The objective of this paper is to assess the capabilities of a hybrid BANS-LES approach DDES coupled with algebraic BANS turbulence transition models SST KD and SST alg-gamma, allowing the prediction of the laminar-turbulent transition (LTT). The approach is applied to calculations of flows around stationary and rotating cylinders as well as a tandem of stationary cylinders. It is shown that for the simulations of the flows under consideration, this approach significantly outperforms the standard SST DDES (within the standard SST DDES it is assumed that the flow is completely turbulent, and the LTT is not taken into account). At the same time, the obtained computational results depend significantly on the choice of the LTT model, and neither of the two models has a clear advantage in terms of agreement between the computational results and experimental data.

The paper presents the results of a computational study of the effect of the longitudinal pressure gradient (PG) on the position of the laminar-turbulent transition (LTT) in the boundary layer on a smooth plate and on a plate with local surface irregularity. For a smooth plate, the calculations were performed using both the method developed by the authors, based on the Global Stability Analysis (GSA) of the laminar boundary layer, and other known methods that take into account the LTT. The results obtained varied significantly for different methods and differed from the more reliable GSA results, which questions the accuracy of these methods. The studies have proved that it is possible to perform a total evaluation of the LTT position shift by adding the shift for a smooth plate due to changes in the PG value and the shift for a plate with irregularity on its surface in the absence of PG.

Представлены результаты всестороннего тестирования четырех недавно предложенных алгебраических моделей ламинарно-турбулентного перехода (ЛТП), которые существенно превосходят дифференциальные модели ЛТП по экономичности, потенциально не уступая им по точности. Выбранные для оценки модели SST KD, SST k$\gamma$, SST alg-$\gamma$ и SA BCM были реализованы в академическом коде NTS и верифицированы путем сравнения полученных результатов с опубликованными результатами авторов моделей. Базу для тестирования моделей путем сравнения результатов расчетов с экспериментом составили пограничные слои при отсутствии и наличии градиента давления и различных уровнях турбулентности набегающего потока, четыре крыловых профиля, при обтекании которых реализуются различные сценарии ЛТП, и тандем крыловых профилей. Обнаружено, что при использовании моделей SA BCM и SST k$\gamma$ при низких уровнях турбулентности положение перехода может зависеть от начального приближения, что не позволяет рекомендовать их для использования в инженерных приложениях. Наилучшие результаты, сравнимые по точности с результатами дифференциальных моделей, получены с использованием модели SST alg-$\gamma$.

The article investigates the feasibility of Large Eddy Simulation methods to accurately compute the flow around the Ahmed car body at 25^∘ slant angle. The flow is computed at two different Reynolds numbers and with different turbulence modeling concepts using a large variety of grids. Issues associated with the accurate computation of the separation at the slant onset will be discussed in detail.

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.

Reliable prediction of the effect of surface irregularities on laminar-turbulent transition (LTT) is of great importance for many industrial applications. At low levels of free-stream turbulence typical of external aerodynamics, the primary mechanism of LTT is associated with the so-called convective instability of the Tollmien-Schlichting waves. In this paper, a non-empiric methodology based on Global Stability Analysis, which has been developed and validated previously to predict the evolution of these waves and the location of the LTT on a smooth flat plate, is applied to evaluation of this effect for backward- and forward- facing steps of different heights and locations. The results obtained are analyzed and compared with results of 2D time-accurate unsteady Navier-Stokes simulations, as well as with available experimental data and with the semi-empiric “variable N-factor” method.

The article presents numerical simulation of turbulent flow in a rotating rectangular 90° bend channel using the WMLES method, and the effect of rotation on the flow structure is studied. The article also presents a study of the accuracy of various semi-empirical turbulence models for closing the Reynolds equations for flows of this type by comparison with the WMLES results for the cases with and without rotation.

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.

This paper presents the results of extensive testing of four recently proposed algebraic laminar-turbulent transition (LTT) models, which are significantly more computationally effective than differential models, while being potentially equally accurate. The models chosen for evaluation, namely, SST KD, SST kγ, SST alg-γ, and SA BCM, are implemented in the in-house code NTS and verified by comparing the obtained results with those published by the models’ authors. The experimental database used for the evaluation of the models includes transitional boundary layers at different free-flow turbulence intensities with and without the pressure gradient, four airfoil flows with different LTT scenarios, and a tandem of two airfoils. It is found that at low levels of turbulence, the results of the SA BCM and SST kγ models may depend on the initial approximation, which does not allow them to be recommended for engineering applications. The best results, comparable in accuracy to those of differential models, are obtained using the SST alg-γ model.

Global Stability Analysis (GSA) is a powerful and efficient tool for studying various forms of instability developing in laminar and turbulent flows. A key element of the GSA is the generalized eigenvalue problem. To solve this problem, the so-called matrix-forming approach is most often used, which implies the explicit formation of the Jacobian matrix of the right-hand sides of the fluid motion equations and the direct solution of corresponding eigenvalue problem. However, this approach requires a lot of computer memory to store elements of the LU-factorized Jacobian matrix. In the present study, based on examples of GSA conducted for a few 2D and 3D flows of various complexity, specific RAM requirements for the matrix-forming approach to GSA and their dependence on the size and type (2D or 3D) of the flows under consideration are defined. This allows an estimate of the maximum size of the GSA problem, which solution is possible on the cluster Tornado of the Supercomputer Center “Politechnichesky” and on other supercomputers with a similar architecture.

In the paper, the two main approaches to calculating the Jacobian of the Navier- Stokes equations, namely, the continuum (CA) and discrete (DA) approaches, have been directly compared for the first time. The DA to calculating this Jacobian was implemented based on in-house finite-volume code for hydrodynamics simulation (in addition to the already existing CA). The DA was successfully verified by comparison between the obtained numerical result and that of solving the transient Navier-Stokes equations. The comparison of these approaches was carried out using the example of a laminar flow past a cylinder by a perfect gas at the near-critical Reynolds numbers (Re = 50 and 60). It was established that the CA predicted the growth rate of perturbations more accurately, while the DA did their frequency and amplitude in toto. The results obtained allow to assert that both CA and DA are equivalent in terms of accuracy, and the choice of a particular approach for analyzing the stability may be determined by other criteria, e. g., ease of implementation, computational work and so on.

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 Direct Numerical and Large Eddy Simulation study is conducted to establish the NASA CS0 diffuser as a test case for scale-resolving simulation methods and to evaluate the ability of such simulations to accurately predict flows with adverse pressure gradients and shallow separation from a smooth surface. The results of fine grid studies are in a good agreement with experimental data and substantially supplement them. These data are used as a basis for testing of LES on reduced grids, using different combinations of wall treatments and turbulence model formulations.

В работе проведено численное моделирование турбулентного течения во вращающемся канале прямоугольного сечения с поворотом на 90° методом WMLES, исследовано влияние вращения на структуру течения. Выполнено исследование точности различных полуэмпирических моделей турбулентности для замыкания уравнений Рейнольдса для течений данного типа путем сравнения с результатами WMLES как при наличии вращения, так и при его отсутствии.

Reliable prediction of effect of surface irregularities on laminar-turbulent transition (LTT) is of great importance for many industrial applications. At low levels of free-stream turbulence typical of external aerodynamics, a primary mechanism of LTT is associated with the so-called convective instability of the Tolmien-Schlichting waves. In the present paper, a non-empiric methodology for numerical prediction of these waves evolution and LTT position based on the Global Stability Analysis, which is developed and validated previously for a smooth flat plate, is applied to evaluation of this effect for backward- and forward-facing steps with different heights and locations. Obtained results are analyzed and compared with available experimental data and with the results of semi-empiric “variable N-factor” method.

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.

Представлена вычислительная методология, предназначенная для расчета пространственной эволюции волн Толлмина-Шлихтинга и показателя роста их амплитуды в существенно непараллельных потоках, базирующаяся на глобальном анализе устойчивости стационарных решений полной системы уравнений Навье-Стокса для сжимаемого газа. Описаны три этапа этой методологии (получение стационарного решения, проведение глобального анализа его устойчивости и постпроцессинг полученных результатов), и приведены результаты ее валидации путем сравнения результатов расчета характеристик волн Толлмина-Шлихтинга на плоской пластине с соответствующими результатами классической теории устойчивости в локально-однородном приближении. Представлен пример расчета обтекания пластины с прямоугольной выемкой, иллюстрирующий возможность применения предложенной методологии к непараллельным течениям.

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.