Numerical simulation of fully nonlinear irregular wave tank in three dimension

A fully nonlinear irregular wave tank has been developed using a three‐dimensional higher‐order boundary element method (HOBEM) in the time domain. The Laplace equation is solved at each time step by an integral equation method. Based on image theory, a new Green function is applied in the whole fluid domain so that only the incident surface and free surface are discretized for the integral equation. The fully nonlinear free surface boundary conditions are integrated with time to update the wave profile and boundary values on it by a semi‐mixed Eulerian–Lagrangian time marching scheme. The incident waves are generated by feeding analytic forms on the input boundary and a ramp function is introduced at the start of simulation to avoid the initial transient disturbance. The outgoing waves are sufficiently dissipated by using a spatially varying artificial damping on the free surface before they reach the downstream boundary. Numerous numerical simulations of linear and nonlinear waves are performed and the simulated results are compared with the theoretical input waves. Copyright © 2006 John Wiley & Sons, Ltd.     

A numerical‐variational procedure for laminar flow in curved square ducts

A new numerical method is presented for the solution of the Navier–Stokes and continuity equations governing the internal incompressible flows. The method denoted as the CVP method consists in the numerical solution of these equations in conjunction with three additional variational equations for the continuity, the vorticity and the pressure field, using a non‐staggered grid. The method is used for the study of the characteristics of the laminar fully developed flows in curved square ducts. Numerical results are presented for the effects of the flow parameters like the curvature, the Dean number and the stream pressure gradient on the velocity distributions, the friction factor and the appearance of a pair of vortices in addition to those of the familiar secondary flow. The accuracy of the method is discussed and the results are compared with those obtained by us, using a variation of the velocity–pressure linked equation methods denoted as the PLEM method and the results obtained by other methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Studies on the law of laminar helical flow of power-law fluid in eccentric annuli

According to the principle of fluid mechanics,the law of laminar,helical flow of power-law fluid in eccentric annuli is studied extensively in this paper.The apparent viscosity,velocities distribution of laminar helical flow of power-law fluid are discussed and calculating methods of flow rate and pressure loss are presented.The factors influencing flow are also analysed.On the basis of theoretical studies some new results of the present paper are compared with the theories of the helical flow of the power-law fluid in concentric annuli.The test verified that theoretical formulas in this article are proper and general.They can be used for calculating hydraulic parameters in drilling engineering.     

Numerical simulation of laminar flow past a circular cylinder with slip conditions

The no‐slip condition is an assumption that cannot be derived from first principles and a growing number of literatures replace the no‐slip condition with partial‐slip condition, or Navier‐slip condition. In this study, the influence of partial‐slip boundary conditions on the laminar flow properties past a circular cylinder was examined. Shallow‐water equations are solved by using the finite element method accommodating SU/PG scheme. Four Reynolds numbers (20, 40, 80, and 100) and six slip lengths were considered in the numerical simulation to investigate the effects of slip length and Reynolds number on characteristic parameters such as wall vorticity, drag coefficient, separation angle, wake length, velocity distributions on and behind the cylinder, lift coefficient, and Strouhal number. The simulation results revealed that as the slip length increases, the drag coefficient decreases since the frictional component of drag is reduced, and the shear layer developed along the cylinder surface tends to push the separation point away toward the rear stagnation point so that it has larger separation angle than that of the no‐slip condition. The length of the wake bubble zone was shortened by the combined effects of the reduced wall vorticity and wall shear stress which caused a shift of the reattachment point closer to the cylinder. The frequency of the asymmetrical vortex formation with partial slip velocity was increased due to the intrinsic inertial effect of the Navier‐slip condition. Copyright © 2011 John Wiley & Sons, Ltd.     

Effects of temperature-dependence of viscosity and viscous dissipation on laminar flow heat transfer in circular tubes

Heat transfer effects of variable viscosity and viscous dissipation for heated developing laminar flows in circular tubes have been investigated. Three studies are reported covering a comprehensive range of input data for the case of constant wall heat flux. Initially the program was used to predict the effect on heat transfer of temperature-dependent viscosity via a general temperature power relation. In addition, predictions were made for nine particular fluids covering a range of Prandtl numbers from 0.025 to 12 500, and a range of Brinkman numbers from 1.8 × 10^?10 to 6.8 × 10³. A more detailed study was made for two particular oils covering a range of practical interest. For the liquids considered their viscosity temperature-dependence resulted in enhancement of heat transfer, whereas for fluids with a Prandtl number <200 the effect of viscous dissipation was negligible, and for fluids of a Brinkman number > × 10^?2 the outcome was a reduction of heat transfer. A numerical instability problem occurred for situations of very high viscous dissipation which limited the length of duct that could be examined.     

Very large‐scale computation of very small‐scale motions in a fully developed pipe flow

Local isotropy theory is examined using direct numerical simulation in a fully developed pipe flow at two Reynolds numbers Re_τ=1285.6 and 684.8. The approach to local isotropy is assessed with reference to the two Kolmogorov classical equations for longitudinal and transverse velocity structure functions. The results for the second‐order longitudinal structure functions in both the dissipative and inertial ranges indicate an improved agreement with the local isotropy hypothesis as the centreline is approached. However, the transverse structure functions satisfy isotropy neither in the dissipative range or in the inertial range. The distribution of the longitudinal and transverse structure functions also shows a substantial Reynolds number dependance in the logarithmic region of the flow and beyond. The results for the third‐order longitudinal structure function demonstrate an increased Reynolds number influence, and a deteriorating tendency to local isotropy for large separations. Contour images of axial velocity differences in the dissipative and inertial ranges have exhibited interesting patterns in relation to those of the instantaneous axial velocity. Finally, the results obtained in this investigation are in very good agreement with other published experimental and numerical data on channel and duct flows. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical simulation of two‐dimensional laminar slot‐jet impingement flows confined by a parallel wall

Two‐dimensional laminar incompressible impinging slot‐jet is simulated numerically to gain insight into flow characteristics.Computations are done for vertically downward‐directed slot‐jets impinging on a plate at the bottom and confined by a parallel surface on top. The behaviour of the jet with respect to aspect ratio (AR) and Reynolds number (Re) are described in detail. The computed flow patterns for various AR (2–5) and for a range of jet‐exit Reynolds numbers (100–500) are analysed to understand the flow characteristics. The transient development of the flow is also simulated for AR = 4 and Re = 300. It is found that the reattachment length is dependent on both AR and Reynolds number for the range considered. The correlation for reattachment length is suggested. The maximum resultant velocity V_rmax and its trajectory is reported. A detailed study of horizontal velocity profile at different downstream locations is reported. It is found that the effect of Reynolds number and AR is significant to the bottom wall vorticity in the impingement and wall jet regions. Copyright © 2007 John Wiley & Sons, Ltd.     

Numerical investigation of fully developed turbulent fluid flow and heat transfer in a square duct

Three-dimensional fully developed turbulent fluid flow and heat transfer in a square duct are numerically investigated with the author's anisotropic low-Reynolds-number k-ε turbulence model. Special attenton has been given to the regions close to the wall and the corner, which are known to influence the characteristics of secondary flow a great deal. Hence, instead of the common wall function approach, the no-slip boundary condition at the wall is directly used. Velocity and temperature profiles are predicted for fully developed turbulent flows with constant wall temperature. The predicted variations of both local wall shear stress and local wall heat flux are shown to be in close agreement with available experimental data. The present paper also presents the budget of turbulent kinetic energy equation and the systematic evaluation for existing wall function forms. The commonly adopted wall function forms that are valid for two-dimensional flows are found to be inadequate for three-dimensional turbulent flows in a square duct.     

Numerical solution of Navier-stokes equations for laminar fluid flow in rows of plates in staggered arrangement

Laminar fluid flow in rows of plate elements with staggered arrangement has been investigated by solving the complete Navier-Stokes equations using numerical methods. The results have been compared with those obtained on the basis of boundary-layer simplifications. The theoretical pressure-drop values compare well with available numerical and experimental data     

Thermally developing flow in finned double‐pipe heat exchanger

A numerical solution of the convective heat transfer in the thermal entry region of the finned double‐pipe is carried out for the case of hydro‐dynamically fully developed flow when subjected to uniform wall temperature boundary condition. Adaptive axial grid size is used in order to cater for the variation of large solution gradients in the axial direction. It has been observed that the thermal entrance region is highly effective and there is a substantial enhancement in the heat transfer coefficient. A maximum of 76.4877% increase has been observed in the thermal entrance region as compared with the fully developed region for 24 fins and H*=0.6 when R?=0.25, whereas for R?=0.5 the maximum increase is 75.0308% for the same number of fins of same height. It has been observed that no geometry consistently perform better throughout the entrance region. However, the geometries that have optimal performance in the fully developed region perform better in the developing region on average terms. Results show that the Nusselt number and the thermal entrance length are dependent upon various geometrical parameters such as ratio of radii of the inner and the outer pipe, fin height and the number of fins. The limiting case results match well with the literature results. This validates our numerical procedure and computer code. Copyright © 2010 John Wiley & Sons, Ltd.     

Numerical study of magnetohydrodynamic laminar flow separation in a channel with smooth expansion

The flow of an electrically conducting incompressible viscous fluid in a plane channel with smooth expansion in the presence of a uniform transverse magnetic field has been analysed. A solution technique for the governing magnetohydrodynamic equations in primitive variable formulation has been developed. A co‐ordinate transformation has been employed to map the infinite irregular domain into a finite regular computational domain. The governing equations are discretized using finite‐difference approximations in staggered grid. Pressure Poisson equation and pressure correction formulae are derived and solved numerically. It is found that with increase in the magnetic field, the size of the flow separation zone diminishes and for sufficiently large magnetic field, the separation zone disappears completely. The peak u‐velocity decreases with increase in the magnetic field. It is also found that the asymmetric flow in a symmetric geometry, which occurs at moderate Reynolds numbers, becomes symmetric with sufficient increase in the transverse magnetic field. Thus, a transverse magnetic field of suitable strength has a stabilizing effect in controlling flow separation, as also in delaying the transition to turbulence. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical investigation of a laminar pulsating flow in a rectangular duct

A pulsating laminar flow of a viscous, incompressible liquid in a rectangular duct has been studied. The motion is induced under an imposed pulsating pressure difference. The problem is solved numerically. Different flow regimes are characterized by a non‐dimensional parameter based on the frequency (ω) of the imposed pressure gradient oscillations and the width of the duct (h). This, in fact, is the Reynolds number of the problem at hand. The induced velocity has a phase lag (shift) with respect to the imposed pressure oscillations, which varies from zero at very slow oscillations, to 90° at fast oscillations. The influence of the aspect ratio of the rectangular duct and the pulsating pressure gradient frequency on the phase lag, the amplitude of the induced oscillating velocity, and the wall shear were analyzed. Copyright © 1999 John Wiley & Sons, Ltd.     

Modelling of two‐dimensional laminar flow using finite element method

In this paper, a Galerkin weighted residual finite element numerical solution method, with velocity material time derivative discretisation, is applied to solve for a classical fluid mechanics system of partial differential equations modelling two‐dimensional stationary incompressible Newtonian fluid flow. Classical examples of driven cavity laminar flow and laminar flow past a cylinder are presented. Numerical results are compared with data found in the literature. Copyright © 1999 John Wiley & Sons, Ltd.     

The influence of an abrupt convergence on heat transfer in circular ducts: a theoretical assessment

This is a theoretical assessment of the postulation made by Barozzi et al, of separation in laminar flow in a circular duct caused by an abrupt entry. Using sets of data supplied by Barozzi, predictions have been made using a program developed by Collins. The effects of viscosity variation with temperature, and of natural convection, are quantified for the flow of water in a vertical tube. The results are consistent with the discussion of Barozzi et al, and tend to confirm the presence of a definite abrupt entry effect     

Numerical prediction of laminar flow and heat transfer characteristics in a tube fitted with regularly spaced twisted-tape elements

By numerically solving the Navier-Stokes and energy equations in their three-dimensional parabolic form, the friction and heat transfer characteristics are predicted for laminar flow in a circular tube fitted with regularly spaced twisted-tape elements that are connected by circular rods. The predictions have agreed closely with the experimental data for water. It is shown that a strong L/D effect is associated with the configuration under consideration. By extending the predictions outside the range of experimental data, it is found that considerably enhanced thermohydraulic performance is achievable by increasing the number of turns on the tape elements, by reducing the connecting rod diameter, and at high fluid Prandtl numbers.     

Numerical simulation of circulation in gas-liquid column reactors: isothermal, bubbly, laminar flow

The gas-liquid flow inside a circular, isothermal column reactor with a vertical axis has been studied using numerical simulations. The flow is assumed to be in the laminar, bubbly flow regime which is characterized by a suspension of discrete air bubbles in a continuous liquid phase such as glycerol water. The mathematical formulation is based on the conservation of mass and momentum principle for the liquid phase. The gas velocity distribution is calculated via an empirically prescribed relative velocity as a function of void fraction. The interface viscous drag forces are prescribed empirically. For some cases a profile shape is assumed for the void ratio distribution. The influence of various profile shapes is investigated. The results are compared with those where the void ratio distribution is calculated from the conservation of mass equation. The mathematical model has been implemented by modifying a readily available computer code for single-phase newtonian fluid flows. The numerical discretization is based on a finite volume approach. The predictions show a good agreement with measurements. The circulation pattern seems not to be so sensitive to the actual shape of the void fraction profiles, but the inlet distribution of it is important. A significantly different flow pattern results when the void fraction distribution is calculated from the transport equation, as compared to those with a priori prescribed profiles. When the void fraction is uniformly distributed over the whole distributor plate, no circulation is observed. Calculations also show that even the two-phase systems with a few discrete bubbles can be simulated successfully by a continuum model.     

Computations of a laminar backward‐facing step flow at Re=800 with a spectral domain decomposition method

The two‐dimensional laminar incompressible flow over a backward‐facing step is computed using a spectral domain decomposition approach. A minimum number of subdomains (two) is used; high resolution being achieved by increasing the order of the basis Chebyshev polynomial. Results for the case of a Reynolds number of 800 are presented and compared in detail with benchmark computations. Stable accurate steady flow solutions were obtained using substantially fewer nodes than in previously reported simulations. In addition, the problem of outflow boundary conditions was examined on a shortened domain. Because of their more global nature, spectral methods are particularly sensitive to imposed boundary conditions, which may be exploited in examining the effect of artificial (non‐physical) outflow boundary conditions. Two widely used set of conditions were tested: pseudo stress‐free conditions and zero normal gradient conditions. Contrary to previous results using the finite volume approach, the latter is found to yield a qualitatively erroneous yet stable flow‐field. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical study of turbulent flow over two‐dimensional surface‐mounted ribs in a channel

This study accurately predicts the cases of turbulent flow around a surface‐mounted two‐dimensional rib with varying lengths. The numerical method employs a differencing scheme for integrating the elliptic Reynolds‐averaged Navier–Stokes equations and the continuity equation. A two‐equation k–ε turbulence model is employed to simulate the turbulent transport quantities and close the solving problem. The near‐wall regions of the separated sides of the rib are resolved by a near‐wall model of a two‐layer approach instead of the wall function approximation. Computations for flow over a surface‐mounted rectangular rib are conducted for the variations in the rib lengths. Results indicate that upstream of the obstacle, the length of the recirculating region remains unchanged with varying rib lengths; while the downstream length of the recirculating region is a strong function of rib length and changes nearly linearly for the varying lengths of B/H=0.1 to B/H=4.0. Reattachment on top of the rib, owing to its increasing length, affects the downstream boundary layer development. Copyright © 1999 John Wiley & Sons, Ltd.     

Effect of duct velocity profile and buoyancy‐induced flow on efficiency of transient hydrodynamic removal of a contaminant from a cavity

This paper describes a preliminary numerical analysis of the effect of duct velocity profile and buoyancy‐induced flow generated by the heat source on hydrodynamic removal of contaminants contained in cavities. The process of fluid renewal in a cavity is modelled via a numerical solution of the Navier–Stokes equations coupled with the energy equation for transient flows. The foulant has the same density as the fluid in the duct and the duct velocity profile is considered to be Poiseuille flow and Couette flow, respectively. The results show that the change in Grashof number and duct flow velocity profile causes a dramatic difference in the observed flow patterns and cleaning efficiency. From a cleaning perspective, the results suggest that Couette flow at higher value of Grashof number becomes more effective in further purging of contaminated fluid from a cavity. Copyright © 2004 John Wiley & Sons, Ltd.