scholarly journals Optical tweezers-based velocimetry: a method to measure microscale unsteady flows

2020 ◽  
Vol 61 (9) ◽  
Author(s):  
P. Ghoddoosi Dehnavi ◽  
D. Wei ◽  
M.-E. Aubin-Tam ◽  
D. S. W. Tam
Keyword(s):  
Optical Tweezers ◽  
Laser Power ◽  
Stokes Equations ◽  
Unsteady Flows ◽  
Research Data ◽  
Steady Flows ◽  
Bead Size ◽  
Micro Piv ◽  
Numerical Predictions ◽  
Passive Tracers

Abstract In the study of micro-scale biological flows, velocimetry methods based on passive tracers, such as micro-PIV and micro-PTV, are well established to characterize steady flows. However, these methods become inappropriate for measuring unsteady flows of small amplitude, because, on these scales, the motion of passive tracers cannot be distinguished from Brownian motion. In this study, we use optical tweezers (OTs) in combination with Kalman filtering, to measure unsteady microscopic flows with high temporal accuracy. This method is referred to as optical tweezers-based velocimetry (OTV). The OTV method measures the nanometric displacements of a trapped bead, and predicts the instantaneous velocity of the flow by employing a Kalman filter. We discuss the accuracy of OTV in measuring unsteady flows with 1.5–70 $$\upmu$$ μ m s$$^{-1}$$ - 1 amplitudes and 10–90 Hz frequencies. We quantify how the bead size and the laser power affect the velocimetry accuracy, and specify the optimal choices for the bead size and laser power to measure different unsteady flows. OTV accurately measures unsteady flows with amplitudes as small as 3–6 $$\upmu$$ μ m s$$^{-1}$$ - 1 . We compare the accuracy of OTV and micro-PTV, and characterize the flow regime for which OTV outperforms micro-PTV. We also demonstrate the robustness of OTV by measuring the unsteady flow created by the cilia of green alga Chlamydomonas reinhardtii, and comparing with numerical predictions based on Stokes equations. An open-source implementation of the OTV software in Matlab is available through the 4TU.Centre for Research Data. Graphic abstract

Numerical Solutions of the Viscous Flow Equations for a Class of Closed Flows

1965 ◽  
Vol 69 (658) ◽  
pp. 714-718 ◽  
Author(s):  
Ronald D. Mills
Keyword(s):  
Moving Boundary ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Steady Flows ◽  
Flow Equations ◽  
Steady Streaming ◽  
Difference Formula ◽  
Surface Passing

The Navier-Stokes equations are solved iteratively on a small digital computer for the class of flows generated within a rectangular “cavity” by a surface passing over its open end. Solutions are presented for depth/breadth ratios ƛ=0.5 (shallow), 10 (square), 20 (deep) and Reynolds number 100. Flow photographs ore obtained which largely confirm the predicted flows. The theoretical velocity profiles and pressure distributions through the centre of the vortex in the square cavity are calculated.In an appendix an improved finite difference formula is given for the vorticity generated at a moving boundary.Since Thorn began his pioneering work some thirty-five years ago the number of numerical solutions which have been obtained for the equations of incompressible viscous fluid motion remains small (see bibliographies of Thom and Apelt, Fromm). The known solutions are principally for steady streaming flows, although two methods have now been used with success for non-steady flows (Payne jets and Fromm flow past obstacles). By contrast this paper is concerned with the class of closed flows generated in a rectangular region of varying depth/breadth ratio by a surface passing over an open end. This problem has been considered for a number of reasons.

scholarly journals Modeling of Tip Clearance Flows Through an Improved 3-D Pressure Correction Navier-Stokes Solver

1993 ◽  
Author(s):  
N. Lymberopoulos ◽  
K. Giannakoglou ◽  
I. Nikolaou ◽  
K. D. Papailiou ◽  
A. Tourlidakis ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Navier Stokes ◽  
Special Treatment ◽  
Pressure Correction ◽  
Compressor Rotor ◽  
Numerical Predictions ◽  
Correction Technique

Mechanical constraints dictate the existence of tip clearances in rotating cascades, resulting to a flow leakage through this clearance which considerably influences the efficiency and range of operation of the machine. Three-dimensional Navier-Stokes solvers are often used for the numerical study of compressor and turbine stages with tip-clearance. The quality of numerical predictions depends strongly on how accurately the blade tip region is modelled; in this respect the accurate modelling of tip region was one of the main goals of this work. In the present paper, a 3-D Navier-Stokes solver is suitably adapted so that the flat tip surface of a blade and its sharp edges could be accurately modelled, in order to improve the precision of the calculation in the tip region. The adapted code solves the fully elliptic, steady, Navier-Stokes equations through a space-marching algorithm and a pressure correction technique; the H-type topology is retained, even in cases with thick leading edges where a special treatment is introduced herein. The analysis is applied to two different cases, a linear cascade and a compressor rotor, and comparisons with experimental data are provided.

scholarly journals Critical slope for laminar transcritical shallow-water flows

2015 ◽  
Vol 783 ◽  
Author(s):  
O. Thual ◽  
L. Lacaze ◽  
M. Mouzouri ◽  
B. Boutkhamouine
Keyword(s):  
Stokes Equations ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Critical Surface ◽  
Steady Flows ◽  
Surface Slope ◽  
Critical Height ◽  
Navier Stokes Equations ◽  
Shallow Water Flows ◽  
Critical Slope

Backwater curves denote the depth profiles of steady flows in a shallow open channel. The classification of these curves for turbulent regimes is commonly used in hydraulics. When the bottom slope $I$ is increased, they can describe the transition from fluvial to torrential regimes. In the case of an infinitely wide channel, we show that laminar flows have the same critical height $h_{c}$ as that in the turbulent case. This feature is due to the existence of surface slope singularities associated to plug-like velocity profiles with vanishing boundary-layer thickness. We also provide the expression of the critical surface slope as a function of the bottom curvature at the critical location. These results validate a similarity model to approximate the asymptotic Navier–Stokes equations for small slopes $I$ with Reynolds number $Re$ such that $Re\,I$ is of order 1.

scholarly journals Development of An Integrated Numerical Model for Simulating Wave Interaction with Permeable Submerged Breakwaters Using Extended Navier–Stokes Equations

2020 ◽  
Vol 8 (2) ◽  
pp. 87 ◽  
Author(s):  
Paran Pourteimouri ◽  
Kourosh Hejazi
Keyword(s):  
Porous Medium ◽  
Wave Propagation ◽  
Numerical Model ◽  
Analytical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Stokes Wave ◽  
Navier Stokes Equations ◽  
Numerical Predictions ◽  
The Impact

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

Some numerical experiments on developing laminar flow in circular-sectioned bends

1985 ◽  
Vol 154 ◽  
pp. 357-375 ◽  
Author(s):  
J. A. C. Humphrey ◽  
H. Iacovides ◽  
B. E. Launder
Keyword(s):  
Shear Stress ◽  
Laminar Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Inviscid Flow ◽  
Streamwise Velocity ◽  
Navier Stokes ◽  
Dean Number ◽  
Navier Stokes Equations ◽  
Numerical Predictions

The paper reports numerical solutions to a semi-elliptic truncation of the Navier–Stokes equations for the case of developing laminar flow in circular-sectioned bends over a range of Dean numbers. The ratios of bend radius to pipe radius are 7:1 and 20:1, corresponding with the configurations examined experimentally by Talbot and his co-workers in recent years. The semi-elliptic treatment facilitates a much finer grid than has been possible in earlier studies. Numerical accuracy has been further improved by assuming radial equilibrium over a thin sublayer immediately adjacent to the wall and by re-formulating the boundary conditions at the pipe centre.Streamwise velocity profiles at Dean numbers of 183 and 565 are in excellent agreement with laser-Doppler measurements by Agrawal, Talbot & Gong (1978). Good, albeit less complete, accord is found with the secondary velocities, though the differences that exist may be mainly due to the difficulty of making these measurements. The paper provides new information on the behaviour of the streamwise shear stress around the inner line of symmetry. Upstream of the point of minimum shear stress, our numerical predictions display a progressive shift towards the result of Stewartson, Cebici & Chang (1980) as the Dean number is successively raised. Downstream of the minimum, however, in contrast with the monotonic approach to an asymptotic level reported by Stewartson, the numerical solutions display a damped oscillatory behaviour reminiscent of those from Hawthorne's (1951) inviscid-flow calculations. The amplitude of the oscillation grows as the Dean number is raised.

Tip Leakage Flow in Axial Compressors

1991 ◽  
Vol 113 (2) ◽  
pp. 252-259 ◽  
Author(s):  
J. A. Storer ◽  
N. A. Cumpsty
Keyword(s):  
Pressure Field ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Tip Clearance ◽  
Leakage Flow ◽  
Tip Leakage Flow ◽  
Local Pressure ◽  
Flow Measurements ◽  
Tip Leakage ◽  
Numerical Predictions

Experimental measurements in a linear cascade with tip clearance are complemented by numerical solutions of the three-dimensional Navier–Stokes equations in an investigation of tip leakage flow. Measurements reveal that the clearance flow, which separates near the entry of the tip gap, remains unattached for the majority of the blade chord when the tip clearance is similar to that typical of a machine. The numerical predictions of leakage flow rate agree very well with measurements, and detailed comparisons show that the mechanism of tip leakage is primarily inviscid. It is demonstrated by simple calculation that it is the static pressure field near the end of the blade that controls chordwise distribution of the flow across the tip. Although the presence of a vortex caused by the roll-up of the leakage flow may affect the local pressure field, the overall magnitude of the tip leakage flow remains strongly related to the aerodynamic loading of the blades.

Simulating Periodic Unsteady Flows Using Cubic-Spline Based Time Collocation Method

2013 ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Collocation Method ◽  
Stokes Equations ◽  
Differential Quadrature Method ◽  
Unsteady Flows ◽  
Cubic Spline ◽  
Navier Stokes ◽  
Transonic Compressor ◽  
Compressor Rotor ◽  
Time Marching ◽  
Flow Variables

Time periodical unsteady flows are typical in turbomachinery. Simulating such flows using conventional time marching approach is most accurate but extremely time consuming. In order to achieve a better balance between accuracy and computational expenses, a cubic-spline based time collocation method is proposed. In this method, the time derivatives in the Navier-Stokes equations are obtained by using the differential quadrature method, in which the periodical flow variables are approximated by cubic-splines. Thus, the computation of a time-periodical flow is substituted by several coupled quasi-steady flow computations at sampled instants. The proposed method is then validated against several typical turbomachinery periodical unsteady flows, i.e., transonic compressor rotor flows under circumferential inlet distortions, single stage rotor-stator interactions and IGV-rotor interactions. The results show that the proposed cubic-spline based time collocation method with appropriate time sampling can well resolve the dominant unsteady effects, whilst the computational expenses are kept much less than the traditional time-marching simulation. More importantly, this paper provides a framework on the basis of time collocation method in which one may choose more compatible test functions for the concerned specific unsteady flows so that the better modeling of the flows can be expected.

Influence of laser power on stiffness calibration of optical tweezers

2016 ◽  
Vol 37 (6) ◽  
pp. 517-522
Author(s):  
Zhang Yuling ◽  
Zhou Zhehai ◽  
Zhu Lianqing
Keyword(s):  
Optical Tweezers ◽  
Laser Power

Numerical Solution of Incompressible Unsteady Flows in Turbomachinery

2000 ◽  
Vol 123 (3) ◽  
pp. 680-685 ◽  
Author(s):  
L. He ◽  
K. Sato
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Time Stepping ◽  
Incompressible Viscous Flow ◽  
Dual Time Stepping

A three-dimensional incompressible viscous flow solver of the thin-layer Navier-Stokes equations was developed for the unsteady turbomachinery flow computations. The solution algorithm for the unsteady flows combines the dual time stepping technique with the artificial compressibility approach for solving the incompressible unsteady flow governing equations. For time accurate calculations, subiterations are introduced by marching the equations in the pseudo-time to fully recover the incompressible continuity equation at each real time step, accelerated with a multi-grid technique. Computations of test cases show satisfactory agreements with corresponding theoretical and experimental results, demonstrating the validity and applicability of the present method to unsteady incompressible turbomachinery flows.

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