Aerodynamic Mitigation of Mechanical Constraints in Small Compressor Blade Profiles

Liquid film atomization from trailing edges is found in numerous applications. These include air blast atomization in pre-filming type fuel injectors and shedding from airfoils. This study investigates the effect of trailing edge thickness on liquid sheet breakup and droplet formation using NACA0012 airfoils with rounded trailing edges of 0.5 mm, 1.0 mm, and 2.0 mm, in high-speed airflow of up to 175 m/s. Water was introduced on the airfoil surface through 26 holes, each 0.5 mm in diameter and spaced 1 mm apart. These holes were located at 65 mm upstream of the trailing edge along the approximately 100 mm chord length. Three liquid flow rates, i.e., 1.4 cm3/(s·cm), 2.0 cm3/(s·cm), and 2.6 cm3/(s·cm) were tested. A variety of experimental techniques were implemented to analyze liquid film breakup and droplet behavior. High-speed video imaging captured film flow on the surface, the accumulation of liquid, ligament formation, and breakup at the trailing edge. Microscopic high-speed imaging was used to observe droplet behavior as a function of distance downstream of the trailing edge. This imaging reveals the transition from ligament formation to secondary atomization to the final droplet size distribution with downstream distance. At 70 mm downstream, atomization is essentially complete, and Laser Diffraction is also used to measure droplet Sauter mean diameters (SMD). The results show that thicker trailing edges and higher liquid mass flow rates promote liquid accumulation at the trailing edge. This, in turn, leads to increased ligament length and sheet breakup time. In the region just downstream of the ligament breakup, droplet sizes increase with increasing trailing edge thickness and liquid volume flow rate. Once the secondary atomization is complete (∼70 mm from the trailing edge), the drop sizes were found to be less affected by the trailing edge thickness and liquid flow and mainly determined by the air velocity. An analysis of variance was performed and a model to predict SMD as a function of weber number, air to liquid mass flow rate, downstream distance and trailing edge thickness was developed. Liquid film thickness as a characteristics length scale was selected as it directly influences the liquid accumulation and maximum ligament breakup length.

Modern gas turbines operate at high temperatures, which exceed the endurance limit of material, and therefore the turbines components are cooled by the air taken from the compressor. The cooling provides positive impact on lifetime of GT has negative impact on its performance. In convection-cooled turbine blade the coolant is usually discharged through the trailing edge and it leads to limitation on the minimal size of trailing edge and thereby negatively affects the losses. Moreover, the injection of cooling air in the turbine disturbs the main flow, and may lead to additional increase of losses, and the trailing edge loss is a significant part of the overall loss in modern gas turbines. This study comprises investigations of losses in cooled blades. Four cascades with different unguided part of aerofoil with and without coolant injection were studied both experimentally and numerically. This analysis provides split of losses caused by different factors, and offers the opportunities for efficiency and lifetime improvements of real engine designs/upgrades. In particular it is shown that an increase in the unguided turning angle results in a reduction of loss in case of relatively thick trailing edge. It is also shown that injection through the trailing edge slot parallel to the main flow leads to neutral loss impact and even loss reduction in subsonic range and loss increase in the supersonic range of exit Mach numbers.

The effect of nozzle trailing edge thickness on broadband acoustic radiation and the production of tones is investigated for coannular nozzles. Experiments were performed for a core nozzle trailing edge thickness between 0.38 mm and 3.17 mm. The on-set of discrete tones was found to be predominantly affected by the velocity ratio, the ratio of the fan velocity to the core velocity, although some dependency on trailing edge thickness was also noted. For a core nozzle trailing edge thickness greater than or equal to 0.89 mm, tones were produced for velocity ratios between 0.91 and 1.61. For a constant nozzle trailing edge thickness, the frequency varied almost linearly with the core velocity. The Strouhal number based on the core velocity changed with nozzle trailing edge thickness and varied between 0.16 and 0.2 for the core nozzles used in the experiments. Increases in broadband noise with increasing trailing edge thickness were observed for tone producing and non-tone producing conditions. A variable thickness trailing edge (crenellated) nozzle resulted in no tonal production and a reduction of the broadband trailing edge noise relative to that of the corresponding constant thickness trailing edge.

Conventional airliners use two to four engines in a Cayley-type arrangement to provide thrust, and the thrust is concentrated right behind the engine. Distributed propulsion is the idea of redistributing the thrust across most, or all, of the wingspan of an aircraft. This can be accomplished by using several large engines and using a duct to spread out the exhaust flow to form a jet-wing or by using many small engines spaced along the span of the wing. Jet-wing distributed propulsion was originally suggested as a way to improve propulsive efficiency. A previous study at Virginia Tech assessed the potential gains in propulsive efficiency. The purpose of this study was to assess the performance benefits of jet-wing distributed propulsion. The Reynolds-averaged, finitevolume, Navier-Stokes code GASP was used to perform parametric computational fluid dynamics (CFD) analyses on two-dimensional jet-wing models. The jet-wing was modeled by applying jet boundary conditions on the trailing edges of blunt trailing edge airfoils such that the vehicle was self-propelled. As this work was part of a BlendedWing-Body (BWB) distributed propulsion multidisciplinary optimization (MDO) study, two airfoils of different thickness were modeled at BWB cruise conditions as examples. One airfoil, representative of an outboard BWB wing section, was 11% thick. The other airfoil, representative of an inboard BWB wing section, was 18% thick. Furthermore, in an attempt to increase the propulsive efficiency, the trailing edge thickness of the 11% thick airfoil was doubled in size. The studies show that jet-wing distributed propulsion can be used to obtain propulsive efficiencies on the order of turbofan engine aircraft. If the trailing edge thickness is expanded, then jet-wing distributed propulsion can give improved propulsive efficiency. However, expanding the trailing edge must be done with care, as there is a drag penalty.

This paper describes a direct numerical simulation (DNS) study of turbulent flow over a rectangular trailing edge at a Reynolds number of 1000, based on the freestream quantities and the trailing edge thickness h; the incoming boundary layer displacement thickness '* is approximately equal to h. The time-dependent inflow boundary condition is provided by a separate turbulent boundary layer simulation which is in good agreement with existing computational and experimental data. The turbulent trailing edge flow simulation is carried out using a parallel multi-block code based on finite difference methods and using a multi-grid Poisson solver. The turbulent flow in the near-wake region of the trailing edge has been studied first for the effects of domain size and grid resolution. Then two simulations with a total of 256 2 512 2 64 (~ 8.42106) and 512 2 1024 2 128 (~ 6.72107) grid points in the computational domain are carried out to investigate the key flow features. Visualization of the instantaneous flow field is used to investigate the complex fluid dynamics taking place in the near-wake region; of particular importance is the interaction between the large-scale spanwise, or Karman, vortices and the small-scale quasi-streamwise vortices contained within the inflow boundary layer. Comparisons of turbulence statistics including the mean flow quantities are presented, as well as the pressure distributions over the trailing edge. A spectral analysis applied to the force coefficient in the wall normal direction shows that the main shedding frequency is characterized by a Strouhal number based on h of approximately 0.118. Finally, the turbulence kinetic energy budget is analysed.

The aim of this experimental study is to scrutinize the flow in the vicinity of a non zero thickness trailing edge, i.e. just upstream and downstream of the base, using Laser Doppler Anemometry. Indeed, boundary layer surveys as well as wake surveys have been performed for different thicknesses and shapes of trailing edges. Experiments have been conducted with two-dimensional trailing edges in both two- and threedimensional flows. Much of the discussion presented in this paper is relevant to flow field modification induced by thick cambered trailing edges.

Numerical Investigation of the Effect of Trailing Edge Shape on Surface-Piercing Propeller Performance

To mitigate the erosion issue in steam turbines, it is crucial to suppress the formation of coarse droplets spreading from the trailing edge upstream as well as from the shroud wall. The droplet size will be highly dependent on the trailing edge shapes and wettability, while the quantitative measurement under well-controlled flow conditions is limited, and hence, the theoretical prediction model including the effect of controlled trailing edge has yet established. We have developed an experimental setup, in which the shearing gas is fully developed and the liquid sheet on a wall is in uniform thickness along the transversal direction, allowing for the quantitative and general discussion from the wavy liquid sheets to the fragmenting droplet in a consistent manner. Here, we perform the visualization experiment on an acrylic pipe flow at the trailing edge thickness of 0.5 mm, 1.0 mm, and 2.0 mm, and the tapered angle of 10 deg and 30 deg, and at the wettability of hydrophobic condition. We successfully quantify the extending ligament from the trailing edge and the following droplet statistics using a high-speed imaging technique. By implementing the hydrophobic tapered wall, we clearly find that the circumferential wavelength between two ligaments on the trailing edge becomes short by minimizing the accumulated liquid on the edge stimulated by the Rayleigh-Taylor instability, leading to the formation of small droplets and suppression of coarse droplets. We finally formulate a theoretical model to predict the mean/maximum droplet sizes and distributions with considering the shape of trailing edge and wettability, which is validated by the present experimental results.

An experimental investigation was made on a turbulent boundary layer near the trailing edge on a long flat plate with a blunt trailing edge. The flow was controlled by an additional splitter plate attached to the trailing edge along the wake center line. The length of the splitter plate, l, was varied from 0.3 to 3 times the trailing edge thickness, h. Measurement of fluctuating velocity was made under the freestream zero pressure gradient. Almost independent of the installation of the splitter plate, the turbulent intensity and the Reynolds shear stress in the inner layer decreased when approaching the trailing edge of the flat plate (x / h=0), compared with that in the fully-developed turbulent boundary layer under the zero pressure gradient. The only exception was the distribution at x / h=0 near the wall in the case without the splitter plate (l / h=0), where the degree of the decrease in u rms / Ue was relatively small, and v rms / Ue and -uv / Ue2 were larger than those of the zero pressure gradient. The effect of l / h on turbulent quantities was shown just upstream of the trailing edge upon close comparison, and was classified into two groups: l / h<1 and l / h≥1. The tendency of the turbulent energy production terms approaching x / h=0 coincided with the decrease in the streamwise turbulent intensity and in the Reynolds shear stress.

An experimental investigation has been made for a turbulent boundary layer near the trailing edge on a long flat plate. The flow was controlled by an additional splitter plate fitted to the trailing edge along the wake center line. The length of the splitter plate, l, was varied from a half, to five times the trailing edge thickness, h. Measurements of base pressure behind the trailing edge and of mean velocity and pressure distribution in the turbulent boundary layer on the flat plate were made under the freestream zero-pressure gradient. The absolute value of base pressure coefficient of the long flat plate was considerably smaller than that of the short flat plate (bluff body) without splitter plate (l/h=0). A significant increase in the normalized base pressure coefficient (about 50% as same as short one) was achieved with the splitter plate (l/h≥1) fitted to the long flat plate. Within an inner layer in the turbulent boundary layer near the trailing edge, mean velocity increased than that in the upstream position, especially in the case without splitter plate. With splitter plate, however, the base pressure rise made mean velocity distribution come closer to that of fully developed turbulent boundary layer. In the case of l/h≥1, the affected range of acceleration decreased from 10 h upstream of the trailing edge without splitter plate to 5 h upstream.

As a straightforward consequence of dimensional analysis, the frequency of vortex phenomena increases proportionally with the flow velocity, and is inversely proportional to its size. Thus, while draft tube surges are in the Hertz range—the characteristic length being the runner diameter, Von Karman eddies are basically determined by a trailing edge thickness, and due to the smaller size their frequency is well in the audible range. The Von Karman eddies have to be minimized by using particular profiles for the trailing edges, in particular in the stay vanes and runner blades, or otherwise the lock-in effect and the narrow-band character of the phenomenon may put the structural safety at risk.

Trailing edge loss is one of the main sources of loss for transonic turbine blades, contributing typically 1/3 of their total loss. Transonic trailing edge flow is extremely complex, the basic flow pattern is understood but methods of predicting the loss are currently based on empirical correlations for the base pressure. These correlations are of limited accuracy. Recent findings that the base pressure and loss can be reasonably well predicted by inviscid Euler calculations are justified and explained in this paper. For unstaggered choked blading, it is shown that there is a unique relationship between the back pressure and the base pressure and any calculation that conserves mass, energy and momentum should predict this relationship and the associated loss exactly. For realistic staggered blading, which operates choked but with subsonic axial velocity, there is also a unique relationship between the back pressure and the base pressure (and hence loss) but the relationship cannot be quantified without knowing a further relationship between the base pressure and the average suction surface pressure downstream of the throat. Any calculation that conserves mass, energy and momentum and also predicts this average suction surface pressure correctly will again predict the base pressure and loss. Two-dimensional Euler solutions do not predict the suction surface pressure exactly because of shock smearing but nevertheless seem to give reasonably accurate results. The effects of boundary layer thickness and trailing edge coolant ejection are considered briefly. Coolant ejection acts to reduce the mainstream loss. It is shown that suction surface curvature downstream of the throat may be highly beneficial in reducing the loss of blades with thick trailing edges operating at high subsonic or low supersonic outlet Mach numbers.

The paper presents some experiments concerning the trailing edge flow of transonic turbine bladings. The experiments are conducted on a model simulating very closely the flow in the overhang section of convergent turbine cascades. The first test series simulates cascade flow conditions with shock free flow in the overhang section (limit load conditions), while the second test series simulates cascade flow conditions characterized by trailing edge shock interferences with the flow in the overhang section. Particular attention is given to the trailing edge separation shock and the length of the isobaric trailing edge base region. The test results indicate that the strength of the separation shock for the rounded trailing edge is of the same order as the strength of the lip shock found by Merzkirch for sharp-edged wedges. The length of the isobaric base region is only 60 to 80 percent of the trailing edge thickness, while the pressure recovery region is about twice as long as the constant pressure region. From an analysis of the flow parameters influencing the base pressure, it is concluded that the boundary-layer shape factor plays a significant role in establishing the base pressure.

The geometric effects of Coanda trailing edges on the aerodynamic performance of an airfoil are numerically evaluated for a range of different freestream Mach numbers and momentum coefficients. A Circulation control (CC) airfoil with a circular trailing edge (ACTE) proves to have better control effectiveness at low subsonic freestream speeds (Mach = 0.1). A CC airfoil having an elliptic trailing edge (AETE) outperforms the ACTE at high subsonic flow conditions. The occurrence of C μ-stall for the AETE is greatly postponed, and meanwhile the maximum net lift coefficient increment achieved for the AETE (Δ C L = 0.51) is slightly higher than that of the ACTE (Δ C L = 0.50) at Mach 0.6. Compared to the ACTE, the AETE is found to have better control consistency at different operating velocities and better control stability when the Coanda jet is supersonic. Through careful consideration of the aerodynamic performance and the control effects, the most appropriate axial ratio for an AETE ellipse is within the interval from 1.5 to 2. Finally, the flow field instability phenomenon and the jet detachment induced by the supersonic Coanda jet are investigated. A self-sustained shock-wave instability phenomenon without jet detachment is first observed in this paper.

The capability of three different perturbation approaches to tackle airframe noise problems is studied. The three approaches represent different levels of complexity and are applied to trailing edge noise problems. In the Euler-perturbation approach the linearized Euler equations without sources are used as governing acoustic equations. The sound generation and propagation is studied for several trailing edge shapes (blunt, sharp, and round trailing edges) by injecting upstream of the trailing edge test vortices into the mean-flow field. The efficiency to generate noise is determined for the trailing edge shapes by comparing the different generated sound intensities due to an initial standard vortex. Mach number scaling laws are determined varying the mean-flow Mach number. In the second simulation approach an extended acoustic analogy based on acoustic perturbation equations (APEs) is applied to simulate trailing edge noise of a flat plate. The acoustic source terms are computed from a synthetic turbulent velocity model. Furthermore, the far field is computed via additional Kirchhoff extrapolation. In the third approach the sources of the extended acoustic analogy are computed from a Large Eddy Simulation (LES) of the compressible flow problem. The directivities due to a modeled and a LES based source, respectively, compare qualitatively well in the near field. In the far field the asymptotic directivities from the Kirchhoff extrapolation agree very well with the analytical solution of Howe. Furthermore, the sound pressure spectra can be shown to have similar shape and magnitude for the last two approaches.