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The problem of the geodynamo is simple to formulate (Why does the Earth possess a magnetic field?), yet it proves surprisingly hard to address. As with most geophysical flows, the fluid flow of molten iron in the Earth's core is strongly influenced by the Coriolis effect. Because the liquid is electrically conducting, it is also strongly influenced by the Lorentz force. The balance is unusual in that, whereas each of these effects considered separately tends to impede the flow, the magnetic field in the Earth's core relaxes the effect of the rapid rotation and allows the development of a large-scale flow in the core that in turn regenerates the field. This review covers some recent developments regarding the interplay between rotation and magnetic fields and how it affects the flow in the Earth's core.
This review provides a comprehensive analysis of the literature on vortex-induced vibration (VIV) of flexible circular cylinders in cross-flow. It delves into the details of the underlying physics governing the VIV dynamics of cylinders characterized by low mass damping and high aspect ratio, subject to both uniform and shear flows. It compiles decades of experimental investigations, modeling efforts, and numerical simulations and describes the fundamental findings in the field. Key focal points include but are not limited to amplitude–frequency response behavior, the relationship between the distributed loading acting on the cylinder and the trajectories and the near wake structures around the cylinder, the existence of traveling waves, the identification of power-in/power-out regions, and the modal overlapping and mode competition phenomena.
Turbulence is often studied by tracking its spatiotemporal evolution and analyzing the dynamics of its different scales. The dual to this perspective is that of an observer who starts from measurements, or observations, of turbulence and attempts to identify their back-in-time origin, which is the foundation of data assimilation. This back-in-time search must contend with the action of chaos, which obfuscates the interpretation of the observations. When the available measurements satisfy a critical resolution threshold, the influence of chaos can be entirely mitigated and turbulence can be synchronized to the exact state–space trajectory that generated the observations. The critical threshold offers a new interpretation of the Taylor microscale, one that underscores its causal influence. Below the critical threshold, the origin of measurements becomes less definitive in regions where the flow is inconsequential to the observations. In contrast, flow events that influence the measurements, or are within their domain of dependence, are accurately captured. The implications for our understanding of wall turbulence are explored, starting with the highest density of measurements that entirely tame chaos and proceeding all the way to an isolated measurement of wall stress. The article concludes with a discussion of future opportunities and a call to action.
Chemical gradients, the spatial variations in chemical concentrations and components, are omnipresent in environments ranging from biological and environmental systems to industrial processes. These thermodynamic forces often play a central role in driving transport processes taking place in such systems. This review focuses on diffusiophoresis, a phoretic transport phenomenon driven by chemical gradients. We begin by revisiting the fundamental physicochemical hydrodynamics governing the transport. Then we discuss diffusiophoresis arising in flow systems found in natural and artificial settings. By exploring various scenarios where chemical gradients are encountered and exploited, we aim to demonstrate the significance of diffusiophoresis and its state-of-the-art development in technological applications.
Ice structures such as accretion on airplanes, wires, or roadways; ice falls; ice stalactites; frozen rivers; and aufeis are formed by the freezing of capillary flows (drops, rivulets, and films). To understand these phenomena, a detailed exploration of the complex coupling between capillary flow and solidification is necessary. Among the many scientific questions that remain open in order to understand these problems are the confinement of the thermal boundary layer by the free surface, the interaction between a freezing front and a free surface, the effect of freezing on the contact line motion, etc. This review focuses mainly on water and ice, discussing the theoretical framework and recent developments in the main areas of the freezing–capillarity interaction. The text deeply explores the freezing of a moving drop or a rivulet and the fundamental problem of wetting water on ice. Additionally, it highlights some of the main open questions on the subject.
The environmental setting of the Dead Sea combines several aspects whose interplay creates flow phenomena and transport processes that cannot be observed anywhere else on Earth. As a terminal lake with a rapidly declining surface level, the Dead Sea has a salinity that is close to saturation, so that the buoyancy-driven flows common in lakes are coupled to precipitation and dissolution, and large amounts of salt are being deposited year-round. The Dead Sea is the only hypersaline lake deep enough to form a thermohaline stratification during the summer, which gives rise to descending supersaturated dissolved-salt fingers that precipitate halite particles. In contrast, during the winter the entire supersaturated, well-mixed water column produces halite. The rapid lake level decline of O(1 m/year) exposes vast areas of newly formed beach every year, which exhibit deep incisions from streams. Taken together, these phenomena provide insight into the enigmatic salt giants observed in the Earth's geological record and offer lessons regarding the stability, erosion, and protection of arid coastlines under sea level change.
By imploding fuel of hydrogen isotopes, inertial confinement fusion (ICF) aims to create conditions that mimic those in the Sun's core. This is fluid dynamics in an extreme regime, with the ultimate goal of making nuclear fusion a viable clean energy source. The fuel must be reliably and symmetrically compressed to temperatures exceeding 100 million degrees Celsius. After the best part of a century of research, the foremost fusion milestone was reached in 2021, when ICF became the first technology to achieve an igniting fusion fuel (thermonuclear instability), and then in 2022 scientific energy breakeven was attained. A key trade-off of the ICF platform is that greater fuel compression leads to higher burn efficiency, but at the expense of amplified Rayleigh–Taylor and Richtmyer–Meshkov instabilities and kinetic-energy-wasting asymmetries. In extreme cases, these three-dimensional instabilities can completely break up the implosion. Even in the highest-yielding 2022 scientific breakeven experiment, high-atomic-number (high-Z) contaminants were unintentionally injected into the fuel. Here we review the pivotal role that fluid dynamics plays in the construction of a stable implosion and the decades of improved understanding and isolated experiments that have contributed to fusion ignition.
Our understanding of respiratory flow phenomena has been consolidated over decades with the exploration of in vitro and in silico canonical models that underscore the multiscale fluid mechanics spanning the vast airway complex. In recent years, there has been growing recognition of the significant intersubject variability characterizing the human lung morphometry that modulates underlying canonical flows across subjects. Despite outstanding challenges in modeling and validation approaches, exemplified foremost in capturing chronic respiratory diseases, the field is swiftly moving toward hybrid in silico whole-lung simulations that combine various model classes to resolve airflow and aerosol transport spanning the entire respiratory tract over cumulative breathing cycles. In the years to come, the prospect of accessible, community-curated datasets, in conjunction with the use of machine learning tools, could pave the way for in silico population-based studies to uncover unrecognized trends at the population level and deliver new respiratory diagnostic and pulmonary drug delivery endpoints.
Lagrangian averaging theories, most notably the generalized Lagrangian mean (GLM) theory of Andrews and McIntyre, have been primarily developed in Euclidean space and Cartesian coordinates. We reinterpret these theories using a geometric, coordinate-free formulation. This gives central roles to the flow map, its decomposition into mean and perturbation maps, and the momentum 1-form dual to the velocity vector. In this interpretation, the Lagrangian mean of any tensorial quantity is obtained by averaging its pull-back to the mean configuration. Crucially, the mean velocity is not a Lagrangian mean in this sense. It can be defined in a variety of ways, leading to alternative Lagrangian mean formulations that include GLM and Soward and Roberts's volume-preserving version. These formulations share key features that the geometric approach uncovers. We derive governing equations both for the mean flow and for wave activities constraining the dynamics of the perturbations. The presentation focuses on the Boussinesq model for inviscid rotating stratified flows and reviews the necessary tools of differential geometry.
When flowing through narrow channels or constrictions, many-body systems exhibit various flowing patterns, yet they can also get stuck. In many of these systems, the flowing elements remain as individuals (they do not aggregate or merge), sharing strong analogies among each other. This is the case for systems as contrasting as grains in a silo and pedestrians passing through tight spaces. Interestingly, when these entities flow within a fluid medium, numerous similarities persist. However, the fluid dynamics aspects of such clogging events, such as interstitial flow, liquid pressure, and hydrodynamic interactions, has only recently begun to be explored. In this review, we describe parallels with dry granular clogging and extensively analyze phenomena emerging when particles coexist with fluid in the system. We discuss the influence of diverse flow drive, particle propulsion mechanisms, and particle characteristics, and we conclude with examples from nature.
Publication date: 30 January 2025
Source: Computers & Fluids, Volume 287
Author(s): Lan Jiang, Jie Wu, Liming Yang, Qiushuo Qin
Publication date: 30 January 2025
Source: Computers & Fluids, Volume 287
Author(s): Xiaoyang Xu, Wei Yu
Publication date: 30 January 2025
Source: Computers & Fluids, Volume 287
Author(s): A. Karimi Noughabi, M. Leer, I. Wlokas, A. Kempf
Publication date: 30 January 2025
Source: Computers & Fluids, Volume 287
Author(s): André F.P. Ribeiro, Thomas Leweke, Aliza Abraham, Jens N. Sørensen, Robert F. Mikkelsen
Publication date: 30 January 2025
Source: Computers & Fluids, Volume 287
Author(s): Yiqiu Jin, Yiqing Shen, Guowei Yang, Guannan Zheng
Publication date: 30 January 2025
Source: Computers & Fluids, Volume 287
Author(s):
Publication date: Available online 10 December 2024
Source: Computers & Fluids
Author(s): Paul Over, Sergio Bengoechea, Thomas Rung, Francesco Clerici, Leonardo Scandurra, Eugene de Villiers, Dieter Jaksch
Publication date: Available online 11 December 2024
Source: Computers & Fluids
Author(s): Michael Deligant, Carlos Romero, Xesus Nogueira, Luis Ramirez, Mathieu Specklin, Farid Bakir, Sofiane Khelladi
Publication date: Available online 11 December 2024
Source: Computers & Fluids
Author(s): Abdallah ElSherbiny, Sébastien Leclaire
Publication date: Available online 11 December 2024
Source: Computers & Fluids
Author(s): M. Girfoglio, A. Quaini, G. Rozza
We investigate the macro-element hybridized discontinuous Galerkin (HDG) method that combines advantages of continuous and discontinuous finite elements for compressible flow analysis. To efficiently handle large systems, we focus on computational strategies at the level of the direct local solver and the matrix-free iterative global solver. Our test simulations show that the macro-element HDG method is efficient for moderate polynomial degrees, balances local and global operations, and compared to standard HDG reduces the global system size and the number of solver iterations.
The macro-element variant of the hybridized discontinuous Galerkin (HDG) method combines advantages of continuous and discontinuous finite element discretization. In this paper, we investigate the performance of the macro-element HDG method for the analysis of compressible flow problems at moderate Reynolds numbers. To efficiently handle the corresponding large systems of equations, we explore several strategies at the solver level. On the one hand, we utilize a second-layer static condensation approach that reduces the size of the local system matrix in each macro-element and hence the factorization time of the local solver. On the other hand, we employ a multi-level preconditioner based on the FGMRES solver for the global system that integrates well within a matrix-free implementation. In addition, we integrate a standard diagonally implicit Runge–Kutta scheme for time integration. We test the matrix-free macro-element HDG method for compressible flow benchmarks, including Couette flow, flow past a sphere, and the Taylor–Green vortex. Our results show that unlike standard HDG, the macro-element HDG method can operate efficiently for moderate polynomial degrees, as the local computational load can be flexibly increased via mesh refinement within a macro-element. Our results also show that due to the balance of local and global operations, the reduction in degrees of freedom, and the reduction of the global problem size and the number of iterations for its solution, the macro-element HDG method can be a competitive option for the analysis of compressible flow problems.
The study proposed a new correction of non-equilibrium terms for the k−ω$$ k-\omega $$ turbulence model. The suggested method of correcting the non-equilibrium effect can be useful in the future to formulate high-speed models based on all turbulent mechanisms.
The goal of this research is to propose a new modification of a non-equilibrium effect in the k−ω$$ k-\omega $$ turbulence model to better predict high-speed turbulent flows. For that, the two local compressibility coefficients are included in the balance production/dissipation terms in a specific dissipation rate equation. The specific dissipation rate reacts to changes in the local Mach number and density through these local coefficients. The developed model is applied to the numerical simulation of the spatial supersonic turbulent airflow with round hydrogen injection. In that, the effects of the proposed turbulence model on the flow field behavior (shock wave and vortex formations, shock wave/boundary layer interaction, and mixture layer) are studied via the solution of three-dimensional Favre-averaged Navier–Stokes equations with a third-order Essentially Non-Oscillatory scheme. A series of numerical experiments are performed, in which an allowable range of local constants by comparing results with experimental data is obtained. The non-equilibrium modification by simultaneous decrease of the turbulence kinetic energy and increase of the specific dissipation rate gives a good agreement of the hydrogen depth penetration with experimental data. Also, the numerical experiment of the supersonic airflow with a nitrogen jet shows wall pressure distribution is consistent well with experimental data.
The paper presents an improved approach for modelling multi-component gas mixtures based on quasi-gasdynamic equations. The proposed numerical algorithm is implemented as a reactingQGDFoam solver based on the open-source OpenFOAM platform. This solver has been extensively validated and verified through a variety of well-described test problems. The stability and convergence parameters of the proposed numerical algorithm are determined. The simulation results are found to be in agreement with analytical solutions and experimental data.
The paper presents an improved approach for modeling multicomponent gas mixtures based on quasi-gasdynamic equations. The proposed numerical algorithm is implemented as a reactingQGDFoam solver based on the open-source OpenFOAM platform. The following problems have been considered for validation: the Riemann problems, the backward facing step problem, the interaction of a shock wave with a heavy and a light gas bubble, the unsteady underexpanded hydrogen jet flow in an air. The stability and convergence parameters of the proposed numerical algorithm are determined. The simulation results are found to be in agreement with analytical solutions and experimental data.
Response surface method-based hydraulic performance optimization of a single-stage centrifugal pump.
In this article, the response surface approach was employed to enhance the hydraulic performance of the pump at the rated point. Specifically, an approximate link between the design head and efficiency of the single-stage centrifugal pump and the parameters of the impeller's design was established. The first step in creating a one-factor experimental design involved selecting significant geometric variables as factors. Decision variables such as the number of blades, flow rate, and rotation were chosen due to their significant impact on hydraulic performance, while head and efficiency were considered as responses. Subsequently, the best-optimized values for each level of the parameters were identified using response surface analysis and a central composite design. The impeller schemes of the Design-Expert software were evaluated for head and efficiency using Computational fluid dynamics, and a total of 20 experiments were conducted. The simulated results were then validated with experimental data. Through the analysis of the individual parameters and the approximation model, the ideal parameter combination that increased head and efficiency by 7.90% and 2.06%, respectively, at the rated value was discovered. It is worth noting that in cases of a high rate of flow, the inner flow was also enhanced.
This paper highlights the impact and importance of including turbulence effects on topology optimization of compressible flow. The study proposes a novel approach based on Favre-Averaged Navier–Stokes equations and the compressible version of the Spalart–Allmaras model and solves first the compressible turbulent adjoint model by coupling dolphin adjoint from FEniCS and OpenFOAM software. Examples demonstrate the effects of turbulence on compressible flow and analyze industrial cases such as pipes, diffusers and mixers chambers where non-intuitive and efficient designs are presented.
Turbulence significantly influences fluid flow topology optimization, and this has already been verified under the incompressible flow regime. However, the same cannot be said about the compressible flow regime, in which the density field now affects and couples all of the fluid flow and turbulence equations and makes obtaining the adjoint model, which is necessary for topology optimization, extremely difficult. Up to now, the turbulence phenomenon has still not been considered in compressible flow topology optimization, which is what is being proposed and analyzed here. Rather than being based in the Reynolds-Averaged Navier–Stokes (RANS) equations which are defined only for incompressible flow, the equations are now based on the Favre-Averaged Navier–Stokes (FANS) equations, which are the counterpart of the RANS equations for compressible flow and feature different dependencies and terms. The compressible turbulence model being considered is the compressible version of the Spalart–Allmaras model, which differs from the usual Spalart–Allmaras model, since now there are some new spatially varying density and specific heat terms that depend on the primal variables and that act over some of the turbulence terms of the overall model. The adjoint equations are obtained by using an automatic differentiation scheme through a coupled software platform. The optimization algorithm is IPOPT, and some examples are presented to show the effect of turbulence in the compressible flow topology optimization.
We introduce semi-implicit Lagrangian Voronoi approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier–Stokes equations, which combines semi-implicit time marching with time-dependent Voronoi tessellations with topology changes. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and play the role of the generators of the computational mesh. The velocity field is projected onto a divergence-free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multiphase flows.
We introduce semi-implicit Lagrangian Voronoi approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier–Stokes equations, which combines the efficiency of semi-implicit time marching schemes with the robustness of time-dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection-based Arbitrary-Lagrangian-Eulerian schemes, we need no remapping stage. A semi-implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence-free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi-phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no-slip and free-slip boundary conditions.
This paper presents a comprehensive numerical investigation of the performance of pulsating heat pipes (PHPs) within nuclear reactor cooling systems. A volume of fluid (VOF) method was used to simulate the complex multiphase flow, providing detailed insights into fluid distribution, phase interactions, and temperature variations under different operating conditions. The simulations revealed distinct phase separation and convective flow patterns that enhance heat transfer efficiency, which is critical for optimizing thermal management in nuclear reactors. Additionally, artificial neural network (ANN) models were employed to predict volume fractions and wall temperatures, achieving high accuracy with R 2 values of 0.99 and 0.98, respectively, and low mean absolute errors (MAE). The ANN models also reduced computational time by 90% compared to traditional numerical simulations. These findings highlight the potential of PHPs to improve heat transfer in nuclear systems and demonstrate the practicality of ANN models for real-time thermal optimization. The research contributes to enhancing the safety and efficiency of nuclear reactor cooling systems, with broader implications for thermal management across various engineering applications.
Using the finite-volume approach on a staggered mesh, we derive semidiscrete system for the transient incompressible Navier–Stokes equations. The calculation of the cell-face fluxes present in the semidiscrete system is carried out by solving suitably defined non-linear boundary value problems(BVP). Depending on physics based treatment of the source, three complete flux approximation schemes are derived and implemented on fluid flow benchmark problems.
We construct novel flux approximation schemes for the semidiscretized incompressible Navier–Stokes equations by finite-volume method on a staggered mesh. The calculation of the cell-face fluxes has been done by solving appropriate local non-linear boundary value problems (BVP). Consequently, the cell-face fluxes are represented as the sum of a homogeneous and an inhomogeneous flux; the homogeneous part represents the contribution of convection and viscous-friction, while the inhomogeneous part represents the contribution of the source terms. We derive three flux approximation schemes to include the impact of the source terms on the numerical fluxes. The first one is based on a homogeneous 1-D local BVP without source. The second scheme is based on an inhomogeneous 1-D local BVP considering only the pressure gradient term in the source. Finally, a complete flux scheme is derived which is based on an inhomogeneous 2-D local BVP. It takes into account both the gradient of the cross-flux and the pressure gradient in the source term. The numerical validation of the schemes is done for the benchmark lid-driven cavity flow for considerably high Reynolds$$ \mathrm{Reynolds} $$ numbers along with a numerical convergence test for the exact solution of the Taylor–Green vortex problem.
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Alexander A. Belozerov, Natalia B. Petrovskaya, Yulii D. Shikhmurzaev
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Mahmoud Shaqfa, Gary P.T. Choi, Guillaume Anciaux, Katrin Beyer
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Luan F. Santos, Joseph Mouallem, Pedro S. Peixoto
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Arijit Sinhababu, Shyamprasad Karagadde
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Allen Alvarez Loya, Daniel Appelö, William D. Henshaw
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Shinya Maeyama, Tomo-Hiko Watanabe, Motoki Nakata, Masanori Nunami, Yuuichi Asahi, Akihiro Ishizawa
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Jonathan Palafoutas, David A. Velasco Romero, Romain Teyssier
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Changqing Ye, Shubin Fu, Eric T. Chung, Jizu Huang
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Xuelian Bao, Chun Liu, Yiwei Wang
Publication date: 1 February 2025
Source: Journal of Computational Physics, Volume 522
Author(s): Maxime Jonval, Ibtihel Ben Gharbia, Clément Cancès, Thibault Faney, Quang-Huy Tran
Fully-convolutional neural networks (FCN) were proven to be effective for predicting the instantaneous state of a fully-developed turbulent flow at different wall-normal locations using quantities measured at the wall. In Guastoni et al. (J Fluid Mech 928:A27, 2021. https://doi.org/10.1017/jfm.2021.812), we focused on wall-shear-stress distributions as input, which are difficult to measure in experiments. In order to overcome this limitation, we introduce a model that can take as input the heat-flux field at the wall from a passive scalar. Four different Prandtl numbers \(Pr = \nu /\alpha = (1,2,4,6)\) are considered (where \(\nu \) is the kinematic viscosity and \(\alpha \) is the thermal diffusivity of the scalar quantity). A turbulent boundary layer is simulated since accurate heat-flux measurements can be performed in experimental settings: first we train the network on aptly-modified DNS data and then we fine-tune it on the experimental data. Finally, we test our network on experimental data sampled in a water tunnel. These predictions represent the first application of transfer learning on experimental data of neural networks trained on simulations. This paves the way for the implementation of a non-intrusive sensing approach for the flow in practical applications.
The dynamic characteristics of mode behavior in a low-speed, single-stage axial compressor are crucial for studying linear stall inception. An input–output analysis framework has been established, enabling the introduction of forcing into the compressor system and identifying the most energetic mode. Both standard and compressed input–output analysis are conducted to explore sensitive forcing positions and flow variables, with opposition control employed to suppress energy gain. As throttling progresses, a shift in high energy gain distribution from high-order to first-order circumferential modes is observed, with two distinct branches emerging across the domain of circumferential mode numbers and forcing frequencies. Compressed input–output analysis shows that limiting the forcing range to the shroud, from the inlet to the rotor blade section, is sufficient to excite the energetic mode in the current cases. Subsequently, opposition control is applied at the shroud to suppress energy amplification and modulate stall propensity within these two distinct branches. The results reveal that axial velocity control reduces energy amplification and suppresses perturbation modes related to stall inception. A comprehensive assessment of componentwise energy amplification is conducted, considering various variable forcing. The predicted results indicate that velocity perturbations are the predominant factors influencing the resolvent mode distribution pattern. Moreover, opposition control significantly impacts the critical branch associated with stall inception.
We study the pressure-driven steady gas flow, imposed by temperature or density gradients, over a backward-facing step in a two-dimensional microchannel. Focusing on the near-free-molecular regime of high Knudsen ( \(\textrm{Kn}\) ) numbers, the problem is analyzed asymptotically based on the Bhatnagar, Gross and Krook kinetic model, and supported by numerical Discrete Velocity Method and Direct Simulation Monte Carlo calculations. The wall conditions are formulated using the Maxwell model, superposing specular and diffuse surface conditions. The asymptotic solution contains the leading-order free-molecular description and a first-order integral representation of the near-free-molecular correction. Our results indicate that flow separation at the step can occur at arbitrarily large (yet finite) Knudsen numbers in channels with specular surfaces (i.e., having an accommodation coefficient of \(\alpha = 0\) ), driven by temperature differences between the inlet and outlet reservoirs. It is then shown that detachment is significantly suppressed by density variations between reservoirs and partially diffuse surfaces (with \(\alpha \gtrsim 0.3\) ). While the mass flow rate in a specular channel decreases with decreasing \(\mathrm {Kn\gg 1}\) in a density-driven setup (in line with the Knudsen Paradox), it increases in a temperature-driven flow. The results are obtained for arbitrary differences between the inlet and outlet reservoir equilibrium properties, and are rationalized using the linearized problem formulation.
A methodology to numerically assess wall-curvature effects in boundary layers is introduced. Wall curvature, which directly induces streamline curvature, is associated with several changes in boundary-layer flow. By necessity, a local radial pressure gradient emerges to balance mean flow turning. Moreover, a streamwise (wall-tangential) pressure gradient can appear for configurations with non-constant wall curvature or a particular freestream condition; zero pressure gradient is a special case. In laminar concave flow, the Görtler instability and the associated Taylor-Görtler vortices destabilize the flow and promote laminar-turbulent transition, whereas in the fully turbulent regime, unsteady coherent structures formed by the centrifugal instability mechanism dramatically redistribute turbulent shear stress. One difficulty of assessing centrifugal effects on boundary layers is that they often appear simultaneously with other phenomena, such as a streamwise pressure gradient, making their individual evaluation often ambiguous. For numerical studies of transitional and turbulent boundary layers, it is therefore beneficial to understand the interactive nature of such coupled effects for generic configurations. A methodology to do so is presented, and is verified using the case of a subsonic, compressible turbulent boundary layer. Four direct numerical simulations have been computed, forming a \(2{\times }2\) matrix of turbulent boundary-layer states; namely with and without concave wall curvature, each having a zero and a non-zero streamwise-pressure-gradient realization. The setup and accompanying procedures to determine appropriate boundary conditions are discussed, and the methodology is evaluated through analysis of the mean flow fields. Differences in mean flow properties such as wall shear stress and boundary-layer thickness due to either streamwise pressure gradient or wall curvature are shown to be remarkably independent of one another.
We investigate scenarios, where only sparse wall shear stress measurements are available, while accurate wall shear stress and velocity profiles are sought. Applying discrete adjoint-based data assimilation, with only near-wall measurements, accurate wall shear stress profiles are achieved at the expense of unrealistic velocity profiles. We therefore add and employ internal reference data generated by performing a relatively cheap hybrid simulation. We modified the dual-mesh hybrid LES/RANS framework recently proposed by Xiao and Jenny (J Comput Phys 231(4):1848–1865, 2012, https://doi.org/10.1016/j.jcp.2011.11.009) by loosely coupling under-resolved LES in the interior with steady RANS near the walls. The framework was developed in OpenFOAM and tested for flow over periodic hills with Re = 10,595. Results show that the devised framework outperforms conventional dual-mesh hybrid LES/RANS and standalone sparse wall-data assimilated RANS models. Graphical abstract Horizontal mean velocity component \(U_{1}\) (top plot) and wall shear stress (friction coefficient \(C_{f}\) ) profiles at the lower wall (bottom plot) obtained with S-RANS and assimilation of sparse wall shear stress data
An exact parallel algorithm of dynamic mode decomposition (DMD) with Hankel matrices for large-scale flow data is proposed. The proposed algorithm enables the DMD and the Hankel DMD for large-scale data obtained by high-fidelity flow simulations, such as large-eddy simulations or direct numerical simulations using more than a billion grid points, on parallel computations without any approximations. The proposed algorithm completes the computations of the DMD by utilizing block matrices of \(X^TX\in \mathbb {R}^{k\times k}\) (where \(X\in \mathbb {R}^{n\times k}\) is a large data matrix obtained by high-fidelity simulations, the number of snapshot data is \(n > rsim 10^9\) , and the number of snapshots is \(k\lesssim O(10^3)\) ) without any approximations: for example, the singular value decomposition of X is replaced by the eigenvalue decomposition of \(X^TX\) . Then, the computation of \(X^TX\) is parallelized by utilizing the domain decomposition often used in flow simulations, which reduces the memory consumption for each parallel process and wall-clock time in the DMD by a factor approximately equal to the number of parallel processes. The parallel computation with communication is performed only for \(X^TX\) , allowing for high parallel efficiency under massively parallel computations. Furthermore, the proposed exact parallel algorithm is extended to the Hankel DMD without any additional parallel computations, realizing the Hankel DMD of large-scale data collected by over a billion grid points with comparable cost and memory to the DMD without Hankel matrices. Moreover, this study shows that the Hankel DMD, which has been employed to enrich information and augment rank, is advantageous for large-scale high-dimensional data collected by high-fidelity simulations in data reconstruction and predictions of future states (while prior studies have reported such advantages for low-dimensional data). Several numerical experiments using large-scale data, including laminar and turbulent flows around a cylinder and transonic buffeting flow around a full aircraft configuration, demonstrate that (i) the proposed exact parallel algorithm reproduces the existing non-parallelized Hankel DMD, (ii) the Hankel DMD for large-scale data consisting of over a billion grid points is feasible by using the proposed exact parallel algorithm with high parallel efficiency on more than 6 thousand CPU cores, and (iii) the Hankel DMD has advantages for high-dimensional data such as \(n > rsim 10^9\) .
Dynamics of a multiphase flow phenomenon involving water (at top), molten metal (at bottom), and vapor (between them), was numerically studied using volume of fluid method. Multiphase flow systems like this are present in a wide range of industrial applications and natural phenomena and are extensively investigated because of their potential to produce energy. This work pays special attention to the interface shape because of its influence on heat transfer rate. An approach, new for systems larger than drop scale, which consists in the construction of an interface shape diagram based on Reynolds (Re) and Bond (Bo) dimensionless numbers is proposed. The presented model demonstrated good capability to discern the governing forces such as viscous, inertial, and surface tension. The most favorable interface shapes for efficient premixing of phases involved were identified. The premixing significance lies in its determining role in steam explosion generation. Moreover, the effect of density ratio and triggering pressure is examined. In addition, Kelvin–Helmholtz and Rayleigh–Taylor fragmentation mechanisms were observed, and their preponderance was analyzed. The results obtained were validated with previous experimental data available in the literature finding good agreement. This proposal aims to provide useful information to enhance our understanding of this phenomenon from a fundamental perspective, applicable to further numerical and experimental studies in different research areas.
An inviscid vortex shedding model is numerically extended to simulate falling flat plates. The body and vortices separated from the edge of the body are described by vortex sheets. The vortex shedding model has computational limitations when the angle of incidence is small and the free vortex sheet approaches the body closely. These problems are overcome by using numerical procedures such as a method for a near-singular integral and the suppression of vortex shedding at the plate edge. The model is applied to a falling plate of flow regimes of various Froude numbers. For \(\text {Fr}=0.5\) , the plate develops large-scale side-to-side oscillations. In the case of \(\text {Fr}=1\) , the plate motion is a combination of side-to-side oscillations and tumbling and is identified as a chaotic type. For \(\text {Fr}=1.5\) , the plate develops to autorotating motion. Comparisons with previous experimental results show good agreement for the falling pattern. The dependence of change in the vortex structure on the Froude number and its relation with the plate motion is also examined.
The generation mechanism of wall heat flux is one of the fundamental problems in supersonic/hypersonic turbulent boundary layers. A novel heat decomposition formula under the curvilinear coordinate was proposed in this paper. The new formula has wider application scope and can be applied in the configurations with grid deformed. The new formula analyzes the wall heat flux of an interaction between a shock wave and a turbulent boundary layer over a compression corner. The results indicated good performance of the formula in the complex interaction region. The contributions of different energy transport processes were obtained. While the processes by the mean profiles such as molecular stresses and heat conduction, can be ignored, the contributions by the turbulent fluctuations, such as Reynolds stresses and turbulent transfer of heat flux, were greatly increased. Additionally, the pressure work is another factor that affects the wall heat flux. The pressure work in the wall-normal direction is concentrated close to the reattachment point, while the pressure work in the streamwise direction acts primarily in the shear layer and the reattachment point.
The aerodynamic and aeroacoustic performance of a low-aspect-ratio ( \(\hbox {AR}=0.2\) ) pitching foil during dynamic stall are investigated numerically with focus on the effects of trailing edge serrations. A hybrid method coupling an immersed boundary method for incompressible flows with the Ffowcs Williams–Hawkings acoustic analogy is employed. Large eddy simulation and turbulent boundary layer equation wall model are also employed to capture the turbulent effects. A modified NACA0012 foil with a rectangular trailing edge flap attached to the trailing edge (baseline case) undergoing pitching motion is considered. Trailing edge serrations are applied to the trailing edge flap and their effects on the aerodynamic and aeroacoustic performance of the oscillating airfoil are considered by varying the wave amplitude ( \(2h^*= 0.05, 0.1\) , and 0.2) at a Reynolds number of 100,000 and a Mach number of 0.05. It is found that the reduction of the sound pressure level at the dimensionless frequency band \(St_{b}\in [1.25,4]\) can be over 4 dB with the presence of the trailing edge serrations ( \(2h^*=0.1\) ), while the aerodynamic performance and its fluctuations are not significantly altered except a reduction around 10% in the negative moment coefficient and it fluctuations. This is due to the reduction of the average spanwise coherence function and the average surface pressure with respect to that of the baseline case, suggesting the reduction of the spanwise coherence and the noise source may result in the noise reduction. Analysis of the topology of the near wake coherent structure for \(2h^*=0.1\) reveals that the alignment of the streamwise-oriented vortex with the serration edge may reduce the surface pressure fluctuation.
