On the Scaling of Aeroelastic Parameters for High Pressure Applications in Centrifugal Compressors

2016 ◽  
Author(s):  
Florian Fruth ◽  
Peter Jeschke ◽  
Holger Franz
Keyword(s):  
Reynolds Number ◽  
Density Ratio ◽  
Development Stage ◽  
Flow Coefficient ◽  
Mode Shapes ◽  
Centrifugal Compressors ◽  
Reynolds Number Effects ◽  
Flow Through ◽  
Higher Temperature ◽  
Temperature Levels

A centrifugal compressor has been evaluated numerically for the scalability of aeroelastic parameters for different pressure levels. By maintaining the flow coefficient, as done in the development process, comparable aerodynamics for the compressor cases have been generated ranging from 0.96 bar to 40 bar inlet pressure. It has been found, that the mean static pressure as well as the aerodynamic damping can be scaled by the inlet density ratio. The gained results proofed for this case to be sufficient in magnitude and distribution for an early development stage. Harmonic pressure scaling for centrifugal compressors however has resulted in non-negligible errors. The origin of changes for the setup presented is found in the variation of Reynolds number. Especially the hub and tip sections are influenced and therefore also the secondary flow through the impeller tip gap. This generally results in lower scalability after the transition from axial to radial flow. Hence impeller trailing edge mode shapes have to be considered carefully. The Reynolds number effects become smaller however for higher temperature levels, reducing the scaling errors.

Reynolds Number Effects on Regenerative Pump Performance

1987 ◽  
Vol 109 (4) ◽  
pp. 392-395 ◽  
Author(s):  
J. W. Hollenberg
Keyword(s):  
Reynolds Number ◽  
Scaling Behavior ◽  
Flow Coefficient ◽  
Maximum Efficiency ◽  
Number Range ◽  
Design Point ◽  
Reynolds Number Range ◽  
Lower Reynolds Number ◽  
Reynolds Number Effects ◽  
Torque Coefficient

Reynolds number effects on the performance of a conventional design regenerative pump were investigated, using glycerine-water mixtures, between an impeller tip speed Reynolds number, RT, of 5.0×103 (all glycerine) and 1.6×106 (all water). Results show that the maximum efficiency, nm, can be expressed in terms of an output to loss ratio, nm/1−nm, which varies as RT0.203 for 2.0×104 < RT < 1.6×106 and as RT1.156 for RT < 2.0×104. These results are consistent with efficiency behavior reported in similar investigations on other types of turbomachines. Further, the design point flow coefficient increased over the range of Reynolds number investigated, while the design point head coefficient exhibited a maximum within this range. In addition, marked departure from scaling behavior occurred in the lower Reynolds number range. Finally, the correlation among torque coefficient, head coefficient, and flow coefficient previously established by the author was further verified and followed scaling behavior for the higher Reynolds number range.

A New Appraisal of Reynolds Number Effects on Centrifugal Compressor Performance

1979 ◽  
Vol 101 (3) ◽  
pp. 384-392 ◽  
Author(s):  
F. J. Wiesner
Keyword(s):  
Reynolds Number ◽  
Centrifugal Compressor ◽  
Performance Test ◽  
Flow Coefficient ◽  
Performance Parameters ◽  
Empirical Methods ◽  
Reynolds Number Effects ◽  
Significant Performance ◽  
Compressor Performance ◽  
Overall Performance

This paper summarizes the results of an investigation into the effects of Reynolds number on the performance of centrifugal compressor stages, using a computer program for the detailed prediction of component and overall performance characteristics. This investigation included wide variation of stage geometries, speeds, and fluid conditions, resulting in diffuser inlet absolute Reynolds number variations over the range from 5 × 102 to 5 × 108. The computer results indicate that variations in Reynolds number and in relative roughness will produce variations in all significant performance parameters: the flow coefficient, the work coefficient, and the efficiency. Correlations of these results with various sources of test data on single and multistage centrifugal compressors produce very satisfactory comparisons. As a result of this study, improved empirical methods are recommended for making practical adjustments of compressor performance with variation in Reynolds number. These recommendations should be taken into account in the modernization of all centrifugal compressor performance test codes such as those formulated by ASME and ISO.

Friction Factor for Isothermal and Nonisothermal Flow Through Porous Media

1977 ◽  
Vol 99 (3) ◽  
pp. 367-373 ◽  
Author(s):  
J. C. Koh ◽  
J. L. Dutton ◽  
B. A. Benson ◽  
A. Fortini
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Friction Factor ◽  
Nonisothermal Flow ◽  
Flow Through Porous Media ◽  
Gaseous Flow ◽  
Pressure Drops ◽  
Flow Through ◽  
Temperature Levels ◽  
Nonisothermal Conditions

Measurements were performed to determine the pressure drops for gaseous flow through porous materials of different microstructures, porosities, and thickness under isothermal and nonisothermal conditions at various temperature levels. Results were satisfactorily correlated by a simple equation relating the friction factor to the Reynolds number and porosities.

Influence of Reynolds Number on the Performance of Process Centrifugal Compressors

2016 ◽  
Author(s):  
Yan Liu ◽  
Li-hua Tao ◽  
Jian Wang ◽  
Yang Wang ◽  
Xue-jun Wang ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Flow Coefficient ◽  
Design Parameters ◽  
Centrifugal Compressors ◽  
Empirical Formulas ◽  
Design Point ◽  
Reliable Performance ◽  
High Reynolds ◽  
Large Flow

Over the past 60 years, effects of changes in Reynolds number on performance of centrifugal compressors have been widely investigated. However most of cases deal with those compressors with small or medium flow coefficients. Studies on the influence of Reynolds number on centrifugal compressors with large flow coefficients and high machine Mach number are rarely seen in the literature. This paper deals with two types of centrifugal compressors. One type of compressor (Model 1) has a relatively large capacity with high machine Mach number. The flow coefficient and machine Mach number are 0.16 and 1.05 respectively at the design condition. Those design parameters for the other type of compressor (Model 2) are 0.11 and 0.7 respectively. Both experimental and numerical results show that with increase in Re, aerodynamic performance of centrifugal compressors is improved. However, to what extent that improvement is gained depends on properties of the baseline compressor. When Reynolds number of Model 1 becomes about 5 times large due to increase in the inlet pressure, its polytropic efficiency is only improved 0.7% at the design point in experiment. Flow field inside the impeller is similar to its prototype. For Model 2, when Reynolds number becomes 1.78 times large due to scaling up, the polytropic efficiency of the enlarged one is improved about 2% at the design point. These results demonstrate that for a compressor with large flow coefficient and high machine Mach number, i.e. originally high Reynolds number, the influence of Reynolds number on its performance is limited. In addition to experiment and CFD, two empirical formulas are applied to work out performance correction due to a change in Reynolds number for Model 1 and Model 2. Although CFD results are more accurate than the empirical results, empirical formula is still useful to get relatively reliable performance correction.

Effect of Heterogeneity on the Non-Darcy Flow Coefficient

1999 ◽  
Vol 2 (03) ◽  
pp. 296-302 ◽  
Author(s):  
Ganesh Narayanaswamy ◽  
Mukul M. Sharma ◽  
G.A. Pope
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Porous Media ◽  
Pressure Drop ◽  
Characteristic Length ◽  
Flow Coefficient ◽  
Darcy Flow ◽  
Liquid Saturation ◽  
Flow Through ◽  
Heterogeneous Formation

Summary An analytical method for calculating an effective non-Darcy flow coefficient for a heterogeneous formation is presented. The method presented here can be used to calculate an effective non-Darcy flow coefficient for heterogeneous gridblocks in reservoir simulators. Based on this method, it is shown that the non-Darcy flow coefficient of a heterogeneous formation is larger than the non-Darcy flow coefficient of an equivalent homogenous formation. Non-Darcy flow coefficients calculated from gas well data show that non-Darcy flow coefficients obtained from well tests are significantly larger than those predicted from experimental correlations. Permeability heterogeneity is a very likely reason for the differences in non-Darcy flow coefficients often seen between laboratory and field data. Introduction In this paper, we present an analytical method for calculating an effective non-Darcy flow coefficient for a heterogeneous reservoir. The effect of heterogeneity on the non-Darcy flow coefficient is also shown using numerical simulations. Non-Darcy flow coefficients calculated from the analysis of welltest data from a gas condensate field are compared with experimental correlations. Such a comparison allows us to more accurately assess the importance of non-Darcy flow in gas condensate reservoirs. Literature Review As early as 1901, Reynolds observed, in his classical experiments of injecting dye into water flowing through glass tubes, that after some high flowrate, flow rate was no longer proportional to the pressure drop. Forchheimer1 also observed this phenomena and proposed the following quadratic equation to express the relationship between pressure drop and velocity in a porous medium: d P d r = μ k u + β ρ u 2 . ( 1 ) This equation has come to be known asForchheimer's equation. At low Reynolds number (creeping flow conditions), the above equation reduces to Darcy's law. Tek2 developed a generalized Darcy equation in dimensionless form which predicts the pressure drop with good agreement over all ranges of Reynolds numbers. Katz et al.3 attributed the phenomenon of non-Darcy flow to turbulence. Tek et al.4 proposed the following correlation for?: β = 5.5 × 10 9 k 5 / 4 ϕ 3 / 4 . ( 2 ) Gewers and Nichol5 conducted experiments on microvugular carbonate cores to measure the non-Darcy flow coefficient. They also studied the effect of the presence of a second static fluid phase and the effect on plugging due to fines migration. They found that ? decreases and then increases with liquid saturation. Wong6 studied the effect of a mobile liquid saturation on ?. He used distilled water as the liquid phase and water saturated nitrogen as the gas phase on the same cores used by Gewers and Nichol. He plotted ? vs liquid saturation and found that there is an eight-fold increase in ? when the liquid saturation increases from 40% to 70%. He concluded that ? can be approximately calculated from the dry core experiments by using the effective gas permeability. Geertsma7,8 introduced an empirical relationship between ?,k and ? based on a combination of experimental data and dimensional analysis. He noted that the observed departure from Darcy's law was due to the convective acceleration and deceleration of the fluid particles. He also defined a new Reynolds number as ?k??/?, and suggested the following correlation for ? with a constant C (k is in ft 2, ?is in 1/ft). β = C k 0.5 ϕ 5.5 . ( 3 ) For the case of gas flowing through a core with a static liquid phase, he suggested the following correlation: β = C ( k k r g ) 0.5 [ ϕ ( 1 − S w ) ] 5.5 . ( 4 ) Phipps and Khalil9 proposed a method for determining the exponent in a Forchheimer-type equation. Firoozabadi and Katz10 presented are view of the theory of high velocity gas flow through porous media. Evanset al.11 reviewed the various correlations. They conducted an experimental study of the effect of the immobile liquid saturation and suggested a correlation based on dimensional analysis. Nguyen12performed an experimental study of non-Darcy flow through perforations on a synthetic core using air. These experiments showed that non-Darcy flow exists in the convergence zone and the perforation tunnel. Results of this study showed that Darcy flow equations can over predict well productivity by as much as 100%. Jones13 conducted experiments on 355 sandstone and 29 limestone cores. These tests were done for various core types: vuggy limestones, crystalline limestones, and fine grained sandstones. He presented the following correlation: β = 6.15 × 10 10 k − 1.55 . ( 5 ) He also points out that the group ?k? which is the characteristic length used for defining a Reynolds number for porous media, should be proportional to the characteristic length k/ϕ. He developed an approximate multilayer flow model that demonstrates that the departure from the above relation is due to permeability variations. Jones suggested that heterogeneity may be the reason why all correlations involving ? exhibit so much scatter.

Small Turbomachinery Compressor and Fan Aerodynamics

1973 ◽  
Vol 95 (3) ◽  
pp. 251-256 ◽  
Author(s):  
R. C. Pampreen
Keyword(s):  
Reynolds Number ◽  
Test Results ◽  
Centrifugal Compressors ◽  
Reynolds Number Effects ◽  
Compressor Performance ◽  
Compressor Efficiency

This paper discusses aerodynamic considerations in the design of small turbomachinery axial and centrifugal compressors and fans. Test results are presented to show the effect of scaling on compressor performance. Correlations are presented which relate compressor efficiency to Reynolds Number and clearance. It is shown that clearance effects are more prominent when scaling designs, and Reynolds Number effects are more prominent as density is lowered.

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.

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