Frequency response and instantaneous temperature profile of cold-wire sensors for fluid temperature fluctuation measurements

The information of the wire response is necessary for the estimation of corrections and uncertainty of temperature measurements. This paper describes the theoretical response of cold-wire sensors to temperature fluctuations in a fluid flow. Existing transfer functions of cold wires are approximate and implicit functions of frequency. We present the exact solutions of heat conduction equations for a cold wire and stubs taking account of the prong effect. Because the solutions have simple forms of elementary functions, we can easily calculate the frequency response of cold wires. Sample calculations are given under several typical conditions. Also, the instantaneous temperature profiles of a cold wire are obtained for the first time.     

Frequency response of a cold-wire in a flow seeded with oil particles

Experiments have been carried out to investigate the effects of aging on the frequency response of a fine cold-wire located in a flow seeded with oil particles used for laser Doppler anemometry. Transfer functions are shown to depend strongly on the running time. Photo-micrographs show that the contamination effect is due to discrete droplets, the diameter of which increases with running time. Reduction of frequency response is shown to affect at first the high-frequency range and then an intermediate range of frequencies that are larger than the inverse of the oil droplets time constant. Good agreement is found between experimental results and predictions derived from a simple model of the contaminated wire. This contamination process requires testing and cleaning the wire steadily in order to keep a significant frequency response and, if needed, to correct temperature fluctuations.     

Notch-root plastic response by temperature measurement

It is an experimental fact that the majority of the irreversible work of plastic deformation in metals is converted to heat. Under adiabatic conditions the spatial distribution of heating is indicative of the spatial distribution of plastic work. Tiny thermocouples welded directly to a metal surface were found to provide adequate measurement speed and sensitivity to detect the temperature change associated with plastic deformation. An array of thermocouples was used with some success in determining plastic-zone size. The heating response was used to study notch-root plastic deformation following overloads and following various post-overload heat treatments. The notch-root plastic response was correlated directly with the notch-root residual-stress level. The degree of stress relief as a function of time and temperature found in the notched members studied agrees well with predictions made using the Larson-Miller parameter and relaxation data on other steels. The deformation response in notched-member tests following stress relief is in qualitative agreement with that predicted by mechanics analysis of cracked bodies done by others.     

Holo-interferometric measurement of the thermal deformation response to power dissipation in multilayer printed wiring boards

A comprehensive evaluation of the thermally induced warping in two microcircuit modules of differing substructure has been made using holographic interferometry. The measured out-of-plane displacement pattern for the ‘symmetric/large-hole’ module was found to be very simple, stable, and repeatable, while for the ‘asymmetric/small-hole’ module it appeared to be highly complex, of changing shape and stable only after several test cycles. Quantitative analysis of these results demonstrate that changes in the internal structure of the multilayer printed wiring board can have a significant impact on the loadings experienced by solder-post connections between the chip carrier and the printed wiring board during normal power cycles. These include changes in the bending pattern sufficient to almost halve the peak Mode B (bending) deformations of the solder posts. At the same time, the associated decreases in local deformation and deformation gradients result in a 33-percent decrease in the peak Mode C (tensile) deformation of these same critical connections.     

Performance of a probe for measuring turbulent energy and temperature dissipation rates

A probe consisting of four X-wires (a total of eight hot wires operated in constant temperature mode) and two pairs of parallel cold wires (operated in constant current mode) is in principle capable of providing simultaneous data for the instantaneous energy and temperature dissipation rates. To evaluate the performance of this probe, measurements have been made in decaying turbulence downstream of a grid/screen combination. The directly measured mean values of the energy and temperature dissipation rates are compared with those obtained from the streamwise decay rates of the mean turbulent energy and temperature variance. The probe also yields all three fluctuating vorticity components; after applying spatial resolution corrections, their spectra are in close agreement with isotropic calculations over nearly all wavenumbers. Both the vorticity variance and the mean energy dissipation rate exhibit the same power-law decay rate. Transport equations for the mean energy and temperature dissipation rates are satisfied to within ᆞ%.     

Testing of a hot- and cold-wire probe to measure simultaneously the speed and temperature in supercritical CO2 flow

The use of hot-wire anemometry in carbon dioxide flow under supercritical conditions has been analyzed and implemented for the first time. A two-sensor probe to simultaneously measure streamwise velocity and temperature in this flow has been designed and constructed. A calibration and test flow loop that can provide supercritical state conditions above the critical point has been also designed, fabricated and tested. The temperature and velocity flow fields of the flow loop can be varied at constant pressure. It has been found that, above the pseudo-critical temperature, the velocity sensor response fits King’s cooling law with a high correlation coefficient. The dependence of the King’s law parameters on temperature can be accurately presented with second or higher order polynomial or exponential fits, depending on the extent of the temperature range. Below the pseudocritical temperature the data is scattered, and the variation with temperature of the King’s law parameters, determined from calibration, is irregular. The influence on this data scatter of the strong variation of the fluid properties near the critical point is analyzed, and a possibility to reduce it is proposed. The temperature sensor response both above and below the pseudocritical temperature is similar to the response under normal conditions. It is linear with a very high correlation coefficient between the calibration data and the fitted curve. It is also shown that the temperature response is not affected by variation of the flow’s speed.     

EXPERIMENTAL STUDY OF MEASUREMENT FOR DISSIPATION RATE SCALING EXPONENT IN HEATED WALL TURBULENCE

Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region . Longitudinal velocity and temperature have been measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is studied because of the existence of organized coherent structure burst process in the near wall region . The scaling law of coarse-grained dissipation rate structure function is foun     

Transport equations for the mean energy and temperature dissipation rates in grid turbulence

 Simultaneous measurements of velocity and temperature fluctuations were made in the turbulent flow downstream of a grid-heated screen combination. The magnitudes of n and m, the power-law exponents for the decay of turbulent energy and temperature variances, are nearly equal. This approximate equality is in conformity with the locations of the peaks in the three-dimensional turbulent energy and temperature spectra. The values of n and m are consistent with the isotropic forms of the transport equations for the mean turbulent energy and temperature variance. They are also consistent, allowing for the measurement accuracy, with the isotropic forms of the equations for the mean turbulent energy and temperature dissipation rates. Received: 20 October 1998 / Accepted: 26 March 1999     

The temperature field in rotational rheometers and flow curve correction for viscous dissipation

A solution is presented for incompressible non-Newtonian liquids of the one-dimensional stationary temperature field which arises due to heat dissipation between two concentric cylinders, the outer fixed and thermostated, the inner rotating at a constant angular velocity. The object of the study is to outline a simple procedure for determining the temperature rise of the liquid and, primarily, to ascertain the corrections of the consistent variables and D which enable the experimenter to rectify the rheogram on the basis of measurement of the shear stress and the angular velocity . The results obtained are summarized in graphical form as diagrams of the temperature and velocity fields and, to facilitate practical application of the correction procedure, in a table relating the dimensionless temperature function (, n, ) to the geometry , the flow behaviour index n, and the coefficient of temperature rise and showing the function (1) as well.List of symbols a radius of the inner cylinder - b radius of the outer cylinder - constant angular velocity of the inner cylinder - r* dimensionless radial coordinate r/b - * dimensionless angular velocity of the liquid - K fluid consistency index - n flow behaviour index - dimensionless temperature rise (T–T ₀)/T ₀ - T temperature of measured liquid (K) - T ₀ temperature of the thermostated bath - Br Brinkman criterion - _f thermal conductivity of liquid - C constant of integration - coefficient of sensitivity in consistency-temperature law - coefficient of sensitivity divided by flow behaviour index: /n - (r*) dimensionless temperature function - coefficient of temperature rise; =Br· - ratio of the radii of inner and outer cylinder - T(1) temperature on the inner wall of the outer cylinder, i.e. for r*=1 - outer cylinder wall thickness - coefficient of heat transfer - q heat flux - k overall heat transfer coefficient - h height of measured liquid - _s thermal conductivity of the outer cylinder - (1) derivative of the dimensionless temperature function at point r*=1 - dimensionless heat transfer constant - _i (r*) dimensional temperature function calculated for isothermal wall; T(1)=T ₀ - dynamic viscosity - _i () maximum value of the dimensionless temperature function - dimensionless symbol — ratio of C/C ₀ - D rate of shear - shear stress - rate of shear (not considering dissipation) - shear stress (not considering dissipation) - D ⁺ rate of shear corrected for the inner cylinder temperature - ⁺ shear stress on the inner cylinder obtained by measurement on the rheometer used - _j rate of shear on the inner cylinder for j-th measurement referred to a single constant temperature     

Calibration of a temperature dissipation probe in decaying grid turbulence

A four cold-wire probe, which allows all three components of the temperature dissipation rate ? _θ to be measured, is “calibrated” in decaying grid turbulence, where <? _θ >, the mean value of ? _θ , can be determined accurately from the decay of the temperature variance <θ ²>. The probe yields values of the three components of <? _θ > which are in reasonable agreement with local isotropy, in the range x ₁/M?50. The pdfs and spectra of the three temperature derivatives also satisfy local isotropy reasonably well.     

Improvement in use of photometric methods for measurement of birefringence

Visual or graphical determination of isochromatic order in photoelastic models is not sufficiently accurate for many photoelastic observations. This is especially true in the long-wavelength spectral region where fringe orders are low and photometric devices must be used for observation. In such cases, some method of fractional-fringe measurement is required. The Tardy and Sénarmont methods are often chosen for convenience, with preference given to the Sénarmont method because of smaller system error. These methods are based on detection of the analyzer angle at which the light transmitted through the given point in the model is minimum. The experimental problem is poorly conditioned, and the procedure is incompatible with nonideal light-sensing apparatus. The equations of the Sénarmont technique show that the intensity of radiation is an even function of the rotation of the analyzer from the position which produces minimum intensity. The indeterminacy in the measurement of minimum-intensity angle may be reduced by observing the angles at which the intensity reaches arbitrary values greater than minimum. The average of two such readings on both sides of the minimum-intensity angle provides an improved measurement of this angle. Best results are obtained if observations are made where the intensity reaches half its maximum value. For a signal-to-noise ratio of 1000, this procedure improves results by a factor of 16. Improvement is greater asS/N is increased.     

粘滞和粘弹性阻尼器减震结构的随机响应特性

利用积分型本构关系,针对带支撑任意线性粘滞和粘弹性阻尼器单自由度耗能结构,建立了微分和积分混合地震响应方程;基于随机平均分析法,推导出耗能结构振幅与相位瞬态联合概率密度函数、位移与速度瞬态联合概率密度函数、位移与速度瞬态响应方差、振幅动力可靠性、振幅首超时间任意阶统计矩的一般解析解;给出了带支撑广义Maxwell阻尼器和广义微分模型阻尼器耗能结构上述各种随机响应特性,从而建立了带支撑任意线性粘滞和粘弹性阻尼器单自由度减震结构的各种随机响应特性分析的统一解析解法。     

多自由度Maxwell阻尼器减震结构(Ⅰ)——随机响应特性

对多自由度带支撑Maxwell粘滞阻尼器减震结构的随机响应特性进行了系统研究。建立了结构一般运动方程;将运动方程按原结构振型展开,将运动方程化为振型广义坐标的微分和积分混合地震响应方程组;基于多自由度随机平均法理论,获得了结构随机平均It方程组的解析式,推导出耗能结构各振型振子的振幅与相位瞬态联合概率密度函数、位移与速度瞬态联合概率密度函数、位移与速度瞬态响应方差的一般解析解;根据SRSS组合方法,给出了耗能结构随机地震响应方差的一般解析式,从而建立了此类耗能结构随机响应特性分析的完备解析解法。     

Analysis of errors in the measurement of energy dissipation with two-point LDA

In the present study, an attempt has been made to identify and quantify, with a rigorous analytical approach, all possible sources of error involved in the estimation of the fluctuating velocity gradients when a two-point laser Doppler velocimetry (LDV) technique is employed. Measurements were carried out in a grid-generated turbulence flow where the local dissipation rate can be calculated from the decay of kinetic energy. An assessment of the cumulative error determined through the analysis has been made by comparing the values of the spatial gradients directly measured with the gradient estimated from the decay of kinetic energy. The main sources of error were found to be related to the length of the two control volumes and to the fitting range, as well as the function used to interpolate the correlation coefficient when the Taylor length scale are estimated.

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An analytical solution for the temperature profiles during injection molding,including dissipation effects

An analytical solution is obtained for the stationary temperature profile in a polymeric melt flowing into a cold cavity, which also takes into account viscous heating effects. The solution is valid for the injection stage of the molding process. Although the analytical solution is only possible after making several (at first sight) rather stringent assumptions, the calculated temperature field turns out to give a fair agreement with a numerical, more realistic approach. Approximate functions were derived for both the dissipation-independent and the dissipation-dependent parts which greatly facilitate the temperature calculations. In particular, a closed-form expression is derived for the position where the maximum temperature occurs and for the thickness of the solidified layer.The expression for the temperature field is a special case of the solution of the diffusion equation with variable coefficients and a source term.Nomenclature a thermal diffusivity [m²/s] - c specific heat [J/kg K] - D channel half-height [m] - L channel length [m] - m 1/ - P pressure [Pa] - T temperature [°C] - T _W wall temperature [°C] - T _i injection temperature [°C] - T _A Br independent part of T - T _B Br dependent part of T - T ^core asymptotic temperature - v _z() axial velocity [m/s] - W channel width [m] - x cross-channel direction [m] - z axial coordinate [m] - (x) gamma function - (a, x) incomplete gamma function - M(a, b, x) Kummer function - small parameter - () temperature function - thermal conductivity [W/mK] - viscosity [Pa · s] - ₀ consistency index - power-law exponent - density [kg/m] - similarity variable Dimensionless variables Br Brinkman number - Gz Graetz number -      

High data density temperature measurement for quasi steady-state flows

A new optical instrument, the liquid crystal point diffraction interferometer (LCPDI), is used to measure the temperature distribution across a heated chamber filled with silicone oil. Data taken using the LCPDI are compared to equivalent measurements made with a traversing thermocouple and the two data sets show excellent agreement. This instrument maintains the compact, robust design of Linnik's point diffraction interferometer and adds to it phase stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wavefronts with very high data density and with automated data reduction.     

阻尼耗能减振框架结构地震作用振动方程求解及地震反应分析Calculation of vibration equation and analysis of seismic response for damping energy dissipation frame structure

研究了设置耗能阻尼器框架的地震作用振动方程求解及该结构的地震反应。框架结构设置耗能阻尼器后,振动方程的阻尼矩阵不再对振型具有正交性,本文对该振动方程给出了状态方程直接积分法,并与传统强制解耦法进行了比较分析,结果表明强制解耦法对结构第一阶振动反应求解偏差较小,而对于高阶振动反应差别较大,并且强制解耦法高估了阻尼器的减震效果。继而采用状态方程直接积分法对设置有粘滞阻尼器的框架结构进行了地震反应分析,探讨了阻尼器位置对框架结构地震反应的影响,结果表明设置有阻尼器的楼层减振效果明显,未设置阻尼器的楼层减振效果差别较大,甚至有可能出现楼层层间侧移增大的现象,由此提出耗能阻尼器应在结构中合理设置。     

光纤陀螺惯性测量组合的数字温控系统设计

光纤陀螺惯性测量组合的测量精度会受到环境温度变化的影响。采用温度控制手段能够有效解决这一问题。提出了一种基于分级控制、分段控制和闭环控制思想的温控方案,并在此基础上设计了一种DSP＋FPGA架构的数字温度控制电路,实现了温控电路的整体结构和工作流程,说明了以FuzzyPID算法为核心的温度控制算法原理。试验结果表明,系统具有速度快、精度高等优点,为解决惯性测量组合启动后缩短惯性器件热平衡过程,迅速进入稳定工作状态提供了一种实用方法,也为类似的惯性测量组合温度控制系统提供了有益参考。     

两位置法快速测定近钻头惯性测量模块的温漂模型

近钻头惯性测量模块(Near-bit Inertial Measurement,NIM)用于石油钻井中实时测量导向外套的姿态角,是导向钻进闭环控制中的重要组成部分。它采用三轴加速度计组合测量重力加速度实现姿态角测量。为了提高加速度计在工作温度范围内的测量精度,需对其进行温漂模型标定。针对三轴加速度计组合的传统12位置翻滚温度模型测定方法存在耗时长、操作效率低的局限性,提出一种新的加速度计三轴组合温度模型标定方法——两位置法,并通过实验验证了温度补偿的效果。在10℃~150℃的温度范围内,补偿后加速度的测量精度达5×10~(-4)g,完全满足NIM测量姿态角的要求。     

Simultaneous measurements of temperature and its dissipation using pairs of parallel cold wires

 The link between fluctuations of a passive scalar and its dissipation is an important problem for various aspects of turbulent flow modelling both with and without chemical reaction. This paper first reports experimental methods for simultaneous measurements of the three derivatives involved in temperature dissipation using cold wire probes in a boundary layer over a weakly heated flat plate. Particular attention is paid to the determination of the optimal length and spacing between sensors, including a four-wire probe of fixed dimensions, for such gradient measurements. Corrections to be applied to account for the effect of the fixed geometry are analyzed. Results about joint statistics, including conditional temperature pdfs, between the scalar and its dissipation are then reported and compared to previous results which mainly concerned conditional dissipation rates. Received: 15 October 1996 / Accepted: 13 January 1997