Considerations for ISO 9300: The Effects of Roughness and Form on the Discharge Coefficient of Toroidal-Throat Sonic Nozzles

Author(s):  
Jeff Gibson ◽  
David Stewart ◽  
Neil Barton

The effect of roughness and form was investigated for toroidal-throat sonic nozzles, using both experimental and computational techniques. Eight, 10 mm diameter nozzles were specially made to investigate the effects of deviating from ISO 9300; these nozzles were measured for diameter, axial profile, roughness and roundness in order to assess the effects on discharge coefficient, Cd. Flow calibrations have revealed that roughness effects are negligible for Ra/d ≤ 4.5×10−5 (three times the limit of ISO 9300) in the turbulent regime (Re > 106), in keeping with previously published data taken in the laminar regime. Test data from three unpolished nozzles, of average Ra of ∼ 0.3 μm, also demonstrated that excellent reproducibility in Cd vs. Re (≤ 0.04%) might be achieved without the need for polishing. Data is also presented from recent primary gravimetric calibrations of NEL’s 16 reference nozzles. The data supports the proposed equation for normally machined nozzles over the Reynolds number range tested (0.17×106 < Re < 17×106), with the standard deviation from the ISO/CD 9300 curve being 0.27% (k = 2; 95% confidence) over the range 0.35×106 < Re < 17×106, provided d ≥ 3.8 mm.

1978 ◽  
Vol 100 (3) ◽  
pp. 299-307 ◽  
Author(s):  
S. H. Alvi ◽  
K. Sridharan ◽  
N. S. Lakshmana Rao

Loss characteristics of sharp-edged orifices, quadrant-edged orifices for varying edge radii, and nozzles are studied for Reynolds numbers less than 10,000 for β ratios from 0.2 to 0.8. The results may be reliably extrapolated to higher Reynolds numbers. Presentation of losses as a percentage of meter pressure differential shows that the flow can be identified into fully laminar regime, critical Reynolds number regime, relaminarization regime, and turbulent flow regime. An integrated picture of variation of parameters such as discharge coefficient, loss coefficient, settling length, pressure recovery length, and center line velocity confirms this classification.


Author(s):  
Noriyuki Furuichi ◽  
Kar-Hooi Cheong ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
...  

Discharge coefficients for three flow nozzles based on ASME PTC 6 are measured under many flow conditions at AIST, NMIJ and PTB. The uncertainty of the measurements is from 0.04% to 0.1% and the Reynolds number range is from 1.3×105 to 1.4×107. The discharge coefficients obtained by these experiments is not exactly consistent to one given by PTC 6 for all examined Reynolds number range. The discharge coefficient is influenced by the size of tap diameter even if at the lower Reynolds number region. Experimental results for the tap of 5 mm and 6 mm diameter do not satisfy the requirements based on the validation procedures and the criteria given by PTC 6. The limit of the size of tap diameter determined in PTC 6 is inconsistent with the validation check procedures of the calibration result. An enhanced methodology including the term of the tap diameter is recommended. Otherwise, it is recommended that the calibration test should be performed at as high Reynolds number as possible and the size of tap diameter is desirable to be as small as possible to obtain the discharge coefficient with high accuracy.


Author(s):  
Noriyuki Furuichi ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
Kazuo Shibuya

The discharge coefficients of the throat tap flow nozzle based on ASME PTC 6 are measured in wide Reynolds number range from Red=5.8×104 to Red=1.4×107. The nominal discharge coefficient (the discharge coefficient without tap) is determined from the discharge coefficients measured for different tap diameters. The tap effects are correctly obtained by subtracting the nominal discharge coefficient from the discharge coefficient measured. Finally, by combing the nominal discharge coefficient and the tap effect determined in three flow regions, that is, laminar, transitional and turbulent flow region, the new equations of the discharge coefficient are proposed in three flow regions.


1992 ◽  
Vol 114 (4) ◽  
pp. 521-526 ◽  
Author(s):  
D. G. Shombert

Fluid dynamic properties of Dacron vascular grafts were studied under controlled steady-flow conditions over a Reynolds number range of 800 to 4500. Knitted and woven grafts having nominal diameters of 6 mm and 10 mm were studied. Thermal anemometry was used to measure centerline velocity at the downstream end of the graft; pressure drop across the graft was also measured. Transition from laminar flow to turbulent flow was observed, and turbulence intensity and turbulent stresses (Reynolds normal stresses) were measured in the turbulent regime. Knitted grafts were found to have greater pressure drop than the woven grafts, and one sample was found to have a critical Reynolds number (Rc) of less than one-half the value of Rc for a smooth-walled tube.


Author(s):  
Ioannis Ieronymidis ◽  
David R. H. Gillespie ◽  
Peter T. Ireland ◽  
Robert Kingston

This paper presents detailed pressure measurements and discharge coefficient data for a long, low aspect ratio manifold; part of a novel blade cooling scheme. The cooling geometry, in which a series of racetrack passages are connected to a central plenum, provides high heat transfer coefficients in regions of the blade in good thermal contact with the outer blade surface. The Reynolds number changes along its length because of the ejection of fluid through a series of 19 transfer holes in a staggered arrangement, which are used to connect ceramic cores during the casting process. For rotation number RN = 0 the velocity down each hole remains almost constant. A correlation between hole discharge coefficient and Velocity Head Ratio is also presented. Pressure loss coefficients in the passage and through the holes are also discussed. A High Pressure (HP) rig was tested to investigate compressibility effects and expand the inlet Reynolds number range. A CFD model was validated against the experimental data, and then used to investigate the effects of rotation on the hole discharge coefficients. Results are presented for an inlet Reynolds number of 43477. At an engine representative rotation number of 0.08 corresponding buoyancy number of 0.17 there was little effect of rotation. However, at high rotational speeds secondary flows in the cooling passage and the exit plenum greatly reduce the hole discharge coefficient by increasing the local cross flow at the hole entrances and capping the hole exits in a manner similar to that seen in leading edge film-cooling geometries.


1968 ◽  
Vol 183 (1) ◽  
pp. 591-602 ◽  
Author(s):  
G. S. Vasy ◽  
L. J. Kastner ◽  
J. C. McVeigh

The characteristics of the orifice meter are well known and have been thoroughly explored by a number of investigators over a considerable range of Reynolds numbers, yet the low Reynolds number range—i.e. below ( Re D = 4000, where ( Re) D is the upstream pipe Reynolds number, has received comparatively little attention, although recent work by two of the authors has supplemented the available data substantially. This work concentrates on very accurate measurements with small diameter orifices, but where less exacting standards of metering accuracy, e.g. ±2-2 1/2 per cent, can be allowed, a closer analysis reveals that there is a choice of orifice profiles which can be used successfully. Consideration is also given to the recommendations of the various standardizing bodies for the allowable tolerances in the diameter of the pipeline in which the orifice meter is situated. These tolerances are often unnecessarily severe and a ‘tolerance number’ depending upon discharge coefficient and the area ratio of orifice to pipe is suggested.


2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Noriyuki Furuichi ◽  
Kar-Hooi Cheong ◽  
Yoshiya Terao ◽  
Shinichi Nakao ◽  
Keiji Fujita ◽  
...  

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.


Author(s):  
Margaret Msongi Mkhosi ◽  
Richard Denning ◽  
Shoichiro Nakamura

The pebble bed modular reactor (PBMR) is a high temperature gas-cooled reactor which uses helium gas as a coolant. The PBMR design relies on the excellent heat transfer properties of graphite and a fuel design that is inherently resistant to the release of the radioactive material up to high temperatures. The safety characteristics of the PBMR concept are excellent. However, a very strong safety case will have to be made if a new generation of reactors is to be successfully introduced to a concerned public. Until recent developments in computational fluid dynamics methods, computer speed, and data storage, the coupled thermal-hydraulic, chemical, and mass transport phenomena could not be treated in an integrated analysis. This paper addresses one aspect of the interplay between the details of fluid flow and aerosol transport within the complex geometry of the pebble bed core. A very large quantity of graphite dust is produced by the interaction among the pebbles. The potential for the deposition of radionuclides on the surface of dust particles and their subsequent transport as aerosols is substantial. This effort focuses on the inertial deposition of these aerosols within the pebble bed. Inertial deposition in the low Reynolds number regime of laminar flow in pebble beds has been explored previously, but with less powerful computational techniques. Some experimental data are also available in this regime. No analyses or experimental data are available in the high Reynolds number turbulent regime in which the PBMR operates. This paper describes results of analyses of inertial deposition obtained with the FLUENT computational fluid dynamics code. The objective of the analysis is to obtain an expression for deposition within an asymptotic unit cell, removed from the boundary conditions at the entrance to the array. The results of analyses performed at different velocities and fluid densities in the turbulent regime were correlated against a modified Stokes number. The deposition correlation is well represented by the integral form of the normal distribution. Deposition for the time-averaged flow was found to be insensitive to the flow model. In the laminar regime, FLUENT results were found to be in agreement with earlier published results and experimental data. The stochastic behavior of eddies was also simulated within FLUENT using the k–ε model. Eddy-enhanced deposition results in greater deposition at all aerosol sizes in comparison with the time-averaged results, with significant deposition of aerosols predicted for small aerosol sizes. However, it is likely that these results are quite sensitive to the modeling of turbulence and they must be considered preliminary.


1960 ◽  
Vol 82 (3) ◽  
pp. 729-733 ◽  
Author(s):  
M. Bogema ◽  
P. L. Monkmeyer

Tests have been conducted to determine the usefulness of the quadrant edge orifice as a fluid-metering device for low Reynolds number flow. As a result of numerous laboratory tests to determine the behavior of the discharge coefficient with changing Reynolds number, the following are discussed: The range of constant discharge coefficient, reproducibility of orifice plates, diameter ratio effects, upstream roughness effects, reinstallation effects, and effects of pressure tap location.


1984 ◽  
Vol 106 (2) ◽  
pp. 489-498 ◽  
Author(s):  
H. Simon ◽  
A. Bu¨lska¨mper

This paper summarizes the results of systematic investigations into the Reynolds number effects. It is based on performance map measurements carried out on a compressor test rig which was constructed primarily for this purpose. The measurements were performed for stages with different flow coefficients (0.004 ≦ φ1 ≦ 0.05), with different gases (air, nitrogen, helium, freon) and in the inlet pressure range 0.2 bar ≦ p1 ≦ 40 bar. By analogy with the turbulent flow in technically rough pipes, semi-empirical correlations are derived concerning the effects of the Reynolds number and the relative surface roughness on the characteristic performance parameters (efficiency, flow coefficient, head coefficient, work coefficient). For the detailed design calculation of individual stages, provision is made for the different effects on the hydraulic flow losses and the disk friction losses. Simplified correlations are given for the conversion of characteristics measured during thermodynamic performance tests. The correlations are applied to various single and multistage compressors, and the results compared with measured performance characteristics in the Reynolds number range 6 × 103 ≦ Ret ≦ 1.1 × 107. The good correspondence obtained forms the basis for recommending the application of these simplified relationships for the improvement of centrifugal compressor performance test codes (e.g. ASME PTC-10 and ISO TC 118).


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