Two-dimensional Numerical Simulation Of Flow Research Articles

内部にバッハ・勾玉型ロータを有する 直線翼ダリウス型風車の性能評価

The straight Darrieus type wind turbine, which is expected to use for dispersed power source in urban site, has low performance especially at low tip speed ratio. In this paper, we suggested new type inner rotor to increase the power coefficient over wide range of tip speed ratio. The new type inner rotor, called “Bach – Comma shaped rotor”, is consist of a combination with cylindrical outer shape and Bach type inner shape. The Bach type shape has straight part to gain more torque from the wind than the classical Savonius bucket. The outer cylindrical shape inhibit the flow separation on the blade and rise the power coefficient. It was verified that the “Bach – Comma shaped rotor” is valid for increase the power coefficient over wide range of tip speed ratio by performing both two-dimensional numerical simulations of flow and the torque measurement experiments under the wind-tunnel.

Two-dimensional numerical simulation of flow around three-stranded rope

Three-stranded rope is widely used in fishing gear and mooring system. Results of numerical simulation are presented for flow around a three-stranded rope in uniform flow. The simulation was carried out to study the hydrodynamic characteristics of pressure and velocity fields of steady incompressible laminar and turbulent wakes behind a three-stranded rope. A three-cylinder configuration and single circular cylinder configuration are used to model the three-stranded rope in the two-dimensional simulation. The governing equations, Navier-Stokes equations, are solved by using two-dimensional finite volume method. The turbulence flow is simulated using Standard κ-e model and Shear-Stress Transport κ-ω (SST) model. The drag of the three-cylinder model and single cylinder model is calculated for different Reynolds numbers by using control volume analysis method. The pressure coefficient is also calculated for the turbulent model and laminar model based on the control surface method. From the comparison of the drag coefficient and the pressure of the single cylinder and three-cylinder models, it is found that the drag coefficients of the three-cylinder model are generally 1.3–1.5 times those of the single circular cylinder for different Reynolds numbers. Comparing the numerical results with water tank test data, the results of the three-cylinder model are closer to the experiment results than the single cylinder model results.

Study of the flow around a cylinder from the subcritical to supercritical regimes

The objective of the present simulations is to evaluate the applicability of the standard k-e turbulence model in engineering practice in the subcritical to supercritical flow regimes. Two-dimensional numerical simulations of flow around a circular cylinder at Re=1x105, 5x105 and 1x106 , had been performed using Unsteady Reynolds-Averaged Navier Stokes (URANS) equations with the standard k-e turbulence model. Solution verification had been studied by evaluating grid and time step size convergence. For each Reynolds number, several meshes with different grid and time step size resolutions were chosen to calculate the hydrodynamic quantities such as the time-averaged drag coefficient, root-mean square value of lift coefficient, Strouhal number, the coefficient of pressure on the downstream point of the cylinder, the separation angle. By comparing the values of these quantities of adjacent grid or time step size resolutions, convergence study has been performed. Solution validation is obtained by comparing the converged results with published numerical and experimental data. The deviations of the values of present simulated quantities from those corresponding experimental data become smaller as Reynolds numbers increases from 1x105 to 1x106. This may show that the standard k-e model with enhanced wall treatment appears to be applicable for higher Reynolds number turbulence flow.

Numerical Simulations of Flow around Square Cylinder Using an Iterative High Order Difference Scheme

A time dependent two-dimensional numerical simulation of flow around a rectangular cylinder is conducted using a particular high order compact finite difference method. The current forth-order compact scheme is implemented for the simulation of flow around bluff bodies for the first time. This formulation offers a semiexplicit method for the solution of Navier-Stokes equations in stream function-vorticity form and based on a nine point difference scheme with uniform grid spacing. The main advantage of the suggested method is its fast convergence and high accuracy. The proposed numerical method combines the enhanced Fourni’e’s forth order scheme with a semi-explicit formulation. By this combination, very accurate results can be obtained with a relatively coarse mesh in a short time. Uniform grids are applied with this high performance algorithm, and the accuracy of the scheme is proved using the benchmark problem of incompressible laminar flow around a rectangular cylinder at medium and high Reynolds numbers. Current results have good agreement with other numerical and experimental values. Generally, it is shown that, using the high order finite difference method demonstrates fairly competitive results for the current problem.

Hydraulic control of continuously stratified flow over an obstacle

AbstractMotivated by the laboratory experiments of Browand & Winant (Geophys. Fluid Dyn., vol. 4, 1972, pp. 29–53), a series of two-dimensional numerical simulations of flow past a cylinder of diameter $d$ are run for different values of the approach Froude number ${\mathit{Fr}}_{o} = U/ Nd$ between $0. 02$ and $0. 2$ at $\mathit{Re}= O(100)$. The observed flow is characterized by blocking and upstream influence in front of the cylinder and by relatively thin, fast jets over the top and bottom of the cylinder. This continuously stratified flow can be understood in terms of an inviscid non-diffusive integral inertia–buoyancy balance reminiscent of reduced-gravity single-layer hydraulics, but one where the reduced gravity is coupled to the thickness of the jets. The proposed theoretical framework describes the flow upstream of the obstacle and at its crest. The most important elements of the theory are the inclusion of upstream influence in the form of blocked flow within an energetically constrained depth range and the recognition that the flow well above and well below the active, accelerated layers is dynamically uncoupled. These constraints determine, through continuity, the transport in the accelerated layers. Combining these results with the observation that the flow is asymmetric around the cylinder, i.e. hydraulically controlled, allows us to determine the active layer thicknesses, the effective reduced gravity and thus all of the integral flow properties of the fast layers in good agreement with the numerically computed flows.

Numerical Study of Capillary Flow in Microchannels With Alternate Hydrophilic-Hydrophobic Bottom Wall

A two-dimensional numerical simulation of flow in patterned microchannel with alternate layers of different sizes of hydrophilic and hydrophobic surfaces at the bottom wall is conducted here. The effect of specified contact angle and working fluid (de-ionized (DI) water and ethanol) on capillary phenomena is observed here. The volume of fluid method is used for simulating the free surface flow in the microchannel. Meniscus profiles with varying amplitude and shapes are obtained under the different specified surface conditions. Nonsymmetric meniscus profiles are obtained by changing the contact angles of the hydrophilic and hydrophobic surfaces. A meniscus stretching parameter is defined here and its relation to the capillary phenomena in the microchannel is discussed. Flow variation increases as the fluid traverses alternately between the hydrophilic and hydrophobic regions. The pattern size and the surface tension of the fluid are found to have significant influence on the capillary phenomena in the patterned microchannel. Smaller pattern size produces enhanced capillary effect with DI water, whereas no appreciable gain is observed for ethanol. The magnitude of maximum velocity along the channel height varies considerably with the pattern size and the contact angle. Also, the rms velocity is found to be higher for smaller alternate patterned microchannel. The meniscus average velocity difference at the top and bottom walls increases for a dimensionless pattern size of 0.6 and thereafter it decreases with the increase in pattern size in the case of DI water with hydrophilic-hydrophobic pattern. Using such patterned microchannel, it is possible to manipulate and optimize fluid flow in microfluidic devices, which require enhanced mixing for performing biological reactions.

Applicability of linear type revised k–ε models to flow over topographic features

Accurate prediction of the wind energy distribution over terrains is essential for the appropriate selection of a suitable site for a wind power plant. This paper presents two-dimensional numerical simulations of flow over three common types of topographic features, i.e., a hill and two types of slopes (up-slope and down-slope). In a previous investigation by the present authors [Lun, Y.F., Mochida, A., Murakami, S., Yoshino, H., Shirasawa, T., 2003. Numerical simulation of flow over topographic features by revised k– ε models. J. Wind Eng. Ind. Aerodyn. 91(1–2), 231–245], the revised k–ε model proposed by P.A. Durbin [1996. Technical note: on the k–ε stagnation point anomaly. Int. J. Heat Fluid Flow 17, 89–90] was applied to flow prediction over a hill. Although, this model works well for flow around bluff bodies, a limitation was revealed in the area downstream of the hill. In this study, two new revised k–ε models proposed by Y. Nagano, H. Hattori and T. Irikado [2001. Prediction of flow over a complex terrain using turbulence model. In: Proceedings of the TED-Conference’01, JSME, in Japanese] and by Y. Nagano and H. Hattori [2003. A new low-Reynolds-number turbulence model with hybrid time-scales of mean flow and turbulence for complex wall flows. In: Proceedings of the Fourth International Symposium on Turbulence, Heat and Mass Transfer, Antalya, Turkey, October 12–17, 2003], i.e., the Ω and S–Ω models, were employed. These models are based on a mixed-time-scale concept. Their performance in predicting flow over various topographic features, namely a hill, up-slope and down-slope, was investigated. The problem of the Durbin model was corrected by the Ω model. However, a drawback of the Ω model was found in the upstream region. A new model, the S–Ω model, was introduced and was found to correct this problem. The S–Ω model showed best agreement with experiments for the hill case and the slope cases.

Numerical simulation of flow over topographic features by revised k-ϵ models : Lun, Y. F. et al. Journal of Wind Engineering and Industrial Aerodynamics, 2003, 91, (1–2), 231–245

The accurate prediction of the wind energy distribution over terrains is important for making an appropriate selection of a suitable site for installing wind power plant. In this study, two-dimensional numerical simulations of flow over two common types of topographic features, i.e. a cliff and a hill, are presented. Three types of turbulence models, namely standard k-e and its revised linear form (Durbin model) as well as a revised nonlinear form (Shih model) are employed in this work. The performance of these models in predicting flow over these features is investigated. The accuracy of the prediction by using a z 0 type wall function to reproduce the effect of surface roughness on flowfield from these turbulence models is also examined.

Numerical simulation of flow over topographic features by revised k– ε models

The accurate prediction of the wind energy distribution over terrains is important for making an appropriate selection of a suitable site for installing wind power plant. In this study, two-dimensional numerical simulations of flow over two common types of topographic features, i.e. a cliff and a hill, are presented. Three types of turbulence models, namely standard k– ε and its revised linear form (Durbin model) as well as a revised nonlinear form (Shih model) are employed in this work. The performance of these models in predicting flow over these features is investigated. The accuracy of the prediction by using a z 0 type wall function to reproduce the effect of surface roughness on flowfield from these turbulence models is also examined.

Numerical simulation of the flow and heat transfer around a cylinder with a pulsating approaching flow at a low Reynolds number

Two-dimensional numerical simulations of flow and heat transfer around a cylinder at a Reynolds number Re= 100 have been performed in order to investigate the effect of imposed inlet velocity pulsation on the heat transfer and flow fields. First the code is validated against existing results from the literature and then several external frequencies are examined. The numerical results confirm the existence of a vortex shedding lock-on regime where the wake behaves in a very ordered manner (completely periodic). Outside the lock-on region the flow is quasiperiodic. The length and centre of the mean recirculating zone downstream of the cylinder are also affected by the external pulsation. Regarding heat transfer, the results indicate that by imposing an external velocity pulsation, the root mean square (r.m.s.) of the local Nusselt number Nu increases, but the mean value increases only in the area downstream of the separation point. The mechanism responsible for this is identified: hot fluid is engulfed by stronger vortices (compared with the steady approaching flow case) shed from the upper and lower side of the cylinder and returned close to the downstream stagnation point. This mechanism also explains the observed variation in Nu with time. In the front part of the cylinder, the Nu varies almost sinusoidally and closely follows the imposed external velocity pulsation. The results indicate also that there is a range of external frequencies where the time and spatially averaged Nu number is maximized.

Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders

It has been known for some time that two-dimensional numerical simulations of flow over nominally two-dimensional bluff bodies at Reynolds numbers for which the flow is intrinsically three dimensional, lead to inaccurate prediction of the lift and drag forces. In particular, for flow past a normal flat plate (International Symposium on Nonsteady Fluid Dynamics, edited by J. A. Miller and D. P. Telionis, 1990, pp. 455–464) and circular cylinders [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)], it has been noted that the drag coefficient computed from two-dimensional simulations is significantly higher than what is obtained from experiments. Furthermore, it has been found that three-dimensional simulations of flows lead to accurate prediction of drag [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)]. The underlying cause for this discrepancy is that the surface pressure distribution obtained from two-dimensional simulations does not match up with that obtained from experiments and three-dimensional simulations and a number of reasons have been put forward to explain this discrepancy. However, the details of the physical mechanisms that ultimately lead to the inaccurate prediction of surface pressure and consequently the lift and drag, are still not clear. In the present study, results of two-dimensional and three-dimensional simulations of flow past elliptic and circular cylinders have been systematically compared in an effort to pinpoint the exact cause for the inaccurate prediction of the lift and drag by two-dimensional simulations. The overprediction of mean drag force in two-dimensional simulations is directly traced to higher Reynolds stresses in the wake. It is also found that the discrepancy in the drag between two-dimensional and three-dimensional simulations is more pronounced for bluffer cylinders. Finally, the current study also provides a detailed view of how the fluctuation, which are associated with the Kármán vortex shedding in the wake, affect the mean pressure distribution and the aerodynamic forces on the body.

Numerical simulation of solute transport in rough fractures : J Geophys Res V96, NB3, March 1991, P4157–4166

Parallel plate models are inadequate to describe the hydraulic and transport properties of natural fractures with rough surfaces. A two-dimensional numerical simulation of flow and solute migration in a fracture with fractal surfaces is presented. The macroscopic transport properties of the fractures are derived by comparison of the numerical simulations to predictions of a one-dimensional advection dispersion model. This makes it possible to determine effective dispersivities and solute velocities for the mathematically generated surfaces. The effects of adsorption, travel distance and channeling phenomena on the transport properties are examined. The modeling indicates that the effective velocity of the solute differs from that of the average fluid particle due to transverse and longitudinal dispersion and diffusion. These conclusions agree with field measurements of flow and transport in fractures.