Cascade Of Airfoils Research Articles

Dynamic mode decomposition analysis of plasma aeroelastic control of airfoils in cascade

A dynamic mode decomposition (DMD) is carried out for the flow field in a compressor cascade with plasma actuators employed for aeroelastic control. Numerical assessments performed in previous works have shown that alternate triggering of pressure side/suction side actuators installed at the trailing edge of the blades can effectively reduce vibratory loads and enlarge the flutter boundaries of a linear compressor cascade. With the twofold aim of obtaining an in-depth understanding of the flow physics associated to plasma actuation and ultimately developing an optimized control law for the actuators, the dominant structures of the pressure field are extracted via a dynamic mode decomposition. The decomposition is conducted on the actuated and non-actuated pressure fields at several inter blade phase angles. The fundamental effects of plasma actuations on the flow field, and in turn on the blade loading, are identified and discussed. The procedure allows obtaining an useful picture of the main fluid mechanic phenomena associated to plasma aeroelastic control on turbomachinery blades. Additionally, the DMD spectrum and its coherence are analysed, yielding a wider energetic spread over high-order modes for the plasma-actuated case, in comparison to the clean cascade.

Rapid method of Predicting the Subsonic Flutter Stability of AGTE Axial-Flow Compressor Blade Cascades. Part 2. Mathematical Implementation of Method and its Potentional Application

The paper considers the implementation of the rapid method of predicting the dynamic stability of the compressor blade assemblies against subsonic flutter. The first flexural mode of blade vibrations is analyzed at the design stage for a wide range of the angle of attack based on the developed database of the critical values of the reduced vibration frequency in straight cascades of blade airfoils. The multiple regression equation is developed that depends on the relative blade spacing and stagger angle of the straight cascade of blade airfoils, coefficient of the flexural-torsional coupling of the blade, and angle of attack with the correlation factor of the studied parameters in the range of 0.92–0.98. Using the obtained equation, the numerical program has been developed for the determination of the dynamic stability limit against subsonic flutter for the first flexural mode of the blade vibrations. The program allows one to find the numerical values of critical reduced frequencies as the characteristics of its dynamic stability and determine their dependence on the angle of attack. The results of practical application of the developed program are presented using the assessment of the dynamic stability of the flexural mode of axial compressors in four modern aircraft gas-turbine engines. It is shown that at the design engine stage it is possible to select the reduced vibration frequencies of the blade assembly for the specified geometry of its peripheral sections and angle of attack of the inflow upon the condition of the occurrence of subsonic flutter.

РЕЗУЛЬТАТЫ ОЦЕНКИ ДИНАМИЧЕСКОЙ УСТОЙЧИВОСТИ К ДОЗВУКОВОМУ ФЛАТТЕРУ ЛОПАТОЧНЫХ ВЕНЦОВ КОМПРЕССОРОВ НЕКОТОРЫХ АВИАЦИОННЫХ ГАЗОТУРБИННЫХ ДВИГАТЕЛЕЙ

The paper outlines the results of the investigation on the verification of the express method of prediction of dynamic stability for subsonic flutter using the blade assemblies of individual stages of the compressor of some types of aircraft gas-turbine engines at different modes of their operation. The paper gives a brief overview of the basic concepts of the developed express estimation method, possibilities of the determination of the stability limit for the blade assemblies for a subsonic flutter, as well as the results of the assessment of the dynamic stability of the compressor stages of some modern aircraft gas-turbine engines. Firstly, the reduced frequencies of vibrations of the blade assemblies under investigation and their critical values coincide practically. The mentioned critical values were determined from the test data for the straight cascades of the blade airfoils corresponding to two sections of the height of the blade airfoil portion. Hence it follows that the task can be solved employing only gas-dynamic parameters of the flow for one of the sections of the airfoil within the specified range of its height. Secondly, the prediction of dynamic stability for the subsonic flutter of the blade assemblies of separate compressor stages of some types of aircraft gas-turbine engines and the comparison of the obtained results with the data of bench tests, as well as the data obtained using other methods, were made. It was implied that the developed method allows one to determine the flutter limit with high accuracy, as well as make an optimal selection of the values of the reduced frequency of the blade vibrations for the specified range of the angle of attack of the sections of the blade assemblies upon the condition of its occurrence. Thirdly, the possibility to determine the nature of vibration excitation for the blade assemblies is considered using the analysis of the initiation of cracks in the blade root of the first compressor stage of the high-pressure gas-turbine engine. Moreover, it is shown that at large angles of attack (≥ 10°) an insignificant displacement of the dynamic stability limit of the blade assemblies may occur in the direction of large values of the reduced frequency of their vibrations.

Modelling of Vane and Rotor Blade Rows in Simulations of Gas Turbine Performance

Abstract A method of modelling of nozzle and rotor blade rows of gas turbine dedicated to simulations of gas turbine performance is proposed. The method is applicable especially in early design stage when many of geometric parameters are yet subject to change. The method is based on analytical formulas derived from considerations of flow theory and from cascade experiments. It involves determination of parameters of gas flow on the mean radius of blade rows. The blade row gas exit angle, determined in turbine design point is a basis for determination of details of blade contour behind the throat position. Throat area is then fixed based on required maximum mass flow in critical conditions. Blade leading edge radius is determined based on flow inlet angle to the blade row in the design point. The accuracy of analytical formulas applied for definition of blade contour details for assumed gas exit angle was verified by comparing the results of analytical formulas with CFD simulations for an airfoil cascade. Losses of enthalpy due to non-isentropic gas flow are evaluated using the analytical model of Craig and Cox, based on cascade experiments. Effects of blade cooling flows on losses of total pressure of the gas are determined based on analytical formulas applicable to film cooling with cooling streams blowing from discrete point along blade surface, including leading and trailing edges. The losses of total pressure due to film cooling of blades are incorporated into the Craig and Cox model as additional factor modifying gas flow velocities.

An experience-independent inverse design optimization method of compressor cascade airfoil

Most of the inverse design methods of turbomachinery experience the shortcoming where the target aerodynamic parameters need to be manually specified depending on the designers’ experience and insight, making the design result aleatory and even deviated from the real optimal solution. To tackle this problem, an experience-independent inverse design optimization method is proposed and applied to the redesign of a compressor cascade airfoil in this study. The experience-independent inverse design optimization method can automatically obtain the target pressure distribution along the cascade airfoil through the genetic algorithm, rather than through the manual specification approach. The shape of cascade airfoil is then solved by the adjoint method. The effectiveness of the experience-independent inverse design optimization method is demonstrated by two inverse design cases of the compressor cascade airfoil, i.e. the inverse design of only the suction surface and the inverse design of both the suction and pressure surfaces. The results show that the proposed inverse design method is capable of significantly improving the aerodynamic performance of the compressor cascade. At the examined flow condition, a thin airfoil profile is beneficial to flow accelerations near the leading edge and flow separation avoidance near the trailing edge. The proposed inverse design method is quite generic and can be extended to the three-dimensional inverse design of advanced compressor blades.

Performance Analysis of Elliptic-Profile Airfoil Cascade for Designing Reversible Axial Flow Fans

Because reversible fans must be able to provide similar performance in either rotation direction, they need to have completely symmetrical blades. In the present study, an elliptic profile with its maximum thickness of 8% chord length at the middle of the chord line is studied. For verification, the NACA 0012 airfoil was once analyzed two-dimensionally in the isolated formation and once in cascade formation with 0.55 and 0.83 solidities, and the obtained results were compared with numerical and experimental results. Three well-known Reynolds-averaged Navier–Stokes turbulence models including Spalart–Allmaras, realizable , and shear-stress transport were used to find the suitable turbulence method. After making sure of the accuracy of the modeling procedure, lift and drag coefficients were calculated for the elliptic profile for a wide range of velocities, solidities, and angles of attack. A number of issues not previously addressed in detail by previous works, such as the important stall phenomenon at low solidities, were solved, and the obtained aerodynamic coefficients were corrected by considering the occurrence of the stall. Finally, the method of using the colored cube for the design procedure of these blades was also proposed to reduce the gap between the design and the desired outcome.

Effect of Planar Member Cross-Section on Cascade Fin Aerodynamics

Grid fins are unconventional control and lifting surfaces consisting of an outer frame supporting an inner grid of small chord intersecting planar surfaces. Credited for their enhanced lifting characteristics at high angles of attack and wider Mach number regimes, minuscule hinge moments, and increased drag, these have been used in numerous aerospace applications. Removal of their cross-members leads to its simplified variant called cascade fins. The present study carries out numerous viscous computational fluid dynamics simulations at subsonic speed and high angles of attack to investigate and compare the impact of the horizontal planar member cross-sectional shape on cascade fin aerodynamics by elucidating the effects of using a NACA 0012 airfoil cross-section instead of a rectangular cross-section and varying the gap between their members. Appreciably higher aerodynamic efficiency attributed to drag reduction and comparable lifting characteristics along with steeper and hastened stall characteristics was deciphered for airfoil cascades. It was also found that optimally reducing the gap alleviates the stall tendency. These trends were further explained using pressure distribution plots and flow visualization analysis for the respective variant. Thus, planar member cross-section and gap selection should be done based on the aerodynamic efficiency requirement, desired maneuverability, and manufacturing cost.

Determination of the Subsonic Flutter Stability Boundary of Blade Rows at Large Angles of Attack

This paper presents an experimental-and-numerical method for determination of the subsonic flutter stability boundary of blade rows at large angles of incident flow. The aerodynamic test rig for determining the unsteady aerodynamic loads is described. The test results are presented for a straight cascade of airfoils in a wide range of variation in the angle of attack and reduced vibration frequency, based on which the regularities in the effect of the angle of attack on the subsonic flutter stability boundary of blading are established.

Aerodynamic Influence of Oscillating Adjacent Airfoils in a Linear Compressor Cascade

Turbomachinery aeroelasticity is gaining renewed interest in the light of current trends, which tend toward thinner blade designs that are not only highly loaded, but also have minimal weight. This necessitates studies of many unsteady aerodynamic phenomena that now occur in acute forms. The present paper investigates the aerodynamic influence of vibrating blades in a compressor cascade using a two-dimensional cascade of airfoils subjected to controlled oscillation. In particular, the pressure distribution and moment on a given airfoil, when its two neighboring airfoils are oscillating sinusoidally at specified phase-difference angles, are investigated. The experimental results are used to establish the relation between the pressure field experienced by the central airfoil and the phase difference between the oscillating blades. The computational results are used additionally to study the secondary phenomenon of flow separation observed when the pressure distribution is such that the local flow incidence to the stationary airfoil is increased. Both the effects are examined quantitatively from the point of the flow being governed by the axial pressure gradient, showing how the geometry of the boundaries, together with the localized flow accelerations, can affect the global flowfield to cause varying amplitudes and phases of unsteadiness in the load.

Advanced Endwall Contouring for Loss Reduction and Outflow Homogenization for an Optimized Compressor Cascade

The following paper deals with the development of an optimized non-axisymmetric endwall contour for reducing the total pressure loss and for homogenizing the outflow of a highly-loaded compressor cascade. In contrast to former studies using a NACA-65 K48 cascade airfoil this study starts with the design of a new high-performance airfoil which is based on the aerodynamic boundary conditions of the NACA-65 K48 cascade. This new airfoil is then used as a basis. Optimizations of the airfoil and of the endwall contour are performed using the German Aerospace Center (DLR) in-house tool AutoOpti and the RANS (Reynolds-averaged Navier-Stokes)-solver TRACE (Turbomachinery Research Aerodynamic Computational Environment). Three operating points at an inflow Mach number of 0.67 with different inflow angles are used to secure a wide operating range. The optimized endwall contour changes the secondary flow in such a way that the corner stall is reduced which, in turn, significantly reduces the total pressure loss. The endwall contour in the outflow region leads to a considerable homogenization of the outflow in the near wall region. Using non-axisymmetric endwall shaping demonstrates a valuable measure to further improve highly-efficient compressor blading on the vane level.

Influence of various design parameters and unsteady flow on the fluid–structure interaction of a lightly cambered blade in a cascade

The aim of this paper is to report the results of the fluid–structure interaction study of a lightly cambered blade in a cascade under the influence of various inflow conditions and structural parameters, in a cost–effective manner. This work could be viewed as a preliminary design tool that provides the behavioral trend of the blade motion which will be useful when a detailed analysis has to be performed. The methodology employed to formulate the aerodynamic model for lightly cambered airfoils follows the Whitehead's aerodynamic theory for a cascade of flat plates. The aerodynamic loads acting on a blade in a cascade of airfoils are computed to provide the required conditions for the structural model. The aeroelastic model thus formulated is employed to predict the structural response of a blade in a cascade subjected to both steady and unsteady flows. The possibilities of a blade undergoing pure bending or torsion, or coupled bending–torsion flutter are investigated in the present study. The utility of the already developed aerodynamic model is demonstrated by investigating the structural behavior of three different blade curvature profiles – Double Circular Arc (DCA), NACA 65, and NACA a=1.0 mean lines. The effects of various blade structural parameters such as mechanical damping, center of gravity and elastic axis offset, and cascade geometric parameters such as stagger angle and blade spacing on the blade aeroelastic response are analyzed. The flutter boundary for a range of frequency ratios is then examined. It has been found that compressor blades with frequency ratios close to unity are vulnerable to coupled bending–torsion flutter under the influence of an incoming steady flow. The growing torsional vibrations are in general registered for higher values of air velocity compared to the range of velocities favoring bending flutter. The influence of different compressor unsteady flows – rotating stall and surge, on the aeroelastic behavior of a lightly cambered blade is also examined in the present study.

FLOW MODELLING AT COMPRESSOR CASCADE WITH TURBULATORS ON BLADE SURFACE

The research of boundary layer control at compressor blade row is actually. It is practical interest to solve the problem of providing of gas-dynamic stability of compressors of gas turbine engines. Aim of work is to investigate the effect of the placement density of turbulators on blade surface at the loss level at the critical flow mode. Flow at airfoil cascade with different placement densities is studied in work. Roughness elements were placed at the entrance of the blade witch was 30% of the surface area of the blade. The characteristics of airfoil cascades at placement density coefficient 0.36, 0.24, 0.18 were investigated. Shape of roughness element is hemisphere. Using of roughness elements at the entrance of the blade with a placement density coefficient 0.18…0.36 lead to a decreasing in value of total pressure loss coefficient at critical flow mode from 0.084…0.12 (for cascade with smooth blades) to 0.03…0.041

Area Schedule Based Design of High-Pressure Recovery Radial Diffusion Systems

High-pressure ratio centrifugal compressors require advanced diffusion systems to achieve enhanced efficiencies set by future turbocharger applications. To address the shortcomings of the commonly used channel diffuser and airfoil cascade design perspectives, a streamtube based area schedule is adopted paying special attention to the diffuser entry region. It is shown that the diffusion in the semivaneless space, controlled chiefly by inlet flow angle and the vane suction side geometry, plays a key role in improving diffuser performance. Removing excess thickness from the suction side eliminates flow overspeed, increases effective diffusion length, and leads to higher pressure recovery at reduced stagnation pressure loss. The pressure side thickness distribution controls the channel area schedule. Thin leading edges (LEs) ensure smooth flow area transition into the channel and reduce the vane upstream influence, mitigating high-cycle fatigue related mechanical issues.

Effect of Leading-Edge Tubercles on Compressor Cascade Performance

Tubercles are modifications to the leading edge of an airfoil in the form of blunt wave-like serrations. Several studies on the effect of tubercles on isolated airfoils have shown a beneficial effect in the poststall regime as reduced drag and increased lift, leading to a delay of stall. The prospect of delaying stall is particularly attractive to designers of axial compressors in gas turbines, because this leads to designs with higher loading and therefore higher pressure rise with fewer number of stages. In the present study, experiments were performed on a cascade of airfoils with a NACA 65209 profile with different tubercle geometries. The measurements were made over an exit plane using a five-hole probe to compare the cascade performance parameters. Additionally, hot-wire measurements were taken near the blade surface to understand the nature of the flow in the region close to the tubercles. Oil-flow visualization on the cascade end wall reveals the flow through the passage of blades with and without tubercles. For the cascade considered, the estimated stall angle for the best performing set of blades is found to increase up to 8.6 deg from that of the unmodified blade of 6.0 deg. Application of such structures in axial compressor blades may well lead to suppression of stall in axial compressors and extend the operating range.

Experimental Investigation of Louver Cooling Scheme on Gas Turbine Stator

An experimental investigation has been conducted to investigate the film cooling performance of the louver scheme over the surface of a gas turbine stator using a transient thermochromic liquid crystal technique. A two-dimensional airfoil cascade has been employed during the study. The exit Reynolds number based on the true chord length is 1.5E5 and the exit Mach number is 0.23. Two rows of an axially oriented louver scheme are distributed on both suction and pressure sides in a staggered arrangement. The effect of hole location on the cooling performance is investigated for each row individually; then row interaction is investigated at four different blowing ratios ranging from 1 to 2 and a 0.9 density ratio. The detailed local performance distribution and the lateral-averaged normalized performance are presented over both sides of the vane in terms of heat transfer coefficient and cooling effectiveness. The louver scheme provides a better cooling performance compared with the similar cylindrical scheme of the same base diameter at the same cooling amount. The blowing ratio does not influence significantly the performance for the louver scheme due to the considerable decrease in the jet momentum that impedes the jet lift-off at exit. The location of the scheme exit has a high impact on the cooling performance as it affects the development of the boundary layer. The double injection on the pressure side provides a superior effectiveness due to the blockage of the mainstream by the coolant injected from the first row. The louver scheme provides higher net heat flux reduction, which suits the cooling capacity needed for the next generation of gas turbines.

Time-domain inflow boundary condition for turbulence–airfoil interaction noise prediction using synthetic turbulence modeling

The present paper deals with development of the synthetic turbulence inflow boundary condition (STIBC) to predict inflow broadband noise generated by interaction between turbulence and an airfoil/a cascade of airfoils in the time-domain. The STIBC is derived by combining inflow boundary conditions that have been successfully applied in external and internal computational aeroacoustics (CAA) simulations with a synthetic turbulence model. The random particle mesh (RPM) method based on a digital filter is used as the synthetic turbulence model. Gaussian and Liepmann spectra are used to define the filters for turbulence energy spectra. The linearized Euler equations are used as governing equations to evaluate the suitability of the STIBC in time-domain CAA simulations. First, the velocity correlations and energy spectra of the synthesized turbulent velocities are compared with analytic ones. The comparison results reveal that the STIBC can reproduce a turbulent velocity field satisfying the required statistical characteristics of turbulence. Particularly, the Liepmann filter representing a non-Gaussian filter is shown to be effectively described by superposing the Gaussian filters. Each Gaussian filter has a different turbulent kinetic energy and integral length scale. Second, two inflow noise problems are numerically solved using the STIBC: the turbulence–airfoil interaction and the turbulence-a cascade of airfoils interaction problems. The power spectrum of noise due to an isolated flat plate airfoil interacting with incident turbulence is predicted, and its result is successfully validated against Amiet׳s analytic model (Amiet, 1975) [4]. The prediction results of the upstream and downstream acoustic power spectra from a cascade of flat plates are then compared with Cheong׳s analytic model (Cheong et al., 2006) [30]. These comparisons are also in excellent agreement. On the basis of these illustrative computation results, the STIBC is expected to be applied to investigate more complicated inflow noise problems including the effects of non-uniform mean flow, nonlinear interaction, and real airfoil shapes.

Influence of setting angle of the airfoil cascade on the flow «choking» regimes in the blade channel

The emergence of “choking” regimes of last stages leads to the stall in the blade rows of first stages, appearance of rotating stall and surge, and is one of the main causes of reduced GTE effectiveness on the off-design operating conditions. The paper deals with investigating the impact of setting angle in the airfoil cascade at the critical flow regime. To solve this problem, a series of gas-dynamic calculations for compressor airfoil cascade with different setting angles γ=30º, γ=40º, γ=50º, γ=60º, γ=70º was carried out. The computational domain for this problem consists of one blade and one blade channel. To solve this problem, irregular adaptive grid was selected. The turbulent gas flow calculation was performed by numerical solution of the averaged Navier-Stokes equations (Reynolds equations). To close the Navier-Stokes equations, the Menter's SST turbulence model was chosen. The second-order design scheme with the local use of the first-order design scheme was used for the calculation. Comparison of theoretical and experimental research results have shown that the flow nature in the blade channels and boundary layer formation depend strongly on the airfoil setting angle. With a decrease in the airfoil setting angle there is a significant decrease in the relative value of the minimum actual flow area of blade channels (described in aerodynamics as free area), which leads to a decrease in the Mach number value at the cascade entrance, at which the flow “choking” regime in blade channels by air flow occurs. These features should be taken into account in “choking” regime calculations. The obtained generalized characteristics of “choking” regimes of compressor cascades can be used in calculating “choking” regimes of the axial flow compressor stages and determining the boundaries of gas-dynamic stability of multistage axial flow compressors.

Influence of space–chord ratio of the airfoil cascade on the flow «choking» regimes in the blade channel

Gas turbine engines are a major part of propulsion systems of different aircrafts. Gas-dynamic stability of compressors of aircraft GTE is achieved by using various compressor regulation methods to ensure unstalled flow of blade rows in all operation modes of the engine. The loss of gas-dynamic stability of the compressor is caused by flow separation in blade rows and critical flow regimes (flow “choking” regime) in the blade channels of separate stages. So far, flow “choking” regimes in the blade channels are not fully investigated. The effect of the cascade space–chord ratio on flow “choking” regimes in the blade channels of the airfoil cascade was studied in the paper. The authors have proposed a theoretical relationship, allowing to calculate flow “choking” regimes with different space–chord ratio of the airfoil cascade. The authors have performed a series of calculations of flow in airfoil cascades in “choking” regimes using numerical simulation. To close the averaged Navier-Stokes equations, the Menter’s SST model was used. Adaptive irregular computational grid was selected to solve this problem. For the calculation, second-order design scheme with the local use of the first-order design scheme was used. Results of studying the flow in airfoil cascades have shown a significant effect of the stall zone behind the front edge of the blades at negative angles of attack on the flow in the blade channels. Decrease in the actual minimum flow area of the blade channel leads to a reduction in the value of the Mach number Ммах, at which flow “choking” regime in the blade channels by the air consumption occurs. The results have shown that the greater the space–chord ratio of airfoil cascades, the larger the relative influence of the boundary layer thickness on the critical flow regime. Generalized characteristics of “choking” regimes of compressor cascades can be used for calculating “choking” regimes of the axial-flow compressor stages in determining the boundaries of gas-dynamic stability and “choking” boundaries of multi-stage axial-flow compressors.

2D VISCOUS SHAPE DESIGN OPTIMIZATION AND MESH ADAPTATION USING THE ADJOINT METHOD

ABSTRACTThe majority of the adjoint methods applications focus on research in aerodynamic shape design optimization such as flow in airfoil cascade. This paper presents the application of the adjoint method technique in simple test cases of engineering relevance. The goal of this work is to extend the adjoint method into more engineering applications for viscous and incompressible flow, and to further improve the performance. Two test cases of engineering relevance have been selected. (1) Mesh adaptation for 2-D lid-driven cavity. (2) Drag reduction using an optimized upstream rod. The adjoint method has been used to efficiently adapt the 2-D lid-driven cavity mesh to minimize the discretization errors in calculating the swirl number. Based on the adaptation for the sensitivity magnitude, a uniform mesh of 1600 cells has been refined until a total 6586 cells, with finer mesh at the locations of highest sensitivities. The application of the adjoint method for the passive drag reduction problem results in a modified shape and position for the upstream cylinder. This change reduces the drag force on the main cylinder by 46%.

Non-linear singular integral equations analysis for unsteady cascade aeroelasticity applied in turbomachines

A two-dimensional unsteady cascade aeroelasticity is introduced for the investigation of flow fields of turbomachines (gas or steam). Especially, the velocity field around a cascade of airfoils is determined, while such a problem is reduced to the solution of a non-linear multidimensional singular integral equation when considering harmonic time dependence between the motions of adjacent blades of the turbine. Consequently, a general non-linear model is investigated by proposing an “innovative” and “groundbreaking” method. An application is finally presented by considering a special description of the velocity field and therefore such a field is determined for arbitrary geometry and arbitrary interblade phase angle.