An outlook of computational fluid dynamics methods based on the fixed Cartesian grid, especially the immersed boundary (IB) method and related techniques, is provided. The basic idea of IB methods ...and the improvements to maintain consistency of boundary condition and mass conservation, that is the consistent projection method, are discussed. Then, recent examples for particle-laden flows are introduced. To deal with many particles, the immersed solid method is picked up as an efficient alternative to the IB method. In particular, we place focus on the flow and heat transfer of dense mixture of particles and liquid. In such a condition, the flow in narrow gap in between solid interfaces is considered by the lubrication equation. Finally, for further development of application in large-scale turbulent flows laden with particles, the importance of explicitly-defined volume averaging is pointed out based on our recent progress.
•Low dissipation hybrid scheme of WCNS and the central finite difference for multi-component flows.•A new simple discontinuity sensor is composed by the Larsson shock sensor and the material ...interface sensor.•Numerical tests demonstrate the performance of capturing shock waves and low numerical dissipation.
A discontinuity sensor for shock waves and material interfaces is proposed to construct a low dissipative scheme that consists of a weighted compact finite nonlinear scheme (WCNS) and central difference to address compressible multi-component flows. The Harten-Lax-van Leer and contact (HLLC) scheme is applied to capture shock waves through material interfaces. At the material interface, the overestimated quasi-conservative WCNS maintains the equilibriums of velocity, pressure, and temperature. The discontinuity sensor is composed of a Larrson shock sensor and a material interface sensor to distinguish between smooth and discontinuous regions, respectively. In the single-component shock-vortex interaction problem, the present scheme successfully captures shock waves with low numerical dissipation. In the multi-component shock-bubble interaction problem, Richtmyer-Meshkov instability problem, and triple-point problem, the simultaneous capturing of shock waves and material interfaces by the present scheme is demonstrated. The proposed scheme suppresses the numerical oscillation by shock waves and material interfaces; additionally, it successfully reduces the numerical dissipation in smooth regions.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
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.
We proposed a novel numerical method for the reliable prediction of decarburization with CO2. In our method, mass, momentum, and energy conservation equations are solved simultaneously, where the ...reactive mass transfer, compressibility, and moving interface between gas and liquid are fully considered. In the decarburization reaction model, we assumed that the rate-limiting processes are the mass transfer in the gas phase and the interfacial reaction rate. Our method quantitatively well reproduced the total decarburization rates in the crucible of Nomura and Mori’s experiment (Trans. ISIJ, 13 (1973), 265.) using a jet of CO2–CO gas mixture. It was found that the interfacial reaction rate affected the local decarburization reaction rate and the concentration distribution of CO2 and CO near the gas–liquid interface. Thus, the consideration of the interfacial reaction rate is important for the accurate reproduction of the local decarburization phenomena by a gas jet of CO2.
A discrete-forcing immersed boundary method with permeable membranes is developed to investigate the effect of lubrication on the permeations of solute and solvent through membrane. The permeation ...models are incorporated into the discretisation at the fluid cells including the membrane, and discretised equations for the pressure Poisson equation and convection–diffusion equation for the solute are represented with the discontinuities at the membrane. The validity of the proposed method is established by the convergence of the numerical results of the permeate fluxes (solute and solvent) to higher-order analytical models in a lubrication-dominated flow field. As a model of the mass exchange between inside and outside of a biological cell flowing in a capillary, a circular membrane is placed between parallel flat plates, and the effect of lubrication is investigated by varying the distance between the membrane and the walls. The pressure discontinuity near the wall is larger than that at the stagnation point, which is a highlighted effect of lubrication. In the case of a small gap, the solute transport is dominated by convection inside the circular membrane and by diffusion outside. Through the time variation of the concentration in the circular membrane, lubrication is shown to enhance mass transport from/to inside and outside the membrane.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In the framework of local volume-averaging for two-way coupling simulation of particle-laden flows, we have developed a force model that represents the particle reaction to the fluid. By considering ...the stress profile on the surface of finite size particles, our previous model was capable of representing the reaction force distribution even without fully resolving the boundary layer around the particle of comparable size to the grid spacing. In our method, the anisotropy of the surface stress is reasonably taken into account in the reaction force. To extend the applicability for particles smaller than the grid spacing, a smoothing method is developed in a consistent way with the discretization of the numerical simulation. The effectiveness of the smoothing method is demonstrated by applying to the following four fundamental fluid-particle interaction problems; a stationary particle in a uniform flow, a moving particle in a vortical flow, a rotating particle in fluid at rest and a particle suspension in a shear flow. The anisotropic contribution of the reaction force is reasonably represented by the smoothing method applied to the volume averaging technique particularly for rotating particle case. For the suspension in the shear flow, the non-physical effect of the grid size is suppressed by the smoothing method. Therefore, the developed reaction force model is effective for the case that the effects of shear and rotation are dominant.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
•A fluid force model on a non-negligible size particle is constructed based on the volume averaged flow information.•The model based on the disturbed flow worked well for non-uniform and unsteady ...flows.•The undisturbed gradients of pressure and velocity are also estimated.
The relationship between the flow field numerically obtained by the two-way coupling simulation and the fluid force on each particle is discussed. For estimating the fluid force on a particle, the effect of the disturbance by the particle needs to be considered. In the present study, for a particle located in a steady ambient flow, the fluid force is modelled as a function of the averaged velocity and pressure over an explicitly-defined averaging volume in the disturbed field. The gradients of the pressure and velocity induced by the particle are also modelled. It is found that the discretised gradients are almost independent of the distance between the reference points for sufficiently small distances. This fact makes the gradient models independent of the grid width of the two-way coupling simulation. The proposed steady viscous force model implicitly includes the correction terms due to the strain of the undisturbed flow and the history effect as the model is constructed with the disturbed flow. For the radius of the averaging volume smaller than 5 times the particle radius, the present force estimation method based on the disturbed flow particularly works well. The results suggest that the present method is effective in the two-way coupling simulation with the particles of comparable size to the minimum length scale of the background flow.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A new discretization scheme on Cartesian grids, namely, a “consistent direct discretization scheme”, is proposed for solving incompressible flows with convective and conjugate heat transfer around a ...solid object. The Navier–Stokes and the pressure Poisson equations are discretized directly even in the immediate vicinity of a solid boundary with the aid of the consistency between the face-velocity and the pressure gradient. From verifications in fundamental flow problems, the present method is found to significantly improve the accuracy of the velocity and the wall shear stress. It is also confirmed that the numerical results are less sensitive to the Courant number owing to the consistency between the velocity and pressure fields. The concept of the consistent direct discretization scheme is also explored for the thermal field; the energy equations for the fluid and solid phases are discretized directly while satisfying the thermal relations that should be valid at their interface. It takes different forms depending on the thermal boundary conditions: Dirichlet (isothermal) and Neumann (adiabatic/iso-heat-flux) boundary conditions for convective heat transfer and a fluid–solid thermal interaction for conjugate heat transfer. The validity of these discretizations is assessed by comparing the simulated results with analytical solutions for the respective thermal boundary conditions, and it is confirmed that the present schemes also show high accuracy for the thermal field. A significant improvement for the conjugate heat transfer problems is that the second-order spatial accuracy and numerical stability are maintained even under severe conditions of near-practical physical properties for the fluid and solid phases.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
•Spatial variations of heat flux with respect to solid volume fraction are obtained.•The heat fluxes through the fluid and individual particles are visualized.•Effects of heat flux through particles ...and interface are highlighted.
To study the heat transfer in a natural convection under dense particulate condition with finite-size spherical particles of uniform diameter, a direct numerical simulation is conducted. For calculating the momentum-interaction between the particle and fluid, our original immersed solid method is applied. The heat transfer in the particle-dispersed flow is treated in Eulerian way with the interfacial flux decomposition method. The results shows that, with fixing the thermal conductivity ratio (of the solid to the fluid) to be 100, the temporal- and horizontal-average Nusselt number 〈Nu〉t increases monotonically with solid volume fraction (vf) at Rayleigh number Ra = 104, while 〈Nu〉t at Ra = 105 exhibits a local maximum at around vf = 40%, although 〈Nu〉t at Ra = 105 is always larger than that at Ra = 104. The heat flux in the particulate system is decomposed into the contributions by convection and conduction through the particles, fluid and interface, and the result shows that the conduction through the interface is the dominant factor to the vertical heat flux in the media. Through visualization of the heat flux through the particle surface, the importance of directly resolving the local heat conduction within the individual particle and through the interface is highlighted.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
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