Transient temperature measurements in an ideal gas by laser-induced Rayleigh light scattering

Horton, J. F.; Peterson, J. E.

doi:10.1063/1.1149896

Cited by 3 publications

(1 citation statement)

References 11 publications

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“…5,6 ͑2͒ A standard way of calculating mean and variance of a measurand from means and variances of the primarily measured quantities is the method of error propagation found in most textbooks on statistics and probability, 7-10 recommended by international standards, 1 and frequently applied in all fields of science and engineering. [11][12][13][14][15][16] The method provides a convenient tool whenever the first two ͑joint͒ moments of the primarily measured quantities are known, while their joint PDF is unknown, a case frequently encountered in practice. Evolving from a ͑usually first-order͒ Taylor approximation of the measurement function, the method can only yield approximate results.…”

Section: Introductionmentioning

confidence: 99%

Accuracy of error propagation exemplified with ratios of random variables

Winzer

2000

Review of Scientific Instruments

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A quantum central limit theorem for sums of independent identically distributed random variables On the statistical errors in the estimate of acoustical energy density by using two microphones in a one dimensional fieldThe method of error propagation provides a convenient tool for calculating mean and variance of a measurand from means and variances of primarily measured quantities. However, being based on a ͑usually first-order͒ Taylor approximation of the measurement function, it only yields approximate results with unknown accuracy. We develop a method for estimating the accuracy of ͑Nth-order͒ error propagation for an arbitrary number of correlated random quantities, and apply our findings to the ratio of two random variables ͑RVs͒. A comparison with some analytically solved expressions for certain probability density functions ͑PDFs͒ as well as with some computer simulations reveals the excellent quality of our estimates as long as the involved PDFs are not significantly skew. For the ratio of two RVs it turns out that conventional, first-order error propagation is safely applicable ͑with about 1% accuracy͒ as long as the denominator's mean is larger than about 12 times its standard deviation. Using second-order error propagation, the approximation for the ratio's mean can be refined, yielding 1% accuracy if the denominator's mean is larger than about four times its standard deviation.

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Section: Introductionmentioning

confidence: 99%

Accuracy of error propagation exemplified with ratios of random variables

Winzer

2000

Review of Scientific Instruments

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Flow Visualizations and Transient Temperature Measurements in an Axisymmetric Impinging Jet Rapid Thermal Chemical Vapor Deposition Reactor

Mathews

Peterson

2002

Journal of Heat Transfer

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Carrier gas flow in a rapid thermal chemical vapor deposition (RTCVD) reactor was studied using flow visualization and laser induced Rayleigh light scattering (RLS). The flow field consists of a downward axisymmetric jet of carrier gas impinging on a wafer which undergoes transient heating. Flow visualization results showed three stable flow regimes as the surface rose from ambient to high temperature: momentum dominated, buoyancy dominated, and a second momentum dominated regime at high temperature; each separated by unstable, chaotic flows. RLS temperature measurements provided transient gas temperature histories, documenting flow visualization results. Regions of momentum dominated, buoyancy dominated, and unstable flows were defined as a function of Grashof number, Reynolds number, pressure, and wafer temperature.

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Rayleigh Light Scattering Measurements of Transient Gas Temperature in a Rapid Chemical Vapor Deposition Reactor

Horton

Peterson

1999

Journal of Heat Transfer

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A laser-induced Rayleigh light scattering (RLS) system was used to measure transient gas temperatures in a simulated rapid chemical vapor deposition (RCVD) reactor. The test section geometry was an axisymmetric jet of carrier gas directed down, impinging on a heated wafer surface. RLS was used to measure instantaneous gas temperature at several locations above the wafer as it was heated from room temperature to 475 K. Gas flow rate and wafer temperature correspond to jet Reynolds number Rei=60, wafer maximum Grashof number GrH=4.4×106, and maximum mixed convection parameter GrH/Rei2=1200; all conditions typical of impinging jet reactors common in the numerical literature. Uncertainty of RLS transient temperature from a propagated error analysis was ±2–4 K. Peak gas temperature fluctuations were large (in the order of 25 to 75 °C). Both flow visualization and RLS measurements showed that the flow field was momentum dominated prior to heating initiation, but became unstable by GrH/Rei2=5. It then consisted of buoyancy-induced plumes and recirculations. Up to the peak wafer temperature, the flow field continued to be highly three-dimensional, unsteady, and dominated by buoyancy. RLS measurements are shown to provide information on carrier gas instantaneous temperature and flow field stability, both critical issues in RCVD processing. [S0022-1481(00)02401-4]

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Transient temperature measurements in an ideal gas by laser-induced Rayleigh light scattering

Cited by 3 publications

References 11 publications

Accuracy of error propagation exemplified with ratios of random variables

Accuracy of error propagation exemplified with ratios of random variables

Flow Visualizations and Transient Temperature Measurements in an Axisymmetric Impinging Jet Rapid Thermal Chemical Vapor Deposition Reactor

Rayleigh Light Scattering Measurements of Transient Gas Temperature in a Rapid Chemical Vapor Deposition Reactor

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