An Extended Three-Control-Volume Theory for Circumferentially-Grooved Liquid Seals

1996 ◽  
Vol 118 (2) ◽  
pp. 276-285 ◽  
Author(s):  
O. R. Marquette ◽  
D. W. Childs
Keyword(s):  
Control Volume ◽  
Current Theory ◽  
Flow Section ◽  
Leakage Flow ◽  
Centrifugal Pumps ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Through Flow ◽  
Control Volumes ◽  
Theoretical Results

Circumferentially-grooved seals are used in centrifugal pumps to reduce leakage flow. They can also have a significant impact on pump rotordynamic characteristics. Florjancic (1990) developed an analysis for leakage and rotordynamic coefficients, using a partition of the seal into three control volumes. This paper presents a new theory, based on an extension of Florjancic’s work (1990) for circumferentially-grooved liquid seals. The current theory differs from Florjancic’s analysis in the retention of transfer momentum terms and the introduction of diverging flow in the through-flow section within a seal groove. Validation of the new analysis is achieved through a comparison with existing experimental data taken from Kilgore (1988), and Florjancic (1990). Theoretical results are reasonable and consistent; i.e., a modification in the seal parameters induces a correct evolution of the rotordynamic coefficients. Direct and cross-coupled stiffness coefficients are slightly underpredicted, whereas the direct damping coefficient is underpredicted within 40 percent. Leakage flow predictions are very good.

Optimum incidence angle in centrifugal pumps and radial inflow turbines

1998 ◽  
Vol 212 (2) ◽  
pp. 97-107 ◽  
Author(s):  
G Ardizzon ◽  
G Pavesi
Keyword(s):  
Incidence Angle ◽  
Theoretical Method ◽  
Centrifugal Pumps ◽  
Numerical Computations ◽  
Through Flow ◽  
Inlet Conditions ◽  
Theoretical Results

A theoretical method is presented for establishing the optimum incidence angle in outward- and inward-flow runners. Relative through-flow and eddy vortex are considered separately in order to examine their influence on the vane inlet conditions. The action of the counter-rotating vortex and of the blade camber is analysed and an algorithm is given for the evaluation of the optimum incidence angle. The validity of the procedure is finally verified by comparing the theoretical results with experimental observations and with numerical computations.

Static and Rotordynamic Characteristics for a New Hole-Pattern Annular Gas Seal Design Incorporating Larger Diameter Holes

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Michael Vannarsdall ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Low Frequency ◽  
Hole Diameter ◽  
Commercial Application ◽  
Manufacturing Cost ◽  
Large Hole ◽  
Rotordynamic Coefficients ◽  
Stability Performance ◽  
Seal Design ◽  
Control Volumes

To reduce manufacturing cost and time, a new larger-diameter hole-pattern seal incorporating hole diameters of 12.27 mm, versus prior hole diameters of 3.175 mm has been proposed. The 12.27 mm hole-diameter seal had substantially better stability performance with higher effective damping and a markedly lower crossover frequency. It had negative direct stiffness coefficients at low frequency, while the 3.175 mm hole-diameter seal did not. Predictions for the rotordynamic coefficients of this new seal were made based on a two-control-volume model developed by Kleynhans and Childs in 1997. The two control volumes consisted of a through-flow control-volume and a control-volume B that extended from the surface of the stator at the top of the holes to the bottom of holes. Predictions agreed poorly with measured results, because the model used, assumes gas flows only radially within control-volume B. With the large hole-diameters axial and circumferential flow is readily accomplished. Compared to the prior 3.175 mm hole-diameter seals, the 12.27 mm hole-diameter seal design leaked approximately 37.5% more which probably precludes its commercial application. Leakage for the seal was well predicted. Although the larger hole diameters were initially proposed to reduce costs, the fabrication was more challenging than originally thought. The larger holes could not be manufactured with a single pass. Hence, manufacturing costs and time were not reduced.

scholarly journals Development of a One-Dimensional Model for the Prediction of Leakage Flows in Rotating Cavities Under Non-Uniform Tangential Pressure Distribution

2019 ◽  
Vol 4 (3) ◽  
pp. 19
Author(s):  
Giulio Cantini ◽  
Simone Salvadori ◽  
Massimiliano Insinna ◽  
Giorgio Peroni ◽  
Gilles Simon ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Control Volume ◽  
Performance Estimation ◽  
Leakage Flow ◽  
Centrifugal Pumps ◽  
One Dimensional ◽  
Leakage Flows ◽  
Aspect Ratios

Regenerative pumps are characterized by a low specific speed that place them between rotary positive displacement pumps and purely radial centrifugal pumps. They are interesting for many industrial applications since, for a given flow rate and a specified head, they allow for a reduced size and can operate at a lower rotational speed with respect to purely radial pumps. The complexity of the flow within regenerative machines makes the theoretical performance estimation a challenging task. The prediction of the leakage flow rate between the rotating and the static disks has the greatest impact on the prediction of global performance. All the classical approaches to the disk clearance problem assume that there is no relevant circumferential pressure gradient. In the present case, the flow develops along the tangential direction and the pressure gradient is intrinsically non-zero. The aim of the present work is to develop a reliable approach for the prediction of leakage flows in regenerative pumps. A preliminary numerical simulation on a virtual model of a regenerative pump where the disk clearance is part of the control volume has been performed for three different clearance aspect ratios. The outcome of that campaign allowed the authors to determine the behavior of the flow in the cavity and choose correctly the baseline hypotheses for a mathematical-physical method for the prediction of leakage flows. The method assumes that the flow inside of the disk clearance is two-dimensional and can be decomposed into several stream-tubes. Energy balance is performed for each tube, thus generating a system that can be solved numerically. The new methodology was tuned using data obtained from the numerical simulation. After that, the methodology was integrated into an existing one-dimensional code called DART (developed at the University of Florence in cooperation with Pierburg Pump Technology Italy S.p.A.) and the new algorithm was verified using available numerical and experimental data. It is here demonstrated that an appropriate calibration of the leakage flow model allows for an improved reliability of the one-dimensional code.

Measurements Versus Predictions for Rotordynamic and Leakage Characteristics of a Convergent-Tapered, Honeycomb-Stator/Smooth-Rotor Annular Gas Seal

2008 ◽  
Author(s):  
Daniel E. van der Velde ◽  
Dara W. Childs
Keyword(s):  
Control Volume ◽  
Excitation Frequency ◽  
Test Fluid ◽  
Low Frequencies ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Direct Stiffness ◽  
Honeycomb Seals ◽  
Excitation Frequencies ◽  
The Cross

Measured results are presented for rotordynamic coefficients and leakage rates for two honeycomb-stator seal geometries, a convergent-tapered honeycomb seals (CTHC) and a constant-clearance honeycomb seals (CCHC) tested by Sprowl and Childs in 2007. The rotor diameter was 114.3 mm (4.500 in). The CTHC seals had inlet and exit clearances of 0.334 and 0.204 mm, respectively. The CCHC seal had a constant clearance of 0.204 mm. Honeycomb cells had depths of 3.175 mm (0.125 in) and widths of 0.79 mm (0.031 in). Measurements are reported with air as the test fluid, zero preswirl, ω = 20,200 rpm, a supply pressure of 69 bar (1,000 psi) and supply temperature of 18°C (64.4°F) for both seal geometries. The test pressure ratios are 0.5 for the CCHC seal, and 0.46 for the CTHC seal. The tapered seal leaks about 20% more than the constant-clearance seal. Measured and predicted dynamic coefficients are strong functions of excitation frequency. The measured direct stiffness coefficient was higher for the tapered seal at all excitation frequencies, including a projection to zero frequency, where the CCHC seal was on the order of −2MN/m versus roughly +13MN/m for the tapered seal. The CTHC seal had higher cross-coupled stiffness coefficients than the CCHC seal at all excitation frequencies. The CCHC and CTHC seals had comparable direct damping out to ∼80 Hz. For higher excitation frequencies, the CTHC seal had larger direct damping values. The effective damping Ceff combines the positive effect of direct damping and the destabilizing effect of cross-coupled-stiffness coefficients. It is negative at low frequencies and becomes positive for higher frequencies. The frequency at which it changes sign is called the cross-over frequency. The CCHC had a lower cross-over frequency (better from a stability viewpoint) and higher Ceff values out to ∼80 Hz. At higher excitation frequencies from ∼120Hz onward, the tapered seal has higher effective damping values. Kleynhans and Childs’ 1997 two-control-volume model did a generally good job of predicting the direct stiffness coefficients of both seals. It closely predicted the cross-coupled stiffness coefficients for the CCHC seal but substantially under predicted the values for the CTHC seal. It under predicted the direct damping for the CCHC seal at frequencies below ∼120Hz, but did a good job for higher frequencies. It under predicted direct damping for the CTHC seal at all frequencies. For the CCHC seal, the model did a good job of predicting Ceff at all frequencies and also accurately predicted the cross-over frequency. For the CTHC seal, the model accurately predicted the cross-over frequency but over predicted Ceff below the cross-over frequency (the seal was more destabilizing than predicted) and under predicted Ceff at higher frequencies.

scholarly journals Influence of Seal Cavity Leakage Flow on Compressor Performance Investigated with a Circumferentially Averaged Method

2021 ◽  
Vol 11 (2) ◽  
pp. 780
Author(s):  
Dong Liang ◽  
Xingmin Gui ◽  
Donghai Jin
Keyword(s):  
Flow Field ◽  
Pressure Ratio ◽  
Interaction Mechanism ◽  
Main Flow ◽  
Leakage Flow ◽  
Destructive Effect ◽  
Through Flow ◽  
Compressor Performance ◽  
Overall Performance ◽  
Flow Blockage

In order to investigate the effect of seal cavity leakage flow on a compressor’s performance and the interaction mechanism between the leakage flow and the main flow, a one-stage compressor with a cavity under the shrouded stator was numerically simulated using an inhouse circumferentially averaged through flow program. The leakage flow from the shrouded stator cavity was calculated simultaneously with main flow in an integrated manner. The results indicate that the seal cavity leakage flow has a significant impact on the overall performance of the compressor. For a leakage of 0.2% of incoming flow, the decrease in the total pressure ratio was 2% and the reduction of efficiency was 1.9 points. Spanwise distribution of the flow field variables of the shrouded stator shows that the leakage flow leads to an increased flow blockage near the hub, resulting in drop of stator performance, as well as a certain destructive effect on the flow field of the main passage.

Defining the Thermodynamic Efficiency in a Wave Rotor

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Shining Chan ◽  
Huoxing Liu ◽  
Fei Xing
Keyword(s):  
Gas Turbine ◽  
Control Volume ◽  
Thermodynamic Efficiency ◽  
Wave Rotor ◽  
Wave Rotors ◽  
Compression And Expansion ◽  
Efficiency Estimation ◽  
Parametric Analyses ◽  
Control Volumes ◽  
Thermodynamic Processes

A wave rotor enhances the performance of a gas turbine with its internal compression and expansion, yet the thermodynamic efficiency estimation has been troubling because the efficiency definition is unclear. This paper put forward three new thermodynamic efficiency definitions to overcome the trouble: the adiabatic efficiency, the weighted-pressure mixed efficiency, and the pressure pre-equilibrated efficiency. They were all derived from multistream control volumes. As a consequence, they could correct the efficiency values and make the values for compression and expansion independent. Moreover, the latter two incorporated new models of pre-equilibration inside a control volume, and modified the hypothetical “ideal” thermodynamic processes. Parametric analyses based on practical wave rotor data demonstrated that the trends of those efficiency values reflected the energy losses in wave rotors. Essentially, different thermodynamic efficiency definitions indicated different ideal thermal cycle that an optimal wave rotor can provide for a gas turbine, and they were recommended to application based on that essence.

Prediction of Rotordynamic Performance of Smooth Stator-Grooved Rotor Liquid Annular Seals Utilizing Computational Fluid Dynamics

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Farzam Mortazavi ◽  
Alan Palazzolo
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Excitation Frequency ◽  
Computationally Efficient ◽  
Operational Conditions ◽  
Rotordynamic Coefficients ◽  
Stiffness Coefficients ◽  
Liquid Seal ◽  
Frequency Ratios ◽  
Annular Seals

Circumferentially grooved, annular liquid seals typically exhibit good whirl frequency ratios (WFRs) and leakage reduction, yet their low effective damping can lead to instability. The current study investigates the rotordynamic behavior of a 15-step groove-on-rotor annular liquid seal by means of computational fluid dynamics (CFD), in contrast to the previous studies which focused on a groove-on-stator geometry. The seal dimensions and working conditions have been selected based on experiments of Moreland and Childs (2016, “Influence of Pre-Swirl and Eccentricity in Smooth Stator/Grooved Rotor Liquid Annular Seals, Measured Static and Rotordynamic Characteristics,” M.Sc. thesis, Texas A&M University, College Station, TX). The frequency ratios as high as four have been studied. Implementation of pressure-pressure inlet and outlet conditions make the need for loss coefficients at the entrance and exit of the seal redundant. A computationally efficient quasi-steady approach is used to obtain impedance curves as functions of the excitation frequency. The effectiveness of steady-state CFD approach is validated by comparison with the experimental results of Moreland and Childs. Results show good agreement in terms of leakage, preswirl ratio (PSR), and rotordynamic coefficients. It was found that PSR will be about 0.3–0.4 at the entrance of the seal in the case of radial injection, and outlet swirl ratio (OSR) always converges to values near 0.5 for current seal and operational conditions. The negative value of direct stiffness coefficients, large cross-coupled stiffness coefficients, and small direct damping coefficients explains the destabilizing nature of these seals. Finally, the influence of surface roughness on leakage, PSR, OSR, and stiffness coefficients is discussed.

Numerical prediction of the performance of gas-lubricated spiral groove thrust bearings

1997 ◽  
Vol 211 (2) ◽  
pp. 117-128 ◽  
Author(s):  
Y Yue ◽  
T. A. Stolarski
Keyword(s):  
Control Volume ◽  
Numerical Procedure ◽  
Operating Conditions ◽  
Hydrodynamic Bearings ◽  
Thrust Bearings ◽  
Flow Balance ◽  
Control Volumes ◽  
Volume Method ◽  
Spiral Angle ◽  
Spiral Grooves

The objective of this paper is to develop an accurate numerical procedure for the analysis of nominally flat contacts with spiral grooves lubricated by gases. The numerical procedure, which is based on the control-volume method, enables the solutions of the non-linear Reynolds equation to be obtained without limitation in geometry and operating conditions. Satisfactory flow balance was achieved on the control volumes as well as on the whole boundary and the method was proved to be very accurate. Convergence of the method was quick for any compressibility number. Three types of contact with spiral grooves were analysed. They were hydrodynamic bearings without interior chambers, hydrodynamic bearings with interior chambers and hybrid bearings. The effects of spiral angle, groove geometry (length, depth and width) and compressibility on performances were investigated for all possible designs.

Impact of Frequency Dependence of Gas Labyrinth Seal Rotordynamic Coefficients on Centrifugal Compressor Stability

2010 ◽  
Author(s):  
Giuseppe Vannini ◽  
Manish R. Thorat ◽  
Dara W. Childs ◽  
Mirko Libraschi
Keyword(s):  
Molecular Weight ◽  
Numerical Model ◽  
Control Volume ◽  
Labyrinth Seal ◽  
Labyrinth Seals ◽  
Frequency Dependent ◽  
Rotordynamic Coefficients ◽  
Frequency Independent ◽  
Rotor Surface ◽  
Independent Model

A numerical model developed by Thorat & Childs [1] has indicated that the conventional frequency independent model for labyrinth seals is invalid for rotor surface velocities reaching a significant fraction of Mach 1. A theoretical one-control-volume (1CV) model based on a leakage equation that yields a reasonably good comparison with experimental results is considered in the present analysis. The numerical model yields frequency-dependent rotordynamic coefficients for the seal. Three real centrifugal compressors are analyzed to compare stability predictions with and without frequency-dependent labyrinth seal model. Three different compressor services are selected to have a comprehensive scenario in terms of pressure and molecular weight (MW). The molecular weight is very important for Mach number calculation and consequently for the frequency dependent nature of the coefficients. A hydrogen recycle application with MW around 8, a natural gas application with MW around 18, and finally a propane application with molecular weight around 44 are selected for this comparison. Useful indications on the applicability range of frequency dependent coefficients are given.

A Comparison of Rotordynamic-Coefficient Predictions for Annular Honeycomb Gas Seals Using Three Different Friction-Factor Models

2002 ◽  
Vol 124 (3) ◽  
pp. 524-529 ◽  
Author(s):  
Rohan J. D’Souza ◽  
Dara W. Childs
Keyword(s):  
Friction Factor ◽  
Flow Model ◽  
Factor Model ◽  
Control Volume ◽  
Bulk Flow ◽  
Shear Stresses ◽  
Steam Turbines ◽  
Frequency Range ◽  
Rotordynamic Coefficients ◽  
Rotordynamic Coefficient

A two-control-volume bulk-flow model is used to predict rotordynamic coefficients for an annular, honeycomb-stator/smooth-rotor gas seal. The bulk-flow model uses Hirs’ turbulent-lubrication model, which requires a friction factor model to define the shear stresses at the rotor and stator wall. Rotordynamic coefficients predictions are compared for the following three variations of the Blasius pipe-friction model: (i) a basic model where the Reynolds number is a linear function of the local clearance, fs=ns Rems (ii) a model where the coefficient is a function of the local clearance, and (iii) a model where both the coefficient and exponent are functions of the local clearance. The latter models are based on data that shows the friction factor increasing with increasing clearances. Rotordynamic-coefficient predictions shows that the friction-factor-model choice is important in predicting the effective-damping coefficients at a lower frequency range (60∼70 Hz) where industrial centrifugal compressors and steam turbines tend to become unstable. At a higher frequency range, irrespective of the friction-factor model, the rotordynamic-coefficient predictions tend to coincide. Blasius-based Models which directly account for the observed increase in stator friction factors with increasing clearance predict significantly lower values for the destabilizing cross-coupled stiffness coefficients.

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