Yohei Morinishi

Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows

The form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by Morinishi et al. [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 124 (1998) 90], and fully conservative finite difference schemes suitable for shock-free unsteady compressible flow simulations are proposed. Commutable divergence, advective, and skew-symmetric forms of convective terms are defined by including the temporal derivative term for compressible flow. These forms are analytically equivalent if the continuity is satisfied, and the skew-symmetric form is secondary conservative without the aid of the continuity, while the divergence form is primary conservative. The relations between the present and existing quasi-skew-symmetric forms are also revealed. Commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system, and they are fully conservative provided that the corresponding discrete continuity is satisfied. In addition, a semi-discrete convection scheme suitable for compact finite difference is presented based on the skew-symmetric form. The conservation properties of the present schemes are demonstrated numerically in a three-dimensional periodic inviscid flow. The proposed fully discrete fully conservative second-order accurate scheme is also used to perform the DNS of compressible isotropic turbulence and the simulation of open cavity flow.

Effect of rheological properties on drag reduction in turbulent boundary layer flow

Direct numerical simulation of a zero-pressure gradient drag-reducing turbulent boundary layer of viscoelastic fluids was systematically performed at the momentum-thickness Reynolds number Reθ0=500 and Weissenberg number We=25 using constitutive equation models such as the Oldroyd-B, the finitely extensible nonlinear elastic Peterlin model at the maximum chain extensibility parameters L2=100, 1000, and 10 000, and the Giesekus model at the mobility factors α=0.01, 0.001, and 0.0001, where the ratios of solvent viscosity to zero shear rate solution viscosity, β, were 0.9, 0.99, and 0.999. For the case that the elongational viscosity for the steady elongational flow was identical, the streamwise variation in the drag reduction (DR) was thoroughly investigated, and then the effects of rheological properties such as the elongational and shear viscosities and the first and the second normal stress differences on DR were clarified. It is found that the streamwise profile of DR shifts downstream with the decreas...

Skew-symmetric convection form and secondary conservative finite difference methods for moving grids

The secondary conservative finite difference method for the convective term is recognized as a useful tool for unsteady flow simulations. However, the secondary conservative convection scheme and associated skew-symmetric form have not been extended to those for moving grids. In this study, the skew-symmetric form and the secondary conservative convection schemes for ALE type moving grid simulations are proposed. For the moving grid simulations, the geometric conservation law (GCL) for metrics and the Jacobian is known as a mathematical constraint for capturing a uniform flow. A new role of the GCL is revealed in association with the commutability and conservation properties of the convection schemes. The secondary conservative convection schemes for moving grids are then constructed for compressible and incompressible flows, respectively. For compressible flows, it is necessary to introduce a shock capturing method to resolve discontinuities. However, the shock capturing methods do not work well for turbulent flow simulations because of their excessive numerical dissipation. On the other hand, the secondary conservative finite difference method does not work well for flows with discontinuities. In this study, we also present a computational technique that combines the shock capturing and the secondary conservative finite difference methods. In order to check the commutability and conservation properties of the convection schemes, numerical tests are done for compressible and incompressible inviscid periodic flows on moving grids. Then, the reliabilities of the schemes are demonstrated on the piston problem, the flow around pitching airfoil, and the flow around an oscillating square cylinder.

An Experimental Study on Opening Delay of a Reed Valve for Reciprocating Compressors

Automatic reed valves are widely used to control refrigerant gas flow in reciprocating compressors for automotive air conditioners. The oil film in the clearance between the reed and the valve seat causes a delay in opening of the valve. This opening delay of the discharge valve leads to over compression, which increases losses such as friction in sliding components and gas overheating. Therefore it is important to understand the behavior both of the oil film and the elastic reed deformation in order to reduce losses due to the delay. This study aims to develop an experimental setup that enables simultaneous visualization of the oil film rupture and measurement of the reed deformation, and to observe this behavior during the valve opening process. The gas-compression stroke is simulated by controlling compressed air with an electromagnetic valve. The oil film rupture is visually observed using a high speed camera through a special valve seat made of glass. The total deformation of the cantilever reed is identified by multipoint strain measurement with 12 strain gauges. The experiment finds that the opening process is divided into four stages. In the first stage, the reed remains stuck to the seat and deforms while the bore pressure increases. In the second stage, cavitation occurs in the oil film and the film starts to rupture. In the third stage, the oil film ruptures and the bore pressure starts to decrease. Finally, in the fourth stage, the reed is separated from the seat and the gas flows through the valve. Reducing the reed/seat contact area changes the reed deformation in the first stage, thereby increasing the reed/seat distance and realizing an earlier oil film rupture and a shorter delay.Copyright

Dynamics of falling droplet and elongational properties of dilute nonionic surfactant solutions with drag-reducing ability

The dynamics of the falling droplet through a nozzle for dilute nonionic surfactant (oleyl-dimethylamine oxide, ODMAO) aqueous solutions with viscoelastic and drag-reducing properties were investigated at different concentrations of ODMAO solutions Cs = 500, 1000, and 1500 ppm by weight. The effects of the flow rate and tube outer diameter on the length of the filament, which was the distance between the tube exit and the lower end of a droplet at the instant when the droplet almost detached from the tube, were clarified by flow visualization measurements by a high-speed video camera. Two types of breaking-off processes near the base of the droplet and within the filament were classified by the Ohnesorge number Oh and the Weber number We. In the regime of the higher Oh and We, the length of the filament became drastically larger at Cs = 1000 and 1500 ppm, whose high spinnability represented the strong viscoelasticity of ODMAO solutions. In the case where the filament was broken up near the lower end of th...

Streamwise variations of turbulence statistics up to maximum drag reduction state in turbulent boundary layer flow due to surfactant injection

We investigate streamwise variations of turbulence statistics in the wide range of drag reduction (DR) up to the maximum drag reduction (MDR; DR ≥ 60%) state for the turbulent boundary layer flow due to surfactant injection. One-component laser-Doppler velocimetry (LDV) measurements show that the DR is drastically varied from the low drag reduction (LDR) to the high drag reduction (HDR) regions and is saturated in the MDR region, and such variation is sensitive to the free-stream velocity and dependent on the process of diffusion of injected surfactant solution. Both two-component LDV measurements and particle image velocimetry (PIV) measurements clarify that the mean velocity in wall units agrees with the so-called Virk’s ultimate profile in the MDR region, where both wall-normal turbulence intensity and the Reynolds shear stress with outer scaling are considerably suppressed compared to those in the LDR and HDR regions, while the maximum of streamwise turbulence intensity is comparable with that of water. Such behavior is independent of flow types such as internal and external flows and kinds of additives such as polymer and surfactant. The principal axis angle in joint probability density function of streamwise and wall-normal velocity fluctuations near the wall is the most promising index as the amount of DR based on the LDR, HDR, and MDR. The PIV measurements also show that the sheet-like structures in the HDR and MDR regions expand to around the maximum location of streamwise turbulence intensity, at which spanwise length scales are evaluated.We investigate streamwise variations of turbulence statistics in the wide range of drag reduction (DR) up to the maximum drag reduction (MDR; DR ≥ 60%) state for the turbulent boundary layer flow due to surfactant injection. One-component laser-Doppler velocimetry (LDV) measurements show that the DR is drastically varied from the low drag reduction (LDR) to the high drag reduction (HDR) regions and is saturated in the MDR region, and such variation is sensitive to the free-stream velocity and dependent on the process of diffusion of injected surfactant solution. Both two-component LDV measurements and particle image velocimetry (PIV) measurements clarify that the mean velocity in wall units agrees with the so-called Virk’s ultimate profile in the MDR region, where both wall-normal turbulence intensity and the Reynolds shear stress with outer scaling are considerably suppressed compared to those in the LDR and HDR regions, while the maximum of streamwise turbulence intensity is comparable with that of wate...

Improving computational accuracy in dissipative particle dynamics via a high order symplectic method

This study was focused on improving the numerical accuracy of the dissipative particle dynamics simulation via modifying its numerical time integration scheme. Despite the integration of the pairwise Langevin part dealt with by most of the previous studies, we paid attention to the improvement of the standard Liouville part. The numerical accuracy was measured by the configurational temperature in this study. Employing a fourth order symplectic scheme showed a significant improvement of the numerical accuracy for the simulations especially with a large time increment when comparing it with existing schemes, which indicates that enough resolution in time was attained when our modified scheme was employed. In addition, a set of simulations was performed for a wider range of time increments than previous studies. The results showed that the computational error demonstrated different orders of accuracy for different time increment ranges, which led to the fact that the dominant effect on the error is conservative and random forces for the large and small increment ranges.

A Stable Compact Finite Difference Method With Skew-Symmetric Form for LES of Variable Density Flows

The objective of this study is to develop a reliable high-order numerical method for the large eddy simulation (LES) of variable density flows. To improve both the numerical accuracy and stability, we use the compact finite difference method (compact FDM) for the transport equation of compressible flows, in which the skew-symmetric form of the convection term is adopted. In the LES of turbulent flows, the reliability of computational results depends strongly on both the reliability of the subgrid scale (SGS) model and the accuracy of the numerical method. First, the reliability is investigated by performing numerical simulations with unresolved grid resolution for compressible turbulent channel flows without SGS models. Then, we perform the LES of compressible turbulent channel flows with several dynamic and non-dynamic SGS models, and compare turbulence statistics with the corresponding DNS data.Copyright

Streamwise Variations in Turbulence Statistics in Drag-Reducing Turbulent Boundary Layer of Viscoelastic Fluids

Direct numerical simulation (DNS) of a zero-pressure gradient drag-reducing turbulent boundary layer of viscoelastic fluids was performed at the different Weissenberg number We = 25, 50, 75, and 100 using the FENE-P model. The increase in We, i.e. the relaxation time leads to the larger maximum of trace of conformation tensor in upstream region, and to the larger maximum of drag reduction ratio DR in downstream region, in which the trace of conformation tensor decreases gradually in the streamwise direction, while the DR increases. The trace of conformation tensor is anticorrelated with DR, While the phase difference between DR and streamwise turbulence intensity becomes larger with the increase in We. Streamwise variations in DR, turbulence statistics and structures are so different between We = 25 and We = 50 to 100, and the difference is elucidated by using the active and hibernating turbulence mechanism of Xi and Graham (2010b) for the minimal channel flow. At We = 25, the locally high and low wall-shear stress regions show larger scale compared to Newtonian fluid. On the other hand, at We = 50, regions of active and hibernating turbulence become obscurer, while the mechanism itself is unchanged.Copyright