A new model of fluid flow to determine pressure balance characteristics

Some projects such as the EUROMET project 463 have underlined the lack of agreement between experimental measurements and calculations by the finite element method (FEM), used to determine the piston fall rate of a high-pressure balance used in primary standards. This is significant because the piston fall rate is an essential parameter to characterize experimentally the mean gap between the piston and the cylinder and to determine the effective area (A p) at each pressure (p) point. By improving the method used to estimate the piston fall rate it is possible to improve the determination of the gap, the effective area and consequently the pressure distortion coefficient. One possible cause of the lack of agreement between the calculated and measured piston fall rates could be inappropriate modelling of the fluid flow. In fact, the former quasi-1D Stokes model assimilates the gap between the piston and the cylinder as formed by two parallel walls, which is an approximation. In addition, the velocity of the piston wall was neglected. In order to evaluate the influence of this model, the equations of the fluid flow are modified and are presented in this paper. Equations that were defined in a parallel-plane model are defined in an annular gap model. In addition to this, corrections due to the velocity of the piston wall are inserted. This research work is applied on a Desgranges et Huot DH 7594 piston-cylinder unit of PTB with a pressure up to 1 GPa, in the continuity of the EUROMET project 463 in order to quantify the influence of each correction that has been inserted in the new equations. This is carried out using the FEM. This analysis will allow us to evaluate the improvement of our knowledge of the behaviour of piston gauges and consequently to better evaluate the uncertainties due to the models.Laboratoire National d'Essais-LN

Experimental study of blade thickness effects on the global and local performances of a Controlled Vortex Designed axial-flow fan

The purpose of this work is to study the effects of blade thickness on the performances of an axial-flow fan. Two fans that differ only in the thickness of their blades were studied. The first fan was designed to be part of the cooling system of an automotive vehicle power unit and has very thin blades. The second fan has much thicker blades compatible with the rotomoulding conception process. The global performances of the fans were measured in a test bench designed according to the ISO-5801 standard. The curve of aerodynamics characteristics (pressure head versus ow-rate) is slightly steeper for the fan with thick blades, and the nominal point is shifted towards lower flow-rates. The efficiency of the thick blades fan is lower than the efficiency of the fan with thin blades but remains high on a wider flow-rate range. The mean velocity field downstream of the rotors are very similar at nominal points with less centrifugation for the thick blades fan. The thick blades fan moreover maintains an axial exit-flow on a wider range of flow-rates. The main dierences concern local properties of the flow: Phase-averaged velocities and wall pressure fluctuations strongly differ at the nominal flow-rates. The total level of fluctuations is lower for the thick blades fan that for the thin blades fan and the spectral decomposition of the wall fluctuations and velocity signals reveal more harmonics for the thick blades fan, with less correlation between the different signals. For this kind of turbomachinery, the use of thick blades could lead to a good compromise between aerodynamic and acoustic performances, on a wider operating range

Experimental study of blade rigidity effects on the global and the local performances of a thick blades axial-flow fan

An experimental investigation on the aerodynamic performances of thick blades axial-flow fans was carried out in this study. Two fans are considered, the first one is rotomoulded (in plastic) and the second one is milled (in aluminium). Both have exactly the same shape, excepting that the rotomoulded fan has hollow blades. They were designed from an existing fan (manufactured by plastic injection process) used in the cooling system of an automotive vehicle power unit. As far as shape is concerned, the only difference between the two first fans and the traditional injected fan is the blade thickness, whereas as far as rigidity is concerned, the only difference between the rotomoulded and the milled fans is the ability of the rotomoulded fan to be deformed easier than the milled fan. The aim of this study is to determine on the one hand the influence of the blade thickness and on the other hand the way the deformation of the hollow blades may affect the global and the local performances. The global performances of the fans were measured in a test bench designed according to the ISO 5801 standards. The curve of the aerodynamics characteristics (pressure head versus flow rate) and of the global efficiency are slightly lower for the rotomoulded fan. The wall pressure fluctuations were also investigated for three flow rates: one corresponding to the maximum efficiencies of both fans and two others corresponding to an under-flow and an over-flow rate. The power spectral density (PSD) levels, estimated by the Welch method, are between six and nine times higher for the rotomoulded fan at nominal flow rate. At partial flow rate, however, the PSD levels are close for both fans

Numerical investigation of the real and ideal gap profiles in the calculation of the pressure distortion coefficient and piston fall rate of an LNE 200 MPa pressure balance

This paper aims to investigate, by means of numerical simulation, the effect of gap profiles on the calculation of the pressure distortion coefficient (λ) and the piston fall rate (vf) of two piston-cylinder units used in a Laboratoire National de Métrologie et d'Essais (LNE) 200 MPa pressure balance. The ideal mean gap width between the piston and the cylinder was obtained after measuring the piston fall rate at a low pressure, while the piston radius was obtained from the cross-float experiments at a low pressure. The real gap width was obtained from dimensional measurements by measuring the diameter and straightness of the piston and the cylinder. The piston and cylinder radial distortions were calculated using the finite element method. The pressure distribution in the gap was calculated on the basis of the Navier-Stokes equation for Newtonian viscous flow. The results such as pressure distributions, radial distortions, the pressure distortion coefficient and the piston fall rate were presented for the free-deformation operating mode of the assemblies. The calculation resulted in ideal and real gap profiles indicating that the average pressure distortion coefficient was in good agreement within 0.017 × 10-6 MPa-1 and the calculations of piston fall rate depended on the gap profile especially at the inlet and outlet zones of the engagement length.Laboratoire National de Métrologie et d'Essai

Properties of estimators of parameters in logistic regression models

Properties of various types of estimators of the regression coefficients in linear logistic regression models are considered. The estimators include those based on maximum likelihood, minimum chi-square and weighted least squares. Theoretical approximations to the biases of the estimators are developed. The results of a large scale simulation investigation evaluating the moment properties of the estimators are presented for the case of a logistic model with a single explanatory variable