High Subsonic Regime Research Articles

Design, Multi-Point Optimization, and Analysis of Diffusive Stator Vanes to Enable Turbine Integration Into Rotating Detonation Engines

Abstract Pressure gain combustion is considered a possible path toward improved thermal cycle efficiency and reduced carbon emissions. However, ad hoc turbine designs are required to maximize the thermodynamic potential; the new turbomachinery should be suited for the oscillations in flow conditions generated by the detonation combustor, which are very different from conventional gas turbines. This paper investigates the design, optimization, and analysis of diffusive stator vanes operating under large inlet flow angles in the high-subsonic regime. First, the design methodology is outlined, focusing on the geometric requirements to ingest high Mach number flow and the parametric modeling of the endwall and the 3D vane pressure and suction sides. Then, the impact of the inlet flow angle on the flow field and vane design is studied through a multi-point, multi-objective optimization with three different inlet angles, performed using steady Reynolds-averaged Navier–Stokes simulations. Remarkable reductions in pressure loss and stator-induced rotor forcing are attained while maintaining an extensive operating envelope and high flow turning. Moreover, several design guidelines are provided based on the analysis of the optimized geometries. Finally, the effectiveness of the proposed methodology is verified with an unsteady assessment of the baseline and optimized vane designs.

Design Optimization of Blade Tip in Subsonic and Transonic Turbine Stages—Part I: Stage Design and Preliminary Tip Optimization

Abstract Rotor blade tip has significant influence on turbine stage aerodynamics and heat transfer. Most previous efforts have been based on low-speed cascade settings. However, more recent research on transonic blade tips exhibits distinctive flow features with qualitatively different performance sensitivities. These prompt two key issues of interest on the related flow conditioning. First, the contrast between a low-speed flow and a transonic regime highlights the less studied high-subsonic flow regime, closely relevant to many realistic turbine designs. Second, the relative casing movement and upstream inflow conditions, known to have non-negligible effects, indicate the need to examine a rotor blade tip in a realistic stator–rotor stage environment, which is also lacking. To elaborate the Mach number effect in the flow regimes of practical interest, we aim to examine a high subsonic stage in a direct and consistent comparison with a transonic one. To this end, a high subsonic stage (exit Mach number of 0.7) and a transonic (exit Mach number of 1.1) are designed at the same Reynolds number with a three-dimensional parameterization and meshing system. The tip squealer height is used as a representative parameter to investigate the sensitivity of the stage aerothermal performance. The multi-objective optimization using the Kriging surrogated model is employed to identify the Pareto fronts for the stage efficiency and the heat transfer. The comparison of the optimized results between these two stages shows distinctively different trends in the performance variation with the squealer height. The efficiency of the subsonic stage increases with the squealer height reaching a plateau. In contrast, the efficiency in the transonic stage first increases and then drops to the level comparable to that of a flat tip. Significantly, the present results indicate, for the first time, that the squealer tip in a transonic stage may not be as effective as in a subsonic stage. On the other hand, for heat transfer, sensitivity variations are more complex. The overall heat load and the local nonuniformity lead to qualitatively different sensitivities with the squealer height, as well as completely incomparable Pareto fronts. These observed heat transfer sensitivities raise the question on how to effectively conduct a combined aerodynamic and heat transfer performance design optimization. The authors subsequently resort further aerothermal physics analyses described in a companion paper as Part II of the two-part article. In Part II, the physical interpretation of the contrasting aero-efficiency sensitivities for the two stages, as well as a physical understanding leveraged selection of the objective function for such combined blade tip aerothermal optimization will be presented.

Recent Applications of System Identification Techniques at IPEV

This paper presents an overview of the system identification techniques developed and applied at the Flight Test and Research Institute during the last decade. System identification techniques have been used extensively to obtain aerodynamic models for a flight-test simulator, which was developed in house and specifically tailored for flight-test instruction and preparation for actual test flights. The methods applied were mostly the output error for data compatibility check and equation error in the time domain for model structure selection and parameter estimation. The most relevant applications are summarized in this paper, including identification of a high angle of attack model with compressibility effects for a jet trainer; estimation of drag polars at high subsonic regime for a jet fighter; identification of aerodynamic model in real-time for a propeller-driven fighter; application of flight-path reconstruction techniques to spin tests, in order to correct errors in the air data sensors; and identification of power effects on the longitudinal stability of a propeller-driven trainer. The examples show that system identification has become crucial to 1) obtain accurate aerodynamic models for training in the flight-test simulator and 2) develop more efficient flight-test techniques.

A computational aeroelastic framework based on high-order structural models and high-fidelity aerodynamics

A computational framework for high-fidelity static aeroelastic analysis is presented. Aeroelastic analysis traditionally employs a beam stick representation for the structure and potential, inviscid and irrotational flow assumptions for the aerodynamics. The unique contribution of this work is the introduction of a high-order structural formulation coupled with a high-fidelity method for the aerodynamics. In more details, the Carrera Unified Formulation coupled with the Finite Element Method is implemented to model geometrically complex composite, laminated structures as equivalent bi-dimensional plates. The open-source software SU2 is then used for the solution of the aerodynamic fields. The in-house fluid-structure coupling algorithm is based on the Moving Least Square technique. The paper contains a thorough validation of each disciplinary solver of the aeroelastic framework, and provides a few application test cases. For an unswept, untapered and isotropic wing, it was found that the method provides results in agreement with predictions from models based on potential flow theory for moderate freestream velocities. Departures were reported for very low speed and in the high-subsonic regime, alerting the need of adopting high-fidelity flow solutions at these flow conditions. The computational framework was then applied to the static aeroelastic tailoring of a composite wing. The paper concludes providing an overview of future implementation steps towards a tool for the seamless analysis of composite structures subject to different flow conditions, from low to high speed.

Air combat training – high energy at lowest cost

PurposeThe purpose of this paper is to reduce the exploitation cost below the standard supersonic training aircraft. The idea will benefit from the latest aerodynamic software and modern avionics, allowing to use much lighter trainer (due to using composite materials and minimizing on board avionic systems), and hence, decreasing the fuel consumption and cost of operation. The need to reform advanced jet training also covers the “red air” missions (manned targets for exercise and training). Red air missions need dedicated more realistic and less costly platforms. However, this makes sense only if the performance of these platforms is comparable to a front-line combat aircraft, particularly in terms of high specific excess power (SEP) and high levels of agility. Failure to address this issue would lead to unrealistic training scenarios and a negative training experience.Design/methodology/approachThe paper focuses on required research and the feasibility studies of a low-cost operationally effective solution for air combat pilot training, combining a very agile air platform, fully dedicated to training, and a flexible, interoperable, integrated training system (ITS) using simulations to provide a complete Live Virtual Constructive (LVC) solution. This study will explore innovations applicable to the learning and maintaining of skills, develop a first pilot physiological survey and propose a follow-up program aimed at developing a fully European air combat training service by 2028 or beyond.FindingsThe volume inside the SEP envelope shows the available SEP potential depending on Mach number and Altitude: SEP is directly representative for climb rate and acceleration or a combination of both. The surface of the volume represents steady-state conditions, i.e. at 1 g (no turns), enabling us to conclude that supersonic trainer and fighter present high energy potentials (SEP) required in air combat manoeuvres and that a subsonic trainer cannot match those qualities and does not fulfil advanced trainer requirements.Practical implicationsA major difficulty for the air forces in their training syllabus lies in the fact that in peacetime supersonic flight is restricted to dedicated areas or over the sea. However, a real beyond visual range fight can often start in the supersonic and continue into the high subsonic regime after a few minutes. Therefore, this novel trainer superior performance in the transonic region will bring the following advantages, for example in the rare opportunities to train in the lower supersonic regime, it can provide similar performance like combat aircraft and in the usual advanced training in the high subsonic regime, this novel trainer offers excellent realistic performance in a region where the conventional advanced trainer performance collapses beyond Mach 0.8 and does not provide realistic training results. The feasibility study shall be executed in close cooperation between User (Requirements) and Study Team (Solutions). The early conceptual design with basic layout and data (T/W and W/L) is key for operational utility and must be addressed with the User right at the beginning. The users are therefore offered early participation in the requirements development.Originality/valueThe presented methodology is an original approach to the combat pilot training. The core of the methodology is a study of a solution that aims to reduce training costs through an affordable operational air vehicle and an agile ITS. This goal will be reached by a design methodology that will concentrate the innovation and the developments to the critical issues for the concept (aerodynamics, propulsion, simulated weapon system, ITS architecture, etc.): the remaining topics will be adapted from existing solution, optimizing the development.

High subsonic flow of an organic vapor past a circular cylinder

A circular cylinder was tested in the cross-flow of an organic vapor (Novec™ 649) and of air over the subsonic (M < 0.4) and high subsonic (0.4 < M < 0.8) speed range in a continuously running pressurized closed-loop wind tunnel test facility. Time-averaged pressure measurements gave information on surface pressure distributions, and the corresponding drag and base pressure drag coefficients were obtained. Due to the charging of the wind tunnel, different values of the compressibility factor (0.876 < Z < 0.999) could be achieved for the organic vapor flow. This enabled in combination with the results for air an assessment of the impact of non-ideal gas dynamics on the form drag of a cylinder in the considered highly subsonic flow regime. The new experimental data were compared with available literature results. Changes in surface pressure distribution at higher subsonic velocities were identified and discussed. It was found that non-ideal gas effects did not strongly affect the overall drag. The variation of drag coefficient over the Mach number range was comparable with literature data for ideal-gas compressible flow, including shock-less and intermittent shock wave, and permanent shock wave flows regimes. At Mach 0.4, the flow of Novec™ 649 was in the shock-less regime and exhibited a pronounced dependency on the Reynolds number. An increase in drag was observed at Mach 0.6 which was attributed to the commencement of vortex shedding. Non-ideal thermodynamics only affected the flow locally and a reduction of the critical pressure coefficient in the high subsonic flow regime was observed in the surface pressure distribution. However, this mechanism did not alter significantly the overall drag behavior.Graphic abstractDrag coefficient CD against Re for several Mach numbers M and comparison with available literature results obtained for air (colored symbols indicate different Mach number clusters)

An experimental parametric study on planar sheared wings tip devices for low-to-moderate aspect ratio wings

PurposeThe purpose of this study is to investigate the aerodynamic characteristics of a low-to-moderate-aspect-ratio, tapered, untwisted, unswept wing, equipped of sheared wing tips.Design/methodology/approachIn this work, wind tunnel tests were made to study the influence in aerodynamic characteristics over a typical low-to-moderate-aspect-ratio wing of a general aviation aircraft, equipped with sheared – swept and tapered planar – wing tips. An experimental parametric study of different wing tips was tested. Variations in its leading and trailing edge sweep angle as well as variations in wing tip taper ratio were considered. Sheared wing tips modify the flow pattern in the outboard region of the wing producing a vortex flow at the wing tip leading edge, enhancing lift at high angles of attack.FindingsThe induced drag is responsible for nearly 50% of aircraft total drag and can be reduced through modifications to the wing tip. Some wing tip models present complex geometries and many of them present benefits in particular flight conditions. Results have demonstrated that sweeping the wing tip leading edge between 60 and 65 degrees offers an increment in wing aerodynamic efficiency, especially at high lift conditions. However, results have demonstrated that moderate wing tip taper ratio (0.50) has better aerodynamic benefits than highly tapered wing tips (from 0.25 to 0.15), even with little less wing tip leading edge sweep angle (from 57 to 62 degrees). The moderate wing tip taper ratio (0.50) offers more wing area and wing span than the wings with highly tapered wing tips, for the same aspect ratio wing.Originality/valueAlthough many studies have been reported on the aerodynamics of wing tips, most of them presented complex non-planar geometries and were developed for cruise flight in high subsonic regime (low lift coefficient). In this work, an exploration and parametric study through wind tunnel tests were made, to evaluate the influence in aerodynamic characteristics of a low-to-moderate-aspect-ratio, tapered, untwisted, unswept wing, equipped of sheared wing tips (wing tips highly swept and tapered).

Wall pressure fluctuations induced by a single stream jet over a semi-finite plate

This work provides an experimental investigation into the interaction between a jet flow and a semi-finite plate parallel to the jet. Wall pressure fluctuations have been measured in a high compressible subsonic regime and for different distances between the jet and the plate trailing edge. The experiment has been carried out in the ISVR anechoic Doak Laboratory at the University of Southampton, using wall pressure transducers flush mounted on the plate surface. Signals were acquired in the stream-wise direction along the jet centreline and in the span-wise direction in a region close to the trailing edge. The radial position of the flat plate was fixed very close to the jet axis to simulate a realistic jet–wing configuration. The plate was moved axially in order to investigate four different jet-trailing edge distances and to include measurements upstream of the nozzle exhaust. The acquired database was analyzed in both the frequency and the time domains providing an extensive statistical characterization in terms of spectral uni– and multi–variate quantities as well as high order statistical moments. A wavelet analysis was performed as well to investigate the time evolution of the wall pressure events.

Use of computational fluid dynamics to implement an aerodynamic inverse design method based on exact Riemann solution and moving wall boundary

An aerodynamic inverse design method, which is used in compressors, is introduced in this paper. This inverse design method is based on the exact solution of the local Riemann problem on moving blade surfaces. Furthermore, an improved relaxation factor is added to control the induced velocity for reasonable deformation sizes in different cases. The viscous flow analysis and the inverse design are integrated in the computational fluid dynamics software ANSYS Fluent using the dynamic mesh user-defined function, which reduces the time spent on remeshing the computational domain. A compressor cascade is taken to illustrate the effect of this inverse design method. Using the compressor model, the case of a different loading pattern design under a high subsonic flow regime and the case of a loading smooth design under a transonic flow regime have proved the capability of this inverse design method to realize the prescribed pressure loading distribution.

On the subsonic near-wake of a space launcher configuration with exhaust jet

The Ariane 5 failure flight 157 made clear that the loads in the base region of space launcher configurations were underestimated and its near-wake dynamics required more attention. In the recent years, many studies have been published on buffet/buffeting in the critical high subsonic flow regime. Nevertheless, not much experimental data are available on the interaction of the ambient flow with an exhaust jet over a wide subsonic Mach number range. Further, a preceding study without exhaust jet revealed questions regarding a similar distribution of the velocity and Reynolds stress in the near-wake if scaled with the reattachment length. Consequently, a generic space launcher configuration featuring a cold, supersonic, over-expanded jet is investigated experimentally in the vertical test section Cologne (VMK) by means of particle image velocimetry (PIV) for five subsonic Mach numbers ranging from 0.5 to 0.9 with corresponding Reynolds numbers between Re_{text {D}}=0.8times 10^6 to 1.6times 10^6. The velocity and Reynolds stress distribution are provided for the near-wake flow and additionally for the incoming boundary layer. Just as in the preceding study, self-similar features are found in the flow field as long as the separated shear layer reattaches on the solid nozzle wall. Substantial changes are then measured for an alternating (hybrid) reattachment between the solid nozzle wall and supersonic exhaust jet as found for Mach 0.8, one of them being the increased axial turbulence in the recirculation bubble due to a ‘dancing’ large-scale, clockwise-rotating vortex.Graphic abstract

Magnetic Suspension and Balance System for High-Subsonic Wind Tunnel

A magnetic suspension and balance system (MSBS) was successfully developed for suspending a model against a high-subsonic flow. In the high-subsonic regime, the aerodynamic loads acting on the model increase with increasing flow speed and the fluctuation forces increase accordingly. The pitch/yaw directional instability of the model increases in the high-subsonic regime. To solve these problems, the power of the amplifiers and the controlling frequency of an MSBS for a 10 cm low-speed wind tunnel were increased to improve the control system response. A magnetic field was also introduced to compensate for the directional instability of the model by increasing the output of the front drag coil and decreasing that of the rear drag coil. This modification of the magnetic field enabled an ogive-cylinder model with a diameter of 10 mm and a length of 156 mm to be suspended in the MSBS up to a Mach number of 0.6.

Parametric optimization of high aspect ratio wing using surrogate model

Wing is an important component of airborne glide vehicle which provide the major portion of lift force to be generated and at the same time lift is to be produced with minimum drag. In this paper an optimum design is evolved to provide a high aerodynamically efficient wing in high subsonic regime and at the same time it is subjected to constraints like, it should provide the minimum lift (lateral acceleration as per the guidance demand) to perform flight manoeuvres. The main objective of the work is to maximize the Lift-to-Drag ratio of the wing at a design point subjected to minimum lift requirement. This aerodynamic efficiency (L/D) decides the range performance of a glide vehicle. Wing parameters like span, chord at root, taper ratio and sweep back angle are subjected to optimizer with limits to obtain the best design while the airfoil NACA651 - 412 is same for all the cases. This paper presents the study carried out using design of experiments, surrogate model, evolutionary optimization approach and gradient based optimization approach using MATLABTMsolver.

Assessment of Transition Modeling and Compressibility Effects in a Linear Cascade of Turbine Nozzle Guide Vanes

The flow field in a linear cascade of highly loaded turbine nozzle guide vanes (NGVs) has been numerically investigated at low and high-subsonic regime, i.e., exit isentropic Mach number of M2is = 0.2 and 0.6, respectively. Extensive experimental data are available for an accurate assessment of the numerical procedure. Aerodynamic measurements include not only vane loading and pressure drop in the wake but also local flow features such as boundary layer behavior along both pressure and suction sides of the vane, as well as secondary flow structures downstream of the trailing edge (TE). Simulations were performed by using two computational fluid dynamics (CFD) codes, a commercial one and an open-source based in-house code. Besides computations with the well-established shear-stress transport (SST) k–ω turbulence model assuming fully turbulent flow, transition models were taken into account in the present study. The original version of the γ–Reθ model of Menter was employed. Suluksna–Juntasaro correlations for transition length (Flenght) and transition onset (Fonset) were also tested. The main goal was to establish essential ingredients for reasonable computational predictions of the cascade aerodynamic behavior, under both incompressible and compressible regime. This study showed that transition modeling should be coupled with accurate profiles of inlet velocity and turbulence intensity to get a chance to properly quantify aerodynamic losses via CFD method. However, additional weaknesses of the transition modeling have been put forward when increasing the outlet Mach number.

Transonic limit cycle oscillation behavior of an aeroelastic airfoil with free-play

The limit cycle oscillation (LCO) behaviors of an aeroelastic airfoil with free-play for different Mach numbers are studied. Euler equations are adopted to obtain the unsteady aerodynamic forces. Aerodynamic and structural describing functions are employed to deal with aerodynamic and structural nonlinearities, respectively. Then the flutter speed and flutter frequency are obtained by V-g method. The LCO solutions for the aeroelastic airfoil obtained by using dynamically linear aerodynamics agree well with those obtained directly by using nonlinear aerodynamics. Subsequently, the dynamically linear aerodynamics is assumed, and results show that the LCOs behave variously in different Mach number ranges. A subcritical bifurcation, consisting of both stable and unstable branches, is firstly observed in subsonic and high subsonic regime. Then in a narrow Mach number range, the unstable LCOs with small amplitudes turn to be stable ones dominated by the single degree of freedom flutter. Meanwhile, these LCOs can persist down to very low flutter speeds. When the Mach number is increased further, the stable branch turns back to be unstable. To address the reason of the stability variation for different Mach numbers at small amplitude LCOs, we find that the Mach number freeze phenomenon provides a physics-based explanation and the phase reversal of the aerodynamic forces will trigger the single degree of freedom flutter in the narrow Mach number range between the low and high Mach numbers of the chimney region. The high Mach number can be predicted by the freeze Mach number, and the low one can be estimated by the Mach number at which the aerodynamic center of the airfoil lies near its elastic axis. Influence of angle of attack and viscous effects on the LCO behavior is also discussed.

Numerical Investigation of Cowl Lip Adjustments for a Rocket-Based Combined-Cycle Inlet in Takeoff Regime

AbstractNumerical integration simulations were performed on a ready-made central strut-based rocket-based combined-cycle (RBCC) engine operating in the ejector mode during the takeoff regime. The effective principles of various cowl lip positions and shapes on the inlet operation and the overall performance of the entire engine were investigated in detail. Under the static condition, reverse cowl lip rotation in a certain range was found to contribute comprehensive improvement to the RBCC inlet and the entire engine. However, the reverse rotation of the cowl lip contributed very little enhancement of the RBCC inlet under the low subsonic flight regime and induced extremely negative impacts in the high subsonic flight regime, especially in terms of a significant increase in the drag of the inlet. Changes to the cowl lip shape provided little improvement to the overall performance of the RBCC engine, merely shifting the location of the leeward area inside the RBCC inlet, as well as the flow separation and eddy, but not relieving or eliminating those phenomena. The results of this study indicate that proper cowl lip rotation offers an efficient variable geometry scheme for a RBCC inlet in the takeoff regime.

Numerical Study of a Boundary Layer Bleedfor a Rocket-Based Combined-Cycle Inlet in Ejector Mode

AbstractFully integrated numerical simulations were performed for a ready-made central strut-based rocket-based combined-cycle (RBCC) engine operating in ejector mode, and the applicability of using a boundary layer bleed in the RBCC inlet designed for supersonic speeds was investigated in detail. The operational mechanism of the boundary layer bleed and its effects on the RBCC inlet and the engine under different off-design conditions in ejector mode were determined. The boundary layer bleed played different roles in the RBCC inlet for different flight regimes. When the RBCC engine took off, some air was entrained into the inlet through the bleed block, thereby inducing significant flow separation and a low-speed vortex, which deteriorated the inner flow and reduced the entraining air mass flow rate: thus, the total pressure loss increased and extra drag was exerted on the inlet. In the low subsonic regime, the bleed block had almost no impact on the RBCC engine and its inlet. However, as the RBCC engine accelerated into a high subsonic flight regime, the boundary layer bleed had a clearly positive effect, comprehensively improving the performance of the RBCC inlet. A boundary layer bleed operation strategy for the RBCC inlet in ejector mode was also developed in this study.

Experimental investigation of the effects of blowing conditions and Mach number on the unsteady behavior of coolant ejection through a trailing edge cutback

The present paper shows the results of an experimental investigation into the unsteadiness of coolant ejection at the trailing edge of a highly loaded nozzle vane cascade. The trailing edge cooling scheme features a pressure side cutback with film cooling slots, stiffened by evenly spaced ribs in an inline configuration. Cooling air is also ejected through two rows of cylindrical holes placed upstream of the cutback. Tests were performed with a low inlet turbulence intensity level (Tu1=1.6%), changing the cascade operating conditions from low speed (M2is=0.2) up to high subsonic regime (M2is=0.6), and with coolant to main stream mass flow ratio varied within the 0.5–2.0% range. Particle Image Velocimetry (PIV) and flow visualizations were used to investigate the unsteady mixing process taking place between coolant and main flow downstream of the cutback, up to the trailing edge. For all the tested conditions, the results show the presence of large coherent structures, which presence is still evident up to the trailing edge. Their shape and direction of rotation change with injection conditions, as a function of coolant to mainstream velocity ratio, strongly influencing the thermal protection capability of the injected coolant flow. The Mach number increase is only responsible for a positioning of such vortical structures closer to the wall, while the Strouhal number almost remains unchanged.

Control of the antisymmetric mode (m = 1) for high Reynolds axisymmetric turbulent separating/reattaching flows

The separated flow over a three-dimensional axisymmetric step controlled by means of continuous jets is investigated numerically at a high subsonic regime using Zonal Detached Eddy Simulation (ZDES). The main objective is here to analyze the influence of two controlled devices acting in different regions of the separated flow, i.e., in the shear layer or in the recirculation area. Contrary to most flow control strategies that aim at reducing the drag, the final purpose of this study consists in controlling the antisymmetric azimuthal mode (m=1) responsible for side loads occurring on a massively separated afterbody. Thus, the design of controlled cases has been motivated both by a literature review which is detailed but especially by the previous identification of a potential area of receptiveness linked to an absolutely unstable area. The related achievement expected lies in increasing the three-dimensionality of the flow but decreasing its large scale coherence. For both controlled configurations, instantaneous, statistical, and fluctuating properties are scrutinized. In particular, the analysis exhibits that the backflow has to be considered stronger in time compared to its mean and broadly distributed in space which impacts the amount of energy needed to counteract this backflow and thus to control the flow. Then, a two-point spectral analysis is performed on the entire wall of interest of the afterbody providing a spatial representation of the fluctuating energy for a selected frequency. This last investigation permits to understand the influence of the control on the mechanisms related to the dimensionless frequency StD=0.2 and its associated antisymmetric mode. Finally, this analysis permits to predict the effect of the control on the change in the nature of the instability contained in the potentially receptive zone transitioning from fully absolute to fully convective.

Effect of compressibility on the global stability of axisymmetric wake flows

We study the linear dynamics of global eigenmodes in compressible axisymmetric wake flows, up to the high subsonic regime. We consider both an afterbody flow at zero angle of attack and a sphere, and find that the sequence of bifurcations destabilizing the axisymmetric steady flow is independent of the Mach number and reminiscent of that documented in the incompressible wake past a sphere and a disk (Natarajan &amp; Acrivos, J. Fluid Mech., vol. 254, 1993, p. 323), hence suggesting that the onset of unsteadiness in this class of flows results from a global instability. We determine the boundary separating the stable and unstable domains in the (M, Re) plane, and show that an increase in the Mach number yields a stabilization of the afterbody flow, but a destabilization of the sphere flow. These compressible effects are further investigated by means of adjoint-based sensitivity analyses relying on the computation of gradients or sensitivity functions. Using this theoretical formalism, we show that they do not act through specific compressibility effects at the disturbance level but mainly through implicit base flow modifications, an effect that had not been taken into consideration by previous studies based on prescribed parallel base flow profiles. We propose a physical interpretation for the observed compressible effects, based on the competition between advection and production of disturbances, and provide evidence linking the stabilizing/destabilizing effect observed when varying the Mach number to a strengthening/weakening of the disturbance advection mechanism. We show, in particular, that the destabilizing effect of compressibility observed in the case of the sphere results from a significant increase of the backflow velocity in the whole recirculating bubble, which opposes the downstream advection of disturbances.

Elephant modes and low frequency unsteadiness in a high Reynolds number, transonic afterbody wake

Experiments and large eddy numerical simulation of a fully turbulent afterbody flow in the high subsonic regime, typical of that developing in the wake of a space launcher, exhibit a large-scale low frequency oscillation of the wake. In the present paper, we investigate to what extent the existence of the synchronized oscillations can be interpreted, at the high Reynolds numbers prevailing in this class of flows, by a local stability analysis of the mean flow, as measured in experiments or computed in numerical simulations. This analysis shows the presence of a pocket of absolute instability in the near wake, slightly detached from the body. The global frequency is strikingly well predicted by the absolute frequency at the upstream station of marginal absolute instability, this frequency selection being in agreement with the theory of nonlinear global modes. This result strongly suggests that a so-called elephant mode is responsible for the intense oscillations observed in the lee of space launcher configurations.