Transonic Flow Research Articles

Transfer Learning for Flow Reconstruction Based on Multifidelity Data

Reduced-order modeling for multifidelity flow reconstruction offers increased accuracy while saving cost in data generation. The key to obtaining successful multifidelity models lies in properly capturing the correlation between low-fidelity and high-fidelity data. In this work, we propose to apply transfer learning to discover representative features that better correlate the multifidelity data to improve the accuracy in multifidelity flow reconstruction. Essentially, transfer learning facilitates the modeling task through transferring the knowledge learned in a related task, thus improving model performance in multifidelity problems. In particular, a typical class of transfer learning based on domain adaptation is introduced to discover domain-invariant features from the flow data of multiple sources. Two transfer learning frameworks via either the transfer component analysis or the geodesic flow kernel are established, providing different concepts to match transferred features between multifidelity data. Thereafter, the transferred features can be used as inputs to build the bridge function between low-fidelity and high-fidelity data for flow reconstruction. The proposed transfer learning methods are tested by various cases with increasing complexity, including heat convection, the Burgers equation, and transonic flows past a NACA0012 airfoil and an ONERA M6 wing. Advantages of the proposed transfer learning method to obtain better feature representations and to help construct more accurate multifidelity models for flow reconstruction are presented.

Viscoelastic transition in transonic flow focusing

Thin jets are necessary for several technological applications. They can be produced with larger orifices by hydrodynamic focusing with an outer faster gas stream (Flow Focusing), which prevents clogging issues. In this work, we show how the addition of a small and adequate amount of a low molecular weight polymer triggers a viscoelastic transition in the meniscus, resulting in significantly thinner and longer jets

Characterization Of Shock Buffet On A Supercritical 2D Airfoil In Transonic Flow

The transonic flow over the supercritical OAT15A airfoil is investigated experimentally. Using time-resolved focusing schlieren sequences, we extracted the temporal evolution of the chordwise shock location for a wide range of combinations of Mach number and angle of attack. Based on this data, we identified the conditions of pre-buffet, buffet onset, fully-established buffet, and buffet-offset behavior. Key parameters characterizing most pronounced buffet behavior are presented and quantified in terms of the shock amplitude, its variation over multiple buffet cycles, and the associated frequency of the periodic shock oscillation. Fully-established buffet is identified at a Mach number of 0.72 and angle of attack of 5 deg. It is demonstrated that these operating conditions are characterized by a quasi-sinusoidal shock oscillation at a distinct frequency of 113 Hz, in good agreement with previous studies. This analysis reveals that the harmonic shock oscillation spanning a range of about 16.5% of the airfoil chord is accompanied by a coupled large-scale variation of the global flow topology. Both instantaneous and mean velocity components in the chordwise and vertical directions are discussed for representative phases of the buffet cycle. Instantaneous vector fields of both components provide insight into the flow organization throughout the buffet cycle and allow to identify the streamwise distance traveled by the shock wave within a full cycle. We can thus precisely capture the state of the shock wave and quantify the evolution of the shock-induced separation and the size of the turbulent wake. Severe variations of the flow topology are induced by the large-scale upstream and downstream shock displacement. The results show that incidents of massive flow separation are observed for shock positions being close to the upstream limit, and more general, that the wake influence is more pronounced when induced by an upstream traveling shock wave. Phase-averaged velocity profiles at significant locations along the airfoil suction side complement this analysis. Characteristic sets of velocity profiles are discussed in detail that allow to uniquely describe the development of the flow in each phase of the buffet cycle. Detailed contours and profiles of both velocity and Reynolds shear stress contributions across the wake region highlight the strong downstream influence the shock-induced turbulent wake. Phases of severe flow separation result in reverse flow persisting until the trailing edge which further substantiates the induced momentum deficit.

PIV investigations of shock-buffet dynamics on a supercritical airfoil with a pitching degree of freedom

The interaction between the transonic flow around a spring mounted OAT15A airfoil model and the resulting pitching motion of the model was investigated with the goal of understanding the dynamics of the occurring phenomena. The experiments were performed at free-stream Mach numbers from 0.70 to 0.77 and at a Reynolds number of Rec ≈ 3 × 10^6. The dominant structural frequency of the airfoil’s pitch motion was adjusted to be in the range of the natural buffet frequency of the flow with inhibited pitching motion of the model. The variation of the Mach number allowed for an investigation in the pre-buffet, buffet and post-buffet regime. A periodic pitch motion with an amplitude of the angle of attack of up to ±1.17° was observed for buffeting flow conditions while it was significantly less in pre-buffet and post-buffet conditions. Velocity field measurements by means of high repetition rate particle image velocimetry (PIV) were used to capture the motion of the shock and to determine the state of the boundary layer flow for the different phases of the model motion. For the Mach number range Ma = 0.72 − 0.75 the change of the angle of attack and the shock position correlate strongly with each other. From the measurements, the delay of both quantities during the coupled motion could be determined.

Analysis Of PIV Images Of Transonic Buffet Flow By Recurrent Deep Learning Based Optical Flow Prediction

In the past few years, several algorithms have been proposed that leverage deep learning techniques within the data analysis workflow of particle-image velocimetry (PIV) experiments. This emerging body of work has shown that deep learning has the potential to match or outperform state-of-the-art classical algorithms in terms of efficiency, accuracy, and spatial resolution. Due to the significant relevance of PIV experiments in the broader fluid mechanics community, progress in PIV processing approaches based on state-of-the-art machine learning tools has a major impact across a range of problems in applied physics and engineering where velocity components of flow fields need to be determined. In contrast to existing methods, these approaches are general, near-automated and yield per-pixel flow estimates. Primary work on deep learning for PIV is promising, but important questions concerning the application to challenging engineering problems remain open and more scientific analyses are necessary to substantiate the general confidence amongst practitioners in such neural network based tools. This motivates us to employ a novel deep learning based PIV approach called RAFT-PIV to a challenging application of a recent research subject. That is, we use our neural optical flow approach to evaluate Background-Oriented Schlieren (BOS) and PIV images obtained by measurements of the transonic flow around a supercritical DRA-2303 profile and demonstrate that it can be used as a direct one-to-one replacement for standard cross-correlation based counterparts.

Tối ưu hóa biên dạng cánh máy bay trong dòng chảy cận âm

This paperpresents a method to optimize the wing profile RAE2822 in transonic flow by a surrogate-based optimization method. The problem is solved for the profile with given parameters of angle of attack, Mach number, ambient temperature and Reynolds number using open source software SU2 (Stanford University Unstructured). The surrogate based optimizationmethod with only two parameters of perturbation functions provides a solution for increasing aerodynamic quality of the wing profile by reducing drag and keeping lift above a specified value. The obtained results are the basis for studying wing optimization in the preliminary design stage.

The rise and fall of banana puree: Non-Newtonian annular wave cycle in transonic self-pulsating flow

We reveal mechanisms driving pre-filming wave formation of the non-Newtonian banana puree inside a twin-fluid atomizer at a steam–puree mass ratio of 2.7%. Waves with a high blockage ratio form periodically at a frequency of 1000 Hz, where the collapse of one wave corresponds to the formation of another (i.e., no wave train). Wave formation and collapse occur at very regular intervals, while instabilities result in distinctly unique waves each cycle. The average wave angle and wavelength are 50° and 0.7 nozzle diameters, respectively. Kelvin–Helmholtz instability (KHI) dominates during wave formation, while pressure effects dominate during wave collapse. An annular injection of the puree into the steam channel provides a wave pool, allowing KHI to deform the surface; then, steam shear and acceleration from decreased flow area lift the newly formed wave. The onset of flow separation appears to occur as the waves' rounded geometry transitions to a more pointed shape. Steam compression caused by wave sheltering increases pressure and temperature on the windward side of the wave, forcing both pressure and temperature to cycle with wave frequency. Wave growth peaks at the nozzle exit, at which point the pressure build-up overcomes inertia and surface tension to collapse and disintegrate the wave. Truncation of wave life by pressure build-up and shear-induced puree viscosity reduction is a prominent feature of the system, and steam turbulence does not contribute significantly to wave formation. The wave birth-death process creates bulk system pulsation, which, in turn, affects wave formation.

Physics-aware reduced-order modeling of transonic flow via β -variational autoencoder

Autoencoder-based reduced-order modeling (ROM) has recently attracted significant attention, owing to its ability to capture underlying nonlinear features. However, two critical drawbacks severely undermine its scalability to various physical applications: entangled and therefore uninterpretable latent variables (LVs) and the blindfold determination of latent space dimension. In this regard, this study proposes the physics-aware ROM using only interpretable and information-intensive LVs extracted by β-variational autoencoder, which are referred to as physics-aware LVs throughout this paper. To extract these LVs, their independence and information intensity are quantitatively scrutinized in a two-dimensional transonic flow benchmark problem. Then, the physical meanings of the physics-aware LVs are thoroughly investigated and we confirmed that with appropriate hyperparameter β, they actually correspond to the generating factors of the training dataset, Mach number, and angle of attack. To the best of our knowledge, our work is the first to practically confirm that β-variational autoencoder can automatically extract the physical generating factors in the field of applied physics. Finally, physics-aware ROM, which utilizes only physics-aware LVs, is compared with conventional ROMs, and its validity and efficiency are successfully verified.

Large-eddy simulations and modal reconstruction of laminar transonic buffet

Transonic buffet refers to the self-sustained periodic motion of shock waves observed in transonic flows over wings and can limit the flight envelope of aircraft. Based on the boundary layer characteristics at the shock foot, buffet has been classified as laminar or turbulent and the mechanisms underlying the two have been proposed to be different (Dandois et al., J. Fluid Mech., vol. 18, 2018, pp. 156–178). The effect of various flow parameters (freestream Mach and Reynolds numbers and sweep and incidence angles) on laminar transonic buffet on an infinite wing (Dassault Aviation's supercritical V2C aerofoil) is reported here by performing large-eddy simulations (LES) for a wide range of parameters. A spectral proper orthogonal decomposition identified the presence of a low-frequency mode associated with buffet and high-frequency wake modes related to vortex shedding. A flow reconstruction based only on the former shows periodic boundary-layer separation and reattachment accompanying shock wave motion. A modal reconstruction based only on the wake mode suggests that the separation bubble breathing phenomenon reported by Dandois et al. is due to this mode. Together, these results indicate that the physical mechanisms governing laminar and turbulent buffet are the same. Buffet was also simulated at zero incidence. Shock waves appear on both aerofoil surfaces and oscillate out of phase with each other indicating the occurrence of a Type I buffet (Giannelis et al., Aerosp. Sci. Technol., vol. 18, 2018, pp. 89–101) on a supercritical aerofoil. These results suggest that the mechanisms underlying different buffet types are the same.

Comparative study of inner–outer Krylov solvers for linear systems in structured and high-order unstructured CFD problems

Advanced Krylov subspace methods are investigated for the solution of large sparse linear systems arising from stiff adjoint-based aerodynamic shape optimization problems. A special attention is paid to the flexible inner–outer GMRES strategy combined with most relevant preconditioning and deflation techniques. The choice of this specific class of Krylov solvers for challenging problems is based on its outstanding convergence properties. Typically in our implementation the efficiency of the preconditioner is enhanced with a domain decomposition method with overlapping. However, maintaining the performance of the preconditioner may be challenging since scalability and efficiency of a preconditioning technique are properties often antagonistic to each other. In this paper we demonstrate how flexible inner–outer Krylov methods are able to overcome this critical issue. A numerical study is performed considering either a Finite Volume (FV), or a high-order Discontinuous Galerkin (DG) discretization which affect the arithmetic intensity and memory-bandwidth of the algebraic operations. We consider test cases of transonic turbulent flows with RANS modeling over the two-dimensional supercritical OAT15A airfoil and the three-dimensional ONERA M6 wing. Benefits in terms of robustness and convergence compared to standard GMRES solvers are obtained. Strong scalability analysis shows satisfactory results. Based on these representative problems a discussion of the recommended numerical practices is proposed.

A Riemann–Hilbert Type Problem for the Generalized Cauchy–Riemann Equation with Supersingular Points on a Half-Plane

For an equation with the Cauchy–Riemann operator having strong isolated point singularities in the lowest coefficient, an integral representation of the solution is found in the class of bounded functions at infinity, and a Riemann–Hilbert type problem on a half-plane is investigated. Specialists are well aware about the important role played in applications by I.N. Vekua’s theory of generalized analytic functions of an equation in the case when the coefficients and the right-hand side of the generalized Cauchy–Riemann system belong to the class of summable functions. It is deeply linked with many areas of analysis, geometry and mechanics, including quasi-conformal maps, surface theory, shell theory, and gas dynamics. In particular, it is widely used in modeling transonic gas flows, states of momentless stressed equilibrium of convex shells, and many other processes. The Vekua–Pompeiu integral plays a key role in this theory. When the lowest coefficient has strong singularities, some researchers believe that the Vekua–Pompeiu integral, which is main research engine in the theory of generalized analytic functions, cannot be applied. By using the Vekua–Pompeiu integral, we have succeeded in constructing solutions of the Cauchy–Riemann system the lowest coefficient of which contains strong isolated point singularities in an infinite domain. A Riemann–Hilbert type problem on a half-plane is investigated for the equation under consideration by using an explicit integral representation.

Numerical Investigation of the Influence of Air Contaminants on the Interfacial Heat Transfer in Transonic Flow in a Compressor Rotor

Atmospheric air is a commonly used working fluid in turbomachinery. The air typically contains a certain amount of suspended solid particles, as well as water in the form of vapor or droplets. In the current paper, we focus on the numerical modeling of humid air transonic flow in turbomachinery. In this paper we demonstrate a rarely considered, but as presented herein important influence of air humidity, pollution and liquid water content on the performance of the first stage of the gas turbine compressor and turbofan engine fan (NASA rotors 37 and 67). We also discuss the impact of the interfacial heat transfer associated with steam condensation or water evaporation on the distribution of stagnation parameters at the rotor outlet, the rotor performance, and flow conditions, as well as losses. Results demonstrate the impact of the number of pollution particles and water droplets on the compression process in the analyzed rotors, especially on the Mach number distribution in the blade-to-blade channel. In this paper we highlight that the air pollution and liquid water content, together with such physical phenomena as steam condensation or water droplets evaporation, exert a significant influence on work parameters, losses and efficiency, and thus should be considered in high-velocity airflow simulations.

Structural stability of transonic shock flows with external force in a divergent 3-D axisymmetric perturbed nozzle

This paper concerns with the structural stability of the transonic shock for steady Euler flows with external force in a divergent 3-D axisymmetric perturbed nozzle. We first establish the existence and uniqueness of spherical symmetric transonic shock solution to steady isentropic Euler system with external force by prescribing suitable exit pressure at the exit of a straight divergent nozzle when the incoming flow at the entrance is spherical symmetric supersonic flow. Then we investigate the stability of this spherical symmetric transonic shock solution to the 3-D axisymmetric steady isentropic Euler system with external force when the incoming supersonic flow and the nozzle boundary and the exit pressure and the external force are suitable perturbed. One of new ideas in the analysis is to use the deformation-curl decomposition provided in [21] to deal with the transonic shock problem.

Computational Study of a Local Fractional Tricomi Equation Occurring in Fractal Transonic Flow

Abstract In this paper, we present the application of local fractional methods in combination with the local fractional Sumudu transform (LFST) for a local fractional Tricomi equation (LFTE). The numerical simulations for obtained results are presented for the local fractional Tricomi equation with different initial conditions on the Cantor set. The computational approach shows that the implemented methods are very impressive to derive solutions for a local fractional Tricomi equation. Moreover, the solutions obtained by using these schemes are in quite good agreement with already computed solutions in the literature.

Fast Predictions of Aircraft Aerodynamics Using Deep-Learning Techniques

The numerical analysis of aerodynamic components based on the Reynolds–averaged Navier–Stokes equations has become critical for the design of transport aircraft but still entails large computational cost. Simulating a multitude of different flow conditions with high-fidelity methods as required for loads analysis or aerodynamic shape optimization is still prohibitive. Within the past few years, the application of machine learning methods has been proposed as a potential way to overcome these shortcomings. This is leading toward a new data-driven paradigm for the modeling of physical problems. The objective of this paper is the development of a deep-learning methodology for the prediction of aircraft surface pressure distributions and the rigorous comparison with existing state-of-the-art nonintrusive reduced-order models. Bayesian optimization techniques are employed to efficiently determine optimal hyperparameters for all deep neural networks. Three data-driven methods which are Gaussian processes, proper orthogonal decomposition combined with an interpolation technique, and deep learning are investigated. The results are compared for a two-dimensional airfoil case and the NASA Common Research Model transport aircraft as a relevant three-dimensional case. Results show that all methods are able to properly predict the surface pressure distribution at subsonic conditions. In transonic flow, when shock waves and separation lead to nonlinearities, deep-learning methods outperform the others by also capturing the shock wave location and strength accurately.

Study on influencing factors of trailing edge flow characteristics of transonic micro turbine rotor

In order to meet the needs of the development of high-performance micro-engine, the micro-turbine is faced with the technical challenge of high-load and transonic flow. At present, the flow characteristics and loss mechanism of high-load micro-impeller are not clear. In this paper, the flow characteristics of high-load micro-turbine rotor are studied. The results show that the loss in rotor trailing edge is the main factor that affect the operation of the micro transonic turbine, and the key to reduce the loss is to reduce the wake diffusion range and the Mach number in front of the extended shock wave. By adjusting the local curvature of the front in front of the incident point of the back-extension wave in the throat of the suction surface, the convergent-divergent ratio is in the range of 1.04 ~ 1.08. Meanwhile, the Mach number of wave front can be reduced by 3.4% and the reflection of trailing edge inward extension can be effectively suppressed, and the total rotor pressure loss coefficient can be reduced by 14.1% at most. The thickness has an important effect on the wave strength and wake loss in the trailing edge. When the relative thickness of the trailing edge decreases by 50%, the maximum Mach number on the suction surface decreases by 7.8%, the turbine stage efficiency increases by 1.92%, and the relative thickness of trailing edge is 0.124~0.185, the studied micro-transonic turbine performs better.

Flow Characteristic Study of High-speed Cavity Based on Detached-eddy Simulations

The cavity is widely used in the advanced flight vehicle. However, there are also some new aerodynamic characteristic when cavity is exposed in high-speed flow. The flow characteristic of high-speed cavity is studied in this paper based on detached-eddy simulation method. The M219 cavity benchmark under transonic flow is used as the validation case for numerical methods and grid strategy. Comparison of predicted sound pressure levels and spectra against the wind tunnel experiment has proved that the numerical methods capture the major oscillation dynamics inside the cavity. The aerodynamic characteristic of cavity with a store is investigated in this paper, there are three vortexes in the cavity and the main vortex in the middle rotates around the store. The shear layer breaks earlier compared with clean cavity due to the turbulent flow around the store. However, the small store has little influence to the sound pressure level of cavity.

Unexpected stability of micrometer weakly viscoelastic jets

We study experimentally the stability of micrometer weakly viscoelastic jets produced with transonic flow focusing. Highly stable jets are formed when a low molecular weight polymer is added to water at a given low concentration, and the injected flow rate is reduced to its minimum value. In this case, the capillary instability is delayed, and the jet breakup occurs at distances from the ejector of the order of tens of thousands the jet diameter. The results indicate that the intense converging extensional flow in the ejection point builds up viscoelastic stress that does not relax in the jet even for times much longer than the polymer relaxation time. We hypothesize that the drag (shear) force exerted by the outer gas stream prevents the stress relaxation. It is also possible that partial polymer entanglement at the jet emission point contributes to this effect. We measure the jet length and the diameter at the ejector orifice and breakup point. The diameter takes values just above 2 μm at the breakup point regardless of the liquid flow rate and gas pressure.

A Numerical Investigation of the Dominant Characteristics of A Transonic Flow Over A Hemispherical Turret

The transonic characteristics of a flow over a hemispherical turret with a freestream Mach number M∞ of 0.8 are numerically studied. The flow field is simulated using the improved delayed detached eddy simulation (IDDES) with a modified sub-grid scale. The results using the adopted medium and fine grids, including for the mean pressure coefficients and the incoming boundary layer, match experimental data very well. It is observed that the wake fluctuates periodically as the shock moves upstream and downstream. The dominant flow characteristics are identified along with their frequencies. The first two proper orthogonal decomposition (POD) modes show a lateral shift of the wake, fluctuating at a Strouhal number (St) of 0.15–0.2. Modes 3 and 4 show a wall-normal fluctuation of the wake with St of 0.35. A dynamic mode decomposition (DMD) gives St values of the lateral shift and wall-normal fluctuation of 0.1813 and 0.3467, respectively.

An experimental and simulated investigation into the validity of unrestricted blast wave scaling models when applied to transonic flow in complex tunnel environments

Since the inception of high explosives as an industrial tool, significant efforts have been made to understand the flow of energy from an explosive into its surroundings to maximize work produced while minimizing damaging effects. Many tools have been developed over the past century, such as the Hopkinson–Cranz (H-C) Scaling Formula, to define blast wave behavior in open air. Despite these efforts, the complexity of wave dynamics has rendered blast wave prediction difficult under confinement, where the wave interacts with reflective surfaces producing complex time-pressure waveforms. This paper implements two methods to better understand blast overpressure propagation in a confined tunnel environment and establish whether scaled tests can be performed comparatively to costly full-scale experiments. Time–pressure waveforms were predicted using both a 1:10 scaled model and three-dimensional air blast simulations conducted in Ansys Autodyn. A comparison of the reduced scale model simulation with a full-scale blast simulation resulted in self-similar overpressure waveforms when employing the H-C scaling model. Experimental overpressure waveforms showed a high level of correlation between the reduced scale model and simulations. Additionally, peak overpressure, duration, and impulse values were found to match within tolerances that are highly promising for applying this methodology in future applications. Using this validated relationship, the simulated model and reduced scale tests were used to predict an overpressure waveform in a full-scale underground mine opening to within 2.12%, 2.91%, and 7.84% for peak overpressure, time of arrival, and impulse, respectively. This paper demonstrates the effectiveness of scaled, blast models when predicting blast wave parameters in a confined environment.