To see the other types of publications on this topic, follow the link: Non-linear Stokes flow.
Journal articles on the topic 'Non-linear Stokes flow'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 journal articles for your research on the topic 'Non-linear Stokes flow.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.
1
Sakthivel, R., S. Vengadesan, and S. K. Bhattacharyya. "Application of non-linear k-e turbulence model in flow simulation over underwater axisymmetric hull at higher angle of attack." Journal of Naval Architecture and Marine Engineering 8, no. 2 (November 22, 2011): 149–63. http://dx.doi.org/10.3329/jname.v8i2.6984.
Full textAbstract:
This paper addresses the Computational Fluid Dynamics Approach (CFD) to simulate the flow over underwater axisymmetric bodies at higher angle of attacks. Three Dimensional (3D) flow simulation is carried out over MAYA Autonomous Underwater Vehicle (AUV) at a Reynolds number (Re) of 2.09×106. These 3D flows are complex due to cross flow interaction with hull which produces nonlinearity in the flow. Cross flow interaction between pressure side and suction side is studied in the presence of angle of attack. For the present study standard k-ε model, non-linear k-ε model models of turbulence are used for solving the Reynolds Averaged Navier-Stokes Equation (RANS). The non-linear k-ε turbulence model is validated against DARPA Suboff axisymmetric hull and its applicability for flow simulation over underwater axisymmetric hull is examined. The non-linear k-ε model performs well in 3D complex turbulent flows with flow separation and flow reattachment. The effect of angle of attack over flow structure, force coefficients and wall related flow variables are discussed in detail. Keywords: Computational Fluid Dynamics (CFD); Autonomous Underwater Vehicle (AUV); Reynolds averaged Navier-Stokes Equation (RANS); non-linear k-ε turbulence modeldoi: http://dx.doi.org/10.3329/jname.v8i2.6984 Journal of Naval Architecture and Marine Engineering 8(2011) 149-163
2
Lee, S., H. Cho, H. Kim, and S. J. Shin. "Time-domain non-linear aeroelastic analysis via a projection-based reduced-order model." Aeronautical Journal 124, no. 1281 (July 20, 2020): 1798–818. http://dx.doi.org/10.1017/aer.2020.59.
Full textAbstract:
ABSTRACTThe aeroelastic phenomenon of limit-cycle oscillations (LCOs) is analysed using a projection-based reduced-order model (PROM) and Navier–Stokes computational fluid dynamics (CFD) in the time domain. The proposed approach employs incompressible Navier–Stokes CFD to construct the full-order model flow field. A proper orthogonal decomposition (POD) of the snapshot matrix is conducted to extract the POD modes and corresponding temporal coefficients. The POD modes are directly projected to the incompressible Navier–Stokes equation to reconstruct the flow field efficiently. The methodology is applied to a plunging cylinder and an aerofoil undergoing LCOs. This scheme decreases the computational time while preserving the capability to predict the flow field accurately. The ROM is capable of reducing the computational time by at least 70% while maintaining the discrepancy within 0.1%. The causes of LCOs are also investigated. The scheme can be used to analyse non-linear aeroelastic phenomena in the time domain with reduced computational time.
3
Palaniappan, D., S. D. Nigam, and T. Amaranath. "A theorem for a fluid Stokes flow." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 35, no. 3 (January 1994): 335–47. http://dx.doi.org/10.1017/s0334270000009334.
Full textAbstract:
AbstractA sphere theorem for non-axisymmetric Stokes flow of a viscous fluid of viscosity μe past a fluid sphere of viscosity μi is stated and proved. The existing sphere theorems in Stokes flow follow as special cases from the present theorem. It is observed that the expression for drag on the fluid sphere is a linear combination of rigid and shear-free drags.
4
SINAYOKO, SAMUEL, A. AGARWAL, and Z. HU. "Flow decomposition and aerodynamic sound generation." Journal of Fluid Mechanics 668 (December 3, 2010): 335–50. http://dx.doi.org/10.1017/s0022112010004672.
Full textAbstract:
An approximate decomposition of fluid-flow variables satisfying unbounded compressible Navier–Stokes equations into acoustically radiating and non-radiating components leads to well-defined source terms that can be identified as the physical sources of aerodynamic noise. We show that, by filtering the flow field by means of a linear convolution filter, it is possible to decompose the flow into non-radiating and radiating components. This is demonstrated on two different flows: one satisfying the linearised Euler equations and the other the Navier–Stokes equations. In the latter case, the corresponding sound sources are computed. They are found to be more physical than those computed through classical acoustic analogies in which the flow field is decomposed into a steady mean and fluctuating component.
5
NOBLE, DAVID R., and DAVID J. HOLDYCH. "FULL NEWTON LATTICE BOLTZMANN METHOD FOR TIME-STEADY FLOWS USING A DIRECT LINEAR SOLVER." International Journal of Modern Physics C 18, no. 04 (April 2007): 652–60. http://dx.doi.org/10.1142/s0129183107010905.
Full textAbstract:
A full Newton lattice Boltzmann method is developed for time-steady flows. The general method involves the construction of a residual form for the time-steady, nonlinear Boltzmann equation in terms of the probability distribution. Bounce-back boundary conditions are also incorporated into the residual form. Newton's method is employed to solve the resulting system of non-linear equations. At each Newton iteration, the sparse, banded, Jacobian matrix is formed from the dependencies of the non-linear residuals on the components of the particle distribution. The resulting linear system of equations is solved using a direct solver designed for sparse, banded matrices. For the Stokes flow limit, only one matrix solve is required. Two dimensional flow about a periodic array of disks is simulated as a proof of principle, and the numerical efficiency is carefully assessed. For the case of Stokes flow (Re = 0) with resolution 251×251, the proposed method performs more than 100 times faster than a standard, fully explicit implementation.
6
Iannelli, Joe. "An exact non-linear Navier-Stokes compressible-flow solution for CFD code verification." International Journal for Numerical Methods in Fluids 72, no. 2 (September 7, 2012): 157–76. http://dx.doi.org/10.1002/fld.3731.
Full text
7
Akhmetov, Vadim. "Stability of counter vortex flows in hydraulic engineering construction." E3S Web of Conferences 97 (2019): 05004. http://dx.doi.org/10.1051/e3sconf/20199705004.
Full textAbstract:
In the framework of linear theory, the stability of counter vortex flows with respect to non-axisymmetric perturbations is investigated numerically. The main flow field calculation results have been obtained as the solutions of the Navier-Stokes equations. The amplification coefficients are calculated, the regions of instability of the flow are defined.
8
HEATON, C. J., J. W. NICHOLS, and P. J. SCHMID. "Global linear stability of the non-parallel Batchelor vortex." Journal of Fluid Mechanics 629 (June 15, 2009): 139–60. http://dx.doi.org/10.1017/s0022112009006399.
Full textAbstract:
Linear stability of the non-parallel Batchelor vortex is studied using global modes. This family of swirling wakes and jets has been extensively studied under the parallel-flow approximation, and in this paper we extend to more realistic non-parallel base flows. Our base flow is obtained as an exact steady solution of the Navier–Stokes equations by direct numerical simulation (with imposed axisymmetry to damp all instabilities). Global stability modes are computed by numerical simulation of the linearized equations, using the implicitly restarted Arnoldi method, and we discuss fully the numerical and convergence issues encountered. Emphasis is placed on exploring the general structure of the global spectrum, and in particular the correspondence between global modes and local absolute modes which is anticipated by weakly non-parallel asymptotic theory. We believe that our computed global modes for a weakly non-parallel vortex are the first to display this correspondence with local absolute modes. Superpositions of global modes are also studied, allowing an investigation of the amplifier dynamics of this unstable flow. For an illustrative case we find global non-modal transient growth via a convective mechanism. Generally amplifier dynamics, via convective growth, are prevalent over short time intervals, and resonator dynamics, via global mode growth, become prevalent at later times.
9
Ulker, Erman, Sıla Ovgu Korkut, and Mehmet Sorgun. "Computational analysis of turbulent flow through an eccentric annulus under different temperature conditions." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 9 (September 3, 2018): 2189–207. http://dx.doi.org/10.1108/hff-01-2018-0040.
Full textAbstract:
Purpose The purpose of this paper is to solve Navier–Stokes equations including the effects of temperature and inner pipe rotation for fully developed turbulent flow in eccentric annuli by using finite difference scheme with fixing non-linear terms. Design/methodology/approach A mathematical model is proposed for fully developed turbulent flow including the effects of temperature and inner pipe rotation in eccentric annuli. Obtained equation is solved numerically via central difference approximation. In this process, the non-linear term is frozen. In so doing, the non-linear equation can be considered as a linear one. Findings The convergence analysis is studied before using the method to the proposed momentum equation. It reflects that the method approaches to the exact solution of the equation. The numerical solution of the mathematical model shows that pressure gradient can be predicted with a good accuracy when it is compared with experimental data collected from experiments conducted at Izmir Katip Celebi University Flow Loop. Originality/value The originality of this work is that Navier–Stokes equations including temperature and inner pipe rotation effects for fully developed turbulent flow in eccentric annuli are solved numerically by a finite difference method with frozen non-linear terms.
10
ANGUIANO, MARÍA. "Homogenization of a non-stationary non-Newtonian flow in a porous medium containing a thin fissure." European Journal of Applied Mathematics 30, no. 2 (February 5, 2018): 248–77. http://dx.doi.org/10.1017/s0956792518000049.
Full textAbstract:
We consider a non-stationary incompressible non-Newtonian Stokes system in a porous medium with characteristic size of the pores ϵ and containing a thin fissure of width ηϵ. The viscosity is supposed to obey the power law with flow index$\frac{5}{3}\leq q\leq 2$. The limit when size of the pores tends to zero gives the homogenized behaviour of the flow. We obtain three different models depending on the magnitude ηϵwith respect to ϵ: if ηϵ≪$\varepsilon^{q\over 2q-1}$the homogenized fluid flow is governed by a time-dependent non-linear Darcy law, while if ηϵ≫$\varepsilon^{q\over 2q-1}$is governed by a time-dependent non-linear Reynolds problem. In the critical case, ηϵ≈$\varepsilon^{q\over 2q-1}$, the flow is described by a time-dependent non-linear Darcy law coupled with a time-dependent non-linear Reynolds problem.
11
Ahlkrona, Josefin, and Malte Braack. "Equal-Order Stabilized Finite Element Approximation of the p-Stokes Equations on Anisotropic Cartesian Meshes." Computational Methods in Applied Mathematics 20, no. 1 (January 1, 2020): 1–25. http://dx.doi.org/10.1515/cmam-2018-0260.
Full textAbstract:
AbstractThe p-Stokes equations with power-law exponent {p\in(1,2)} describes non-Newtonian, shear-thinning, incompressible flow. In many industrial applications and natural settings, shear-thinning flow takes place in very thin domains. To account for such anisotropic domains in simulations, we here study an equal-order bi-linear anisotropic finite element discretization of the p-Stokes equations, and extend a non-linear Local Projection Stabilization to anisotropic meshes. We prove an a priori estimate and illustrate the results with two numerical examples, one confirming the rate of convergence predicted by the a-priori analysis, and one showing the advantages of an anisotropic stabilization compared to an isotropic one.
12
Mohyud-din, Syed Tauseef, Umar Khan, Naveed Ahmed, and M. M. Rashidi. "Stokes’ first problem for MHD flow of Casson nanofluid." Multidiscipline Modeling in Materials and Structures 13, no. 1 (June 12, 2017): 2–10. http://dx.doi.org/10.1108/mmms-03-2016-0014.
Full textAbstract:
Purpose The purpose of this paper is to present investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate using Buongiorno’s model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticle fraction are passively controlled on the boundary rather than actively. Design/methodology/approach The partial differential equations governing the flow are reduced to a system of non-linear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters are provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers. Findings A revised model for Stokes’ first problem in nanofluids is presented in this paper. This model considers a zero flux condition at the boundary. Governing equations after implementing the similarity transforms get converted into a system of non-linear ordinary differential equations. Numerical solution using RK-Fehlberg method is also carried out. Emerging parameters are analyzed graphically. Figures indicate a quite significant change in concentration profile due to zero flux condition at the wall. Originality/value This work can be extended for other problems involving nanofluids for the better understanding of different properties of nanofluids.
13
Saroha, Sagar, Sawan S. Sinha, and Sunil Lakshmipathy. "Evaluation of PANS method in conjunction with non-linear eddy viscosity closure using OpenFOAM." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 3 (March 4, 2019): 949–80. http://dx.doi.org/10.1108/hff-09-2018-0529.
Full textAbstract:
Purpose In recent years, the partially averaged Navier–Stokes (PANS) methodology has earned acceptability as a viable scale-resolving bridging method of turbulence. To further enhance its capabilities, especially for simulating separated flows past bluff bodies, this paper aims to combine PANS with a non-linear eddy viscosity model (NLEVM). Design/methodology/approach The authors first extract a PANS closure model using the Shih’s quadratic eddy viscosity closure model [originally proposed for Reynolds-averaged Navier–Stokes (RANS) paradigm (Shih et al., 1993)]. Subsequently, they perform an extensive evaluation of the combination (PANS + NLEVM). Findings The NLEVM + PANS combination shows promising result in terms of reduction of the anisotropy tensor when the filter parameter (fk) is reduced. Further, the influence of PANS filter parameter f on the magnitude and orientation of the non-linear part of the stress tensor is closely scrutinized. Evaluation of the NLEVM + PANS combination is subsequently performed for flow past a square cylinder at Reynolds number of 22,000. The results show that for the same level of reduction in fk, the PANS + NLEVM methodology releases significantly more scales of motion and unsteadiness as compared to the traditional linear eddy viscosity model (LEVM) of Boussinesq (PANS + LEVM). The authors further demonstrate that with this enhanced ability the NLEVM + PANS combination shows much-improved predictions of almost all the mean quantities compared to those observed in simulations using LEVM + PANS. Research limitations/implications Based on these results, the authors propose the NLEVM + PANS combination as a more potent methodology for reliable prediction of highly separated flow fields. Originality/value Combination of a quadratic eddy viscosity closure model with PANS framework for simulating flow past bluff bodies.
14
Breit, Dominic, Bianca Stroffolini, and Anna Verde. "Non-stationary flows of asymptotically Newtonian fluids." Communications in Contemporary Mathematics 20, no. 02 (November 29, 2017): 1750006. http://dx.doi.org/10.1142/s0219199717500067.
Full textAbstract:
We study nonlinear parabolic Stokes systems with an asymptotically linear structure. This refers to the slow flow of a non-Newtonian fluid with Newtonian behavior for large shear rates. We show that the symmetric gradient of the velocity field is locally bounded in space-time.
15
Sun, Wei, and Liping Xu. "Improvement of corner separation prediction using an explicit non-linear RANS closure." Journal of the Global Power and Propulsion Society 5 (April 7, 2021): 50–65. http://dx.doi.org/10.33737/jgpps/133913.
Full textAbstract:
In this paper, an investigation into the effect of explicit non-linear turbulence modelling on anisotropic turbulence flows is presented. Such anisotropic turbulence flows are typified in the corner separations in turbomachinery. The commonly used Reynolds-Averaged Navier-Stokes (RANS) turbulence closures, in which the Reynolds stress tensor is modelled by the Boussinesq (linear) constitutive relation with the mean strain-rate tensor, often struggle to predict corner separation with reasonable accuracy. The physical reason for this modelling deficiency is partially attributable to the Boussinesq hypothesis which does not count for the turbulence anisotropy, whilst in a corner separation, the flow is subject to three-dimensional (3D) shear and the effects due to turbulence anisotropy may not be ignored. In light of this, an explicit non-linear Reynolds stress-strain constitutive relation developed by Menter et al. is adopted as a modification of the Reynolds-stress anisotropy. Coupled with the Menter’s hybrid "k-ω" ⁄"k-ε" turbulence model, this non-linear constitutive relation gives significantly improved predictions for the corner separation flows within a compressor cascade, at both the design and off-design flow conditions. The mean vorticity field are studied to further investigate the physical reasons for these improvements, highlighting its potential for the widespread applications in the corner separation prediction.
16
NISHIYAMA, TAKAHIRO. "Meromorphic non-integrability of a steady Stokes flow inside a sphere." Ergodic Theory and Dynamical Systems 34, no. 2 (April 2012): 616–27. http://dx.doi.org/10.1017/etds.2012.130.
Full textAbstract:
AbstractThe non-existence of a real meromorphic first integral for a spherically confined steady Stokes flow of Bajer and Moffatt is proved on the basis of Ziglin’s theory and the differential Galois theory. In the proof, the differential Galois group of a second-order Fuchsian-type differential equation associated with normal variations along a particular streamline is shown to be a special linear group according to Kovacic’s algorithm. A set of special values of a parameter contained in the Fuchsian-type equation is studied by using the theory of elliptic curves. For this set, a computer algebra system is used in part of Kovacic’s algorithm.
17
Sayma, A. I., M. Vahdati, and M. Imregun. "Turbine forced response prediction using an integrated non-linear analysis." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 214, no. 1 (March 1, 2000): 45–60. http://dx.doi.org/10.1243/1464419001544133.
Full textAbstract:
The forced response due to flow defects caused by the upstream blade rows is predicted for two turbines: intermediate pressure (IP) and low pressure (LP). The prediction method is based on an advanced numerical tool where the compressible viscous flow field is modelled by solving Favre-averaged Navier-Stokes equations with the Baldwin and Barth turbulence model. The flow solution is coupled to a modal model of the structure and information is exchanged every time step between the fluid and the structural domains. The hybrid unstructured mesh is moved at each time step to follow the structural motion using a spring analogy. For the IP turbine, the method was used to rank two different designs of nozzle guide vanes. For the LP turbine, special emphasis was placed on predicting vibration amplitudes due to high and low engine order excitations. Predictions and measurements were found to be in good agreement for both turbines. Due to insufficient experimental data, it was difficult to assess the accuracy of the low engine order computations, although it was shown that the model was capable of undertaking such a task.
18
SARKAR, KAUSIK, and WILLIAM R. SCHOWALTER. "Deformation of a two-dimensional viscous drop in time-periodic extensional flows: analytical treatment." Journal of Fluid Mechanics 436 (June 10, 2001): 207–30. http://dx.doi.org/10.1017/s0022112001004013.
Full textAbstract:
In Sarkar & Schowalter (2001), we reported results from numerical simulations of drop deformation in various classes of time-periodic straining flows at non-zero Reynolds number. As often occurs, analytical solutions provide more effective understanding of the structure and significance of a phenomenon. Here we describe drop deformation predicted from analytical solutions to linear time-periodic straining flows. Three different limiting cases are considered: an unsteady Stokes flow that retains all but the nonlinear advection terms, a Stokes flow that neglects inertia altogether, and an inviscid potential flow. The first limit is in clear contrast to the common approach in emulsion literature that resorts almost always to the Stokes flow assumption. The analysis clearly shows the forced–damped mass–spring system underlying the physical phenomena, which distinguishes it from the inertialess Stokes flow. The potential flow also depicts resonance, albeit of an undamped system, and provides an important limit of the problem. The drop deformation is assumed to be small, and a perturbative approach has been employed. The first-order problem has been solved to arrive at either an evolution equation (in Stokes and potential flow limits) or the long-time periodic drop response (for unsteady Stokes analysis). The analytical results compare satisfactorily with those obtained from the numerical simulation in Sarkar & Schowalter (2001), and the resonance characteristics are quantitatively explained. The three different solutions are compared with each other, and the results are presented for different parameters such as frequency, interfacial tension, viscosity ratio, density ratio and Reynolds number. Furthermore, the simple ODE model presented in the Appendix of Sarkar & Schowalter (2001) is shown to explain the asymptotic limits of the present solution.
19
PIGEONNEAU, FRANCK, and FRANÇOIS FEUILLEBOIS. "Collision of drops with inertia effects in strongly sheared linear flow fields." Journal of Fluid Mechanics 455 (March 25, 2002): 359–86. http://dx.doi.org/10.1017/s002211200100742x.
Full textAbstract:
The relative motion of drops in shear flows is responsible for collisions leading to the creation of larger drops. The collision of liquid drops in a gas is considered here. The drops are small enough for the Reynolds number to be low (negligible fluid motion inertia), yet large enough for the Stokes number to be possibly of order unity (non-negligible inertia in the motion of drops). Possible concurrent effects of Van der Waals attractive forces and drop inertia are taken into account.General expressions are first presented for the drag forces on two interacting drops of different sizes embedded in a general linear flow field. These expressions are obtained by superposition of solutions for the translation of drops and for steady drops in elementary linear flow fields (simple shear flows, pure straining motions). Earlier solutions adapted to the case of inertialess drops (by Zinchenko, Davis and coworkers) are completed here by the solution for a simple shear flow along the line of centres of the drops. A solution of this problem in bipolar coordinates is provided; it is consistent with another solution obtained as a superposition of other elementary flow fields.The collision efficiency of drops is calculated neglecting gravity effects, that is for strongly sheared linear flow fields. Results are presented for the cases of a simple linear shear flow and an axisymmetric pure straining motion. As expected, the collision efficiency increases with the Stokes numbers, that is with drop inertia. On the other hand, the collision efficiency in a simple shear flow becomes negligible below some value of the ratio of radii, regardless of drop inertia. The value of this threshold increases with decreasing Van der Waals forces. The concurrence between drop inertia and attractive van der Waals forces results in various anisotropic shapes of the collision cross-section. By comparison, results for the collision efficiency in an axisymmetric pure straining motion are more regular. This flow field induces axisymmetric sections of collision and strong inertial effects resulting in collision efficiencies larger than unity. Effects of van der Waals forces only appear when one of the drops has a very low Stokes number.
20
Orazzo, A., G. Coppola, and L. de Luca. "Disturbance energy growth in core–annular flow." Journal of Fluid Mechanics 747 (April 10, 2014): 44–72. http://dx.doi.org/10.1017/jfm.2014.155.
Full textAbstract:
AbstractThe linear stability of the horizontal pipe flow of an equal density oil–water mixture, arranged as acore–annular flow(CAF), is here reconsidered from the point of view of non-modal analysis in order to assess the effects of non-normality of the linearized Navier–Stokes operator on the transient evolution of small disturbances. The aim of this investigation is to give insight into physical situations in which poor agreement occurs between the predictions of linear modal theory and classical experiments. The results exhibit high transient amplifications of the energy of three-dimensional perturbations and, in analogy with single-fluid pipe flow, the largest amplifications arise for non-axisymmetric disturbances of vanishing axial wavenumber. Energy analysis shows that the mechanisms leading to these transient phenomena mostly occur in the annulus, occupied by the less viscous fluid. Consequently, higher values of energy amplifications are obtained by increasing the gap between the core and the pipe wall and the annular Reynolds number. It is argued that these linear transient mechanisms of disturbance amplification play a key role in explaining the transition to turbulence of CAF.
21
Wang, Kai, Shiting Wen, Rizwan Zahoor, Ming Li, and Božidar Šarler. "Method of regularized sources for axisymmetric Stokes flow problems." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (May 3, 2016): 1226–39. http://dx.doi.org/10.1108/hff-09-2015-0397.
Full textAbstract:
Purpose – The purpose of this paper is to find solution of Stokes flow problems with Dirichlet and Neumann boundary conditions in axisymmetry using an efficient non-singular method of fundamental solutions that does not require an artificial boundary, i.e. source points of the fundamental solution coincide with the collocation points on the boundary. The fundamental solution of the Stokes pressure and velocity represents analytical solution of the flow due to a singular Dirac delta source in infinite space. Design/methodology/approach – Instead of the singular source, a non-singular source with a regularization parameter is employed. Regularized axisymmetric sources were derived from the regularized three-dimensional sources by integrating over the symmetry coordinate. The analytical expressions for related Stokes flow pressure and velocity around such regularized axisymmetric sources have been derived. The solution to the problem is sought as a linear combination of the fields due to the regularized sources that coincide with the boundary. The intensities of the sources are chosen in such a way that the solution complies with the boundary conditions. Findings – An axisymmetric driven cavity numerical example and the flow in a hollow tube and flow between two concentric tubes are chosen to assess the performance of the method. The results of the newly developed method of regularized sources in axisymmetry are compared with the results obtained by the fine-grid second-order classical finite difference method and analytical solution. The results converge with a finer discretization, however, as expected, they depend on the value of the regularization parameter. The method gives accurate results if the value of this parameter scales with the typical nodal distance on the boundary. Originality/value – Analytical expressions for the axisymmetric blobs are derived. The method of regularized sources is for the first time applied to axisymmetric Stokes flow problems.
22
Hosseini, Reza, Sadegh Poozesh, and Saeed Dinarvand. "MHD Flow of an Incompressible Viscous Fluid through Convergent or Divergent Channels in Presence of a High Magnetic Field." Journal of Applied Mathematics 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/157067.
Full textAbstract:
The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear equation has been solved analytically using a very efficient technique, namely, differential transform method (DTM). The DTM solution is compared with the results obtained by a numerical method (shooting method, coupled with fourth-order Runge-Kutta scheme). The plots have revealed the physical characteristics of flow by changing angles of the channel, Hartmann and Reynolds numbers.
23
BROOKER, A. M. H., J. C. PATTERSON, and S. W. ARMFIELD. "Non-parallel linear stability analysis of the vertical boundary layer in a differentially heated cavity." Journal of Fluid Mechanics 352 (December 10, 1997): 265–81. http://dx.doi.org/10.1017/s0022112097007258.
Full textAbstract:
A non-parallel linear stability analysis which utilizes the assumptions made in the parabolized stability equations is applied to the buoyancy-driven flow in a differentially heated cavity. Numerical integration of the complete Navier–Stokes and energy equations is used to validate the non-parallel theory by introducing an oscillatory heat input at the upstream end of the boundary layer. In this way the stability properties are obtained by analysing the evolution of the resulting disturbances. The solutions show that the spatial growth rate and wavenumber are highly dependent on the transverse location and the disturbance flow quantity under consideration. The local solution to the parabolized stability equations accurately predicts the wave properties observed in the direct simulation whereas conventional parallel stability analysis overpredicts the spatial amplification and the wavenumber.
24
Mandal, Shubhadeep, Uddipta Ghosh, and Suman Chakraborty. "Effect of surfactant on motion and deformation of compound droplets in arbitrary unbounded Stokes flows." Journal of Fluid Mechanics 803 (August 19, 2016): 200–249. http://dx.doi.org/10.1017/jfm.2016.497.
Full textAbstract:
This study deals with the motion and deformation of a compound drop system, subject to arbitrary but Stokesian far-field flow conditions, in the presence of bulk-insoluble surfactants. We derive solutions for fluid velocities and the resulting surfactant concentrations, assuming the capillary number and surface Péclet number to be small, as compared with unity. We first focus on a concentric drop configuration and apply Lamb’s general solution, assuming the far-field flow to be arbitrary in nature. As representative case studies, we consider two cases: (i) flow dynamics in linear flows and (ii) flow dynamics in a Poiseuille flow, although for the latter case, the concentric configuration does not remain valid in general. We further look into the effective viscosity of a dilute suspension of compound drops, subject to linear ambient flow, and compare our predictions with previously reported experiments. Subsequently, the eccentric drop configuration is addressed by using a bipolar coordinate system where the far-field flow is assumed to be axisymmetric but otherwise arbitrary in nature. As a specific example for eccentric drop dynamics, we focus on Poiseuille flow and study the drop migration velocities. Our analysis shows that the presence of surfactant generally opposes the imposed flows, thereby acting like an effective augmented viscosity. Our analysis reveals that maximizing the effects of surfactant makes the drops behave like solid particles suspended in a medium. However, in uniaxial extensional flow, the presence of surfactants on the inner drop, in conjunction with the drop radius ratio, leads to a host of interesting and non-monotonic behaviours for the interface deformation. For eccentric drops, the effect of eccentricity only becomes noticeable after it surpasses a certain critical value, and becomes most prominent when the two interfaces approach each other. We further depict that surfactant and eccentricity generally tend to suppress each other’s effects on the droplet migration velocities.
25
Hack, M. J. Philipp, and Tamer A. Zaki. "Modal and non-modal stability of boundary layers forced by spanwise wall oscillations." Journal of Fluid Mechanics 778 (August 3, 2015): 389–427. http://dx.doi.org/10.1017/jfm.2015.387.
Full textAbstract:
Modal and non-modal perturbation growth in boundary layers subjected to time-harmonic spanwise wall motion are examined. The superposition of the streamwise Blasius flow and the spanwise Stokes layer can lead to strong modal amplification during intervals of the base-flow period. Linear stability analysis of frozen phases of the base state demonstrates that this growth is due to an inviscid instability, which is related to the inflection points of the spanwise Stokes layer. The generation of new inflection points at the wall and their propagation towards the free stream leads to mode crossing when tracing the most unstable mode as a function of phase. The fundamental mode computed in Floquet analysis has a considerably lower growth rate than the instantaneous eigenfunctions. Furthermore, the algebraic lift-up mechanism that causes the formation of Klebanoff streaks is examined in transient growth analyses. The wall forcing significantly weakens the wall-normal velocity perturbations associated with lift-up. This effect is attributed to the formation of a pressure field which redistributes energy from the wall-normal to the spanwise velocity perturbations. The results from linear theory explain observations from direct numerical simulations of breakdown to turbulence in the same flow configuration by Hack & Zaki (J. Fluid Mech., vol. 760, 2014a, pp. 63–94). When bypass mechanisms are dominant, the flow is stabilized due to the weaker non-modal growth. However, at high amplitudes of wall oscillation, transition is promoted due to fast growth of the modal instability.
26
Tagawa and Song. "Stability of an Axisymmetric Liquid Metal Flow Driven by a Multi-Pole Rotating Magnetic Field." Fluids 4, no. 2 (April 21, 2019): 77. http://dx.doi.org/10.3390/fluids4020077.
Full textAbstract:
The stability of an electrically conducting fluid flow in a cylinder driven by a multi-pole rotating magnetic field is numerically studied. A time-averaged Lorentz force term including the electric potential is derived on the condition that the skin effect can be neglected and then it is incorporated into the Navier-Stokes equation as a body force term. The axisymmetric velocity profile of the basic flow for the case of an infinitely long cylinder depends on the number of pole-pairs and the Hartmann number. A set of linearized disturbance equations to obtain a neutral state was successfully solved using the highly simplified marker and cell (HSMAC) method together with a Newton–Raphson method. For various cases of the basic flow, depending on both the number of pole-pairs and the Hartmann number, the corresponding critical rotational Reynolds numbers for the onset of secondary flow were obtained instead of using the conventional magnetic Taylor number. The linear stability analyses reveal that the critical Reynolds number takes its minimum at a certain value of the Hartmann number. On the other hand, the velocity profile for cases of a finite length cylinder having a no-slip condition at the flat walls generates the Bödewadt boundary layers and such flows need to be computed including the non-linear terms of the Navier-Stokes equation.
27
Alam, M., S. Saha, and R. Gupta. "Unified theory for a sheared gas–solid suspension: from rapid granular suspension to its small-Stokes-number limit." Journal of Fluid Mechanics 870 (May 15, 2019): 1175–93. http://dx.doi.org/10.1017/jfm.2019.304.
Full textAbstract:
A non-perturbative nonlinear theory for moderately dense gas–solid suspensions is outlined within the framework of the Boltzmann–Enskog equation by extending the work of Saha & Alam (J. Fluid Mech., vol. 833, 2017, pp. 206–246). A linear Stokes’ drag law is adopted for gas–particle interactions, and the viscous dissipation due to hydrodynamic interactions is incorporated in the second-moment equation via a density-corrected Stokes number. For the homogeneous shear flow, the present theory provides a unified treatment of dilute to dense suspensions of highly inelastic particles, encompassing the high-Stokes-number rapid granular regime ($St\rightarrow \infty$) and its small-Stokes-number counterpart, with quantitative agreement for all transport coefficients. It is shown that the predictions of the shear viscosity and normal-stress differences based on existing theories deteriorate markedly with increasing density as well as with decreasing Stokes number and restitution coefficient.
28
Kang, Kean Lee, Richard Ashworth, and Shahid Mughal. "Stabilization of crossflow instability with plasma actuators: Linearized Navier–Stokes simulations." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 234, no. 1 (April 15, 2019): 68–78. http://dx.doi.org/10.1177/0954410019842033.
Full textAbstract:
This paper describes work carried out within the European Union (EU)-Russia Buterfli project to look at the control of transition-causing “target” stationary cross flow vortices, by the use of distributed plasma actuation to generate sub-dominant “killer” modes. The objective is to use the “killer” modes to control the “target” modes through a non-linear stabilizing mechanism. The numerical modelling and results are compared to experimental studies performed at the TsAGI T124 tunnel for a swept plate subject to a favorable pressure gradient flow. A mathematical model for the actuator developed at TsAGI was implemented in a linearized Navier–Stokes (LNS) solver and used to model and hence predict “killer” mode amplitudes at a measurement plane in the experiment. The LNS analysis shows good agreement with experiment, and the results are used as input for non-linear parabolized stability equation (PSE) analysis to predict the effect of these modes on crossflow transition. Whilst the numerical model indicates a delay in transition, experimental results indicated an advance in transition rather than delay. This was determined to be due to actuator-induced unsteadiness arising in the experiment, resulting in the generation of travelling crossflow disturbances which tended to obscure and thus dominate the plasma stabilized stationary disturbances.
29
COIMBRA, C. F. M., and R. H. RANGEL. "General solution of the particle momentum equation in unsteady Stokes flows." Journal of Fluid Mechanics 370 (September 10, 1998): 53–72. http://dx.doi.org/10.1017/s0022112098001967.
Full textAbstract:
The general solution of the particle momentum equation for unsteady Stokes flows is obtained analytically. The method used to obtain the solution consists of applying a fractional-differential operator to the first-order integro-differential equation of motion in order to transform the original equation into a second-order non-homogeneous equation, and then solving this last equation by the method of variation of parameters. The fractional differential operator consists of a three-time-scale linear operator that stretches the order of the Riemann–Liouville fractional derivative associated with the history term in the equation of motion. In order to illustrate the application of the general solution to particular background flow fields, the particle velocity is calculated for three specific flow configurations. These flow configurations correspond to the gravitationally induced motion of a particle through an otherwise quiescent fluid, the motion of a particle caused by a background velocity field that accelerates linearly in time, and the motion of a particle in a fluid that undergoes an impulsive acceleration. The analytical solutions for these three specific cases are analysed and compared to other solutions found in the literature.
30
Mei, Y., and A. Guha. "Implicit numerical simulation of transonic flow through turbine cascades on unstructured grids." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 219, no. 1 (February 1, 2005): 35–47. http://dx.doi.org/10.1243/095765005x6926.
Full textAbstract:
Numerical simulation of the compressible flow through a turbine cascade is studied in the present paper. The numerical solution is performed on self-adaptive unstructured meshes by an implicit method. Computational codes have been developed for solving Euler as well as Navier-Stokes equations with various turbulence modelling. The Euler and Navier-Stokes codes have been applied on a standard turbine cascade, and the computed results are compared with experimental results. A hybrid scheme is used for spatial discretization, where the inviscid fluxes are discretized using a finite volume method while the viscous fluxes are calculated by central differences. A MUSCL-type approach is used for achieving higher-order accuracy. The effects of the turbulent stress terms in the Reynolds-averaged Navier-Stokes equations have been studied with two different models: an algebraic turbulence model (Baldwin-Lomax model) and a two-equation turbulence model ( k-ɛ model). The system of linear equations is solved by a Gauss-Seidel algorithm at each step of time integration. A new treatment of the non-reflection boundary condition is applied in the present study to make it consistent with the finite volume flux calculation and the implicit time discretization.
31
Schmid, Peter J., and Dan S. Henningson. "Optimal energy density growth in Hagen–Poiseuille flow." Journal of Fluid Mechanics 277 (October 25, 1994): 197–225. http://dx.doi.org/10.1017/s0022112094002739.
Full textAbstract:
Linear stability of incompressible flow in a circular pipe is considered. Use is made of a vector function formulation involving the radial velocity and radial vorticity only. Asymptotic as well as transient stability are investigated using eigenvalues and ε-pseudoeigenvalues, respectively. Energy stability is probed by establishing a link to the numerical range of the linear stability operator. Substantial transient growth followed by exponential decay has been found and parameter studies revealed that the maximum amplification of initial energy density is experienced by disturbances with no streamwise dependence and azimuthal wavenumber n = 1. It has also been found that the maximum in energy scales with the Reynolds number squared, as for other shear flows. The flow field of the optimal disturbance, exploiting the transient growth mechanism maximally, has been determined and followed in time. Optimal disturbances are in general characterized by a strong shear layer in the centre of the pipe and their overall structure has been found not to change significantly as time evolves. The presented linear transient growth mechanism which has its origin in the non-normality of the linearized Navier–Stokes operator, may provide a viable process for triggering finite-amplitude effects.
32
Barna, Imre Ferenc, Gabriella Bognar, and Krisztian Hriczo. "SELF-SIMILAR ANALYTIC SOLUTION OF THE TWO-DIMENSIONAL NAVIER-STOKES EQUATION WITH A NON-NEWTONIAN TYPE OF VISCOSITY." Mathematical Modelling and Analysis 21, no. 1 (January 26, 2016): 83–94. http://dx.doi.org/10.3846/13926292.2016.1136901.
Full textAbstract:
We investigate Navier-Stokes (NS) and the continuity equations in Cartesian coordinates and Eulerian description for the two dimensional incompressible nonNewtonian fluids. Due to the non-Newtonian viscosity we consider the Ladyzenskaya model with a non-linear velocity dependent stress tensor. The key idea is the multidimensional generalization of the well-known self-similar Ansatz, which has already been used for non-compressible and compressible viscous flow studies. Geometrical interpretations of the trial function are also discussed. Our recent results are compared to the former Newtonian ones.
33
Bayona Roa, Camilo Andrés, Joan Baiges, and R. Codina. "Variational multi-scale finite element approximation of the compressible Navier-Stokes equations." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (May 3, 2016): 1240–71. http://dx.doi.org/10.1108/hff-11-2015-0483.
Full textAbstract:
Purpose – The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated. Design/methodology/approach – The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion. Findings – Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state. Originality/value – A complete investigation of the stabilized formulation of the compressible problem is addressed.
34
Yang, Jianhong, Gang Lei, and Jianwei Yang. "Two-Scale Picard Stabilized Finite Volume Method for the Incompressible Flow." Advances in Applied Mathematics and Mechanics 6, no. 5 (October 2014): 663–79. http://dx.doi.org/10.4208/aamm.2013.m153.
Full textAbstract:
AbstractIn this paper, we consider a two-scale stabilized finite volume method for the two-dimensional stationary incompressible flow approximated by the lowest equal-order element pairP1—P1which do not satisfy the inf-sup condition. The two-scale method consist of solving a small non-linear system on the coarse mesh and then solving a linear Stokes equations on the fine mesh. Convergence of the optimal order in theH1-norm for velocity and theL2-norm for pressure are obtained. The error analysis shows there is the same convergence rate between the two-scale stabilized finite volume solution and the usual stabilized finite volume solution on a fine mesh with relationh = (H2). Numerical experiments completely confirm theoretic results. Therefore, this method presented in this paper is of practical importance in scientific computation.
35
Zimmermann, R., and S. Görtz. "Improved extrapolation of steady turbulent aerodynamics using a non-linear POD-based reduced order model." Aeronautical Journal 116, no. 1184 (October 2012): 1079–100. http://dx.doi.org/10.1017/s0001924000007491.
Full textAbstract:
AbstractA reduced-order modelling (ROM) approach for predicting steady, turbulent aerodynamic flows based on computational fluid dynamics (CFD) and proper orthogonal decomposition (POD) is presented. Model-order reduction is achieved by parameter space sampling, solution space representation via POD and restriction of a CFD solver to the POD subspace. Solving the governing equations of fluid dynamics is replaced by solving a non-linear least-squares optimisation problem. The method will be referred to as LSQ-ROM method. Two approaches of extracting POD basis information from CFD snapshot data are discussed: POD of the full state vector (global POD) and POD of each of the partial states separately (variable-by-variable POD). The method at hand is demonstrated for a 2D aerofoil (NACA 64A010) as well as for a complete industrial aircraft configuration (NASA Common Research Model) in the transonic flow regime by computing ROMs of the compressible Reynolds-averaged Navier-Stokes equations, pursuing both the global and the variable-by-variable POD approach. The LSQ-ROM approach is tried for extrapolatory flow conditions. Results are juxtaposed with those obtained by POD-based extrapolation using Kriging and the radial basis functions spline method. As a reference, the full-order CFD solutions are considered. For the industrial aircraft configuration, the cost of computing the reduced-order solution is shown to be two orders of magnitude lower than that of computing the reference CFD solution.
36
Nandeppanavar, Mahantesh M., Rama Subba Reddy Gorla, and S. Shakunthala. "Magneto-hydrodynamic Blasius flow and heat transfer from a flat plate in the presence of suspended carbon nanofluids." Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems 232, no. 1 (December 7, 2017): 31–40. http://dx.doi.org/10.1177/2397791417744702.
Full textAbstract:
In this article, we have discussed the effect of external magnetic field and other governing parameters on the flow and heat transfer in the presence of suspended carbon nanotubes over a flat plate. The governing equations of flow and heat transfer are derived from the Navier–Stokes and Prandtl boundary layer concept. The derived governing equations of flow and energy are non-linear partial differential equation, and these equations are converted into non-linear ordinary differential equations with corresponding boundary conditions using some suitable similarity transformations and are solved numerically using fourth-order Runge–Kutta method with efficient shooting technique. Effects of governing parameters on flow and heat transfer are shown through various graphs and explained with physical interpretation in detail. This study has applications in glass-fiber production and technology. On observing the results of this study, we can conclude that external magnetic field shows opposite behaviors on velocity and temperature and it enhances the rate of heat transfer.
37
Popkov, V. I., V. I. Astafiev, V. P. Shakshin, and S. V. Zatsepina. "Conjugate Solutions of Navier-Stokes Equation with Deformed Pore Structure." Bulletin of Mathematical Sciences and Applications 8 (May 2014): 30–48. http://dx.doi.org/10.18052/www.scipress.com/bmsa.8.30.
Full textAbstract:
Within the framework of block self-organizing of geological bodies with use of deformation theory the mathematical solution of a problem for effective final speed is proposed. The analytical and numerical integrated solutions of Navier-Stokes equation for deformable porous space were obtained. The decisions of multi-scaled regional problems «on a flow basis» were also presented: from lithology of rock space - to a well and from a well - to petro-physics. The evolutionary transformation of the linear solution of the equation on mass conservation up to the energetically stable non-linear solution of the equation on preserving the number of movements is also offered. Basing upon the analytical solution of Navier-Stokes equation and model of A.N. Kolmogorov we have obtained the energy model of turbulence pulsing controlled chaos, conjugated with risk stability of average well inflow and cluster structure of Earth defluidization.
38
Gomatam, Sreekar, S. Vengadesan, and S. K. Bhattacharyya. "Numerical simulations of flow past an autonomous underwater vehicle at various drift angles." Journal of Naval Architecture and Marine Engineering 9, no. 2 (December 24, 2012): 135–52. http://dx.doi.org/10.3329/jname.v9i2.12567.
Full textAbstract:
Three dimensional (3D) flow past an Autonomous Underwater Vehicle (AUV) is simulated using a Computational Fluid Dynamics (CFD) approach at a Reynolds (Re) number of 2.09x106. A non-linear k-? (NLKE) turbulence model is used for solving the Reynolds Averaged Navier-Stokes (RANS) equations. The effect of control surfaces over the flow, the flow interaction between the hull and the appendages at various Angles of Attack (AoA) and the effect of the symmetry plane is studied. Flow structure, variation of flow variables and force distribution for various AoA are presented and discussed in detail.DOI: http://dx.doi.org/10.3329/jname.v9i2.12567 Journal of Naval Architecture and Marine Engineering 9(2012) 135-152
39
Aziz, Taha, A. Aziz, and C. M. Khalique. "Exact Solutions for Stokes’ Flow of a Non-Newtonian Nanofluid Model: A Lie Similarity Approach." Zeitschrift für Naturforschung A 71, no. 7 (July 1, 2016): 621–30. http://dx.doi.org/10.1515/zna-2016-0031.
Full textAbstract:
AbstractThe fully developed time-dependent flow of an incompressible, thermodynamically compatible non-Newtonian third-grade nanofluid is investigated. The classical Stokes model is considered in which the flow is generated due to the motion of the plate in its own plane with an impulsive velocity. The Lie symmetry approach is utilised to convert the governing nonlinear partial differential equation into different linear and nonlinear ordinary differential equations. The reduced ordinary differential equations are then solved by using the compatibility and generalised group method. Exact solutions for the model equation are deduced in the form of closed-form exponential functions which are not available in the literature before. In addition, we also derived the conservation laws associated with the governing model. Finally, the physical features of the pertinent parameters are discussed in detail through several graphs.
40
Budarin, Vitaliy. "Analyzing the influence of a particle's linear and angular velocity on the equations of liquid motion." Eastern-European Journal of Enterprise Technologies 1, no. 5 (109) (February 26, 2021): 23–30. http://dx.doi.org/10.15587/1729-4061.2021.225209.
Full textAbstract:
This paper has analyzed the equation of motion in terms of stresses (Navier), as well as its two special cases for an incompressible viscous current. One is the Stokes (Navier-Stokes) equation, and the other was derived with fewer restrictions. It has been shown that the Laplace equation of linear velocity can be represented as a function of two variables ‒ the linear and angular speed of particle rotation. To describe the particle acceleration, all motion equations employed a complete derivative from speed in the Gromeka-Lamb form, which depends on the same variables. Taking into consideration the joint influence of linear and angular velocity allows solving a task of the analytical description of a turbulent current within the average model. A given method of analysis applies the provision of general physics that examines the translational and rotational motion. The third type of mechanical movement, oscillatory (pulsation), was not considered in the current work. A property related to the Stokes equation decomposition has been found; a block diagram composed of equations and conditions has been built. It is shown that all equations for viscous liquid have their own analog in a simpler model of non-viscous fluid. That makes it easier to find solutions to the equations for the viscous flow. The Stokes and Navier equations were used to solve two one-dimensional problems, which found the distribution of speed along the normal to the surface at the flow on a horizontal plate and in a circular pipe. Both solution methods produce the same result. No solution for the distribution of speed along the normal to the surface in a laminar sublayer could be found. A relevant task related to the mathematical part is to solve the problem of closing the equations considered. A comparison of the theoretical and empirical equations has been performed, which has made it possible to justify the assumption that a rarefied gas is the Stokes liquid
41
Shobukhov, Andrey. "Mathematical Model for the Electrokinetic Instability of Electrolyte Flow." EPJ Web of Conferences 224 (2019): 02003. http://dx.doi.org/10.1051/epjconf/201922402003.
Full textAbstract:
We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.
42
Kendall, S. R., and H. V. Rao. "Detection of multiple solutions using a mid-cell back substitution technique applied to computational fluid dynamics." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 214, no. 11 (November 1, 2000): 1401–7. http://dx.doi.org/10.1243/0954406001523371.
Full textAbstract:
Computational models for fluid flow based on the Navier-Stokes equations for compressible fluids led to numerical procedures requiring the solution of simultaneous non-linear algebraic equations. These give rise to the possibility of multiple solutions, and hence there is a need to monitor convergence towards a physically meaningful flow field. The number of possible solutions that may arise is examined, and a mid-cell back substitution technique (MCBST) is developed to detect and avoid convergence towards apparently spurious solutions. The MCBST was used successfully for flow modelling in micron-sized flow passages, and was found to be particularly useful in the early stages of computation, optimizing the speed of convergence.
43
DiBenedetto, Michelle H., and Nicholas T. Ouellette. "Preferential orientation of spheroidal particles in wavy flow." Journal of Fluid Mechanics 856 (October 12, 2018): 850–69. http://dx.doi.org/10.1017/jfm.2018.738.
Full textAbstract:
We report a theoretical study of the angular dynamics of small, non-inertial spheroidal particles in a linear wave field. We recover the observation recently reported by DiBenedetto et al. (J. Fluid Mech., vol. 837, 2018, pp. 320–340) that the orientation of these spheroids tends to a stable limit cycle consisting of a preferred value with a superimposed oscillation. We show that this behaviour is a consequence of finite wave amplitude and is the angular analogue of Stokes drift. We derive expressions for both the preferred orientation of the particles, which depends only on particle shape, and the amplitude of the oscillation about this preferred value, which additionally depends on the wave parameters and the depth of the particle in the water column.
44
Sekrieru, G. V. "NALYSIS OF FORMATION OF VISCOUS HEAT CONDUCTING GAS FLOWSFOR SMALL PERTURBATIONS OF PARAMETERS." EurasianUnionScientists 5, no. 5(74) (June 14, 2020): 61–66. http://dx.doi.org/10.31618/esu.2413-9335.2020.5.74.757.
Full textAbstract:
Formation of one-dimensional flows arising as a result of interaction of a viscous heat-conducting gas and a heat-conducting wall in the process of reflection of a normally incident weak shock wave is considered. Formation of the flow field with small perturbations of parameters is studied on the basis of the Navier -Stokes equations linearized around the values of the parameters in the initial state, and the wall temperature distribution is modeled by linear heat equation. Analytical solutions of the linearized system of equations are obtained that allow one to analyze the influence of viscosity, thermal conductivity, and other factors on the formation of a continuous flow field structure with the formation of dissipative and ideal inviscid and non-heat-conducting zones.
45
Izumi, Tomoki, and Junya Mizuta. "Numerical model for non-Darcy flow through coarse porous media using the moving particle simulation method." Thermal Science 22, no. 5 (2018): 1955–62. http://dx.doi.org/10.2298/tsci171231271i.
Full textAbstract:
A numerical model for non-Darcy flow, which occurs when water moves through coarse porous media under high Reynolds number, is developed. The governing equation for incompressible viscous flow through porous media is composed of a continuity equation and a momentum equation, which is the Navier-Stokes equation with an additional non-linear resistance term based on Forchheimer?s law. For the discretization scheme, moving particle simulation method is employed. In order to assess the model validity, seepage experiments in different kinds of coarse porous media are implemented, and then reproducibility of the numerical results is examined. From the results, it is found that the computational flow velocities at middle part of porous media are in good agreement with experimental ones while velocities at outflow end are overestimated.
46
ABID, MALEK. "Nonlinear mode selection in a model of trailing line vortices." Journal of Fluid Mechanics 605 (May 23, 2008): 19–45. http://dx.doi.org/10.1017/s0022112008001377.
Full textAbstract:
Nonlinear mode selection, from initial random Gaussian field perturbations, in a model of trailing line vortices (swirling jets), in the breakdown regime, is addressed by direct numerical simulations with a Reynolds number equal to 1000. A new concept of mode activity in the nonlinear evolution is introduced. The selected modes, according to their activities, are reported and related to strain eigenvectors (with maximum eigenvalues) of the basic flow corresponding to the trailing line vortex under consideration. The selected modes are also related to results from the linear eigenmode (exponential growth) instability theory using the concept of dispersion relation envelope. It is found that the global mode hypothesis of the linear eigenmode theory is violated near the flow axis when the swirl number increases. However, far from the flow axis the linear eigenmode theory is in good agreement with the nonlinear evolution in the breakdown regime. The discrepancy between the nonlinear evolution and the linear eigenmode theory is related to the transient growth of optimal perturbations resulting from the non-normality of the linearized Navier–Stokes equations about shear flows. A clear distinction between an eigenmode, an optimal perturbation (non-modal) and a direct numerical simulation (DNS) mode is made. It is shown that the algebraic (transient) growth contributions from the inviscid continuous spectrum could trigger nonlinearities near the flow axis. The DNS mode selected in the nonlinear regime coincides with the long-wave eigenmode benefiting from the algebraic growth in the linear regime. This eigenmode is different from the short-wave eigenmode with the absolute maximum exponential growth. Although it is promoted by transients, in the linear regime, the long-wave component is selected nonlinearly.
47
Del Negro, C., L. Fortuna, and A. Vicari. "Modelling lava flows by Cellular Nonlinear Networks (CNN): preliminary results." Nonlinear Processes in Geophysics 12, no. 4 (May 19, 2005): 505–13. http://dx.doi.org/10.5194/npg-12-505-2005.
Full textAbstract:
Abstract. The forecasting of lava flow paths is a complex problem in which temperature, rheology and flux-rate all vary with space and time. The problem is more difficult to solve when lava runs down a real topography, considering that the relations between characteristic parameters of flow are typically nonlinear. An alternative approach to this problem that does not use standard differential equation methods is Cellular Nonlinear Networks (CNNs). The CNN paradigm is a natural and flexible framework for describing locally interconnected, simple, dynamic systems that have a lattice-like structure. They consist of arrays of essentially simple, nonlinearly coupled dynamic circuits containing linear and non-linear elements able to process large amounts of information in real time. Two different approaches have been implemented in simulating some lava flows. Firstly, a typical technique of the CNNs to analyze spatio-temporal phenomena (as Autowaves) in 2-D and in 3-D has been utilized. Secondly, the CNNs have been used as solvers of partial differential equations of the Navier-Stokes treatment of Newtonian flow.
48
Yang, Jie, and Song Ping Wu. "An Immersed Boundary Method for Compressible Flows with Complex Boundaries." Applied Mechanics and Materials 477-478 (December 2013): 281–84. http://dx.doi.org/10.4028/www.scientific.net/amm.477-478.281.
Full textAbstract:
An immersed boundary method based on the ghost-cell approach is presented in this paper. The compressible Navier-Stokes equations are discretized using a flux-splitting method for inviscid fluxes and second-order central-difference for the viscous components. High-order accuracy is achieved by using weighted essentially non-oscillatory (WENO) and Runge-Kutta schemes. Boundary conditions are reconstructed by a serial of linear interpolation and inverse distance weighting interpolation of flow variables in fluid domain. Two classic flow problems (flow over a circular cylinder, and a NACA 0012 airfoil) are simulated using the present immersed boundary method, and the predictions show good agreement with previous computational results.
49
Martin, N., and J. Monnier. "Of the gradient accuracy in Full-Stokes ice flow model: basal slipperiness inference." Cryosphere Discussions 7, no. 4 (August 5, 2013): 3853–97. http://dx.doi.org/10.5194/tcd-7-3853-2013.
Full textAbstract:
Abstract. This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. We quantify the ability to identify the basal slipperiness for such methods with a non-linear friction law. The complete adjoint problem is solved and a comparison with the so called "self-adjoint" method, neglecting the viscosity dependency to the velocity, common in glaciology, is carried out. A lower bound of identifiable wavelengths of 10 ice thickness in the friction coefficient is established, when using the full adjoint method, while the "self-adjoint" method is limited to a maximum of 20 ice thickness wavelengths. In addition, the full adjoint method demonstrates a better robustness and reliability for the parameter identification process. The derivation of the adjoint model using algorithmic differentiation leads to formulate a generalization of the "self-adjoint" approximation towards an incomplete adjoint method, adjustable in precision and computational burden.
50
CARNEVALE, G. F., R. C. KLOOSTERZIEL, P. ORLANDI, and D. D. J. A. van SOMMEREN. "Predicting the aftermath of vortex breakup in rotating flow." Journal of Fluid Mechanics 669 (January 11, 2011): 90–119. http://dx.doi.org/10.1017/s0022112010004945.
Full textAbstract:
A method for predicting the outcome of vortex breakup in a rotating flow is introduced. The vortices dealt with here are subject to both centrifugal and barotropic instabilities. The prediction of the aftermath of the breakup relies on knowing how both centrifugal and barotropic instabilities would equilibrate separately. A theoretical model for non-linear equilibration in centrifugal instability is wedded to two-dimensional simulation of barotropic instability to predict the final vortices that emerge from the debris of the original vortex. This prediction method is tested against three-dimensional Navier–Stokes simulations. For vortices in which a rapid centrifugal instability triggers a slower barotropic instability, the method is successful both qualitatively and quantitatively. The skill of the prediction method decreases as the time scales of the two instabilities become comparable.