Cascade Of Airfoils Research Articles

Detached eddy simulation of the rotor-stator interaction phenomenon in a moving cascade of airfoils

Flow inside turbomachinery is fairly complex in general, due to the geometry complexity and the intrinsic structure of the flow. Rotor-Stator Interaction (RSI) has a strong influence on the machine behavior, especially when the machine is operating in off-design conditions, where flow complexity increases due to the presence of boundary layer detachment influencing the general flow pattern and creating pressure pulses that can enhance the RSI behavior. These interactions can have a significant impact on the vibrational and acoustical characteristics of the machine. For gaining insight in the RSI characteristics and the behavior of a turbomachinery under this kind of flow interaction, in this work the RSI generated between a moving cascade of airfoils and fixed flat plate located downstream was studied by means of Computational Fluid Dynamics (CFD) using Detached Eddy Simulation (DES). The upstream boundary layer influence on the wake of the moving cascade, and the subsequent wake-boundary layer interaction between the cascade and a fixed flat plate downstream were obtained and compared against experimental and previous numerical results (obtained with Eddy Viscosity Models). Design and off-design conditions were modeled and a detailed comparison between them has been made. To analyze in detail the flow pattern, mean and fluctuating velocities were obtained and compared against experimental results. Furthermore, results concerning to turbulence intensity were compared against an experimental database.

난류-캐스케이드 상호작용 소음 예측을 위한 Perfectly Matched Layer을 이용한 내부 입/출구 정상유동 경계조건의 개발

It is essential for the accurate time-domain prediction of broadband noise due to turbulence-cascade interaction to develop inflow/outflow boundary conditions to satisfy the following three requirements: to maintain the back ground mean flow, to nonreflect the outgoing disturbances and to generate the specified input gust. The preceding study showed that perfectly matched layer(PML) boundary condition was successfully applied to absorb the outgoing disturbances and to generate the specified gust in the time-domain computations of broadband noise due to interaction of incident gust with a cascade of flat-plates. In present study, PML boundary condition is extended in order to predict steady mean flow that is needed for the computation of noise due to interaction of incident gust with a cascade of airfoils. PML boundary condition is originally designed to absorb flow disturbances superimposed on the steady meanflow in the buffer zone. However, the steady meanflow must be computed before PML boundary condition is applied on the flow computation. In the present paper, PML equations are extended by introducing source term to maintain desired mean flow conditions. The extended boundary condition is applied to the benchmark problem where the meanflow around a cascade of airfoils is predicted. These illustrative computations reveal that the extended PML equations can effectively provide and maintain the target meanflow.

Lifing Requirement Based Turbine Airfoil Mass Estimation Method in Conceptual Aero-Engine Design

The presented paper describes a method developed by MTU Aero Engines to estimate the mass of turbine blades during multidisciplinary conceptual design studies based on a prescribed airfoil lifetime (Klingels, 2009, “Vordimensionierung von Turbinenschaufeln unter Berücksichtigung der Missionsanforderungen,” MTU Aero Engines, Technical Paper No. M09TET-0028, and Weisser, M., 2010, Erstellung und Implementierung eines erweiterten regelbasierten Verfahrens zur Schaufelauslegung mit Kühlluftmengenbestimmung in der Triebwerksvorauslegung, Diploma thesis, Institute of Aircraft Propulsion Systems, Universität Stuttgart, Stuttgart). For a given material, the target lifetime can be translated into a maximally allowable material temperature and stress level. While the latter has to be maintained by an appropriate mechanical design of the turbine blades, the material temperature needs to be established by sufficient cooling air. The predominant life-limiting effects are taken into account to determine the allowable temperatures and stresses as an accumulation of the varying operating condition over a flight cycle. The applicable stress levels are then used to calculate the necessary radial area distribution of the airfoil and by this a prediction of its mass is possible. Furthermore, the methodology estimates the required amount of cooling air per airfoil cascade from the computed material temperatures. Example calculations are presented and discussed which illustrate design trends and the benefits which are gained from the proposed method.

Third‐order sensitivity analysis for robust aerodynamic design using continuous adjoint

SUMMARYRobust design problems in aerodynamics are associated with the design variables, which control the shape of an aerodynamic body, and also with the so‐called environmental variables, which account for uncertainties. In this kind of problems, the set of design variables, which leads to optimal performance, taking into account possible variations in the environmental variables, is sought. One of the possible ways to solve this problem is by means of the second‐order second‐moment approach, which requires first‐order and second‐order derivatives of the objective function with respect to the environmental variables. Should the minimization problem be solved using a gradient‐based method, algorithms for the computation of up to third‐order sensitivity derivatives (twice with respect to the environmental variables and once with respect to the shape controlling design variables) must be devised. In this paper, a combination of the continuous adjoint variable method and direct differentiation to compute the third‐order sensitivities is proposed. This is shown to be the most efficient among all alternative methods provided that the environmental variables are much less than the design ones. Apart from presenting the method formulation, this paper focuses on the assessment of the so‐computed up‐to third‐order mixed derivatives through comparison with costly finite‐difference schemes. To this end, the robust design of a two‐dimensional duct is performed. Then, using the validated method, the robust design of a two‐dimensional cascade airfoil is demonstrated. Although both cases are handled as inverse design problems, the method can be extended to other objective functions or three‐dimensional problems in a straightforward manner. Copyright © 2012 John Wiley & Sons, Ltd.

An assessment of the laminar kinetic energy concept for the prediction of high-lift, low-Reynolds number cascade flows

The laminar kinetic energy (LKE) concept has been applied to the prediction of low-Reynolds number flows, characterized by separation-induced transition, in high-lift airfoil cascades for aeronautical low-pressure turbine applications. The LKE transport equation has been coupled with the low-Reynolds number formulation of the Wilcox's k − ω turbulence model. The proposed methodology has been assessed against two high-lift cascade configurations, characterized by different loading distributions and suction-side diffusion rates, and tested over a wide range of Reynolds numbers. The aft-loaded T106C cascade is studied in both high- and low-speed conditions for several expansion ratios and inlet freestream turbulence values. The front-loaded T108 cascade is analysed in high-speed, low-freestream turbulence conditions. Numerical predictions with steady inflow conditions are compared to measurements carried out by the von Kármán Institute and the University of Cambridge. Results obtained with the proposed model show its ability to predict the evolution of the separated flow region, including bubble-bursting phenomenon and the formation of open separations, in high-lift, low-Reynolds number cascade flows.

Unsteady gasdynamics of a linear cascade of airfoils executing small harmonic vibrations

Numerical modeling of inviscid compressible gas flow past a linear cascade of airfoils executing small harmonic translational and rotational vibrations is carried out. The control volume method on moving unstructured grid structures is used for discretization of basic equations. The influence of the frequency and phase characteristics of the airfoils on the pressure distribution over their surface and the lift coefficient is investigated. The results of numerical calculations are compared to the available calculated and experimental data.

Aerodynamic design using the truncated Newton algorithm and the continuous adjoint approach

AbstractIn this paper, the so‐called ‘continuous adjoint‐direct approach’ is used within the truncated Newton algorithm for the optimization of aerodynamic shapes, using the Euler equations. It is known that the direct differentiation (DD) of the flow equations with respect to the design variables, followed by the adjoint approach, is the best way to compute the exact matrix, for use along with the Newton optimization method. In contrast to this, in this paper, the adjoint approach followed by the DD of both the flow and adjoint equations (i.e. the other way round) is proved to be the most efficient way to compute the product of the Hessian matrix with any vector required by the truncated Newton algorithm, in which the Newton equations are solved iteratively by means of the conjugate gradient (CG) method. Using numerical experiments, it is demonstrated that just a few CG steps per Newton iteration are enough. Considering that the cost of solving either the adjoint or the DD equations is approximately equal to that of solving the flow equations, the cost per Newton iteration scales linearly with the (small) number of CG steps, rather than the (much higher, in large‐scale problems) number of design variables. By doing so, the curse of dimensionality is alleviated, as shown in a number of applications related to the inverse design of ducts or cascade airfoils for inviscid flows. Copyright © 2011 John Wiley & Sons, Ltd.

Detailed study of the rotor-stator interaction phenomenon in a moving cascade of airfoils

In turbomachinery the Rotor-Stator Interaction (RSI) is an important phenomenon that has a strong influence on the machine behavior. These interactions can have a significant impact on the vibrational and acoustical characteristics of the machine. Unsteadiness and turbulence play a fundamental role in complex flow structure and the use of Computational Fluid Dynamics (CFD) is becoming a usual requirement in design in turbomachinery due to the difficulties and high cost of the necessary experiments needed to identify RSI phenomena. The flow inside a turbomachinery working under design condition is complex but apparently, when working under off-design conditions, it becomes more complex due to the boundary layer separation phenomena. Therefore, the choice of an appropriate turbulence model is far from trivial and a suitable turbulence modeling plays a very important role for successful CFD results. In this work the RSI generated between a moving cascade of blades and fixed flat plate located downstream were studied by means of CFD modeling and compared against experimental results. Design and off-design conditions were modeled and a detailed comparison between them has been made. To analyze in detail the flow pattern, mean velocities in the boundary layer were obtained and compared against experimental results. Furthermore, results concerning to turbulence intensity were compared against an experimental database. It was observed that for each operating condition, the flow in the cascade show special features. For flow inside the turbomachine under design conditions there is no separation, the wake is thin and the characteristic length of the eddies is small. For off-design conditions, there is a large separation and the wake is thick with large eddies. The results obtained can be used to obtain a deeper insight into the RSI phenomena.

Distributed evolutionary algorithms with hierarchical evaluation

A distributed evolutionary algorithm is presented that is based on a hierarchy of (fitness or cost function) evaluation passes within each deme and is efficient in solving engineering optimization problems. Starting with non-problem-specific evaluations (using surrogate models or metamodels, trained on previously evaluated individuals) and ending up with high-fidelity problem-specific evaluations, intermediate passes rely on other available lower-fidelity problem-specific evaluations with lower CPU cost per evaluation. The sequential use of evaluation models or metamodels, of different computational cost and modelling accuracy, by screening the generation members to get rid of non-promising individuals, leads to reduced overall computational cost. The distributed scheme is based on loosely coupled demes that exchange regularly their best-so-far individuals. Emphasis is put on the optimal way of coupling distributed and hierarchical search methods. The proposed method is tested on mathematical and compressor cascade airfoil design problems.

Aerodynamic characteristics of a thin airfoil cascade in an ideal incompressible flow with separation from the leading edges

A new method of solving the problem of separation flow past a cascade of thin airfoils is proposed. The method is based on the model of separated flow past a single airfoil in which vortex wakes shed from the airfoil edges are modeled by vortex layers with time-averaged intensities. Under the assumption of a small deviation of the freestream angle α from the “impactless entry” angle α0 the singular integral equation governing the flow kinematics is closed by a dynamic equation. It is shown that the separation effect on the time-averaged aerodynamic characteristics of the cascade is associated with the total pressure loss due to the flow energy expenditure on the vortex wake formation. The aerodynamic characteristics of the cascade calculated with and without account for flow separation differ by the second-order quantity ɛ = α − α0.

Decomposition of modal acoustic power due to cascade–turbulence interaction

This paper investigates the modal acoustic power (MAP) generated by a cascade of flat-plate airfoils interacting with homogeneous, isotropic turbulence. The basic formulation for the upstream and downstream acoustic power based on the analytical theory of Smith [Discrete frequency sound generation in axial flow turbomachines, Reports and Memoranda no. 3709, Aeronautical Research Council, 1972] and its generalization to broadband noise due to Cheong et al. [High frequency formulation for the acoustic power spectrum due to cascade–turbulence interaction. Journal of the Acoustical Society of America 119 (2006) 108–122]. The MAP has been expressed as the sum of cut-on acoustic modes, whose modal power is the product of three terms: a term that specifies the wavenumber distribution of mean square velocity, a sound power factor that specifies the efficiency of radiation, and an acoustic blade response function. The effect of these terms on the MAP is discussed in detail in this paper. The acoustic blade response functions are found to determine the modal lines of minimum sound power in mode-frequency maps of the MAP. The upstream sound power factor is less than the downstream power factor, which is generally large, especially away from the cut-off frequency. Both power factors are small for modes close to cut-off. Modes close to cut-off, therefore, do not contribute significantly to the radiated acoustic power in the downstream direction, even though the modal pressure amplitude for these modes is high since they are excited close to resonance. For an isotropic turbulent gust, the mean square velocity wave number spectrum reduces only the magnitude of the MAP without altering the distribution of power in the frequency-mode map.

Numerical Investigation of Tandem Airfoils for Subsonic Axial-Flow Compressor Blades

The tandem airfoil has potential to do more work as a compressor blade than a single airfoil without incurring significantly higher losses. Although tandem blades are sometimes employed as stators, they have not been used in any known commercial rotors. While the long-term goal for this program is development of a commercially viable tandem rotor, this paper discusses tandem airfoils in subsonic, shock-free rectilinear cascade flow. Existing literature data on tandem airfoils in rectilinear cascades have been compiled and presented in a Lieblein loss versus loading correlation. Large scatter in the data gave motivation to conduct an extensive 2D computational fluid dynamics (CFD) study evaluating the overall performance as a function of the relative positions of the forward and aft airfoils. CFD results were consistent with trends in the open literature, both of which indicate that a properly designed tandem airfoil can outperform a comparable single airfoil on and off design. The general agreement of the CFD and literature data serves as a validation for the computational approach.

205 航空エンジン用高負荷低圧タービン翼面上境界層の非定常挙動に関する実験及びCFD(流体工学II)

205 航空エンジン用高負荷低圧タービン翼面上境界層の非定常挙動に関する実験及びCFD(流体工学II)

The continuous direct-adjoint approach for second order sensitivities in viscous aerodynamic inverse design problems

A novel continuous adjoint approach for the computation of the second order sensitivities of the objective function used in inverse design problems is proposed. In the framework of the Newton method, the proposed approach can be used to efficiently cope with inverse design problems in viscous flows, where the target is a given pressure distribution along the solid walls. It consists of two steps and will, thus, be referred to as the direct-adjoint approach. At the first step, the direct differentiation method is used to compute the first order sensitivities of the flow variables with respect to the design variables and build the gradient of the objective function. At the second step, the adjoint approach is used to compute the second order sensitivities. The final Hessian expression is free of field integrals and its computation requires the solution of N + 1 equivalent flow (system) solutions for N design variables. Since the CPU cost of using the Newton method, with exact gradient and Hessian data at each cycle, becomes prohibitively high, an approach that computes the exact Hessian only once and then updates it in an approximated manner through the BFGS formula, is used instead. The accuracy of the Hessian matrix components, computed using the direct-adjoint approach is demonstrated on the inverse design of a diffuser and a cascade airfoil.

Aerodynamics lattices profiles Gas Mechanic

It was a short review of all means, which allow providing a steady flow in the gas turbine engine. It was proposed to consider the airfoil cascade with gas-mechanical regulation as an object with definite aerodynamic characteristics. On the base of the computation of the gas flow through airfoil cascade for different flow operating modes and taking into account the torque of external force, aerodynamic characteristics of the airfoil cascade with gas-mechanical regulation in wide diapason of inlet angel were made. Their comparison with aerodynamic characteristics of unmovable airfoil cascade confirms big advantage of airfoil cascade with gas-mechanical regulation. First of all their characteristics are stable in all possible diapason of inlet flow angel. That gives a chance to solve all problems of gas-dynamics stability and injectivity of a gas turbine engine.

Analytical Modeling of Turbine Cascade Leading Edge Heat Transfer Using Skin Friction and Pressure Measurements

The flow near the leading edge stagnation line of a plane turbine cascade airfoil is analyzed using measurements, analytical modeling, and computational fluid dynamics modeling. New measurements of skin friction and pressure are used to show that the aerodynamics of the leading edge, within what we call the stagnation region, are well described by an exact analytical solution for laminar stagnation-point or Hiemenz flow. The skin friction measurements indicate the extent of the stagnation region. The same parameters that characterize Hiemenz flow also characterize stagnation-point potential flow. The thermal resistance of the laminar momentum boundary layer in Hiemenz flow is absent in the inviscid solution. Consequently, the heat transfer in stagnation-point potential flow is greater than the heat transfer in Hiemenz flow. Based on measurements from an earlier study, the highest heat transfer levels in the cascade occur along the leading edge stagnation line. Stagnation-point potential flow provides a close, upper bound for the measured heat transfer at this small but critical location within the stagnation region. This paper describes how to apply the analytical model for predicting cascade stagnation-line heat transfer using only surface pressure calculations.

A multilevel approach to single- and multiobjective aerodynamic optimization

An optimization platform with multilevel structure, which is capable of efficiently solving design-optimization problems in aerodynamics, is proposed. The multilevel structure relies on a two-way regular exchange of information between successive search levels. Each level can be associated with a different evaluation software, different problem parameterization and/or different search tool, for the minimization of the same objective function(s). The combination of some or all of the aforementioned strategies is possible, although beyond the scope of this paper. The basic optimization tool, which is associated with at least one of the levels, is a metamodel-assisted evolutionary algorithm; candidate solutions that have previously been examined are memorized and serve to train radial basis function networks, operating as local surrogate evaluation models. To handle multiobjective optimization problems with different search techniques at each level, we hybridize an evolutionary algorithm that computes the front of Pareto optimal solutions at the lower level(s) with a gradient-based method at the upper level, for the purpose of refinement through local search. In aerodynamic optimization, the adjoint method is used to compute the gradient of the objective function. For the gradient method to apply to a front of solutions rather than a single individual, an approximation of the SPEA-2 utility function gradient needs to be devised. The multilevel platform is demonstrated on mathematical problems as well as the design of isolated and compressor cascade airfoils.

Mathematical modeling of the sound induced in a subsonic flow around cascades in relative motion

A method of mathematical modeling of the tonal sound induced by the unsteady aerodynamic interaction of two plane airfoil cascades in a subsonic flow and in uniform relative motion in the direction of their fronts is developed. The method is based on the numerical integration of the unsteady flow equations using a simplified model for the periodic system of edge wakes shed from the airfoils of the first (leading) cascade in the viscous flow and acting on the second (trailing) cascade. An analysis of the distinctive features of the flow under consideration demonstrates the efficiency of the model proposed.

평판 에어포일 캐스케이드와 입사 난류의 상호작용에 의한 광대역 소음의 모달 음향 파워 특성

This paper investigates the modal acoustic power by a cascade of flat-plate airfoils interacting with homogeneous, isotropic turbulence. Basic formulation for the acoustic power upstream and downstream is based on the analytical theory of Smith and its generalization due to Cheong et al. The acoustic power spectrum has been expressed as the sum of cut-on acoustic modes, whose modal power is the product of three terms: a turbulence series, an upstream or downstream power factor and an upstream or downstream acoustic response function. The effect of these terms in the modal acoustic power has been examined. For isotropic turbulence gust, the turbulent series are only reducing factor of the modal acoustic power. The power factor tends to reduce the modal acoustic power in the upstream direction, although the power factor is liable to increase the modal acoustic power in the downstream direction. The modes close to cut-off are decreasing strongly, especially in the downstream direction. Therefore the modes close to cut-off don't contribute highly to the radiated acoustic power in the downstream direction, although the modal acoustic pressure is high for these modes.

Studies on High-Lift LP Turbine Airfoils of Aero Engines (Understanding of Boundary Layer Transitional Behaviour on Time-Space Diagram under the High Lift and Ultra High Lift Conditions)

This paper details experimental studies on the flow field around a linear cascade of low-pressure turbine airfoils whose solidity is changeable. Highly loaded low-pressure turbine (LPT) blades are one of the key paths to successful future aero-engines, however these blades are usually accompanied with separation bubble, eventually leading to the increase in aerodynamic performance. The purpose of this study is therefore to clarify any favorable effects of incoming wakes upon the aerodynamic loss of high-lift or ultra high-lift rotor blade cascade through the measurements of wake-affected boundary layers including separation bubble under low Reynolds number conditions. Cylindrical bars on the timing belts work as wake generator to emulate upstream stator wakes that impact the rotor blade. Hot-wire probe measurement is conducted over the blade suction surface to understand to what extent and how the incoming wakes affect the boundary layers containing separation bubble. Time-dependent transitional behaviors due to the wake passing are examined through the detailed inspection of several composite maps of flow properties displayed on time-space diagrams.