A swinging arm calibration method for low velocity hot-wire probe calibration

This paper describes a swinging arm calibration facility for the calibration of hot-wire probes at low velocities. During the motion of the probe the anemometer signal is recorded digitally using pre-set angle positions for the start and stop of the data acquisition. The evaluation method described in this paper is based on an integral procedure over a fixed, known probe path length. Tests in the velocity range 1 to 6 m/s demonstrated a high degree of repeatability of the calibration results. Furthermore, the test facilities can easily be adjusted for other low velocity ranges.     

A simple pendulum technique for the calibration of hot-wire anemometers over low-velocity ranges

A method for low velocity calibration of hot-wire anemometers, in which the probe is mounted on a pendulum arm, is presented. The calibration constants are determined from recorded traces of the anemometer signal obtained in the forward swing of the pendulum with the probe mounted at two different radii along the arm. Typical calibration results are presented and the use of a modified King's law in the low Reynolds number range is discussed.List of Symbols A, B, n calibration constants in King's law - E anemometer voltage output - E ₀ anemometer voltage output for zero flow velocity - Re Reynolds number - r radius along the pendulum arm - T period of oscillation of the pendulum arm - t time - U velocity - y ⁺ non-dimensional distance from the wall Greek Symbols root mean square of the velocity difference in half the forward swing - angular position of pendulum - angular velocity of pendulum arm Financial support for this work was provided by the Natural Sciences and Engineering Research Council of Canada and by the Atomic Energy of Canada Limited.     

The calibration of (multi-) hot-wire probes. 1. Temperature calibration

We study the performance of the classical relation for the correction for ambient temperature drift of the signal of a hot-wire anemometer and the influence of practical assumptions. It is shown that most methods to estimate the operational temperature via the temperature/resistance coefficient lead to underestimation of the operational temperature and thus to overcorrection of signals for temperature drift. We found that, in the presence of a sensible heat flow, temperature fluctuations cannot be sufficiently removed from the hot-wire signal when one relies on temperature/resistance coefficients from literature. When only slow temperature drift is involved, most literature values give a satisfactory temperature correction, but this depends on the specific combination of a probe and a literature reference. Therefore it is generally advisable to calibrate the value. A method that uses a ratio of (measured) resistances as a function of temperature, which does not require estimation of the operational temperature of the wire, is shown to depend crucially on a parasitic resistance of a few tenths of an ohm. This parameter can be found by optimizing its value using data from a collection of velocity calibrations at different temperatures. This additional calibration alone suffices to estimate the operational temperature of the wire via optimization. A quick calibration procedure (15 min) is proposed and tested.     

An experimental approach to the calibration and use of triple hot-wire probes

A method of calibrating and extracting velocities from arbitrary geometry triple hot-wire probes has been developed and tested. The three-step procedure involves experimental determination of an accurate cooling law for each wire in the array, use of these models to develop a set of tables relating anemometer output to flow velocity input, and a table look-up procedure to extract the velocities. The functional form for the cooling law can be arbitrarily chosen and these equations are never directly inverted. Solutions are tabulated making use of special variable transformations that separate the dependence on flow angle and velocity magnitude. Errors in the table look-up procedure are commensurate with those in exact inversion techniques. Most of the error arises from accurate determination of the cooling laws. An application to turbulent boundary layer measurements is presented as an example of the use of the method.     

关于虚拟激励法的一个注记

从具有随机频率与随机相位的随机谐和函数出发,证明了当随机频率与相位均为均匀分布而随机幅值与功率谱密度平方根成正比时,该随机过程的功率谱即精确地等于目标功率谱.进而表明:只需遍历频率区间,即可由单一谐和函数激励下的响应幅值给出响应的功率谱密度,从而揭示了虚拟激励法的物理意义.研究还表明:为了给出结构响应的功率谱密度,实际...     

A note on the method of weighted difference

In this short paper, we introduce a new difference approximation for singular perturbation problem and prove the necessary condition of uniform convergence. Selecting apposite weight factor, we obtain the same difference schemes as in the case of Ilin’s method.     

A time-resolved hot-wire shear stress probe for turbulent flow: use of laminar flow calibration

A specially-designed rotating rig for producing near Couette flow was used in the calibration of a marginally elevated hot-wire shear stress probe. The probe was then used for measurements in both the turbulent boundary layer and pipe flows. Results showed that the mean wall shear stress can be accurately predicted and the near wall statistical quantities of intensity, skewness and flatness of shear stress fluctuations concurred well with previous works, thereby supporting the notion of a time-resolved shear stress probe for turbulent flows.     

A note on delta-perturbation expansion method

ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙＢｅｎｄｅｒｅｔａｌ.[1]ｐｒｏｐｏｓｅｄａｎｅｗｐｅｒｔｕｒｂａｔｉｏｎｔｅｃｈｎｉｑｕｅｂａｓｅｄｏｎａｎａｒｔｉｆｉｃｉａｌｐａｒａｍｅｔｅｒδ .Ｔｈｅｉｄｅａｉｓｑｕｉｔｅｓｉｍｐｌｅ .Ｃｏｎｓｉｄｅｒ,ｆｏｒｅｘａｍｐｌｅ ,ｔｈｅＤｕｆｆｉｎｇｅｑｕａｔｉｏｎｗｉｔｈｏｕｔａｓｍａｌｌｐａｒａｍｅｔｅｒｕ″+ｕ+ 1 0ｕ3=0 .　　Ｗｅｒｅｐｌａｃｅｔｈｅｎｏｎｌｉｎｅａｒｕ3ｂｙａｎｏｔｈｅｒｔｅｒｍｕ1+δ,ｗｈｉｃｈｃｏｎｔａｉｎｓｔｈｅｐａｒａｍｅｔｅ…     

The calibration of (multi-)hot-wire probes. 2. Velocity-calibration

We review a set of velocity calibration methods for one popular configuration of a four-hot-wire probe with the aim of finding a method of estimating with 10% accuracy (based on full scale) the mean flow vector, the rms of the turbulent velocity component and the associated linearized anisotropy invariants. We performed full 3D velocity calibrations of a classic and a sub-miniature probe. With a calibrated King/Jørgensen model and with an interpolation scheme in the real calibrations, we simulated calibrations and (anisotropic) turbulence measurements. Analysis of the idealized and of the realistic simulation data showed that the lookup-table method is the only good tool for processing hot-wire measurements. Polynomial models give large systematic errors. The King/Jørgensen model can only be used for qualitative ends, but it forms a good basis for a simulation-based assessment of the quality of a measured calibration set. Our results indicate that the experimental results reported in the literature, and which were based on hot-wire measurements, may require a reassessment of the calibration method.     

A calibration technique for multiple-sensor hot-wire probes and its application to vorticity measurements in the wake of a circular cylinder

A calibration technique for multiple-sensor hot-wire probes is presented. The technique, which requires minimal information about the probe geometry, is tested using a four-sensor and a twelve-sensor probe. Two data reduction algorithms are introduced. The first one assumes a uniform velocity over the probe sensing-volume and is applied to the four-sensor probe measurements. The second one assumes a uniform velocity gradient over the sensing volume of the probe. The procedure, when applied to the twelve-sensor probe, is shown to measure the velocity gradient components successfully. In both algorithms, the unknowns (velocity and velocity gradient components) are obtained by solving the resulting systems of nonlinear algebraic equations in a least-squares sense. The performances of the probes and the algorithms are tested with measurements in the wake of a circular cylinder. The statistics and spectra show that the twelve-sensor probe is successful in the simultaneous measurement of all three components of the velocity and all three components of the vorticity vectors.     

A fast simple hot-wire method of determining the mean velocity vector of complex three-dimensional flows

A fast and simple method of determining the mean velocity vector of complex three-dimensional flow fields is outlined. Straight and slanted single hot-wires are rotated in two perpendicular planes. This method increases the angular resolution, which is of importance in flow situations where one of the velocity components dominates and the other changes rapidly from one point to another. The method was calibrated in a wind tunnel and assessed in the internal flow field at the outlet of a fan in a defroster channel. It is shown that the hot-wire method yields good agreement with corresponding flow visualizations determined using a textile thread, and an integration of the measured mean flow yields a flow rate which agrees within a few percent with corresponding direct measurements on an orifice plate.     

A note on Ligtenberg's reflective moiré method

A new arrangement of the optical components of the Ligtenberg reflective moiré method is proposed whereby the line density of the reference grating can be varied continuously. As a result, the sensitivity of the method can be changed at will to suit the particular problem under study.     

关于《再论约束最小二乘法》的注记

约束最小二乘法在计算力学和工程问题的理论研究和实际应用中都起到重要的作用。本文借助矩阵广义奇异值分解的方法，研究了一般矩阵的约束最小二乘问题，给出了一般矩阵约束最小二乘问题的算法，推广了文献[1]的结果。     

A simplified, flow-based calibration method for stereoscopic PIV

An improvement of the process of stereo-PIV calibration is presented. The central feature of the proposed technique is that the calibration of the stereoscopic system is based upon the measurement of a calibrated flow. This is achieved through an initial two-dimensional calibration of the measurement plane using a single target point, followed by a perspective and laser sheet thickness optimization that makes use of the measurement of a known reference flow, e.g., a uniform flow. This technique results in planar domain, three-component (2D–3C) measurements with a simpler calibration phase, which delivers uncompromised accuracy, compensates for the mechanical misalignment and eliminates the errors deriving from the classical target plate dot identification. The technique is particularly well suited for towing tanks and other large facilities, and is applied to the vortex system shed from an underwater bridge sail.     

An oscillating hot-wire technique for resolving the magnitude and direction of velocity measurements using single hot-wire sensors

Thermal anemometry is a classic flow-velocity measurement technique that is known to suffer from the inability to discern the flow direction. The current paper describes an innovative approach whereby an oscillating hot wire is used to extract velocity direction and magnitude information from single hot-wire measurements. It is shown that the new sensor operates in one of two modes depending on the velocity amplitude of the wire oscillation. Furthermore, results from applying the technique to measure the phase-averaged velocity in an oscillating pipe flow experiment are presented. The results from the hot-wire measurements show good agreement with those from laser Doppler velocimetery measurements in the same facility.     

Simulation and calibration of granules using the discrete element method

The discrete element method (DEM), developed by Cundall and Strack (1979) to solve geomechanical problems, is used to simulate the mechanical behavior of granules. According to the DEM, an individual granule can be modeled as a realistic mechanical system consisting of primary particles bonded by interaction forces.Granulometric properties of the model material, zeolite 4A, have been measured to determine their macro properties. To investigate the compression behavior, a compression test was performed using a strength tester on single granules between two pistons. A modeled granule consisting of more than 22,000 primary particles was generated. The micro properties of the modeled granule have been precisely set to allow its macro properties to be equivalent to the macro properties of zeolite 4A granules. To calibrate the mechanical properties, diametrical compression was simulated using two rigid walls stressed at a constant stressing velocity. The force–displacement curve of the modeled granule at compression has been calibrated by the experimental curve of zeolite 4A.