Hybrid Laminar Flow Control Research Articles

Energy Absorption Properties of 3D-Printed Polymeric Gyroid Structures for an Aircraft Wing Leading Edge

Laminar flow offers significant potential for increasing the energy efficiency of future transport aircraft. At the Cluster of Excellence SE2A—Sustainable and Energy-Efficient Aviation—the laminarization of the wing by means of hybrid laminar flow control (HLFC) is being investigated. The aim is to maintain the boundary layer as laminar for up to 80% of the chord length of the wing. This is achieved by active suction on the leading edge and the rear part of the wing. The suction panels are constructed with a thin micro-perforated skin and a supporting open-cellular core structure. The mechanical requirements for this kind of sandwich structure vary depending on its position of usage. The suction panel on the leading edge must be able to sustain bird strikes, while the suction panel on the rear part must sustain bending loads from the deformation of the wing. The objective of this study was to investigate the energy absorption properties of a triply periodic minimal surface (TPMS) structure that can be used as a bird strike-resistant core in the wing leading edge. To this end, cubic-sheet-based gyroid specimens of different polymeric materials and different geometric dimensions were manufactured using additive manufacturing processes. The specimens were then tested under quasi-static compression and dynamic crushing loading until failure. It was found that the mechanical behavior was dependent on the material, the unit cell size, the relative density, and the loading rate. In general, the weight-specific energy absorption (SEA) at 50% compaction increased with increasing relative density. Polyurethane specimens exhibited an increase in SEA with increasing loading rate, as opposed to the specimens of the other investigated polymers. A smaller unit cell size induced a more consistent energy absorption, due to the higher plateau force.

Investigation of Hybrid Laminar Flow Control Capabilities from the Flight Envelope Perspective

The present work conducts a multifidelity aerodynamic design of a medium-range commercial aircraft wing featuring hybrid laminar flow control (HLFC) technology. The design was performed to investigate the capabilities of the HLFC, considering the entire design flight envelope, low-speed performance requirements, and various potential mission scenarios. A combination of medium-fidelity aerodynamic design tools for laminar flow control using MSES-COCO-LILO, CFD RANS for high-lift cases, the quasi-three-dimensional for database generations, and SUAVE for mission analysis were used to design and assess aircraft’s performance with the HLFC wing. Studies of the design objective demonstrated a conflict between friction and compressibility drag that strongly affects the design objective function and the wing performance at various off-design conditions. A strong dependence of HLFC on flight conditions was observed to indicate technology performance limitations and a tradeoff between airplane emissions, range, and costs. Finally, a comparison of medium- and low-fidelity performance results showed deviations in the design fuel burn of 4%, a minimum possible harmonic range difference of 3%, and direct operating costs of 2%. The outcome suggests the need for better compressibility and parasite drag models for early design stages to accurately model the HLFC technology without introducing complicated methods at the first sizing steps.

Aircraft Wing Design for Extended Hybrid Laminar Flow Control

Laminar flow offers significant potential for increasing the energy-efficiency of future transport aircraft. The German Cluster of Excellence SE2A is developing a new approach for hybrid laminar flow control. The concept aims to maintain laminar flow up to 80% of the chord length by integrating suction panels at the rear part of the wing, which consist of a thin suction skin and a supporting core structure. This study examines effects of various suction panel configurations on wing mass and load transfer for an all-electric short-range aircraft. Suction panel material, as well as thickness and relative density of the suction panel core are modified in meaningful boundaries. Suction panels made from Ti6Al4V offer the most robust design resulting in a significant increase in wing mass. For the studied configurations, they represent up to 33.8% of the mass of the wingbox. In contrast, panels made from Nylon11CF or PU1000 do not significantly increase the wing mass. However, the use of these materials raises questions about their robustness under operational conditions. The results demonstrate that the choice of material strongly influences the load path within the wing structure. Ti6Al4V suction panels provide sufficient mechanical properties to significantly contribute to load transfer and buckling stiffness. Locally, the share of load transfer attributed to the suction panel exceeds 50%. In contrast, compliant materials such as Nylon11CF or PU1000 are inherently decoupled from load transfer. Unlike the thickness of the suction skin, the relative density of the core structure strongly affects the wrinkling stiffness. However, wrinkling failure did not appear critical for the examined suction panel configurations. In the present study, the mechanical properties of Ti6Al4V cannot fully be exploited. Therefore, compliant suction panels made from Nylon11CF are preferred in order to achieve a lightweight solution, provided that they meet operational requirements.

Receptivity and Stability Theory Analysis of a Transonic Swept Wing Experiment

Surface suction provides an efficient way to delay boundary layer transitions. In order to verify the suction effects and determine the mechanism of suction control in transonic swept wing boundary layers, wind tunnel transition measurements in a hybrid laminar flow control (HLFC) wind tunnel model uses an infrared thermography technique in the Aircraft Research Association (ARA) 2.74 m × 2.44 m low turbulence level transonic wind tunnel. Based on the experimental data of stationary crossflow dominant transitions without and with surface suction in transonic swept wing boundary layers, in this paper, the effects on the receptivity and linear and nonlinear evolution of stationary crossflow vortices have been analyzed with the consideration of curvature. Theoretical analysis agreed with the experimental observations in regard to the transition delay caused by boundary layer suction near the leading-edge region.

Design of Hybrid-Laminar-Flow-Control Wing and Suction System for Transonic Midrange Aircraft

Hybrid laminar flow control (HLFC) has shown significant promise in the viscous drag reduction of aircraft. However, the use of HLFC for commercial applications requires further simplification. The current study proposes tools for the conceptual design of transonic HLFC wing and suction system. In the first part of the study, airfoil sections for the wing are optimized for minimum total drag using a multi-objective genetic algorithm approach at six spanwise locations. The induced drag of the wing is estimated using a vortex lattice method solver. In the second part of the study, suction system design is performed using ASPeCT, an in-house solver for HLFC system design. A simplified inner structure for the suction system is proposed, which can be integrated easily within the wing structure. A total drag penalty approach is proposed to establish a tradeoff between matching the target suction distribution and the complexity of the suction system. Finally, the additional weight and off-design performance of the suction system are analyzed for a ±0.1 change in the design lift coefficient. A maximum fuel reduction of 7% can be expected with the HLFC system taking into account the additional weight added and power off-take from the engine.

Aerodynamic drag reduction through a hybrid laminar flow control and variable camber coupled wing

This paper presents computational fluid dynamics (CFD) results of a transonic transport aircraft wing, featuring a hybrid laminar flow control (HLFC) and variable camber (VC) technology coupling. The goal of the paper is a quantitative assessment of synergistic effects for aerodynamic drag reduction, when combining the possibility of actively shaping the surface pressure distribution of the wing through VC with the passive natural laminar flow aspect of HLFC. Modeling approaches for both VC integration, achieved through deflections of an Adaptive Dropped Hinge Flap (ADHF), and boundary layer suction into a CFD workflow are presented. Transition prediction is accomplished with the γ−Reθ+Cross-flow(CF) transition turbulence model, and linear stability theory (LST) coupled to a two-N-factor transition prediction method. Both methods reflect synergy-driven effects. While the extent of laminar flow predicted by the γ−Reθ+CF model is limited, both favorable ADHF settings and boundary layer suction lead to an overall drag reduction. This is correspondingly reflected through the analyses via LST. Furthermore, the latter predicts a pronounced downstream shift in transition position with increasing suction strength, where the inherent differentiation of transition mechanisms in the two-N-factor method between Tollmien-Schlichting (TSI) and cross-flow instabilities (CFI) reflects a marked reduction in TSI N-factors with increasing ADHF deflection angles. Even though N-factors associated to CFI partially increase through ADHF deflections, the intended synergistic effects are represented throughout the investigated parameter range, leading to an increase in the extent of laminar flow for adequate ADHF deflection angles.

Multidisciplinary Design Optimization of Transonic Wings with Boundary-Layer Suction

A quasi-three-dimensional aerodynamic solver is developed for the aerodynamic analysis of wings in a transonic regime that is able to capture the effect of BLS in hybrid laminar flow control (HLFC) application or transition to turbulent flow for natural laminar flow (NLF). The tool provides accurate results, but without the high computational cost of high-fidelity tools. The solver combines the use of an Euler flow solver characterized by an integral boundary-layer method and linear stability analysis using a approximation for transition prediction. In particular, a conical transformation is adopted, including the determination of the shock-wave position. The solver is implemented in a multidisciplinary design optimization (MDO) framework, including wing weight estimation and aircraft performance analysis. The framework consists of different modules: aerodynamics, structure, suction system analysis, and performance evaluation. Using a genetic algorithm and considering HLFC technology, wing MDO has been performed to find the optimum wing planform and airfoil shape. A backward-swept wing (BSW) aircraft, developed inside the Cluster of Excellence–Sustainable and Energy Efficient Aviation (A) is studied. Novel technologies such as active flow control, limited maximum load factors due to load alleviation, and novel materials allow a fuel weight reduction of 6%.

Development of a medium/long-haul reference aircraft

For the evaluation of future aircraft architectures or novel technologies, a well-understood and sound reference to compare to is essential to prove the impact of intended changes. A reference aircraft serves as a basis for calibration of the aircraft and is used as a starting point for subsequent investigations, sensitivity studies or optimizations. The prime need for such a reference arose from the European Clean-Sky-2 project HLFC-Win (Hybrid Laminar Flow Control—Wing), where no industrial reference data for a conventional aircraft were available. The project investigates a HLFC system integrated into the wing aiming to reduce the wing drag and consequently reducing the fuel consumption. Therefore, this paper presents the D300-XRF1 designed by DLR, which is based on the AIRBUS research aircraft XRF1 (eXternal Research Forum). It is intended to be used as a reference aircraft database representing aircraft for medium- and long-range missions. A variable fidelity multidisciplinary design analysis and optimization (MDAO) aircraft design environment is set up to provide a consistent estimate of the geometry, mass breakdown, propulsion system, aerodynamics and aircraft performance. A conceptual aircraft design tool is utilized in the aircraft design environment to initialize the process, and higher-fidelity modules are used to enhance the results. The presented results describe the overall aircraft characteristics of the D300-XRF1 based on 2010 entry into service technology level and is offered to be used as a reference within the aviation research community, hopefully reducing similar design efforts in other research projects.The aircraft operates at a design cruise Mach number of 0.83, has a design range of 5500 NM and transports a payload of 31.5 t (300 PAX at 105 kg/PAX). The D300-XRF1 serves as a consistent reference aircraft database and provides a holistic overview of the aircraft’s performance that has been presented to and approved by AIRBUS. Therefore, this reference aircraft design can be used for future studies and to assess new technologies on a sophisticated level.

Hybrid Laminar Flow Control Optimizations for Infinite Swept Wings

Maintaining the laminar flow on surfaces through active control is a significantly promising technique for reducing fuel burn and alleviating environmental concerns in commercial aviation. However, there is a lack of systematic parameter studies for the hybrid laminar flow control (HLFC) together with natural laminar flow (NLF). To address this need, we optimize the infinite swept wings with different sweep angles and at various conditions, including different Mach numbers, Reynolds numbers, and lift coefficients. The Reynolds-averaged Navier-Stokes (RANS) solver coupled with the linear stability theory is applied for the laminar-turbulent transition prediction, and the traditional optimization method based on evolutionary algorithms is applied for laminar flow wing optimization. The optimization results found that HLFC is required when the NLF fails at a larger sweep angle (35°) and Reynolds number ( 20 × 10 6 ). The lower pressure peak with boundary-layer suction is found to delay the transition of the regional aviation condition. Besides, the pressure distribution of HLFC is similar to NLF results at the lower Reynolds number ( 10 × 10 6 ) or sweep angle (25°), i.e., a gentle negative pressure gradient near the leading edge and a small favorable pressure gradient behind it. Clarifying the characteristics of laminar flow wings will advance the application of the laminar flow technique within its field.

Design Exploration of Transonic Airfoils for Natural and Hybrid Laminar Flow Control Applications

Designing transonic laminar swept wing at high Reynolds numbers is challenging due to the premature flow transition from the prominent crossflow instabilities (CFIs). Hence, natural laminar flow (NLF) wings are limited to lower sweep angles. In this study, hybrid laminar flow control (HLFC) is used to extend this limit to design low-drag transonic infinite wing. A multi-objective genetic algorithm with competing drag components as objectives is used to design NLF and HLFC airfoils. Optimal design is a tradeoff between the drag reduction from skin friction drag, pressure drag, and suction drag, and does not resemble initial airfoils. Airfoil shape and suction distribution are coupled and optimized simultaneously. Euler flow solver with integral boundary-layer method is coupled with a higher-fidelity Linear Stability Analysis using 2.5D approximation for transition prediction. At wing sweep of 22.5°, Mach number of 0.78, and Reynolds number of 30 million, optimum NLF airfoil has 27% lower drag than an optimum turbulent airfoil. The optimum HLFC airfoil showed a 25% lower total drag than the NLF airfoil. A higher optimum sweep angle was observed for low-drag HLFC airfoil (20.5°) in comparison to the NLF airfoil (16.8°) and both favored an undercut on the lower surface to dampen CFI.

The Aircraft Family Concepts for an Advanced Technology Regional Aircraft

The aim of this work is to make a feasibility study of the aircraft family concepts using a combined Hybrid Laminar Flow Control - Variable Camber Wing (HLFC-VCW) for a high subsonic Advanced Technology Regional Aircraft (ATRA). The prediction of ATRA’s performance used computational fluid dynamic and empirical methods. The aircraft family concept using a combined HLFC–VCW is feasible for the ATRA aircraft family from an aerodynamic point of view.

Inverter prototype development for HLFC compressor applications

A key component in Hybrid Laminar Flow Control (HLFC) is a turbo-compressor, which requires an inverter. However, a harsh environment in combination with restrictive boundary conditions make the inverter design very challenging. Moreover, aviation certification standards have to be considered. By reason of its growing significance, a Model-Based Systems Engineering (MBSE) approach is described to break the HLFC system requirements down to the lower level of the inverter. Using the acquired set of requirements, the design of an inverter prototype was initiated. For this, the compressor motor, a Permanent Magnet Synchronous Motor (PMSM) running up to 150,000 text {min}^{text {-1}} at a power of more than 5 kW, was characterized by measurements. Thereafter, a control concept was elaborated and implemented on a preliminary electronics. In the end, feasibility tests were conducted on a testbed, whose results match well with the theory.

Design and power calculation of HLFC suction system for a subsonic short-range aircraft

Hybrid laminar flow control (HLFC) can be a possible solution for future sustainable energy-efficient aviation. The current study proposes a MATLAB-based numerical tool for the design of the suction system for an airfoil optimized for a subsonic short-range HLFC application. Considerable energy losses may occur when the air passes through the perforated metallic outer surface and the inner structure of the suction system. A semi-empirical approach is used to design a layout that provides a target suction velocity based on measured pressure losses through porous medium and substructures. Flowbench measurements were performed on 3D-printed internal core test samples to quantify the pressure losses that can be used to create a lower pressure below the porous sheet matching the target suction velocity. The actual suction realized on the airfoil using this substructure concept has a discrete nature that increases with the distance between two adjacent walls. Finally, the suction system’s power requirement is calculated. The power requirement for distributed suction accounts for the pressure loss characteristics of the porous material, the internal core structure, and throttling holes. However, the study does not include the ducting losses from the substructure to the compressor. Approximately 80% of the total suction power is utilized to eject the sucked air back to the freestream conditions for a system with a compressor and propulsive system efficiency equal to one. The study analyses the performance of the designed internal core layout to different flight conditions and addresses the suction power requirement variation with lift coefficient and flight altitude.

Analysis and Uncertainty Quantification of a Hybrid Laminar Flow Control System

This study aims to quantify suction velocities for hybrid laminar flow control of a vertical fin by taking data and model uncertainties into account. Because suction velocities cannot be measured directly, they are calculated using the Darcy–Forchheimer model, which needs the pressure distribution and porosity characteristics as input. Uncertainties in the pressure distribution are characterized using a novel data fusion method incorporating wind-tunnel and numerical data. Furthermore, geometrical uncertainties of the airfoil that alter the pressure distribution are considered. Two methods are proposed to model the porosity characteristics of the surface: one of which uses a local representation, and the other a global representation. In addition, the modeling error of the Darcy–Forchheimer model is estimated. These input uncertainties are quantified and propagated by Monte Carlo sampling through the Darcy–Forchheimer model. It reveals that local information on the porosity characteristics is essential for accurate suction velocity estimates for this specific application. A sensitivity study shows that the most influential contribution to the variance of suction velocities is the uncertainty in the porosity characteristics, followed by uncertainties in the pressure distribution. The model error and uncertainties in the reference pressure are shown to have a negligible influence.

Numerical analyses of a reference wing for combination of hybrid laminar flow control and variable camber

The objective of the LuFo VI-1 project CATeW (Coupled Aerodynamic Technologies for Aircraft Wings) consists in multifidelity analyses to assess the potential for aerodynamic efficiency increase by combined application of hybrid laminar flow control and variable camber technologies to the wing of a transonic transport aircraft. Individually, both technologies have proven to lead to major aerodynamic drag reductions. An evaluation of the coupled technologies is, therefore, expected to show an even higher potential due to synergy effects. To derive conclusions on system level, low-fidelity (LowFi) overall aircraft design methodologies will be applied for the analysis of a medium haul reference aircraft in the course of the project, while complex aerodynamic phenomena are modelled with high-fidelity (HiFi) computational fluid dynamics methods. The paper at hand presents results of aerodynamic analyses on both fidelity levels for the wing of the turbulent reference configuration CATeW-01, featuring the technology combination as a retrofit. Furthermore, this work encompasses adaptations and implementations performed within both the LowFi and HiFi toolchains. The LowFi toolchain already incorporates several modules for the proposed technology combination. A short presentation of the LowFi-toolchain is given, along with the modeling approach in the HiFi framework using mesh deformations and a mass flux boundary condition. Comparative studies of the turbulent flow field around the wing show good agreement of predicted load distributions in both numerical frameworks, studies based upon the HiFi approach attest the potential for efficiency increase due to the variable camber technology, incorporated by means of Adaptive Dropped Hinge Flap (ADHF) deflections. Considering the coupled application, four different constant suction mass flow rates are examined, where the maximum mass flow causes laminar flow extending over the entire suction panel, thus moving the transition location from the wing’s leading edge to the end of the suction panel. When being coupled with ADHF deflections, again the variable camber technology leads to a reduction of the wing’s pressure drag component with the simultaneous application of boundary layer suction further promoting drag reduction with increasing suction rate. While the combined application shows no mutual inhibition, major reciprocal effects are not directly observable when applying the combination as a retrofit to the reference configuration CATeW-01. This is mainly attributed to the limited extend of laminar flow, thus indicating the necessity for optimization in wing geometry and operating parameters, to achieve extensive areas of laminar flow and to promote the aspired synergy effects.

Introducing variance-based global sensitivity analysis for uncertainty enabled operational and economic aircraft technology assessment

Assessing the efficacy of aircraft and technologies is a crucial step in the aeronautic product development. Due to their prospective nature, such analyses are subject to various uncertainties, which decrease their transparency and can act as a barrier for innovation. Therefore, a comprehensive and systematic inclusion of uncertainties is needed. For the use case of this paper being Hybrid Laminar Flow Control (HLFC), these comprise a number of inputs from different domains such as the design, operation, environment, or economics, leading to the underlying research question: Which parameters contribute to what extent to the output uncertainty of HLFC efficacy? To answer this, this paper introduces variance based global sensitivity analyses (GSA) in combination with a discrete event simulation framework. Considered outputs of the assessment comprise the Net Present Value (NPV) as an economic metric as well as the fuel efficiency as an operational performance indicator. A first monte-carlo simulation revealed an equivocal assessment outcome with ΔNPV values ranging from −$11M up to +$22M. Results of a subsequent GSA reveal the cruise mach speed being the dominant element (39%) in this overall uncertainty, followed by the lack of knowledge in specific fuel consumption penalty (23%) and overall drag reduction potential (9%). Furthermore, this study includes an applied comparison of different GSA methods, i.e. Fourier Amplitude Sensitivity Test and the Sobol' method. While computed sensitivity indices are fairly equal among all alternatives, the lack of quantification of higher order terms of certain methods may pose a disadvantage if interaction effects are high. The contribution of this study helps to direct further research and development efforts regarding HLFC, e.g. to focus on a robust and aerodynamically less sensitive airfoil design. More generally, the use of GSA methods and further uncertainty quantification efforts in prospective assessments can significantly improve the trust in the analysis and with that, help in terms of a commercially successful HLFC development.

Stochastic Investigation on the Robustness of Laminar-Flow Wings for Flight Tests

Natural laminar-flow (NLF) wings and hybrid laminar-flow control (HLFC) wings are efficient drag reduction technologies. It is vital to develop robust laminar-flow wings to research the stochastic characteristics of both NLF and HLFC wings and reveal the generation mechanism for differences in their statistical responses. Wing-glove flight experiments and deterministic numerical simulations using the method with a suction-velocity model are performed, which are in good agreement. Uncertainty and correlation analyses based on nonintrusive polynomial chaos expansion are then performed to evaluate the influence of operational and geometric uncertainties. The simulations indicate that operational condition uncertainties have a greater impact on their statistical responses. Pressure coefficients near the leading edge and end region of the favorable pressure gradient are the most sensitive to disturbances in the angle of attack (AOA) and Mach number, respectively. Whereas HLFC wings significantly delay the laminar–turbulent transition, NLF wings may have better robustness against disturbances if the development of Tollmien–Schlichting (TS) waves is not completely suppressed in the suction region. This is because disturbances affect statistical responses of HLFC wings by changing both the local pressure gradients and suction coefficient distributions. Positive correlations between the AOA, local pressure gradients, and suction coefficients amplify the influence of AOA disturbances. Meanwhile, Mach-number disturbances have negative and positive correlations with local pressure gradients and suction coefficients, respectively. The opposite correlation weakens the influence of Mach-number disturbances.

Experimental investigation of hybrid laminar flow control by a modular flat plate model in the DNW-NWB

To determine the characteristics of new suction concepts for hybrid laminar flow control (HLFC) a modular flat plate wind tunnel model is investigated in the DNW-NWB wind tunnel facility. This approach allows detailed examination of suction characteristics in consideration of realistic boundary layer flow conditions. The following evaluation reveals the effects of joining methods between successive panels and other surface disturbances of porous materials and underlying chambers on HLFC techniques. After successful measurements with and without suction panels, this paper compares experimental results with theoretical and numerical approaches and draws conclusions from N-factor results and boundary layer (BL) measurements.

Multidisciplinary design optimisation of a fully electric regional aircraft wing with active flow control technology

AbstractThe German research Cluster of Excellence SE2A (Sustainable and Energy Efficient Aviation) is investigating different technologies to be implemented in the following decades, to achieve more efficient air transportation. This paper studies the Hybrid Laminar Flow Control (HLFC) using boundary layer suction for drag reduction, combined with other technologies for load and structural weight reduction and a novel full-electric propulsion system. A multidisciplinary design optimisation framework is presented, enabling physics-based analysis and optimisation of a fully electric aircraft wing equipped with HLFC technologies and load alleviation, and new structures and materials. The main focus is on simulation and optimisation of the boundary layer suction and its influence on wing design and optimisation. A quasi three-dimensional aerodynamic analysis is used for drag estimation of the wing. The tool executes the aerofoil analysis using XFOILSUC, which provides accurate drag estimation through boundary layer suction. The optimisation is based on a genetic algorithm for maximum take-off weight (MTOW) minimisation. The optimisation results show that the active flow control applied on the optimised geometry results in more than 45% reduction in aircraft drag coefficient, compared to the same geometry without HLFC technology. The power absorbed for the HLFC suction system implies a battery mass variation lower than 2%, considering the designed range as top-level requirement (TLR).

Coupled Boundary-Layer Suction and Airfoil Optimization for Hybrid Laminar Flow Control

The present work incorporates the effects of boundary-layer suction in designing airfoils for hybrid laminar flow control application. The overall airfoil shape, the suction velocity distribution, and its location are optimized for minimum total drag while sustaining laminar flow over 80% of the airfoil top surface. Nondominated Sorting Genetic Algorithm II is used with the aerodynamic load computations from XFOILSUC and transition prediction from the improved Van Ingen method. The airfoil is designed for short-range subsonic conditions for three design lift-coefficient scenarios: 1) 0.4, 2) in the range of 0.3–0.7, and 3) in the range of 0.3–0.7 with suction onset at midchord. The optimized airfoil for scenario 3, with suction onset at midchord, results in a thicker airfoil with natural laminar flow (NLF) on the upper surface comparable to NLF airfoils. The total drag reduces by one-third due to the effects of suction. On the other hand, without limiting the suction onset (scenario 2), a thinner airfoil with longer NLF on the bottom surface and lower total drag is obtained. Optimum suction onset location is predicted to be at 30% of the chord. Suction is also observed to improve the drag bucket at off-design conditions.