Transonic Flow Research Articles

Exact compressible transport equation for the unresolved stresses and PANS-RSM simulation of transonic buffet

The exact compressible-flow tensorial transport-equations for the unresolved stresses of the density-weighted filtered (Favre) velocity field are reformulated without using mixed Favre-Reynolds central moments. The exact equation for the dissipation-rate of the unresolved turbulent-kinetic-energy is derived for constant density-flow and extended to compressible flows invoking Morkovin's hypothesis. The term-by-term correspondence of the transport equations for the unresolved stresses and dissipation-rate with the corresponding exact transport equations for the Reynolds stresses and turbulence-kinetic-energy dissipation-rate is exploited to derive the closure for the subgrid-scales (SGS) equations by applying the partially averaged Navier-Stokes (PANS) framework to an underlying Reynolds-stress model (RSM). The paper assesses the prediction of transonic buffet on the OAT15A supercritical airfoil using a PANS–RSM approach. Experimental data for transonic buffet flow around the supercritical OAT15A airfoil are compared with computations, using both PANS-RSM and Reynolds averaged Navier-Stokes (RANS-RSM), demonstrating the potential of PANS–RSM to predict the low-frequency self-sustained shock-wave oscillations.

Dynamic characteristic of transonic aeroelasticity affected by fluid mode in pre-buffet flow

Transonic aeroelasticity remains a significant challenge in aerospace. The coupling mechanism of aeroelastic problems involving the coexistence of fluid modes and multiple structural modes still needs further investigation. For this purpose, we analysed the dynamic characteristic of a two-degree-of-freedom (2DOF) NACA0012 airfoil in pre-buffet flow. First, we constructed an aeroelastic reduced-order model, which can represent near-unstable transonic flow using the dominant fluid mode. Then, the flutter mechanism was investigated by studying the main eigenvalues of the model that vary with the natural pitching frequency. The results revealed that the existence of the fluid mode transitions the transonic flutter type from coupled-mode flutter to single-DOF (SDOF) flutter, which leads to a reduction in the flutter boundary. Under the effect of the fluid mode, the system produces six aeroelastic phenomena at different structural natural frequencies, including SDOF heaving/pitching flutter, heaving/pitching instability within coupled-mode flutter, forced vibration and stable state. Moreover, we identified two types of SDOF flutter in the 2DOF system. The first type corresponds to the traditional SDOF flutter, where the coupling of other modes has a small impact on the system's stability in most cases. However, within specific ranges of natural frequencies, this type of SDOF flutter may disappear due to coupling with other modes. The second type of SDOF flutter is characterized by strong coupling dominated by the unstable mode. It arises from the interaction among the flow, heaving and pitching modes, and does not manifest in the absence of any of these modes.

Three-Dimensional Flutter Numerical Simulation of Wings in Heavy Gas and Transonic Flutter Similarity Law Correction Method

Wind tunnel testing is a crucial method for studying aircraft flutter. Using heavy gas as the wind tunnel medium can mitigate the escalating issue of test models being overweight as advanced aircraft develop. This paper employs an analytical method for numerical calculations of three-dimensional (3D) wing flutter based on fluid–structure interaction (FSI). Flutter calculations for the Goland wing are conducted, and the results in the air medium are consistent with the literature. In contrast, significant differences in flutter behavior are observed in the heavy gas R134a medium. Compared to air, when the model reaches a critical state in R134a, the incoming flow velocity is lower, the incoming flow density is approximately 3 to 5 times air, and the incoming flow dynamic pressure is about 1.1 to 1.2 times that of air. The correction of heavy gas flutter data is crucial for wind tunnel testing. This paper proposes a correction method based on the unsteady transonic flow similarity law proposed by Bendiksen under quasi-steady conditions. Attempts are made to revise relevant published wind tunnel tests and heavy gas flutter calculation results. The transonic flutter similarity law effectively explains the flutter similarity of rigid models in both heavy gas and air media. Still, it fails in cases with highly reduced frequencies and low mass ratios, such as those encountered with flexible wings.

Impact of annular nanosecond plasma actuators on drag reduction in transonic flow

During the last few decades, plasma actuators have emerged as promising devices for aerodynamic flow control. This study focuses on the use of nanosecond plasma actuators for such purposes. A thermal phenomenological model is employed to simulate the effects of these actuators. The propagation of shock waves and their interactions for two specific geometries of plasma actuators, linear and annular plasma synthetic jet actuators, are examined here. A comparative analysis of the performance of these two configurations is presented. Furthermore, the geometric characteristics and temperature model are analyzed to provide insights that can be applied to practical problems. The influence of the actuators on a projectile in the transonic flow is also investigated. The results of the present study show that actuators placed in the conical and cylindrical regions of the object do not contribute to drag reduction. Conversely, actuators positioned at the boat-tail and base of the object effectively reduce drag. This drag reduction is primarily attributed to thermal disturbances in the separation area. Additionally, it is observed that the effects of shock waves and their interaction with stationary waves around the projectile are negligible in terms of drag force reduction.

Mode decomposition to identify oscillation patterns of flexible aeroshell

Flexible aeroshells, featuring deformable membrane surfaces supported by pressurized gas, offer a novel re-entry system for high-altitude deceleration during re-entry. The flexibility of structural components introduces unique challenges in predicting aerodynamic behavior, as deformations can significantly alter the flow field, affecting pressure distribution and potentially causing aerodynamic instabilities. Therefore, coupled analysis is crucial to ensure the performance reliability of inflatable aeroshells. This study investigates the unsteady aerodynamic behavior, considering structural deformation in a two-way partitioned coupled manner in transonic flow. The dominant deformation patterns are identified using dynamic mode decomposition and the greedy compressive sensing algorithm. The findings reveal that the primary deformation pattern combines axial deformation and swing oscillation. The dominant oscillation frequencies remain different from the eigenfrequencies, indicating that the aerodynamic force is the primary driving force of such oscillations. The time evolution of these dominant modes indicates purely oscillatory behavior rather than increasing or decreasing trends. These insights are critical for the design and reliability assessment of inflatable aeroshells in varying aerodynamic environments.

High-order discontinuous Galerkin method with immersed boundary treatment for compressible flows on parallel adaptive Cartesian grids

Adaptive mesh refinement (AMR) technology and high-order methods are important means to improve the quality of simulation results and have been hotspots in the computational fluid dynamics community. In this paper, high-order discontinuous Galerkin (DG) and direct DG (DDG) finite element methods are developed based on a parallel adaptive Cartesian grid to simulate compressible flow. On the one hand, a high-order multi-resolution weighted essentially nonoscillatory limiter is proposed for DG and DDG methods. This limiter can enhance the stability of DG/DDG methods for compressible flows dominated by shock waves. It is also compact, making it suitable for the implementation of AMR with frequent refinement/coarsening. On the other hand, a coupling method of DG and immersed boundary method is proposed to simulate flow around objects. Due to the compactness of DG, the physical quantities of image points can be directly obtained through the DG/DDG polynomial of the corresponding cells. It avoids the wide interpolation stencil of traditional IBM and makes it more suitable for the parallel adaptive Cartesian grid framework in this paper. Finally, the performance of the proposed method is verified through typical two- and three-dimensional cases. The results indicate that the method proposed in this paper has low numerical dissipation in smooth areas and can effectively handle compressible flow dominated by discontinuities. Moreover, for transonic flow over a sphere, the error of results between the proposed method and direct numerical simulation is within 1%, fully validating the accuracy of the method presented in this paper.

Quantitative and Qualitative Experimental Assessment of Water Vapor Condensation in Atmospheric Air Transonic Flows in Convergent–Divergent Nozzles

Atmospheric air, being also a moist gas, is present as a working medium in various areas of technology, including the areas of airframe aerodynamics and turbomachinery. Issues related to the condensation of water vapor contained in atmospheric air have been intensively studied analytically, experimentally and numerically since the 1950s. An effort is made in this paper to present new, unique and complementary results of the experimental testing of moist air expansion in the de Laval nozzle. The results of the measurements, apart from the static pressure distribution on the nozzle wall and the images obtained using the Schlieren technique, additionally contain information regarding the quantity and quality of the condensate formed due to spontaneous condensation at the transition from the subsonic to the supersonic flow in the nozzle. The liquid phase was identified using the light extinction method (LEM). The experiments were performed for three geometries of convergent–divergent nozzles with different expansion rates of 3000, 2500 and 2000 s−1. It is shown that as the expansion rate increases, the phenomenon of water vapor spontaneous condensation appears closer to the critical cross-section of the nozzle. A study was performed of the impact of the air relative humidity and pollution on the process of condensation of the water vapor contained in the air. As indicated by the results, both these parameters have a significant effect on the flow field and the pressure distribution in the nozzle. The results of the experimental analyses show that in the case of the atmospheric air flow, in addition to the pressure, temperature and velocity, other parameters must also be taken into account as boundary parameters for possible numerical analyses. Omitting information about the air humidity and pollution can lead to incorrect results in numerical simulations of transonic flows of atmospheric air. The presented results of the measurements of the moist air transonic flow field are original and fill the research gap in the field of experimental studies on the phenomenon of water vapor spontaneous condensation.

Spherical accretion onto higher-dimensional Reissner–Nordström black hole

Abstract We obtain relativistic solutions of spherically symmetric accretion by a dynamical analysis of a generalised Hamiltonian for higher-dimensional Reissner–Nordström (RN) Black Hole (BH). We consider two different fluids namely, an isotropic fluid and a non-linear polytropic fluid to analyse the critical points in a higher-dimensional RN BH. The flow dynamics of the fluids are studied in different spacetime dimensions in the framework of Hamiltonian formalism. The isotropic fluid is found to have both transonic and non-transonic flow behaviour, but in the case of polytropic fluid, the flow behaviour is found to exhibit only non-transonic flow, determined by a critical point that is related to the local sound speed. The critical radius is found to change with the spacetime dimensions. Starting from the usual four dimensions it is noted that as the dimension increases the critical radius decreases, attains a minimum at a specific dimension (D > 4) and thereafter increases again. The mass accretion rate for isotropic fluid is determined using Hamiltonian formalism. The maximum mass accretion rate for RN BH with different equations of state parameters is studied in addition to spacetime dimensions. The flow behaviour and mass accretion rate for a change in BH charge is also studied analytically. It is noted that the maximum mass accretion rate in a higher-dimensional Schwarzschild BH is the lowest, which however, increases with the increase in charge parameter in a higher-dimensional RN BH.

Research and Analysis of the Small Disturbance Equation in Subsonic, Transonic, and Supersonic Regimes

This paper explores the application of the Small Disturbance Equation (SDE) across subsonic, transonic, and supersonic flow regimes. Derived from the Euler and Navier-Stokes equations, the SDE offers an efficient framework for analyzing aerodynamic behaviors, particularly through the utilization of discretization techniques and iterative solving methods executed in Python. The study assesses the accuracy and limitations of the SDE in detailing essential flow characteristics, revealing that while the equation performs effectively in subsonic and transonic flows, it encounters challenges in supersonic regimes. Nonlinear effects such as shock waves significantly hinder its performance at high speeds. Compared with conventional computational fluid dynamics (CFD) methods, the SDE stands out in scenarios where computational efficiency is paramount. However, its limitations in handling high-speed flows must be carefully considered, highlighting the need for further refinement in its application to supersonic dynamics. This analysis suggests that while the SDE is beneficial for certain aerodynamic studies, its scope and utility are constrained by the inherent complexities of high-speed fluid dynamics.

Convective vortices in collapsing stars

Abstract Recent studies show that non-radial structures arising from massive star shell convection play an important role in shaping core-collapse supernova explosions. During the collapse phase, convective vortices generate acoustic waves that interact with the supernova shock. This amplifies turbulence in the post-shock region, contributing to explosion. We study how various physical parameters influence the evolution of these convective vortices during stellar collapse using simplified simulations. We model the collapsing star with a transonic Bondi flow and represent convection as solenoidal velocity perturbations. Our results are consistent with previous studies, demonstrating that the peak perturbation amplitude scales linearly with the pre-collapse convective Mach number and inversely with the angular wavenumber of convection. While the shell radius and width primarily determine the timescale of accretion, they have little impact on the peak perturbation amplitudes. Finally, we show that when the convective Mach number is below approximately 0.2, the dynamics remain within the linear regime.

Point-enhanced convolutional neural network: A novel deep learning method for transonic wall-bounded flows

Low order models can be used to accelerate engineering design processes. Ideally, these surrogates should meet the conflicting requirements of large design space coverage, high accuracy and fast evaluation. Within the context of aerospace applications at transonic conditions, this can be challenging due to the associated non-linearity of the flow regime. Different methods have been investigated in the past to predict the flow-field around shapes such as airfoils or cylinders. However, they usually have reduced spatial resolution, limiting the prediction capabilities within the boundary layer which is of interest for transonic wall-bounded flows. This work proposes a novel Point-Enhanced Convolutional Neural Network (PCNN) method that combines the advantages of the well-established PointNet and convolutional neural network approaches. The PCNN model has relatively low memory requirements in the training process, preserves the spatial correlation in the domain and has the same resolution as a traditional computational method. The architecture is used for the flow-field prediction of civil aero-engine nacelles in which it is demonstrated that the flow features of peak isentropic Mach number (Mis), pre-shock isentropic Mach number and shock location (X/Lnac) are captured within ΔMis = 0.02, ΔMis=0.04, ΔX/Lnac=0.007, respectively. The PCNN model successfully predicts the integral parameters of the boundary layer, in which the incompressible displacement thickness, momentum thickness and shape factor are typically within 5% of the CFD. Overall, the PCNN method is demonstrated for transonic wall-bounded flows for a range of flow physics that include shock waves and shock-induced separation.

The Influence of Bleed Position on the Stability Expansion Effect of Self-Circulating Casing Treatment

The self-circulating casing treatment can effectively expand the stable working range of the compressor, with little impact on its efficiency. With a single-stage transonic axial flow compressor NASA (National Aeronautics and Space Administration) Stage 35 as the research object, a multi-channel unsteady numerical calculation method was used here to design three types of self-circulating casing treatment structures: 20% Ca (axial chord length of the rotor blade tip), 60% Ca, and 178% Ca (at this time, the bleed position is at the stator channel casing) from the leading edge of the blade tip. The effects of these three bleed positions on the self-circulating stability expansion effect and compressor performance were studied separately. The calculation results indicate that the further the bleed position is from the leading edge of the blade tip, the weaker the expansion ability of the self-circulating casing treatment, and the greater the negative impact on the peak efficiency and design point efficiency of the compressor. This is because the air inlet of the self-circulating casing with an air intake position of 20% Ca is located directly above the core area of the rotor blade top blockage, which can more effectively extract low-energy fluid from the blockage area. Compared to the other two bleed positions, it has the greatest inhibitory effect on the leakage vortex in the rotor blade tip gap and has the strongest ability to improve the blockage at the rotor blade tip. Therefore, 20% Ca from the leading edge of the blade tip has the strongest stability expansion ability, achieving a stall margin improvement of 11.28%.

Numerical investigation of the influence of suction surface synthetic jet on the performance of transonic axial flow compressor

In order to investigate the effect of suction surface synthetic jet on the aerodynamic performance of transonic axial compressor, Rotor35 was used for numerical simulation. The results show that at four different positions, the stability margin of the compressor is slightly reduced by suction surface excitation, but there is an optimal position that can improve the compressor total pressure ratio and efficiency. At this position, there is little change in the total pressure ratio at the peak efficiency, and the efficiency is improved by 0.58%. The total pressure ratio and efficiency of the design point are increased by 0.18% and 0.55%, respectively. The periodic excitation of synthetic jet can effectively separate the suction surface and reduce the separation loss, which is the reason for the improvement of compressor efficiency. However, for the transonic compressor, synthetic jet on the suction surface obstructs the radial migration vortex that reaches the tip to the exit, but cause it to gather in the tip channel, resulting in the blockage and reduction of the stability margin of the compressor. In order to take into account the stability margin of the compressor, the coupled flow control is carried out by combining the casing treatment with synthetic jet on the suction surface. The results show that the flow margin of the compressor is increased by 8.76%, the total pressure ratio is increased by 1.76%, and the efficiency is only decreased by 0.13%. In coupled flow control, the suction and injection effects of the casing treatment can make up for the negative influence of synthetic jet on the tip flow, effectively improve the tip flow and expand the stable working range of the compressor. Compared with flow control that only carries out casing treatment, coupled flow control can exert the advantages of synthetic jet suppressing suction surface separation, reduce shock loss, outlet loss and casing treatment loss, and make up for the shortage of excessive efficiency reduction after casing treatment, which is the main reason for the improvement of compressor performance.

Introduction of oblique plane waves through a forcing source term in Euler equations

The propagation of shock waves generated by a transonic flow at the tip of a propeller blade is numerically calculated in order to determine the pressure footprint on an aircraft fuselage. An academic case is first proposed to validate the methodology. An incoming signal is built up as oblique harmonic plane waves. The signal is introduced in the computational domain using a Gaussian volume forcing term in the conservation of mass and energy equations. The Euler equations are solved in two dimensions using finite-difference schemes with low dispersion and dissipation. Selective filtering has also been integrated in the algorithm to remove grid-to-grid oscillations. The numerical solution is compared to an analytical solution based on the tailored Green function. An illustration for a realistic open rotor is then considered. The pressure signal near the blade tip, determined from a preliminary RANS simulation, is introduced using a volume source in a solver of the Euler equations.

Wind tunnel wall interference correction for transonic airfoils with data-reduced ensemble Kalman filter

The uncertain factors in wind tunnel experiments, especially the interference effects, will cause the flow around the test model to differ from that under the free flow condition. The wind tunnel wall interference effects are challenging to be eliminated, especially in transonic flow regions where classical linear correction methods are ineffective. To address this issue, an efficient wind tunnel wall interference correction framework based on data assimilation is proposed for steady and shock buffet flows around the airfoils in the transonic region in this work. The ensemble Kalman filter (EnKF) is used to find the combination of inflow conditions, which minimizes the differences between the pressure coefficients measured in the wind tunnel experiment and those estimated by computational fluid dynamics (CFD). The polynomial chaos expansion method is used to propagate uncertainty in the forecast step of the EnKF in order to improve efficiency. Typical wind tunnel wall interference correction problems are studied, including two steady cases: the transonic flow around the Royal Aircraft Establishment 2822 (RAE2822) and the National Aerospace Laboratory 7301 (NLR7301) airfoils, and one unsteady case: the transonic shock buffet on the National Aeronautics and Space Administration supercritical (phase 2)-0714 (NASA SC(2)-0714) airfoil. It is demonstrated that with the corrected Mach number and angle of attack, the estimated CFD results are in better agreement with the measured experimental data than traditional linear methods and the computational efficiency is improved compared to the original EnKF.

Scaling law of aero-optical steady-distortion for hemisphere-on-cylinder conformal-window turrets across the subsonic, transonic, and supersonic flows

Scaling law of aero-optical steady-distortion for hemisphere-on-cylinder conformal-window turrets across the subsonic, transonic, and supersonic flows

Surface roughness effects in a transonic axial flow compressor operating at near-stall conditions

Surface roughness is a major contributor to performance degradation in gas turbine engines. The fan and the compressor, as the first components in the engine's air path, are especially vulnerable to the effects of surface roughness. Debris ingestion, accumulation of grime, dust, or insect remnants, typically at low atmospheric conditions, over several cycles of operation are some major causes of surface roughness over the blade surfaces. The flow in compressor rotors is inherently highly complex. From the perspective of the component designers, it is, thus, important to study the effect of surface roughness on the performance and flow physics, especially at near-stall conditions. In this study, we examine the effect of surface roughness on flow physics such as shock-boundary layer interactions, tip and hub flow separations, the formation and changes in the critical points, and tip leakage vortices among other phenomena. Steady and unsteady Reynolds Averaged Navier Stokes calculations are conducted at near-stall conditions for smooth and rough National Aeronautics and Space Administration rotor 67 blades. Surface streamlines, Q-criterion, and entropy contours aid in analyzing the flow physics qualitatively and quantitatively. It is observed that from the onset of stall, to fully stalled conditions, the blockage varies from 21.7% to 59.6% from 90% span to the tip in the smooth case, and from 40.5% to 75.2% in the rough case. This significant blockage, caused by vortex breakdown and chaotic flow structures, leads to the onset of full rotor stall.

Numerical study on transonic shock wave buffeting of airfoil

Abstract Modern transportation aircraft typically cruise at transonic speeds. However, under a specific combination of incoming flow Mach numbers and angles of attack, periodic self-excited oscillations of shock waves can lead to unsteady aerodynamic loads, causing sustained vibrations in the aircraft, which is known as transonic shock wave buffeting. Buffeting loads significantly impact the fatigue life of the aircraft’s structural materials and its handling performance. In severe cases, it causes structural damage or even leads to flight safety incidents, so we should pay more attention to transonic shock wave buffeting when focusing on aeronautical engineering. This paper employs computational fluid dynamics technology for calculations to solve the Navier-Stokes equations, using the SST k-ω turbulence model to numerically simulate the steady flow field, and further employing the detached eddy simulation (DES) method to study and analyze the buffeting initiation mechanism and flow field characteristics of the NACA0012 airfoil’s transonic unsteady flow. By applying the DES method, the results demonstrate an accurate prediction of the buffeting onset boundary of the airfoil compared to wind tunnel experimental data. The research findings on the initiation mechanism and load characteristics of transonic buffeting provide a theoretical basis for optimizing the aerodynamic performance of aircraft during transonic flight and offer guidance for engineering issues such as buffeting load mitigation.

Position query-guided cross-modal flow field prediction model of a transonic compressor cascade

The gradient of flow parameters in a transonic compressor cascade flow field varies significantly, especially in the region of shock waves, which causes a significant challenge to its high-precision flow field prediction. In this study, the position query-guided cross-modal flow field prediction model (PGCM) is proposed to effectively predict the flow field parameter distribution of a transonic compressor cascade. The PGCM utilizes the self-attention mechanism for the global and deep geometric feature extraction of configurations, which contributes to an in-depth understanding of the spatial relationships between coordinate points within the flow field, accurately capturing and analyzing the structural complexity of a compressor cascade flow. In addition, the PGCM integrates the cross-attention mechanism that establishes correlations between different input sequences, which enhances the performance of the model in querying and interpreting flow parameters at specific coordinates. The flow field prediction models are developed to predict the flow parameter distributions of different cascade geometries at Mach numbers of 0.78 and 0.93, respectively. The validation results indicate that the PGCM performs significantly better than the existing convolutional neural network and vision transformer, especially in the prediction of the pressure coefficient Cp distribution. The PGCM is adaptable to the variation of flow conditions and geometrical configurations efficiently and accurate in predicting the flow field of a compressor cascade. This paper demonstrates the promising potential of conducting the multi-modal information fusion to enhance the capability of flow field prediction.

Event-Based Measurement of Aeroelastic Structure in High-Speed Flow

In high-speed aerodynamics research, point sensors are ideal for embedding in test models but lack spatial resolution, whereas high-speed cameras offer spatiotemporally resolved measurement but involve significant footprint, cost, and data size. To address these tradeoffs, this study explores the application of nascent event-based cameras for high-speed tests. Event-based cameras support continuous, data-sparse kilohertz-equivalent imaging at 720p resolution, on form factors as small as 36 mm and 40 grams in mass, combining the benefits of point sensors and high-speed cameras. However, these attributes come from asynchronous pixels that necessitate unique operating and postprocessing approaches. Here, the authors adapted event-based cameras for two-/three-dimensional photogrammetric tracking of aeroelastic structures, demonstrating an event-based workflow and two tracking algorithms (mean-shift filtering and circle fit). Bench-top validations achieved three-dimensional precision of 0.35 mm/s on 20 mm/s motion across a 259 mm field of view, while two-dimensional measurements of an aeroelastic titanium panel in Mach 0.76 transonic flow successfully identified millimeter-scale vibrations at 43.7, 120, and 270 Hz, validated against a laser displacement and high-speed camera. The transonic test’s raw data were 145.8 MB on the event-based camera, compared to 88.5 GB on the high-speed camera. The presented results demonstrated the viability of event-based techniques in high-speed aerodynamic testing, while highlighting challenges such as polarity switching and pixel latency.