Flow Nozzles With Zero Beta Ratio

1964 ◽  
Vol 86 (3) ◽  
pp. 538-540 ◽  
Author(s):  
Hans J. Leutheusser
Keyword(s):  
Experimental Data ◽  
Satisfactory Agreement ◽  
Discharge Coefficient ◽  
Theoretical Equation ◽  
Analytical Expression ◽  
Discharge Coefficients ◽  
Analytical Work

An analytical expression for the discharge coefficient of ASME long-radius flow nozzles with zero beta ratio is presented. The latter condition corresponds to the installation of a metering nozzle at the outlet from a very large supply reservoir. The prediction of the theoretical equation is compared with experimentally determined discharge coefficients for nozzles of this type. Reference is made to analytical work in this field by other investigators and conclusions are drawn as to the degree of analytical sophistication required in order to obtain satisfactory agreement between analytical and experimental data.

Discharge coefficients for ogee weirs including the effects of a sloping upstream face

2020 ◽  
Vol 20 (4) ◽  
pp. 1493-1508 ◽  
Author(s):  
Farzin Salmasi ◽  
John Abraham
Keyword(s):  
Gene Expression ◽  
Experimental Data ◽  
Regression Analysis ◽  
Discharge Coefficient ◽  
Gene Expression Programming ◽  
Linear Interpolation ◽  
Performance Criteria ◽  
Upstream Face ◽  
Discharge Coefficients ◽  
Regression Techniques

Abstract Discharge coefficients (C0) for ogee weirs are essential factors for predicting the discharge-head relationship. The present study investigates three influences on the C0: effect of approach depth, weir upstream face slope, and the actual head, which may differ from the design head. This study uses experimental data with multiple non-linear regression techniques and Gene Expression Programming (GEP) models that are applied to introduce practical equations that can be used for design. Results show that the GEP method is superior to the regression analysis for predicting the discharge coefficient. Performance criteria for GEP are R2 = 0.995, RMSE = 0.021 and MAE = 0.015. Design examples are presented that show that the proposed GEP equation correlates well with the data and eliminates linear interpolation using existing graphs.

New Discharge Coefficient of Throat Tap Nozzle Based on ASME Performance Test Code 6 for Reynolds Number From 2.4 × 105 to 1.4 × 107

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Noriyuki Furuichi ◽  
Kar-Hooi Cheong ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
...  
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Discharge Coefficient ◽  
Performance Test ◽  
Reynolds Numbers ◽  
Experimental Results ◽  
National Metrology Institute ◽  
Reference Curve ◽  
Number Range ◽  
Discharge Coefficients

The throat tap nozzle of the American Society of Mechanical Engineers performance test code (ASME PTC) 6 is widely used in engineering fields, and its discharge coefficient is normally estimated by an extrapolation in Reynolds number range higher than the order of 107. The purpose of this paper is to propose a new relation between the discharge coefficient of the throat tap nozzle and Reynolds number by a detailed analysis of the experimental data and the theoretical models, which can be applied to Reynolds numbers up to 1.5 × 107. The discharge coefficients are measured for several tap diameters in Reynolds numbers ranging from 2.4 × 105 to 1.4 × 107 using the high Reynolds number calibration rig of the National Metrology Institute of Japan (NMIJ). Experimental results show that the discharge coefficients depend on the tap diameter and the deviation between the experimental results and the reference curve of PTC 6 is 0.75% at maximum. New equations to estimate the discharge coefficient are developed based on the experimental results and the theoretical equations including the tap effects. The developed equations estimate the discharge coefficient of the present experimental data within 0.21%, and they are expected to estimate more accurately the discharge coefficient of the throat tap nozzle of PTC 6 than the reference curve of PTC 6.

Discharge Coefficients for Circular Side Outlets

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Laszlo Czetany ◽  
Peter Lang
Keyword(s):  
Experimental Data ◽  
Genetic Algorithm ◽  
Least Squares ◽  
Discharge Coefficient ◽  
Nonlinear Least Squares ◽  
Fluid Distribution ◽  
Vast Amount ◽  
Discharge Coefficients ◽  
New Equation

Fluid distributors are widely used in various industrial and ventilation applications. For the appropriate design of such distributors, the discharge coefficient has to be known to predict the energy and fluid distribution performance. Despite the vast amount of experimental data published, no generally applicable equations are available. Therefore, a new equation is presented for sharp-edged circular side outlets, which can be widely used for calculating the discharge coefficient. The equation is developed by regression with nonlinear least squares combined with genetic algorithm on experimental data available in the literature. The equation covers a wider range than the others presented in the literature.

A Versatile Analytical Expression for the Inverse Abel Transform Applied to Experimental Data with Noise

2008 ◽  
Vol 62 (6) ◽  
pp. 701-707 ◽  
Author(s):  
Shuiliang Ma ◽  
Gming Hon Gao ◽  
Guangjun Zhang ◽  
Lin Wu
Keyword(s):  
Experimental Data ◽  
Abel Transform ◽  
Analytical Expression

SEMIEMPIRICAL SCF–LCAO–MO TREATMENT OF THIOPHENE, FURAN, AND PYRROLE

1965 ◽  
Vol 43 (5) ◽  
pp. 1569-1576 ◽  
Author(s):  
N. Solony ◽  
F. W. Birss ◽  
John B. Greenshields
Keyword(s):  
Experimental Data ◽  
Satisfactory Agreement ◽  
Electronic Structures ◽  
Spectroscopic Data ◽  
Variable Parameter ◽  
Coulomb Repulsion ◽  
Resonance Integral ◽  
Electronic Transitions ◽  
The Core ◽  
Lcao Mo

The semiempirical SCF–LCAO–MO method of Pariser–Parr–Pople is utilized in the study of the π-electronic structures of thiophene, furan, and pyrrole. The core Hamiltonian expansion contains a Uz++ term, the potential due to the ionized hetero-atom contributing two electrons to the π-system. The γzz, one-center coulomb repulsion integral for the hetero-atom is evaluated from the experimental spectroscopic data only. With the resonance integral βczc as the only variable parameter, the calculated π*–π electronic transitions are in a satisfactory agreement with the experimental data.

Statistical Design of Fatigue Experiments

1952 ◽  
Vol 19 (1) ◽  
pp. 109-113
Author(s):  
Waloddi Weibull
Keyword(s):  
Experimental Data ◽  
Statistical Design ◽  
Testing Time ◽  
Optimum Distribution ◽  
Analytical Expression ◽  
Optimum Choice ◽  
Stress Levels ◽  
Parameter Values ◽  
Applied Stresses

Abstract An analytical expression connecting fatigue lives with applied stresses, and methods for computing the values of its parameters from experimental data are given. Formulas for estimating the uncertainty of computed parameter values, caused by scatter of loads and fatigue lives, for optimum distribution of specimens, and for optimum choice of stress levels, are deduced. Testing time and costs may be reduced by more than 40 per cent by using the formulas.

Unsteady Numerical Simulation of the Flow in a Direct Transfer Pre-Swirl System

2008 ◽  
Author(s):  
Fabio Ciampoli ◽  
Nicholas J. Hills ◽  
John W. Chew ◽  
Timothy Scanlon
Keyword(s):  
Discharge Coefficient ◽  
Direct Transfer ◽  
Elementary Model ◽  
Discharge Coefficients ◽  
Significant Difference ◽  
Aero Engine ◽  
Velocity Coefficient ◽  
Unsteady Numerical Simulation ◽  
Unsteady Effects ◽  
Cooling Air

Results of fully unsteady numerical simulations of the flow in a direct transfer pre-swirl system are presented and compared with previously published experimental data from an aero-engine representative rig. The conditions considered include those where strong unsteady effects were observed experimentally. Two different rig builds are considered, with the main difference being in the design of the pre-swirl nozzles. The agreement between calculation and experiment is very good in terms of nozzle and receiver hole discharge coefficients and in identifying significant unsteady effects at certain conditions. Predicted cooling air delivery temperatures are lower than those measured. This may be due to heat transfer and other effects in the rig which have not been modelled. Present unsteady results also show agreement, where appropriate, with earlier steady CFD and an elementary model. Both calculations and measurements show similar performance in terms of delivery temperature for the two different builds studied, despite significant difference in pre-swirl nozzle discharge coefficients for the two builds. The calculations indicate that this is associated with the nozzle velocity coefficient being considerably higher than the discharge coefficient in one case.

Gas transport in a model derived from Hansen-Ampaya anatomical data of the human lung

1976 ◽  
Vol 41 (1) ◽  
pp. 115-119 ◽  
Author(s):  
M. Paiva ◽  
L. M. Lacquet ◽  
L. P. van der Linden
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Satisfactory Agreement ◽  
Dead Space ◽  
Empirical Formula ◽  
Molecular Diffusion ◽  
Human Lung ◽  
Gas Transport ◽  
Gas Mixing ◽  
Anatomical Data

The anatomical data of the human lung published by Hansen and Ampaya are used in a model of gas transport in the lung. The Bohr dead space is calculated from solutions of a transport equation where diffusivity is given by an empirical formula obtained by Sherer et al. A satisfactory agreement is found with experimental data obtained from simultaneous washouts of H2 and SF6 for respiratory frequencies ranging between 15 and 60 min-1 and tidal volumes between 200 and 1,800 ml. The results support the idea that molecular diffusion is the main but not the only physical phenomenom which intervenes in gas mixing during breathing.

A Method for Correlating the Influence of External Crossflow on the Discharge Coefficients of Film Cooling Holes

2000 ◽  
Vol 123 (2) ◽  
pp. 258-265 ◽  
Author(s):  
D. A. Rowbury ◽  
M. L. G. Oldfield ◽  
G. D. Lock
Keyword(s):  
Gas Turbine ◽  
Film Cooling ◽  
Discharge Coefficient ◽  
Guide Vane ◽  
Discharge Coefficients ◽  
Nozzle Guide Vane ◽  
Aero Engine ◽  
Nozzle Guide ◽  
Film Cooling Holes ◽  
Asme Paper

An empirical means of predicting the discharge coefficients of film cooling holes in an operating engine has been developed. The method quantifies the influence of the major dimensionless parameters, namely hole geometry, pressure ratio across the hole, coolant Reynolds number, and the freestream Mach number. The method utilizes discharge coefficient data measured on both a first-stage high-pressure nozzle guide vane from a modern aero-engine and a scale (1.4 times) replica of the vane. The vane has over 300 film cooling holes, arranged in 14 rows. Data was collected for both vanes in the absence of external flow. These noncrossflow experiments were conducted in a pressurized vessel in order to cover the wide range of pressure ratios and coolant Reynolds numbers found in the engine. Regrettably, the proprietary nature of the data collected on the engine vane prevents its publication, although its input to the derived correlation is discussed. Experiments were also conducted using the replica vanes in an annular blowdown cascade which models the external flow patterns found in the engine. The coolant system used a heavy foreign gas (SF6 /Ar mixture) at ambient temperatures which allowed the coolant-to-mainstream density ratio and blowing parameters to be matched to engine values. These experiments matched the mainstream Reynolds and Mach numbers and the coolant Mach number to engine values, but the coolant Reynolds number was not engine representative (Rowbury, D. A., Oldfield, M. L. G., and Lock, G. D., 1997, “Engine-Representative Discharge Coefficients Measured in an Annular Nozzle Guide Vane Cascade,” ASME Paper No. 97-GT-99, International Gas Turbine and Aero-Engine Congress & Exhibition, Orlando, Florida, June 1997; Rowbury, D. A., Oldfield, M. L. G., Lock, G. D., and Dancer, S. N., 1998, “Scaling of Film Cooling Discharge Coefficient Measurements to Engine Conditions,” ASME Paper No. 98-GT-79, International Gas Turbine and Aero-Engine Congress & Exhibition, Stockholm, Sweden, June 1998). A correlation for discharge coefficients in the absence of external crossflow has been derived from this data and other published data. An additive loss coefficient method is subsequently applied to the cascade data in order to assess the effect of the external crossflow. The correlation is used successfully to reconstruct the experimental data. It is further validated by successfully predicting data published by other researchers. The work presented is of considerable value to gas turbine design engineers as it provides an improved means of predicting the discharge coefficients of engine film cooling holes.

Influence of Flow Characteristics on the Discharge Coefficient of a Multiperforated Wall

2005 ◽  
Author(s):  
Jean-Louis Champion ◽  
Pasquale Di Martino ◽  
Xavier Coron
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
General Expression ◽  
Discharge Coefficient ◽  
Flow Characteristics ◽  
Coolant Flow ◽  
Asymptotic Value ◽  
Rate Of Increase ◽  
Classical Correlations

The aim of this study is to determine the discharge coefficient of a multiperforated wall sample designed by AVIO, and more precisely to show the influence of each surrounding flow (inside holes, coolant and main flows). Results obtained are compared to correlations from literature. As previously observed, it is found that the discharge coefficient is strongly dependent on the Reynolds number relative to the hole flow (Reh). The influence of the coolant flow has been proved. The comparison with classical correlations shows many differences: i) on the expected asymptotic value ii) on the rate of increase for the lowest values of Reh. This influence is not taken into account by classical correlations deduced from experiments carried out without crossflow. Based on our experiments, we determined a general expression of Cd. Experimental data are fitted with a function of type Cd = A(1−exp(−B.Reh)), where A and B are expressed as functions of the Reynolds number (Re2) of the coolant flow.

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