scholarly journals Experimental Investigations on Leakages in Positive Displacement Machines

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Hitesh H. Patel ◽  
Vikas J. Lakhera
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Pressure Ratio ◽  
Flow Coefficient ◽  
Experimental Investigations ◽  
Mean Deviation ◽  
Leakage Flow ◽  
Positive Displacement ◽  
Flow Through ◽  
The Mean

The clearance gaps in positive displacement machines such as compressors, pumps, expanders, and turbines are critical for their performance and reliability. The leakage flow through these clearances influences the volumetric and adiabatic efficiencies of the machines. The extent of the leakage flow depends on the size and shape of clearance paths and pressure differences across these paths. Usually, the mass flow through the gaps is estimated using the isentropic nozzle equation with the flow coefficients applied to correct for the real flow conditions. However, the flow coefficients applied generally do not take into account the shape and size of these leakage paths. For that reason, a proper understanding of the relationship between flow coefficients and shape parameters is crucial for an accurate prediction of leakage flows. The present study investigates the influence of the various dimensionless parameters such as Reynolds number, Mach number, and pressure ratio on the flow coefficients for circular and rectangular clearance shapes. The flow coefficients are determined by comparing the experimental values obtained in an experimental test rig and the flow rates obtained from the isentropic nozzle equation. It is observed that in the case of circular clearances, the mean deviation of the experimental leakage results (in comparison to the analytical results using isotropic nozzle equations) is +9.1%, which is significantly lower than the mean deviation (+20.5%) in the case of rectangular clearance leakages. The study indicates that the isentropic nozzle equation method is more suitable for predicting the leakages through the circular clearances and needs modifications for consideration of the rectangular clearances. Using regression analysis, empirical correlations are developed to predict the flow coefficient in terms of Reynolds number, Mach number, pressure ratio, aspect ratio, and β ratio, which are found to match within ±6.4 percent of the numerical results for the rectangular clearance and within the range of -3.6 percent to +5.1 percent of the numerical result for the circular clearance. The empirical relationships presented in this study can be extended to evaluate the flow coefficients in a positive displacement machine.

Investigation of the 3D Unsteady Rotor Pressure Field in a HP Turbine Stage

2002 ◽  
Author(s):  
E. Valenti ◽  
J. Halama ◽  
R. De´nos ◽  
T. Arts
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Pressure Field ◽  
Pressure Ratio ◽  
Turbine Stage ◽  
Time Resolved ◽  
Mach Number Distribution ◽  
Rotor Surface ◽  
Exit Mach Number ◽  
Unsteady Pressure Measurements

This paper presents steady and unsteady pressure measurements at three span locations (15, 50 and 85%) on the rotor surface of a transonic turbine stage. The data are compared with the results of a 3D unsteady Euler stage calculation. The overall agreement between the measurements and the prediction is satisfactory. The effects of pressure ratio and Reynolds number are discussed. The rotor time-averaged Mach number distribution is very sensitive to the pressure ratio of the stage since the incidence of the flow changes as well as the rotor exit Mach number. The time-resolved pressure field is dominated by the vane trailing edge shock waves. The incidence and intensity of the shock strongly varies from hub to tip due to the radial equilibrium of the flow at the vane exit. The decrease of the pressure ratio attenuates significantly the amplitude of the fluctuations. An increase of the pressure ratio has less significant effect since the change in the vane exit Mach number is small. The effect of the Reynolds number is weak for both the time-averaged and the time-resolved rotor static pressure at mid-span, while it causes an increase of the pressure amplitudes at the two other spans.

The Impact of Manufacturing Variations on Performance of a Transonic Axial Compressor Rotor

2018 ◽  
Author(s):  
Marcus Lejon ◽  
Niklas Andersson ◽  
Lars Ellbrant ◽  
Hans Mårtensson
Keyword(s):  
Flow Field ◽  
Geometric Mean ◽  
Pressure Ratio ◽  
Axial Compressor ◽  
Mean Deviation ◽  
Design Intent ◽  
Compressor Rotor ◽  
Measuring Machine ◽  
The Mean ◽  
The Impact

In this paper, the impact of manufacturing variations on performance of an axial compressor rotor are evaluated at design rotational speed. The geometric variations from the design intent were obtained from an optical coordinate measuring machine and used to evaluate the impact of manufacturing variations on performance and the flow field in the rotor. The complete blisk is simulated using 3D CFD calculations, allowing for a detailed analysis of the impact of geometric variations on the flow. It is shown that the mean shift of the geometry from the design intent is responsible for the majority of the change in performance in terms of mass flow and total pressure ratio for this specific blisk. In terms of polytropic efficiency, the measured geometric scatter is shown to have a higher influence than the geometric mean deviation. The geometric scatter around the mean is shown to impact the pressure distribution along the leading edge and the shock position. Furthermore, a blisk is analyzed with one blade deviating substantially from the design intent, denoted as blade 0. It is shown that the impact of blade 0 on the flow is largely limited to the blade passages that it is directly a part of. The results presented in this paper also show that the impact of this blade on the flow field can be represented by a simulation including 3 blade passages. In terms of loss, using 5 blade passages is shown to give a close estimate for the relative change in loss for blade 0 and neighboring blades.

Effects of Pressure Ratio and Rotational Speed on Leakage Flow and Cavity Pressure in the Staggered Labyrinth Seal

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Zhigang Li ◽  
Jun Li ◽  
Xin Yan ◽  
Zhenping Feng
Keyword(s):  
Experimental Data ◽  
Numerical Simulations ◽  
Rotational Speed ◽  
Stokes Equations ◽  
Pressure Ratio ◽  
Labyrinth Seal ◽  
Flow Coefficient ◽  
Leakage Flow ◽  
Cavity Pressure ◽  
Cavity Structure

Effects of pressure ratio and rotational speed on the leakage flow and cavity pressure characteristics of the rotating staggered labyrinth seal were investigated by means of experimental measurements and numerical simulations. The rotating seal test rig with turbine flowmeter and pressure measuring instruments was utilized to investigate the leakage flow of the staggered labyrinth seal at eight pressure ratios and five rotational speeds. The repeatability of the experimental data was demonstrated by three times measurements at different pressure ratios and fixed rotational speed. The three-dimensional Reynolds-averaged Navier–Stokes equations and standard k-ε turbulent model were also applied to study the leakage flow characteristics of the staggered labyrinth seal at the experimental conditions. The validation of the numerical approach was verified through comparison of the experimental data. The detailed flow field in the staggered labyrinth seal was illustrated according to the numerical simulations. The experimental and numerical results show that the leakage flow coefficient increases with increasing pressure ratio at the fixed rotational speed and is more sensitive to the smaller pressure ratio. The influence of rotational speed on the leakage flow coefficient is not obvious in the present rotational speed limitations. The cavity pressure coefficient in the staggered labyrinth seal decreases and is significantly influenced by the cavity structure along the flow direction.

An Investigation on Turbine Tip and Shroud Heat Transfer

2003 ◽  
Vol 125 (3) ◽  
pp. 513-520 ◽  
Author(s):  
Kam S. Chana ◽  
Terry V. Jones
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Guide Vane ◽  
Pressure Ratio ◽  
Experimental Investigations ◽  
Inlet Temperature ◽  
Turbine Stage ◽  
Pressure Distributions ◽  
Engine Design ◽  
Nozzle Guide

Detailed experimental investigations have been performed to measure the heat transfer and static pressure distributions on the rotor tip and rotor casing of a gas turbine stage with a shroudless rotor blade. The turbine stage was a modern high pressure Rolls-Royce aero-engine design with stage pressure ratio of 3.2 and nozzle guide vane (ngv) Reynolds number of 2.54E6. Measurements have been taken with and without inlet temperature distortion to the stage. The measurements were taken in the QinetiQ Isentropic Light Piston Facility and aerodynamic and heat transfer measurements are presented from the rotor tip and casing region. A simple two-dimensional model is presented to estimate the heat transfer rate to the rotor tip and casing region as a function of Reynolds number along the gap.

scholarly journals THE EFFECT OF CONVERGENT-DIVERGENT NOZZLE PROFILE ON ITS PERFORMANCE

2019 ◽  
Vol 19 (1) ◽  
pp. 14-43
Author(s):  
Arkan Al-Taie ◽  
Hussien W Mashi ◽  
Ali M Hadi
Keyword(s):  
Mach Number ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Sharp Decrease ◽  
Inlet Pressure ◽  
Ansys Fluent ◽  
Static Pressure Distribution ◽  
Flow Parameters ◽  
Sudden Rise ◽  
Flow Through

The paper presents the effect of convergent-divergent nozzles profile across specified inlet pressures values from (1.5 bar-4 bar), with constant back pressure of (1 bar). The flow of air through three convergent-divergent nozzles was studied theoretically. The flow was assumed to be one-dimensional, adiabatic and reversible (isentropic). The flow parameters like static pressure ratio and Mach number were analyzed. The flow parameters were obtained in term of area ratio along the nozzle. MATLAB code was built in order to find the Mach number along the nozzles, by using Newton-Raphson method. The shockwave position inside the nozzles was determined, using "analytic method". ANSYS fluent 18 was used to simulate the flow through the three nozzles. Two- dimensional, turbulent and viscous models were utilized to solve the governing equations. K-? model was used to model the turbulent effect. The results concluded that, reduction in inlet pressure can not affect the flow upstream the throat. Also the shockwave appearance can be noticed by a sudden rise in static pressure associated with a sharp decrease in Mach number. Shockwave moves toward the throat by reduction the inlet total pressure .By comparison the static pressure distribution along the three nozzles where can be deduced that the profile has an effect on the flow character i.e. (static pressure Mach no).The best performance among the nozzles is the performance of nozzle (N1), which (75%) of its length work as nozzle at the lowest inlet pressure of (1.5bar) while (44% and 60%) of the nozzles length for (N2 and N3) respectively work as the nozzle.

scholarly journals Velocity fluctuations generated by the flow through a random array of spheres: a model of bubble-induced agitation

2017 ◽  
Vol 823 ◽  
pp. 592-616 ◽  
Author(s):  
Zouhir Amoura ◽  
Cédric Besnaci ◽  
Frédéric Risso ◽  
Véronique Roig
Keyword(s):  
Reynolds Number ◽  
Volume Fraction ◽  
Experimental Investigations ◽  
Sphere Diameter ◽  
Spatial Fluctuation ◽  
Average Flow Velocity ◽  
Random Array ◽  
Time Fluctuation ◽  
Flow Through ◽  
Non Gaussian

This work reports an experimental investigation of the flow through a random array of fixed solid spheres. The volume fraction of the spheres is 2 %, and the Reynolds number $Re$ based on the sphere diameter and the average flow velocity is varied from 120 to 1040. Using time and spatial averaging, the fluctuations have been decomposed into two contributions of different natures: a spatial fluctuation that accounts for the strong inhomogeneity of the flow around each sphere, and a time fluctuation that comes from the instability of the flow at large enough Reynolds numbers. The evolutions of these two contributions with the Reynolds number are different, so that their relative importance varies. However, when each is normalized by using its own variance and the integral length scales of the fluctuations, their spectra and probability density functions (PDFs) are almost independent of $Re$. The spatial fluctuation mostly comes from the velocity deficit in the wakes of the spheres, and is thus dominated by scales larger than one or two sphere diameters. It is found to be responsible for the asymmetry of the PDFs of the vertical fluctuations and of the major part of the anisotropy level between the vertical and the horizontal components of the fluctuations. The time fluctuation dominates at scales smaller than the integral length scale. It is isotropic and its PDFs, well described by an exponential distribution, are non-Gaussian. The spectra of the spatial and the time fluctuations both show an evolution as the power $-3$ of the wavenumber, but not exactly in the same subrange. All these properties are found in remarkable agreement with the results of both experimental investigations and large eddy simulations (LES) of a homogeneous bubble swarm. This confirms that the main mechanism responsible for the production of bubble-induced fluctuations is the interaction of the velocity disturbances caused by obstacles immersed in a flow and that the structure of this agitation is weakly dependent on the precise nature of the obstacles. The understanding and the modelling of the agitation generated by the motion of a dispersed phase, such as the bubble-induced agitation, therefore require one to distinguish between the roles of these two contributions.

scholarly journals New Perspective for Heat Transfer Evaluation During Film Condensation Inside Tubes

2021 ◽  
Vol 39 (2) ◽  
pp. 390-402
Author(s):  
Yanán Camaraza-Medina
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Single Phase ◽  
Film Condensation ◽  
Mean Deviation ◽  
Two Phase ◽  
Wide Range ◽  
The Mean ◽  
Vertical Tubes

This paper presents the main results of the research developed by the author in his postdoctoral investigations on heat transfer calculations during film condensation inside tubes. The elements studied are combined in an analysis expression that provides a reasonable fit with the available experimental data, which includes a total of 22 fluids, including water, refrigerants and a wide range of organic substances, which condense inside horizontal, inclined and vertical tubes. These experimental data were obtained from the reports of 33 sources. Available data covers tube diameters from 2 to 50 mm, mass flow rates from 3 to 850 kg/(m2s), reduced pressures ranging from 0.0008 to 0.91, values for single-phase from 1 to , Reynolds number for two-phase from 900 to 594390, Reynolds number for single-phase from 65 to 84950 and vapor quality from 0.01 to 0.99. The mean deviation found for the analyzed data for horizontal tubes was 13.4%, while for the inclined and vertical tubes data the mean deviation was 14.9%. In all cases, the agreement of the proposed model is good enough to be considered satisfactory for practical design.

Moderate Reynolds number flows through periodic and random arrays of aligned cylinders

1997 ◽  
Vol 349 ◽  
pp. 31-66 ◽  
Author(s):  
DONALD L. KOCH ◽  
ANTHONY J. C. LADD
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Volume Fraction ◽  
Unit Length ◽  
Reynolds Numbers ◽  
Moderate Reynolds Number ◽  
Random Arrays ◽  
Flow Through ◽  
The Mean ◽  
Square Array

The effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders is investigated. Numerical simulations using a lattice-Boltzmann formulation are performed for Reynolds numbers up to about 180.The magnitude of the drag per unit length on cylinders in a square array at moderate Reynolds number is strongly dependent on the orientation of the drag (or pressure gradient) with respect to the axes of the array; this contrasts with Stokes flow through a square array, which is characterized by an isotropic permeability. Transitions to time-oscillatory and chaotically varying flows are observed at critical Reynolds numbers that depend on the orientation of the pressure gradient and the volume fraction.In the limit Re[Lt ]1, the mean drag per unit length, F, in both periodic and random arrays, is given by F/(μU) =k1+k2Re2, where μ is the fluid viscosity, U is the mean velocity in the bed, and k1 and k2 are functions of the solid volume fraction ϕ. Theoretical analyses based on point-particle and lubrication approximations are used to determine these coefficients in the limits of small and large concentration, respectively.In random arrays, the drag makes a transition from a quadratic to a linear Re-dependence at Reynolds numbers of between 2 and 5. Thus, the empirical Ergun formula, F/(μU) =c1+c2Re, is applicable for Re>5. We determine the constants c1 and c2 over a wide range of ϕ. The relative importance of inertia becomes smaller as the volume fraction approaches close packing, because the largest contribution to the dissipation in this limit comes from the viscous lubrication flow in the small gaps between the cylinders.

Flow in a Channel With Longitudinal Ribs

1994 ◽  
Vol 116 (2) ◽  
pp. 233-237 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Reynolds Number ◽  
Eigenfunction Expansion ◽  
Complex Geometry ◽  
Parallel Plates ◽  
Match Method ◽  
Mean Velocity ◽  
Longitudinal Ribs ◽  
Flow Through ◽  
The Mean ◽  
Wetted Perimeter

The laminar, viscous flow between parallel plates with evenly spaced longitudinal ribs is solved by an eigenfunction expansion and point-match method. The ribs on both plates may be symmetrically placed or staggered. For a given pressure gradient, the mean velocity is plotted as a function of the geometric parameters. We find the wetted perimeter and the friction factor—Reynolds number product are unsuitable parameters for the flow through ducts of complex geometry.

Study for the Gas Flow Through a Critical Nozzle

2003 ◽  
Author(s):  
Heuy Dong Kim ◽  
Jae Hyung Kim ◽  
Kyung Am Park
Keyword(s):  
Reynolds Number ◽  
Mass Flow ◽  
Gas Flow ◽  
Critical Pressure ◽  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Nozzle Throat ◽  
Critical Nozzle ◽  
Flow Through ◽  
Diffuser Angle

The critical nozzle is defined as a device to measure the mass flow with only the nozzle supply conditions, making use of flow choking phenomenon at the nozzle throat. The discharge coefficient and critical pressure ratio of the gas flow through the critical nozzle are strongly dependent on Reynolds number, based on the diameter of nozzle throat and nozzle supply conditions. Recently a critical nozzle with small diameter is being extensively used to measure mass flow in a variety of industrial fields. For low Reynolds numbers, prediction of the discharge coefficient and critical pressure is very important since the viscous effects near walls significantly affect the mass flow through critical nozzle, which is associated with working gas consumption and operation conditions of the critical nozzle. In the present study, computational work using the axisymmetric, compressible, Navier-Stokes equations is carried out to predict the discharge coefficient and critical pressure ratio of gas flow through critical nozzle. In order to investigate the effect of the working gas and turbulence model on the discharge coefficient, several kinds of gases and several turbulence models are employed. The Reynolds number effects are investigated with several nozzles with different throat diameter. Diffuser angle is varied to investigate the effects on the discharge coefficient and critical pressure ratio. The computational results are compared with the previous experimental ones. It is known that the standard k-ε turbulence model with the standard wall function gives a best prediction of the discharge coefficient. The discharge coefficient and critical pressure ratio are given by functions of the Reynolds number and boundary layer integral properties. It is also found that diffuser angle affects the critical pressure ratio.

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