Propagating structures in wall-bounded turbulent flows

Hydraulic and heat transfer processes play a very important role in the design and prototyping of aerospace technology. In most cases this technique works under non-isothermal conditions. Non-isothermal conditions may significantly affect heat transfer and hydrodynamic process. Fundamental research of Non-isothermal turbulent flow is required for further engineering modeling. Models for unsteady processes calculation must be based on fundamental turbulent structure research. Moscow Aviation Institute National Research University (MAI) has been building non-isothermal turbulent flow structures since 1989. An experimental facility was designed to provide gas flow heating. Experimental data of a turbulent gas flow structure in isothermal and non-isothermal conditions are presented. The frequency spectra of axial and radial velocity pulsations are based on experimental data received. The results of experimental turbulent flow research demonstrate fundamental non-isothermal processes influence on the flow structure. The main results of non-isothermal experimental research show that there are three specific zones in turbulent flow structure: wall area, maximal turbulent structure transformation and flow core. The analysis of non-isothermal conditions influence on turbulent pulsations generation and development mechanisms is presented. The results show significant distinction in turbulent flow spectra between isothermal and non-isothermal conditions. The present paper describes a method of experimental research, methodology of data processing and non-isothermal turbulent flow spectra results.

Coherent structures in turbulent square duct flow

The near-wall, subgrid-scale (SGS) model [Chung and Pullin, Large-eddy simulation and wall-modeling of turbulent channel flow, J. Fluid Mech. 631, 281--309 (2009)] is used to perform large-eddy simulations (LES) of the incompressible developing, smooth-wall, flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. The composite SGS-wall model is presently incorporated into a computer code suitable for the LES of developing flat-plate boundary layers. This is then used to study several aspects of zero- and adverse-pressure gradient turbulent boundary layers. First, LES of the zero-pressure gradient turbulent boundary layer are performed at Reynolds numbers Reθ based on the free-stream velocity and the momentum thickness in the range Reθ = 103 - 1012. Results include the inverse skin friction coefficient, √2/Cf, velocity profiles, the shape factor H, the Karman constant, and the Coles wake factor as functions of Reθ. Comparisons with some direct numerical simulation (DNS) and experiment are made, including turbulent intensity data from atmospheric-layer measurements at Reθ = O(106. At extremely large Reθ, the empirical Coles-Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot of itself probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that the LES is suggestive of the asymptotic, infinite Reynolds-number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum Reθ of the present simulations appears to be limited by machine precision and it is speculated, but not demonstrated, that even larger Reθ could be achieved with quad- or higher-precision arithmetic. Second, the time series velocity signals obtained from LES within the logarithmic region of the zero-pressure gradient turbulent boundary layer are used in combination with an empirical, predictive inner--outer wall model [Marusic et al., Predictive model for wall-bounded turbulent flow, Science 329, 193 (2010)] to calculate the statistics of the fluctuating streamwise velocity in the inner region of the zero-pressure gradient turbulent boundary layer. Results, including spectra and moments up to fourth order, are compared with equivalent predictions using experimental time series, as well as with direct experimental measurements at Reynolds numbers Reτ based on the friction velocity and the boundary layer thickness, Reτ =7,300, 13,600 and 19,000. LES combined with the wall model are then used to extend the inner-layer predictions to Reynolds numbers Reτ =62,000, 100,000 and 200,000 that lie within a gap in log(Reτ) space between laboratory measurements and surface-layer, atmospheric experiments. The present results support a log-like increase in the near-wall peak of the streamwise turbulence intensities with Reτ and also provide a means of extending LES results at large Reynolds numbers to the near-wall region of wall-bounded turbulent flows. Finally, we apply the wall model to LES of a turbulent boundary layer subject to an adverse pressure gradient. Computed statistics are found to be consistent with recent experiments and some Reynolds number similarity is observed over a range of two orders of magnitude.

High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations. This paper provides a detailed comparison of the effectiveness of entropy stable discontinuous Galerkin methods for the stabilization of compressible (wall-bounded) turbulent flows. For this investigation, an entropy stable discontinuous Galerkin spectral element method is applied on Gauss–Legendre and Gauss–Lobatto nodes. In the compressible regime, an additional stabilization technique for shock capturing based on a convex blending of a low-order finite volume with the high-order discontinuous Galerkin operator is utilized. The present investigation provides a systematic study from convergence tests, to the Taylor–Green vortex and finally to a more intricate turbulent wall-bounded 3D diffuser flow, encompassing both weakly compressible and compressible regimes. The comparison demonstrates that the DGSEM on Gauss–Lobatto nodes is generally less accurate for an equal amount of degrees of freedom. Conversely, it is faster than the DGSEM on Gauss—Legendre nodes due to a less severe time step restriction and simpler numerical operator. A performance comparison reveals that the DGSEM on Gauss–Lobatto nodes generally outperforms the DGSEM on Gauss nodes for underresolved turbulence in the subsonic regime on a periodic domain. Conversely, the opposite effect can be observed for wall-bounded flows as well as the supersonic regime, the latter depending of course on the chosen shock-capturing scheme. To the author’s knowledge, this is the first time for which a comparison of entropy stable DGSEM on Gauss–Lobatto and Gauss–Legendre has been performed for compressible, wall-bounded turbulent flows with separation.

Generating inflow fields for scale-resolving simulations of turbulent flow is crucial for a wide range of applications and is an active area of research. In this thesis, a method for inflow generation employing a precursor turbulent channel flow simulation is proposed. A procedure for determining the parameters of the precursor simulation based on the properties of the inflow is given. To evaluate the performance of the method, results from a simulation of a flat-plate zero-pressure-gradient turbulent boundary layer are analysed. The adaption length is quantified in terms of the development of integral quantities and the statistical moments of the velocity field. The performance is also compared with that of a state-of-the-art rescaling method for the generation of inflow data. It is shown that both approaches result in adaption lengths of comparable sizes, which makes the proposed method an attractive alternative due to its conceptual simplicity and robustness.As part of the work on inflow generation, a Python package, eddylicious, was developed. The purpose of the package is to be a framework within which various generation methods can be implemented. The package is available online under an open-source license. An overview of the architecture and currently implemented functionality of the package is given in this thesis.Furthermore, the results of a preparatory study on large-eddy simulation of wall-bounded turbulent flows are discussed. Fully-developed turbulent channel flow is used as a model problem, and the general-purpose computational fluid dynamics solver OpenFOAM is employed. The accuracy of the results with respect to the resolution of the computational mesh is analysed. Several modelling approaches for the subgrid scale stresses are considered.

A new statistical coherent structure (CS), the velocity–vorticity correlation structure (VVCS), using the two-point cross-correlation coefficient $R_{ij}$ of velocity and vorticity components, $u_i$ and $\omega _j~ (i, j = 1, 2, 3)$, is proposed as a useful descriptor of CS. For turbulent channel flow with the wall-normal direction $y$, a VVCS study consists of using $u_i$ at a fixed reference location $y_r$, and using $|R_{ij} (y_r; x, y, z)|\geqslant R_0$ to define a topologically invariant high-correlation region, called $\mathit{VVCS}_{ij}$. The method is applied to direct numerical simulation (DNS) data, and it is shown that the $\mathit{VVCS}_{ij}$ qualitatively and quantitatively captures all known geometrical features of near-wall CS, including spanwise spacing, streamwise length and inclination angle of the quasi-streamwise vortices and streaks. A distinct feature of the VVCS is that its geometry continuously varies with $y_r$. A topological change of $\mathit{VVCS}_{11}$ from quadrupole (for smaller $y_r$) to dipole (for larger $y_r$) occurs at $y^{+}_r=110$, giving a geometrical interpretation of the multilayer nature of wall-bounded turbulent shear flows. In conclusion, the VVCS provides a new robust method to quantify CS in wall-bounded flows, and is particularly suitable for extracting statistical geometrical measures using two-point simultaneous data from hotwire, particle image velocimetry/laser Doppler anemometry measurements or DNS/large eddy simulation data.

Turbulent wall-bounded flows are dominated by the structure and dynamics of coherent motions. Therefore, in order to understand the mechanics of turbulence, it is essential to understand how coherent structures are generated, evolve and dissipate. This thesis has two parts: firstly a digital holography-based three-component - three-dimensional velocimetry method is developed and assessed to enable the measurement of turbulent flows; secondly, since due to COVID-19 restrictions this methodology could not be employed to study wall-bounded flows, high-resolution 2-component - 2-dimensional velocity measurements of a high Reynolds number turbulent boundary layer flow is used to analyse and reveal how coherent structures affect the viscous drag exerted by the fluid on the wall.

Opposition control is a simple method used to attenuate near-wall turbulence and reduce drag in wall-bounded turbulent flows [H. Choi, P. Moin, and J. Kim, J. Fluid Mech. 262, 75 (1994)]. This method employs blowing and suction at the wall in opposition to the wall-normal fluid velocity a small distance from the wall. Results from direct numerical simulations of turbulent channel flow indicate that, when the control at the wall is based on detection of the wall-normal velocity in a plane sufficiently close to the wall, the opposition control strategy establishes a “virtual wall,” i.e., a plane that has approximately no through flow, halfway between the detection plane and the wall. As a consequence, drag is reduced about 25%. When the detection plane is at a greater distance from the wall, a virtual wall is not established, and the blowing and suction increase the drag significantly.

Premixed turbulent flame blowoff velocity correlation based on coherent structures in turbulent flows

We summarize the results of our recent work that show the logarithmic region of the streamwise turbulent intensity in wall-bounded turbulent flows. We extract the three-dimensional structures of the intense streamwise velocity fluctuations in the instantaneous flow field obtained from direct numerical simulation data of turbulent boundary layer at \(Re_\tau \approx 1000\). The identified structures are physically attached to the wall, and their height (\(l_y\)) spans from the buffer layer to the boundary layer thickness. Their length and width scale with \(l_y\) and the population density function of the tall attached structures (\(290< l_y^+ < 550\)) is inversely proportional to \(l_y\), reflecting Townsend’s attached-eddy hypothesis. We conditionally average the streamwise turbulent intensity associated with the tall attached structures and show the existence of the logarithmic region. This logarithmic behavior is further verified by examining the diagnostic function.

The excellent drag reduction effect of the bubble drag reduction technique has been proved through many experiments since it was proposed. In this paper, the authors investigate the bubble-turbulence interaction and the corresponding drag reduction effect with a two-way coupled Euler–Lagrange code. The liquid phase is simulated by using a large eddy simulation method with the immersed bubbles treated using a nonlinear collision model to accurately simulate the bubble–wall interaction. A Gaussian distributed method is adopted to obtain the void fraction and interphase forces in the two-way coupled algorithm. Two typical wall-bounded turbulent flow problems (turbulent channel flow and boundary layer flow) are simulated to validate the accuracy and stability in bubbly flows and investigate the drag reduction mechanism. First, the effect of bubbles on the turbulent flow is studied in the channel flow cases in which the bubbles are observed attaching to the upper plate and swaying in the spanwise direction. In this case, Reynolds stress near the wall is decreased, which contributes to the drag reduction. Moreover, drag reduction of a turbulent boundary layer flow with bubble injection is studied in which the drag reduction under different air flow rates is in good agreement with experimental results. The contribution of turbulence and different liquid forces to the migration of bubbles away from the wall is investigated. The bubble trajectory in the turbulent boundary layer is divided into three distinct stages and discussed in detail finally.

Computational modeling is an important tool to understand and stabilize transient turbulent fluid flow in the continuous casting of steel to minimize defects. The current work combines the predictions of two steady Reynolds-averaged Navier–Stokes (RANS) models, a “filtered” unsteady RANS model, and two large eddy simulation (LES) models with ultrasonic Doppler velocimetry (UDV) measurements in a small-scale liquid GaInSn model of the continuous casting mold region fed by a bifurcated well-bottom nozzle with horizontal ports. Both mean and transient features of the turbulent flow are investigated. LES outperformed all models while matching the measurements, except in locations where measurement problems are suspected. The LES model also captured high-frequency fluctuations, which the measurements could not detect. Steady RANS models were the least accurate methods. Turbulent velocity variation frequencies and energies decreased with distance from the nozzle port regions. Proper orthogonal decomposition analysis, instantaneous velocity patterns, and Reynolds stresses reveal that velocity fluctuations and flow structures associated with the alternating-direction swirl in the nozzle bottom lead to a wobbling jet exiting the ports into the mold. These turbulent flow structures are responsible for patterns observed in both the time average flow and the statistics of their fluctuations.

The current work qualitatively surveys the phenomenon of polymer drag reduction from the standpoint of the salient coherent motions in the near-wall region of wall-bounded turbulent flows. In an attempt to make the work self-containing, turbulence is introduced phenomenologically in terms of the scale separation concept. In concert with this theme, the idea of drag crisis is then developed in terms of reduction in this scale separation. Leveraging such a perspective, it is explained how the polymer chain dynamics spatiotemporally modulate the near-wall structure of turbulent boundary layers to affect drag reduction. To this end, a sea of literature pertaining to coherent motions in Newtonian wall-bounded flows is juxtaposed with the turbulence-inhibiting characteristics of polymer chains to develop a polymer-modified version for the near-wall cycle of turbulence generation and its sustenance. The future of polymer drag reduction, in light of the current state of knowledge and contemporary challenges, is also discussed.

Heat transfer and flow structure in laminar and turbulent flows in a rectangular channel with longitudinal vortices

The concept of coherent structure in turbulent flow is a revolutionary idea which is being developed by evolutionary means. The main objective of this review is to list some solid achievements, showing what can be done by using the concept of coherent structure that cannot be done without it. The nature of structure is described in terms of some related concepts, including celerity, topology, and the phenomenon of coalescence and splitting of structure. The main emphasis is on the mixing layer, as the one flow whose structure is well enough understood so that technical applications are now being made in problems of mixing and chemistry. An attempt is made to identify some conceptual and experimental obstacles that stand in the way of progress in other technically important flows, particularly the turbulent boundary layer. A few comments are included about the role of structure in numerical simulations and in current work on manipulation and control of turbulent flow. Some recent developments are cited which suggest that the time is nearly right for corresponding advances to occur in turbulence modeling.