that Spalart-Allmaras turbulence model is adequate for this type of flow field except at locations where the tip leakage vortex of one blade interacts with the wake of a following blade. This situation may prevail for blades with longer span and/or in the far wake. Prediction of such an interaction presents a challenge to RANS computations. The effects of blade span on the flow structure have been also investigated. Two cascades with blades of aspect ratios of 0.5 and 1.0 are considered. By comparing pressure distributions on the blade, it is shown that the aspect ratio has strong effects on loading distribution on the blade although the tip gap height is very small (0.016 chord). Grid convergence study has been carried out with three different grids for pressure distributions and limiting streamlines on the end wall. / Ph. D.

The unsteady behavior of a tip leakage flow downstream of a simulated axial compressor rotor has been studied. The Virginia Tech low speed linear cascade wind tunnel was adapted to model the unsteady tip leakage flow produced by a rotor operating in the vortical wakes of a set of stator vanes. The cascade, consisting of 8 GE rotor B blades, has adjustable tip gap, inlet angle of 65.1 degrees, turning angle of 11.8 degrees and solidity of 1.076. The cascade Reynolds number, based on blade chord, was 393,000. A moving end wall was used to simulate the relative motion between rotor and casing, and vortex generators attached to the moving end wall were used to produce an idealized periodic unsteady vortical inflow similar to that shed by the junction of a row of inlet guide vanes. Measurements of the vortical inflow to the cascade produced by the generators and of the mean blade loading at the mid span are presented. The periodic and aperiodic behavior of the tip leakage flow downstream of the cascade, produced by this vortical disturbance, is also presented using phase and time averaged 3-component turbulence and pressure fluctuation measurements. These measurements are made for tip gap from 0.83% to 3.3% chord and streamwise locations from 0.772% to 1.117% blade spacing axially downstream of the cascade. The phase averaged inflow measurements reveal that the inflow produced by the vortex generators consists of a pair asymmetric counter-rotating vortices embedded in a thin (4.6% chord) endwall boundary layer. The vortices extend some 7.4% chord from the end wall. Their strength is about two orders smaller than the typical circulation of the tip leakage vortices produced by the cascade. Phase averaged single point three component hot-wire measurements downstream of the cascade reveal that the vortical inflow is, however, capable of producing significant large scale fluctuations in the size, strength, structure and position of the tip leakage vortex. These effects increase in magnitude with increase of tip gap. For small tip gaps these effects appear to be due to simple superposition between the inflow vortices and the tip leakage vortex. However for larger tip gaps these effects appear primarily a consequence of the inflow vortices interfering with the shedding of circulation from the blade tip. The fact that the circulation fluctuation is consistent with the inviscid unsteady loading prediction suggests that the inviscid response may be a major mechanism for generating the tip leakage unsteadiness. Although there is large periodic fluctuation in the tip leakage flow disturbed by the inflow, there is a larger aperiodic component. Two point correlation measurements and linear stochastic estimation are used to reveal the structure of this aperiodic part for a tip gap of 3.3% chord. The aperiodic fluctuation, containing most of the turbulence energy, is found appearing to be organized structures in large scale, and making the estimated instantaneous velocity field significantly different from the phase averaged periodic velocity field. Phase averaged pressure fluctuation measurements made using a microphone in the tip leakage vortex downstream of the cascade reveal that there are significant periodic fluctuating pressure waves and intense mean square fluctuation of the aperiodic fluctuating pressure. They are consistent with the measured periodic flow and aperiodic flow field respectively. These microphone measurements are validated using fluctuating pressure gradient estimates determined from the hot-wire measurements. / Ph. D.

The interaction between rotor blade tip leakage vortex and inflow disturbances, such as encountered in shrouded marine propulsors, was simulated in the Virginia Tech Linear Cascade Wind Tunnel equipped with a moving endwall system. Upstream of the blade row, idealized periodic inflow unsteadiness was generated using vortex generator pairs attached to the endwall at the same spacing as the blade spacing. At three tip gap settings, 1.7%c, 3.3%c and 5.7%c, the flow near the lower endwall of the center blade passage was investigated through three-component mean velocity and turbulence distributions measured by four-sensor hotwires. Besides time-averaged data, the measurements were processed for phase-locked analysis, with respect to pitchwise locations of the vortex generators relative to the blade passage. Moreover, surface pressure distributions at the blade tip were acquired at eight tip gaps from 0.87%c to 12.9%c. Measurements of pressure-velocity correlation were also performed with wall motion but without inflow disturbances. Achieved in this study is an understanding of the characteristics and structures of the tip leakage vortex at its initial formation. The mechanism of the tip leakage vortex formation seems to be independent of the tip gap setting. The tip leakage vortex consists of a vortical structure and a region of low streamwise-momentum fluid next to the endwall. The vortical structure is initially attached to the blade tip that creates it. This structure picks up circulation shed from that blade tip, as well as those from the endwall boundary layer, and becomes stronger with downstream distance. Partially induced by the mirror images in the endwall, the vortical structure starts to move across the passage resulting in a reduction in its rotational strength as the cross sectional area of the vortex increases but little circulation is added. The larger the tip gap, the longer the vortical structure stays attached to the blade tip, and the stronger the structure when it reaches downstream of the passage. Phased-averaged data show that the inflow disturbances cause small-scale responses and large-scale responses upstream and downstream of the vortex shedding location, respectively. This difference in scale is possibly dictated by a variation in the shedding location since the amount of circulation in the vortex is dependent on this location. The inflow disturbances possibly cause a variation in the shedding location by manipulating the separation of the tip leakage flow from the endwall and consequently the flow's roll-up process. Even though this manipulation only perturbs the leakage flow in a small scale, the shedding mechanism of the tip leakage vortex amplifies the outcome. / Ph. D.

This dissertation presents the results from an experimental study of three-dimensional turbulent tip gap flow in a linear cascade wind tunnel with 3.3% chord tip clearance with and without moving endwall simulation. Experimental measurements have been completed in Virginia Tech low speed linear cascade wind tunnel. A 24" access laser-Doppler velocimeter (LDV) system was developed to make simultaneous three-velocity-component measurements. The overall size of the probe is 24"à 37"à 24"and measurement spatial resolution is about 100 μm. With 24" optical access distance, the LDV probe allows measurements to be taken from the side of the linear cascade tunnel instead of through the bottom of the tunnel floor. The probe has been tested in a zero-pressure gradient two-dimensional turbulent boundary layer. Experimental measurements (oil flow visualization, pressure measurement, and LDV measurement) for the stationary wall captured the major flow structures of the tip leakage flow in the linear compressor cascade, such as tip leakage vortex, tip leakage vortex separation and tip separation vortex. Large velocity gradients in the tip leakage vortex separation, tip leakage vortex, and tip separation vortex regions generate large production of the Reynolds stresses and turbulent kinetic energy. One of the most interesting features of the tip leakage flow is the bimodal velocity probability histograms of the v component due to the unsteady motion of the flow in the interaction region between the tip leakage vortex and tip leakage jet. The tip separation vortex, tip leakage vortex separation, and tip leakage vortex contain most of turbulent kinetic energy and generate the highest dissipation rate. Relative motion of the endwall significantly affects the tip gap flow structures, especially in the near wall region. Compared to the stationary wall case, velocity gradients in the near wall region for the moving wall case are much smaller and lower velocity gradients in the near wall region cause the low production of Reynolds stresses and turbulent kinetic energy. Similar to the stationary wall case, high Reynolds stresses and turbulent kinetic energy values are mainly located in the vicinity of the tip leakage vortex and tip separation vortex region. The bimodal velocity probability histograms of the v component are also found at the same locations. The tip separation vortex with most of the turbulent kinetic energy generates the highest dissipation rate. The dissipation rate in the tip leakage vortex region is reduced with the decrease of turbulent kinetic energy under the moving wall effect. / Ph. D.

This thesis presents some results from an experimental study of three-dimensional turbulent tip gap flows in the linear cascade wind tunnel, for two different tip gap clearances (t/c=1.65% and 3.3%). The experiments focus on near-wall flow field measurements for the stationary wall and moving wall, and static pressure measurement on the low end-wall for the stationary wall case. The representative flows were pressure driven, three-dimensional turbulent boundary layers in the linear cascade tunnel for the stationary wall case, and the combination of the pressure driven and shear driven flow for the moving wall case. Several experimental techniques are used in the studies: a three-orthogonal-velocity-component fiber-optic laser Doppler anemometer (3D-LDA) system, surface oil flow visualization, and a scanivalve system for static pressure measurement through pressure ports on the end-wall. From the details of the oil flow visualization pattern on the end-wall, some features of the passage flow, cross flow, and the tip leakage vortex in this cascade flow were captured. Oil flow visualization on the blade surface reveals the reattachment of the tip leakage vortex on the blade surface. The static pressure results on the lower end-wall and mid-span of the blade show huge pressure drop on the lower end-wall from the pressure side to the suction side of the blade and from mid-span to the lower end wall. The end-wall skin friction velocity is calculated from near-wall LDA data and pressure gradient data using the near-wall momentum equation. The statistics of Reynolds stresses and triple products in two-dimensional turbulent boundary layer and three-dimensional turbulent boundary layer was examined using a velocity fluctuation octant analysis in three different coordinates (the wall collateral coordinates, the mid tip gap coordinates, and the local mean flow angle coordinates). The velocity fluctuation octant analysis for the two-dimensional turbulent boundary layer reveals that ejections of the low speed streaks outward from the wall and the sweeps of high speed streaks inward toward the wall are the dominant coherent motions. The octant analysis for the three-dimensional turbulent boundary layer in the tip gap shows that the dominant octant events are partially different from those in the two-dimensional turbulent boundary layer, but ejection and sweep motions are still the dominant coherent motions. For the three-dimensional turbulent boundary layer in the moving wall flow, the near-wall shear flow reinforces the sweep motion to the moving wall and weakens the out-ward ejection motion in the shear flow dominant region. Between the passage flow and the shear flow, is the interaction region of the high speed streaks and the low speed streaks. This is the first time that the coherent structure of the three-dimensional turbulent boundary in the linear cascade tip gap has been studied. / Master of Science

The effects of serrated trailing edge designs, designed for noise reduction, on the flow-field downstream of an idealized aircraft engine fan blade row were investigated in detail. The measurements were performed in the Virginia Tech low speed linear cascade tunnel on one set of baseline GE-Rotor-B blades and four sets of GE-Rotor-B blades with serrated trailing edges. The four serrated blade sets consisted of two different serration sizes (1.27 cm and 2.54 cm) and for each different serration size a second set of blades with added trailing edge camber. The cascade row consisted of 8 GE-Rotor-B blades and 7-passages with adjustable tip gap settings. It had an inlet angle of 65.1º, stagger angle of 56.9º and a turning angle of 11.8º. The tunnel was operated with a tip gap setting of 1.65% chord, with a Reynolds number based on the chord of 390,000. Blade loading measurements performed on each set of blades showed that it was slightly dependent on the serration shape. As the serration size was increased the blade loading decreased, but adding droop increased the blade loading. The Pitot-static cross-sections showed that flow-fields near the upper and lower endwalls cascade tunnel were similar with the baseline or the serrated blade downstream of the blade row. In the wake region, the individual trailing edge serrations tips and valleys could be seen. As the wake convected downstream, the individual tips and valleys became less visible and the wake was more uniform in profile. The tip leakage vortex was only minimally affected by the trailing edge serrations. This conclusion was further reinforced by the three-component hot-wire cross-sectional measurements that were performed from the lower endwall to the mid-span of the blade. These showed that the mean streamwise velocity, turbulence kinetic energy and turbulence kinetic energy production in the tip leakage region were nearly the same for all four serrated blades as well as the baseline. The vorticity in this region was a more dependent on the serration shape and as a result increased with serration size compared to the baseline. Mid-span measurements performed with the three-component hot-wire showed the spreading rate of the wake and the decay rate of the wake centerline velocity deficit increased with serration size compared to the baseline case. Drooping of the trailing edge only minimally improved the spreading and decay rates. This improvement in these rates was predicted to reduce the tonal noise at the leading edge of the downstream stator vane because the periodic fluctuation associated with the sweeping of the rotor blade wakes across it, was due to the pitchwise variation in the mean streamwise velocity. The wakes were further compared to the mean velocity and turbulence profiles of plane wakes, which the baseline and the smallest serration size agreed the best. As the serration size was increased and drooping was added, the wakes became less like plane wakes. Spectral plots at the wake centerline in all three velocity directions showed some evidence of coherent motion in the wake as a result of vortex shedding. / Master of Science

This dissertation presents results from a thorough study of the tip-gap turbulent flow structure in a low-speed linear compressor cascade wind tunnel at Virginia Tech that includes a moving belt system to simulate the relative motion between the tip and the casing. The endwall pressure measurements and the surface oil flow visualizations were made on a stationary endwall to obtain the flow features and to determine the measurement profiles of interest. A custom-made miniature 3-orthogonal-velocity-component fiber-optic laser-Doppler velocimetry (LDV) system was used to measure all three components of velocity within a 50 mm spherical measurement volume within the gap between the endwall and the blade tip, mainly for the stationary wall with 1.65% and 3.30% tip gaps as well as some initial experiments for the moving wall. Since all of the vorticity in a flow originates from the surfaces under the action of strong pressure gradient, it was very important to measure the nearest-wall flow on the endwall and around the blade tip. The surface skin friction velocity was measured by using viscous sublayer velocity profiles, which verified the presence of an intense lateral shear layer that was observed from surface oil flow visualizations. All second- and third-order turbulence quantities were measured to provide detailed data for any parallel CFD efforts. The most complete data sets were acquired for 1.65% and 3.30% tip gap/chord ratios in a low-speed linear compressor cascade. This study found that tip gap flows are complex pressure-driven, unsteady three-dimensional turbulent flows. The crossflow velocity normal to the blade chord is nearly uniform in the mid tip-gap and changes substantially from the pressure to suction side. The crossflow velocity relies on the local tip pressure loading that is different from the mid-span pressure loading because of tip leakage vortex influence. The tip gap flow is highly skewed three-dimensional flow throughout the full gap. Normalized circulation within the tip gap is independent of the gap size. The tip gap flow interacts with the primary flow, separates from the endwall, and rolls up on the suction side to form the tip leakage vortex. The tip leakage vortex is unsteady from the observation of the TKE transport vector and oil flow visualizations. The reattachment of tip separation vortex on the pressure side strongly depends on the blade thickness-to-gap height ratio after the origin of tip leakage vortex but is weakly related to it before the origin of tip leakage vortex for a moderate tip gap. Other than the nearest endwall and blade tip regions, the TKE does not vary much in tip gap. The tip leakage vortex produces high turbulence intensities. The tip gap flow correlations of streamwise and wall normal velocity fluctuations decrease significantly from the leading edge to the trailing edge of the blade due to flow skewing. The tip gap flow is a strongly anisotropic turbulent flow. Rapid distortion ideas can not apply to it. A turbulence model based on stress transport equations and experimental data is necessary to reflect the tip gap flow physics. For the moving endwall, relative motion skews the inner region flow and is decorrelated with the outer layer flow. Hence, the TKE and correlations of streamwise and wall normal velocity fluctuations decrease. / Ph. D.

L’écoulement de jeu dans les compresseurs axiaux est étudié à l’aide de la Zonal Detached Eddy Simulation (ZDES). L’objectif consiste à évaluer la capacité de méthodes hybrides URANS/LES à simuler l’écoulement de jeu d’un compresseur axial réaliste afin de mieux comprendre la physique de cet écoulement, notamment son comportement au vannage ainsi que l’effet de sillages venant du stator amont sur le rotor aval. Après avoir choisi la méthode hybride ZDES, un banc d’essai numérique est défini afin de simuler le premier rotor du compresseur de recherche CREATE. Ce banc a la particularité de pouvoir prendre en compte les effets instationnaires venant de la roue directrice d’entrée (RDE), notamment son sillage ainsi que les tourbillons générés en pied et en tête. Basé sur des critères de maillage ZDES, il est utilisé pour évaluer cette méthode comparativement aux méthodes classiques RANS et URANS. La ZDES est validée par étape jusqu’à une analyse spectrale de l’écoulement de jeu se basant sur des données expérimentales. Elle s’est révélée capable de capturer plus précisément l’intensité et la position des phénomènes instationnaires rencontrés en tête du rotor, notamment le tourbillon de jeu. Les densités spectrales de puissance analysées montrent que cela est dû en partie à une meilleure prise en compte du transfert d’énergie des grandes vers les petites structures de l’écoulement avant leur dissipation. De plus, l’écart entre les approches s’accentue lorsque le tourbillon de jeu traverse le choc en tête. Proche pompage, les effets d’interaction entre le choc, le tourbillon de jeu, la couche limite carter et le tourbillon venant de la tête de la RDE sont amplifiés. Le décollement de la couche limite carter s’accentue et une inversion locale de l’écoulement est observée. De plus, le tourbillon de jeu s’élargit et est dévié vers la pale adjacente, ce qui intensifie le phénomène de double écoulement de jeu. L’interaction du tourbillon venant de la tête de la RDE avec le choc et le tourbillon de jeu du rotor est ensuite étudiée au point de dessin. Un battement du tourbillon de jeu est rencontré lors de l’interaction de ce tourbillon avec le tourbillon de tête de la RDE, ce qui diminue le double écoulement de jeu. / The tip-leakage flow in axial compressors is studied with the Zonal Detached Eddy Simulation (ZDES). This study aims at evaluating the capability of hybrid URANS/LES methods to simulate the tip-leakage flow within a realistic axial compressor in order to better understand the involved physics, especially the behaviour of the flow near surge and the effects of stator wakes on the downstream rotor. Once the ZDES method is chosen, a numerical test bench is defined to simulate the first rotor of the research compressor CREATE. This bench takes into account the unsteady effects of the Inlet Guide Vane (IGV), such as its wake as well as vortices generated at the IGV hub and tip. It is based upon ZDES meshing criteria and is used to evaluate this method compared to classic RANS and URANS approaches. A method validation is carried out up to a spectral analysis compared to experimental data. The ZDES is capable to capture more accurately the intensity and position of the unsteady phenomena encountered in the tip region, especially the tip-leakage vortex. The power spectral densities highlight that this partly originates from a better capture of the energy transfer from large to small structures until their dissipation. The discrepancy between the methods is accentuated as the tip-leakage vortex crosses the shock. Near the surge line, the interactions between the shock, the tip-leakage vortex, the boundary layer developing on the shroud and the vortex generated by the IGV tip are amplified. The boundary layer on the shroud separates earlier and a local flow inversion occurs. Besides, the tip-leakage vortex widens and is deflected toward the adjacent blade. This strengthens the double leakage. At the design operating point, the interaction of the IGV tip vortex with the shock and the rotor tip vortex is studied. A vortex flutter is observed as the IGV tip vortex arrives on the rotor blade and stretches the rotor tip vortex. This phenomenon decreases the double leakage.

<p dir="ltr">Gas turbines are widely used to provide propulsion, electrical-power, and mechanical power. Though tremendous advances have been made since Frank Whittle’s patent of a turbojet in 1930 and Hans von Ohain’s patent of the first operational turbojet in 1936, industry still has aggressive goals on improvements in efficiency and service life. One area where further advances are needed is better control of the flow across the gap between the blade tip and the shroud, referred to as tip-leakage flow (TLF). This is because TLF accounts for up to one-third of the aerodynamic losses in a turbine stage.</p><p dir="ltr">In this study, hybrid LES-RANS based on IDDES and steady RANS based on the SST turbulence model were used to study the compressible flow in a 1.5-stage turbine with geometry and operating conditions that are relevant to power-generation gas turbines. The focus is on the flow in the tip-gap region that account for the flow features created by the upstream stator vanes, stator-rotor interactions, and downstream stator vanes. Results obtained reveal the flow structures about the tip-gap region and the flow mechanisms that create them. Results obtained also show where steady RANS with mixing plane could predict correctly when compared with results from IDDES that resolve the unsteadiness of the turbulence and the motion of the rotor blades passing the stator vanes. Turbulent statistics from the IDDES were generated to guide the development of better RANS models. Results were also obtained by using RANS to examine the effects of blade loading, where mass flow rate through the 1.5 stage turbine was varied with the rotor’s rotational speed fixed at 3,600 RPM – the speed at which power-generation gas turbines operate in the U.S.</p><p dir="ltr">Key findings are as follows: In the first-stage stator, horseshoe, passage, and corner vortices were found to be confined within 10 to 15% span from the hub and shroud, and both steady RANS and IDDES generated similar results. Steady RANS and IDDES, however, differed considerably in how they predicted the wake downstream of the vane’s trailing edge. This coupled with the use of mixing plane, steady RANS was unable to account for effects of stator-rotor interactions and their effects on the tip-leakage flow. In the rotor, steady RANS predicted passage vortices that extended up to 50% span from the hub and 25% span from the shroud. The flow through the tip gap was found to induce a separation bubble on the blade tip and one large and two small vortical structures on the suction side of the blade and a vortical structure next to the shroud. These structures were found to grow along the axial chord of the blade. Steady RANS also predicted the large tip leakage vortex that contained the fluid from the tip-leakage flow to breakdown. IDDES did not predict the vortex breakdown because all of the coherent vortical structures identified including the separated region on the blade tip were unsteady and constantly shedding. As a result, IDDES predicted much smaller mean passage vortices – albeit the instantaneous structures were nearly as large as those predicted by steady RANS.</p>