We examine effects of the divergence of the viscous terms on the numerical results of an incompressible flow by using an exact solution of the governing equation. When the Poisson equation is solved using fractional steps, the divergence in the velocity field may have nonzero magnitude. It should be noted that the divergence of the viscous terms can be larger than that of the velocity field. We use an exact solution, which is commonly used for benchmarking, to examine the effects of the divergence of the viscous terms. The divergence of the viscous terms affects the equilibrium relations found in the exact solution. In the present numerical results, the divergence of the viscous terms reduces the rate of decay of the kinetic energy and the pressure, and it also causes some harmonic waves in the flow field. We examine these results quantitatively by using approximations to the numerical results. Skewness and kurtosis factors of the physical quantities are also affected by the divergence of the viscous terms. These results show that the divergence of the viscous terms significantly affects the flow field.
Wet-steam flows under high-pressure conditions are numerically investigated using a newly derived condensation model that assumes a real gas and uses a real gas Equation of State (EOS). Under high-pressure conditions, the present condensation model calculates the critical radius of a water droplet that is larger than that of the conventional model. The results indicate that nucleation is initiated farther downstream in the nozzle and the nucleation rate is smaller. Wet-steam nozzle flows under high-pressure conditions are simulated and the results are compared with experimental results. The present model simulates the pressure increase due to the release of latent heat of condensation more accurately than the conventional method based on the ideal gas assumption. The results obtained are also in good agreement with the experimental results.
In this paper, we present a shallow water flow field estimation analysis, based on the Kalman filter FEM, for locating the optimal positions for tidal stream power generation systems. In our flow field analysis, we adopt the shallow water equation as the governing equation. The Galerkin and the selective lumping methods are employed as discretization techniques in space and time, respectively. The Kalman filter theory is applied to estimate the flow field. As a numerical example, we carry out a flow estimation analysis for Tokyo Bay. The high estimation accuracy of the flow field estimation based on the Kalman filter FEM is confirmed by comparison with conventional FEM. The electric power generation potential is also computed using the estimated flow field.
Thixotropy is a common behavior of soft matters widely used in various industries. Numerous models, both empirical and theoretical, have been proposed for different soft matters. In this paper the Maxwell viscoelastic model has been modified by decoupling the second order tensor type equation into vector type equations, without introducing new material parameters or assuming the dependence of the viscosity and/or elasticity on time and/or shear rate. The proposed Maxwell model is known as the vector type Maxwell model while the original one as the second order tensor type Maxwell model. The vector type Maxwell model was applied to both the stationary and the single step shear rate shear flow and the numeric results were compared with the experiments in the literature. It is found that the vector type Maxwell model predicted better both the shear and the normal stresses in the stationary shear flow than the second order tensor type Maxwell model, and the vector type Maxwell fluids may show thixotropic behavior in the single step shear rate flow as observed in experiments.
The operating conditions of Horizontal Axis Wind Turbine (HAWT) are extremely complex in natural surroundings. One of the wind conditions is called extreme wind direction change which has been specified in the International Electrotechnical Commission (IEC) 61400-1 standard. External conditions can generate extreme loads which may affect the power coefficient and the lifetime of HAWTs. This paper attempted to compile the evaluation of the aerodynamic forces acting on a small HAWT under extreme wind direction change condition in the wind tunnel experiments. An Avistar airfoil is used for the two-bladed and three-bladed wind turbines. This study is intended to clarify the load fluctuation when sudden wind direction change reacts to two-bladed and three-bladed wind turbines. A vane system is used to generate the wind direction change. A 6-component balance is used to measure the forces and the moments acting on the entire wind turbine in the three directions of x, y and z-axes. The results show that when the extreme wind direction change is generated, the yaw moment fluctuation amplitude of two-bladed wind turbine is about 39% larger than that of the three-bladed one. The strong dependence of the inflow timing of the wind direction change on the fluctuation amplitude can be seen only for the two-bladed wind turbine.
To control and reduce the rear separation region and the vortex of the free-end surface, a passive flow control method that is to use an inclined flow controlling hole (FCH) passing through the free-end surface to the side of the rear surface was proposed for a low aspect ratio (=1) circular cylinder. The high-speed PIV (Particle Image Velocimetry) measurements were performed at Reynolds number of 8,570 in a circulation water tunnel in order to compare the flow characteristics between the controlling and no-controlling wakes. Furthermore, to study the position effect of the FCH, there kinds of the FCH models were tested. It was found that the fluid flows from the large rear recirculation zone upwards to the small recirculation zone on the free end surface through the FCH. The size of rear recirculation zone was reduced by the FCH cylinders with h = 50 mm, and the FCH cylinders with h = 20 and 35 mm effectively diminished the separation region of the free end surface. Meanwhile, vorticity, Reynolds shear stresses and turbulent kinetic energy were also decreased by the FCH cylinders with h = 50 mm comparing with the standard cylinder and other FCH models. Spectral analyses suggest that the dominate frequency of vortex shedding from the cylinder surface increases.
A large-scale perpendicular cavitating vortices (PCVs), at the trailing edge of attached cavitation on the blade suction side near the tip region, has been found recently due to the great impact on performance breakdown in an axial waterjet pump. However, the trajectory and dynamics of this structure have been given scant attention. In this study, some visualized experiments were carried out to elucidate the PCVs for different conditions. The high-speed imaging coupled with numerical computations show that the vortical cloud cavitation is induced by the combination of tip leakage vortex (TLV) and radial re-entrant jets from the hub to blade tip. Moreover, the trajectory and intensity of PCVs depend on the operating conditions strongly, whether the other parameters, e.g. blade number and blade geometries, are modified. When taken the blade number into consideration, as a consequence of flow passage width and blade loading distributions, the dynamics and strength of PCVs vary considerably. Furthermore, an optimum clearance geometry is seen to eliminate corner vortex and clearance cavitation when the clearance edge is rounded on the pressure side. However, the more intensive tip leakage vortex cavitation is observed due to the increased amount of leakage flux. Additionally, in the original blade with sharp edges, the PCVs is relative weak and has a loose structure, resulting in the multiple interaction with the next blade. These phenomenon are responsible for the severe performance degradation and flow instabilities in the tip region of an axial-flow pump.
The yaw angle (φ) effect on riblets are investigated by parametrically conducted direct numerical simulation (DNS). Three configurations are adopted: standard straight riblet, sinusoidal riblet, and modified sinusoidal riblet. The height of the side wall in the modified sinusoidal riblet is lowered toward the node of the sinusoidal curve to reduce the pressure drag, whereas the riblet height is maintained at the anti-node as it has been reported to be the most effective for straight or traditional sinusoidal riblets. This study is the first investigation on yaw angle effect on both traditional and modified sinusoidal riblets. The increase and decrease in drag caused by riblets are calculated by comparing the drag of the upper and lower walls in a channel. To reproduce inclined flow, pressure gradients Pg cosφ and Pg sinφ are applied in the x and z directions, respectively, where Pg is the pressure gradient applied in the x direction in the zero-yaw-angle case as the driving force. Under moderate misalignment of φ ≤ 10°, straight riblet is more robust than the other two configurations against the change of yaw angle. Nevertheless, the drag-reducing performance of both the traditional and modified sinusoidal riblets is still maintained. It should be noted that the total drag reduction rates of the modified sinusoidal riblet are better than those of the traditional sinusoidal riblet. Under larger misalignment of φ = 20°, the total drag reduction rates of the three configurations are similarly degraded. To discuss the reason for the change of drag-reducing performance, the contributions of the pressure drag and friction drag to the total drag reduction rates, which cannot be measured separately, are investigated by DNS.
The present paper discusses acceleration in the swimming of a small three-dimensional fish with two motions, carangiform and anguilliform. Flow fields generated by fish deformations are investigated numerically by the constrained interpolation profile method in combination with an immersed boundary method. The three-dimensional vortical structure visualized using a second invariant and the pressure field around the fish body show that a fish with anguilliform motion accelerates more rapidly than one with carangiform motion because of a larger thrust due to the strong transverse vortex in the wake of the fish and a large pressure variation around the fish body. It is also found that the time variations of inline swimming speed of a small fish and the fluid force acting on it can be estimated using a free-fall model, and the fluid force can be expressed by a linear function of the fish speed. This function consists of a thrust part that is independent of fish speed and a viscous drag part that is proportional to fish speed. Thus, time histories of swimming speed, swimming distance, and fluid force can be predicted by simple functions from rest to terminal speed.
In this study, vorticity dissipation phenomenon within a curved shear layer while Karman vortices are formed behind a body was investigated experimentally based on time variation of energy dissipation function distribution. The vorticity dissipation within a separated shear layer would be caused by viscous effect associated with shear strain in the process of pairing between two vortices formed by Kelvin-Helmholtz instability. Therefore, in this experiment, the vortex pairing phenomenon within a separated shear layer was reproduced within a centrifugally stable curved free shear layer. Time variation of velocity distribution in one period of vortex pairing process was obtained by means of L.D.V. and phase ensemble averaging technique. By differentiating the velocity distribution for each phase of pairing process, time varying distributions of vorticity, shear strain rate and energy dissipation function were obtained and investigated. As the results, it was found that the strong shear strain occurs and energy is dissipated significantly when the vortices are started to starch in the process of pairing. Also, it was found that the diffusion of vorticity from the vortices to surrounding irrotational fluid becomes significant after the vortices are fully stretched, instead of in the process of stretching. Moreover, it was found that the energy dissipation by shear strain is almost ended when the pairing vortices align vertically, that is defined as the "merging location."
We propose a unified interpolation stencil that is used for a ghost-cell immersed boundary method to satisfy wall boundary conditions in Cartesian-based numerical simulation of fluid flow with complex boundaries. As other ghost-cell methods do, the numerical boundary point is considered in the solid region and the required velocity is interpolated directly from the proximate points in the fluid region. In this paper, we propose a unified interpolation scheme based on a sequence of one-dimensional interpolations. Different interpolation stencils are examined and their convergence rates are compared by solving a benchmark problem on the flow between the concentric cylinders. In contrast to typical standard stencils, the proposed ones are versatile and do not require to be altered according to the irregularities in boundary shape. Namely, the boundary condition can be accurately imposed with a unique stencil for all numerical boundary points while preserving the convergence rate of the flow solver. Performance of the proposed method is studied by solving two-dimensional incompressible flows around a circular cylinder, a square cylinder, and a square cylinder inclined with respect to the main flow. Comparison with the existing numerical and experimental data shows good agreement, which confirms the capability of the proposed method.
We investigated atomized spray droplet size from multi-hole nozzles for direct injection gasoline (DIG) engines. Our findings showed that the droplet size can be described by the nozzle-hole geometry. For the DIG engine, adequate spray pattern and finely atomized spray are important to achieve low emission or/and low fuel consumption. As an injector for DIG engines, multiple holes (multi-hole) type nozzle is typically used because of adaptability of spray pattern. The multi-hole type spray has been generally used for Diesel engines, and the characteristics have been investigated in earlier studies. However, multi-hole nozzles for DIG engines require narrow spacing as fuel passage just upstream of the orifice hole. The narrow fuel passage affects spray characteristics including droplet size. This makes droplet size prediction and designing orifice geometry difficult, thus the narrow passage geometry needs to be incorporated as a design parameter. We therefore investigated relation between droplet size and nozzle geometry both experimentally and theoretically. Experimentally, we evaluated an experimental dataset which was done in previous work in which the spray droplet size from the fabricated test sample nozzles, and determined the relationship parameters between nozzle geometries, flow rate, and droplet size. The experimental result in which its pressure range was 1 to 15MPa showed that velocity at outlet of orifice-hole is a dominant factor to determine droplet size, and that the velocity has a correlation with the nozzle geometry. Theoretically, we focused on a pressure-drop at the narrow passage, which can describe velocity at the outlet of the orifice-hole. Finally, theoretical approach described the droplet size by using the orifice geometries incorporating the parameter of narrow passage.
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