Viscous Flow Computations Research Articles

Pressure based finite volume method for calculation of compressible viscous gas flows

A pressure based, iterative finite volume method is developed for calculation of compressible, viscous, heat conductive gas flows at all speeds. The method does not need the use of under-relaxation coefficient in order to ensure a convergence of the iterative process. The method is derived from a general form of system of equations describing the motion of compressible, viscous gas. An emphasis is done on the calculation of gaseous microfluidic problems. A fast transient process of gas wave propagation in a two-dimensional microchannel is used as a benchmark problem. The results obtained by using the new method are compared with the numerical solution obtained by using SIMPLE (iterative) and PISO (non-iterative) methods. It is shown that the new iterative method is faster than SIMPLE. For the considered problem the new method is slightly faster than PISO as well. Calculated are also some typical microfluidic subsonic and supersonic flows, and the Rayleigh–Bénard convection of a rarefied gas in continuum limit. The numerical results are compared with other analytical and numerical solutions.

Steady saturation distribution in hydrophobic gas-diffusion layers of polymer electrolyte membrane fuel cells: A pore-network study

A pore-network model is developed to simulate liquid water transport in a hydrophobic gas-diffusion layer (GDL) during the operation of polymer electrolyte membrane fuel cells (PEMFCs). The steady saturation distribution in GDLs is determined through a numerical procedure using a pore-network model combined with invasion-percolation path-finding and subsequent viscous two-phase flow calculation. The simulation results indicate that liquid water transport in hydrophobic GDLs is a strongly capillary-driven process that almost reaches the pure invasion-percolation limit with zero capillary number. A uniform flux condition is found to better reflect the actual phenomenon occurring at the inlet boundary for liquid water entering a GDL than a uniform pressure condition. The simulation further clarifies the effect of the invaded pore fraction at a uniform-flux inlet boundary in modifying water transport in GDLs. Finally, the effect of the GDL thickness on the steady saturation distribution is investigated.

Remapping-free ALE-type kinetic method for flow computations

Based on the integral form of the fluid dynamic equations, a finite volume kinetic scheme with arbitrary control volume and mesh velocity is developed. Different from the earlier unified moving mesh gas-kinetic method [C.Q. Jin, K. Xu, An unified moving grid gas-kinetic method in Eulerian space for viscous flow computation, J. Comput. Phys. 222 (2007) 155–175], the coupling of the fluid equations and geometrical conservation laws has been removed in order to make the scheme applicable for any quadrilateral or unstructured mesh rather than parallelogram in 2D case. Since a purely Lagrangian method is always associated with mesh entangling, in order to avoid computational collapsing in multidimensional flow simulation, the mesh velocity is constructed by considering both fluid velocity (Lagrangian methodology) and diffusive velocity (Regenerating Eulerian mesh function). Therefore, we obtain a generalized Arbitrary-Lagrangian–Eulerian (ALE) method by properly designing a mesh velocity instead of re-generating a new mesh after distortion. As a result, the remapping step to interpolate flow variables from old mesh to new mesh is avoided. The current method provides a general framework, which can be considered as a remapping-free ALE-type method. Since there is great freedom in choosing mesh velocity, in order to improve the accuracy and robustness of the method, the adaptive moving mesh method [H.Z. Tang, T. Tang, Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal. 41 (2003) 487–515] can be also used to construct a mesh velocity to concentrate mesh to regions with high flow gradients.

An immersed boundary/level-set method for incompressible viscous flows in complex geometries with good conservation properties

This paper concerns the development of a new Cartesian grid / immersed boundary (IB) method for the computation of incompressible viscous flows in irregular geometries. In IB methods, the computational grid is not aligned with the irregular boundary, and of upmost importance for accuracy and stability is the discretization in cells which are “cut" by the boundary. In this paper, we present an IB method (the LS-STAG method) based on the Cartesian MAC method where the irregular boundary is represented by its level-set function. This implicit representation of the immersed boundary enables us to discretize efficiently the fluxes in the cut-cells by imposing the strict conservation of total kinetic energy at the discrete level. The accuracy and robustness of our method are assessed on benchmark flows.

Inverse design of transonic airfoils using genetic algorithm and a new parametric shape method

The inverse design of transonic airfoils is carried out using genetic algorithm and different shape parameterization methods. A new technique for airfoil shape parameterization is presented considering the features of the transonic flow. The method is then applied to several airfoil inverse design problems with defined geometry or surface pressure distributions. The influence of parametric shape methods on the accuracy and computational cost of the design process are investigated for inviscid and viscous flow problems. The fitness function evaluation is carried out using an unstructured grid finite volume flow solver. It is shown that the new shape parameterization method is able to reduce the total computational time by about 50% in the inverse design of transonic airfoils, particularly when viscous flow calculations are concerned.

An immersed boundary/level-set method for incompressible viscous flows in complex geometries with good conservation properties

This paper concerns the development of a new Cartesian grid / immersed boundary (IB) method for the computation of incompressible viscous flows in irregular geometries. In IB methods, the computational grid is not aligned with the irregular boundary, and of upmost importance for accuracy and stability is the discretization in cells which are “cut by the boundary. In this paper, we present an IB method (the LS-STAG method) based on the Cartesian MAC method where the irregular boundary is represented by its level-set function. This implicit representation of the immersed boundary enables us to discretize efficiently the fluxes in the cut-cells by imposing the strict conservation of total kinetic energy at the discrete level. The accuracy and robustness of our method are assessed on benchmark flows.

Geometrical Installation and Deformation Effects in High-Lift Flows

For a three-dimensional half-model high-lift configuration in a wind-tunnel environment, flow separation near maximum lift is influenced by the presence of geometric details. To examine the influence of these details, three computationalfluid dynamics based studies are carried out. The objective is to examine the influence of pressure tube bundles, wind-tunnel walls andmodelmounting, and the effect ofmodel deformation for a high-lift wind-tunnel halfmodel. Viscous flow computations for a high-lift configuration including pressure tubes and wind-tunnel walls (and model mounting) are performed. Experiences gathered with these flow computations are reported and comparisons to wind-tunnel experiments are made. Four methods are deployed in order to study aeroelastic effects, namely, a lifting surface based aeroelastic method and three fully coupledmethods. Three structural models of a high-lift wing are developed. Experiences with three fully coupled methods are reported and benefits and shortcomings are identified. It is concluded that geometrical installation and deformation effects for a half-model high-lift wing in a wind-tunnel environment are significant. The mounting of the half-model has the most significant effect on the aerodynamic coefficients.

Flow-induced forces arising during the impact of two circular cylinders

This paper presents numerical simulations of two-dimensional incompressible flow around two circular cylinders in relative motion, which may result in impact. Viscous flow computations are carried out using a streamfunction–vorticity method for two equal-diameter cylinders undergoing a two-dimensional impact in otherwise stationary fluid and for cases of similar impact of two cylinders in a steady incident flow. These results are supported by potential flow calculations carried out using a Möbius conformal transformation and infinite arrays of image singularities. The inviscid flow results are compared with other published work and show that the inviscid forces induced on the cylinders have an inverse square root singularity with respect to the time to impact. All impacts considered in this paper result from steady motion of the cylinders along the line joining their centres.

Deriving mathematical manoeuvring models for bare ship hulls using viscous flow calculations

To assess the manoeuvrability of ships at the early design stage, reliable simulation models are required. Traditionally, these tools have used empiric descriptions of the forces and moments on the ship’s hull. However, nowadays new computational techniques are available enabling more reliable predictions of the manoeuvring behaviour of ships. In this article, a mathematical manoeuvring model to predict the forces and moments on a bare ship hull is presented. Special attention is paid to application in simulators in which also astern or sideways manoeuvring should be possible. The hydrodynamic derivatives in this model were determined by a hybrid approach using results of viscous flow calculations supplemented by semi-empirical methods. It was demonstrated that this approach leads to a considerable improvement in the prediction of the forces and moments on the ship compared to using conventional empiric derivatives published in the literature.

Development of CMPS Method for Accurate Water-Surface Tracking in Breaking Waves

A Corrected Moving Particle Semi-implicit (CMPS) method is proposed for the accurate tracking of water surface in breaking waves. The original formulations of standard MPS method are revisited from the view point of momentum conservation. Modifications and corrections are made to ensure the momentum conservation in a particle-based calculation of viscous incompressible free-surface flows. A simple numerical test demonstrates the excellent performance of the CMPS method in exact conservation of linear momentum and significantly enhanced preservation of angular momentum. The CMPS method is applied to the simulation of plunging breaking and post-breaking of solitary waves. Qualitative and quantitative comparisons with the experimental data confirm the high capability and precision of the CMPS method. A tensor-type strain-based viscosity is also proposed to further enhanced CMPS reproduction of a splash-up.

Flow over a thin circular disk at low to moderate Reynolds numbers

Computation of viscous flow over a circular disk of aspect ratio 10 (thickness/diameter) in the Reynolds number (Re) range of 10 to 300 was performed. The following flow regimes were observed: (I) steady axisymmetric flow whenRe< 135, with the presence of a toroidal vortex behind the disk; (II) regular bifurcation with loss of azimuthal symmetry but with planar symmetry and a double-threaded wake, for 135 ≤Re< 155; (III) three-dimensional flow with periodic shedding of double-sided hairpin-shaped vortex structures and periodic motion of the separation region for 155 ≤Re< 172; (IV) regular shedding of double-sided hairpin-shaped vortex structures with planar and spatio-temporal symmetry for 172 ≤Re< 280; (V) periodic three-dimensional flow with irregular rotation of the separation region whenRe= 280–300. This transition process for the disk differs from that for the sphere as we observe a loss of the symmetry plane in Regime III due to a twisting motion of the axial vorticity strands in the wake of the disk. The periodic flow was characterized by double-sided hairpin structures, unlike the one-sided vortex loops observed for the sphere. This resulted in the drag coefficient oscillating at twice the frequency of the axial velocity. In Regime IV, the vortex loops were shed from diametrically opposite locations and with equal strength, resulting in the lift coefficient oscillating symmetrically about a zero mean. These results imply the presence of spatio-temporal symmetry.

Residual layer thickness in nanoimprint

A refined coarse-grain method for simultaneous calculation of the resist viscous flow in nanoimprint lithography and the stamp/substrate deformation is presented. The method has been realized in an...

A residual-based scheme for computing compressible flows on unstructured grids

A second-order residual-based compact scheme, initially developed for computing flows on Cartesian and curvilinear grids, is extended to general unstructured grids in a finite-volume framework. The scheme is applied to the computation of several inviscid and viscous compressible flows governed by the Euler and Navier–Stokes equations. Its efficiency and accuracy properties are compared with those of conventional second-order upwind schemes based on variable reconstruction.

Viscous-flow calculations for bare hull DARPA SUBOFF submarine at incidence

By order of the Defence Materiel Organisation (DMO) of the Royal Netherlands Navy (RNLN) the Maritime Research Institute Netherlands (MARIN) conducts studies regarding the hydrodynamics and manoeuvring capabilities of submarines. Together, they are actively involved in the Submarine Hydrodynamics Working Group (SHWG). The SHWG is a group of international navies from Australia, Canada, Germany, France, UK, USA and The Netherlands. In general, the navies team up with local research institutes. Informal meetings are held every eighteen months to discuss non-classified subjects related to hydrodynamics of submarines. Within the SHWG, a study was initiated to assess the state-of-the-art in computations of viscous flows around a submarine and to accelerate and improve research and development of numerical submarine hydrodynamics. In the study, a common testcase was defined for which each navy was asked to generate predictions based on their best approach in viscous-flow calculations. The central question in the study is to demonstrate the capability of viscous-flow solvers to reproduce the flow field around and the forces acting on a submarine hull form. This article presents the work conducted by the Dutch team.

REFINED SIMULATION OF SOLITARY PLUNGING BREAKER BY CMPS METHOD

As a meshfree particle method, the Moving Particle Semi-implicit (MPS) method is ideally suited for simulating the complicated behaviour of water surface with fragmentation. In this paper, the original formulations of MPS method are revisited from the view point of momentum conservation. Modifications and corrections are made to ensure the momentum conservation in a particle-based calculation of viscous incompressible free-surface flows. The excellent performance of Corrected MPS (CMPS) method in the exact (and nearly exact) conservation of linear (and angular) momentum is shown by a simple numerical test. The CMPS method is then applied to the simulation of wave breaking and post-breaking. Refined simulation of a solitary plunging breaker and resultant splash-up is demonstrated through comparisons with experiment. A tensor-type strain-based viscosity is also proposed for further enhanced CMPS reproduction of splash-up.

Computations of the propeller open water characteristics using the SOLAGA computer program. Predictions of the cavitation phenomenon

This paper presents the theoretical model and numerical methods which are applied in computer program SOLAGA for computations of viscous flow around ship propeller as well as for modelling of cavitation phenomenon. The model presented in the article is based on mass conservation equation and Reynolds averaged Navier-Stokes equation, the turbulent viscosity is approximated with the use of Spalart-Allmaras turbulent model. The numerical model used for solving the system of main equations is based on Finite Volume Method. The procedures for cavitation predictions applied in the SOLAGA program are based on travelling bubble model. This paper presents the results of computations of KT, KQ characteristics for conventional and skewed propeller. The results are compared with the data obtained from experiment. The results of computation of cavitation for the skewed propeller are presented as well.

1706 半開放形プロペラファンの三次元空力設計(S19-1 流体機械に関連した流動現象とその解析・計測(1)ファン内流れの計測と解析,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

A three-dimensional aerodynamic design method for half-ducted propeller fan has been presented. The half-ducted propeller fan has internal and external flow feature. It is important to take into account non-uniform meridional flow distributions around it. The present design method consists of two parts: a three-dimensional inverse design of fan rotor blade and an axisymmetric viscous flow calculation on the meridional plane. Continuing the process between the blade design using the three-dimensional inverse design method and the evaluation of the viscous flow fields around the rotor using the axisymmetric viscous flow calculation, the blade shape matching the flow fields around the rotor is converged. It is found that the present design method is useful to the half-ducted propeller fan design tool.

Quasi‐gasdynamic numerical algorithm for gas flow simulations

AbstractThe quasi‐gasdynamic equation system and the numerical algorithm for non‐stationary viscous gasdynamic flow calculations are presented. The quasi‐gasdynamic equation system generalizes the Navier–Stokes equations and differs from it by the additional dissipative terms. The numerical examples are presented. Copyright © 2007 John Wiley & Sons, Ltd.

Two-dimensional Stokes flow driven by elliptical paddles

A fast and accurate numerical technique is developed for solving the biharmonic equation in a multiply connected domain, in two dimensions. We apply the technique to the computation of slow viscous flow (Stokes flow) driven by multiple stirring rods. Previously, the technique has been restricted to stirring rods of circular cross section; we show here how the prior method fails for noncircular rods and how it may be adapted to accommodate general rod cross sections, provided only that for each there exists a conformal mapping to a circle. Corresponding simulations of the flow are described, and their stirring properties and energy requirements are discussed briefly. In particular the method allows an accurate calculation of the flow when flat paddles are used to stir a fluid chaotically.

Improving longitudinal motion prediction of hybrid monohulls with the viscous effect

A new method improves prediction of the motion of a hybrid monohull in regular waves. Stem section hydrodynamic coefficients of a hybrid monohull with harmonic oscillation were computed using the Reynolds Averaged Navier-Stokes Equations (RANSE). The governing equations were solved using the finite volume method. The VOF method was used for free surface treatment, and RNGK-ɛ turbulence model was employed in viscous flow calculation. The whole computational domain was divided into many blocks each with structured grids, and the dynamic process was treated with moving grids. Using a 2-D strip method and 2.5D theory with the correction hydrodynamic coefficients allows consideration of the viscous effect when predicting longitudinal motion of a hybrid monohull in regular waves. The method is effective at predicting motion of a hybrid monohull, showing that the viscous effect on a semi-submerged body cannot be ignored.