A new application of differential interferometry for stress analysis

In the past, differential interferometry has found interesting applications in gas dynamics. The gradients of density could be measured in gas flows. Now, a first trial is made to extend this method to the experimental treatment of stress problems. A Wollaston prism with polarizing elements is used in the optical arrangement. This prism combines two beams of light which have penetrated the model at locally separated points. A field of interference fringes can be produced behind the Wollaston prism. The deflections of the different conjugated light beams, which are caused by the deformed elements of the model, lead to a shifting of the interference fringes. A Stress Differential-interferometer Law is derived theoretically in order to interpret the optical data According to this theory, the optical effect caused by the deflection in this arrangement is proportional to the gradient of the sum of principal stresses. A calibration test is performed by using a circular disk, this method is applied to a circular ring for measuring the stress gradients. Under special conditions, interference fringes could be produced which represent the loci of equal stress gradient. Plexiglas plane models are loaded diametrically by single loads. The experimental results verify the statements of the developed theory.     

Development and Application of a Novel Technique for Direct Heat Flux Measurements in Turbomachinery Flows

The high performance and efficiency of modern gas turbines are only possible with temperatures inside the engine exceeding the allowed material temperatures in some areas by several hundred degrees. Therefore effective cooling methods are one of the key factors for the success of these engines. In order to achieve reliable predictions of the heat load of rotor or stator blades numerous research activities were performed to understand the nature of heat transfer in complex unsteady flows. Even numerical methods have made significant progress in recent years detailed experimental data are still necessary for validation and further development of the engines and the design tools. Here a new method to directly measure the heat flux at the material surface and accurately determine the heat transfer coefficienth is presented. The new sensor is based on the anisotropic characteristics of single crystals and allows the determination of the time varying heat flux on the surface of a model turbine airfoil. This feature is of special interest to study the influence of periodically disturbed flow conditions on the heat transfer characteristics of cooled turbine blades. The working principle of an anisotropic heat flux (AHF) sensor is briefly described together with the design of the actual sensor used in this study. Prior to the application of the sensor in a cascade test rig, comprehensive test of the sensor, the electronics and the data acquisition system were performed using a pulsed laser beam as heat source. To test the sensor under realistic conditions a large number of sensor was installed in a test blade and heat transfer measurements were performed in a cascade test rig equipped with a spoke-wheel wake generator. The results showed good agreement in the time mean results compared with standard techniques. Additionally time resolved data could be extracted from the sensor signals providing detailed information on the unsteady heat transfer characteristics and boundary layer development. This revised version was published online in July 2006 with corrections to the Cover Date.     

Absolute phase measurement in extrinsic Fabry-Perot optical fiber sensors using multiple path-match conditions

This paper describes the use of the first and second optical return paths in a moderate-to-high finesse Fabry-Perot sensor to measure the absolute phase in extrinsic Fabry-Perot interferometry (EFPI) sensors. A path-matched differential interferometry (PMDI) using a highfinesse EFPI sensors, a low-finesse Fabry-Perot readout interferometer and a broadband light source consisting of amplified spontaneous emission (ASE) from an erbium-doped fiber amplifier (EDFA) is used to illustrate the idea. The first and second multiple paths in the Fabry-Perot readout sensor are used to provide two distinct path-match conditions from the same scanning Fabry-Perot readout interferometer. The difference in fringe numbers between the centers of two orders of interference fringe packets formed by the distinct path-match conditions makes possible a simple method of measuring the cavity length of EFPI sensors, which in turn can be used to measure absolute phase and the corresponding strain. Sensor cavity length measurement using the multiple return paths in the high-finesse Fabry-Perot sensor is correlated to that measurement using the modulation transfer function found using an optical spectrum analyzer; the multiple return path technique is then used to make strain measurements on a cantilever beam. Comparisons with resistance strain gage measurements are favorable. Characterization tests indicate that the proposed technique has a cavity length measurement resolution on the order of 1.1 μm, which translates to a strain resolution of 28 με for a 4-cm gage length sensor.     

Measurement techniques for unsteady flows in turbomachines

 The growing interest for unsteady flows in turbomachines over the last two decades has led to an intensive development of fast response measurement techniques, capable of resolving with high frequency phenomena related to inlet distortion, rotating stall and blade row interference effects with blade passing frequencies ranging from 3 to 30 kHz. This development was favoured by major advances in sensor technology and data acquisition systems. The paper reviews the progress in fast response measurement techniques for high speed turbomachinery and application with emphasis on fast response pressure and temperature probes and blade surface sensors including pressure, heat transfer and shear stress determination. Received: 9 November 1998/Accepted: 21 September 1999     

A film-based wall shear stress sensor for wall-bounded turbulent flows

In wall-bounded turbulent flows, determination of wall shear stress is an important task. The main objective of the present work is to develop a sensor which is capable of measuring surface shear stress over an extended region applicable to wall-bounded turbulent flows. This sensor, as a direct method for measuring wall shear stress, consists of mounting a thin flexible film on the solid surface. The sensor is made of a homogeneous, isotropic, and incompressible material. The geometry and mechanical properties of the film are measured, and particles with the nominal size of 11 μm in diameter are embedded on the film’s surface to act as markers. An optical technique is used to measure the film deformation caused by the flow. The film has typically deflection of less than 2% of the material thickness under maximum loading. The sensor sensitivity can be adjusted by changing the thickness of the layer or the shear modulus of the film’s material. The paper reports the sensor fabrication, static and dynamic calibration procedure, and its application to a fully developed turbulent channel flow at Reynolds numbers in the range of 90,000–130,000 based on the bulk velocity and channel full height. The results are compared to alternative wall shear stress measurement methods.     

An advanced thin foil sensor concept for heat flux and heat transfer measurements in fully turbulent flows

A double layer hot film with two 10 μm nickel foils, separated by a 25 μm polyimide foil is used as a multi-purpose sensor. Each foil can be operated as a (calibrated) temperature sensor in its passive mode by imposing an electric current small enough to avoid heating by dissipation of electrical energy. Alternatively, however, each foil can also serve as a heater in an active mode with electric currents high enough to cause Joule heating. This double foil sensor can be used as a conventional heat flux sensor in its passive mode when mounted on an externally heated surface. Together with the wall and free stream temperature this measured heat flux will provide the local heat transfer coefficient In fully turbulent flows it alternatively can be operated in an active mode on a cold, i.e. not externally heated surface. Then, by heating the upper foil, a local heat transfer is initiated from which the local heat transfer coefficient h can be determined, once the lower foil is heated to the same temperature as the upper one, thus acting as a counter-heater. The overall concept behind this mode of measurement is based on the local character of heat transfer in fully turbulent flows which turns out to be almost independent of the upstream thermal events.     

Thermal convection in a Hele-Shaw cell under the action of centrifugal forces

The action of centrifugal forces on convective flows in a Hele-Shaw cell is studied experimentally and theoretically for a pulsing point heat supply from below. The dependence of convection on certain factors associated with imperfection of the experimental set-up is considered. The prospects of using experimental data and numerical simulation for the design of a sensor of inertial accelerations are discussed.     

Probabilistic mapping of adiabatic horizontal two-phase flow by capacitance signal feature clustering

In order to better quantify two-phase flow regime transitions, a sensor is developed which measures the electric capacitance of two-phase flows. A large number of experiments are done with air–water flow in a 9 mm ID horizontal tube. Based on a multivariate analysis, the most suitable sensor signal parameters are selected for building a flow regime classifier. This classifier is based on a fuzzy c-means clustering algorithm together with a regression technique. The output of the algorithm is used to create a probabilistic flow regime map. A comparison between a visual classification based on high speed camera images and the outcome of the flow regime classifier shows a remarkable agreement. The flow regime transitions are further quantified and discussed based on the probabilistic information and the sensor signal characterization. Probabilistic mapping makes it possible to combine flow regime dependent correlations in the two-phase flow models for heat transfer and pressure drop with smooth and appropriately quantified transitions from one flow regime to another.     

Non-contact boundary layer profiler using low-coherence self-referencing velocimetry

A spatially self-referencing velocimetry system based on low-coherence interferometry has been developed. The measurement technique is contactless and relies on the interference between back-reflected light from an arbitrary reference surface and seeding particles in the flow. The measurement location and the flow velocity are measured relative to the reference surface’s location and velocity, respectively. Scanning of the measurement location along the beam direction does not require mechanical movement of the sensor head. The reference surface (which can move or vibrate relative to the sensor head) can be either an external object or the surface of a body over which measurements are to be performed. The absolute spatial accuracy and the spatial resolution only depend on the coherence length of the light source (tens of microns for a superluminescent diode). The prototype is an all-fiber assembly. An optical fiber of arbitrary length connects the self-contained optical and electronics setup to the sensor head. Proof-of-principle measurements in water (Taylor–Couette flow) and in air (Blasius boundary layer) are reported in this paper.     

Measurements of cross-sectional instantaneous phase distribution in gas–liquid pipe flow

Two novel complementing methods that enable experimental study of gas and liquid phases distribution in two-phase pipe flow are considered. The first measuring technique uses a wire-mesh sensor that, in addition to providing data on instantaneous phase distribution in the pipe cross-section, also allows measuring instantaneous propagation velocities of the phase interface. A novel algorithm for processing the wire-mesh sensor data is suggested to determine the instantaneous boundaries of gas–liquid interface. The second method applied here takes advantage of the existence of sharp visible boundaries between the two phases. This optical instrument is based on a borescope that is connected to a digital video camera. Laser light sheet illumination makes it possible to obtain images in the illuminated pipe cross-section only. It is demonstrated that the wire-mesh-derived results based on application of the new algorithm improve the effective spatial resolution of the instrument and are in agreement with those obtained using the borescope. Advantages and limitations of both measuring techniques for the investigations of cross-sectional instantaneous phase distribution in two-phase pipe flows are discussed.     

Gauge finite element method for incompressible flows

A finite element method for computing viscous incompressible flows based on the gauge formulation introduced in [Weinan E, Liu J‐G. Gauge method for viscous incompressible flows. Journal of Computational Physics (submitted)] is presented. This formulation replaces the pressure by a gauge variable. This new gauge variable is a numerical tool and differs from the standard gauge variable that arises from decomposing a compressible velocity field. It has the advantage that an additional boundary condition can be assigned to the gauge variable, thus eliminating the issue of a pressure boundary condition associated with the original primitive variable formulation. The computational task is then reduced to solving standard heat and Poisson equations, which are approximated by straightforward, piecewise linear (or higher‐order) finite elements. This method can achieve high‐order accuracy at a cost comparable with that of solving standard heat and Poisson equations. It is naturally adapted to complex geometry and it is much simpler than traditional finite element methods for incompressible flows. Several numerical examples on both structured and unstructured grids are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

Holographic sensor for measurement of wall velocity gradients

Time-resolved measurements of skin friction and boundary layer turbulence are important to the design of more fuel efficient aircraft. In this paper we describe the design and testing of a holographic fan fringe sensor that can non-intrusively measure time-resolved velocity gradients near an aerodynamic surface. The holographic sensor produces a set of optical interference fringes inside the viscous sub-layer that form a fan rather than a linear array. Particles scattering light in the sub-layer produce a Doppler frequency that is a direct measurement of the velocity gradient and is proportional to aerodynamic shear stress and skin friction. The holographic recording condenses the optics necessary to form the fringes into a small 3–5 mm package, eliminates the need for optical access from behind the model, and produces a compact and robust sensor.     

Feasability study of wall shear stress imaging using microstructured surfaces with flexible micropillars

A new optical sensor technique based on a sensor film with arrays of hair-like flexible micropillars on the surface is presented to measure the temporal and spatial wall shear stress field in boundary layer flows. The sensor principle uses the pillar tip deflection in the viscous sublayer as a direct measure of the wall shear stress. The pillar images are recorded simultaneously as a grid of small bright spots by high-speed imaging of the illuminated sensor film. Two different ways of illumination were tested, one of which uses the fact that the transparent pillars act as optical microfibres, which guide the light to the pillar tips. The other method uses pillar tips which were reflective coated. The tip displacement field of the pillars is measured by image processing with subpixel accuracy. With a typical displacement resolution on the order of 0.2 m, the minimum resolvable wall friction value is _w20 mPa. With smaller pillar structures than those used in this study, one can expect even smaller resolution limits.     

Heat transfer measurements in fully turbulent flows: basic investigations with an advanced thin foil triple sensor

In a former article in this journal a double layer hot film with two 10 μm nickel foils, separated by a 25 μm polyimide foil was introduced as a multi-purpose sensor. Each foil can be operated as a (calibrated) temperature sensor in its passive mode by imposing an electric current small enough to avoid heating by dissipation of electrical energy. Alternatively, however, each foil can also serve as a heater in an active mode with electric currents high enough to cause Joule heating. This double foil sensor can be used as a conventional heat flux sensor in its passive mode when mounted on an externally heated surface. In fully turbulent flows it alternatively can be operated in an active mode on a cold, i.e. not externally heated surface. Then, by heating the upper foil, a local heat transfer is initiated from which the local heat transfer coefficient h can be determined, once the lower foil is heated to the same temperature as the upper one, thus acting as a counter-heater. For further investigations with respect to the underlying sensor concept a triple sensor has been built which consists of three double layer film sensors very close to each other. Various aspects of heat transfer measurements in active modes can be addressed by this sensor.     

Planar gas flows with weak energy supply

Perfect gas flows in an unlimited space, which occur during rectilinear motion of a system of distributed heat sources, are investigated. The next modes in order of growth of the number M are examined: the heat conductive, convective, subsonic, transonic, supersonic, hypersonic. Examples of computations are presented. Flows with distributed heat sources attract ever-increasing attention. Such flows are important, e.g., in the problem of radiation propagation [1–5], in the analysis of a gasdynamic laser resonator and the optical characteristics of a ray [6]. Changes in the density because of absorption of the ray energy, which can result in an essential redistribution of the radiation intensity, are of great interest in these problems. Theoretical investigations of a general nature with distributed heat supply [7–10] are also important for the development of further applications. Gas flows for a given distribution of relatively weak heat sources switched on at a certain time are examined in this paper.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 95–102, September–October, 1978.     

A radiation and convection fluxmeter for high temperature applications

Heat flux is an essential parameter for the diagnostic of thermal systems. In high temperature industrial environment, there are difficulties in measuring incident radiation heat flux as well as in differentiating between the convective and radiative components of heat flux on the heat transfer surface. A new method for heat flux measurement is being developed using a porous sensing element. The gas stream flowing through the porous element is used to measure the heat received by the sensor surface exposed to the hot gas environment. A numerical model of sensor with appropriate boundary condition has been developed in order to perform analysis of possible options regarding its design. The analysis includes: geometry of element, physical parameters of gas and solid and gas flow rate through the porous element. For the optimal selection of parameters, an experimental set-up was designed, including the sensor element with respective cooling and monitoring systems and a high temperature radiation source. The experimental set-up was used to obtain calibration curves for a number of sensors. The linear dependency of the heat flux and respective temperature difference of the gas were verified. The accuracy analysis of the sensor reading has proved high linearity of the calibration curve and accuracy of ±5%.     

Optical method for measuring the distribution of a solid admixture in two-phase flows

We discuss an optical method for measuring the density distribution of a solid admixture with a narrow particle-size distribution function by the intensity of the scattered light. A comparison of measurements made by the optical method and by a probe shows the suitability of the optical method for a number of types of two-phase flows.     

Effect of dissipative processes on compression flows in a plasma accelerator channel

Plasma flows in coaxial channels with a truncated central electrode are accompanied by compression and heating of the plasma on the channel axis [1–4]. Such flows were calculated in [1, 4] within the framework of a simple MHD model and by simple numerical methods and, accordingly, the results reflect only the basic qualitative characteristics of compression flows. Below, these flows are investigated in greater detail on the basis of a more accurate physical model with allowance for the finite conductivity, heat conduction and radiation of the plasma and impurities. The cases of anisotropic and classical isotropic heat conduction are considered. The numerical method employed is based on two finite-difference schemes: SHASTA-FCT [5–7] and TVD [8, 6]. The main advantage of these methods is the high resolution of the shock waves and contact discontinuities, which is highly desirable in describing compression flows. The calculations relate to the case of a fully ionized hydrogen plasma.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 102–109, May–June, 1991.In conclusion, the author wishes to express his gratitude to K. V. Brushlinskii and A. I. Morozov for frequent discussions and to K. P. Gorshenin for the use of his calculation results.