The goal of developing a coupling methodology for the design of shape-adaptive compressor blades is to provide a multidisciplinary design tool, covering aspects from aerodynamics and structural design during all design stages, in order to produce compressor blades capable of having an optimal aerodynamic performance at different flight phases, while guaranteeing structural integrity. The design method is generalized and can be applied to multiple types of blade geometries and aim at different shape adaption scenarios. However, as previously mentioned, for this paper the exemplary focus lies on the first-stage compressor blades of the NASA 67 rotor and is described in detail for such a case.
At a first level and as a first step, the off-design operating conditions along with the reference blade geometry are transferred to the aerodynamic design space. Within the aerodynamic design, first ideal inflow as well as flow deflection requirements for the off-design operating conditions are derived, using a streamline curvature calculation (as explained in
Section 2.2.1). Simultaneously, a first qualitative assessment of the feasible deformations through the piezoceramic actuation is conducted for the structural design for different actuator configurations (
Figure 2). Therefore, the reference blade and initial ideal target shapes are taken as input to analyze the different possibilities for structural morphing and calculating the achievable shapes.
Once simulated, the morphing shape results of the preliminary analysis are sent back to the aerodynamic analysis, where the achievable deformations are evaluated according to aerodynamic design criteria. A comparison of the spanwise deformation requirements with the structurally feasible deformations reveals adjustment requirements for the structural adaption concept as well as for the meridional design. In an iterative procedure, the actuator configuration and the aerodynamic vortex design are modified until a sufficient accordance between aerodynamic requirements and structurally feasible deformations is achieved. Within the actuation optimization, geometric parameters, such as the number of necessary actuators, their size and positions, the material properties and fiber orientations of the actuation fabric and the material possibilities for the blade itself, are covered.
The second step or level of the coupled design process focuses on the detailed analysis of the aerodynamic profile sections, comparing the reference blade performance to that of the structurally achievable morphing shapes. With the meridional design finalized and a preliminary actuator configuration selected, the rotor blade is re-designed by varying the camber design according to the aerodynamically predicted inflow as well as flow deflection variations. The derived target shapes are then transferred to the structural design, represented by the right side in
Figure 1, to provide an orientation for the structural deformations. The ideal target design also serves as an input for the second coupling step, the simulative performance evaluation, wherein a detailed performance analysis of the aerodynamic target design as well as of the morphed blade is conducted. To reduce calculation effort and time within this coupling step, a representative Q3D (quasi-three-dimensional) evaluation approach is introduced on the aerodynamic side. By focusing on a tip section of the shape-adaptive system, the variation in profile performance through shape morphing can be evaluated, without relying on an expensive 3D flow analysis. Even though this analysis only gives a result for the tip section, it already sets a good reference for performance values and for assessing the agreement in morphing design requirements between structure and aerodynamics, especially due to the transonic flow behavior in the upper area of the rotor.
The design process is repeated for every pre-defined adaption scenario in order to evaluate the suitability of actuation concepts for different aerodynamic off-design requirements. The iterative character of the design methodology, with a three-step coupling approach of increasing fidelity, allows a continuous interaction between aerodynamic design and structural morphing conditions throughout the entire design process. With the introduction of a representative evaluation approach through Q3D simulations, the base for an efficient coupled optimization routine is additionally set.
2.1. Selection of the NASA 67 Rotor as Test Case and Reference Design
The NASA 67 rotor is a widely researched test case rotor developed by NASA and used since the 1980s for diverse modeling and experimental scenarios [
22,
23]. The rotor was originally used to collect tangential and axial velocities measured with the help of a laser anemometer (LA). Through these measurements, stream-wise and pitch-wise flow data were made available, offering insights into the detailed aerodynamic performance of the rotor. The front stage rotor was chosen for this study because the geometry design data as well as the flow data in the meridional design plane are well documented by Hathaway and Strazisar in [
22], offering an extensive data base for referencing and evaluating the aerostructural design methodology. Additionally, the transonic and supersonic regions, with a peak relative tip Mach number of 1.38, offer a high potential for the application of shape morphing. Because the blade shock interaction is highly sensitive towards small changes in blade profile geometry, shape morphing is expected to have a high impact on the rotor performance.
For the transformation of the NASA 67 rotor into a shape-adaptive system, the original geometry data are extracted, refined and smoothed. Due to the low resolution of the rotor leading and trailing edges, circles are iteratively fitted until a tangential transition between suction and pressure sides is achieved.
By remodeling the original reference geometry with a parabolic mean camber line [
24] and a CSM (Class Shape/Class Form function Methodology) thickness distribution [
25], the adaptability of the reference design and the flexibility for the creation of aerodynamic redesigns is increased. Additionally, relevant blade profile design parameters, such as the turning angle, stagger angle and leading and trailing-edge metal angles, can be derived as reference values for the aerodynamic redesign methodology. The placement of the profile reference sections for the rotor design is an important coupling parameter between aerodynamic pre-design, structural deformation simulation and evaluation. They are kept constant as a common reference throughout the coupled design process. For the modeling of the reference geometry, the number of reference sections is increased by interpolating the derived design parameters in radial direction. Thereby, 20 equally spaced streamlines with a linear slope within the blade row are created in the meridional design plane and defined as reference locations for the profile section throughout the shape adaption process (as explained in
Section 2.2.1.).
After remodeling the reference geometry, the stage performance is evaluated in a CFD simulation. For the simulation, a structured mesh is created in AutoGrid with a y+ value of approximately 1 at the blade’s surface, the hub and the shroud end wall. For the stationary simulation of the speed line at design speed, a k-ω turbulence model is selected, and the static outlet pressure is iteratively increased until simulation divergence predicts the simulative onset of stall. Based on the simulated operating range and speed line, where the red dot marks the literature design point, different adaption scenarios are derived, which then serve as input for the aerodynamic design methodology (
Figure 3). Three shape adaption scenarios are exemplarily selected for this study.
2.4. Aero-Structural Coupling in the Meridional Plane
For the comparison of aerodynamically required deformations and structural feasible morphing, the deformed grid data from the FEM simulation are analyzed according to aerodynamic design criteria and angular definitions (
Figure 5). At this point in the coupling methodology, two challenges occur. Since the blade has been deformed, the structure of the exportable FEM data does not exactly follow the aerodynamic input. Furthermore, since FEM calculations do not need as much detail as flow simulations do, the mesh resolution of the FEA is much coarser than the one required for detailed CFD simulations, especially at the leading- and trailing-edge areas. To overcome these challenges, a further post-processing of the mesh grid data is required, prior to the aerostructural coupling. Since the numbering of the grid points follows an internal indexing set up by the Ansys Mechanical modules, the grid points have to be assigned back to the original aerodynamic design sections in the meridional plane. By keeping the blade sections throughout the structural analysis, the sorting process is simplified. With the blade sections separated and radially sorted, the 3D sections are transformed back into the 2D design plane to calculate the spanwise blade staggering of the deformed geometry and to rotate the blade profiles back into design position (
Figure 6). Furthermore, a separation of the suction and pressure sides is necessary to allow blade camber reengineering for every profile section. Calculating the chordwise slope of the re-engineered profile camber yields variation of the leading-edge and trailing-edge camber angles
αi due to the shape morphing, and the structurally feasible turning variation ΔΔ
φ can be calculated according to
Figure 5. The feasible variation in section-wise blade turning is then directly compared with the desired aerodynamic target design requirements.
The three predefined shape adaption scenarios are separately analyzed, comparing the aerodynamically derived flow angles with the feasible structural deformations induced by the piezoceramic actuator configurations. In order to evaluate the pressure rise capability of the morphed rotor blade, the required variation in flow deflection ΔΔ
β is compared to the achievable morphing of the blade turning ΔΔ
φ (
Figure 18). Additional to the deflection requirement, the variation of the leading-edge metal angle
κ1 has to match the altered inflow angle
β1, in order to achieve the mass flow required by the adaption scenarios (
Figure 19).
The iterative character of the design methodology becomes directly apparent when the feasible deformations are generally compared to the flow deflection requirement of the
PM scenario with a standard free vortex law, as shown in
Figure 18, left. While the variation in flow deflection requirements is highest towards the blade hub, the hub sections remain nearly undeformed due to the blade clamping into the hub. Instead, the achievable deformations increase towards the blade tip, where for all actuation concepts the highest morphing potential is visible. This poses a major conflict for aerostructural coupling and for the creation of aerodynamic target designs. To match the deformation pattern, the hub loading for the new design point is altered by varying the n-factor of the vortex design (equation 1), until the aerostructural contradiction is reduced to a minimum, without exceeding the blade loading limits defined by the diffusion number. Thereby, the best agreement between aerodynamic requirements and an actuation configuration can be identified for the following simulative evaluation. For the
PM- and the
PR- scenario, the pressure ratio for the redesign is increased, causing a spanwise raise in deflection requirement. By unloading the hub of the redesigned rotor, the deformation requirement at the hub shifts towards the blade tip. As the actuation concept with two actuators, a zero degree fiber orientation, expansion of the suction-side actuator and compression of the pressure-side actuator yields the overall highest variation of blade turning, an n-factor of
n = 0.79 is selected for both scenarios to match the feasible deformation distribution conveniently.
Similar to the previous two adaption scenarios, a constant vortex design for the
MF redesign results in the highest deformation requirement towards the hub (
Figure 18, right). As an increased mass flow is selected for this adaption scenario, while the pressure ratio remains constant, the required spanwise blade turning has to be reduced compared to the reference design. This determines an increase in hub loading, which is limited by the diffusion number, and the exclusion of a spanwise altering deformation requirement. With these limitations, n-factors higher than 1.1 are not feasible from a structural standpoint, leaving the free vortex design with
n = 1.1 as the best option for the
MF redesign (Equation (1)). With this option, a deviation between aerodynamic design requirements and structural deformation feasibility remains. Additional to a deviation in turning requirement at the blade hub, a reproduction of the structurally feasible deformations towards the blade tip is not entirely possible without causing a spanwise altering deformation requirement. As a compromise, an actuation concept with two expanded actuators, a 45° suction-side and a 135° pressure-side fiber orientation seems to be best suited for this adaption scenario.
With the preliminary selection of vortex design and actuation configuration based on the turning variation as the driving coupling parameter, the incidence through shape adaption represents an additional quality criterion for the evaluation of the accordance between aerodynamic target design and structurally feasible deformations.
For the quantification of the spanwise shape adaption incidence, the variation of the relative inflow angle, Δ
β1, according to the SLC solution is compared to the structural variation of the leading-edge metal angle, Δ
κ1, which, again, is a result of the leading-edge camber angle variation Δα
1 as well as the stagger angle variation Δ
λ (
Figure 5).
The shape adaption incidence allows a further evaluation of the spanwise deviation between inflow angle variation and feasible leading-edge metal angle morphing. An elevated incidence would diminish the rotor efficiency through increased profile losses up to unstable operating conditions in the selected adaption scenario and should therefore be minimized.
For the
PM scenario, the highest shape adaption incidence occurs in the subsonic blade hub area, where the rotor is expected to show an increased incidence tolerance. Towards the transonic and supersonic inflow regimes of the upper rotor sections, the shape adaption incidence decreases (
Figure 19). This is beneficial for the selected actuation concept, since the transonic and supersonic profile sections are highly sensitive towards increased inflow incidence. However, an elevated incidence tolerance, especially for the subsonic rotor sections, should be considered for the reference design of a shape-adaptive compressor stage. Comparing the same actuation concepts to the
PR redesign with
n = 0.79 yields a reversed spanwise shape adaption incidence distribution. The incidence is moderate in the hub area, with a minimum at approximately 45% rotor height and a maximum of 1.4° at the supersonic blade tip section (
Figure 19). This contradicts the suitability of the available actuation concepts, as the selected design point might not be achievable, due to increased profile losses in the tip region of the deformed rotor.
The increased design point mass flow in the MF scenario causes a decrease in the spanwise leading-edge metal angle over all blade sections, with a maximum of 3.2° at approximately 45% rotor height. Only a minor improvement is achievable through a vortex law alteration towards an increased hub loading. Since the variation in relative inflow angle Δβ1 is dominant for this adaption scenario, this result indicates that the initially specified mass flow variation of 2.75 kg/s is not feasible through shape adaption. However, the selected actuation concept (nact = 2, o1 = 45°, o2 = 135°, both actuators expanded) achieves a reduction of shape adaption incidence in the rotor tip region and is therefore selected for a further simulative investigation.
2.5. Representative Simulative Evaluation
Under the assumption of a non-deformable thickness distribution throughout the adaption process, only the deformed and re-engineered blade camber is extracted from the FEM-post data to prepare the second step in the coupling methodology. The second level of coupling starts once the conceptual design phase of the morphing blade has been concluded and a qualitative compromise of possible spanwise morphing distributions has been found. For the aerodynamic redesign, the vortex designs are chosen according to the available and feasible deformations.
Depending on the adaption scenario, one of the free blade morphing parameters
fc,
xc or
λ is specified, defining the others through the required blade turning and inflow angle. With the highest deformations concentrated in the blade tip region, leaving the lower blade sections basically undeformed, the transonic behavior of the blade profiles plays a major role, emphasizing the maximum camber position
xc as the active design parameter. In order to control the flow acceleration towards a compression shock and to reduce suction-side curvature beyond the leading edge, a rearward shift of
xc is implemented for the tip sections of the rotor. Between 70% rotor height and blade hub, the maximum camber position is kept constant. Combined with an increase or decrease in the maximum camber, depending on the specified flow deflection requirement, the camber design is derived for all sections (Equation (5)). With
xc and
fc defined through the turning requirement, the blade camber leading-edge angle is fixed, and the required spanwise stagger angle can be calculated for each section (Equation (9)). With the projection of the profile sections on the meridional reference streamlines, aerodynamic target rotor designs are derived for the three selected adaption scenarios. In
Figure 20,
Figure 21 and
Figure 22, the redesigned target shapes are represented by
Section 2 at 95% of the rotor height and compared to the reference design as well as to the best suited structural deformation, selected in the first coupling step.
Based on the deformation results presented in
Figure 18 and
Figure 19, it can be assumed that for all actuation concepts, the highest deformations occur towards the rotor blade tip. Under this assumption, a preliminary Q3D simulation methodology for the detailed aerodynamic evaluation of the deformed profile performance is implemented in the design methodology. With the deformations highest towards the blade tip and the transonic and supersonic aerodynamic behavior highly sensitive towards small variations in the rotor geometry, a tip section is selected for the representative approach. Since the tip vortex dominates the surroundings of the blade tip, the second profile section at 95% blade height is chosen for the representative approach. The mean streamline for the creation of the simulation domain is derived from the design point SLC solution and interpolated on the reference blade section, defined preliminarily to the deformation study. In order to account for 3D effects, such as channel wall tapering, end wall boundary layer formation and compressibility effects, the AVDR distribution is derived from the reference flow data [
3] and rebuilt with a hyperbolic modeling approach, introduced in [
15]. The AVDR distribution is transformed into a CFD domain thickness distribution, which is then orthogonally added onto the mean streamline to create the radial boundaries of the simulation domain (
Figure 20). With the simulation domain modeled, the deformed profile sections are projected onto the conical mean streamline within the blade row to finalize the Q3D simulation domain setup.
Analogous to the 3D-CFD stage simulation of the reference geometry, a k-ω turbulence model and a structured mesh is used. For the radial domain limits, a frictionless moving wall is assumed, while only one rotor section is simulated with periodic boundary conditions in circumferential direction. The Q3D performance analysis is applied to all actuation concepts and compared to the performance of the reference design for an initial evaluation of the aerodynamic effects of the piezoceramic actuation. Based on the first coupling step and according to
Table 3, suitable actuation configurations are then compared to the performance of the aerodynamic target designs (
Figure 21).
For the
PM scenario, the mass flow reduction leads to a stronger staggering of the blade profiles, amplified by the reduced leading-edge camber angle due to the rearward relocation of the maximum camber. This also decreases suction-side curvature beyond the leading edge, as the profile cambering is now concentrated at the rear end of the profile, following the classic wedge-shaped profile designs for transonic and supersonic inflow conditions [
29]. Compared to the actuator configuration, which yields the highest turning adaption, the stagger angle variation is negligible, while the leading-edge metal angle morphing visible in
Figure 22 is mainly achieved through the increased camber angle at the leading edge. Although the blade profile turning is increased through the piezoceramic actuation, no increase in achievable pressure ratio is predicted in the Q3D simulative approach (
Figure 21, middle). Only a slight shift of the unique incidence condition by less than 0.5° is visible, caused by the variation of the leading-edge metal angle. By considering the profile losses, it becomes evident that the effect of the increased blade turning is diminished by the elevated shock losses due to the higher suction-side curvature and the amplified pre-shock flow acceleration. Compared to the performance of the aerodynamic target shape, the inflow angle variation and the achievable variation in profile pressure ratio are too small to achieve the selected adaption scenario though shape morphing.
For the
PR scenario, the required variation of the stagger angle is compensated by the leading-edge metal angle reduction due to the rearward shift of the maximum camber position. The twist of the target shape remains nearly constant compared to the reference geometry. Although the deformed profile sections (
Figure 23) seem to fit the aerodynamic target shape better than those of the
PM scenario, the required pressure rise is not achievable due to the increased shock losses (
Figure 21). Additionally, the shift of the unique incidence condition is too high for the adaption scenario, where the mass flow, and therefore the unique incidence angle, should remain constant, as indicated by the performance of the aerodynamic target shape.
The aerodynamic simulation for the
MF target design predicts a 1.5° decrease in unique incidence angle due to the increased design point mass flow. Additionally, the pressure ratio is increased compared to the reference design, which results from the lower profile loss values predicted by the Q3D simulation (
Figure 21). Again, the alteration of the maximum camber position towards the trailing edge in combination with a turning reduction and therefore a reduction of the suction-side curvature has a positive influence on the shock-induced profile losses (
Figure 24). The selected actuation concept shows a similar trend, with a slight increase in achievable pressure ratio and a 0.25° reduction of the unique incidence angle. However, the achievable deformations are too small to reach the pre-defined mass flow of the adaption scenario, indicating the requirement for an increased deformability of the reference blade design. For the selected actuation concept (
nact = 2,
o1 = 45°,
o2 = 135°), the actuation mechanism can be switched from expansion to compression, reversing the deformation of the leading-edge metal angle. This increases the total achievable variation of the unique incidence angle to 0.52°, with a compressed actuation corresponding to a
MF adaption scenario with reduced design point mass flow (
Figure 21).