Unsteady Viscous Flow Research Articles

Combined effects of viscous dissipation and MHD on free convection flow past a semi-infinite vertical plate with variable surface temperature in the presence of heat source

An unsteady MHD laminar viscous dissipative fluid flow past a semi-infinite vertical plate with variable surface temperature in the presence of heat source is considered in the present analysis. The present approach transforms the governing boundary layer equations into nondimensional form using the appropriate nondimensional quantities, which is valid in the free convection region. The resulting governing equations are solved numerically using the Crank–Nicolson method, an efficient implicit finite-difference scheme. Numerical results are obtained and presented in the form of local as well as average shearing stress, local and average heat transfer rate, velocity and temperature during the transient period. The present results are compared with the available results in the literature and are found to be in an excellent agreement.

Meshfree simulation of flow around airfoil using different turbulent models

The moving least square meshfree method is used to solve the Reynolds-averaged Navier-Stokes equations with two different turbulence models: the renormalisation group (RNG) k-ε model and the Wilcox k-ω model. The moving least square approach with clouds-of-points reconstruction, which can provide results from highly anisotropic clouds of points, is adopted to approximate the spatial derivatives. Both the subsonic and transonic viscous flows around RAE2822 airfoil are simulated. The pressure coefficients of the airfoil surface are calculated, the Mach number contours of the flow fields are presented, and the mean velocity profiles of the boundary layer at different locations are investigated. Some unsteady viscous flow simulation results are also presented. The simulation results show a good agreement with the experiment results and other numerical simulation results. Overall, the simulation results demonstrate that the proposed meshfree numerical algorithm is accurate and capable of modelling turbulence flows around airfoils.

Unsteady viscous MHD flow over a permeable curved stretching/shrinking sheet

Purpose The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically. Design/methodology/approach The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined. Findings Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter. Originality/value The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

Numerical investigations on cavitation intensity for 3D homogeneous unsteady viscous flows

The cavitation erosion remains an industrial issue. In this paper, we deal with the cavitation intensity which can be described as the aggressiveness - or erosive capacity - of a cavitating flow. The estimation of this intensity is a challenging problem both in terms of modelling the cavitating flow and predicting the erosion due to cavitation. For this purpose, a model was proposed to estimate cavitation intensity from 3D unsteady cavitating flow simulations. An intensity model based on pressure and void fraction derivatives was developped and applied to a NACA 65012 hydrofoil tested at LMH-EPFL (École Polytechnique Fédérale de Lausanne) [1]. 2D and 3D unsteady cavitating simulations were performed using a homogeneous model with void fraction transport equation included in Code_Saturne with cavitating module [2]. The article presents a description of the numerical code and the physical approach considered. Comparisons between 2D and 3D simulations, as well as between numerical and experimental results obtained by pitting tests, are analyzed in the paper.

A comparison of Rosenbrock and ESDIRK methods combined with iterative solvers for unsteady compressible flows

In this article, we endeavour to find a fast solver for finite volume discretizations for compressible unsteady viscous flows. Thereby, we concentrate on comparing the efficiency of important classes of time integration schemes, namely time adaptive Rosenbrock, singly diagonally implicit (SDIRK) and explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) methods. To make the comparison fair, efficient equation system solvers need to be chosen and a smart choice of tolerances is needed. This is determined from the tolerance TOL that steers time adaptivity. For implicit Runge-Kutta methods, the solver is given by preconditioned inexact Jacobian-free Newton-Krylov (JFNK) and for Rosenbrock, it is preconditioned Jacobian-free GMRES. To specify the tolerances in there, we suggest a simple strategy of using TOL/100 that is a good compromise between stability and computational effort. Numerical experiments for different test cases show that the fourth order Rosenbrock method RODASP and the fourth order ESDIRK method ESDIRK4 are best for fine tolerances, with RODASP being the most robust scheme.

URANS Studies of Effect of Eccentricity on Ship–Lock Interactions

The unsteady viscous flow around a 12000TEU ship model entering the Third Set of Panama Locks with different eccentricity is simulated by solving the unsteady Reynolds averaged Navier–Stokes (RANS) equations in combination with the [Formula: see text]SST turbulence model. Overset grid technology is utilized to maintain grid orthogonality and the effects of the free surface are taken into account. The hydrodynamic forces, vertical displacement as well as surface pressure distribution are predicted and analyzed. First, a benchmark test case is designed to validate the capability of the present methods in the prediction of the viscous flow around the ship when maneuvering into the lock. The accumulation of water in front of the ship during entry into a lock is noticed. A set of systematic computations with different eccentricity are then carried out to examine the effect of eccentricity on the ship–lock hydrodynamic interaction.

Study on the Aerodynamic Characteristics of Tunnel and Metro Station with PSD During High-speed Train Passing Tunnel

A numerical simulation on the 3D compressible viscous unsteady flow field induced by a high-speed subway train, while it’s passing by the platform screen door of subway station, is presented in the paper. The research on transient pressure in tunnel due to changes of positions of platform screen door is proceeded in order to design platform screen doors for underground stations of Dong-guan to Huizhou inter-city rail traffic. Result shows that the platform is subjected to aerodynamic compression and tension cycle loads all the time. And compression load is larger than tension load. The maximum and minimum pressure values in absolute terms got from measuring points of the whole station decrease gradually along the direction train going ,no matter whether the platform screen door is fixed or not. The absolute values of maximum and minimum pressure of piston wind generated at platform screen door are decreasing while the spacing between platform screen door and platform becomes wider. The pressure value of air at exit is larger than that of air at entrance. As for a high-speed subway station, it is a practicable way to set air shafts at entrance and exit of station to mitigate pressure of air in station and tunnel. The pressure value of air could have a 10 to 15 percent reduction if there is an air shaft. Besides, the platform screen door can be installed in half tall of PSD.

Numerical simulations of viscous flow around the obliquely towed KVLCC2M model in deep and shallow water

By solving the unsteady Reynolds averaged Navier–Stokes (RANS) equations in combination with the k-ω SST turbulence model, the unsteady viscous flow around the obliquely towed tanker KVLCC2M model in both deep and shallow waters is simulated and the hydrodynamic forces, the surface pressure distribution, and the wake field are calculated. The overset grid technology is used to avoid the grid distortion in large drift angle cases. The effects of the free surface are taken into account. At the first stage, the deep water cases with five oblique angles are designed as the benchmark test cases. The predicted wake field, the surface pressure distribution and the hydrodynamic forces acting on the hull agree well with the corresponding experimental data, implying the capability of the present method in the prediction of the viscous flow around the tanker drifting in shallow water. A set of systematic computations with varying water depths and drift angles are then carried out to study the viscous flow around the model drifting in shallow water. The forces and moments, as well as the surface pressure distribution are predicted and analyzed. The most significant changes such as the increased stagnation pressure in the bow, the acceleration of the flow along the ship's sides and in the gap between ship and seabed, the lower hull pressure and finally, the stronger vortices along the bilges and weaker vortices with larger diameters in the wake are noticed.

Unsteady self-similar viscous flow near a stagnation point

The problem of unsteady viscous incompressible fluid flow near a stagnation point is considered. Self-similar solutions describing plane and axisymmetric flows are constructed.

A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier–Stokes equations

SummaryA fourth‐order finite‐volume method for solving the Navier–Stokes equations on a mapped grid with adaptive mesh refinement is proposed, implemented, and demonstrated for the prediction of unsteady compressible viscous flows. The method employs fourth‐order quadrature rules for evaluating face‐averaged fluxes. Our approach is freestream preserving, guaranteed by the way of computing the averages of the metric terms on the faces of cells. The standard Runge–Kutta marching method is used for time discretization. Solutions of a smooth flow are obtained in order to verify that the method is formally fourth‐order accurate when applying the nonlinear viscous operators on mapped grids. Solutions of a shock tube problem are obtained to demonstrate the effectiveness of adaptive mesh refinement in resolving discontinuities. A Mach reflection problem is solved to demonstrate the mapped algorithm on a non‐rectangular physical domain. The simulation is compared against experimental results. Future work will consider mapped multiblock grids for practical engineering geometries. Copyright © 2016 John Wiley & Sons, Ltd.

Numerical prediction of hydrodynamic forces on a berthed ship induced by a passing ship in different waterway geometries

An investigation has been conducted to quantify the effect of waterway geometry on the form and magnitude of forces and moment experienced by a berthed ship due to a passing ship. By using the dynamic mesh technique and solving the unsteady RANS equations in conjunction with a RNG k-e turbulence model, numerical simulation of the three-dimensional unsteady viscous flow around a passing ship and a berthed ship in different waterway geometries is conducted, and the hydrodynamic forces and moment acting on the berthed ship are calculated. The proposed method is verified by comparing the numerical results with existing empirical curves and a selection of results from model scale experiments. The calculated interaction forces and moment are presented for six different waterway geometries. The magnitude of the peak values and the form of the forces and moment on the berthed ship for different cases are investigated to assess the effect of the waterway geometry. The results of present study can provide certain guidance on safe maneuvering of a ship passing by a berthed ship.

Effects of MHD on the Unsteady Thin Flow of Non-Newtonian Oldroyd –B Fluid over an Oscillating Inclined Belt Through a Porous Medium

The unsteady (MHD) thin film flow of an incompressible Oldroyd -B fluid over an oscillating inclined belt making a certain angle with the horizontal through a porous mediumis analyzed .The analytical solution of velocity field is obtained by a semi-numerical technique optimal homotopy asymptotic method (OHAM) .Finally the influence of various dimensionless parameters emerging in the model on velocity field is analyzed by graphical illustrations. I. Introduction In everyday life and in engineering flow of non-Newtonian fluid are frequently occurred .It is ubiquitous in nature and technologies .Therefore ,to understand there mechanics is essential in most application .Most of it problems appeared in several examples are polymer solution ,paints ,certain oils ,exocitic lubricants ,colloidal and suspension solutions , clay coatings and cosmetic products .In non-Newtonian fluids Thin film flows have a large varying of practical applications in nonlinear science and engineering industries . For modeling of non-Newtonian Fluid flow problem we used several model like (second grade, third grade , Maxwell fluid ,Oldroyd-B ) ..ect fluid model by which we got linear or nonlinear ordinary differential equation or partial differential equations which may be solved exactly, analytically or numerically. For solution of these problems different varieties of methods are used, in which (ADM,VAM,HAM,HPM,OHAM) are frequently used. In this work we have modeled a partial differential equations by using oldroyd-B fluid model. Solution of the problem is obtained by using OHAM. Fetecau et al. (3) studied the exact solutions of an Oldroyd-B fluid over a flat plate on constantly accelerating flow. In the following year, Fetecau et al. (4) obtained the exact solutions of the transient oscillating motion of an Oldroyd-B fluids in cylindrical domains. Haitao and Mingyu (5) investigated the series solution of an Oldroyd-B fluid by using the sine and Laplace transformations for the plane Poiseuille flowand plane couette flow. Lie L. (7) studied the effect of MHD flow for an Oldroyd-B fluid between two oscillating cylinders .Khan et al. Burdujan (2) discussed the solution for the flow of an incompressible Oldroyd-B fluid between two cylinders . Shahid et al. (12) studied the solution of the steady and unsteady flow of Oldroyd-B fluid by using Laplace and Fourier series. Shah et al. (13) studied the solution by using OHAM of thin film flow of third grade fluid on moving inclined plane. Marinca et al. (11) studied the approximate solution of non-linear steady flow of fourth grade fluid by using OHAM. Marinca et al (10) discussed the approximate solution of the unsteady viscous flow over a shrinking cylinder by using OHAM method . Kashkari (6) studied the OHAM solution of nonlinear Kawahara equation. For comparison HPM, VHPM and VIM method is used but OHAM ismore successful method. . Anakira et al. (1) the analytical solution of delay differential equation by using OHAM. Mabood et al. (8,9) investigated the approximate solution of non-linear Riccati differential equation by using OHAM . Taza Gul (14) studied the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. In this paper , we study the unsteady (MHD) thin film flow of an incompressible Oldroyd -B fluid over an oscillating inclined belt making a certain angle with the horizontal in porous medium . the solution of velocity field is obtained by using a semi-numerical technique optimal homotopy asymptotic method (OHAM). Finally, we analyzed the influence of various dimensionless parameters emerging in the model on velocity field is analyzed by graphical illustrations.

The impact of valve simplifications on left ventricular hemodynamics in a three dimensional simulation based on in vivo MRI data

Left ventricle (LV) fluid dynamics and the function of its valves have a crucial impact on clinical diagnosis, treatment and prosthesis design. In this paper, we simulated left ventricular flow using 3D computational fluid dynamics (CFD) based on geometrical and deformational information obtained from MRI. Time variant smoothed LV shapes were extracted from MR images. Corresponding deformation data was interpolated using a cubic-spline interpolation. To evaluate valve influence on LV flow, we compared two planar valve models: physiologically corrected gradually opening/closing model and a simple on/off model. Endocardial displacement was applied to fluid boundary using fluid–structure interaction (FSI) approach. Arbitrary Lagrangian–Eulerian (ALE) formulation was used for unsteady incompressible viscous Newtonian blood flow in the fluid domain. Comparison of results for LV flow with two valve models demonstrated a clear distinction between pressure distribution, velocity distribution, vortex formation/growth/vanishing and energy dissipation especially in the filling phase. Consequently, LV flow simulation by ignoring geometrical details of valves׳ model may lead to non-realistic results in some aspects.

Numerical Investigation of Transient Flow in a Prototype Centrifugal Pump during Startup Period

AbstractTransient performance of pumps during transient operating periods, such as startup and stopping, has drawn more and more attentions recently due to the growing engineering needs. During the startup period of a pump, the performance parameters such as the flow rate and head would vary significantly in a broad range. Therefore, it is very difficult to accurately specify the unsteady boundary conditions for a pump alone to solve the transient flow in the absence of experimental results. The closed-loop pipe system including a centrifugal pump is built to accomplish the self-coupling calculation. The three-dimensional unsteady incompressible viscous flow inside the passage of the pump during startup period is numerically simulated using the dynamic mesh method. Simulation results show that there are tiny fluctuations in the flow rate even under stable operating conditions and this can be attributed to influence of the rotor–stator interaction. At the very beginning of the startup, the rising speed of the flow rate is lower than that of the rotational speed. It is also found that it is not suitable to predict the transient performance of pumps using the calculation method of quasi-steady flow, especially at the earlier period of the startup.

Unsteady Self-Similar Viscous Flow Near a Critical Point

Unsteady Self-Similar Viscous Flow Near a Critical Point

Meshfree Simulation of Flow around Airfoil using Different Turbulent Models

The moving least square meshfree method is used to solve the Reynolds-averaged Navier-Stokes equations with two different turbulence models: the renormalisation group (RNG) k-e model and the Wilcox k-ω model. The moving least square approach with clouds-of-points reconstruction, which can provide results from highly anisotropic clouds of points, is adopted to approximate the spatial derivatives. Both the subsonic and transonic viscous flows around RAE2822 airfoil are simulated. The pressure coefficients of the airfoil surface are calculated, the Mach number contours of the flow fields are presented, and the mean velocity profiles of the boundary layer at different locations are investigated. Some unsteady viscous flow simulation results are also presented. The simulation results show a good agreement with the experiment results and other numerical simulation results. Overall, the simulation results demonstrate that the proposed meshfree numerical algorithm is accurate and capable of modelling turbulence flows around airfoils.

Causal mechanisms in airfoil-circulation formation

In this paper, we trace the dynamic origin, rather than any kinematic interpretations, of lift in two-dimensional flow to the physical root of airfoil circulation. We show that the key causal process is the vorticity creation by tangent pressure gradient at the airfoil surface via no-slip condition, of which the theoretical basis has been given by Lighthill [“Introduction: Boundary layer theory,” in Laminar Boundary Layers, edited by L. Rosenhead (Clarendon Press, 1963), pp. 46–113], which we further elaborate. This mechanism can be clearly revealed in terms of vorticity formulation but is hidden in conventional momentum formulation, and hence has long been missing in the history of one’s efforts to understand lift. By a careful numerical simulation of the flow around a NACA-0012 airfoil, and using both Eulerian and Lagrangian descriptions, we illustrate the detailed transient process by which the airfoil gains its circulation and demonstrate the dominating role of relevant dynamical causal mechanisms at the boundary. In so doing, we find that the various statements for the establishment of Kutta condition in steady inviscid flow actually correspond to a sequence of events in unsteady viscous flow.

Dynamic behaviour of high- bypass- ratio turbofan carbon fiber-reinforced plastic blade ubder unsteady airloads

The dynamic behavior of vibrating blades of an advanced high- bypass- ratio turbojet engine wide-chord fan under unsteady air loads has been researched. Unsteady air loads occur because of the flow around the impeller situated in the air inlet in the case of strong crosswind. These loads affect the blade dynamic behavior and could lead to increasing of the blade vibration amplitude and the stress in the blades. Blade dynamic behavior is investigated on the basis of 3D high-level gas-dynamic and finite-element models. The gas-dynamic model takes into account unsteady viscous 3D air flows. The strength model takes into account geometrical non-linearity and anisotropy of the composite material. The Cobra software package developed at CIAM and based on Godunov’s method is used for aerodynamic research and obtaining unsteady aerodynamic loads. The ANSYS package of finite-element analysis is used to solve the mechanical problem. The paper deals with both forced vibrations of a blade under given cyclic aerodynamic loads and vibrations with account for the fluid-structure interaction (FSI) of the structure and the flow of titanium and carbon-fiber-reinforced blades. The results of investigations have been compared. The differences between the results of solving the task of forced vibrations and vibrations with FSI, as well as the differences between the results obtained for blades of the same configuration but made of different materials are presented.

Stability and Conservation Properties of Collocated Constraints in Immersogeometric Fluid-Thin Structure Interaction Analysis

AbstractThe purpose of this study is to enhance the stability properties of our recently-developed numerical method [D. Kamensky, M.-C. Hsu, D. Schillinger, J.A. Evans, A. Aggarwal, Y. Bazilevs, M.S. Sacks, T.J.R. Hughes, “An immersogeometric variational framework for fluid-structure interaction: Application to bioprosthetic heart valves”, Comput. Methods Appl. Mech. Engrg., 284 (2015) 1005–1053] for immersing spline-based representations of shell structures into unsteady viscous incompressible flows. In the cited work, we formulated the fluid-structure interaction (FSI) problem using an augmented Lagrangian to enforce kinematic constraints. We discretized this Lagrangian as a set of collocated constraints, at quadrature points of the surface integration rule for the immersed interface. Because the density of quadrature points is not controlled relative to the fluid discretization, the resulting semi-discrete problem may be over-constrained. Semi-implicit time integration circumvents this difficulty in the fully-discrete scheme. If this time-stepping algorithm is applied to fluid-structure systems that approach steady solutions, though, we find that spatially-oscillating modes of the Lagrange multiplier field can grow over time. In the present work, we stabilize the semi-implicit integration scheme to prevent potential divergence of the multiplier field as time goes to infinity. This stabilized time integration may also be applied in pseudo-time within each time step, giving rise to a fully implicit solution method. We discuss the theoretical implications of this stabilization scheme for several simplified model problems, then demonstrate its practical efficacy through numerical examples.

Novel structured dynamic mesh generation for CFD analysis of scroll compressors

In order to improve the simulation accuracy of scroll compressors, a novel mesh-generation method of structured dynamic mesh (SDM) is proposed for fluid domains of scroll compressors in this paper. High-quality and density meshes are generated using the SDM in the fluid domains, especially in the flank meshing clearance between wrap profiles in the orbiting and fixed scrolls. The mesh generation process is presented, including scroll solid boundary of fluid domains, structured mesh dividing method in normal and tangent direction, and motion equations of each layer of nodes. Based on the SDM, numerical simulation of an unsteady compressible viscous turbulent flow with moving boundaries in the working process of scroll compressors is carried out, and the overall flow distributions of pressure, temperature and velocity are obtained. The study results show that the numerical simulation using the SDM is more accurate than using the existing unstructured dynamic mesh. The results are significant to predict, exhibit and reveal flow fields in the fluid domain of scroll compressors.