Experiments and simulations of MEMS thermal sensors for wall shear-stress measurements in aerodynamic control applications

MEMS thermal shear-stress sensors exploit heat-transfer effects to measure the shear stress exerted by an air flow on its solid boundary, and have promising applications in aerodynamic control. Classical theory for conventional, macroscale thermal shear-stress sensors states that the rate of heat removed by the flow from the sensor is proportional to the 1/3-power of the shear stress. However, we have observed that this theory is inconsistent with experimental data from MEMS sensors. This paper seeks to develop an understanding of MEMS thermal shear-stress sensors through a study including both experimental and theoretical investigations. We first obtain experimental data that confirm the inadequacy of the classical theory by wind-tunnel testing of prototype MEMS shear-stress sensors with different dimensions and materials. A theoretical analysis is performed to identify that this inadequacy is due to the lack of a thin thermal boundary layer in the fluid flow at the sensor surface, and then a two-dimensional MEMS shear-stress sensor theory is presented. This theory incorporates important heat-transfer effects that are ignored by the classical theory, and consistently explains the experimental data obtained from prototype MEMS sensors. Moreover, the prototype MEMS sensors are studied with three-dimensional simulations, yielding results that quantitatively agree with experimental data. This work demonstrates that classical assumptions made for conventional thermal devices should be carefully examined for miniature MEMS devices

A thin rivulet or ridge subject to a uniform transverse\ud shear stress at its free surface due to an external airflow

We use the lubrication approximation to analyse three closely related problems involving a thin rivulet or ridge (i.e. a two-dimensional droplet) of fluid subject to a prescribed uniform transverse shear stress at its free surface due to an external airflow, namely a rivulet draining under gravity down a vertical substrate, a rivulet driven by a longitudinal shear stress at its free surface, and a ridge on a horizontal substrate, and find qualitatively similar behaviour for all three problems. We show that, in agreement with previous numerical studies, the free surface profile of an equilibrium rivulet/ridge with pinned contact lines is skewed as the shear stress is increased from zero, and that there is a maximum value of the shear stress beyond which no solution with prescribed semi-width is possible. In practice, one or both of the contact lines will de-pin before this maximum value of the shear stress is reached, and so we consider situations in which the rivulet/ridge de-pins at one or both contact lines. In the case of de-pinning only at the advancing contact line, the rivulet/ridge is flattened and widened as the shear stress is increased from its critical value, and there is a second maximum value of the shear stress beyond which no solution with a prescribed advancing contact angle is possible. In contrast, in the case of de-pinning only at the receding contact line, the rivulet/ridge is thickened and narrowed as the shear stress is increased from its critical value, and there is a solution with a prescribed receding contact angle for all values of the shear stress. In general, in the case of de-pinning at both contact lines there is a critical “yield” value of the shear stress beyond which no equilibrium solution is possible and the rivulet/ridge will evolve unsteadily. In an Appendix we show that an equilibrium rivulet/ridge with prescribed flux/area is quasi-statically stable to two-dimensional perturbations

Wall Orientation and Shear Stress in the Lattice Boltzmann Model

The wall shear stress is a quantity of profound importance for clinical diagnosis of artery diseases. The lattice Boltzmann is an easily parallelizable numerical method of solving the flow problems, but it suffers from errors of the velocity field near the boundaries which leads to errors in the wall shear stress and normal vectors computed from the velocity. In this work we present a simple formula to calculate the wall shear stress in the lattice Boltzmann model and propose to compute wall normals, which are necessary to compute the wall shear stress, by taking the weighted mean over boundary facets lying in a vicinity of a wall element. We carry out several tests and observe an increase of accuracy of computed normal vectors over other methods in two and three dimensions. Using the scheme we compute the wall shear stress in an inclined and bent channel fluid flow and show a minor influence of the normal on the numerical error, implying that that the main error arises due to a corrupted velocity field near the staircase boundary. Finally, we calculate the wall shear stress in the human abdominal aorta in steady conditions using our method and compare the results with a standard finite volume solver and experimental data available in the literature. Applications of our ideas in a simplified protocol for data preprocessing in medical applications are discussed.Comment: 9 pages, 11 figure

Immersed boundary method predictions of shear stresses for different flow topologies occuring in cerebral aneurysms

A volume-penalizing immersed boundary method is presented that facilitates the computation of incompressible fluid flow in complex flow domains. We apply this method to simulate the flow in cerebral aneurysms, and focus on the accuracy with which the flow field and the corresponding shear stress field are computed. The method is applied to laminar, incompressible flow in curved cylindrical vessels and in a model aneurysm. The time-dependent shear stress distributions over the vessel walls are visualized and interpreted in terms of the flow fields that develop. We compute shear stress levels at two different Reynolds numbers, corresponding to a steady and an unsteady flow. In the latter situation strong fluctuations in the shear stress are observed, that may be connected to raised risk-levels of aneurysm rupture

Incompressible viscous flow near the leading edge of a flat plate admitting slip

The shear stress at the leading edge, calculated on basis of the Navier-Stokes equations and the no-slip boundary condition, approaches infinity. However, taking into account the mean free path of the molecules, which implies admitting a certain slip, the shear stress becomes inversely proportional to the square root of the Knudsen number κ if κ→0. κ is defined as the ratio between the mean free path and the viscous length. The new boundary condition modifies the shear stress only within the Knudsen region of which the size is of the order of 3 to 4 times the mean free path.

Growth and shear loss characteristics of an aerobic biofilm : a thesis submitted in partial fulfilment of the requirements for the degree of Master of Technology in Biotechnology at Massey University

The application of biofilms in fermentation and waste treatment processes has been increasingly considered in recent years due to several inherent advantages over suspended growth systems. For example, they enable higher biomass hold-up providing larger quantity of cell per unit reactor volume which allows high loading rates. The biofilm systems, with fixed or immobilised cells, avoid washout conditions. The often difficult problems of sludge thickening, separation, recycle, and wasting associated with suspended growth systems are eliminated for biofilm systems. However, the major drawback lies in the control of film thickness in order to maintain high reactor productivities. The attached film thickness depends on both the biological parameters such as growth rate, and physical parameters such as hydrodynamic shear. The understanding of the growth and shear loss characteristics is a prerequisite for effective film thickness control. The main objective of this work therefore is to investigate the growth and shear loss characteristics of an aerobic biofilm utilizing phenol in a concentric cylindrical bioreactor. The growth and detachment of the biofilm was studied at different shear stresses, and their relationships were established. Detachment by shear was studied under two different conditions. One was examined simultaneously with growth under a constant shear stress where the biofilm detachment and growth occurred at the same time in the bioreactor. The other was examined via a separate shear test performed on the biofilm initially grown at a shear stress lower than that applied during the test. A method for measuring the torque exerted on the biofilm surface was first developed to enable computation of the related shear stress necessary for the study. The effect of film thickness on torque at film surface for a constant rotational speed was not significant. Shear stress can be conveniently determined from a quadratic relationship between torque and rotational speed for the range of film thickness studied. The substrate consumption is directly proportional to film thickness up to about 0.050 to 0.100 mm only, and beyond that it becomes independent of film thickness. The mass transfer resistance in the liquid phase appears to reach a minimum at shear stress greater than 3.44 N/m2 coinciding with the maximum steady-state substrate removal rate. The shear loss resistance of the biofilm increases with increasing shear stress during growth. The ultimate shear loss rate and shear stress relationship follows approximately: Rs = (40.82 – 2.750+0.1502 – 31.83e-0.610 ) × 10-2 The net growth rate varies with shear stress according to a parabolic function which predicts a shear stress of 19 N/m2 is required to achieve zero net growth. The biofilm-support adhesion must remain stronger than the film layer adhesion, otherwise, detachment will occur at the film-support interface rendering it impossible to control the film thickness