Evaluation of Cavitation in Hydraulic Turbomachinery Using STAR-CCM+

Transcription

1 Evaluation of Cavitation in Hydraulic Turbomachinery Using STAR-CCM+ Dr. Edward M. Bennett Vice President of Fluids Engineering Mechanical Solutions, Inc. Whippany, NJ07981 USA 7 March, Apollo Drive, Whippany, New Jersey Tel: (973) Fax: (973) Website:

2 The Company Mechanical Solutions, Incorporated (MSI) is an Engineering firm headquartered in Whippany, New Jersey USA. MSI specializes in fluid machinery design, fluid dynamic analysis, and mechanical engineering design and analysis. Further information regarding MSI can be found at

3 AGENDA Introduction to the challenges of cavitation in hydraulic turbomachinery Benefits of STAR-CCM+ in addressing cavitating CFD analyses Cavitation examples Double suction pump Dissolved gas in an axial pump Cavitation instabilities in an axial inducer Cavitation erosion prediction in a Francis turbine Conclusions

4 Cavitation Definition Cavitation is the formation and disappearance of bubbles caused by the change in pressure in the fluid domain. It is a thermodynamic non-reversible process Bramanti(2005)

5 Cavitation in Hydraulic Turbomachinery Cavitation in turbomachinery is often characterized by two variables Net Positive Suction Head NPSH = (P t1 Pva por ) ρg Cavitation Number σ = (P t1 P vapor ), where 1 2 ρ l U 1 P t1 is inlet or exit total pressure P vapor is vapor pressure of fluid at a given temperature ρ is the density of the liquid(subscript l is for liquid) U 1 is the rotational velocity 2

6 Negative Effects of Cavitation in Hydraulic Machinery Performance, Capacity and Range Vibration and Noise Dissolved or Entrained Gas in Fluid Cavitation Instabilities Cavitation Surge Alternate Blade Cavitation Rotating Cavitation Stall Auto-Oscillation Erosion and Corrosion Rotordynamic Instabilities

7 Performance, Capacity and Range Visser(2005)

8 Dissolved or Entrained Gas in Fluid Some fluids have dissolved gas or entrained gas embodied in the liquids. The gaseous cavitation that occurs when the gas comes out of solution, due to low pressure can have a negative impact on performance, in addition to the negative effects of vapor cavitation. Wood et al(1998)

9 Cavitation Instabilities Cavitation is inherently unstable and unsteady. As the formation grows, unstable effects, such as stall and auto-oscillation can have a profound impact on the operation and mechanical integrity of hydraulic turbomachinery Bramanti(2005)

10 Erosion and Corrosion The collapse of bubbles on a surface can create damage, eroding and corroding the metals in the stationary and rotating components. Visser(2005)

11 Benefits of STAR-CCM+ STAR-CCM+ has the necessary features to analyze the most complex cavitating flows in hydraulic turbomachinery Advanced geometry modeling and CAD capture Sophisticated unstructured meshing to fully resolve cavitating regions with detailed accuracy. Relevant physical models to capture advanced flow physics Unsteady CFD model Unsteady cavitation model Advanced turbulence models Advanced multiphase models to capture dissolved gas and gas entrainment Post-processing tools that facilitate flow diagnosis and optimization Animation tools to facilitate diagnosis of cavitation instabilities

12 Case Studies Double Suction Pump Dissolved Gas in Axial Pump Cavitation Instabilities in Axial Inducer Erosion in Francis Turbine

13 Double-Suction Pump

14 Double Suction Pump A complex centrifugal pump designed to enhance cavitation performance Flow Physics Complex, transient flow through 360 degrees Stationary and rotating domains Unsteady cavitation Relevant STAR-CCM+ features to facilitate a solution Unsteady flow solver Unsteady cavitation model Unsteady stationary/rotating interfaces Advanced unstructured CFD meshing from CAD geometry Parallel capability for large size and economical time to solution

15 Flowpath Geometry Suction Inlet Volute Impeller

16 Mesh in STAR-CCM+ Note: Single-vane mesh for impeller was cyclically patterned and fused to ensure mesh uniformity.

17 STAR-CCM+ Mesh Statistics Region Vertex Count Cell Count Suction 4,898,638 1,459,107 Impeller 6,945,706 2,639,844 Volute 2,929, ,935 TOTAL 14,774,181 5,010,886

18 STAR-CCM+ Model Setup SST k-ω turbulence model Segregated flow solver 2 nd -order convection scheme Multi-phase Volume of Fluid (VOF) model Rayleigh-Plesset cavitation model Boundary conditions: - Inlet total pressure via pressure reference point - Rotating speed on Impeller region - Inlet and exit mass flow Transient timestep set to match 360 steps per revolution 20 inner iterations per timestep Simulation ran until residual plots and monitor value plots (such as pressure, torque and mass flow) were judged to have settled

19 Velocity Flowfield

20 Pressure Contours

21 Streamlines

22 Vapor Fraction Contours Inlet Total Pressure 175 kpa Inlet Total Pressure 80 kpa Inlet Total Pressure 40 kpa Inlet Total Pressure 27 kpa

23 Comparison of Cavitation Breakdown Curves

24 Comparison of Cavitation Breakdown Curves

25 Comparison of Cavitation Breakdown Curves

26 Flow Animations Flow animations can be an invaluable tool in assessing cavitating flows in pumps. Flow symmetry can be determined qualitatively as well as quantitatively. Cavitation can be observed in other components than the impeller, such as the radial inlet, or diffuser passage. STAR-CCM+ provides post-processing that facilitate excellent flow animations.

27 Cavitation Animation

28 Cavitation Animation

29 Low NPSHr Axial Pump with Dissolved Gas An axial pump was designed for an industrial application. The pump had to operate with a low Net Positive Suction Head (NPSH) The pump satisfied the requirements, but did not have the NPSHr margin predicted. An investigation was conducted to determine the source of the variance.

30 Axial Pump Flowpath Geometry Outlet Pipe Impeller Elbow Inlet Pipe

31 Axial Pump Mesh

32 Mesh Statistics Domain Vertex Count Cell Count INLET PIPE 38,564 13,776 IMPELLER 4,437,083 1,518,888 ELBOW 371, ,099 OUTLET PIPE 24,366 18,120 TOTAL 4,871,022 1,668,883

33 CFD Model Setup Realizable k-ε turbulence model Segregated flow solver with 2 nd -order convection scheme VOF multiphase model with Rayleigh-Plesset cavitation model Water and water vapor at 68 F as working fluids Boundary conditions: - Stagnation inlet - Rotating speed on Impeller region - Exit mass flow Transient timestep set to match 360 steps per revolution 20 iterations per step Simulation ran until residual plots and monitor value plots (such as pressure, torque and mass flow) were judged to have settled

34 Axial Pump Streamlines

35 Axial Pump Cavitation

36 Axial Pump Animation Vortex Rope

37 Predicted Cavitation Breakdown Curves

38 Inclusion of Dissolved Gas Customer testing demonstrated cavitation breakdown was greater than the predicted value. The water used for the test was left alone in a tank for several days to eliminate entrained air; however, the water was not deaerated for the test Air dissolved in water was hypothesized as a potential source of variance between the test and the CFD, which considered no dissolved air in the solution. Dissolved gas model added to CFD setup Based on Henry s Law Water replaced with mixture of water and air (1.2%) Water vapor replaced with mixture of vapor and air Model was rerun at 100% flow with previous boundary conditions

39 Axial Pump Cavitation with Dissolved Gas

40 Cavitation Breakdown Curves with Dissolved Gas Inclusion of dissolved air causes pump to have a greater NPSHr, within 2% of test results.

41 Axial Inducer with Cavitation Instabilities Axial inducers are used to boost pressure and improve cavitation performance They are used in the following applications. High energy pumps Rocket turbopumps LNG pumps Fire suppression pumps

42 Axial Inducer Axial inducers are used in rocket turbopumps and high energy density industrial pumps Inducers act as boost pumps to the main head producing impeller. They can operate at higher cavitation levels since their power level is only a fraction of the main impeller. The large axial inlet facilitates lower velocities at the throat and can swallow more cavitating vapor Cavitating Inducer (Brennen(1994)

43 Axial Inducer Test Case Test inducer described in Bennett(2009) serves as test case Test case based upon NASA FASTRAC LOX inducer Test geometry developed using CFturbo design software

44 Inducer Test Geometry Inlet Volute Inducer Bladeless Impeller Passage

45 Inducer Mesh Single-vane sector mesh for inducer was patterned and fused to ensure mesh uniformity

46 Mesh Statistics Domain Cells Faces Vertexes Inlet 122, , ,844 Inducer 1,250,682 5,806,662 3,763,724 Impeller 129, , ,244 Volute 84, , ,411 TOTAL 1,587,276 7,174,848 4,566,223

47 Inducer CFD Model Setup SST k-ω turbulence model (with curvature correction) Segregated flow solver (2 nd order) Volume of Fluid (VOF) multiphase model (2 nd order) Water and vapor as constant-density fluids at K - Saturation pressure of Pa Boundary conditions: - Stagnation inlet at 1000 kpa (Sequentially lowered) rpm rotating speed - Outlet mass flow rate corresponding to m 3 /s Transient timestep of 3.333e-5 s (360 per revolution) 1e-4 limit for residual convergence of inner iterations Simulation ran until and monitor value plots (such as pressure, torque and mass flow) were judged to have settled

48 Inducer Performance Summary Suction Specific Speed NPSHa [m] Inlet Total Pressure [kpa] Outlet Total Pressure [kpa] Inducer Head [m] Inducer Torque [N-m] Inducer Efficiency % % % % % % % % All results were averaged over several revolutions (as many as 27 for highly-cavitating cases)

49 Inducer NPSH Breakdown Curve

50 Inducer Cavitation 20 kpa inlet total pressure 0.3 vapor fraction isosurface

51 Inducer Pressure Probe Locations

52 Inducer Probe Traces

53 Inducer Probe FFT Analysis Multiples of Vane Pass 0.26Ω, potential auto-oscillation

54 Typical Pump Cavitation Instability Frequencies Bramanti(2005)

55 Animation of Inducer at Inlet Pressure = 20 kpa

56 Animation of Inducer at Inlet Pressure = 12 kpa

57 Cavitation in Francis Turbine

58 Cavitation in Francis Turbine Erosion takes place when vapor bubbles collapse near a wall Quantitative analysis is difficult because erosion is a slow process, so a qualitative approach is preferable Several functions can be evaluated and plotted on the walls to calibrate against experimental data (if available) Vapor bubble radius Rate of change of vapor bubble radius Rate of change of vapor bubble volume Second derivative of vapor bubble volume with respect to time

59 Rate of Change of Bubble Radius The general Rayleigh-Plesset equation is: p vapor p local ρ liquid = R d2 R dt dr dt 2 + 4ν liquid R dr dt + 2σ ρ liquid R The single-component bubble growth rate can be estimated using the inertia-controlled growth model, which discounts viscous and surface tension effects. Therefore: dr dt = sign(p vapor p local ) 2 3 p vapor p local ρ liquid Erosion rate could be proportional to rate of bubble collapse.

60 Rate of Change of Bubble Radius

61 Rate of Change of Bubble Volume The seed-based cavitation model proposes the following volume relation between vapor and liquid phases: V vapor = n 0 V liquid 4 3 πr3, where n 0 is the seed density, or the number of bubbles per unit volume. It also states that: α vapor = V vapor V total = V vapor V vapor + V liquid = n 0 V liquid 4 3 πr3 n 0 V liquid 4 3 πr3 + V liquid = n πr3 n πr3 + 1 Therefore: R = α vapor n π(1 α vapor) 1 3

62 Rate of Change of Bubble Volume The rate of change of bubble volume is then: dv vapor dt = n 0 (1 α vapor )4πR 2 dr dt at which point one can plug in the above equations for R and dr dt. dv vapor dt = n 0 1 α vapor 4π α vapor n π 1 α vapor 2 3 sign(p vapor p local ) 2 3 p vapor p local ρ liquid

63 Rate of Change of Bubble Volume

64 Second derivative of bubble volume with respect to time Presume that erosion is proportional to d2 V dt 2. From the equation for bubble volume, it follows that: d 2 V dt 2 = d2 R 4πR2 dt 2 + 8πR dr dt 2 To simplify, one can dismiss the d2 R dr dt2 term, since is only a function of dt pressure, which is not changing in a quasi-steady flow. Therefore: d 2 V vapor dt 2 8πR dr dt at which point one can again plug in the equations for R and dr dt. 2

65 Second derivative of bubble volume with respect to time

66 Cavitation Erosion Summary

67 Quantitative Runner Erosion Prediction Visser(2005) Method involves the use of surface cavity length, fluid and metal properties, and basic hydraulic properties of the runner flow domain

68 Quantitative Runner Erosion Prediction Typical MSI Erosion Rate Spreadsheet

69 CONCLUSIONS STAR-CCM+ is an extremely valuable tool for analyzing the flow through hydraulic turbomachinery The unsteady cavitation model has been successful in resolving the various forms of cavitation that are specific to hydraulic turbomachinery

70 Acknowledgment Mechanical Solutions is grateful for the ongoing support and technical service provided by CD-adapco.

71 References 1. Bennett, E., Advanced Methodology for Low NPSH Axial Pump Inducers, ASME Fluids Engineering Division Summer Meeting, Bramanti, C., Experimental Study of Cavitation and Flow Instabilities in Space Rocket Turbopumps and Hydrofoils, University of Pisa Doctoral Dissertation, Wood, D., et al, Application Guidelines for Pumping Liquids That Have a Large Dissolved Gas Content, 15 th Texas A&M Pump Symposium, Visser, F., Cavitation in Centrifugal Pumps and Prediction Thereof, Tutorial, 2005 ASME Fluids Engineering Division Summer Conference, 2005.