Relevant bibliographies by topics / Non-linear Stokes flow

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Non-linear Stokes flow'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Non-linear Stokes flow"

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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.

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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
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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.

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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.
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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.

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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.
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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.

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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.
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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.

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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.
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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.

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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.

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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.
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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.

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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.
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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.

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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.
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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.

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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.
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Dissertations / Theses on the topic "Non-linear Stokes flow"

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Helanow, Christian. "Basal boundary conditions, stability and verification in glaciological numerical models." Doctoral thesis, Stockholms universitet, Institutionen för naturgeografi, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-141641.

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To increase our understanding of how ice sheets and glaciers interact with the climate system, numerical models have become an indispensable tool. However, the complexity of these systems and the natural limitation in computational power is reflected in the simplifications of the represented processes and the spatial and temporal resolution of the models. Whether the effect of these limitations is acceptable or not, can be assessed by theoretical considerations and by validating the output of the models against real world data. Equally important is to verify if the numerical implementation and computational method accurately represent the mathematical description of the processes intended to be simulated. This thesis concerns a set of numerical models used in the field of glaciology, how these are applied and how they relate to other study areas in the same field. The dynamical flow of glaciers, which can be described by a set of non-linear partial differential equations called the Full Stokes equations, is simulated using the finite element method. To reduce the computational cost of the method significantly, it is common to lower the order of the used elements. This results in a loss of stability of the method, but can be remedied by the use of stabilization methods. By numerically studying different stabilization methods and evaluating their suitability, this work contributes to constraining the values of stabilization parameters to be used in ice sheet simulations. Erroneous choices of parameters can lead to oscillations of surface velocities, which affects the long term behavior of the free-surface ice and as a result can have a negative impact on the accuracy of the simulated mass balance of ice sheets. The amount of basal sliding is an important component that affects the overall dynamics of the ice. A part of this thesis considers different implementations of the basal impenetrability condition that accompanies basal sliding, and shows that methods used in literature can lead to a difference in velocity of 1% to 5% between the considered methods. The subglacial hydrological system directly influences the glacier's ability to slide and therefore affects the velocity distribution of the ice. The topology and dominant mode of the hydrological system on the ice sheet scale is, however, ill constrained. A third contribution of this thesis is, using the theory of R-channels to implement a simple numerical model of subglacial water flow, to show the sensitivity of subglacial channels to transient processes and that this limits their possible extent. This insight adds to a cross-disciplinary discussion between the different sub-fields of theoretical, field and paleo-glaciology regarding the characteristics of ice sheet subglacial hydrological systems. In the study, we conclude by emphasizing areas of importance where the sub-fields have yet to unify: the spatial extent of channelized subglacial drainage, to what degree specific processes are connected to geomorphic activity and the differences in spatial and temporal scales. As a whole, the thesis emphasizes the importance of verification of numerical models but also acknowledges the natural limitations of these to represent complex systems. Focusing on keeping numerical ice sheet and glacier models as transparent as possible will benefit end users and facilitate accurate interpretations of the numerical output so it confidently can be used for scientific purposes.

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.


Greenland Analogue Project
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Ivan, Lucian. "Development of High-order CENO Finite-volume Schemes with Block-based Adaptive Mesh Refinement (AMR)." Thesis, 2011. http://hdl.handle.net/1807/29759.

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A high-order central essentially non-oscillatory (CENO) finite-volume scheme in combination with a block-based adaptive mesh refinement (AMR) algorithm is proposed for solution of hyperbolic and elliptic systems of conservation laws on body- fitted multi-block mesh. The spatial discretization of the hyperbolic (inviscid) terms is based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact least-squares reconstruction technique following from a fixed central stencil with a monotonicity preserving limited piecewise linear reconstruction algorithm. The limited reconstruction is applied to computational cells with under-resolved solution content and the unlimited k-exact reconstruction procedure is used for cells in which the solution is fully resolved. Switching in the hybrid procedure is determined by a solution smoothness indicator. The hybrid approach avoids the complexity associated with other ENO schemes that require reconstruction on multiple stencils and therefore, would seem very well suited for extension to unstructured meshes. The high-order elliptic (viscous) fluxes are computed based on a k-order accurate average gradient derived from a (k+1)-order accurate reconstruction. A novel h-refinement criterion based on the solution smoothness indicator is used to direct the steady and unsteady refinement of the AMR mesh. The predictive capabilities of the proposed high-order AMR scheme are demonstrated for the Euler and Navier-Stokes equations governing two-dimensional compressible gaseous flows as well as for advection-diffusion problems characterized by the full range of Peclet numbers, Pe. The ability of the scheme to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content (i.e., shocks and other discontinuities) is shown for a range of problems. Moreover, the ability to perform mesh refinement in regions of smooth but under-resolved and/or non-smooth solution content to achieve the desired resolution is also demonstrated.
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Books on the topic "Non-linear Stokes flow"

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Yousuff, Hussaini M., and Institute for Computer Applications in Science and Engineering., eds. Non-linear evolution of a second mode wave in supersonic boundary layers. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1989.

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Yousuff, Hussaini M., and Institute for Computer Applications in Science and Engineering., eds. Non-linear evolution of a second mode wave in supersonic boundary layers. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1989.

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Book chapters on the topic "Non-linear Stokes flow"

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Moffatt, H. K., and V. Mak. "Corner Singularities in Three-Dimensional Stokes Flow." In IUTAM Symposium on Non–Linear Singularities in Deformation and Flow, 21–26. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4736-1_3.

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Conference papers on the topic "Non-linear Stokes flow"

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Nieto, César, Henry Power, Mauricio Giraldo, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Boundary Integral Equation Approach for Stokes Flow with Non-Linear Slip Boundary Condition." In ICNAAM 2010: International Conference of Numerical Analysis and Applied Mathematics 2010. AIP, 2010. http://dx.doi.org/10.1063/1.3497909.

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Koh, Wonhyuk, Sungwoo Kang, Myunghwan Cho, and Jung Yul Yoo. "Three-Dimensional Steady Flow in Non-Linear Elastic Collapsible Tubes." In ASME 2009 Fluids Engineering Division Summer Meeting. ASMEDC, 2009. http://dx.doi.org/10.1115/fedsm2009-78343.

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Three-dimensional fluid-structure interaction problem arising from steady flow in non-linear elastic tube is studied numerically by using a finite element software, ADINA. Strain-energy density function is used for non-linear elastic analysis of solid material. Navier-Stokes equation coupled with elastic wall condition is solved for the fluid flow. To simulate interactions between the fluid and the solid domains, arbitrary Lagrangian-Eulerian (ALE) formulation is utilized. For validation, thin-walled linear elastic collapsible tubes is computed and compared with previous numerical results. The tube collapses into the buckling mode N = 2 and the results are in excellent agreement with a previous study. Then, the results for linear elastic tube are compared with those for non-linear elastic tube to show the effects of non-linear elasticity of the wall. The wall material is considered to be non-linear hyperelastic and isotropic. The non-linear elastic wall shows the tendency to preserve its shape more than the linear material. The deformation patterns, pressure distributions of the tube with non-linear elastic material are significantly different from those with linear elastic material.
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Jasak, Hrvoje, and Gregor Cvijetić. "Implementation and Validation of the Harmonic Balance Method for Temporally Periodic Non–Linear Flows." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56254.

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An efficient method for tackling non-linear, temporally–periodic incompressible flows is presented in this paper. Assuming temporally fully periodic flow, Harmonic Balance method deploys Fourier transformation in order to formulate transient problem as a multiple quasi-steady state problems. The method is implemented in OpenFOAM and developed for a general transport equation and incompressible Navier–Stokes equations. Validation is presented on three test cases: oscillating scalar case for scalar transport validation, a flow around a 2D NACA airfoil and a 3D Onera M6 wing for turbulent incompressible Navier–Stokes validation. For all test cases Harmonic Balance results are compared to transient simulation results. Verification of the model is performed by changing the number of harmonics for all test cases.
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Bhattacharjee, Subir, and Noor Al Quddus. "Effects of Non-Linearity of the Momentum Conservation Equation During Electrokinetic Transport in Nano and Microchannels." In ASME 2010 8th International Conference on Nanochannels, Microchannels, and Minichannels collocated with 3rd Joint US-European Fluids Engineering Summer Meeting. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30163.

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Electrokinetic transport phenomena, such as electroosmosis, streaming potential, electrophoresis, and sedimentation potential, are central to many micro- and nano-channel flows. During continuum modeling of such phenomena, incorporation of the electrical body force term can make the fluid momentum conservation equation highly non-linear. This non-linearity is often ignored in small-scale electrokinetic flow modeling because of our implicit reliance on the linearity of the Stokes equations for low Reynolds number flows. In this paper, ramifications of this non-linear Stokes equation in electrokinetic flows will be described with examples of our recent studies on pressure driven flows through porous media for electrokinetic power generation, electroosmotic flow of charged entities in nanochannels, and flow of DNA through self-assembled porous media under pulsed electric fields.
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Polly, James B., and J. M. McDonough. "Application of the Poor Man’s Navier–Stokes Equations to Real-Time Control of Fluid Flow." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63564.

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Control of fluid flow is an important, and quite underutilized process possessing significant potential benefits ranging from avoidance of separation and stall on aircraft wings and reduction of friction factors in oil and gas pipelines to mitigation of noise from wind turbines. But the Navier–Stokes (N.–S.) equations governing fluid flow consist of a system of time-dependent, multi-dimensional, non-linear partial differential equations (PDEs) which cannot be solved in real time using current, or near-term foreseeable, computing hardware. The poor man’s Navier–Stokes (PMNS) equations comprise a discrete dynamical system that is algebraic—hence, easily (and rapidly) solved—and yet which retains many (possibly all) of the temporal behaviors of the full (PDE) N.–S. system at specific spatial locations. In this paper we outline derivation of these equations and present a short discussion of their basic properties. We then consider application of these equations to the problem of control by adding a control force. We examine the range of PMNS equation behaviors that can be achieved by changing values of this control force, and, in particular, consider controllability of this (non-linear) system via numerical experiments. Moreover, we observe that the derivation leading to the PMNS equations is very general, and, at least in principle, it can be applied to a wide variety of problems governed by PDEs and (possibly) time-delay ordinary differential equations such as, for example, models of machining processes.
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Zheng, Yingsong, Jason M. Reese, Thomas J. Scanlon, and Duncan A. Lockerby. "Scaled Navier-Stokes-Fourier Equations for Gas Flow and Heat Transfer Phenomena in Micro- and Nanosystems." In ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2006. http://dx.doi.org/10.1115/icnmm2006-96066.

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A new hydrodynamic model is proposed in order to model critical phenomena in gas flows at the micro- and nanoscale. A scaling is applied to the conventional Navier-Stokes-Fourier equations, mathematically equivalent to using an “effective” viscosity and an “effective” thermal conductivity in the original linear constitutive relations. Expressions for this “effective” viscosity and this “effective” thermal conductivity are obtained from two ideal half-space flow problems: Kramer’s problem, and the temperature jump problem. Our model ensures the correct viscous stress is maintained in the region of the wall in isothermal flow (or the correct heat flux in the pure heat transfer situation); it is only the relationships between stress and the corresponding near-wall strain-rate, and between heat flux and the near-wall temperature gradient, that are altered. The advantage of our model over the traditional linear hydrodynamic model is that the non-equilibrium flow in the Knudsen layer is described. Its advantage over higher-order hydrodynamic models for rarefied gas flows is that no additional boundary conditions are required (although there are minor changes in the slip/jump coefficients), so modifications of current CFD codes to incorporate this new model would be minimal. As an application example, we solve for the velocity profiles and drag force on a micro-sphere moving in a gas at different Knudsen numbers (Kn). For this problem, our model gives excellent results for Kn<0.1 and accptable results up to Kn = 0.25: this is considerably better that the tradition Navier-Stokes model with non-scaled constitutive relations.
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Harvey, Neil W., Martin G. Rose, Mark D. Taylor, Shahrokh Shahpar, Jonathan Hartland, and David G. Gregory-Smith. "Non-Axisymmetric Turbine End Wall Design: Part I — Three-Dimensional Linear Design System." In ASME 1999 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/99-gt-337.

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A linear design system, already in use for the forward and inverse design of three-dimensional turbine aerofoils, has been extended for the design of their end walls. This paper shows how this method has been applied to the design of a non-axisymmetric end wall for a turbine rotor blade in linear cascade. The calculations show that non-axisymmetric end wall profiling is a powerful tool for reducing secondary flows, in particular the secondary kinetic energy and exit angle deviations. Simple end wall profiling is shown to be at least as beneficial aerodynamically as the now standard techniques of differentially skewing aerofoil sections up the span, and (compound) leaning of the aerofoil. A design is presented which combines a number of end wall features aimed at reducing secondary loss and flow deviation. The experimental study of this geometry, aimed at validating the design method, is the subject of the second part of this paper. The effects of end wall perturbations on the flow field are calculated using a 3-D pressure correction based Reynolds Averaged Navier-Stokes CFD code. These calculations are normally performed overnight on a cluster of work stations. The design system then calculates the relationships between perturbations in the end wall and resulting changes in the flow field. With these available, linear superposition theory is used to enable the designer to investigate quickly the effect on the flow field of many combinations of end wall shapes (a matter of minutes for each shape).
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Hirsch, Charles, and Andrei E. Khodak. "Application of Different Turbulence Models for Duct Flow Simulation With Reduced and Full Navier-Stokes Equations." In ASME 1995 International Gas Turbine and Aeroengine Congress and Exposition. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/95-gt-145.

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An S-shaped diffusing duct flow is analysed with various turbulence models: standard high-Reynolds-number k-ε model with wall functions, a low-Reynolds-number k-ε model, and an explicit non-linear algebraic Reynolds stress closure model (ASM). In addition, computations were obtained with parabolic and partially-parabolic approximations along with solutions of the full Navier-Stokes equations. Results of the numerical simulation are compared with LDA measurements of the turbulent flow as reported by Whitelaw and Yu (1993). Detailed comparisons of mean velocity and Reynolds stress distributions are presented. It is shown that the partially-parabolic approach gives a significant improvement over parabolic approximation in predicting mean velocities and pressure distributions. However, the turbulence models used are still not able to reproduce all the observed flow features, although the ASM results appear to be slightly but consistently closer to the experimental data.
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Yang, Ru, and Chin-Sheng Wang. "A Micro-Channel Flow and Heat Transfer Study by Lattice Boltzmann Method." In ASME 2003 1st International Conference on Microchannels and Minichannels. ASMEDC, 2003. http://dx.doi.org/10.1115/icmm2003-1047.

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A Lattice Boltzmann method is employed to investigate the flow characteristics and the heat transfer phenomenon between two parallel plates separated by a micro-gap. A nine-velocity model and an internal energy distribution model are used to obtain the mass, momentum and temperature distributions. It is shown that for small Knudsen numbers (Kn), the current results are in good agreement with those obtained from the traditional Navier-Stokes equation with non-slip boundary conditions. As the value of Kn is increased, it is found that the non-slip condition may no longer be valid at the wall boundary and that the flow behavior changes to one of slip-flow. In slip flow regime, the present results is still in good agreement with slip-flow solution by Navier Stokes equations. The non-linear nature of the pressure and friction distribution for micro-channel flow is gieven. Finally, the current investigation presents a prediction of the temperature distribution for micro-channel flow under the imposed conditions of an isothermal boundary.
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Apte, Shrinivas G., and Brian H. Dennis. "Pseudo Compressible Mixed Interpolation Finite Element Method for Solving Three Dimensional Navier-Stokes Equations." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13484.

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A pseudo compressible finite element method for solving three dimensional incompressible Navier-Stokes equations is presented. A physical problem discretized using tetrahedral elements with linear and quadratic interpolation functions for pressure and velocity variables respectively is then marched in time by using implicit time marching scheme based on finite differencing. The possible formation of indefinite matrix due to incompressibility constraint is avoided by inserting an artificial/pseudo time dependent term (Chorin, 1974) into the continuity equation that is eliminated when steady state is reached. This definite matrix system can then be solved using standard pre-conditioners and iterative solvers. Solutions for pressure driven flows obtained using this method are validated with the ones obtained from a standard problem of flow over a cylinder and also with numerical benchmark case of a 3-D laminar flow around an obstacle. An object oriented C++ program was developed which uses exact integrals of shape functions in its calculations rather than numerical integrations. This program was tested with different values of artificial compressibility factor (β), Reynolds numbers (Re) and grid sizes (number of Elements) and time steps (dt). The effect of these parameters on the the number of linear solver iterations required for convergence is studied efficiently using the non-dimensional numbers Pseudo Compressibility Number (PCN) and Elemental Reynolds Number (ERe). Although the relationship between the linear solver performance and these two non dimensional numbers remain complicated, it is found that there exists an optimum range of PCN as a function of ERe for which the solution convergence can be obtained with the minimum number of iterations.
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