Incompressible Research Articles

Modeling the Unsteady Wake of an Impulsively Started Circular Cylinder Using Refined Potential Flow Theory

Abstract Cylindrical structures find usage in many engineering applications including tethered oil drums and engine canisters slung beneath helicopters in flight. The motion of air around such circular cylindrical structures and the helicopter presents interesting phenomena including flow separation, wakes and turbulence. The physics of these are enshrined in the continuity equation and the Navier-Stokes equations. Therefore, their studies are not only important in mathematics and physics, but they are also required for efficient helicopter operations. In practice, reduced-order models of these operations that take in aerodynamics models of the tethered loads are utilized for stability analysis, flight certification and pilot training because of the prohibitive cost of experimentation and computational analyses of these configurations. However, there is a dearth of realistic analytical models of finite cylinder flows because of the Navier-Stokes problem. Classical potential flow theory provides an avenue to develop such models, but the extant gaps in its predictions significantly preclude its usage for engineering applications. Attempting to bridge these gaps, this article introduces refined potential flow theory in which the governing equations and boundary conditions are satisfied. Viscous effects, fluctuations of the mean flow and three-dimensional effects are also incorporated. For characterization, refined potential flow theory is employed on an incompressible flow over an impulsively started circular cylinder for Reynolds numbers and non-dimensional times in the range 30 < Re < 10^4 and 0.2 ≤ T≤ 77, 047 respectively. There is an excellent prediction of 0.209 for the Strouhal number at Re = 3, 900. At this transitional Reynolds number, the harmonics of the Strouhal frequency are also captured, and the characteristic irregular fluctuations at sub-Strouhal frequencies are discernible in the velocity spectra. As the flow becomes more turbulent, these become more pronounced at Re = 9, 500 when the predicted Strouhal number is within 10% of experimental result. In the fully developed stage, spectra analyses of the wake velocity components at some downstream locations also display Kolmogorov’s Five-Thirds law of homogeneous isotropic turbulence. The present model can thus aid the development of reduced-order models of helicopter operations that feature tethered cylindrical loads.

Theoretical investigation of the convective heat transfer mechanism along a cantilever shape

The present study aims to investigate the steady state mixed convection flow for a viscous incompressible fluid along a cantilever shape. The study has analyzed the impact of mixed convection boundary layer flow behavior and heat transfer characteristic of the cantilever shape. The leading equations for the said problem are the Navier-Stokes and energy equations. These leading equations are converted into ordinary differential equations using the stream function formulation, and the numerical solution is obtained using the shooting technique with BVP4C and built in MATLAB program. The impact of dimensionless parameters such as n, Pr, and λ on the velocity and temperature profile within the boundary layer of the cantilever cylinder is presented graphically. The results for velocity slope and temperature gradient under the effects of various emerging parameters are presented in tables. The study has concluded that mixed convection parameter has a significant impact on the velocity and temperature distribution, as well as on the velocity slope and temperature gradient rates along a cantilever shape geometry. The outcomes of the current study can be utilized for the design and optimization of various engineering devices involving cantilever shapes. Further, research regarding the impact of other parameters on the cantilever shape including heat transfer characteristics can be conducted using the approach presented in this study. The novelty of the current work can be claimed by saying that for reduced gravity, other forces involved in the flow model induced the fluid motion and temperature gradient.

Small-scale turbulent characteristics in transcritical wall-bounded flows

Considerable efforts have been devoted to the understanding of the small-scale characteristics in turbulent flows. While the universality of small-scale quantities has been established for incompressible flows, their extension to high-pressure transcritical flows remains an open area of research. To address this question, we investigate the real-fluid thermodynamic effects on small-scale velocity statistics of high-pressure transcritical wall-bounded turbulence. We show that in the locally isotropic region for transcritical flows, low-order moments of small-scale statistics collapse for all cases and Kolmogorov's (1941) theory holds. However, real-fluid thermodynamic effects introduce deviations in the tails of the probability density function for the velocity derivative and, consequently, high-order moments of velocity gradients and dissipation rate in transcritical flows cannot collapse in the locally isotropic region. Analysis of the intermittency shows that the low-order structure functions in transcritical flows follow extended self-similarity, while the dependence of the intermittency factor on real-fluid effects is observed for high-order structure functions. The real-fluid effects on intermittency are explained by turbulent structures related to rare events. Additionally, the dissipation rate moments for transcritical flows follow a universal scaling with Reynolds number, and the scaling exponents are different from those of incompressible flows. These results extend the small-scale universality in incompressible flows (Schumacher et al., Proc. Natl Acad. Sci. USA, vol. 111, 2014, pp. 10961–10965) to realistic flows with significant changes in thermodynamic properties, and provide a physical underpinning of the scaling laws of small-scale statistics at transcritical conditions.

Evidence of Kelvin-Helmholtz and tearing mode instabilities at the magnetopause during space weather events

Introduction: Kelvin-Helmholtz (KH) and tearing mode (TM) instabilities are one of the most important mechanisms of solar wind energy, momentum and plasma transport within the magnetosphere.Methods: To investigate the conditions under which KHTM instabilities occur in the Earth environment it is fundamental to combine simultaneous multipoint in situ measurements and MHD simulations. We analyzed data from the THEMIS and Cluster spacecraft considering two Space Weather (SWE) events starting with an M2.0 flare event (hereafter Case-1) that occurred on 21 June 2015 and the most-intensive flare (X9.3) of solar cycle 24 that occurred on 6 September 2017 (hereafter Case-2).Results: Our analysis utilized a 2D MHD model for incompressible and viscous flow. The results from Case-1 indicate the presence of KH and TM instabilities, suggesting existence of observed low-amplitude oscillations at the nose of the magnetopause. However, the MHD simulations for Case-2 did not show any evidence of KH vortices, but did reveal the presence of “magnetic island” structures during a low-shear condition. The reconnection rate derived from the observations is compared with the computed one in the presence of developed instabilities inside the Earth’s magnetopause.

Aeroacoustic simulation of human phonation based on the flow-induced vocal fold vibrations including their contact

This paper deals with the numerical simulation of the flow induced sound as generated in the human phonation process including vocal folds (VF) contact. The hybrid approach is used allowing to separate the acoustic and the biomechanical description of the considered problem. The two-dimensional fluid–structure interaction (FSI) problem is modelled by a simplified linear elastic model coupled to the incompressible Navier–Stokes equations in the arbitrary Lagrangian–Eulerian form and special attention is paid to the treatment of the contact problem in the FSI context. Following approach of [Sváček and Horáček, 2021] the incompressible flow model is modified by an addition of fictitious porosity term and the penalization inlet boundary condition is used. Further, the Lighthill acoustic analogy is applied for calculation of sound sources and their propagation through a vocal tract model. All partial differential equations, describing the elastic body vibration, the fluid flow and the acoustics, are approximated by finite element method. Numerical results of one-sided vocal fold paralysis are presented.

Asymptotic analysis of the nonsteady micropolar fluid flow through a system of thin pipes

In this paper, we analyze the time‐dependent flow of an incompressible micropolar fluid in a multiple‐pipe system. Motivated by the applications, we assume that the pipes have circular cross‐section and that the ratio between pipes' thickness and its length is small, denoted by the parameter . Far from the junction, the fluid exhibits different behavior depending on the magnitude of the viscosity coefficients with respect to the small parameter . Focusing on the critical case described by the strong coupling between velocity and microrotation, the complete asymptotic expansion of the solution (up to an arbitrary order) is built. To improve the accuracy of the asymptotic approximation, we introduce the boundary layer correctors near the pipes' ends and take into account the interior layer correction in the vicinity of the junction as well. The convergence is also proved via error estimates, providing the rigorous justification of the proposed effective model.

MICROPOLAR FLUID FLOWS RELATIVE TO A SWARM OF SPHERICAL POROUS SHELLS

This article investigates the creeping axisymmetric flow of an incompressible micropolar fluid past a swarm of porous shells. Employing the Darcy and a transition Brinkman porous layer, the study presents an analytical model that captures the flow behavior by integrating continuity conditions for velocity, normal and tangential stresses, and microrotations at fluid-porous interface regions.Distinct unit cell techniques, including those proposed by Happel, Kuwabara, Kvashnin, and Mehta and Morse, are analyzed to observe the effects of hydraulic resistivity, porous layer thickness, and porosity on the dimensionless drag for a bounded micropolar fluid system. The results, graphically represented in a series of plots, reveal a complex interplay between these parameters, significantly impacting drag forces and providing insight into the hydrodynamics of a swarm of porous particles, akin to that encountered in oral drug delivery systems.The study identifies a general inverse relationship between hydraulic resistivity and drag and highlights the nuanced effects of porous layer thickness and porosity on fluid resistance, with stark contrasts observed among different unit cell models. These findings underscore the importance of the chosen unit cell technique in predicting and optimizing the flow behavior in micropolar fluid systems.

Prandtl-eyring couple stressed flow within a porous region counting homogeneous and heterogeneous reactions across a stretched porous sheet

The movement of a non-Newtonian incompressible Prandtl-Eyring fluid layer over a stretching/shrinking permeable plate is shown in the current work. The flow is stressed by an additional couple stress, altered by a uniform normal magnetic field, and saturated in a permeable material. Heat transmission is demonstrated using a temperature-dependent heat source, an exponential space-dependent heat source, Joule heating, and viscous dissipations. Momentum, energy, and chemical type concentration equations, coupled with appropriate boundary conditions, support the mathematical structure. The novel aspect of the current work comes from considering species mass transfer using heterogeneous and homogeneous biochemical reactions along with the effects of thermal diffusion in the aforementioned flow. The reaction processes are isothermal with identical coefficients of chemical species. The leading nonlinear partial differential equations are transformed into ordinary differential equations utilizing appropriate similarity transformations. The homotopy perturbation method examines these equations. As a result, the primary objective distributions' analytical solutions are derived, and a graphical representation of them is produced to show the effects of the pertinent physical elements. The heterogeneity reaction serves as a dual role parameter in this diffusion, while the homogeneity reaction has been discovered to be a decreasing factor for particle diffusion. The ability of suction or injection via a permeable surface is observed to reduce the velocity and heat transmission, meanwhile, increasing chemical species condensation.

Embedded large eddy simulation of boundary layer transition behind a micro-ramp

Boundary layer transition induced by surface roughness elements plays an important role in aerodynamic and aero-thermodynamic design of subsonic/supersonic/hypersonic vehicles. However, the effect of three-dimensional isolated roughness element in the process of promoting/suppressing boundary layer transition is far from being fully understood, particularly in the incompressible laminar flow. In the present study, the laminar-to-turbulent transition induced by a three-dimensional isolated micro-ramp element immersed in an incompressible laminar boundary layer is investigated numerically. The embedded large eddy simulation (ELES) combining the intermittency transition model and the wall-modeled large eddy simulation (WMLES) S − Ω model is employed for the first time. Numerical results on the time-averaged/instantaneous flow field and the statistical flow fluctuations are analysed and validated thoroughly by the existing experimental measurements. It is found that the interaction of the secondary and the tertiary streamwise vortices causes a high level of wall shear and an inflectional velocity distribution in the near-wall region. An additional eddy system that develops nonlinearly from the unstable inflectional flow may trigger the boundary layer transition. The present study validates that the ELES combined with the WMLES S − Ω model is an efficient simulation tool for industrial wall-bounded flows allowing effective compromise between flexibility, cost, and accuracy.

Performance Comparison of CFD Microbenchmarks on Diverse HPC Architectures

OpenFOAM is a CFD software widely used in both industry and academia. The exaFOAM project aims at enhancing the HPC scalability of OpenFOAM, while identifying its current bottlenecks and proposing ways to overcome them. For the assessment of the software components and the code profiling during the code development, lightweight but significant benchmarks should be used. The answer was to develop microbenchmarks, with a small memory footprint and short runtime. The name microbenchmark does not mean that they have been prepared to be the smallest possible test cases, as they have been developed to fit in a compute node, which usually has dozens of compute cores. The microbenchmarks cover a broad band of applications: incompressible and compressible flow, combustion, viscoelastic flow and adjoint optimization. All benchmarks are part of the OpenFOAM HPC Technical Committee repository and are fully accessible. The performance using HPC systems with Intel and AMD processors (x86_64 architecture) and Arm processors (aarch64 architecture) have been benchmarked. For the workloads in this study, the mean performance with the AMD CPU is 62% higher than with Arm and 42% higher than with Intel. The AMD processor seems particularly suited resulting in an overall shorter time-to-solution.

A boundary element analysis of quasi-potential inviscid incompressible flow in multiply connected airfoil wing

AbstractThe quasi-potential flow in a doubly linked airfoil wing with a sharp trailing edge can be solved using a high-order boundary-element method (BEM). A bicubic Hermite spline interpolation is used to express the unknown, with node derivatives given by finite difference method. The revolutionary traits apply to bleeding-edge settings; specifically, challenges relating to the three-dimensional problem of multiply connected domains are investigated. Numerical validation examples were utilized to assess the implemented BEM approach.

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

A reduction-consistent phase field model for non-isothermal multiphase flows of N immiscible incompressible fluids

In this study, we developed a reduction-consistent phase field model for non-isothermal incompressible N-phase flows. The model is based on the high-order spectral element method. To account for thermocapillary effects, we reformulated the continuum surface force model specifically for N-phase flows. In order to enhance computational efficiency, time-independent coefficient matrices for all variables involved were reconstructed, and an unsymmetrized multifrontal LU factorization was employed to solve the linear algebraic equations, which is derived by discretization. To verify the model effectiveness in calculating surface tension and describing three-phase interfacial dynamics, we conducted several experiments, including the stationary two-droplet example, the three-phase droplet spreading, and the equilibrium morphology of double emulsion droplet. Through these experiments, both the reduction-consistency and robustness of our model were demonstrated. Moreover, we validated the proposed model's applicability to non-isothermal three-phase flows by investigating the thermocapillary migration of single droplet and two droplets of different phases. Notably, we explored the thermocapillary migration of three-phase double droplets, focusing particularly on how the encapsulation process affects overall thermocapillary motion. Our findings indicate that the interaction between the two vortices near the interfaces of the two droplets strongly influences their migration behavior.

A third-order compact finite volume scheme on unstructured grid for fluid flows

The large reconstruction stencil is one of the biggest obstacles in design and implementation of high-order finite volume schemes on unstructured grid. To tackle this problem, a third-order compact reconstruction scheme on unstructured grid is developed on the basis of compact least-squares (CLS) finite volume method. In building the reconstruction polynomial, the general boundary condition is adopted to ensure the unified third-order accuracy in both the internal and boundary cells. The reconstruction polynomial is solved in a semi-implicit sense to ensure high computational efficiency without solving the global linear algebraic equations. The theoretical accuracy order and stability limit are firstly verified by the Fourier analysis. The numerical accuracy and efficiency are then verified and validated with several incompressible and compressible flow cases. This work provides a reference to design and analysis of high-order compact finite volume schemes on unstructured grid with unified accuracy.

On well-posedness of Navier–Stokes variational inequalities

In this paper, well-posedness is carried out on variational inequalities in a general form for the stationary Navier–Stokes equations modeling viscous incompressible fluid flows with a nonsmooth slip boundary condition of friction type. For a special form of the variational inequality commonly studied in existing literature, our proof technique leads to a substantial improvement on the well-posedness condition.

Mixing in Incompressible Flows: Transport, Dissipation, and Their Interplay

Mixing in Incompressible Flows: Transport, Dissipation, and Their Interplay

Folding of a growing hyperelastic sheet in a viscous fluid

Understanding the growth-induced deformation of soft materials in viscous environments is important for a variety of problems in nature and engineering. Here, we focus on the fluid–structure interaction of a hyperelastic sheet growing in an incompressible Newtonian fluid in the Stokes flow regime. We develop a computational framework for simulating this problem, where the isogeometric boundary integral method is used with the Kirchhoff–Love shell formulation and elastic–plastic decomposition of the deformation gradient tensor. We quantify the relative effects of the growth rate, the sheet bending rigidity, and the fluid viscosity on the fold formation and development of the growing sheet. Our results suggest that the viscous resistance to in-plane deformation promotes fold formation, whereas the viscous resistance to out-of-plane deformation suppresses fold development. We also investigate the effects of the thickness and aspect ratio of the rectangular sheet. Finally, we compare the growth- and prestrain-induced deformations to find a common behavior of sheets under viscous environments.

A fully conservative and shift-invariant formulation for Galerkin discretizations of incompressible variable density flow

This paper introduces a formulation of the variable density incompressible Navier-Stokes equations by modifying the nonlinear terms in a consistent way. For Galerkin discretizations, the formulation leads to favorable discrete conservation properties without the divergence-free constraint being strongly enforced. In addition, the formulation is shown to make the density field invariant to global shifts. The effect of viscous regularizations on conservation properties is also investigated. Numerical tests validate the theory developed in this work. The new formulation shows superior performance compared to other formulations from the literature, both in terms of accuracy for smooth problems and in terms of robustness.

A Weighted Shifted Boundary Method for Immersed Moving Boundary Simulations of Stokes' Flow

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests.

Effect of retarded friction and added mass on the swimming speed of a vibrating two-sphere

A theoretical expression is derived for the mechanical contribution to the mean swimming speed of a vibrating two-sphere, consisting of two spheres connected by an elastic spring, and immersed in a viscous incompressible fluid. The spring provides a harmonic potential for oscillations about a mean distance between centers. The system is made to oscillate at a chosen frequency by activating forces which sum to zero. The mechanical contribution to the resulting mean swimming velocity is calculated from the mechanical equations of motion and the corresponding impedance matrix of linear response. The frequency-dependent pair friction coefficients are found from approximate expressions derived earlier. The mechanical contribution is calculated to second order in the amplitude of stroke as a function of the scaling number, a dimensionless combination of size, frequency, and kinematic viscosity. Retarded friction and added mass determine the functional behavior.