May New Proposal A HYBRID COMPUTATIONAL ANALYSIS FOR SHALLOW DEPTH, GROOVED ANNULAR SEALS FOR PUMPS. Luis San Andrés Tingcheng Wu

Transcription

1 New Proposal May 2015 A HYBRID COMPUTATIONAL ANALYSIS FOR SHALLOW DEPTH, GROOVED ANNULAR SEALS FOR PUMPS Luis San Andrés Tingcheng Wu

2 Introduction Circumferentially-grooved seals are widely used in centrifugal pumps to reduce leakage flow. These seals can impact the pump rotordynamics. Multistage Barrel Process Pump Circumferentially Grooved Seal 2

3 Models for prediction of grooved seals force coefficients (1) Bulk-Flow Model Simplify the bulk flow equations with assumptions; Computationally efficient; Require user defined empirical constants (i.e. friction factors). (2) Computational Fluid Dynamics (CFD) Solution Solve Navier Stokes equations with an appropriate turbulence flow model. Perturbation (unsteady motion) difficult for force coefficients. (Long) computation time. 3

4 Bulk Flow Model XLCGrv Marquette and Childs (1996) developed predictive tool XLCGrv, part of XLTRC2 software. Three Control Volume Bulk Flow Model Friction coefficient f=n Re m Experimentally determined (n, m); Computationally efficient; Validated against test data for Halon short length seals L/D <

5 Hirs bulk flow model for friction factor f (1) Mean velocity of flow relative to the surface; Shear stress; Reynolds number for mean flow; Fluid density; Fluid viscosity; film clearance;, Empirical friction factor coefficients. 5

6 Three control volume (CV) Bulk flow model c Flow C= 0.225mm Rotor Velocity Distribution in a grooved seal (CFD) (Groove length 1.6mm, Groove depth 1.6mm) In the groove section, the flow is partitioned into: (1) through-flow section (CV Ⅱ); (2) deep cavity with recirculation zone: a stream line divides flow to the jet sudden expansion (CV Ⅲ). 6

7 XLCGrv predictions for a long seal Predicted force coefficients for a long grooved seal (L/D>1) used to estimate the rotor dynamic performance of a commercial pump. The estimations show no reasonable correlation with shop test results. Assumptions applied in the three control volume bulk flow model (wall shear stress, single vortex, etc.); Friction factor coefficients obtained through test results with short length seals. Precise predictions for pump stability necessitates of a better analysis tool. 7

8 CFD Based Seal Models Solving Navier Stokes equations with an appropriate turbulence flow model could give accurate predictions of dynamic force coefficients (in lieu of test data). CFD Predictions Avoid simplifying assumptions: (wall shear stress, single vortex, etc.) No empirical constants needed; Computationally intensive. Using CFD to predict force coefficients of complex geometry seals is becoming common practice. Forces exerted on the whirling rotor in relative coordinate system 8

9 CFD Based Model Untaroiu et al. (2013) obtained CFD flow solutions to predict the rotor dynamic coefficients of a shallow depth, grooved seal. Fluid induced forces Small amplitude perturbation approach Pressure distribution from full 3D CFD solution Rotordynamic force coefficients Curve fitting of seal reaction forces Ω Ω Seal Geometry L D S ax c n (mm) (mm) (mm) (mm) (mm) (mm) (mm) Ω Ω 9

10 Untaroiu et al. (2013) predictions Dynamic Coefficients From CFD and Bulk-Flow Codes CFD Bulk flow method * K xx = K yy (MN/m) K xy = -K yx (MN/m) C xx = C yy (kn s/m) C xy = - C yx (kn s/m) M xx = M yy (kg) M xy = -M yx (kg) To validate the predictions from CFD method, Untaroiu et al. used predicted dynamic force coefficients to estimate the vibration behavior of a pump. The RD estimations were then compared to the vibration characteristic measured by an OEM. The indirect comparisons indicate that the CFD solution delivers accurate force coefficients. ~13 hours/simulation, NOT computational efficiency * Solution based on SEALS program developed by Childs and Scharrer, Texas A&M University 10

11 CFD Steady state flow for a seal with increasing groove depth Axial velocity (m/s) for increasing groove depth Groove Depth [mm] Groove Length =1.6 mm Groove Length =1.6 mm Seal Length =180mm Rotor Radius =90mm Rotor Speed =2980 RPM Number of Grooves = 55 Radial Clearance c = 0.25 mm m/s Flow Flow in a shallow groove does not show recirculation zone within a cavity. 11

12 New Proposal for A HYBRID COMPUTATIONAL ANALYSIS FOR SHALLOW DEPTH, GROOVED ANNULAR SEALS FOR PUMPS 12

13 Work Proposed for Utilize a steady-state CFD solution for a seal to determine base state flow variables; Apply a bulk-flow perturbation analysis to determine the dynamic coefficients of the seal. Validate and compare the predictions against test data. 13

14 Hybrid Analysis with Bulk-Flow/CFD Methodology Use CFD to calculate the steady state flow; Determine the bulk mean flow variables; Calculate the wall friction factors ( ) and its differences (,, ) from CFD flow field; Apply Bulk Flow Model analysis; Integrate the perturbed pressure field over the surface of the rotor to get fluid forces acting on the rotor: direct estimation of dynamic force coefficients. 14

15 TRC Budget Year I Support for GS (20 h/week) x $ 2,200 x 12 months $ 26,400 Fringe benefits (2.4%) and medical insurance ($150/month) $ 2,434 Tuition & fees three semesters ($363/credit hour) $ 8,712 PC upgrade +monitor $ 1,250 Attend 2 day short-course in CFD analysis $ 3,000 Total Cost: $ 41,875 Modified BF code will enable rapid prediction of rotordynamic coefficients for (shallow depth) grooved seals with various length/width aspect ratio. Validate to test data (if available) to ensure improved accuracy with efficiency. 15

16 Acknowledgement Thanks to the support of Dr. San Andres (PI incentive funds) plus his patience. Questions (?)

17 References: [1] TorishimaPump, 2013, "Multistage Barrel Process Pump, &lvl=3. [2] Nordmann, R., Dietzen, F., Janson, W., Frei, A., and Florjancic, S., 1986, "Rotordynamic Coefficients and Leakage Flow of Parallel Grooved Seals and Smooth Seals, NASA. Lewis Research Center Rotordynamic Instability Problems in High-Performance Turbomachinery, pp [3] Marquette, O., and Childs, D., 1996, "An Extended Three-Control-Volume Theory for Circumferentially Grooved Liquid Seals," Journal of Tribology, 118(2), pp [4] Childs, D. W., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, John Wiley & Sons, Chap.4. [5] Untaroiu, A., Hayrapetian, V., Untaroiu, C. D., Wood, H. G., Schiavello, B., McGuire, J., 2013, "On the Dynamic Properties of Pump Liquid Seals," Journal of Fluids Engineering, 135(5). [6] Migliorini, P. J., Untaroiu, A., Wood, H. G., and Allaire, P. E., 2012, "A Computational Fluid Dynamics/Bulk-Flow Hybrid Method for Determining Rotordynamic Coefficients of Annular Gas Seals," Journal of Tribology, 134(2), pp

18 Three control volume (CV) Bulk flow model Assumptions: Fig.4 Definition of Three Control Volume for Grooved Seal (1) Newtonian and incompressible fluid; (2) Shear stress variation for each control volume ignored and only shear stresses at the boundaries of the control volume are taken into account. (3) There is no mass exchange between CVⅡ and CVⅢ. (4) Pressure variation among groove is ignored. (5) A single-vortex flow evolves within the groove cavity (CVⅢ). 18

19 Bulk Flow Model XLCGrv For Short Length Seals: The friction factor coefficients of XLCGrv are determined by experimental results. For short seals, various experiments (Kilgore,1988) proved its accuracy. Table.1 Seals Tested by Kilgore 19