Turbulent kinetic energy balance measurements in the wake of a low-pressure turbine blade

The turbulent kinetic energy budget in the wake generated by a high lift, low-pressure two-dimensional blade cascade of the T106 profile was investigated experimentally using hot-wire anemometry. The purpose of this study is to examine the transport mechanism of the turbulent kinetic energy and provide validation data for turbulence modeling. Point measurements were conducted on a high spatial resolution, two-dimensional grid that allowed precise derivative calculations. Positioning of the probe was achieved using a high accuracy traversing mechanism. The turbulent kinetic energy (TKE) convection, production, viscous diffusion and turbulent diffusion were all obtained directly from experimental measurements. Dissipation and pressure diffusion were calculated indirectly using techniques presented and validated by previous investigators. Results for all terms of the turbulent kinetic energy budget are presented and discussed in detail in the present work.     

Transient growth mechanisms of low Reynolds number flow over a low-pressure turbine blade

A direct transient growth analysis for three-dimensional perturbations to flow past a periodic array of T-106/300 low-pressure turbine fan blades is presented. The methodology is based on a singular value decomposition of the flow evolution operator, linearised about a steady or periodic base flow. This analysis yields the optimal growth modes. Previous work on global mode stability analysis of this flow geometry showed the flow is asymptotically stable, indicating a non-modal explanation of transition may be more appropriate. The present work extends previous investigations into the transient growth around a steady base flow, to higher Reynolds numbers and periodic base flows. It is found that the notable transient growth of the optimal modes suggests a plausible route to transition in comparison to modal growth for this configuration. The spatial extent and localisation of the optimal modes is examined and possible physical triggering mechanisms are discussed. It is found that for longer times and longer spanwise wavelengths, a separation in the shear layer excites the wake mode. For shorter times and spanwise wavelengths, smaller growth associated with excitation of the near wake are observed.     

涡轮叶片蠕变全过程的修正Graham模型的参数识别

针对定向凝固镍基合金制造的航空发动机涡轮叶片,从涡轮叶片典型部位取材并设计制造模拟试件,在980℃下不同应力水平下进行单轴蠕变试验。对试验数据进行了唯象学的数学描述,并对ANSYS有限元分析软件中Graham蠕变模型进行了修正,使修正后的模型能够比较精确地描述单轴蠕变的全过程。并应用修正Graham模型对试验过程进行数值模拟,研究表明ANSYS有限元模拟蠕变的结果和试验数据吻合较好。这说明了修正Graham模型模拟单轴蠕变过程的合理性,该模型在一定程度上为ANSYS在金属材料蠕变分析方面的二次开发提供了理论基础。     

Two-equation turbulence models for prediction of heat transfer on a transonic turbine blade

Two versions of the two-equation k–ω model and a shear stress transport (SST) model are used in a three-dimensional, multi-block, Navier–Stokes code to compare the detailed heat transfer measurements on a transonic turbine blade. It is found that the SST model resolves the passage vortex better on the suction side of the blade, thus yielding a better comparison with the experimental data than either of the k–ω models. However, the comparison is still deficient on the suction side of the blade. Use of the SST model does require the computation of distance from a wall, which for a multi-block grid, such as in the present case, can be complicated. However, a relatively easy fix for this problem was devised. Also addressed are issues such as (1) computation of the production term in the turbulence equations for aerodynamic applications, and (2) the relation between the computational and experimental values for the turbulence length scale, and its influence on the passage vortex on the suction side of the turbine blade.     

Three-dimensional flow visualization in the wake of a miniature axial-flow hydrokinetic turbine

This paper examines the velocity profile of fuel issuing from a high-pressure single-orifice diesel injector. Velocities of liquid structures were determined from time-resolved ultrafast shadow images, formed by an amplified two-pulse laser source coupled to a double-frame camera. A statistical analysis of the data over many injection events was undertaken to map velocities related to spray formation near the nozzle outlet as a function of time after start of injection. These results reveal a strong asymmetry in the liquid profile of the test injector, with distinct fast and slow regions on opposite sides of the orifice. Differences of ～100 m/s can be observed between the ‘fast’ and ‘slow’ sides of the jet, resulting in different atomization conditions across the spray. On average, droplets are dispersed at a greater distance from the nozzle on the ‘fast’ side of the flow, and distinct macrostructure can be observed under the asymmetric velocity conditions. The changes in structural velocity and atomization behavior resemble flow structures which are often observed in the presence of string cavitation produced under controlled conditions in scaled, transparent test nozzles. These observations suggest that widely used common-rail supply configurations and modern injectors can potentially generate asymmetric interior flows which strongly influence diesel spray morphology. The velocimetry measurements presented in this work represent an effective and relatively straightforward approach to identify deviant flow behavior in real diesel sprays, providing new spatially resolved information on fluid structure and flow characteristics within the shear layers on the jet periphery.     

Three dimensional flow at the junction between a turbine blade and end-wall

A visualization of the flow on the suction side and end-wall of a passage between two neighboring turbine blades is compared with mass (heat) transfer measurements on the same surfaces. Besides the horseshoe and passage vortices, there are several smaller vortices formed near the junction of blade and end-wall whose origins are discussed. The vortices detach from the end-wall and move up the blade's span. These vortices, sometimes in counter rotating pairs, are responsible for substantial local variations of heat transfer.

---

Drei-dimensionale Strömung an der Naht zwischen Turbinenschaufel und Endwand

Zusammenfassung Der Durchfluß auf der Saugseite und an der Endwand eines Kanals zwischen zwei benachbarten Turbinenschaufeln wird sichtbar gemacht und mit gemessenen Massen-(Wärme)strömen der selben Oberflächen verglichen. Neben den hufförmigen Wirbeln und Durchflußwirbeln werden mehrere kleinere Wirbel in der Nähe der Verbindungsstelle von Schaufel und Endwand gebildet und die Ursache ihrer Entstehung wird diskutiert. Die Wirbel lösen sich von der Endwand ab und bewegen sich über die Spannweite der Schaufel. Diese Wirbel, manchmal als gegenläufige rotierende Paare, sind für die wesentlichen lokalen Variationen des Wärmeflusses verantwortlich.

---

Nomenclature AT Attachment line between counter-rotating vortices - C Chord length of the test blade, c.f. Fig. 1 b;C=16.91 cm in the present study - DE Detachment line between pairs of counter-rotating vortices - DL Flow dividing line-line along which surface flow divides into neighboring blade passages - Re ₁ Reynolds number based on cascade inlet velocity and blade chord length,U ₁ C/ - S _s Suction side curvilinear distance from the stagnation line of the test blade (see Fig. 1 b). Note thatS _s /C=1.355 at the trailing edge of the blades in the present study - U ₁ inlet velocity to the cascade - V _h the horseshoe vortex - V _Lc the leading edge corner vortex - V _p the passage vortex - V _ph pressure side leg of the horseshoe vortex - V _pLc pressure side leg of the leading edge corner vortex - V _s1 leading edge stagnation region vortex 1 - V _s2 leading edge stagnation region vortex 2 - V _sc1 suction side corner vortex 1 - V _sc1s portion ofV _sc1 which climbs up the blade suction surface - V _sc2 suction side corner vortex 2 - V _sc3 suction side corner vortex 3 - V _sh suction side leg of the horseshoe vortex - V _sLc suction side leg of the leading edge corner vortex - kinematic viscosity Dedicated to Prof. Dr.-Ing. F. Mayinger's 60th birthday     

涡轮叶片的持久寿命预测模型

镍基高温合金用于制造发动机的高压涡轮叶片.为了提高涡轮叶片持久寿命设计参数选取和设计方法的可靠性,从涡轮叶片代表性部位取材并设计、加工试验试件,进行持久寿命试验.试验过程中记录试件的变形量,进而推算出其蟠变应变,然后利用修正θ-Project Concept法来建立其持久寿命预测方程,并对其进行验证.     

An aerodynamic ROM of the blade subjected to wake based on Fourier method for flow

A reduced-order model (ROM) is presented based on Fourier method for flow to predict aerodynamic forces of blades subjected to periodic time-varying upstream wakes. In the method, a time-varying wake is decomposed into harmonic waves by fast Fourier transformation. Using the Fourier method for flow and neglecting the cross-coupling between harmonics, the aerodynamic forces caused by the wake are represented by a linear combination of harmonics with the same frequencies as the wake. The coefficients of the aerodynamic force harmonics are interpolated at the per-fitted curves of the normalized Fourier coefficients (coefficients of aerodynamic forces harmonics corresponding to a unit simple harmonic excitation)–frequency relationship. A blade example is used to show the ability of the proposed method. The results indicate that the ROM method can predict the aerodynamic forces of blades caused by wakes efficiently and accurately. The amplitude levels of wakes have a linear impact on the accuracy of the ROM. Neglecting the higher-order cross-coupling between the harmonics in the ROM method is acceptable.     

Separation-induced boundary layer transition: Modeling with a non-linear eddy-viscosity model coupled with the laminar kinetic energy equation

We present an effort to model the separation-induced transition on a flat plate with a semi-circular leading edge, using a cubic non-linear eddy-viscosity model combined with the laminar kinetic energy. A non-linear model, compared to a linear one, has the advantage to resolve the anisotropic behavior of the Reynolds-stresses in the near-wall region and it provides a more accurate expression for the generation of turbulence in the transport equation of the turbulence kinetic energy. Although in its original formulation the model is not able to accurately predict the separation-induced transition, the inclusion of the laminar kinetic energy increases its accuracy. The adoption of the laminar kinetic energy by the non-linear model is presented in detail, together with some additional modifications required for the adaption of the laminar kinetic energy into the basic concepts of the non-linear eddy-viscosity model. The computational results using the proposed combined model are shown together with the ones obtained using an isotropic linear eddy-viscosity model, which adopts also the laminar kinetic energy concept and in comparison with the existing experimental data.     

Effects of camberwise varying tip injection on loss and wake characteristics of a low pressure turbine blade

This paper presents the results of an experimental study that investigates the effects of camberwise varying tip injection on the total pressure loss and wake flow characteristics downstream of a row of Low Pressure Turbine (LPT) blades. This injection technique involves spanwise jets at the tip that are issued from a series of holes distributed along the camber line. The injection from each hole is individually and separately controlled using a computer driven solenoid valve and therefore the flow injection geometrical pattern at the tip can be adjusted to any desired variation. Three different injection cases are investigated including triangular, reversed triangular and uniform injection patterns. Here, triangular and reversed triangular cases refer to discrete blowing from the blade tip in which the blowing velocity increases (triangular) or decreases (reverse triangular) linearly from the leading to trailing edge along the camber. For uniform injection, the injection velocity is kept constant for all injection holes. The total mass injection from the tip is kept the same for all injection cases. The experiments are conducted in a continuous-flow wind tunnel with a linear cascade test section and measurements involve Kiel probe traverses 0.5 axial chords downstream of the blades covering a region between 85% and 100% span as well as two-dimensional Particle Image Velocimetry (PIV) measurements on 50%, 85% and 95% spanwise planes. For all injection cases, results show that tip injection reduces the total pressure loss levels in general. Highest measured overall loss reduction occurs in the case of reversed-triangular injection. The least effective waveform is observed to be triangular injection. There is significant reduction in the extent of the low momentum zone of the leakage vortex with injection. This effect is much less pronounced for the passage vortex. On the other hand, complex flow patterns are observed within the passage vortex, especially in the case of reversed-triangular injection, such as a possible embedded vortical structure along the passage vortex core, which creates double peaks in the velocity and turbulent kinetic energy fields.     

Revised Prandtl mixing length model applied to the two-dimensional turbulent classical wake

Previous applications of Prandtl׳s mixing length model to turbulent wake flows, which neglect the kinematic viscosity of the fluid, have underestimated the width of the boundary layer. In this paper, we present a revised Prandtl mixing length model by including the kinematic viscosity of the fluid. We show that this model predicts a boundary that lies outside the one predicted by Prandtl. We also prove that the results for the two models converge for very large Reynolds number wake flows.     

Effects of free stream turbulence on the distribution of heat transfer around turbine blade sections

Local convective heat transfer coefficients to a number of modern gas turbine blade sections have been measured under a wide range of mainstream conditions, from notionally steady flows to highly perturbed turbulent flows. The paper discusses the results and, through a detailed analysis of the pertinent boundary layer flow parameters and their relation to the observed experimental results, tests criteria for the occurrence of transition from laminar to turbulent boundary layers, a factor which all the data from this work confirm as critical in predicting the quantitative effects of mainstream turbulence on heat transfer rates. Artificially induced mainstream turbulence, which is endemic in the flows in a real turbine, enhances significantly the heat transfer rates, especially to the leading edge regions and on the pressure surface, particularly when the acceleration is tending to suppress transition. The results presented here confirm existing criteria for laminarisation and the applicability of some of those available for predicting laminar-turbulent transition. The observations also demonstrate how surface geometry can influence the stability of the flows, and the uncertainties which remain in assessing the effect of Goertler vortices and their role in the convective heat transfer process.     

Effect of finite depth of stratified flow on turbulence formation in the wake of a cylinder

The experimental results of investigating the effect of the finite depth of a linearly stratified flow channel on turbulence formation associated with the horizontal motion of a cylinder are presented. The limits of the interval of internal Froude numbers and dimensionless channel depths (with respect to the cylinder diameter) corresponding to local instabilites in the disturbed flow density distribution, leading to the formation of turbulence, are found. The dynamics of formation of the turbulent zones and their evolution are investigated. Unsteady periodic regimes are found.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 160–163, September–October, 1990.The authors are grateful to A. T. Onufriev for his interest in their work.     

Evaluation of an algebraic model for laminar-to-turbulent transition on secondary flow loss in a low-pressure turbine cascade with an endwall

The predictive qualities of a recently developed algebraic intermittency model for laminar-to-turbulent transition are analysed for the flow through a linear cascade of low-pressure turbine blades with an endwall. Both steady RANS (Reynolds-averaged Navier–Stokes) and time-accurate RANS (URANS) simulations are performed. The results are compared with reference LES (Large Eddy Simulation) by Cui et al. (2017, Numerical investigation of secondary flows in a high-lift low pressure turbine, Int. J. of Heat and Fluid Flow, vol. 63) and results by the local correlation-based intermittency transport model (LCTM) by Menter et al. (2015, A one-equation local correlation-based transition model. Flow Turbul. Combust., vol. 95) for laminar and turbulent endwall boundary layers at the cascade entrance. Good agreement is obtained with the reference LES and with results by the LCTM for the evolution through the cascade of the mass-averaged total pressure loss coefficient and for profiles of pitchwise-averaged total pressure loss coefficient at the cascade exit.