# Showing papers in "Physics of Fluids in 2018"

••

TL;DR: In this paper, the existence of the possible rotational axis is proved through real Schur decomposition, and a fast algorithm for calculating Rortex is also presented, which can reasonably represent the local fluid rotation and provide a new powerful tool for vortex dynamics and turbulence research.

Abstract: A vortex is intuitively recognized as the rotational/swirling motion of the fluids. However, an unambiguous and universally accepted definition for vortex is yet to be achieved in the field of fluid mechanics, which is probably one of the major obstacles causing considerable confusions and misunderstandings in turbulence research. In our previous work, a new vector quantity that is called vortex vector was proposed to accurately describe the local fluid rotation and clearly display vortical structures. In this paper, the definition of the vortex vector, named Rortex here, is revisited from the mathematical perspective. The existence of the possible rotational axis is proved through real Schur decomposition. Based on real Schur decomposition, a fast algorithm for calculating Rortex is also presented. In addition, new vorticity tensor and vector decompositions are introduced: the vorticity tensor is decomposed to a rigidly rotational part and a non-rotationally anti-symmetric part, and the vorticity vector is decomposed to a rigidly rotational vector which is called the Rortex vector and a non-rotational vector which is called the shear vector. Several cases, including the 2D Couette flow, 2D rigid rotational flow, and 3D boundary layer transition on a flat plate, are studied to demonstrate the justification of the definition of Rortex. It can be observed that Rortex identifies both the precise swirling strength and the rotational axis, and thus it can reasonably represent the local fluid rotation and provide a new powerful tool for vortex dynamics and turbulence research.

262 citations

••

TL;DR: In this article, an alternative eigenvector-based definition of Rortex is introduced, in which the direction of the possible axis of the local rotation is determined by the real eigen vector of the velocity gradient tensor.

Abstract: Most of the current Eulerian vortex identification criteria, including the Q criterion and the λci criterion, are exclusively determined by the eigenvalues of the velocity gradient tensor or the related invariants and thereby can be regarded as eigenvalue-based criteria. However, these criteria will be plagued with two shortcomings: (1) these criteria fail to identify the swirl axis or orientation; (2) these criteria are prone to severe contamination by shearing. To address these issues, a new vector named Rortex which represents the local fluid rotation was proposed in our previous work. In this paper, an alternative eigenvector-based definition of Rortex is introduced. The direction of Rortex, which represents the possible axis of the local rotation, is determined by the real eigenvector of the velocity gradient tensor. And then the rotational strength obtained in the plane perpendicular to the possible axis is used to define the magnitude of Rortex. This new equivalent definition allows a much more efficient implementation. Furthermore, a systematic interpretation of scalar, vector, and tensor versions of Rortex is presented. By relying on the tensor interpretation, the velocity gradient tensor is decomposed to a rigid rotation part and a non-rotational part including shearing, stretching, and compression, different from the traditional symmetric and anti-symmetric tensor decomposition. It can be observed that shearing always manifests its effect on the imaginary part of the complex eigenvalues and consequently contaminates eigenvalue-based criteria, while Rortex can exclude the shearing contamination and accurately quantify the local rotational strength. In addition, in contrast to eigenvalue-based criteria, not only the iso-surface of Rortex but also the Rortex vectors and the Rortex lines can be applied to investigate vortical structures. Several comparative studies on simple examples and realistic flows are studied to confirm the superiority of Rortex.

210 citations

••

TL;DR: In this paper, a data-driven model is proposed for the prediction of the velocity field around a cylinder by fusion convolutional neural networks (CNNs) using measurements of the pressure field on the cylinder.

Abstract: A data-driven model is proposed for the prediction of the velocity field around a cylinder by fusion convolutional neural networks (CNNs) using measurements of the pressure field on the cylinder. The model is based on the close relationship between the Reynolds stresses in the wake, the wake formation length, and the base pressure. Numerical simulations of flow around a cylinder at various Reynolds numbers are carried out to establish a dataset capturing the effect of the Reynolds number on various flow properties. The time series of pressure fluctuations on the cylinder is converted into a grid-like spatial-temporal topology to be handled as the input of a CNN. A CNN architecture composed of a fusion of paths with and without a pooling layer is designed. This architecture can capture both accurate spatial-temporal information and the features that are invariant of small translations in the temporal dimension of pressure fluctuations on the cylinder. The CNN is trained using the computational fluid dynami...

195 citations

••

TL;DR: In this article, the results of velocity, temperature, entropy generation, Bejan number, coefficient of skin friction, and local Nusselt number are discussed, showing that the entropy generation rate depends on velocity and temperature distributions.

Abstract: Simultaneous effects of viscous dissipation and Joule heating in flow by rotating disk of variable thickness are examined. Radiative flow saturating porous space is considered. Much attention is given to entropy generation outcome. Developed nonlinear ordinary differential systems are computed for the convergent series solutions. Specifically, the results of velocity, temperature, entropy generation, Bejan number, coefficient of skin friction, and local Nusselt number are discussed. Clearly the entropy generation rate depends on velocity and temperature distributions. Moreover the entropy generation rate is a decreasing function of Hartmann number, Eckert number, and Reynolds number, while they gave opposite behavior for Bejan numbers.

178 citations

••

TL;DR: In this article, the effects of Hall current and radiation on an incompressible viscous and electrically conducting viscous second grade fluid bounded by a loosely packed porous medium were studied, and various parameters on the velocity profiles, the skin friction, temperature field, rate of heat transfer in terms of their amplitude, and phase angles were shown graphically.

Abstract: The effects of radiation and Hall current on an unsteady magnetohydrodynamic free convective flow in a vertical channel filled with a porous medium have been studied. We consider an incompressible viscous and electrically conducting incompressible viscous second grade fluid bounded by a loosely packed porous medium. The fluid is driven by an oscillating pressure gradient parallel to the channel plates, and the entire flow field is subjected to a uniform inclined magnetic field of strength Ho inclined at an angle of inclination α with the normal to the boundaries in the transverse xy-plane. The temperature of one of the plates varies periodically, and the temperature difference of the plates is high enough to induce the radiative heat transfer. The effects of various parameters on the velocity profiles, the skin friction, temperature field, rate of heat transfer in terms of their amplitude, and phase angles are shown graphically.

176 citations

••

TL;DR: In this paper, the improvement of nanofluid heat transfer inside a porous cavity by means of a non-equilibrium model in the existence of Lorentz forces has been investigated by employing control volume based finite element method.

Abstract: In the present article, the improvement of nanofluid heat transfer inside a porous cavity by means of a non-equilibrium model in the existence of Lorentz forces has been investigated by employing control volume based finite element method Nanofluid properties are estimated by means of Koo-Kleinstreuer-Li The Darcy-Boussinesq approximation is utilized for the nanofluid flow Roles of the solid-nanofluid interface heat transfer parameter Nhs, Hartmann number Ha, porosity e, and Rayleigh number Ra were presented Outputs demonstrate that the convective flow decreases with the rise of Nhs, but it enhances with the rise of Ra Porosity has opposite relationship with the temperature gradient

165 citations

••

TL;DR: In this article, the wake of a square cylinder is investigated for Reynolds number Re < 107, and the dependence on Re of the recirculation bubble size or vortex formation length, wake width, shear-layer transition, time-mean drag force, and Strouhal number is discussed in detail.

Abstract: The wake of a square cylinder is investigated for Reynolds number Re < 107. Two-dimensional (2D) laminar simulation and three-dimensional (3D) large-eddy simulation are conducted at Re ≤ 1.0 × 103, while experiments of hotwire, particle image velocimetry, and force measurements are carried out at a higher Re range of 1.0 × 103 < Re < 4.5 × 104. Furthermore, data covering a wide Re range, from 100 to 107, in the literature are comprehensively collected for discussion and comparison purposes. The dependence on Re of the recirculation bubble size or vortex formation length, wake width, shear-layer transition, time-mean drag force, and Strouhal number is discussed in detail, revealing five flow regimes, each having distinct variations of the above parameters. With increasing Re, while the streamwise recirculation size enlarges at Re < 50 (steady flow regime), the vortex formation length reduces at 50 < Re < 1.6 × 102 (laminar flow regime), remains unchanged at 1.6 × 102 < Re < 2.2 × 102 (2D-to-3D transition f...

163 citations

••

TL;DR: In this paper, data-driven machine learning algorithms, random forests and artificial neural network (ANN), are used to establish the subgrid-scale (SGS) model for large-eddy simulation, and a new uniform ANN model is proposed to provide closure for all the components of the SGS stress.

Abstract: Data-driven machine learning algorithms, random forests and artificial neural network (ANN), are used to establish the subgrid-scale (SGS) model for large-eddy simulation. A total of 30 flow variables are examined as the potential input features. A priori tests indicate that the ANN algorithm provides a better solution for this regression problem. The relative importance of the input variables is evaluated by the two algorithms. It reveals that the gradient of filtered velocity and the second derivative of filtered velocity account for a vast majority of the importance. Besides, a pattern is found for the dependence of each component of the SGS stress tensor on the input features. Accordingly, a new uniform ANN model is proposed to provide closure for all the components of the SGS stress, and a correlation coefficient over 0.7 is reached. The proposed new model is tested by large-eddy simulation of isotropic turbulence. By examining the energy budget and the dissipative properties, the ANN model shows good agreement with direct numerical simulation and it provides better predictions than the Smagorinsky model and the dynamic Smagorinsky model. The current research suggests that data-driven algorithms are effective approaches to help us discover knowledge from large amounts of data.

149 citations

••

TL;DR: In this article, the heat generation/absorption and thermo-diffusion on an unsteady free convective MHD flow of radiating and chemically reactive second grade fluid near an infinite vertical plate through a porous medium and taking the Hall current into account have been studied.

Abstract: The heat generation/absorption and thermo-diffusion on an unsteady free convective MHD flow of radiating and chemically reactive second grade fluid near an infinite vertical plate through a porous medium and taking the Hall current into account have been studied. Assume that the bounding plate has a ramped temperature with a ramped surface concentration and isothermal temperature with a ramped surface concentration. The analytical solutions for the governing equations are obtained by making use of the Laplace transforms technique. The velocity, temperature, and concentration profiles are discussed through graphs. We also found that velocity, temperature, and concentration profiles in the case of ramped temperature with ramped surface concentrations are less than those of isothermal temperature with ramped surface concentrations. Also, the expressions of the skin friction, Nusselt number, and Sherwood number are obtained and represented computationally through a tabular form.

141 citations

••

TL;DR: In this paper, the evolution of second-mode instabilities in hypersonic boundary layers and its effects on aerodynamic heating are investigated in a Mach 6 wind tunnel using fast-response pressure sensors, fluorescent temperature-sensitive paint, and particle image velocimetry.

Abstract: The evolution of second-mode instabilities in hypersonic boundary layers and its effects on aerodynamic heating are investigated. Experiments are conducted in a Mach 6 wind tunnel using fast-response pressure sensors, fluorescent temperature-sensitive paint, and particle image velocimetry. Calculations based on parabolic stability equations and direct numerical simulations are also performed. It is found that second-mode waves, accompanied by high-frequency alternating fluid compression and expansion, produce intense aerodynamic heating in a small region that rapidly heats the fluid passing through it. As the second-mode waves decay downstream, the dilatation-induced aerodynamic heating decreases while its shear-induced counterpart keeps growing. The latter brings about a second growth of the surface temperature when transition is completed.

100 citations

••

TL;DR: In this paper, the development of the fluid flow and resultant heat transfer caused by a rotating disk moving vertically upward or downward during an unsteady flow motion is studied, and it is observed that the upward and downward motion of the disk exerts an effect similar to that of the injection/suction through the wall, albeit with observable differences.

Abstract: The object of this study is the development of the fluid flow and resultant heat transfer caused by a rotating disk moving vertically upward or downward during an unsteady flow motion. The problem is formulated such that the similarity equations governing the physical phenomenon eventually reduced to those reported in the traditional viscous pumping study of von Karman for a vertically motionless but still rotating disk. The non-rotating disk with the upward or downward motion leads to the formation of a two-dimensional flow over the disk. Otherwise, the rotation and vertical action of the disk sets up a three-dimensional flow over the surface. It is observed that the upward and downward motion of the disk exerts an effect similar to that of the injection/suction through the wall, albeit with observable differences. Moreover, the viscous pumping is found to be a jet-like radial velocity as the disk moves upward fast. Although the downward movement of the disk suppresses the velocity field, a growth in the boundary layer thickness is anticipated, contrary to the traditional wall suction. The temperature field is shown to be highly dependent on the form of the wall temperature, which is maintained at a time-varying function. Moreover, the impact of the vertical wall movement is observed to be overwhelmed by high disk rotations.

••

TL;DR: In this paper, the authors demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects.

Abstract: In this article, we demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. We demonstrate that an effective eddy-viscosity is predicted by our purely data-driven large eddy simulation framework without explicit utilization of phenomenological arguments. In addition, our data-driven framework precludes the knowledge of true sub-grid stress information during the training phase due to its focus on estimating an effective filter and its inverse so that grid-resolved variables may be related to direct numerical simulation data statistically. The proposed predictive framework is also combined with a statistical truncation mechanism for ensuring numerical realizability in an explicit formulation. Through this, we seek to unite structural and functional modeling strategies for modeling non-linear partial differential equations using reduced degrees of freedom. Both a priori and a posteriori results are shown for a two-dimensional decaying turbulence case in addition to a detailed description of validation and testing. A hyperparameter sensitivity study also shows that the proposed dual network framework simplifies learning complexity and is viable with exceedingly simple network architectures. Our findings indicate that the proposed framework approximates a robust and stable sub-grid closure which compares favorably to the Smagorinsky and Leith hypotheses for capturing the theoretical k−3 scaling in Kraichnan turbulence.

••

TL;DR: In this paper, the effect of different parameters such as Reynolds number (50 ≤ Re ≤ 150), vertical passage ratio (2.0 ≤ M ≤ 4.0), and nanoparticle solid volume fractions (Φ = 0, 0.01, isotherms, and local Nusselt number) on the laminar forced convection heat transfer of nanofluid through a bent channel was numerically investigated.

Abstract: In this paper, the laminar forced convection heat transfer of nanofluid through a bent channel was numerically investigated. The lattice Boltzmann method was used for solving the governing equations in the domain. The effect of different parameters such as Reynolds number (50 ≤ Re ≤ 150), vertical passage ratio (2.0 ≤ M ≤ 4.0), and nanoparticle solid volume fractions (Φ = 0, 0.01, 0.03, 0.05) are analyzed in terms of streamlines, isotherms, and local Nusselt numbers. It was concluded from this study that the local and average Nusselt number increased with increasing nanoparticle volume fraction regardless of Re and M. Moreover, the effect of the nanofluid concentration on the increment of heat transfer was more remarkable at higher values of the Reynolds number. Simulations show that by increasing the Reynolds number or decreasing the vertical passage ratio, the local and average Nusselt number increases.

••

TL;DR: In this paper, a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g(S) is proposed, based on a reformulation of the equation in Cartesian coordinates of the embedding R3.

Abstract: We consider a numerical approach for the incompressible surface Navier-Stokes equation on surfaces with arbitrary genus g(S). The approach is based on a reformulation of the equation in Cartesian coordinates of the embedding R3, penalization of the normal component, a Chorin projection method, and discretization in space by surface finite elements for each component. The approach thus requires only standard ingredients which most finite element implementations can offer. We compare computational results with discrete exterior calculus simulations on a torus and demonstrate the interplay of the flow field with the topology by showing realizations of the Poincare-Hopf theorem on n-tori.

••

TL;DR: In this article, the authors investigate the unsteady hydromagnetic boundary layer flow of a thermally radiating nanofluid past a non-linear stretching sheet embedded in a porous medium in the presence of an externally applied magnetic field along with Navier's velocity slip.

Abstract: The intention behind carrying out this research work is to investigate the unsteady hydromagnetic boundary layer flow of a thermally radiating nanofluid past a non-linear stretching sheet embedded in a porous medium in the presence of an externally applied magnetic field along with Navier’s velocity slip. The governing partial differential equations, defining the flow regime, are transformed into a system of ordinary differential equations by employing suitable similarity transformation. Optimal Homotopy Analysis Method has been incorporated in order to solve the converted non-linear coupled equations. The impact of several regulatory flow parameters on the temperature, velocity, and nanoparticle concentration are explained via graphs, while the variation of some useful engineering quantities such as the Nusselt number, skin friction co-efficient, and Sherwood number are interpreted through tabular values. An analysis regarding entropy generation of the system is also presented. Furthermore, on the numeric data of the skin friction coefficient and Nusselt number, a linear and quadratic multiple linear regression analysis has also been performed. The findings of the present analysis reveal that the velocity slip, unsteadiness and the nonlinearity of the stretching velocity lead to a fall in the velocity profile of the nanofluid.

••

TL;DR: This work presents a study of RBC partitioning based on, for the first time, a direct numerical simulation (DNS) of a flowing cell suspension through modeled vascular networks that are comprised of multiple bifurcations and have topological similarity to microvasculature in vivo.

Abstract: Partitioning of red blood cells (RBCs) at vascular bifurcations has been studied over many decades using in vivo, in vitro, and theoretical models. These studies have shown that RBCs usually do not distribute to the daughter vessels with the same proportion as the blood flow. Such disproportionality occurs, whereby the cell distribution fractions are either higher or lower than the flow fractions and have been referred to as classical partitioning and reverse partitioning, respectively. The current work presents a study of RBC partitioning based on, for the first time, a direct numerical simulation (DNS) of a flowing cell suspension through modeled vascular networks that are comprised of multiple bifurcations and have topological similarity to microvasculature in vivo. The flow of deformable RBCs at physiological hematocrits is considered through the networks, and the 3D dynamics of each individual cell are accurately resolved. The focus is on the detailed analysis of the partitioning, based on the DNS data, as it develops naturally in successive bifurcations, and the underlying mechanisms. We find that while the time-averaged partitioning at a bifurcation manifests in one of two ways, namely, the classical or reverse partitioning, the time-dependent behavior can cycle between these two types. We identify and analyze four different cellular-scale mechanisms underlying the time-dependent partitioning. These mechanisms arise, in general, either due to an asymmetry in the RBC distribution in the feeding vessels caused by the events at an upstream bifurcation or due to a temporary increase in cell concentration near capillary bifurcations. Using the DNS results, we show that a positive skewness in the hematocrit profile in the feeding vessel is associated with the classical partitioning, while a negative skewness is associated with the reverse one. We then present a detailed analysis of the two components of disproportionate partitioning as identified in prior studies, namely, plasma skimming and cell screening. The plasma skimming component is shown to under-predict the disproportionality, leaving the cell screening component to make up for the difference. The crossing of the separation surface by the cells is observed to be a dominant mechanism underlying the cell screening, which is shown to mitigate extreme heterogeneity in RBC distribution across the networks.

••

TL;DR: Proper orthogonal decomposition (POD) is utilized to analyze the wake-dynamics of a low-mass ratio circular cylinder undergoing vortex-induced vibrations in the initial and upper branches (U* = U∞/fND = 4.07, 5.32).

Abstract: Proper orthogonal decomposition (POD) is utilized to analyze the wake-dynamics of a low-mass ratio circular cylinder undergoing vortex-induced vibrations in the initial and upper branches (U* = U∞/fND = 4.07, 5.32). POD allows for characterizing dynamics at frequencies which differ from the cylinder oscillation that cannot be captured with conventional phase-averaging. POD modes contributing to the dominant coherent motions are described in detail. Fourier analysis techniques are used to identify relationships between the POD modes describing non-periodic dynamics linked to the slow-varying base flow and result in a modulation in the strength of vortex shedding. Heuristic models based on mean-field theory are proposed for the POD temporal coefficients. The modelled wake dynamics are found to account for a significant contribution to the Reynolds stresses. In the initial branch, it is found that 6 POD modes are required to capture the salient aspects of the flow, while in the upper branch, 7 modes are required.

••

TL;DR: This study proves that Rortex is invariant under the Galilean transformation and several examples are provided to confirm the conclusion.

Abstract: A new vector named Rortex [C. Liu et al., “Rortex—A new vortex vector definition and vorticity tensor and vector decompositions,” Phys. Fluids 30, 035103 (2018)] was proposed to represent the local fluid rotation in our previous work. However, the Galilean invariance of Rortex is yet to be elaborated. In the present study, we prove that Rortex is invariant under the Galilean transformation and several examples are provided to confirm the conclusion.

••

TL;DR: In this paper, a 3D unified lattice Boltzmann method (LBM) was used to simulate 3D electroconvection in a dielectric liquid lying between two parallel plates.

Abstract: Charge injection induced electroconvection in a dielectric liquid lying between two parallel plates is numerically simulated in three dimensions (3D) using a unified lattice Boltzmann method (LBM). Cellular flow patterns and their subcritical bifurcation phenomena of 3D electroconvection are numerically investigated for the first time. A unit conversion is also derived to connect the LBM system to the real physical system. The 3D LBM codes are validated by three carefully chosen cases and all results are found to be highly consistent with the analytical solutions or other numerical studies. For strong injection, the steady state roll, polygon, and square flow patterns are observed under different initial disturbances. Numerical results show that the hexagonal cell with the central region being empty of charge and centrally downward flow is preferred in symmetric systems under random initial disturbance. For weak injection, the numerical results show that the flow directly passes from the motionless state ...

••

TL;DR: In this article, the complex interaction between a suspended particle and an attached bubble, which is associated with cavitation in silt-laden flow, was investigated with high-speed photography, in which bubbles are generated by underwater electric discharge means.

Abstract: This study aims to elucidate the complex interaction between a suspended particle and an attached bubble, which is associated with cavitation in silt-laden flow. Systematic experiments are performed with high-speed photography, in which bubbles are generated by underwater electric discharge means. The bubble-particle interactions are found to be strongly dependent on two dimensionless parameters, i.e., the particle-bubble size ratio λL and the particle-liquid density ratio λρ. When λρ equals 2.61, the bubble split phenomenon is universally observed and the particle shooting effect (the particle acceleration during bubble expansion and after bubble-particle detachment) becomes more obvious as λL decreases. If λL < ∼0.34, the particle velocity keeps positive (away from the bubble), otherwise the particle velocity drops below zero (toward the bubble) during the bubble collapse phase. As λρ increases, the particle achieves a lower velocity but a higher impulse, and the bubble necking phenomenon is more pronounced. Our boundary integral simulations reproduce the experiments extremely well, including the particle dynamics, the bubble wrapping the particle, the bubble necking and detachment, and the mushroom-shaped bubble. After the bubble-particle detachment, the liquid around the detachment location is drawn inward and collides on the axis of symmetry, leading to the formation of a localized high pressure region between the bubble and the particle, which accelerates the particle for the second time even in the bubble collapse phase.

••

TL;DR: In this article, high-speed schlieren imaging and high-resonance frequency pressure measurements were used to capture the flow features during the shock train movement, and the analysis was extended to complex situations with incident shocks.

Abstract: The oscillation characteristics of the shock train in an isolator have been investigated in a direct-connect wind tunnel at Mach 2.7. High-speed schlieren imaging and high-resonance frequency pressure measurements were used to capture the flow features during the shock train movement. The oscillation features without the effects of incident shocks were analyzed first. As the shock train moved upstream, the low-frequency part of the oscillation was found to develop. The analysis was then extended to complex situations with incident shocks. It was revealed that the shock wave-boundary layer interactions considerably influence the shock train behavior. The interactions were classified into three patterns: (I) single interaction, (II) multi-interactions on the same side, and (III) multi-interactions on different sides. Experimental results indicated that the oscillation could be affected in temporal scale by pattern II and enhanced in spatial scale by pattern III. The data also showed that the pressure rise induced upstream propagates to the exit, causing phase offsets in the wall pressure histories and making the pressure distributions diverge from their stable state. This phenomenon suggested a possible physical mechanism for the oscillation during shock train movement, which was verified by additional tests with large backpressure rising rate. It was found that there exists a critical frequency which is related to the pressure ramping rate during the oscillation. If the dominant frequency of the backpressure varies beyond this critical frequency, the pressure distribution could be forced into a steady state before the oscillation was induced. Otherwise the oscillation could not be suppressed.

••

TL;DR: In this article, the authors proposed an improved reduced-order model based on dynamic mode decomposition (ROM) to model the flow dynamics of the attractor from a transient solution, which is tested in the solution of a NACA0012 airfoil buffeting in a transonic flow.

Abstract: This study proposes an improvement in the performance of reduced-order models (ROMs) based on dynamic mode decomposition to model the flow dynamics of the attractor from a transient solution. By combining higher order dynamic mode decomposition (HODMD) with an efficient mode selection criterion, the HODMD with criterion (HODMDc) ROM is able to identify dominant flow patterns with high accuracy. This helps us to develop a more parsimonious ROM structure, allowing better predictions of the attractor dynamics. The method is tested in the solution of a NACA0012 airfoil buffeting in a transonic flow, and its good performance in both the reconstruction of the original solution and the prediction of the permanent dynamics is shown. In addition, the robustness of the method has been successfully tested using different types of parameters, indicating that the proposed ROM approach is a tool promising for using in both numerical simulations and experimental data.

••

TL;DR: In this article, a mathematical model to study the electroosmotic flow of a viscoelastic fluid in a parallel plate microchannel with a high zeta potential, taking hydrodynamic slippage at the walls into account in the underlying analysis is presented.

Abstract: We present a mathematical model to study the electroosmotic flow of a viscoelastic fluid in a parallel plate microchannel with a high zeta potential, taking hydrodynamic slippage at the walls into account in the underlying analysis. We use the simplified Phan-Thien–Tanner (s-PTT) constitutive relationships to describe the rheological behavior of the viscoelastic fluid, while Navier’s slip law is employed to model the interfacial hydrodynamic slip. Here, we derive analytical solutions for the potential distribution, flow velocity, and volumetric flow rate based on the complete Poisson–Boltzmann equation (without considering the frequently used Debye–Huckel linear approximation). For the underlying electrokinetic transport, this investigation primarily reveals the influence of fluid rheology, wall zeta potential as modulated by the interfacial electrochemistry and interfacial slip on the velocity distribution, volumetric flow rate, and fluid stress, as well as the apparent viscosity. We show that combined with the viscoelasticity of the fluid, a higher wall zeta potential and slip coefficient lead to a phenomenal enhancement in the volumetric flow rate. We believe that this analysis, besides providing a deep theoretical insight to interpret the transport process, will also serve as a fundamental design tool for microfluidic devices/systems under electrokinetic influence.

••

TL;DR: In this paper, the authors investigated an airfoil flow involving a turbulent transition and separations near the stall condition at a high Reynolds number Rec = 2.1 × 106 and provided the wall-resolved large-eddy simulation (LES) database for near-wall models in LES.

Abstract: This paper investigates an airfoil flow involving a turbulent transition and separations near the stall condition at a high Reynolds number Rec = 2.1 × 106 (based on the freestream velocity and the airfoil chord) and provides the wall-resolved large-eddy simulation (LES) database for near-wall models in LES. The present results are compared with the existing experimental and computational data. The wall-resolved LES with the finest mesh (Δξ+,Δη+,Δζ+: chordwise, wall normal, spanwise ≲25, 0.8, 13) and the widest spanwise extent (approximately 5% of the chord length) resolves the key phenomena of the flow (i.e., laminar separation, transition to turbulence, turbulent reattachment, turbulent boundary layer development, and turbulent separation) and well predicts turbulence statistics. The present LES also clarifies unsteady flow features associated with shear-layer instability: the high frequency unsteadiness of St ≃ 130 (based on the freestream velocity and the airfoil chord) at the laminar separation bubble near the leading edge and low frequency unsteadiness of St ≃ 2 at the turbulent separation near the trailing edge. The characteristic frequencies can be scaled to 0.035 and 0.033 by the local momentum thickness and the shear layer velocity which are similar to the natural frequency of the laminar and turbulent shear layer, respectively. With regard to the near-wall modeling in LES, the obtained database indicates that the pressure-gradient term in the mean streamwise-momentum equation is not negligible at the laminar and turbulent separated regions. This fact suggests that the widely used equilibrium wall model is not sufficient, and the inclusion of the pressure-gradient term is necessary for wall modeling in LES of such an airfoil flow. Additionally, influences of computational mesh resolution and spanwise extent on the computational results in wall-resolved LES are investigated.

••

TL;DR: In this paper, the authors developed a model to study the natural convection of a nanofluid between a square enclosure and a circular, an elliptical, or a rectangular cylinder.

Abstract: We develop a model to study the natural convection of a nanofluid between a square enclosure and a circular, an elliptical, or a rectangular cylinder. Using super elliptic functions, the dimensionless governing equations of two-dimensional rectangular coordinates have been transformed into a system of equations valid for the above geometry. The resulting equations are then solved utilizing finite difference technique. We illustrate the flow and heat transfer characteristics of nanofluids with streamlines and isotherms as well as the Nusselt number at the inner and outer cylinders. It is found that the intensity of streamlines becomes stronger with the increase in the volume fraction of nanoparticles and the Rayleigh number. The Nusselt number at the inner and outer cylinders is almost linearly increased for higher values of the volume fraction of nanoparticles while an exponentially increasing tendency is observed with the increase in the Rayleigh number. The distinct findings are that the intensity of the streamlines increases with rectangular, circular, and elliptical inner shapes. Moreover, the Nusselt number at the inner and outer cylinders diminishes with circular, elliptical, and rectangular inner shapes. The acquired knowledge from the results could be used to augment or control the heat transfer of nanofluids and for the advancement of existing technology. Moreover, the present concept of introducing super elliptic functions might be useful to formulate a model for more complex geometry.

••

TL;DR: In this article, an explicit wall model based on a power-law velocity profile is proposed for the simulation of the incompressible flow around airfoils at high Reynolds numbers.

Abstract: In this paper, an explicit wall model based on a power-law velocity profile is proposed for the simulation of the incompressible flow around airfoils at high Reynolds numbers. This wall model is particularly suited for the wall treatment involved in Cartesian grids. Moreover, it does not require an iterative procedure for the friction velocity determination. The validation of this power-law wall model is assessed for Reynolds-averaged Navier-Stokes simulations of the flow around a two-dimensional airfoil using the lattice Boltzmann approach along with the Spalart-Allmaras turbulence model. Good results are obtained for the prediction of the aerodynamic coefficients and the pressure profiles at two Reynolds numbers and several angles of attack. The explicit power-law is thus well suited for a simplified near-wall treatment at high Reynolds numbers using Cartesian grids.

••

TL;DR: In this paper, an unsteady two-dimensional magneto-hydrodynamic (MHD) boundary layer flow of an incompressible electrically conducting fluid over a slippery stretching sheet surrounded in a porous medium is reported.

Abstract: This article reports an unsteady two-dimensional Magneto-hydrodynamic (MHD) boundary layer flow of an incompressible electrically conducting fluid over a slippery stretching sheet surrounded in a porous medium. The Roseland boundary layer approximation with the radiative heat flux is employed within the current analysis. The influence of the velocity slip, thermal radiation, heat source, and buoyancy force is also considered within the current analysis, which makes significant effects on the flow field passages. The unsteady system of non-dimensional partial differential equations (PDEs) with corresponding boundary conditions are solved by implementing the explicit finite difference scheme. In the presence of pertinent parameters such as viscous dissipation, heat source or sink, Prandtl number, Grashof number, thermal radiation, magnetic field, and Darcy number, the accurate movement of the electrically conducting fluid over a slippery sheet is shown graphically in the form of velocity, temperature, skin friction coefficient, and Nusselt number. Unlike the other studies, wherein the system of PDEs is commonly transformed into a system of ordinary differential equations via the similarity transformations, the current study provides an efficient numerical procedure to solve a given system of PDEs without using the similarity transformations which exemplify the precise movement of an electrically conducting fluid over a slippery surface. It has been anticipated that the current boundary layer analysis would provide a platform for solving the system of the nonlinear PDEs of the other unsolved boundary layer models that are associated with the two-dimensional unsteady MHD flow over a slippery stretching surface embedded in a porous medium.

••

TL;DR: In this article, a well-defined texture with streamwise grooves at the walls in which the gas is expected to be entrapped is considered, and a substantial drag reduction is observed which strongly depends on the grooves' dimension and on the solid fraction, i.e., the ratio between the solid wall surface and the total surface of the pipe.

Abstract: The drag reduction induced by superhydrophobic surfaces is investigated in a turbulent pipe flow. Wetted superhydrophobic surfaces are shown to trap gas bubbles in their asperities. This stops the liquid from coming in direct contact with the wall in that location, allowing the flow to slip over the air bubbles. We consider a well-defined texture with streamwise grooves at the walls in which the gas is expected to be entrapped. This configuration is modeled with alternating no-slip and shear-free boundary conditions at the wall. With respect to the classical turbulent pipe flow, a substantial drag reduction is observed which strongly depends on the grooves’ dimension and on the solid fraction, i.e., the ratio between the solid wall surface and the total surface of the pipe’s circumference. The drag reduction is due to the mean slip velocity at the wall which increases the flow rate at a fixed pressure drop. The enforced boundary conditions also produce peculiar turbulent structures which on the contrary d...

••

TL;DR: In this article, an axisymmetric shock-dominated hypersonic laminar separated flow over a double cone is studied for the first time using a combination of time accurate Direct Simulation Monte Carlo (DSMC) calculations, linear global instability analysis, and momentum potential theory (MPT).

Abstract: Unsteadiness of axisymmetric shock-dominated hypersonic laminar separated flow over a double cone is studied for the first time using a combination of time accurate Direct Simulation Monte Carlo (DSMC) calculations, linear global instability analysis, and momentum potential theory (MPT). Close to steady state linear analysis reveals the spatial structure of the underlying temporally stable global modes. At all Reynolds numbers examined, the amplitude functions demonstrate the strong coupling between the separated flow region at the cone junction with the entire shock system, including pressure and temperature waves generated behind the shock and spatially amplified Kelvin-Helmholtz waves. In addition, as the Reynolds number is increased, temporally damped harmonic shock oscillations and multiple-reflected λ-shock patterns emerge in the eigenfunctions. Application of the MPT (valid for both linear and nonlinear signals) to the highest Reynolds number DSMC results shows that large acoustic and thermal potential variations exist in the vicinity of the separation shock, the λ-shock patterns, and the shear layers. It is further shown that the motion of the bow shock system is highly affected by non-uniformities in the acoustic field. At the highest Reynolds number considered here, the unsteadiness is characterized by Strouhal numbers in the shear layer and bow-shock regions and is found to be in qualitative agreement with earlier experimental and numerical work.Unsteadiness of axisymmetric shock-dominated hypersonic laminar separated flow over a double cone is studied for the first time using a combination of time accurate Direct Simulation Monte Carlo (DSMC) calculations, linear global instability analysis, and momentum potential theory (MPT). Close to steady state linear analysis reveals the spatial structure of the underlying temporally stable global modes. At all Reynolds numbers examined, the amplitude functions demonstrate the strong coupling between the separated flow region at the cone junction with the entire shock system, including pressure and temperature waves generated behind the shock and spatially amplified Kelvin-Helmholtz waves. In addition, as the Reynolds number is increased, temporally damped harmonic shock oscillations and multiple-reflected λ-shock patterns emerge in the eigenfunctions. Application of the MPT (valid for both linear and nonlinear signals) to the highest Reynolds number DSMC results shows that large acoustic and thermal poten...

••

TL;DR: In this article, the interaction of a zero pressure gradient turbulent boundary layer flow with a rough permeable surface has been investigated experimentally using a long flat plate equipped with several surface pressure transducers and pressure taps.

Abstract: The interaction of a zero pressure gradient turbulent boundary layer flow with a rough permeable surface has been investigated experimentally. The flow interaction characteristics have been examined using a long flat plate equipped with several surface pressure transducers and pressure taps. Three types of porous materials with different porosities and permeability constants were used in these investigations. To reveal the behavior of turbulent flows over porous surfaces, measurements were performed for the boundary layer growth, energy content of the turbulent structure within the boundary layer, and surface pressure fluctuations, before, over, and after the porous test-section. The interaction of the flow with the porous substrate was found to significantly alter the energy cascade within the boundary layer. Results have also shown that the boundary layer interaction with the rough porous surfaces leads to an increase in the pressure fluctuations exerted on the wall, particularly at low frequencies. The near-field investigations have shown that the penetration of the boundary layer flow into the porous medium can generate an internal hydrodynamic field within the porous medium. This, in turn, reduces the frequency-energy content of the large boundary layer coherent structures and their spanwise correlation length. This study paves the way for further investigation into the interaction of the porous media with different flow fields and development of tailored porous treatments for improving the aerodynamic and aeroacoustic performance of different aero- and hydro-components.