Mean Camber Line Research Articles

Axial flow compressor blade optimization through flexible shape tuning by means of cooperative co-evolution algorithm and adaptive surrogate model

The present study is to explore potential benefits of axial flow compressor blade optimization through a flexible tuning. Modifications of blade sectional profiles and their stacking line can control spanwise blade loading distribution, reduce shock losses, and extend operating flow range. Most previous studies focused on tuning either sectional profiles or stacking line, but little work was conducted by collaboratively varying both, which may be due to abrupt rise of optimization variables and complexity. An efficient optimization method is developed to handle highly nonlinear high-dimension blade optimization problem with simultaneous variation of both sectional profiles and stacking line. It incorporates an improved cooperative co-evolution algorithm optimizer and one-stage expected improvement based adaptive surrogate model. The former decomposes the high-dimension problem into low-dimension subproblems and they can be readily solved; the latter enables the optimizer to jump out of the local minima and conduct the aim-oriented optimal search toward global optimum. A coarse surrogate model is firstly constructed with some DOE samples but it is refined during optimization process with newly identified and evaluated samples. The model prediction accuracy is gradually improved, thus it captures the distinct features (especially global optimum) of optimization problem. Both blade sectional profiles and their spatial positions are simultaneously varied. Four sectional profiles of hub, 33% span, 67% span, and shroud are parameterized, and each is defined by a mean camber line and thickness distribution. Both of them are represented, respectively, by a third-order B-Spline curve. Spatial position of each profile varies in term of sweep and lean. Blade design optimization is conducted for Rotor67 at design flow on a single workstation of Dell 7500. Performance gains are significant: at design flow, overall efficiency and pressure ratio are increased, respectively, by 1.44 and 7.24%; off-design performances are also improved over the entire flow range.

The Research on the Methods of the Aero Engine Blades Evaluation

As an important part of the aero engine, the quality of the blade seriously affects the engine performance, so the inspection method of the blade is significant. Based on the research of the HB 5647-98<<to mark dimensions, tolerances of the vane type and the surface roughness of the blade body>> , this paper concludes different evaluation methods of the blade. The main evaluated parameters include the leading and trailing edge radius, the chord length, the maximum thickness of blade profile, the mean camber line, and the surface twist and so on. Here we mainly discuss the previous three terms. The least square method is adopted to fit the arc of the leading and trailing edge; introduce the projection method to calculate the chord length; at last, we employ the spline fitting method to get the mean line and then obtain the maximum thickness of the blade section.

Comprehensive Application of a First Principles Based Methodology for Design of Axial Compressor Configurations

Axial compressors are widely used in many aerodynamic applications. The design of an axial compressor configuration presents many challenges. It is necessary to retool the design methodologies to take advantage of the improved accuracy and physical fidelity of these advanced methods. Here, a first-principles based multiobjective technique for designing single stage compressors is described. The study accounts for stage aerodynamic characteristics and rotor-stator interactions. The proposed methodology provides a way to systematically screen through the plethora of design variables. This method has been applied to a rotor-stator stage similar to NASA Stage 35. By selecting the most influential design parameters and by optimizing the blade leading edge and trailing edge mean camber line angles, phenomena such as tip blockages, blade-to-blade shock structures and other loss mechanisms can be weakened or alleviated. It is found that these changes to the configuration can have a beneficial effect on total pressure ratio and stage adiabatic efficiency, thereby improving the performance of the axial compression system.

Unsteady Effects on Transonic Turbine Blade-Tip Heat Transfer

In a gas turbine engine the blade tips of the high-pressure turbine are exposed to high levels of convective heat transfer, because of the so-called tip-leakage phenomenon. The blade-lift distribution is known to control the flow distribution in the blade–tip gap. However, the interaction between upstream nozzle guide vanes and the rotor blades produces a time-varying flow field that induces varying flow conditions around the blade and within the tip gap. Extensive measurements of the unsteady blade-tip heat transfer have been made in an engine representative transonic turbine. These include measurements along the mean camber line of the blade tip, which have revealed significant variation in both time-mean and time-varying heat flux. The influences of potential interaction and the vane trailing edge have been observed. Numerical calculations of the turbine stage using a Reynolds-averaged-Navier-Stokes-based computational fluid dynamics code have also been conducted. In combination with the experimental results, these have enabled the time-varying flow field to be probed in the blade-relative frame of reference. This has allowed a deeper analysis of the unsteady heat-transfer data, and the quantification of the impact of vane potential field and vane trailing edge interaction on the tip-region flow and heat transfer. In particular, the separate effects of time-varying flow temperature and heat-transfer coefficient have been established.

Geometric parameter-based optimization of the die profile for the investment casting of aerofoil-shaped turbine blades

Dimensional accuracy is one of the most important criteria in the investment casting of turbine blades for aero engine applications. Although investment casting is an ideal route for producing net-shaped components, it necessitates accurate determination of the casting die profile. To avoid extensive modifications on the die cavity shape, this study proposes a simple but efficient inverse design method that adjusts certain geometric parameters to establish the die profile. Parameterized modeling is achieved by identifying the geometric parameters that describe the mean camber line of the blade profile. Meanwhile, blade shrinkages at different positions are effectively remedied through the adjustment of the parameters using the inverse iteration algorithm proposed in this paper. The relative positions among the cross-sections can also be varied to rectify the twist deformation of the blade, thereby guaranteeing the dimensional accuracy of the turbine blades. The applicability of this method is validated using numerical simulation data and experimental results.

An Optimum-Curved Die-Profile for Investment Casting of Turbo Blades

In order to avoid tremendous modifications of the die cavity for investment casting of turbo blades, this paper proposed an inverse iterative compensation method that adjusts certain geometric parameters to establish the die-profile. The parameterized modeling is achieved by identifying geometric parameters describing the mean camber line; the optimum-curve die-profile can be obtained based on the inverse iteration algorithm. As a result, the dimension precision of turbo blades can be guaranteed. The applicability of this method is validated using numerical simulation data.

A procedure for the design of radial cascade diffusers based on the maximum ratio between flow deflection and total pressure loss coefficient

A design procedure of radial cascade diffusers for incompressible flow, based on the maximum ratio between the flow deflection and the total pressure loss coefficient, is proposed. To achieve such a result, numerical investigations were carried out on several different diffusers at design and off-design operating conditions. Four space chord ratios, with seven blades and nine outlet flow angles were considered. For each diffuser, the optimum performance parameters were correlated to the incoming flow angle and the design variables of the aerofoil cascade. Reynolds number and mean camberline influence were also analysed. Design charts were then produced in order to attain an efficient preliminary design of aerodynamic diffusers without resorting to time-consuming approaches. Finally, auxiliary charts were proposed for predicting the diffuser performance at off-design operating conditions.

Inner Workings of Shrouded and Unshrouded Transonic Fan Blades

This paper reports on the numerical assessment of the differences in aerodynamic performance between part span shrouded and unshrouded fan blades generally found in the first stage of multistage fans in low bypass ratio aircraft engines. Rotor flow fields for both blade designs were investigated at two operating conditions using a three-dimensional viscous flow analysis. Although designed to the same radius ratio, aspect ratio, and solidity, the unshrouded fan rotor had a slightly increased tip speed (+3%) and somewhat lower pressure ratio (−3.2%) due to engine cycle requirements. Even when allowing for these small differences, the analysis reveals interesting differences in the level and in the radial distribution of efficiency between these two rotors. The reason for the improved performance of the shrouded rotor in part can be attributed to the shroud blocking off the radial migration of boundary layer fluid centrifuged from the hub on the suction side. As a result, the shock boundary layer interaction seems to be improved on the shrouded blade. At the cruise condition, the efficiency is the same for both rotors. The slightly better efficiency of the shrouded blade in the outer panel is nullified by the large efficiency penalty in the vicinity of the shroud. As there is no significant radial migration of fluid in the suction side boundary layer, as indicated by the analysis at this condition relative to the design speed case, the benefit due to the shroud is greatly reduced. At this speed and at lower speeds, the shroud becomes a net additional loss for the blade. Also of interest from the numerical results is the indication that significant blade ruggedization penalties to performance can be reduced in the case of the unshrouded blade through custom tailoring of its mean camber line.

A contractive operator solution of an airfoil design inverse problem

AbstractThis paper deals with a numerical method for an airfoil design which was presented in [3, 5]. This method is intended for design of an airfoil from a given velocity distribution along a mean camber line. The method is based on searching for a fixed point of a contractive operator. This operator combines an inexact inverse operator and equations describing the flow. A subsonic flow is assumed, the flow is described by a system of the Euler equations which is solved by an implicit finite volume method. The Newton method is applied to the solution of the nonlinear system. The resulting system of linear algebraic equations is solved by GMRES method, the Jacobian‐free version is described. The inexact inverse operator consists of a middle curve function and a thickness function, both depending on the given velocity distribution. In addition to the velocity distribution the velocity in infinity is given. The angle of attack is determined so that the stagnation point is in a specific position. Successful numerical results are presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Technical Note: Definition of the Mean Camber Line from Airfoil Shapes

Technical Note: Definition of the Mean Camber Line from Airfoil Shapes

Blade-tip heat transfer in a transonic turbine

The blade-tips of high-pressure turbine blades in a gas turbine engine are subjected to strong convective heat transfer and continued to present a significant design challenge to manufacturers. This paper is concerned with developing an understanding of the unsteady flow physics that influences the blade-tip heat transfer. Experimental investigations of bladetip heat transfer and aerodynamics have been conducted in a transonic turbine stage test facility. The data reveal the effect of vane-rotor interactions on the unsteady heat transfer along the blade-tip mean camber line. In particular, the vane shock and potential field interaction establish characteristic unsteady heat transfer signatures at different axial positions along the blade-tip. The fluctuations in heat transfer are discussed in terms of vane-periodic changes in both relative total temperature and aerodynamic conditions.

Experimental Investigation of Diffuser Hub Injection to Improve Centrifugal Compressor Stability

Results from a series of experiments to investigate whether centrifugal compressor stability could be improved by injecting air through the diffuser hub surface are reported. The research was conducted in a 4:1 pressure ratio centrifugal compressor configured with a vane-island diffuser. Injector nozzles were located just upstream of the leading edge of the diffuser vanes. Nozzle orientations were set to produce injected streams angled at −8, 0, and +8 degrees relative to the vane mean camber line. Several injection flow rates were tested using both an external air supply and recirculation from the diffuser exit. Compressor flow range did not improve at any injection flow rate that was tested, and generally diminished as injection rate increased. Compressor flow range did improve slightly at zero injection due to the flow resistance created by injector openings on the hub surface. Resistance and flow range both increased as the injector orientation was turned toward radial. Leading edge loading and semivaneless space diffusion showed trends that are similar to those reported earlier from shroud surface experiments that did improve compressor range. Opposite trends are seen for hub injection cases where compressor flow range decreased. The hub injection data further explain the range improvement provided by shroud-side injection and suggest that stability factors cited in the discussion of shroud surface techniques are valid. The results also suggest that a different application of hub-side techniques may produce a range improvement in centrifugal compressors.

Design Method for Turbomachine Blades With Finite Thickness by the Circulation Method

This paper presents a procedure to extend a recently developed three-dimensional inverse method for infinitely thin blades to handle blades with finite thickness. In this inverse method, the prescribed quantities are the blade pressure loading and the blade thickness distributions, and the calculated quantity is the blade mean camber line. The method is formulated in the fully inverse mode whereby the blade shape is determined iteratively using the flow-tangency condition along the blade surfaces. Design calculations are presented for an inlet guide vane, an impulse turbine blade, and a compressor blade in the two-dimensional inviscid- and incompressible-flow limit. Consistency checks are carried out for these design calculations using a panel analysis method and the analytical solution for the Gostelow profile.

Calculation of transonic flows by a field integral equation method

A field integral equation method is developed to solve the two-dimensional compressible potential equation for transonic flow over airfoils with embedded shocks at subsonic freestream Mach numbers. The perturbation velocities are induced by linear internal source and vorticity distributions on the mean camber line of the airfoil and nonlinear field source distributions external to the airfoil surface. Derivatives are calculated in the computational plane, and those in the physical plane are determined by using the Jacobian of the transformation

Induced-drag characteristics of crescent-moon-shaped wings

Results are presented of a theoretical study conducted to analyze the potential drag reduction characteristics of wings with highly tapered aft-swept tips at subsonic speeds. These planar wings, also named crescent- moon-shaped wings or wings with curved planform, can produce induced drag less than the minimal value ob- tained with the classical unswept elliptical wing for a constant lift and wing span. The induced-drag reduction is the result of the nonplanar wing and wake shape at the angle of attack. For an example wing of aspect ratio 7, the crescent-moon shape provides a reduction in cruise induced drag of 8.0% as compared to an unswept elliptical wing. equal to but not less than the minimum value obtained for the classical straight wing with elliptical loading distribution can be achieved with planar curved planforms. In order to obtain the mimimum value of induced drag for the wing with backward sweep, it may be required to introduce a substantial amount of washout, while for the wing with for- ward sweep, it may be necessary to incorporate washin. The twist requirement has a severe disadvantage, however, because now the minimum induced drag is obtained only at the angle of attack for which the wing twist distribution is optimized. At off-design conditions, drag penalties are in- curred and the induced drag produced by the twisted swept wing will be higher than for the untwisted unswept elliptical wing for a constant lift coefficient. This paper will demonstrate that an untwisted planar crescent-moon wing can be more efficient than an unswept elliptical wing. A computa- tion method that correctly accounts for the influence of the trailing wake must be applied in order to obtain this somewhat unexpected result. Zimmer3'4 demonstrated that crescent-moon planform shapes can significantly reduce the level of induced drag pro- duced by a wing. The results are obtained with a vortex- lattice method that models the lifting surface by its mean camber line and takes into account the nonlinear effect of the trailing vortex sheet. Consequently, the influence of air- foil thickness is assumed to be negligible and the leading- edge suction force is modeled mathematically. Zimmer's work resulted in the Dornier New Technology Wing (Dornier Do-228), which represents a practical (and somewhat com- promised) application of the crescent-moon planform shape. In this study, a nonlinear surface panel method is applied to study the drag characteristics of a crescent-moon-shaped lifting surface of aspect ratio 7. Consequently, no approxima- tions are required to calculate the induced-drag force. Analysis Method

Aerodynamic Design of High-Perf ormance Biplane Wings

LTHOUGH biplanes were quite popular during the early days of aviation, they had virtually disappeared from service by the mid-1930's. The biplane seemed to be plagued by inherently high drag and low maximum lift coefficient. The purpose of the present study was to re-examine the reasons for the biplane's decline. It was found that for any practical biplane configuration, it is possible to design a wing system which has a much lower weight per unit area and which has essentially the same maximum useable lift coefficient as that of a comparable, well-designed, monoplane wing, in either clean or flapped configurations. Improvements in the design of fairings permit large drag reductions, relative to the earlier designs. Because of these improvements, it is possible to design a biplane whose performance is superior, for some applications, to that of a well-designed monoplane. These applications are those for which excellent low-speed maneuverability, good short-field performance, good loadcarrying ability, low cost, and rugged construction are of primary importance.! Content If a biplane wing system is to develop a high CLmax, both wings must stall nearly together. A method presented by Fuchs was used to identify those configurations for which a good stall match could be obtained. Each wing is idealized in this method as a single horseshoe vortex, with the bound part of each vortex located at the center of pressure. Satisfactory stall match was defined as a ratio of leading wing to trailing wing Coequal to unity at an assumed CLmax for the combination. Some results of this analysis are given in Fig. 1, and some nomenclature is defined in the sketch. The airfoil chord lines are parallel; results of this study showed no advantage to be gained from the use of decalage. The geometric stagger angle a for best stall match is quite insensitive to the gap/chord ratio, and it decreases as the aspect ratio increases. The best stall match always corresponds to small values of 0, the aerodynamic stagger angle. The chordwise variation in vertical velocity induced by one airfoil upon the other corresponds to a local curvature of the flow. Since within the framework of thin airfoil theory, this effect is identical to the effect of a change in the mean camber line, it will be referred to as induced camber. Data for NACA airfoils of the four- and five-digit series show increases in the maximum section lift coefficient Cfmax

A Simple Method Calculating Airfoil and Wing Lattice Forms which have Given Pressure Distribution

This paper deals with the problem of constructing the form of airfoil section which has given pressure distribution. The effects of angle of incidence, mean camber and thickness upon the velocity on the surface of airfoil are approximately independent of each other. This fact is utilized and from the difference of velocities on the upper and lower surfaces of the airfoil, the mean camber line and the angle of incidence are determined, while from the mean velocity, the thickness is determined. Although the labour of calculation is little, yet the result is very satisfactory. The above-mentioned method is extended to the case of wing lattice and procedure of calculation is explained.

A Method for obtaining Profile-Form which has Given Surface Pressure Distribution

A method for obtaining the profile-form which has the given surface pressure distribution is stated. The method is based on a theorem about the velocity along a profile and enables us to obtain separately the thickness distribution as well as the mean camber line of the required profile by simple calculations. Therefore, we can easily understand the relation between the pressure distribution and the profile form. Calculation has been made for a Joukowski profile which has the thickness of 11 percent and the camber of 2.5 percent of chord and Munk 6 profile. It showed that the deviation of the calculated form from the exact one was very small, which proves that the present method is very satisfactory for practical use in respect to the facility of calculation and to the accuracy of result.