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Register a new userUnsteady fluid--structure interactions in a soft-walled microchannel: A one-dimensional lubrication model for finite Reynolds number
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We develop a one-dimensional model for the unsteady fluid--structure interaction (FSI) between a soft-walled microchannel and viscous fluid flow within it. A beam equation, which accounts for both transverse bending rigidity and nonlinear axial tension, is coupled to a one-dimensional fluid model obtained from depth-averaging the two-dimensional incompressible Navier--Stokes equations across the channel height. Specifically, the Navier--Stokes equations are scaled in the viscous lubrication limit relevant to microfluidics. The resulting set of coupled nonlinear partial differential equations is solved numerically through a segregated approach employing fully-implicit time stepping. We explore both the static and dynamic FSI behavior of this example microchannel system by varying a reduced Reynolds number $Re$, which necessarily changes the Strouhal number $St$, while we keep the geometry and a modified dimensionless Youngs modulus $Sigma$ fixed. At steady state, an order-of-magnitude analysis (balancing argument) shows that the axially-averaged pressure in the flow, $langle Prangle$, exhibits two different scaling regimes, while the maximum deformation of the top wall of the channel, $H_{mathrm{max}}$, can fall into four different regimes, depending on the magnitudes of $Re$ and $Sigma$. These regimes are physically explained as resulting from the competition between the inertial and viscous forces in the fluid flow as well as the bending resistance and tension in the elastic wall. Finally, the linear stability of the steady inflated microchannel shape is assessed via a modal analysis, showing the existence of many highly oscillatory but stable modes, which further highlights the computational challenge of simulating unsteady FSIs.
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We study fluid-structure interactions (FSIs) in a long and shallow microchannel, conveying a non-Newtonian fluid, at steady state. The microchannel has a linearly elastic and compliant top wall, while its three other walls are rigid. The fluid flowing inside the microchannel has a shear-dependent viscosity described by the power-law rheological model. We employ lubrication theory to solve for the flow problem inside the long and shallow microchannel. For the structural problem, we employ two plate theories, namely Kirchhoff-Love theory of thin plates and Reissner-Mindlin first-order shear deformation theory. The hydrodynamic pressure couples the flow and deformation problem by acting as a distributed load onto the soft top wall. Within our perturbative (lubrication theory) approach, we determine the relationship between flow rate and the pressure gradient, which is a nonlinear first-order ordinary differential equation for the pressure. From the solution of this differential equation, all other quantities of interest in non-Newtonian microchannel FSIs follow. Through illustrative examples, we show the effect of FSI coupling strength and the plate thickness on the pressure drop across the microchannel. Through direct numerical simulation of non-Newtonian microchannel FSIs using commercial computational engineering tools, we benchmark the prediction from our mathematical prediction for the flow rate-pressure drop relation and the structural deformation profile of the top wall. In doing so, we also establish the limits of applicability of our perturbative theory.
Convolutional neural networks (CNNs) have recently been applied to predict or model fluid dynamics. However, mechanisms of CNNs for learning fluid dynamics are still not well understood, while such understanding is highly necessary to optimize the network or to reduce trial-and-errors during the network optmization. In the present study, a CNN to predict future three-dimensional unsteady wake flow using flow fields in the past occasions is developed. Mechanisms of the developed CNN for prediction of wake flow behind a circular cylinder are investigated in two flow regimes: the three-dimensional wake transition regime and the shear-layer transition regime. Feature maps in the CNN are visualized to compare flow structures which are extracted by the CNN from flow at the two flow regimes. In both flow regimes, feature maps are found to extract similar sets of flow structures such as braid shear-layers and shedding vortices. A Fourier analysis is conducted to investigate mechanisms of the CNN for predicting wake flow in flow regimes with different wave number characteristics. It is found that a convolution layer in the CNN integrates and transports wave number information from flow to predict the dynamics. Characteristics of the CNN for transporting input information including time histories of flow variables is analyzed by assessing contributions of each flow variable and time history to feature maps in the CNN. Structural similarities between feature maps in the CNN are calculated to reveal the number of feature maps that contain similar flow structures. By reducing the number of feature maps that contain similar flow structures, it is also able to successfully reduce the number of parameters to learn in the CNN by 85% without affecting prediction performances.
Microfluidic technologies are commonly used for the manipulation of red blood cell (RBC) suspensions and analyses of flow-mediated biomechanics. To enhance the performance of microfluidic devices, understanding the dynamics of the suspensions processed within is crucial. We report novel aspects of the spatio-temporal dynamics of RBC suspensions flowing through a typical microchannel at low Reynolds number. Through experiments with dilute RBC suspensions, we find an off-centre two-peak (OCTP) profile of cells contrary to the centralised distribution commonly reported for low-inertia flows. This is reminiscent of the well-known tubular pinch effect which arises from inertial effects. However, given the conditions of negligible inertia in our experiments, an alternative explanation is needed for this OCTP profile. Our massively-parallel simulations of RBC flow in real-size microfluidic dimensions using the immersed-boundary-lattice-Boltzmann method (IB-LBM) confirm the experimental findings and elucidate the underlying mechanism for the counterintuitive RBC pattern. By analysing the RBC migration and cell-free layer (CFL) development within a high-aspect-ratio channel, we show that such a distribution is co-determined by the spatial decay of hydrodynamic lift and the global deficiency of cell dispersion in dilute suspensions. We find a CFL development length greater than 46 and 28 hydraulic diameters in the experiment and simulation, respectively, exceeding typical lengths of microfluidic designs. Our work highlights the key role of transient cell distribution in dilute suspensions, which may negatively affect the reliability of experimental results if not taken into account.
Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and the pressure Hessian tensor, which we analyze here using direct numerical simulations of isotropic turbulence in periodic domains of up to $12288^3$ grid points, and Taylor-scale Reynolds numbers in the range $140-1300$. We extract the statistics of various terms involved in amplification of strain and additionally condition them on the magnitude of strain. We find that strain is overall self-amplified by the quadratic nonlinearity, and depleted via vortex stretching; whereas pressure Hessian acts to redistribute strain fluctuations towards the mean-field and thus depleting intense strain. Analyzing the intense fluctuations of strain in terms of its eigenvalues reveals that the net amplification is solely produced by the third eigenvalue, resulting in strong compressive action. In contrast, the self-amplification terms acts to deplete the other two eigenvalues, whereas vortex stretching acts to amplify them, both effects canceling each other almost perfectly. The effect of the pressure Hessian for each eigenvalue is qualitatively similar to that of vortex stretching, but significantly weaker in magnitude. Our results conform with the familiar notion that intense strain is organized in sheet-like structures, which are in the vicinity of, but never overlap with regions of intense vorticity due to fundamental differences in their amplifying mechanisms.
An essential ingredient of turbulent flows is the vortex stretching mechanism, which emanates from the non-linear interaction of vorticity and strain-rate tensor and leads to formation of extreme events. We analyze the statistical correlations between vorticity and strain rate by using a massive database generated from very well resolved direct numerical simulations of forced isotropic turbulence in periodic domains. The grid resolution is up to $12288^3$, and the Taylor-scale Reynolds number is in the range $140-1300$. In order to understand the formation and structure of extreme vorticity fluctuations, we obtain statistics conditioned on enstrophy (vorticity-squared). The magnitude of strain, as well as its eigenvalues, is approximately constant when conditioned on weak enstrophy; whereas they grow approximately as power laws for strong enstrophy, which become steeper with increasing $R_lambda$. We find that the well-known preferential alignment between vorticity and the intermediate eigenvector of strain tensor is even stronger for large enstrophy, whereas vorticity shows a tendency to be weakly orthogonal to the most extensive eigenvector (for large enstrophy). Yet the dominant contribution to the production of large enstrophy events arises from the most extensive eigendirection, the more so as $R_lambda$ increases. Nevertheless, the stretching in intense vorticity regions is significantly depleted, consistent with the kinematic properties of weakly-curved tubes in which they are organized. Further analysis reveals that intense enstrophy is primarily depleted via viscous diffusion, though viscous dissipation is also significant. Implications for modeling are nominally addressed as appropriate.
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