A CFD ANALYSIS ANCHORED TO TEST DATA Proceedings of ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition, June 11-15, 2018, Oslo, Norway GT-2018-77140 ON THE LEAKAGE, TORQUE AND DYNAMIC FORCE COEFFICIENTS OF AN AIR IN OIL (WET) ANNULAR SEAL: A CFD ANALYSIS ANCHORED TO TEST DATA Luis San Andrés Mast-Childs Chair Professor Fellow ASME Jing Yang Research Associate Xueliang Lu Research Assistant Turbomachinery Laboratory, Texas A&M University accepted for journal publication Funded by Turbomachinery Laboratory

A need: subsea pumping & compression Wet compression systems a must! Subsea Engineering or SURF Subsea Umbilicals Risers Flowlines High pressure & extreme temperature Cost efficient subsea factories must rely on multiple-phase flow compression and pump systems that reduce tieback systems and perform full flow separation on the sea floor. O&G price will increase! subsea production facilities will be more common (North Sea & Brazil  Gulf of Mexico  Artic) as extreme engineering will enable five year or longer reliability.

Background The need: 5% LVF in wet compressors and up to 90% GVF in pumps. Already known that seals operating under a wet gas or bubbly flow conditions do affect system rotordynamic stability [1-3]. Sound engineering requires to quantify the performance of annular seals under wet gas conditions! Computational Fluid Dynamics (CFD) Test Program and Field Operation Bulk-Flow Model (BFM)

Sparger (mixing) element A Wet Seal Test Rig GVF: gas volume fraction Ps: pressure at inlet plane Pa: ambient pressure= 1 bar(a) Qg: gas flow rate at Ps Ql: liquid flow rate Air Inlet Oil Inlet (ISO VG 10) Sparger (mixing) element GVF at inlet: Supply pressure (Ps) 1.0~3.5 bar Oil ISO VG 10 density(ρl) 830 kg/m3 viscosity (μl) at 34 ºC 10.6 cP Air density (ρg) at 1bar 1.1 kg/m3 viscosity(μg) at 20 ºC 0.02 cP Test seal section journal speed: 3.5 krpm (23.3 m/s)

A Wet Smooth Surface Annular Seal Geometry Rotor diameter D = 2R 127 mm Seal length L 46 mm Clearance Cr 0.203 mm Operation at Inlet pressure PS = 2.5 bar(a) Outlet pressure Pa = 1 bar(a) Shaft speed 3.5 krpm (23 m/s) Inlet pre-swirl Test Data [4] For inlet GVF = 0.9, leakage decreases by 25% and drag power reduces by 85% when compared to flow/power for oil seal. Wet seal force coefficients are frequency dependent and GVF dependent. Test seal shows self-excited acoustic resonance at ~12 Hz (SSV). [4] San Andrés, L., and Lu, X., 2018, “Leakage, Drag Power and Rotordynamic Force Coefficients of an Air in Oil (Wet) Annular Seal,” ASME J. Eng. Gas Turbine Power, 140.

Most important findings for Wet Seal [4] San Andrés, L., and Lu, X., 2018, “Leakage, Drag Power and Rotordynamic Force Coefficients of an Air in Oil (Wet) Annular Seal,” ASME J. Eng. Gas Turbine Power, 140. BEST PAPER AWARD. Paper GT2017-63254 GVF > 0  centering stiffness increases with gas content and hardens with frequency. Leakage decreases with GVF but data collapses into one curve for all pressures and shaft speeds.

Work at the Turbomachinery Laboratory Funded by O&G end users since 2010, two-phase seal flow research at the TurboLab has delivered abundant experimental results applicable to wet compressors and multiple-phase pumps (Childs et al., Morrison et al., San Andres et al.). The unique test programs resolve and anticipate needs of turbomachinery manufacturers and end users.

Contents The aim of this paper To complement experimental work by revealing flow field structures in multiple-phase flow seals through Computational Fluid Dynamics (CFD) and to validate/update engineering (BFM) predictive tools. Contents CFD Setup and Mesh 2D CFD Predictions vs. Test Data CFD Predicted Force Coefficients vs. Test Data A Mystery Unveiled: Stiffness Hardening Effect

CFD Approach and Mesh 3D mesh (node # 1.7 Million) Ansys-Fluent® hosted by TAMU HPRC Multi-phase model Eulerian-Eulerian model Drag model Schiller and Naumann Air in mixture Ideal gas Bubble size 1×10-6 m Laminar flow for oil and mixtures 3D mesh (node # 1.7 Million) Upstream & downstream plenum sections not needed in a laminar flow seal.

CFD vs Tests Static condition(steady flow)

Seal Leakage: CFD vs Tests vs BFM DP = 1.5 bar, rotor speed 3.5 krpm, inlet GVF = 0~1 Fluid GMF Test [g/s] CFD [g/s] BFM Pure oil - 68.0 70.1 70.8 Air in oil   GVF = 0.2 0.0008 66.7 66.9 67.1 GVF = 0.4 0.002 65.0 66.0 64.7 GVF = 0.6 0.005 62.6 64.1 62.0 GVF = 0.8 0.01 55.6 60.3 57.2 GVF = 0.9 0.03 50.0 54.4 52.1 Pure air 23.4 24.5 GMF: mass volume fraction. BFM: mixture bulk flow model [5]. GVF CFD and mixture-BFM leakage reproduce test data [4]. GMF is small (~0.03) even for GVF = 0.9.

CFD Pressure vs. axial length P/Ps Reynolds numbers at inlet For air in oil mixture Rossby # Axial Circ. All GVFs Rea Rec Ro# Oil 17 185 0.09 Air in oil GVF = 0.2 20 0.1 GVF = 0.4 26 GVF = 0.6 38 0.2 GVF = 0.8 71 186 0.4 GVF = 0.9 127 188 0.7 Air 3,278 373 9 Pressure drops linearly  laminar flow. No inlet pressure loss  null direct static stiffness. Flow transitions: circ. > axial at low GVF  axial > circ. as GVF grows.

Drag Power Loss P : CFD vs Test P = TD ·Ω TD: Drag torque. W: rotor speed. Pl : power for oil seal. P : power bubbly seal. CFD: Pl = 538 W Test: Pl = 555 W P/Pl P = (1-GVF) Pl (R2 = 0.99) GVF Drag power decreases linearly with gas content  P ~ (1-GVF) Pl since flow is laminar. CFD drag power agrees with test data.

2D CFD: GVF vs axial length & across clearance At exit plane (z=L): GVF increases as pressure drops. CFD GVF verifies simple formula. For small GVF: thin layer (~ 5% Cr) with GVF > 0.8 near rotor surface  (denser) oil is thrown away from rotor surface (Ro# < 1).

2D CFD: axial velocity W vs length & across gap Same speed for oil & air  homogeneous flow! Increase of GVF  larger axial speed, fastest at the seal exit (since mixture density decreases).

2D CFD: mean circ velocity U vs axial length a=U/(WR) GVF Swirl at inlet =0 For low GVF, (mainly) oil quickly reaches ½ surface speed (a=0.5) near seal inlet  Slow Stokes flow. As air content increases, GVF  1, circumferential speed U takes longer to develop towards a=0.5  Axial flow dominates.

CFD vs Tests Dynamic Force Coefficients

Derivation of Seal Force Coefficients 3D CFD unsteady flow solver Multi-frequency, elliptic orbit method [6] Displacements dx(t), dy(t)) Periodic flow solution: Force (Fx(t), Fy(t)) Fourier Series Decomposition a = Cr /N, b = ½ a Frequency domain: (dx(ω), dy(ω)) and (Fx(ω), Fy(ω)) Seal complex dynamic stiffness: Direct: H=HR + i HI Quadrature: h=hR + i hI HI~ w C  Direct damping C

Force Coefficients for Oil Seal (GVF=0) [7]   Test CFD BFM Analytical K [N/m] - -0.25 -0.14 k [MN/m] 3.8 4.6 4.3 4.5 C [kN-s/m] 20 25.4 23.8 23.4 M [kg] 5.5 7.0 6.3 WFR=k/CΩ 0.52 0.49 0.50 Rotor diameter D 127 mm Seal length L 46 mm Clearance Cr 0.203 mm CFD and BFM validate analytical solution. The gap between CFD, BFM and test data maybe due to inaccurate estimation of clearance (~8% higher will deliver test C, k).

Direct Dynamic Stiffness for Wet Seal DP = 1.5 bar, surface speed=23 m/s, inlet GVF = 0  0.9 [4] CFD HR at 80Hz GVF HR > 0 Centering stiffness > 0 for GVF>0.2  a strong hardening effect. Test stiffness shows peak magnitude at GVF = 0.4, different from CFD and BFM predictions (max. at GVF = 0.2).

Cross-coupled Dynamic Stiffness for Wet Seal DP = 1.5 bar, surface speed=23 m/s, inlet GVF = 0  0.9 Symbol: CFD Line: BFM Test Data [4] BFM prediction a little lower than CFD result. Test stiffness decreases with frequency (ω/Ω <1) and then increases. Not seen in CFD or BFM predictions. CFD hR at 80Hz GVF hR

Direct Damping for Wet Seal DP = 1.5 bar, surface speed=23 m/s, inlet GVF = 0  0.9 [4] BFM < CFD prediction. As GFV increases, direct damping decreases steadily. CFD damping matches well test data for inlet GVF > 0.6. CFD C at 80Hz GVF C~CL (1-GVF)

Effective Damping for Seal Ceff = (C - hR/ω) DP = 1.5 bar, surface speed=23 m/s, inlet GVF = 0  0.9 [4] CFD Ceff at 80Hz GVF Ceff =CL-eff (1-GVF) Effective damping decreases linearly with an increase in gas content. Cross-over frequency is ~ ½ X for oil seal & decreases as GVF grows.

Often large vertical turbines/pumps show SSV (actually a resonance) A common practice is to inject air into the band seal to reduce amplitude of motions.

BFM direct dynamic stiffness Stiffness Hardening Effect A small gas content in an oil stream produces a significant change in direct dynamic stiffness. Hardening exacerbated by excitation frequency. BFM direct dynamic stiffness Air injection increases seal centering stiffness & promotes static stability  An industrial practice explained!

Rationale for Stiffness Hardening Effect DP = 1.5 bar, surface speed=23.3 m/s, inlet GVF = 0  0.9 Sound speed Sound speed ratio a/al Oil κ: bulk modulus ag/al = 0.24 GVF = 1 = 1470 m/s Path of GVF Inlet  Outlet Air γ: gas capacity ratio; R: specific gas constant =353 m/s Air in oil mixture [8] Mixture density A GVF as low as 0.10, produces a 97% drop in sound speed (a = 0.03 al). From seal inlet towards outlet, the mixture sound speed drops while its axial velocity increases. Stiffness hardens due to the quick drop in sound speed brought by a small amount of gas.

GT2018-77140 CONCLUSION ON THE LEAKAGE, TORQUE AND DYNAMIC FORCE COEFFICIENTS OF AN AIR IN OIL (WET) ANNULAR SEAL: A CFD ANALYSIS ANCHORED TO TEST DATA

Conclusion GT2018-77140 CFD predictions (leakage, power loss) agree with test data, and also produce high fidelity flow field variables, including pressure, speeds, and GVF. Operation with a low GVF (< 0.4) produces a significant hardening effect which makes positive the direct stiffness. Test data shows same rapid stiffness increase as GVF 0.2. Stiffness hardening effect is due to the dramatic reduction in sound speed brought by a small amount of gas (fluid becomes more compressible). The combination of test results and CFD and BFM analyses furthers the engineering of seals for wet gas compressors and bubbly liquids in multiple phase pumps.

Questions (?) Acknowledgments Paper GT2018- 77140 Thanks Turbomachinery Laboratory and TAMU High Performance Research Computing (TAMU HPRC) Questions (?) Learn more at http://rotorlab.tamu.edu

References [1] Brenne, L., Bjorge, T., and Gilarranz, J., 2005, “Performance Evaluation of a Centrifugal Compressor Operating under Wet Gas Conditions,” Proc. 34th Turbomachinery Symposium, Houston, TX, September 12-15. [2] Ransom, D., Podesta, L., Camatti, M., Wilcox, M., Bertoneri M., and Bigi, M., 2011, “Mechanical Performance of a Two Stage Centrifugal Compressor under Wet Gas Conditions,” Proc. 40th Turbomachinery Symposium, Houston, TX, September 12-15. [3] Vannini, G, Bertoneri, M., Del Vescovo, G., Wilcox, M., 2014, “Centrifugal Compressor Rotordynamics in Wet Gas Conditions,” Proc. 43rd Turbomachinery Symposium, Houston, TX, September 12-15, pp. 201-220. [4] San Andrés, L., and Lu, X., 2018, “Leakage, Drag Power and Rotordynamic Force Coefficients of an Air in Oil (Wet) Annular Seal,” ASME J. Eng. Gas Turbine Power, 140(1), p. 012505. [5] San Andrés, L., 2012, “Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals,” ASME J. Eng. Gas Turbine Power, 134(2), p. 022503. [6] Li, Z., Li, J., and Feng, Z., 2016, “Comparisons of Rotordynamic Characteristics Predictions for Annular Gas Seals Using the Transient Computational Fluid Dynamic Method Based on Different Single-Frequency and Multi-frequency Rotor Whirling Models ,” J. Tribol., 138(1), p. 011701. [7] San Andrés, L., 2010, Modern Lubrication Theory, “Annular Pressure (Damper) Seals”, Notes 12(a), Texas A&M University Digital Libraries, http://oaktrust.library.tamu.edu/handle/1969.1/93197. [Access Oct. 21, 2017] [8] Andrews, M. J., and O’Rourke, P. J., 1996, “The Multiphase Particle-in-Cell (MP-PIC) Method for Dense Particulate Flows,” Int. J. Multiphase Flow, 22(2), pp. 379–402.

Rotor Whirl Motions with Multi-Frequency Method introduced by Li et al. X Y a = 1.5 μm  Xmax ~ 10%Cr b = 1 μm  Ymax ~ 5%Cr ωi = 20- 280 Hz (14 frequencies, 10 Hz apart) ωi /Ω = 0.12 – 1.68 Input: rotor displacements (X,Y)  output: seal reaction force

Seal Force Components Periodic reaction force fx and fy with multi-frequency ωi x : radial direction y : tangential direction One period of multiple frequency

Force Coefficients Identification Time Domain Fourier Series (K, k) and (C, c) : stiffness and damping force coefficients. Frequency Domain At each frequency (wj): 𝑥 𝑗 =𝑎;  𝑦 𝑗 =𝑏

+ + Mesh Deformation Method Y X Rotor whirl Speed ω Rotor Speed Ω Rotor displaces with distinct specified X, Y  One transient response over a full period (T) delivers seal forces, fr and ft , on rotor surface. Rotor whirl Speed ω + X + Rotor Speed Ω The rotor motion creates a periodic force on the rotor surface.

CFD Settings Gas Model: Ideal CFD Package: ANSYS Fluent ® hosted by TAMU High Performance Computing Center Energy Equation: Fluent® default with adiabatic walls