Cascade Of Airfoils Research Articles

Another look at residual dynamic mode decomposition in the regime of fewer snapshots than dictionary size

Residual Dynamic Mode Decomposition (ResDMD) offers a method for accurately computing the spectral properties of Koopman operators. It achieves this by calculating an infinite-dimensional residual from snapshot data, thus overcoming issues associated with finite truncations of Koopman operators (e.g., Extended Dynamic Mode Decomposition), such as spurious eigenvalues. Spectral properties computed by ResDMD include spectra, pseudospectra, spectral measures, Koopman mode decompositions, and dictionary verification. In scenarios where the number of snapshots is fewer than the dictionary size, particularly for exact DMD and kernelized Extended DMD, ResDMD has traditionally been applied by dividing snapshot data into a training set and a quadrature set. We demonstrate how to eliminate the need for two datasets through a novel computational approach of solving a dual least-squares problem. We analyze these new residuals for exact DMD and kernelized Extended DMD, demonstrating ResDMD’s versatility and broad applicability across various dynamical systems, including those modeled by high-dimensional and nonlinear observables. The utility of these new residuals is showcased through three diverse examples: the analysis of a cylinder wake, the study of airfoil cascades, and the compression of transient shockwave experimental data. This approach not only simplifies the application of ResDMD but also extends its potential for deeper insights into the dynamics of complex systems.

Inverse design optimization of the compressor cascade airfoil assisted by active subspace approach

Inverse design optimization of the compressor cascade airfoil assisted by active subspace approach

Prediction of the Influence of the Inlet End-Wall Boundary Layer on the Secondary Flow of a Low Pressure Turbine Airfoil Using RANS and Large-Eddy Simulations

Abstract This paper analyzes the effect of the inlet end-wall boundary layer on the secondary flow of a low pressure turbine airfoil cascade at Reynolds number 2 × 105 using RANS and implicit large-eddy simulations (LES). The results are compared against experimental data obtained at two low-speed linear cascade facilities, one located at the Whittle Laboratory of the University of Cambridge and the other at the Polytechnic University of Madrid. The RANS turbulence model is the k−ω−γ−Reθt and no sub-grid scale model has been used in the LES. An unstructured mesh of hexahedra and prisms is used, with high order elements used in the boundary layer region to better describe the airfoil shape in the LES. Two inlet end-wall boundary layers that produce different secondary flow patterns are analyzed: a laminar thin velocity profile and a turbulent thick velocity profile with several inlet turbulent intensities. The agreement between LES numerical predictions and experimental measurements of the position and intensity of the secondary vortices is very good for both cases. RANS simulations are much cheaper in terms of computational cost and reasonably predict most of the flow features, except when the inlet turbulence is low and turbulent transition prediction becomes critical. The effect of the inlet velocity profiles and inlet turbulence on the secondary flow structure is quite pronounced. The velocity profile thickness determines the spanwise penetration of the passage vortex, and different inlet turbulence intensities modify its mixing. Higher inlet turbulence intensities lead to a decrease of the secondary losses due to the passage vortex and an increase of end-wall losses.

Development of a Performance-Based Design Technique for an Axial-Flow Fan Unit Using Airfoil Cascades Based on the Blade Strip Theory

Axial-flow fans are widely used as cooling fans in the outdoor units of split-type air conditioners. The design of an axial-flow fan blade involves stacking several airfoils that can be differently designed for each spanwise section. However, the complex flow field around the fan blade, including circumferential and axial flows, presents challenges when applying the single airfoil theory. This study proposed a systematic performance-based design method for axial-flow fans using a cascade of airfoils based on the blade strip theory. The theory characterized the complex three-dimensional flow field driven by an axial-flow fan in terms of a two-dimensional cascade of airfoil flows. Computational fluid dynamics based on finite volume methods were used to predict the flow field and aerodynamic sound sources of an existing low-pressure axial-flow fan partially covered by a fan shroud, and the results were validated against experimental measurements. Three radial locations in the spanwise region from the hub to the blade tip that have a significant impact on aerodynamic performance were selected, and the two-dimensional flow field on a cylindrical surface with a constant radius was extracted from the three-dimensional flow field to characterize the performance of an axial fan. Then, the airfoils at the targeted span locations were optimized for a higher flow rate and greater efficiency via two-dimensional simulations using the cascades of the airfoil, and the selected optimized airfoils were applied to existing fan blades. The effectiveness of the proposed performance-based design method for low-pressure axial-flow fans was validated by the results, which showed that the redesigned fan blades with cascades of airfoils performed as predicted, increasing the intended higher flow rate by about 1%, improving power consumption by 8%, and lowering the overall sound pressure level by 1.5 dBA.

Mesh suitability for CFD simulations performed on axial compressor airfoil cascades

Mesh suitability for CFD simulations performed on axial compressor airfoil cascades

Effects of moving endwall on the unsteadiness of tip leakage flow in compressor cascades

The influence of the moving endwall on the behavior of the tip leakage flow in compressors holds substantial significance. This work investigates the unsteadiness of the compressor's tip leakage flow under the impact of the moving endwall, employing both experimental methods and unsteady Reynolds-averaged Navier–Stokes (URANS) simulations. First, a numerical decomposition technique is proposed to isolate the tip leakage flow within a controlled diffusion airfoil (CDA) cascade. Subsequently, URANS simulations based on the CDA cascade are conducted at various incidence angles (−6° to +7°), tip clearances (clearance to chord: 0.83% to 3.33%), and flow coefficients (0.4 to 0.6), and additional URANS simulations based on the Virginia Tech cascade are also performed. The results indicate that the moving endwall induces a greater inclination of the tip leakage flow in the pitchwise direction, allowing it to impinge upon the pressure side of the adjacent blade. The impingement, if sufficiently intense, leads to the periodic generation of unsteady tip leakage flow by altering the blade loading. Moreover, the degree of unsteadiness diminishes significantly as the endwall speed and clearance height decrease. Additionally, it is observed that the breakdown of the tip leakage vortex does not serve as the root cause of the periodic unsteadiness. These findings underscore the critical role played by the moving endwall in the unsteadiness of the compressor's tip leakage flow.

Investigating horizontal-axis wind turbine aerodynamics using cascade flows

The simplest aerodynamic model of horizontal-axis wind turbines is the blade element momentum theory, which assumes that the blades behave as airfoils, but a correct two-dimensional representation is an infinite cascade of lifting bodies. This study analyzes the conventional and impulse forms of the forces on cascades of airfoils at spacings and pitch angles typical of wind turbine applications. OpenFOAM software was used to simulate steady, incompressible flow at a Reynolds number of 6×106 through cascades of NACA 0012 airfoils. The force equations agree well (less than 1% error) with the forces determined directly from OpenFOAM for four spacing ratios. We concentrate on the “wake vorticity” term, which is ignored in blade element momentum analysis. At a pitch angle of 90°, this term balances the viscous drag when the angle of attack is zero. At zero pitch, which models the outer region of a wind turbine blade at a high tip speed ratio, the term can account for 27% of the axial thrust when the angle of attack is about 4°. The normal force equation, like the angular momentum equation for wind turbines, has no viscous term, which forces the body drag to contribute to the circulation in the wake. It is shown that the airfoil assumption is conservative in that cascade elements have higher lift-to-drag ratios than airfoils at the same angle of attack. An associated result is that separation occurs at higher angles of attack on a cascade element compared to an airfoil.

Time-Inclined Method for High-Fidelity Rotor/Stator Simulations

The application of the time-inclined method in a fourth-order unstructured flux-reconstruction code for turbomachinery is demonstrated. Inviscid and viscous unsteady results due to the interaction of an incoming gust of total pressure with a linear cascade of flat plates and a linear cascade of T106A low-pressure turbine airfoils are reported. The agreement between the time-inclined method and the equivalent full-annulus multipassage solution is very high for both cases. Viscous solutions at Reynolds numbers of 104 and 105 were conducted. A high degree of matching was obtained between the time-inclined and the whole annulus approaches. The limitations of the method are explored and discussed. While the evolution of the unsteady boundary layers created by the interaction with the incoming wakes was very well captured, the mixing associated with the trailing edge vortex shedding was less accurate. The critical parameter controlling the method’s accuracy is the local Strouhal number. It was demonstrated that the benefit of retaining the exact blade count in the simulations overcomes the slight differences in the mixing due to the limitation of the time-inclined method to model viscous effects accurately in all situations.

Mesh convergence error estimations for compressible inviscid fluid flow over airfoil cascades using multiblock structured mesh

This work deals with estimations of errors, which are a consequence of a finite spatial discretisation that appears while solving differential equation numerically. More precisely, it deals with the estimation of errors that occur while computing compressible inviscid fluid flow over 2D airfoil cascades. This flow is described by the 2D Euler equations that are solved by the finite volume method in their conservative form. Numerical computations are performed on structured meshes consisting of four blocks, so the number of cells in the mesh can be easily adjusted. In this work, two estimation methods are used. Firstly, the grid convergence index is used to estimate the amount of cells needed to obtain certain accuracy of the solution. Secondly, the Richardson extrapolation is used to approximate the exact solution from a series of solutions obtained with meshes of different sizes. This analysis is performed on a well-known compressor cascade, which is composed of NACA 65 series airfoils. The obtained results should lead to a reasonable choice of the number of elements in a computational mesh based on the required accuracy of the solution and therefore also to computational time reduction while performing airfoil cascade computations. The results indicate that even for very precision demanding applications, 100 000 is a sufficient number of cells in a mesh.

Performance Investigation of Airfoils for Axial Flow Fans in Low Solidity Cascades Operating at High Inlet Flow Angles

Abstract Axial flow fans are usually characterized by blade sections with low solidity and high inlet flow angles. Two main approaches are followed in the preliminary design phase, to take into account blade interaction effects: the use of available airfoil cascades data (or related correlations) and that of isolated airfoil data together with interference coefficients. The working conditions of low solidity airfoil cascades with highly tangential inflow are not widely studied in the literature, leaving the designer the possibility to rely on limited cascade data or often on the use of isolated airfoil data, with the assumption of negligible interference effects. A systematic investigation of the above working conditions for airfoil cascades is performed with Reynolds-averaged Navier–Stokes simulations. Three different airfoils are used to evaluate the influence of the design lift coefficient and maximum blade thickness. The results provide a better insight into the aerodynamic behavior of airfoil sections in such operating conditions, showing that interactions cannot be neglected. The use of metamodeling coupled with computational fluid dynamics (CFD) simulations is presented as a suitable tool for treating interference effects within the fan design process. The main findings of the present work can be used as a support for design choices as well as for developing design strategies both for the fan blades and for the airfoil sections.

Test problem of the flow modeling in axial compressor cascades

The flow of gas in the flow path of a gas turbine engine (GTE) is accompanied by a rather complex phenomenon. These are a three-dimensional boundary layer, an incoming vortex, a paired vortex, flow turbulence, aerodynamic wakes behind the trailing edge, separation of the boundary layer from the blade surface, pressure pulsations, uneven and unsteady flow, secondary overflows, changes in the angles of flow exit, etc. Flow R&D of a GTE remains a rather complex process, and requires the use of reliable research methods and techniques. Nowadays, two known methods are used to study a gas flow through the flow path of a GTE ˗ experimental and calculated. Calculated, in turn, can be divided into analytical and numerical. An important stage of the numerical experiment is the solution to test problems for the possibility of setting the parameters of the numerical experiment. In this work, two test tasks were carried out. The object of the research was two compressor cascades, consisting of the identical airfoils series KR-33. The profile chord was 52 mm; the pitch cascade was 52 mm. The difference was in the installation angle of these profiles: variant 1 of the compressor cascade has an installation angle of 63.5º; variant 2 of the compressor cascade has an installation angle of 89.5º. A computational domain was constructed for each compressor cascades of airfoils and consisted of 5 million cells. Air under normal atmospheric conditions was chosen as the working fluid. The flow regime of compressor cascades varied in the range of coefficient λ = 0.26…0.9 and λ = 0.265…0.8, where the coefficient λ is the reduced velocity. The unstructured mesh method with an adaptation for the boundary layer was chosen to construct the computational mesh. Such a combination makes it possible to correctly model the flow in the boundary layer near the walls. The turbulence model SST was taken to close the Navier-Stokes equations. A comparison of the results of numerical and physical experiments for two variants of compressor cascades shows that the flow simulation error is less than 5%. Because of the calculation, the choice of this turbulence model for subsequent studies of the flow in the stages of the compressor, fan, and propfan will be justified.

A Comprehensive Analytical Shock Loss Model for Axial Compressor Cascades

AbstractThe approach applied in various research papers that model compressor shock losses is valid only for certain types of airfoil cascades operating in a narrow range of working conditions. Lately, more general shock loss models have been established that cover a wider variety of airfoils and operating regimes. However, owing to the complexity of the studied matter, the majority of such models are, to a certain extent, presented only in a descriptive manner. The lack of specific details can affect the end results when such a model is utilized since improvisation cannot be avoided. Some models also apply complex numerical procedures that can slow the calculations and be a source of computational instability. In this research, an attempt has been made to produce an analytical shock loss model that is simple enough to be described in detail while being universal and robust enough to find wide application in the fields of design and performance analysis of transonic compressors and fans. The flexible description of airfoil geometry encompasses a variety of blade shapes. Both unchoked and choked operating regimes are covered, including a precise prediction of choke occurrence. The model was validated using a number of numerical test cases.

Aero-Structural Coupling Strategy for a Morphing Blade Cascade Study

Abstract The coupling of aerodynamics and structural mechanics is an important step in the design process of aeronautical devices with morphing parts. In this article, a 2D–3D coupling approach is developed to study a morphing blade cascade. Two shape memory alloy actuators are placed on the upper and lower sides of the blade to make possible the change in shape of the leading edge. In the present study, a preliminary design study is conducted by considering a two-dimensional computational fluid dynamics (CFD) analysis of an airfoil cascade coupled with a three-dimensional structural analysis of the whole 3D blade. A methodology is developed to match 2D and 3D meshes such that the aerodynamic loads can be easily transferred to the structural analysis. From there, the deformed blade geometry due to both aerodynamic loads and actuator work can be transferred back to the CFD solver, and the iterative aero-structural coupling loop can be repeated until convergence. The aero-structural coupling strategy developed in this study is also applied to a blade cascade study aiming to improve its performance by morphing the leading-edge of the blade. The results of this application show that by morphing the leading-edge blade of only few millimeters (less than 2 mm), it is possible to achieve a relevant performance improvement in terms of total pressure loss coefficient decrease of about 53% considering off-design conditions.

Experimental Studies of Airfoil Cascades with High Velocity Vector Circulation around the Airfoil

Experimental Studies of Airfoil Cascades with High Velocity Vector Circulation around the Airfoil

Design and validation of a reconfigurable polysonic wind tunnel

A new polysonic wind tunnel has been designed and constructed at Saint Louis University. The flow paths and flow conditioning needs were designed by PhD students and the structural design and manufacturing were accomplished by local pressure vessel and manufacturing firms. Starting with a set of two 25 hp air compressors, an air filter and dryer system with an operating pressure range between 100–200 psia, and a 14 m3 storage tank, the total cost for additional components and labor was on the order of $750,000, where design and installation was completed in approximately 18 months. The facility is uniquely reconfigurable to accommodate straight and curved flow paths, with existing configurations supporting a supersonic shock wave-boundary layer interaction study in a rectangular channel and another study of a transonic linear cascade of high-pressure turbine airfoils. The design process and resulting components are described herein, and include how to improve supersonic nozzle design by adjusting for displacement thickness growth as well as how to diagnose and correct choked flow conditions which existed in the first iteration of the flow path circuit. Results also include a sample schlieren image of a normal shock wave-boundary layer interaction and airfoil static pressure distributions and total pressure ratio across the turbine showing successful configuration implementations.

An adaptive approach to duct optimization of an industrial boiler air supply system using airfoils

The purpose of this paper is to examine the pressure drop caused by placing an airfoil at different angles of attack in the straight part of the rectangular air duct, as the first step of investigating the possibility of using a staggered cascade of airfoils for gradual deflection of the air-flow in radial elbows of an air supply system used in industrial boilers. The initial problem was approached by using the commercial CFD code based on the finite volume method to numerically simulate a 2-D incompressible turbulent flow and by conducting direct experimental measurements in the wind tunnel. The results of CFD simulations have been compared to experimentally measured data for two considered cases of inlet velocities and five different angles of attack. Numerical solutions show an adequate level of agreement with experimental measurements. The obtained results indicate the possibility of using a staggered cascade of airfoils for gradual deflection of the air-flow.

A viscous blade body force model for computational fluid dynamics–based throughflow analysis of axial compressors

In recent years, the computational fluid dynamics (CFD) techniques have attracted enormous interest in the throughflow calculations, and one of the major concerns in the CFD-based throughflow method is the modeling of blade forces. In this article, a viscous blade force model in the CFD-based throughflow program was proposed to account for the loss generation. The throughflow code is based on the axisymmetric Navier–Stokes equations. The inviscid blade force is determined by calculating a pressure difference between the pressure and suction surfaces, and the viscous blade force is related to the local kinetic energy through a skin friction coefficient. The viscous blade force model was validated by a linear controlled diffusion airfoil cascade, and the results showed that it can correctly introduce the loss into the CFD-based throughflow model. Then, the code was applied to calculate the transonic NASA rotor 67, and the calculated results were in good agreement with the measured results, which showed that the calculated shock losses reduce the dependence of the throughflow calculation on the empirical correlation. Last, the 3.5-stage compressor P&W3S1 at 85%, 100%, and 105% of the design speed was performed to demonstrate the reliability of the viscous blade force model in a multistage environment. The results showed that the CFD-based throughflow method can easily predict the spanwise mixing due to the inclusion of the turbulence model, and predicted results were in acceptable agreement with the experimental results. In a word, the proposed viscous blade force model and CFD-based throughflow model can achieve the throughflow analysis with an acceptable level of accuracy and a little time-consuming.

Turbomachine criteria for similarity of natural size proportionality

Introduction. It is possible to give rise to synergy as a result of science-intensive industries combination with innovative eco-technologies for subsoil use only by developing a brand new approach to nature-like auxiliary technologies. Insufficient adaptability of turbomachines that ensure industrial safety increases the production cost of the mining and oil and gas complexes of the Russian Federation by more than 15%, reducing its competitiveness. Research methodology. Based on the hypothesis of the hydrodynamic analogy of the mechanisms of deceleration of the flow around the airfoil and the formation of its profile resistance, Karman's theory of attached and free vortices, the Zhukovsky-Chaplygin-Kutta hypothesis, the method of conformal transformations, the theory of similarity, the method of singular points by Chaplygin S. A., the criteria for the similarity of natural proportionality are obtained, that is, for the hydrodynamic similarity of the mechanism of energy interaction between the blades of the turbomachine impeller and the wing of a bird. Results. It has been proved that the dominant control over the nature-like proportionality of the aerodynamics of turbomachines is the ratio between the speed and flow acceleration circulation around the airfoil. It has been established that the coefficients of the airfoil resistance, lift and aerodynamic quality of the airfoil cascade are hydrodynamic analogs of the coefficients of the circulation of the velocity and acceleration of the flow and their ratio. Conclusions. It has been experimentally confirmed that the use of the proposed criterion of natural proportionality in the design of turbomachines increases their coefficient of aerodynamic adaptability by more than 2 times, increasing the area of economical operation by 83%.

Numerical Investigation of the Turbulent Wake-Boundary Interaction in a Translational Cascade of Airfoils and Flat Plate

Rotor stator interaction (RSI) is an important phenomenon influencing performances in the pump, turbine, and compressor. In this paper, the correlation-based transition model is used to study the RSI phenomenon between a translational cascade of airfoils and a flat plat. A comparison was made between computational results and experimental results. The computational boundary layer velocity is in reasonable agreement with the experimental velocity. The thickness of boundary layer decreases as the RSI frequency increases and it increases as the fluid flows downstream. The spectral plots of velocity fluctuations at leading edge x/c = 2 under RSI partial flow condition f = 20 Hz and f = 30 Hz are dominated by a narrowband component. RSI frequency mainly affects the turbulence intensity in the freestream region. However, it has little influence on the turbulence intensity of boundary layer near the wall. A secondary vortex is induced by the wake–boundary layer interaction and it leads to the formation of a thickened laminar boundary layer. The negative-vorticity wake also facilitates the formation of a thickened boundary layer while the positive-vorticity wake has a similar effect, like a calmed region which makes the boundary layer thinner.

Proper orthogonal decomposition assisted inverse design optimisation method for the compressor cascade airfoil

Inverse design is by far the most physically explicit method in the turbomachinery field for designing a cascade airfoil shape for a prescribed distribution of aerodynamic parameters on the airfoil surface. However, a vital drawback of the available inverse design methods for cascade airfoils is the lack of effective techniques to specify optimal target aerodynamic parameters, particularly optimal pressure distribution on the airfoil surface. This drawback hinders the wide application of inverse design optimisation methods in the turbomachinery field. To overcome this vital drawback, we proposed a proper orthogonal decomposition (POD) assisted inverse design optimisation method for cascade airfoils, in which an optimal pressure distribution on airfoil surface was automatically obtained by solving a direct design optimisation problem and accurately parameterised via the POD method. The effectiveness of the proposed inverse design optimisation method was demonstrated using the inverse designs of a compressor cascade airfoil with two different optimisation objectives. Results highlighted the proposed inverse design method's capability to significantly improve the aerodynamic performance of the compressor cascade. The POD method can provide an adequate and flexible description of airfoil surface pressure distribution with a small number of POD modes. This work is valuable for the further development of inverse design optimisation methods for advanced compressor blades.