: The lack of a standard method for estimating the errors associated with gas turbine performance data has made it impossible to compare measurement systems between facilities, and there has been confusion over the interpretation of error analysis. Therefore, a standard uncertainty methodology is proposed in this Handbook. The mathematical uncertainty model presented is based on two components of measurement error: the fixed (bias) error and the random (precision) error. The result of applying the model is an estimate of the error in the measured performance parameter. The uncertainty estimate is the interval about the measurement which is expected to encompass the true value. The propagation of error from basic measurements through calculated performance parameters is presented. Traceability of measurement back to the National Bureau of Standards and associated error sources is reviewed.

Handbook, Uncertainty in Gas Turbine Measurements

A choked nozzle with an appropriate wall contour has adischarge coefficient, CD, so close to unity that a theoretical calculation of (I—CD) would allow the nozzle to be used as an absolute meter for air flow. The high discharge coefficient results basically from the fact that ∂(ρv)∂p=0 at M=1.Simplified calculations yield formulae for the boundary layer displacement thickness and for the flow reduction resulting from the variation in static pressure across the throat. The optimum profile for the wall at the throat of an absolute meter is suggested to be a circular arc of radius of curvature equal to about twice the throat diameter. For such a meter the theoretical discharge coefficient is found to be within ¼ per cent of 0·995 over a wide range of Reynolds numbers.The uncertainty in the discharge coefficient for a steady flow at Reynolds numbers of 106 and over appears to be less than ±0·15 per cent, both when the boundary layer is known to be entirely turbulent and when it is known to be entirely laminar. When the state of the boundary layer is not known the corresponding figure appears to be ±0·25 per cent. Experimental information might therefore be helpful on transition—under the appropriate conditions of flow unsteadiness and rig vibration. Available experimental results with known boundary layers tend to confirm the theoretical discharge coefficients down to a Reynolds number of 0·4x106.A pressure ratio of about 1·1/1 or less would probably be sufficient to establish fully supersonic flow if the nozzle were followed by a suitable diffuser.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0001924000060905

The Calculation of the Discharge Coefficient of Profiled Choked Nozzles and the Optimum Profile for Absolute Air Flow Measurement

A portable mass spectrometer system is described. The system includes a mass spectrometer device incorporated within an evacuated chamber. The chamber includes a permeable membrane located between the mass spectrometer device and an entrance port to the chamber. Located between the membrane and the entrance port is a valve. The valve is provided in an normally closed state and has an open state, such that, in use, the adoption of the open state allows the flow of the sample into the chamber through the membrane and into contact with the spectrometer device.

Mass spectrometer system

Data are presented which tend to verify the theoretically predicted discharge coefficients for circular-arc venturi flow meters operating in the critical flow regime (sonic) at throat Reynolds numbers above 1.5 105. Extensive analysis of the data is presented using methods that are presently in process of international standardization. The data lend to verify the theoretically predicted decrease of 0.25 percent in the discharge coefficient during transition from laminar to a turbulent boundary layer. The transi­ tion occurred at a throat Reynolds number of 2.2 106, but the transition point probably changes as a function of several influences. The mean line of the measured data fell between the theoretical values for laminar and turbulent boundary layers. The scatter in 55 data points was ±0.212 percent (95 percent confidence level) from the mean line equation for Reynolds numbers from 4-1 10i to 34 lCfi, which included the effects of several variables. Data were obtained from 17 Venturis with throat sizes from 0.15 to 1.37 in. with Beta ratios ranging from 0.014- to 0.25. Four different test gases and three primary flow measurement facilities were used. Additional data are presented extending down to throat Reynolds numbers of 1.8 104 and throat diameters of 0.05 in. which indicate special problems in these regions. The state of the art for measuring venturi throat diameters presented a major limitation to the correlation effort. Cali­ bration is necessary in many cases depending on various parameters and requirements. Additional study is needed to determine the optimum geometrical parameters at low Reynolds numbers, the optimum approach configuration for Beta ratios above 0.1, the effect of surface roughness on the discharge coefficient, and the effect of various operational variables such as flow pulsation and approach velocity profile. Also, a continuous effort should be made to improve the critical flow functions for real gases as better gas property data become available, and to extend these calculations to broader ranges of pressures and temperatures, and to other gases.

Discharge Coefficient Correlations fir Circular-Arc Venturi Flowmeters it Critical (Soiic) Flow

Interference effects of three sonic nozzles of different throat diameters in the same meter tube

Abstract : A venturi contour designed specifically for use at critical flow conditions is described, and a theoretical method is presented for determining the discharge coefficient of this venturi. An experimental investigation was conducted to determine the discharge coefficient of such a venturi, and the results are compared with the theoretical values. This investigation covered a range of Reynolds number from 0.4 x 10 to the 6th power to 5.4 x 10 to the 6th power based on venturi throat diameter. The venturi used had a throat diameter of 5.6436 in. and an airflow capacity of 8.6 lb/sec at an inlet total pressure of one atmosphere and an inlet total temperature of 519 R. The values of discharge coefficient ranged from 0.992 to 0.994, and the theoretically and experimentally determined coefficients agreed within + or - 0.06% over the range of conditions investigated.

Robert E. Smith

Papers

A Theoretical Method of Determining Discharge Coefficients for Venturis Operating at Critical Flow Conditions