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The focused acoustic field formed under the water surface raised by ultrasound exposure was numerically investigated to elucidate the relationship with the surface rising prior to ultrasonic atomization. The effect of surface tension was newly added to the computational scheme constructed in the previous paper (Orisaki and Kajishima, 2022) and the direct numerical simulation based on compressible fluid dynamics was conducted. The water surface above the sound source rises. When the risen surface shape changes into a dome due to the effect of surface tension, the acoustic antinode with strong focusing appears inside the dome and the water surface begins to rise rapidly. In case of the insufficient sound source pressure, the gentle risen surface is kept, and acoustic peak spots remain deep due to the small curvature of the surface. These results suggest that the dome formation increases the acoustic pressure amplitude at the dome center and promotes acoustic cavitation there. On the dome surface, the kinetic energy density with the phase opposite to acoustic pressure increases, which causes the increase in the acoustic radiation pressure.

When an underwater ultrasonic wave is emitted toward an air-water interface, the water surface rises and droplets are generated from the formed fountain. The rising process of water surface was numerically investigated for better understanding the mechanism of ultrasonic fountain prior to the atomization. To analyze the water surface rising that occurs in a very short time, it is necessary to simulate the rapid increase of acoustic radiation pressure and the rapid development of acoustic streaming. Therefore, the direct numerical simulation based on compressible fluid dynamics was carried out. The water surface rising as observed in the formation process of ultrasonic fountain was successfully reproduced. In the region between sound source and water surface, standing wave is established and acoustic kinetic energy density increases significantly while water surface rises with acceleration. The kinetic energy density is associated with the acoustic radiation pressure acted on free surface based on the theory of Yosioka-Kawasima (1955). After the rising speed becomes to be constant, the standing wave fades and the kinetic energy density decreases. These results suggest that the acoustic radiation pressure acted on water surface increases significantly due to temporary resonance and water surface rises rapidly. By drawing a fluid due to rapid rising of water surface, acoustic streaming is induced toward the risen region.

In this study, a large-eddy simulation (LES) is conducted to investigate meandering airflows generated throughout the underbody of a real-shaped train model in open air. In our previous study, this was shown by an LES of airflows around a simplified train model. The shape of the underbody affects the flow. However, thus far, no systematic analyses that consider bogies have been conducted. Our experimental results qualitatively reproduced the power spectra of lateral velocity fluctuations in the underbody obtained using a 1:8.4-scale train model on a moving belt in a wind tunnel. Results on the effects of various bogie shapes suggested that the meandering flow was primarily affected by the time-averaged profile of streamwise velocity. Thus, the effects of the bogie shape on airflow are considerable. Comparing bogie shapes with and without a side cover, that without a side cover generated meandering airflow with a slightly smaller peak frequency than that with a side cover, and a completely smooth bogie generated no meandering airflows. It was confirmed that this LES was useful as a technical tool to develop measures to reduce meandering airflows around high-speed trains.

To clarify the mechanisms underlying airflow-induced vibrations of high-speed trains running through tunnels, large-eddy simulation of a large-scale flow structure around a simplified 6-car train model was conducted. Since actual trains run on one of the double track lines, the position of the train model was made to deviate from the tunnel center and hence the gap between one of the sides of the train and the tunnel wall is narrower than that of the other side. A train running in the open air was also calculated for comparison. The results of this study shed light on the generation mechanism of the pressure fluctuations acting on the side of high-speed trains as follows. Firstly, in the open air, the air velocity in the space between the underbody and the ground gradually decreases from the head toward the tail of the train. Thus, the air velocity is slower than that on both sides of the train, which generates shear flows near the bottom edges of both sides of the train. The shear flows cause large Karman vortex-like vortices (staggered Karman vortex street), which in turn lead to a meandering airflow beneath the underbody of the train. Secondly, in the tunnel, the air velocity not only in the gap between the underbody and the ground but also in the narrower gap between the side of the train and the tunnel wall gradually decreases from the head toward the tail of the train. In the same mechanism as the open air, a meandering airflow is generated throughout the side and underbody of the train and causes pressure fluctuations along the side of the train. Finally, it is demonstrated that the wavelength of pressure fluctuations along the side of the actual train can be estimated from the present LES results.

Large-eddy simulation (LES) of the cavitating turbulent flow around a hydrofoil was conducted. Especially, we focused on the improvement of the reproducibility of the hydrofoil performance under the condition of cavitation when considering the unsteadiness of the flow field sufficiently by LES. The analysis object is the cavitating turbulent flow around a Clark-Y11.7% hydrofoil at the angle-of-attack of 2 degrees. The weak compressibility was taken into account in the governing equation. The cavitation is represented by the cavity source based on the homogeneous fluid model. For LES, the subgrid scale (SGS) eddy viscosity was determined by solving the transport equation of SGS kinetic energy. Typical patterns of cavitation that was observed experimentally for various cavitation number were successfully reproduced: e.g., attached sheet cavitation of steady as well as unsteady modes. The reproducibility of the cavitation characteristics of the hydrofoil was improved in comparison with that by previous Reynolds-averaged turbulence models. In addition, by reducing the cavitation number, the slight increase of lift coefficient was observed before the breakdown. These are due to the streamline curvature around the sheet cavity. We found this feature is related to the unsteady motion of large-scale spanwise vortices. LES revealed that the vortices are intermittently generated by the baroclinic torque originated from the onset of sheet cavitation.

We investigate the drag-reducing performance of a zigzag riblet inspired by the “Miura fold” and its influence on the streamwise vortices above a wall-bounded turbulent flow through direct numerical simulations of channel flows. The employed channel wall geometries are a flat plate, straight riblet, and zigzag riblet. The drag-reducing performance of various zigzag riblets with adjusted configuration parameters is superior or at least comparable to that of the straight riblet. We assume an analogy between the drag reduction mechanisms of spatially periodic forcing and the zigzag riblet, because both methods induce similar sinusoidal velocity profiles. To investigate the characteristics of the zigzag riblets, we apply a conditional sampling technique to the near-wall streamwise vortices that is also applied to the wall-bounded flow under spatially periodic forcing. The flow toward the wall of the rotating motion of a vortex becomes relatively small, as the main flow levitates at the tips of the zigzag riblet. Thus, the ejection increases and the sweep decreases. In the phase where the direction of the induced spanwise velocity coincides with the vortical motion, the latter is weakened because the vortex tilts in the spanwise direction at the phase; then, vortex stretching is suppressed. The zigzag riblet can reduce the drag via a mechanism analogous to active control, such as periodic oscillation. However, the effect of the upward flow is dominant above the zigzag riblet, and the analogous mechanisms are less remarkable. The considered zigzag riblet has potential application as a kind of active feedback control.

A new method for studying the interaction between an elastic object and a fluid has been developed. The fluid phase including solid interface is solved by our immersed solid method of body-force type. In the present study, the fluid-solid interaction force is incorporated into the finite-element method. This process is done by a superposition of the hydrodynamic force field with the solid internal force field. The inter-phase momentum exchange is implemented through the distributed force field shared by both Eulerian and moving Lagrangian references. In this paper, we demonstrate the recent results of our conservative momentum exchange algorithm for the fluid flow bounded by elastic walls. Examples include two-dimensional flows through a gap between modeled vocal cords, and some three-dimensional demonstrations.

Cavitation instability in the turbo-pump can be divided into two different stages: the local instability such as the rotating cavitation and the system instability such as the cavitation surge. In our study, a numerical analysis of cavitating flow in a two-dimensional cascade, which represents the tip region in an inducer of liquid-fuel rocket engine, was conducted to find an indicator of the onset of cavitation surge. The response characteristic of cavitating flow field to three types of inflow boundary conditions was examined: steady inflow, inflow with sinusoidal fluctuation and inflow considering the characteristic of piping system. The last one is modeled by the unsteady Bernoulli's equation. Various cavitation modes that cause local instability and system instability were reproduced by considering flow rate variation in piping system. It is found that the specific mode, which is hidden behind the fluctuation of rotating cavities, is to be developed to the cavitation surge. The frequency of the surge was confirmed to be in the experimentally observed range and the ratio of the surge frequency to the propagating frequency, which is generated by rotating cavitaion, is almost constant while inflow changes.

This study investigates the aerodynamics of an airfoil which passes close to an air-water interface with heaving motions by means of numerical simulation. Simulations are performed by solving the Navier-Stokes equation on a curvilinear coordinate system whose axes fit the moving airfoil surface in contrast to the conventional approaches which neglect the air viscosity. The air-water interface is captured by a CIP method. We show the crucial importance of taking the air viscosity into account for the successful prediction of the airfoil aerodynamics in heaving motions by demonstrating the observation of vortex separations near the leading edge of a NACA0012 airfoil at the Reynolds numbers of 50000 and 66138 based on the viscosity and the density of air and the translational velocity of the airfoil. It is found in this study that the existence of the water surface has a significant impact on the lift force on the heaving NACA0012 airfoil and the deviation of the lift coefficient from the one measured in the simulation conducted in the open space depends not only on the clearance between the airfoil and the water surface but on the mean angle of attack and the phase of the heaving. When the airfoil moves close to the surface, the surface effect on the airfoil-aerodynamics is emphasized due to the squeezed-film damping and the interaction of the separated vortices and the air-water interface. The importance of analyzing the fluid motion of both air and water phases is illustrated by showing that the kinetic energy of the moving airfoil transferred through the the air-water interface is rather significant.

The resolution and efficiency of the finite-difference lattice Boltzmann method (FDLBM) is improved to deal with wall-bounded turbulence, which is characterized by the strong shear and anisotropy. FDLBM puts the merit of LBM, which is the explicit and non-iterative algorithm, into practice on the body-fitted coordinate in the conventional solvers based on Navier-Stokes equation of motion. Thus the performance of FDLBM is mostly affected by the finite-difference scheme for the advection terms of LBM, which has to be an upwind one from a stand point of numerical stability. Particularly in this study, the influences of the the order of accuracy and upwind method are assessed by the direct numerical simulation of fully-developed turbulent flow in a plane channel. We introduce a discretization method with numerical flux similar to the finite-volume method, and a nonlinear scheme which localizes the effect of the numerical diffusion. Our method successfully reproduced the mean velocity and turbulence statistics in comparison with standard database. We confirmed that the nonlinear scheme improved the resolution. Increase of reproducibility with the higher order scheme surpassed increment of its computational cost. The 7th-order scheme, for example, provided a comparable result to that by the 3rd-order scheme using 4 times finer grid, though the calculation time increases just 20 % at the same resolution. This higher-order nonlinear scheme proposed in this study, by reducing the requirement of computational resources, can extend the applicability of LBM for DNS and LES of turbulent flows.

Under a high Schmidt number condition, concentration boundary layers get much thinner than momentum boundary layers. Resolution requirement to numerically capture the steep concentration gradient near an interface is therefore significantly high. This article presents a novel VOF-based method to predict mass transfer from gas-liquid interfaces using a computational grid of a marginal resolution required for the solution of the Navier-Stokes equation. The solution procedure to the mass conservation equation is divided into two steps: the dissolution and diffusion step and the advection step. The concentration profiles near gas-liquid interfaces, which are identified as segments (in case of two-dimensional computations) in each computational cell, are reconstructed in terms of the complementary error function by virtue of the boundary layer approximation to the solution of the unsteady advection-diffusion equation of mass. The amount of dissolution from the interfaces and diffusion in the vicinity of the interfaces is obtained by taking advantage of the reconstructed concentration profile on each interface segment. In the advection step, the un-smoothness of concentration profiles in the interface cells is explicitly taken into consideration by taking full advantage of a VOF advection scheme. The present method is validated in two-dimensional test problems with the Schmidt number of 100 which cover a pure diffusion problem and a mass transfer problem from a freely rising buoyant bubble. The validation shows the present method is capable of resolving a concentration boundary layer which is as thin as a computational cell. The reduction rate in the overall computational cost is O(10-3) compared to one of the conventional methods (Ezu et al., 2011) without the subgrid-scale resolution.

A numerical method for liquid-vapor two-phase flows accompanied by condensation/evaporation is proposed. The phase change model at the vapor-liquid interface, which had been theoretically derived by Sone and Onishi, is coupled with an interface capturing scheme. The model gives the condensation/evaporation rate as boundary conditions. The interface is captured by the volume-of-fluid method associated by the reconstruction scheme, and the scheme to obtain the pressure with consideration for thermodynamics in the vicinity of the interface is employed. These methods are coupled and arranged on the cylindrical coordinate system to appropriately deal with the liquid film flow around a cool cylinder in a natural convection of vapor. The development of a liquid film due to the condensation, the flow in a thin layer and a drop of the distilled liquid are successfully reproduced in our result. The influence of the volumetric conservation is confirmed by comparing the results of condensation case and a non-condensation case. Besides the Nusselt number is in good agreement with a theoretically estimated value.

We performed numerical simulations of a non-steady separated shear layer with and without cavitation to examine the effect on flow dynamics. Particular focus was given to the interaction between vortices and cavitation. In the simulations, streamwise and spanwise vortices generated by the instability of a shear layer flow, typical features in such a flow field, were formed further upstream in cavitating than in non-cavitating flows. In cavitating flows, the vortex shedding frequency and the Reynolds stresses increase, and we observed vortex weakening caused by cavitation. We found that a Burgers-type vortex can become the origin of a cavity. Contrarily, the growth of the cavity attenuates the corresponding vortex. We described this influence of a cavity on a streamwise vortex with a simple inviscid model.

For the application to optimal design and effective operation of air-conditioning system in an aircraft cabin, we propose an indicator to represent the air quality. It was derived from the result of the large-eddy simulation (LES) of turbulent flow with the immersed boundary (IB) method, which took into account the respiration of passengers. The cabin air quality is defined as an oxygen concentration of inhalation air (OCIA) per each breath. Degree of air renewal in reference volume is a dominant factor of air quality, OCIA. Intensity of time-averaged velocities by cross-sectional components closely correlates with the degree of the air replacement, and becomes the most suitable indicator of air quality. In case of decrease of the intensity, each of two different flow conditions, namely stagnation and circular flow just around a mouth, was found out at the reference volume as inactivation elements of the air renewal.

Attention was focused on the statistical properties of pressure fluctuation, which is caused by fine-scale vortices in turbulent flow. The aim is improvement in the prediction of cavitation inception due to fine-scale turbulence vortices, which are usually in subgrid-scale (SGS) in Large-eddy simulation (LES). We conducted a finely-resolved direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer in cavitating and non-cavitating (single-phase) conditions. The result under cavitating condition suggested that low-pressure region corresponding to the core of fine-scale vortices could become an origin of cavitation. We applied filtering technique to DNS database under non-cavitating condition to model the low-pressure region of subfilter vortices observed in result under cavitating condition. Filtering volume is corresponding to that in the probable LES. In fully developed turbulence, proportional relation was found out between intensity of SGS pressure fluctuation and turbulent kinetic energy. In addition, Gaussian profile reasonably approximated instantaneous pressure distribution within a filtering volume. We therefore think the possibility of cavitation inception can be accurately estimated by using the intensity of SGS kinetic energy in couple with filtered pressure field.

Direct numerical simulations (DNS) of turbulent flow through an asymmetric plane diffuser, consisting of a flat wall and an inclined wall, were performed using a high-order finite difference method, to reveal the relationship between turbulence and flow separations under negative pressure gradients. A typical feature of this flow field is the non-steady three-dimensional separation region formed near the inclined wall. At the opening of the diffuser, low speed streaks in wall turbulence cause the initial non-steady separation layer, which includes small-scale reverse flow regions. Because turbulent eddies growing from this initial separation suppress the separated flow, a small reattachment section is formed downstream. When turbulent eddies start to decay and the negative pressure gradient begins to dominate, the flow separates again, and then a large-scale separation region is formed. In summary, the intensity of turbulent eddies affects the formation of the separation and reattachment regions near the inclined wall.

The mechanism of secondary flow was discussed based on a result of LES of turbulent flow in a subchannel. The LES was carried out on the Cartesian grid system using an improved immersed boundary method developed for accurate simulation of complex wall boundary of industrial interest. The method was verified by comparing the LES with a DNS of turbulent flow in a pipe. The LES for the subchannel reasonably reproduced the secondary flow of the second kind. To analyze the mechanism of the secondary flow, a theoretical method was proposed. The result of the analysis indicated that main source of the secondary flow was a non-conservative component of Reynolds stress as was the case for a square duct. The theory suggested that the non-conservative force corresponds to an imbalance between pressure along the wall and Reynolds stress decreasing rapidly near the wall. The present theory will unify an understanding between secondary flows of the first and second kind. The present LES technique and theory are useful for investigating physics in turbulent flow bounded by complex walls.

The direct numerical simulations of turbulent flow in a rotating channel are executed, with the attention on a transient state after an onset of the rotation. Some different rotation numbers which contain 0, 0.5, 1, 2.5 and 5 are tested. To clarify a relationship between rotation numbers and the alteration of turbulence structures, we paid notice to temporal evolutions of wall friction velocities on both sides, volume-averaged velocity, kinetic energy and its production and dissipation. We found that the time evolutions of flow rates indicate non-monotonic behaviors due to the system rotation. The major reason of it is the difference in response of wall friction velocities on both walls. Moreover, we applied an analysis based on the theory of the invariants of Reynolds stress tensor to associate the status of turbulence with turbulence structures. From the result of the analysis, the three-dimensionality of turbulence is emphasized by the system rotation except for the vicinity of the wall on the pressure side. On the suction side, however, flow field indicates the feature of two-dimensionality.

An immersed boundary method is improved and applied to 2-D flow fields involving a single stationary/moving object. The present immersed boundary method employs a body force proportional to a solid volume fraction for coupling the solid and fluid motions at the interface. A hyperbolic-tangent function is newly introduced as a surface digitiser for computing the volume fractions at the interface cells, and this improvement is proved to be efficient for problems involving arbitrary shape object. The present method is applied to a uniform flow field around a circular cylinder and an interaction problem of fluid and free-falling object. The computational results are found to agree with the results by the different methods of the present authors and the results reported in the literatures. Also the computation time is considerably cut down compared to the other methods by the series of improvements to the immersed boundary method.

While the Navier boundary condition, which claims the proportionality between fluid slip velocity and wall shear stress (Qian et al., 2003, Bocquet and Barrat, 2007), was established by Thompson and Troian (1997) for a single-phase Newtonian fluid flowing along an atomically defect-less solid wall under a wide range of shear rate conditions, its validity for flows with a contact line has not been proved yet even for the simplest pairing of a monoatomic fluid and a solid with a face-centered cubic structure. In the studies of Qian et al. (2003, 2006) the static wall shear stress was subtracted in the formulation of their Navier boundary condition, but as we show, it is not physically justified. Ren and E (2007) formulated a Navier boundary condition in terms of the fluid slip velocity and wall shear stress integrated through the region containing the contact line in a similar fashion to the present work, providing no physical grounds regarding their particular choice of the integration region and the interfacial region. We performed molecular dynamics simulations of Couette flows where two immiscible liquids with an identical molecular mass and identical interaction potentials were driven by two parallel solid walls so that steady flows with moving contact lines were formed. Based on the detailed analysis of stress tensor and slip velocity distributions both for static and dynamic cases, we show that the Navier boundary condition should be formulated in terms of the quantities integrated through the fluid-fluid interaction region in the first adsorption layer formed on the solid wall. In order to investigate the relevance of the Navier boundary condition as a boundary condition of the Navier-Stokes equation, the validity of Newton's law of viscosity between the first and second adsorption layers is also examined.

Although the advantage of using arbitrarily-shaped polyhedral meshes for the industrial flow applications is clear, their employment to two-phase flows is rather limited due to difficulty in deriving and implementing algorithms without overwhelming complexity on such meshes. We present a numerical method based on the VOF (Volume of Fluid) method which works on arbitrarily-shaped three-dimensional polyhedral meshes with comparable accuracy to the methods for structured meshes. We extend the THINC (Tangent of Hyperbola Interface Capturing) method and the RDF (Reconstructed Distance Function) method respectively, to solve the advection equation of the color function and to estimate the interface curvature on polyhedral meshes without laborious geometric arithmetics.

An LES was carried out to clarify the mechanism of decaying swirl in a rod-bundle. In our LES, an immersed boundary method was used to treat this complex wall boundary in the Cartesian grid system. A consistent immersed boundary method and a one-equation dynamic SGS model were introduced for an accurate simulation of no-slip wall condition. The Reynolds number based on the bulk velocity, the rod pitch and the kinematic viscosity was approximately 4100. Our computational results were compared well with experimental and computational data obtained in other studies. The results were able to represent the effect of flow geometry: the flow around the mixing-vanes caused the swirl with a large-scale fluctuation enhancing heat transfer; a vortex enhancing enthalpy mixing between channels was produced in the rod gap; this developing vortex and the decreasing wake promoted the decay of the swirl more strongly than in a pipe. The LES technique introduced in this study is useful for designing the spacer by predicting the effect of flow control.

Motion of solid object in fluid is studied in moving frame of reference. Navier-Stokes (N-S) equations in a non-inertial frame of reference is coupled with the equations of linear and angular momentums for the solid object. It is shown that the numerical implementation for solving the non-inertial N-S equations is equivalent to that of the arbitrary Lagrangian-Eulerian (ALE) method. The simulation results by the two methods show reasonable agreements for a 2-D flow field including a cylinder. In the present work, a generalised convective boundary condition is constructed for non-inertial frame of reference. Also, an appropriate boundary condition is proposed for fluid phase based on a least square adjustment (LSA) method. It is shown that the LSA is essential for the non-inertial study fluid-solid interaction. Also, the non-inertial N-S equation is applied to a problem of a concave object falling in a fluid. It is shown that traditional time-advancement schemes undermine the ortho-normality of the rotation matrix, resulting in non-physical deformation of the object. However, our time-advancement procedure with quaternion is found to be robust and effective even under a violent manoeuvre of the object.

The purpose of this study is to develop a numerical method for turbulent flows at low Mach number range. To account for the weak compressibility, we modify the time marching method of the usual incompressible scheme which is based on the elliptic equation for pressure. To deal with high Reynolds number flows appropriately, we propose a new one-equation subgrid scale model (SGS). In this model, the concept of coherent structure function model is introduced to treat the energy transfer from grid scale to SGS portion of turbulence kinetic energy. The feature of our one-equation SGS model is that the energy production rate of SGS kinetic energy is calculated without the dynamic procedure, and any parameters such as the friction velocity on the wall or distance from the wall are not necessary. The new one-equation SGS model is incorporated into the weakly compressible scheme to treat a small density variation. Computational examinations have been conducted for fully developed turbulent flows in a plane channel and turbulent flows around NACA0012 airfoil at low Mach number, and have shown satisfactory results. We show that the consideration of the density variation even in low Mach number flows is essential to reproduce the pressure fluctuation and vortical structure appropriately.

We developed a practical method for the computation of liquid-vapor two-phase flows accompanied by phase change at the interface. In this paper, we propose an intrinsic improvement by introducing a boundary condition at the non-equilibrium interface, which was derived by Sone and Onishi (Journal of the Physical Society of Japan, Vol.44, (1978),pp.1981-1994.) on the basis of the kinetic theory of gases. The boundary condition, which gives the relationship between the phase change rate and the jump in physical properties, was appropriately integrated with a numerical simulation based on continuum mechanics. The interface was captured by the volume-of-fluid (VOF) method with the piecewise linear interface construction (PLIC) scheme to improve the conservation property of volume. This method was applied to simulating film condensation around a horizontal cylinder. Our results showed that heat and fluid phenomena, including condensation to a liquid film, were successfully reproduced. The order of the spatially averaged Nusselt number on the cylinder was in good agreement with the theoretical value. We compared the results of our method with those of a method that obtains the phase change rate without considering the boundary condition on a molecular scale. We found that our method was effective at simulating film condensation.