Lennart Löfdahl

MEMS APPLICATIONS IN TURBULENCE AND FLOW CONTROL

Manufacturing processes that can create extremely small machines have been developed in recent years. Microelectromechanical systems (MEMS) refer to devices that have characteristic length of less than 1 mm but more than 1 μm, that combine electrical and mechanical components and that are fabricated using integrated circuit batch-processing techniques. Electrostatic, magnetic, pneumatic and thermal actuators, motors, valves, gears and tweezers of less than 100 μm size have been fabricated. These have been used as sensors for pressure, temperature, mass flow, velocity and sound, as actuators for linear and angular motions, and as simple components for complex systems such as micro-heat-engines and micro-heat-pumps. In this paper, we focus on the microelectromechanical systems for the diagnosis and control of turbulent shear flows. We survey the status and outlook of microsensors and microactuators as used for those particular applications, and compare the minute devices to their larger cousins. Microsensors can resolve all relevant scales even in high-Reynolds-number turbulent flows. Arrays of microsensors and microactuators make it feasible, for the first time, to achieve effective reactive control targeted toward specific small-scale coherent structures in turbulent wall-bounded flows.

MEMS-based pressure and shear stress sensors for turbulent flows

From a fluid dynamics perspective, the introduction of microelectromechanical systems (MEMS) has considerably broadened the spectrum of workable experiments. A typical MEMS sensor is at least one order of magnitude smaller than traditional sensors used to measure instantaneous flow quantities such as pressure and velocity. The microsensors can resolve all relevant scales even in high-Reynolds-number turbulent flows, and arrays of microsensors make it feasible, for the first time, to achieve complete information on the effective small-scale coherent structures in turbulent wall-bounded flows. In this paper we focus on the use of MEMS for the diagnosis of turbulent shear flows and survey the status and outlook of microsensors as used for measurements of fluctuating wall pressure and wall shear stress, two quantities which we deem particularly difficult to measure with conventional probes. For both wall pressure and wall shear stress sensors, we give general background, design criteria and calibration procedure. Examples of measurements conducted with MEMS-based sensors are provided and the minute devices are compared to their larger cousins.

A similarity theory for the turbulent plane wall jet without external stream

A new theory for the turbulent plane wall jet without external stream is proposed based on a similarity analysis of the governing equations. The asymptotic invariance principle (AIP) is used to require that properly scaled profiles reduce to similarity solutions of the inner and outer equations separately in the limit of infinite Reynolds number. Application to the inner equations shows that the appropriate velocity scale is the friction velocity, u ∗, and the length scale is v / u ∗. For finite Reynolds numbers, the profiles retain a dependence on the length-scale ratio, y + 1/2 = u ∗ y 1/2 / v , where y 1/2 is the distance from the wall at which the mean velocity has dropped to 1/2 its maximum value. In the limit as y + 1/2 → ∞, the familiar law of the wall is obtained. Application of the AIP to the outer equations shows the appropriate velocity scale to be U m , the velocity maximum, and the length scale y 1/2 ; but again the profiles retain a dependence on y + 1/2 for finite values of it. The Reynolds shear stress in the outer layer scales with u 2 * , while the normal stresses scale with U 2 m . Also U m ∼ y n 1/2 where n < −1/2 and must be determined from the data. The theory cannot rule out the possibility that the outer flow may retain a dependence on the source conditions, even asymptotically. The fact that both these profiles describe the entire wall jet for finite values of y + 1/2 , but reduce to inner and outer profiles in the limit, is used to determine their functional forms in the ‘overlap’ region which both retain. The result from near asymptotics is that the velocity profiles in the overlap region must be power laws, but with parameters which depend on Reynolds number y + 1/2 and are only asymptotically constant. The theoretical friction law is also a power law depending on the velocity parameters. As a consequence, the asymptotic plane wall jet cannot grow linearly, although the difference from linear growth is small. It is hypothesized that the inner part of the wall jet and the inner part of the zero-pressure-gradient boundary layer are the same. It follows immediately that all of the wall jet and boundary layer parameters should be the same, except for two in the outer flow which can differ only by a constant scale factor. The theory is shown to be in excellent agreement with the experimental data which show that source conditions may determine uniquely the asymptotic state achieved. Surprisingly, only a single parameter, B 1 = ( U m v / M o )/ ( y + 1/2 M o / v 2 ) n = constant where n ≈ −0.528, appears to be required to determine the entire flow for a given source.

An integrated pressure—flow sensor for correlation measurements in turbulent gas flows

A new integrated pressure—flow sensor has been specially designed for measurements in turbulent gas flows. The pressure sensor is based on polysilicon diaphragm technology and the flow sensor on the gas cooling of a polyimide-insulated heated mass. With a pressure-sensor diaphragm area of 100 μm × 100 μm, a flow-sensor hot-chip area of 300 μm × 60 μm and an edge-to-edge distance of 100 μm between the different sensor areas, the smallest eddies in technically interesting turbulent flows can be resolved and measured. The pressure-sensor design shows a flat frequency response curve within ±2 dB between 10 Hz and 10 kHz with an acoustic sensitivity of 0.9 μV Pa−1 for a supply voltage of 10 V. The flow sensor has a thermal response with a time constant of 7 ms and a response time of 25 μs when the sensor is operated at constant temperature using feedback electronics. The measured steady-state flow-sensor power dissipation in a turbulent wall boundary layer at an overtemperature of 100 °C was P = 34 + 0.4τ00.47 mW where τ0 is the time-average flow-dependent wall shear stress. The integrated sensor has been used for simultaneous measurement of fluctuating pressure and wall shear stress in a turbulent boundary layer yielding pressure—wall shear stress correlation coefficients never previously presented.

Silicon based flow sensors used for mean velocity and turbulence measurements

Small and directional sensitive silicon based sensors for velocity measurements have been designed and fabricated using microelectronic technology. Single-chip as well as double-chip sensors for the determination of mean velocity and turbulent stresses have been developed. To determine the performance of these silicon sensors, comparisons with conventional hot-wire sensors were done in a well-defined two-dimensional turbulent flat plate boundary layer at a constant Reynolds number of 4.2 · 106. All the silicon sensors were found to have a spatial and frequency resolution that makes them suitable for turbulence measurements. In the studied flow field the measured profiles of mean velocities and Reynolds stresses of all silicon sensors show the same accuracy as corresponding hot-wire measurements. The silicon sensors are also shown to operate with good resolution even when the temperature of the heated part of the chip is reduced considerably.

A study of the Blasius wall jet

A plane wall-jet flow is numerically investigated and compared to experiments. The measured base flow is matched to a boundary-layer solution developing from a coupled Blasius boundary layer and Blasius shear layer. Linear stability analysis is performed, revealing high instability of two-dimensional eigenmodes and non-modal streaks. The nonlinear stage of laminar-flow breakdown is studied with three-dimensional direct numerical simulations and experimentally visualized. In the direct numerical simulation, an investigation of the nonlinear interaction between two-dimensional waves and streaks is made. The role of subharmonic waves and pairing of vortex rollers is also investigated. It is demonstrated that the streaks play an important role in the breakdown process, where their growth is transformed from algebraic to exponential as they become part of the secondary instability of the twodimensional waves. In the presence of streaks, pairing is suppressed and breakdown to turbulence is enhanced.

Shear-free turbulence near a wall

The mean shear has a major influence on near-wall turbulence but there are also other important physical processes at work in the turbulence/wall interaction. In order to isolate these, a shear-free boundary layer was studied experimentally. The desired flow conditions were realized by generating decaying grid turbulence with a uniform mean velocity and passing it over a wall moving with the stream speed. It is shown that the initial response of the turbulence field can be well described by the theory of Hunt & Graham (1978). Later, where this theory ceases to give an accurate description, terms of the Reynolds stress transport (RST) equations were measured or estimated by balancing the equations. An important finding is that two different length scales are associated with the near-wall damping of the Reynolds stresses. The wall-normal velocity component is damped over a region extending roughly one macroscale out from the wall. The pressure-strain redistribution that normally would result from the Reynolds stress anisotropy in this region was found to be completely inhibited by the near-wall influence. In a thin region close to the wall the pressure-reflection effects were found to give a pressure-strain that has an effect opposite to the normally expected isotropization. This behaviour is not captured by current models.

Experiments on secondary instability of streamwise vortices in a swept-wing boundary layer

A detailed experimental study on the formation of crossflow vortex mode packets and their high-frequency secondary instability in a swept-wing boundary layer was carried out. Stationary vortex packets are most likely to be generated under natural flight conditions and transition to turbulence is quickest within these disturbances. In the present experiments, different methods of controlled excitation are used so that the crossflow vortex packets are generated by surface-roughness elements and by localized continuous suction. It is found that as the stationary disturbance reaches a significant amplitude, of about 10% of the free-stream velocity, while being below the saturation level, high-frequency secondary instabilities start to grow. Influence of the crossflow vortex packet magnitude on the development of the secondary instability is investigated in detail and below its threshold the crossflow vortex packet was found to be nearly neutrally stable. By studying the unstable packets, the frequency of natural secondary perturbations was identified and the travelling disturbances were forced in a controlled manner by periodic blowing-suction applied locally under the stationary vortex. Two modes of secondary instability were found to develop and the preferred mode was dependent on the properties of the primary stationary disturbance. Additionally, the underlying physics of the process of nonlinear formation and development of the vortices in the boundary layer is clarified. It was observed that the large-amplitude co-rotating vortices may interact, thus reducing their amplitude. Also a large-scale excitation by an isolated roughness element produced two individual stationary crossflow vortex packets at its tips, each with different preferred secondary instability modes.

An Integrated Silicon based Wall Pressure-Shear Stress Sensor for Measurements in Turbulent Flows

By the introduction of silicon micro machining into fluid mechanics the experimentalists have been given a new incentive to carry out measurements of fundamental parameters in turbulent flows. One such unknown parameter is the pressure-velocity correlation (PVC) which turns out to be a key term in the kinetic energy budget as well as in the transport equations for the Reynolds stresses.

A small-size silicon microphone for measurements in turbulent gas flows

Abstract For the first time a silicon microphone specially designed for measurements in turbulent gas flows has been fabricated and tested. The new design, based on surface-micromachining techniques, has a very small pressure-sensitive polysilicon diaphragm of 100 μm side length and 0.4 μm thickness with polysilicon piezoresistive strain gauges. The small diaphragm makes it possible to resolve and measure the pressure fluctuations of the smallest eddies in a turbulent flow. In order to achieve a sufficiently high acoustic pressure sensitivity, a relatively deep (3 μm) cavity is formed below the diaphragm by using the sacrificial-layer etching technique. A special vent channel is designed to give an equalization of the static air pressure between the cavity and the ambient without degrading the dynamic pressure response of the microphone. The device has a very flat frequency-response curve within ±2 dB between 10 Hz and 10 kHz and an acoustic sensitivity of 0.9 μV Pa−1 for a supply voltage of 10 V. It has been shown that the new sensor fulfils the requirements for pressure measurements in turbulence. The microphone frequency response has been calculated using an electrical analogy. Comparisons with experimental data are presented.