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Direct numerical simulation is conducted for a spatially developing shear mixing layer to investigate the spatial transition of the dissipation coefficient of the turbulent kinetic energy, Cϵ. The scaling law suggested by Goto and Vassilicos [Phys. Rev. E 94, 053108 (2016)], C ϵ ∼ R e λ − 1 , holds over a wide area in the upstream region (0.3 ≤ x/L0 ≤ 1.9, where x is the streamwise direction and L0 is the height of the computational domain), and Cϵ takes a constant value in the further downstream region, where Reλ is the turbulent Reynolds number based on Taylor’s microscale. Proper orthogonal decomposition (POD) analysis is performed to investigate the distributions of the streamwise length of the large-scale energy-containing structure, which is estimated from the cycle of the zero-crossing point of the time-series data composed of the sum of the POD modes until the cumulative energy rate exceeds 60 %. It is shown that Cϵ becomes a constant when the distributions of the length of the large-scale structure reach a self-similar state. This result suggests that it is necessary to satisfy the self-similarity of the distribution of the length of the large-scale energy-containing structure in order to apply the condition that Cϵ is a constant.

The necessity of odor sensing has been increasing from environmental and health standpoints. Here, we propose the novel concept of a small device which can select odor molecules based on electrostatic spraying. For high selectivity of the target gas or odor, we conducted computational fluid dynamics coupled with an electrostatic field, as well as measurements by particle image velocimetry and anemometry. The computational model successfully reproduced characteristic features of ionic wind. Different trajectories of charged particles were computationally obtained owing to their electrical mobility. The results imply that different materials might be separated by the arrangement of the collecting electrode.

We propose a numerical method for turbulent reactive flows using a large eddy simulation (LES) based on the approximate deconvolution model (ADM). LES based on the ADM is combined with a Lagrangian notional particle (LP) method for computing reactive flows without using models for chemical source terms. In the LP method, values of scalars are assigned to each particle. The evolutions of Lagrangian particles in physical and scalar composition spaces are modeled by using the mixing model for molecular diffusion and the resolved velocity field of LES. We also propose a particles-interaction mixing model using a mixing volume concept, in which the mixing timescale is determined by relating the decay of scalar variance in the mixing volume to the scalar dissipation rate. The LES-LP method based on the ADM and the mixing model is applied to a planar jet with a second-order reaction for testing the numerical method. The statistics obtained by the LES-LP method are compared with the direct numerical simulation data. The results show that the evolutions of Lagrangian particles are well modeled in the LES-LP method by using the resolved velocity and the mixing model, and this method can accurately predict the statistical properties of reactive scalars. The mixing timescale depends on the distance among the Lagrangian particles. It is also shown that the present mixing model can implicitly take into account the effect of distance among the particles by adjusting the mixing timescale without using any model parameters.

Experimental measurement and numerical simulation are the typical methods employed in flow analysis. Both methods have advantages and disadvantages and it is difficult to correctly reproduce real flows with inherent uncertainties. In order to overcome this problem, measurement-integrated (MI) simulation has been proposed in which measurement and simulation are integrated based on the observer theory. The validity of MI simulation has been proved in several applications. However the feedback law critical in MI simulation has been designed by trial and error based on physical considerations. Development of a general theory for the design of MI simulation is critical for its widespread use. In this study, as a fundamental consideration to construct a general theory of MI simulation, we formulated a linearized error dynamics equation to express time development of the error between the simulation and the real flow, and an equation for eigenvalue analysis. Primary advantage of the proposed method is to provide a framework to design a feedback gain of MI simulation based on a standard linear dynamical system theory. The validity of the method was investigated by comparison of the results of the eigenvalue analysis and those of the numerical experiment for the low-order model problem of the turbulent flow in a square duct with various feedback gains in the case of feedback with all velocity components and two velocity components. From the eigenvalue analysis in the case without feedback, the error dynamics was unstable and the error increased exponentially. When the feedback gain k u > 0.98 with feedback of all velocity components or k u > 1.67 with feedback of u 1 , u 2 velocity components, all eigenvalues were stable. In the numerical experiment, the critical feedback gains obtained from eigenvalue analysis quantitatively agreed with the lower limit of the feedback gain to reduce the steady error in MI simulation. In the comparison of the time constant for the reduction of the error norm, the time constant obtained from the eigenvalue analysis agreed with those from the numerical experiment. The eigenvalue analysis of the linearized error dynamics formulated in this study was effective in evaluation of the effect of the feedback gain of the MI simulation.

Reproduction of the exact structure of real turbulent flows is crucial in many applications. Four Dimensional variation (4D-VAR) is widely used in numerical weather forecasting, but it requires huge computational power to repeatedly solve flow dynamics and its adjoint, and, therefore, is not suitable to apply to problems of real-time flow reproduction such as feedback flow control. Kalman filter and observer, in which numerical solution converges to the real state asymptotically by means of the feedback signal proportional to the difference between the calculated state and the real state, requiring much less computational load than the variational method, are potential candidates to solve the problem. By comparing Kalman filter and observer, the latter has simpler structure retaining essential part of the state estimation. This study deals with a special type of observer, or measurement-integrated simulation (MI simulation), in which a SIMPLER-based flow solver is used as the mathematical model of the system in place of approximate small dimensional linear differential equations usually used in observers. Reproduction of the exact structure of a turbulent flow was investigated by a MI simulation. A numerical experiment was performed for a fully developed turbulent flow in a pipe with a square cross section. The MI simulation was performed with the feedback from the standard solution in the flow domain for the cases using: (1) all velocity components at all grid points, (2) partial velocity components at all grid points, or (3) all velocity components at partial grid points. Convergence of the MI simulation to the standard solution was investigated using the steady error norm for the convergent state and the time constant for the transient state. The result of the MI simulation using all the velocity information exponentially converges to the standard solution with a steady state error reduced from that of the ordinary simulation in a range of the feedback gain. Decreasing the feedback gain reduces the effect of feedback, and a feedback gain which is too large destabilizes the closed loop system, resulting in large error. The time constant decreases almost inversely proportional to the feedback gain as long as the feedback system is stable. For the MI simulation with the feedback using limited information, feedback using two velocity components by omitting one transverse velocity component showed a good result, although the other results were not satisfactory. For the MI simulation with the feedback using limited grid points, the result of the MI simulation applying the feedback at the grid points on every 20th plane in the x1 direction was almost the same as that using all grid points at some feedback gain, while the result with the feedback on the planes skipped in the x2 direction requires 10 times more planes to achieve the same reduction rate.

The swimming properties of a spiral-type magnetic micro-machine were analyzed theoretically using 3D finite volume method. The basic equations of incompressible viscous fluid flow were integrated. The flow field around the micro-machine was calculated to estimate the swimming velocity, thrust, drag, and load torque of a spiral-type magnetic micro-machine. Good agreement was obtained between the experimental and theoretical results in a low Reynolds number. Therefore, the 3D analysis method without any fitting parameters was judged to be established.

In the present study, our aim was to visualise the changes in the left atrial flow during atrial fibrillation (AF)using numerical simulations and an animal experiment. A geometric model of the left atrium (LA) was constructed based on MR images obtained into a computational model created using tetrahedral mesh. A flow simulation was performed using FLUENT. To simulate AF, we added low-amplitude and high-frequency contractions to the sinus rhythm (SR) mode, and subtractedactive contractions while the mitral valve was opening. In a goat model, the intra-left atrial flow was directly visualised with microbubble contrast agents using echocardiography under general anesthesia. The LA was electrically fibrillated during 9 V direct current stimulation of the left atrial wall. SR was recovered soon after the stimulation was terminated. The results of the computer simulation showed that, a small rotational flow present during ventricular diastole disappeared in the AF model. A large number of eddies were evident along the superior left pulmonary vein. During ventricular systole, although a vortex was formed, the density of the streamlines was lower than that observed in the SR model. In the animal experiment, the flow was obscured by local eddies when AF occurred. Some microbubbles remained at the junction of the left atrial body and pulmonary vein. Compared with the SR, the atrial vortices became obscured by an increased number of local eddies along the superior left pulmonary vein when AF was present, after which the intra-left atrial flow became congested.

Erratum to ‘‘Influence of surface model extraction parameter on computational fluid dynamics modeling of cerebral aneurysms’’ [Journal of Biomechanics 45 (2012) 2355–2361] Shunsuke Omodaka , Takashi Inoue , Kenichi Funamoto , Shin-ichirou Sugiyama , Hiroaki Shimizu , Toshiyuki Hayase , Akira Takahashi , Teiji Tominaga a a Department of Neurosurgery, Tohoku University Graduate School of Medicine, 1-1 Seiryo-machi, Aobaku, Sendai, Miyagi 980-8574, Japan b Department of Neurosurgery, Kohnan Hospital, 4-20-1 Nagamachiminami, Taihaku-ku, Sendai, Miyagi 982-8523, Japan c Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, Miyagi 980-8577, Japan d Department of Neuroanesthesia, Kohnan Hospital, 4-20-1 Nagamachiminami, Taihaku-ku, Sendai, Miyagi 982-8523, Japan e Department of Neuroendovascular Therapy, Tohoku University Graduate School of Medicine, 1-1Seiryo-machi, Aobaku, Sendai, Miyagi 980-8574, Japan

Previous applications of QUICK for the discretization of convective transport terms in finite-volume calculation procedures have failed to employ a rigorous and systematic approach for consistently deriving this finite difference scheme. Instead, earlier formulations have been established numerically, by trial and error. The new formulation for QUICK presented here is obtained by requiring that it satisfy four rules that guarantee physically realistic numerical solutions having overall balance. Careful testing performed for the wall-driven square enclosure flow configuration shows that the consistently derived version of QUICK is more stable and converges faster than any of the formulations previously employed. This testing includes the relative evaluation of boundary conditions approximated by second- and third-order finite-difference schemes as well as calculations performed at higher Reynolds numbers than previously reported.