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Shape optimization of a transonic axial compressor rotor operating at the design flow condition has been performed using the response surface method and three-dimensional Navier-Stokes analysis. The three design variables, blade sweep, lean and skew, are introduced to optimize the three-dimensional stacking line of the rotor blade. The objective fu...

## Contexts in source publication

**Context 1**

... blade stacking line is optimized by introducing three shape variables; namely sweep, lean, and skew as shown in Figs. 3-5. A variety of terms have been used to define the stacking line (e.g. sweep, lean, skew etc.) and no consistent nomenclature has emerged. The term of sweep is used to describe movement of airfoil section in the manner shown in Fig. 3. That is, movement parallel to the airfoil chord line is termed sweep. A sweep value, α in Fig. 3, is defined at the rotor tip and normalized by the axial tip chord (= 27.77 mm). The blade sweep is taken to be positive if the airfoil sections are moved in the downstream direction. The line of the swept blade between the rotor tip (α in ...

**Context 2**

... as shown in Figs. 3-5. A variety of terms have been used to define the stacking line (e.g. sweep, lean, skew etc.) and no consistent nomenclature has emerged. The term of sweep is used to describe movement of airfoil section in the manner shown in Fig. 3. That is, movement parallel to the airfoil chord line is termed sweep. A sweep value, α in Fig. 3, is defined at the rotor tip and normalized by the axial tip chord (= 27.77 mm). The blade sweep is taken to be positive if the airfoil sections are moved in the downstream direction. The line of the swept blade between the rotor tip (α in Fig. 3) and hub (= zero) is linearly connected while the gap of the tip clearance is kept ...

**Context 3**

... in Fig. 3. That is, movement parallel to the airfoil chord line is termed sweep. A sweep value, α in Fig. 3, is defined at the rotor tip and normalized by the axial tip chord (= 27.77 mm). The blade sweep is taken to be positive if the airfoil sections are moved in the downstream direction. The line of the swept blade between the rotor tip (α in Fig. 3) and hub (= zero) is linearly connected while the gap of the tip clearance is kept constant. Figure 4, which is top view of the rotor, shows the definition of blade lean (or dihedral). Lean is defined when the blade moves normal to the airfoil chord line. The lean value, β in Fig. 4, is defined at the rotor tip and normalized by the ...

## Citations

... In comparison to a baseline case, FSW gave an increased g tt in Ref. [19], unchanged g ts in Ref. [13], and decreased g tt in Ref. [24]. For BSW, studies reported increased g tt in Ref. [25] as well as decreased g tt in Ref. [24]. Note that these results have been reported for different blades and different flow coefficients. ...

Axial fans with low hub-to-tip diameter ratio are used in many branches of industry. Optimization of their aerodynamic performance is important, for which using sweep, dihedral and skew of the blades' stacking line form an important method. Investigations on axial fans with medium to high hub-to-tip diameter ratio have shown that forward sweep of blades can give improved aerodynamic performance, especially the total-to-total efficiency. However, only few studies for fans with small hub-to-tip diameter ratio have been reported. For such fans, extensive regions of backflow are present behind the fan near the hub. Based on a validated Computational Fluid Dynamics simulation method, effects of sweep, dihedral and skew in axial and circumferential directions (in forward and backward direction) on the aerodynamic performance of small hub-to-tip ratio fans are investigated, with a linear stacking line. Current results show that forward sweep and circumferential skew are beneficial for higher total-to-total efficiency and that higher total-to-static efficiency can be obtained by forward dihedral and axial skew. The backward shape variety generally gives negative aerodynamic effects. Forward sweep and circumferential skew shorten the radial migration path, but more flow separation is present near the hub. With forward dihedral and axial skew the backflow region is reduced in size and axial extent, but a more significant hub corner stall region is found. The pressure reduction due to sweep and dihedral is more limited than what could be expected from wing aerodynamics.

... It is easy to form the large corner separation when the high entropy fluid is accumulated in the suction surface-endwall corner by the cross passage pressure gradient and further decelerated by the axial adverse pressure gradient (Denton 1993). Over the years, substantial efforts have been expended in exploring and investigating the techniques to weaken the corner separation, such as the blade sweeping and leaning design (Jang et al. 2006), the axisymmetric endwall profiling (Kroger et al. 2009), the non-axisymmetric endwall profiling (Reising and Schiffer 2009), the boundary layer suction (Gbadebo et al. 2007), the pulsed jets (Hecklau et al. 2011), and the vortex generator (Hergt et al. 2010). These techniques are different in mechanisms and application scopes. ...

This paper investigates an optimization for the axisymmetric hub-endwall profile of a transonic fan designed for a civil high bypass ratio turbofan engine. A time-saving integrated design optimization method is proposed based on a new hub-endwall profile modification method in combination with a novel two-stage polynomial response surface. The profile modification method is proposed to change the profile of the baseline hub curve by moving three control points, so as to redesign the hub-endwall. The two-stage polynomial response surface is proposed to obtain an accurate high-order polynomial while requiring fewer sampling points, so as to reduce the computational cost. The results show that the integrated design optimization method is suitable and valuable. After optimization, the corner separation of the studied fan is weakened, and the stall margin of the core fan is also enlarged. Moreover, the aerodynamic performance of the core fan at the design speed is improved.

... One change involves the geometry of each section being held constant while the relative position changes; that is, the axial and circumferential offsets of the section constitute the bow and sweep of the blade. [1][2][3] The other approach is to change the shape of central arced curve and thickness distribution in each section, [4][5][6][7] or to change the suction or pressure side profile of each section by means of free curves, [8][9][10] so as to change the blade geometry. The disadvantages of the method mentioned above include a large number of optimization parameters and non-smooth surface. ...

An aerodynamic optimization method for axial flow compressor blades available for engineering is developed in this paper. Bezier surface is adopted as parameterization method to control the suction surface of the blades, which brings the following advantages: (A) significantly reducing design variables; (B) easy to ensure the mechanical strength of rotating blades; (C) better physical understanding; (D) easy to achieve smooth surface. The Improved Artificial Bee Colony (IABC) algorithm, which significantly increases the convergence speed and global optimization ability, is adopted to find the optimal result. A new engineering optimization tool is constructed by combining the surface parametric control method, the IABC algorithm, with a verified Computational Fluid Dynamics (CFD) simulation method, and it has been successfully applied in the aerodynamic optimization for a single-row transonic rotor (Rotor 37) and a single-stage transonic axial flow compressor (Stage 35). With the constraint that the relative change in the flow rate is less than 0.5% and the total pressure ratio does not decrease, within the acceptable time in engineering, the adiabatic efficiency of Rotor 37 at design point increases by 1.02%, while its surge margin 0.84%, and the adiabatic efficiency of Stage 35 0.54%, while its surge margin 1.11% after optimization, to verify the effectiveness and potential in engineering of this new tool for optimization of axial compressor blade.

... In recent years, many research papers on design optimization of turbomachinery blade using computational fluid dynamics (CFD) [4][5][6][7][8][9][10][11] have been published. Oyama et al. [4] performed design optimization of NASA Rotor 67 to reduce entropy production. ...

This paper presents the application of a viscous adjoint method to the multipoint design optimization of a rotor blade through blade profiling. The adjoint method requires about twice the computational effort of the flow solution to obtain the complete gradient information at each operating condition, regardless of the number of design parameters. NASA Rotor 67 is redesigned through blade profiling. A single point design optimization is first performed to verify the effectiveness and feasibility of the optimization method. Then in order to improve the performance for a wide range of operating conditions, the blade is redesigned at three operating conditions: near peak efficiency, near stall, and near choke. Entropy production through the blade row combined with the constraints of mass flow rate and total pressure ratio is used as the objective function. The design results are presented in detail and the effects of blade profiling on performance improvement and shock/tip-leakage interaction are examined.

... Higher performance can be achieved using a proper combination of two orthogonal blade curvatures, i.e., the use of a blade curved both axially and tangentially, as well as swept and leaned at the same time. Peak efficiency increments from 1% to 1.5% were numerically observed using a blade prevalently curved towards the direction of rotor rotation and slightly backward inclined [12,52,107]. ...

Transonic axial flow compressors are fundamental components in aircraft
engines as they make it possible to maximize pressure ratios per stage
unit. This is achieved through a careful combination of both tangential
flow deflections and, above all, by taking advantage of shock wave
formation around the rotor blades. The resulting flow field is really
complex as it features highly three-dimensional inviscid/viscous
structures, strong shock-boundary layer interaction and intense tip
clearance effects which negatively influence compressor efficiency.
Complications are augmented at part load operation, where
stall—related phenomena occur. Therefore, considerable research
efforts are being spent, both numerically and experimentally, to improve
efficiency and stall margin at peak efficiency and near stall operation.
The present work aims at giving a complete review of the most recent
advances in the field of aerodynamic design and operation of such
machines. A great emphasis has been given to highlight the most relevant
contribution in this field and to suggest the prospects for future
developments.

... Higher performance can be achieved using a proper combination of two orthogonal blade curvatures, i.e. the use of a blade curved both axially and tangentially, as well as swept and leaned at the same time. Peak efficiency increments from 1% to 1.5% were numerically observed using a blade prevalently curved towards the direction of rotor rotation and slightly backward inclined (Biollo & Benini, 2008b;Jang et al., 2006;Yi et al., 2006). ...

... Similar results were recently obtained by [11] [12]. It seems that the better performance is associated with a favorable modification of the three-dimensional shock structure, leading to a reduction of the related aerodynamic losses. ...

A newly designed rotor was modeled from the well-known radially stacked NASA rotor 37 by applying a three-dimensional shape to the original blade stacking line. A considerable curvature toward the direction of rotor rotation was given to the new blade. A three-dimensional numerical model, developed and validated using a commercial computational fluid dynamics Reynolds-averaged Navier-Stokes code, was adopted to predict the flowfield inside the new rotor. Steady-viscous-flow calculations were run at the design speed of the baseline configuration. Compared with rotor 37, the new rotor showed a higher efficiency, mainly due to a three-dimensional modification of the shock structure. At the outer span, the new rotor developed a blade-to-blade shock front located more downstream than in the baseline rotor, with a considerable impact on the flowfield near the casing. Computational fluid dynamics How visualizations showed a less detrimental shock/boundary-layer/tip-clearance interaction at low-flow operating conditions, with a considerable reduction of the low-momentum-fluid region after the shock.

... Sweep and lean were parameterized with a parabolic curve. Jang [16] tested sweep, lean and skew effects on an axial compressor case. Ahn et al. [17] used a parabolic profile for the stacking curve. ...

This paper presents an effective and practical shape optimization strategy for turbine stages so as to minimize the adverse effects of three-dimensional flow features on the turbine performance. The optimization method combines a genetic algorithm (GA), with a Response Surface Approximation (RSA) of the Artificial Neural Network (ANN) type. During the optimization process, the individual objectives and constraints are approximated using ANN that is trained and tested using a few three-dimensional CFD flow simulations; the latter are obtained using the commercial package Fluent. The optimization objective is a weighted sum of individual objectives such as isentropic efficiency, streamwise vorticity and is penalized with a number of constraints. To minimize three-dimensional effects, the stator and rotor stacking curves are taken as the design variable. They are parametrically represented using a quadratic rational Bezier curve (QRBC) whose parameters are related to the blade lean, sweep and bow, which are used as the design variables. The described strategy was applied to single and multipoint optimization of the E/TU-3 turbine stage. This optimization strategy proved to be successful, flexible and practical, and resulted in an improvement of around 1% in stage efficiency over the turbine operating range with as low as 5 design variables. This improvement is attributed to the reduction in secondary flows, in stator hub choking, and in the transonic region and the associated flow separation.

... I N RECENT years, shape optimization based on threedimensional flow analysis has been performed in turbomachinery blade shape design, as demonstrated by Papila et al. [1], Gallimore et al. [2], Ahn and Kim [3], Jang and Kim [4], Jang et al. [5,6], Yi et al. [7], Benini and Biollo [8], and Oyama et al. [9], for example. They have investigated compressor optimization for aircraft engine applications using lean and skewed blades for efficiency enhancement. ...

... At the design flow rate (design mass flow=choked mass flow rate 0:965 in Fig. 3), the adiabatic efficiency obtained by the numerical analysis for the reference blade is only 1.3% higher than the experimental efficiency. Further validations of the present numerical procedure are available in [3][4][5][6]. ...

... Fx fx Zx (6) whereFx represents the unknown function and fx is the global model, whereas Zx represents the localized deviations. Zx is the realization of a stochastic process with mean zero and nonzero covariance. ...

A major issue in surrogate model-based design optimization is the modeling fidelity. An effective approach is to employ multiple surrogates based on the same training data to offer approximations from alternative modeling viewpoints. This approach is employed in a compressor blade shape optimization using the NASA rotor 37 as the case study. The surrogate models considered include polynomial response surface approximation, Kriging, and radial basis neural network. In addition, a weighted average model based on global error measures is constructed. Sequential quadratic programming is used to search the optimal point based on these alternative surrogates. Three design variables characterizing the blade regarding sweep, lean, and skew are selected along with the three-level full factorial approach for design of experiment. The optimization is guided by three objectives aimed at maximizing the adiabatic efficiency, as well as the total pressure and total temperature ratios. The optimized compressor blades yield lower losses by moving the separation line toward the downstream direction. The optima for total pressure and total temperature ratios are similar, but the optimum for adiabatic efficiency is located far from them. It is found that the most accurate surrogate did not always lead to the best design. This demonstrated that using multiple surrogates can improve the robustness of the optimization at a minimal computational cost. Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

... Recently, Benini [9] performed a multi-objective design optimization on the NASA Rotor 37 and demonstrated that the overall efficiency can be significantly improved by giving the blade a proper lean toward the direction of rotation, due to a drastic modification in the shock structure (passing from a nearly normal shock to two less-intense oblique shocks) within the blade passage. More recently, the positive impact of lean blade curvature was also confirmed by Jang et al. [10] and Yi et al. [11]. ...

A numerical investigation to understand the impact of leaned blades on the aerodynamic behaviour of transonic axial flow compressor rotors was undertaken. The influence of lean was analyzed using a three-dimensional CFD model, based on the Reynolds-averaged Navier-Stokes equations, which was previously validated against NASA Rotor 37 existing experimental data. Next, two configurations of leaned rotors were modelled from the original Rotor 37 by changing the circumferential curvature of the original stagger line using four control points (located at 0%, 33%, 67% and 100% of the span). All the new transonic rotors were simulated and the results revealed many interesting aspects which are believed to be very helpful to better understand the blade curvature effects on the shock and secondary losses within a transonic rotor.