Dr Demetrios Lefas

Modern flutter solvers act as black boxes, providing little understanding of how a wing’saeroelastic design influences its stability. This paper presents a physical explanation of coupled-mode flutter in which the wing’s natural modes form a hierarchical network connected byaerodynamic forces. Within this "forced-response network", each natural mode behaves as amass–spring–damper system whose "effective natural frequency" varies with the freestreamdynamic pressure due to aerodynamic stiffness. Using URANS calculations of the NASACommon Research Model, an energy analysis shows flutter occurs when one of these effectivenatural frequencies becomes equal to the flutter frequency, causing that natural mode toresonate. The resonance is shown to propagate through the network’s connections, resulting inchanges to all other natural modes that ultimately re-stabilize the wing and produce a humpmode. This explanation allows the influence of each aspect of the wing’s aeroelastic designon stability to be physically understood and quantified. It is shown this enables flutter in arepresentative modern airliner to be distilled to only a few parameters that may be targeted inaerodynamic or structural design. The utility of the analysis is demonstrated by explaining theeffects of changing the natural frequencies, freestream Mach number, and static deformation.

The formation of part-chord shock waves at transonic speeds causes a rapid decrease in the dynamic pressure at which a wing flutters, commonly known as the “transonic dip”. Yet, owing to the complexity of the coupled aeroelastic system, no simple physical explanation has been given for why these shocks are destabilizing. This paper investigates the role of shocks in transonic bending-torsion flutter using three-dimensional unsteady Reynolds-averaged Navier-Stokes calculations of the AGARD 445.6 wing. By performing an energy analysis across different Mach numbers, it is shown that the transonic dip is almost entirely caused by changes in the phase difference between the flutter aeroelastic mode’s bending and torsion motions. A simplified model for the aeroelastic system is then presented, which demonstrates that these changes in bending-torsion phase with Mach number occur predominantly due to changes in a single generalized aerodynamic force (GAF). Through visualizing the unsteady pressures during forced oscillations, the changes in this crucial GAF are directly related to the formation of shocks and the changes in shock structure with Mach number, thereby explaining the role of shocks in producing the transonic dip. Finally, it is demonstrated how this physical understanding may be used to inform structural design changes that improve flutter.

A key problem in transonic compressor and fan design is that although a 3D description of the flow is necessary to correctly capture the shock, accounting for it during the sectional design is difficult because the key driving design parameters are unknown. In this paper, it is shown that for inlet relative Mach numbers between 0.85 and 1.10, the pre-shock Mach number is a function of the 3D streamtube area at the throat At over the inlet area A1. This key finding is based on three key transonic flow features, discussed in detail within this paper, being present together across a wide range of 10,000 representative transonic compressor and fan designs published online.1 This unique wide-ranging web-interactive dataset reveals that the effect of changes in the blade geometry, or the 3D streamtube height, on the transonic flow field is one of the same and can be explained simply by keeping track of the associated changes in At/A1. Surprisingly, the pre-shock Mach number at a given At/A1 is shown to be insensitive to the details of the blade surface geometry. Only geometric design choices made in the preliminary design phase, such as the maximum thickness and inlet relative flow angle, are shown to have a second-order effect. These findings suggest that the sectional design phase should focus solely on achieving the desired spanwise 3D At/A1 distribution. The second half of the paper addresses the level of fidelity necessary when calculating the spanwise 3D At/A1, for it to positively influence design; especially when approaching a Mach number of unity. A key conclusion is that failing to resolve the subtle 3D radial flow changes within the blade passage at the appropriate level of fidelity during the early throughflow multistage compressor design stage could mislead the transonic design process. As a result, for the rapid exploration of future compressor designs, this paper advocates utilizing the more than 10,000 transonic design databse to generate an initial 3D blade, which is then assessed early in the design process using At/A1 extracted from 3D CFD.

This paper describes a simple and efficient physics-based method for designing optimal transonic multistage compressor rotors. The key to this novel method is that the spanwise variation of the parameter which controls the three-dimensional shock structure, the area ratio between the throat and the inlet, ‘Athroat /Ainlet’, is extracted directly from the 3D CFD. The spanwise distribution of the area ratio is then adjusted iteratively to balance the shock structure across the blade span. Because of this, the blade design will be called ‘aerodynamically balanced’. The new designmethod converges in a few iterations and is physically intuitive because it accounts for the real changes in the 3D area ratio that directly controls the shock structure. Specifically, changes in both the spanwise 3D flow and in the rotor’s operating condition; thus aiding designer understanding.

Every supersonic fan or compressor blade row has a streamtube, the “sonic streamtube,” which operates with a blade relative inlet Mach number of one. A key parameter in the design of the “sonic streamtube” is the area ratio between the blade throat area and the upstream passage area, Athroat/Ainlet. In this article, it is shown that one unique value exists for this area ratio. If the area ratio differs, even slightly, from this unique value, then the blade either chokes or has its suction surface boundary layer separated due to a strong shock. Therefore, it is surprising that in practice designers have relatively little problem designing blade sections with an inlet relative Mach number close to unity. This article shows that this occurs due to a physical mechanism known as “transonic relief.”

Transonic fan stall flutter is an aeroelastic instability that constrains fan operability and design. Whilst it is known that the suction surface shock dynamics are a major stabilising contributor to the overall aerodynamic damping, the mechanisms governing their variation with reduced frequency, mode shape composition and throttling remain poorly understood. This two-part paper presents a physics-based explanation of the 3D unsteady flow mechanisms governing shock dynamics. Part I investigates pre-throttle reduced frequencies of 0.15 ≤ 𝑘 ≤ 0.73 and torsional axis locations of 0.5 ≤ 𝑙/𝑐 ≤ 3.0 in combined mode shapes, using unsteady aeroelastic simulations of a low-pressure ratio transonic fan. The results show that the conventional quasi 2D incidence ratio does not uniquely collapse the shock motion phase. Instead, the response is governed by the 3D instantaneous streamtube throat-to-inlet area ratio 𝐴ₜ/𝐴₁, extracted from unsteady CFD throughout the vibration cycle. Decomposing 𝐴ₜ/𝐴₁ into streamtube width and height contributions reveals the physics. The width response is controlled by vibration induced, non-axisymmetric inlet pitch adjustment, whereas the height response is governed by throat pressure variation. Both contributions are independently set by the balance between twist driven passage area variation and plunge driven effective blade speed variation. Their magnitudes and phase offset set 𝐴ₜ/𝐴₁ in a manner that can be physically explained and quantified, enabling control of the stabilising shock contribution. The framework therefore relates structural mode shape and aerodynamic design to shock induced damping and transonic performance.

Transonic fan stall flutter is an aeroelastic instability that constrains fan operability and design. Although the suction-surface shock provides a strongly stabilising aerodynamic-work contribution before flutter onset, the mechanisms by which throttling towards stall weakens this contribution remain poorly understood. This second part of a two-part study investigates shock dynamics across reduced frequencies 0.15 ≤ 𝑘 ≤ 0.73 and torsional-axis locations of 0.5 ≤ 𝑙/𝑐 ≤ 3 in combined mode shapes, using unsteady aeroelastic simulations of a low-pressure-ratio transonic fan. Throttling is shown to reduce shock stabilisation primarily by decreasing the magnitude of the unsteady shock response. This reduction represents the dominant individual contribution to the decrease in overall aerodynamic damping. The instantaneous streamtube throat-to-inlet area ratio, 𝐴ₜ/𝐴₁, introduced in Part I, is used to explain the underlying mechanism. Throttling produces a non-reattaching midspan separation and associated centrifuging streamlines, causing a local post-shock phase reversal that alters the non-axisymmetric passage mass-flow redistribution. By continuity, the inlet mass-flow response shifts in phase, bringing the inlet-pitch variation into closer phase alignment with the blade deflection. This reduces the streamtube width contribution and therefore the magnitude of unsteady 𝐴ₜ/𝐴₁, weakening the stabilising shock response, while the streamtube height contribution changes little. At low 𝑘, the relative width and height contributions to 𝐴ₜ/𝐴₁ become comparable and drive the shock in opposing directions, producing an additional phase rise that can even make the shock destabilising. Steady quasi-three-dimensional calculations confirm that this behaviour arises from the altered composition of 𝐴ₜ/𝐴₁. Overall, the framework directly links separation topology and non-axisymmetric blockage near stall to shock-induced aerodynamic damping.