The film cooling holes in the blade of modern gas turbines have commonly been manufactured by laser drilling, Electric Discharge Machining (EDM), and Additive Manufacturing (AM) in recent years. These manufacturing processes often result in small geometric deviations, such as conical angles, filleted edges, and diameter deviations of the hole, which can lead to deviations on the distribution of adiabatic cooling effectiveness (η) values, the value of the discharge coefficient (C_d), and the characteristic of the in-hole flow field. The current study employed flat plate fan-shaped film cooling holes with length-to-diameter values (L/D) equal to 3.5 and six to investigate the effects of these manufacturing deviations on the distribution of η values, the value of C_d, and the characteristic of in-hole flow field. An Uncertainty Quantification (UQ) analysis using the Polynomial Chaos Expansion (PCE) model was carried out to quantify the uncertainty in the values of η and C_d. The statistical characteristics (mean values, standard deviation (Std) values, and Probability Density Function (PDF) values) of η and C_d were also calculated. The results show that conical angle deviations exert no visible changes on the value of η. However, the C_d value decreases by 6.2% when the conical angle changes from 0–0.5°. The area averaged adiabatic cooling effectiveness ( $\stackrel{=}{\eta }$ ) decreases by 3.4%, while the C_d increases by 15.2% with the filleted edge deviation existing alone. However, the deviation value of $\stackrel{=}{\eta }$ is 7.6%, and that of C_d is 25.7% with the filleted edge deviation and the diameter deviation existing.

The first-stage rotor squealer tip is a key area in gas turbine for both aerodynamic performance and blade cooling tasks, which should be carefully designed. However, harsh operating conditions near the rotor squealer tip can cause the geometry of the squealer tip to degrade, and manufacturing inaccuracies can also cause the squealer tip geometry to deviate from the ideal design. These geometry deviations would change the flow field near the blade tip, which will influence the thermal and aerodynamic performance. Thus, it is important to quantitatively investigate the effects of squealer tip geometry deviation on the aerothermal performance. In this paper, a typical transonic first-stage turbine is employed, and three important geometric features of squealer tip, the tip clearance height (H), the squealer depth (D), and the squealer edge chamfer (R), are selected. An uncertainty quantification process is performed to study the effect of deviation of H, D, and R on the aerothermal performance. Many cases with different geometry features are checked in the current study using 3D Reynolds-averaged Navier–Stokes simulations. A parameter sensitivity analysis using Sobol Indice method is carried out to identify the key parameters to aerothermal performance of the squealer tip. The uncertainty quantification results show that the existence of the tip chamfer reduces the size of separation bubble and the dwelling range of the scraping vortex, thus, the blockage effect of the leakage flow is weakened, which results in larger amount of leakage flow and more mixing loss of squealer tips with edge chamfer than those without edge chamfer. The results of the parameter sensitivity analysis show that the height of tip clearance is the main factor that affects the aerodynamic performance of the squealer tip. This work provides a certain guiding direction for the optimization design of the turbine groove tip.

A New Treatment for Boundary of Laminar Flow Inlet or Outlet in SPH

We present a numerical investigation on the impact of the Coulomb interaction in the spiderlike photoelectron momentum distributions (PMDs) of a hydrogen atom ionized by an intense laser pulse. We have shown, by integrating analytical correction terms into the standard semiclassical rescattering model (SRM) to formulate the Coulomb analytically-corrected SRM (AC-SRM), that the interference fringes manifest a systematic shift along the transverse momentum direction upon considering the Coulomb action. A Coulomb correction to the SRM model has rarely been reported before. Analyses are made by varying physical quantities such as the carrier frequency and initial transverse velocity of the ionized electron. In particular, we decipher the impact of the Coulomb interaction with the classical-action phase map scheme, and demonstrate that this effect is more pronounced for smaller momenta in the spiderlike PMDs. It is proven that the presented AC-SRM is simple and effective in accounting for the Coulomb effect, as an alternative correction due to the Coulomb interaction to the standard SRM theory. Also, our phase map scheme is shown to be more powerful than the plain interference fringes in interrogating the Coulomb effect, especially for the first interference minimum. We anticipate that the present AC-SRM can be useful in investigating other strong field processes where the Coulomb interaction is considered.

本文使用半经典回碰模型和求解含时薛定谔方程的方法数值研究了电离电子的纵向初速度在氢原子的蜘蛛状动量谱干涉结构中的作用。对光电子动量谱的纵向和横向动量分布性质的数值研究结果表明，可以从光电子动量谱的纵向动量分布获取电离电子纵向初速度的信息。研究发现无论将初速度视为多个常数亦或是多段分布，均能重建完整的蜘蛛状干涉结构，可见用常数值来描述电子的初速度有待深入研究。另外，数值求解含时薛定谔方程的结果也与半经典回碰模型的模拟结论相一致，可以互相印证。本文的研究结果表明纵向初速度在强激光脉冲电离产生的光电子动量谱中起着重要作用，速度的分布情况还需结合非绝热过程深入研究。