The results are presented of the numerical experiments aimed at obtaining detailed and reliable data on the mean and turbulent characteristics of the asymmetric curved turbulent wake behind a flat plate (FP) subjected to an adverse pressure gradient (APG). The computations are performed for the model wake configuration designed earlier by the authors with the use of the scale-resolving zonal Reynolds-averaged Navier–Stokes-improved delayed detached-eddy simulation (RANS-IDDES) approach to represent turbulence. The reliability of the obtained results is confirmed by the grid independence of the obtained solutions, and a comparison of these results with the corresponding results of computations performed with the use of various semiempirical RANS models indicates the insufficient accuracy of the latter and the need for their further improvement.

A computational methodology is presented for calculating the spatial evolution of Tollmien–Schlichting (T–S) waves and their amplitude growth-rate factor in substantially nonparallel compressible flows, based on a global stability analysis of stationary solutions of the full Navier–Stokes (N–S) equations. Three stages of this methodology (obtaining a stationary solution, as well as carrying out a global stability analysis and its postprocessing) are described, and the results are presented of its validation based on the comparison of the results of calculating the characteristics of T–S waves on a flat plate with the corresponding results of the classical stability theory in the parallel approximation. An example of calculating the flow around a plate with a rectangular cavity is presented to illustrate the possibility of applying the proposed methodology to nonparallel flows.

The drag crisis in flow past a sphere is modeled within the framework of the recently formulated scale-resolving hybrid RANS−LES approach, which includes a semi-empirical model of laminar-turbulent transition. The calculations performed in a wide Reynolds number range show that the complex model used yields a qualitatively adequate description of all aspects of the drag crisis including such fine effects, as the growth of the side force oscillation amplitude at near-critical Reynolds numbers. At the same time, the results obtained indicate that very fine computation grids should be used for obtaining qualitatively accurate predictions of the critical Reynolds number and the details of laminar-turbulent transition in near-critical flow regimes.

We present the results of an analysis of flows in a gap between the reentry vehicle of a manned spacecraft and the propulsion bay located behind it in the case of their separation due to an emergency situation of the rocket in the active region of its trajectory. Emphasis is placed on different-in-nature oscillation processes occurring in transonic flight regimes. An approach to the estimation of the regimes of self-oscillation existence and their frequencies is proposed on the basis of the problem geometry and the flow conditions.

The work is devoted to the improvement of the k-omega BSL turbulence model for the closure of Reynolds averaged Navier-Stokes (RANS) equations with the use of machine learning (ML) methods. The correction developed for this model enhances its accuracy in cal-culating airfoil flows at stall angles of attack. Testing of the modified model on the flows around different airfoils reveals its superiority for this type of flows. The results demonstrate efficiency of the ML methods for turbulence model improvement.

Представлены результаты анализа исследований течения в зазоре между возвращаемым аппаратом пилотируемого космического корабля и расположенным за ним двигательным отсеком при их разделении в случае аварии ракеты на активном участке траектории. Особое внимание уделено автоколебательным процессам различной природы, возникающим при определенных расстояниях разделения на трансзвуковых режимах полета. Предложен подход к оценке режимов существования и частот автоколебаний на основе геометрии задачи и условий обтекания.

A numerical procedure is presented for computing characteristics of Tollmien- Schlichting (T-S) waves in the course of their downstream evolution. It is based on the Global Stability Analysis of steady solutions of the full compressible Navier-Stokes equations and, therefore, does not have the restrictions associated with the parallel or quasi-parallel flow as-sumptions used in the classical methods of the linear stability analysis based on the boundary layer approximation. Hence, the methodology may be applied not only to simple boundary lay-ers on smooth surfaces but also to non-parallel flows, e.g. those over surfaces with irregularities (steps, gaps, etc.). The developed procedure is validated by the comparison of the computed distribution of the T-S amplification factor (N-factor) in the zero pressure gradient boundary layer with the similar distribution computed based on the solution of the Orr-Sommerfeld equation and is shown to be accurate and robust.

The results of the numerical modeling of the impact of the wakes of the nozzles of an emergency rescue rocket unit (ERRU) on the surface of a manned spacecraft are presented. The calculations are performed in the context of the two-stage zonal RANS-LES methodology proposed and validated by the authors earlier. In this methodology, the wall-modeled LES (WMLES) is based on the well-known eddy-resolving approach IDDES. In this paper, this technique is improved by including in the WMLES-subdomain the first row of the ERRU’s nozzles and performing calculations in the entire (360°) azimuthal domain. This makes it possible to increase the accuracy of the calculations due to a more correct description of the wakes of these nozzles and to analyze the flow around the spacecraft at nonzero angles of attack. The effect of the flight’s Mach number on the amplitude-frequency characteristics of the pressure fluctuations on the surface of the spacecraft, including their alteration at the sonic barrier, is analyzed. In addition, at the transonic Mach number value of M∞ = 0.95, the effects of the angle of attack and the mutual azimuthal position of the nozzles of the first and second rows are studied.

A two-stage RANS-DDES model and the results of calculations of the turbulent trans- and supersonic flow around a manned spacecraft (MSC) in the course of the emergency separation of the reentry module (RM) after actuation of the propulsion device (PD) of the crew’s emergency rescue system (ERS) in the initial flight stage are presented. The study is focused on determining the unsteady aerodynamic and acoustic loads on the screen of the RM and the fairing of the engine compartment (EC). It is shown that the maximum level of the unsteady loads is reached on the fairing of the EC in the region of impingement of the turbulent structures of the shear layer separated from the command module. In addition, it is found that at the transonic flight in the initial stage of the detachment process, self-exciting oscillations are observed in the gap between the RM and the EC.

A comparative study is performed on three different approaches for prediction of transonic buffet onset on infinite swept wings. All three approaches are based on the unsteady Reynolds-averaged Navier–Stokes (URANS) equations, and include: quasi-3D and fully-3D global stability analysis of the corresponding steady 2.5D RANS solutions and direct numerical solution of the 3D URANS equations. The results are presented for an infinite swept wing based on the ONERA OAT15A airfoil section. The quasi-3D stability analysis is shown to be accurate and most efficient and, thus, is best suited for this spanwise-uniform flow. The fully-3D stability analysis ensures the same accuracy, provided that the grid-step in the spanwise direction is sufficiently small. It is much more demanding in terms of computer memory but can be extended to more-general wing configurations. Good agreement is observed between the three approaches in terms of critical conditions for buffet onset and the instability growth characteristics, providing a cross-validation of the methods and an assessment of their computational demands.

We have developed high-fidelity CFD/CAA capability for the prediction of fan tone and broadband noise from an aero-engine. With a zonal URANS—wall-modeled LES approach, referred to as the Improved Delayed Detached Eddy Simulation (IDDES), the entire geometry of NASA's Source Diagnostic Test (SDT) fan rig including the nacelle is solved at approach, cut-back and take-off conditions. Multi-block grids with high-order structured finite-volume schemes are designed to resolve turbulence in the wakes and vortices as well as sound propagation in the bypass duct through the blade rows. By applying the Ffowcs-Williams and Hawkings technique with permeable surfaces, far-field sound-power spectra are computed, and by incorporating with the duct-mode-extraction technique, the radiated sound from the inlet and exhaust is decomposed into duct modes. These predicted fan-noise characteristics as well as aerodynamic performances are validated against NASA’s wind-tunnel test data. The fan-noise associated with the rotor-stator interaction is very well characterized: The tone power levels up to the second blade passing frequencies from both inlet and exhaust are predicted well across the engine speed, and the broadband power spectra are also predicted except for those from the inlet only at supersonic tip Mach numbers.

The paper consists of two parts. The first part presents further evaluation of the prediction capability of an enhanced version of the broadband time-domain impedance model (TDIM) proposed by Dragna, Pineau and Blanc-Benon in 2015, which has been recently developed by the authors (AIAA paper 2020-2535). The model is implemented in the high-fidelity numerical system for aero-engine fan noise computation based of the zonal URANS-WMLES approach to turbulence representation and is validated by a comparison of the URANS and WMLES predictions of sound propagation over a ceramic tubular liner installed in a duct against the NASA experimental data, considered as a standard benchmark for the lined ducts’ acoustics. The present work significantly broadens the validation database for this TDIM by consideration of four different Single-Degree-of-Freedom (SDoF) acoustic liners with the perforated facesheet tested in the Grazing Flow Impedance Tube of the NASA Langley Research Center, which are representative of the liners used for practical turbofan engines. The second part of the paper addresses one of the major obstacles in the time-domain computations of the sound attenuation by the acoustic liners consisting in the development of the spatial hydrodynamic instability over the acoustically treated walls at low acoustic resistance of the liner. In most cases, the growth rate of the instability and its effect on the sound propagation are significantly overemphasized by the CFD. The paper presents a novel volumetric source term (“body force”) aimed at resolving this issue by means of the artificial suppression of the instability instead of trying to microscopically simulate the liner. The proposed body force is shown to ensure elimination of the instability with a minimum deterioration of the prediction of the acoustics and the turbulent characteristics in the framework of the scale-resolving simulations of flows over lined walls.

This study investigates the instabilities of the interstage flow between a rotor and a stator in turbomachinery and evaluates their impact on the fan noise. By viewing the interstage flow as the so-called spiral-Poiseuille flow, linear stability analysis of the incompressible Navier-Stokes equations reveals two distinct instability regimes at the Reynolds numbers up to Re & LE;O(105): The first mode excites disturbances over wide frequencies, including the rotor speed, and forms wavepacket-like structures above the outer-wall boundary layer. The second mode evolves inside the outer-wall boundary layer with slower velocity and possesses much smaller axial wavenumbers. We extract these modes using an approach analogous to dynamic mode decomposition from a database of our improved-delayed-detached eddy simulation solving NASA's turbofan-rig test at low speed. The dynamic mode decomposition technique successfully visualizes these two instability modes even at Re & AP;4x106, and their dispersion relations approximately agree with the characteristics predicted by the linear stability analysis. These analyses suggest that the instabilities amplify coherent disturbances in the rotor wakes and vortices near the tip until they interact with the stator; moreover, coherent structures associated with the second instability may act as stationary objects, possibly resulting in an additional fan-noise source.

We investigate hydrodynamic instabilities in the interstage of a turbofan engine, which potentially amplify the fan noise associated with the rotor-stator interaction. By applying linear stability analysis of the incompressible Navier--Stokes equations to the velocity profiles of two NASA's high-speed fan rigs, Source Diagnostic Test (SDT) and Advanced Ducted Propulsor (ADP), we reveal multiple distinct unstable regimes: The first unstable mode amplifies disturbances right outside the outer-wall boundary layer over a wide mid-frequency range including the rotor speed. The second mode rotates much slower and develops inside the outer-wall boundary layer with a smaller axial wavenumber. In addition, the analysis of ADP indicates an unstable mode near the inner wall. We extract these modes using an approach analogous to dynamic mode decomposition (DMD) from databases of our improved-delayed-detached eddy simulation (IDDES) solving the SDT geometry at approach and cut-back conditions. The extracted modes generally capture the characteristics, e.g.\ the dispersion relations and the eigenfunctions, predicted by the linear stability analysis. At the approach condition, the two unstable modes seem to interact inside the outer-wall boundary layer, while at the cut-back condition, disturbances associated with the first mode migrate away from the outer wall. These trends seem to be consistent with the azimuthal contents of the fan broadband noise simulated using the IDDES and measured using a mode ring.

Global instability analysis is used to investigate the effects of extended regions of laminar flow on both unswept and swept infinite-span wings. The formulation is based on the Reynolds-averaged Navier-Stokes equations and differs from earlier studies on fully turbulent flows in the activation of the trip term in the Spalart-Allmaras eddy-viscosity transport equation. The trip term ensures a rapid transition to turbulence at an arbitrary-specified location on the wing surface, analogous a trip strip in an experiment. A parametric study is conducted for the ONERA OAT15A extruded airfoil, as an example. Results show that an extended region of laminar flow leads to a reduction in the critical angle of attack for the buffet onset, as compared with the fully turbulent conditions. All modes of instability show enhanced growth as a result of the laminar flow. However, increased lift (at fixed angle of attack) associated with an extended region of laminar flow results in a higher lift coefficient at buffet onset as compared with the fully turbulent case. Results show that the laminar flow effects on the buffet onset are linked to the suction-side laminar flow and are largely independent of the boundary-layer state on the pressure side of the wing.

Results are presented of scale-resolving computations of mean and turbulent (including the dissipation rate of turbulent kinetic energy) characteristics of the turbulent wake of a flat plate subjected to adverse pressure gradient (APG). The computations are performed in the framework of a zonal RANS-LES model for two configurations. In the first one, APG is created by a plane symmetric diffuser and in the second one by a system of two pairs of thin liner foils specially designed for this purpose. In the both cases a volumetric synthetic turbulence generator is used for creating turbulent content at the inlet of LES subdomain. High accuracy of results of the simulations is supported by their weak sensitivity to grid-refinement. Obtained detailed data on wakes’ characteristics may be used for validation and improvement of RANS turbulence models as applied to the considered class of flows.

This paper presents two enhancements of the efficient broadband time-domain impedance model proposed by Dragna, Pineau, and Blanc-Benon in 2015. It treats lined walls in the framework of the macros...

The paper presents a bilateral German-Russian project launched in 2017 and aimed at investigation of turbulent wakes in the presence of Adverse Pressure Gradient (APG). Such wakes are a common feature of high-lift wing flows near the maximum lift conditions (take-off and landing), when the wake of the main wing is subjected to APG created by flaps. This type of flow is known to be poorly predicted by available RANS models. Hence, an ultimate goal of the project is their improvement based on a detailed experimental dataset and on results of high-fidelity turbulence resolving simulations providing relevant second moment closure terms not accessible by measurements. After a brief overview of the experimental and numerical parts of the project, the paper focuses on the first zonal RANS-IDDES computations of a wake of the flat plate in APG created by a plane diffuser. These computations performed in the initial stage of the project (before obtaining experimental data) are aimed at evaluating the capability of this approach to ensure the required accuracy with reasonable computational resources. Results of the simulations conducted on 3 grids (18, 30, and 50 million cells) support the credibility of the approach and suggest that it ensures not only virtually grid-independent prediction of the mean flow characteristics of the wake but also the dissipation-rate which is a key quantity in the context of improvement of the Reynolds Stress Transport RANS models. This is achieved, despite a relatively large grid step in the wake region (about 75 Kolmogorov length scales), thanks to computing this quantity based on the balance of the separate terms of the Reynolds stress transport equations.

Results are presented of high-fidelity scale-resolving simulations of the wake flow exposed to adverse pressure gradient (APG). Specifically, zonal RANS-IDDES computations are performed of the flow model designed and manufactured at the Technische Universität Braunschweig in the framework of a joint German-Russian project “Wake in Adverse Pressure gradient”. The model includes a flat plate as the wake generator and two pairs of thin liner foils creating APG. Results of the computations of mean flow characteristics agree with currently available experimental data and differ from those of the RANS predictions. This suggests the necessity of RANS models improvement which is planned to be done with the use of the combined experimental/numerical database on the mean flow and turbulence statistics of the wake accumulated in the course of the project.