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Dynamic Behavior and Response Analysis of Fluid/Tank Systems

Dynamic Behavior and Response Analysis of Fluid/Tank Systems. He Liu, Ph.D., P.E. University Alaska Anchorage Daniel H. Schubert, P.E. Dept. of Environmental Health & Engineering ANTHC.

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Dynamic Behavior and Response Analysis of Fluid/Tank Systems

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  1. Dynamic Behavior and Response Analysis of Fluid/Tank Systems He Liu, Ph.D., P.E. University Alaska Anchorage Daniel H. Schubert, P.E. Dept. of Environmental Health & Engineering ANTHC

  2. Tanks Rupture: A water tank was lifted off a gravel base six to ten inches during an earthquake. After the earthquake, the tank was resting on the gravel base about 12 inches lower (due to buckle) and shifted about an inch to the west.

  3. Courtesy U.C. Berkley

  4. Courtesy U.C. Berkley

  5. Courtesy U.C. Berkley

  6. Courtesy U.C. Berkley

  7. Tank seismic Design Code is mainly based onsimplifiedRigid Tank assumption, and NO fluid/structure interactionincluded • Theoretical solutions are available only for rigidtanks and no interaction • Anapproximate “Cantilever Beam” approach needs numerical proof.

  8. The Approximate“Cantilever-Beam” Approach • For approximate frequencies can be calculated by equation • f’0is the natural frequency of the fluid tank system with roof mass • fo is the natural frequency without the roof • fFB and fSB is the natural frequency of an empty tank with the mass of the roof

  9. Purposes of This Study Use the Finite Element Analysis(FEA) • To evaluate the performance of steel water tanks due to earthquake excitation • To compare results with Design Code of AWWA’s simplified formula’s • To verify the approximate “Cantilever-Beam”approach.

  10. z x y r x R Tank Geometry water level Ht H tb Radius =16 feet Height = 26 feet Water Depth = 24 feet Wall Thickness =0.315in  =0o ts

  11. Modeling Approach I -Tank • Tank wall/roof/base • - shell and beam elements • Fluid • - Fluid 3-D Contained FluidElement • Material Properties - Steel E = 29,000 ksi - Steel density = 7.34x104 lb-sec2/in4 - Fluid density = 0.9345x104 lb-sec2/in4 - Fluid bulk modulus = 30x104 lb/in2

  12. Modeling Approach II - 3-D Contained Fluid Elements • 8 nodes - 3 DOF • Free surface - added spring • Bulk modulus = 30 x 104 lb/in2 • Fluid elements do not attached at tank wall and base • Coincident nodes coupled normal to the interface to allow fluid relative movement in tangential and vertical directions • Free horizontal movement at base

  13. Modeling Approach III - Meshing FEA Models • Because of the system symmetry, one half of the tank is modeled. • Fluid elements are rectangular-brick shaped whenever possible • Number of Fluid Elements in ANSYS Model: - 640, 1280, 2112, 3072 - Based on accuracy and efficiency, 1280 fluid elements was chosen

  14. partially filled with a near incompressible water • water-contained fluid elements • tank--shell and beam elements • interaction between water and tank wall is included

  15. How to verify the numerical solution fromANSYS FEA models?

  16. ANSYS Rigid Tanks Theory Rigid Tanks Yes ANSYS Flexible Tanks Approximate Flexible Tanks Comparison & Conclusion AWWA Simplified “Rigid” Tank Method ANSYS Unanchored

  17. 1st Natural Mode Shape – Water Sloshing One-Cosine Type Sloshing Mode

  18. 2nd Natural Mode Shape – Water Sloshing Two-Cosine Type Sloshing Mode

  19. 3rd Natural Mode Shape – Water Sloshing Three-Cosine Type Sloshing Mode

  20. 4th Natural Mode Shape – Water Sloshing Four-Cosine Type Sloshing Mode

  21. Modal Analysis Results: Comparison of Convective Frequencies No. of Fluid Elements in ANSYSModel Theory (Units: Hz) 640 1280 2112 3072 1st mode 0.299 0.298 0.298 0.298 0.305 2nd mode 0.477 0.476 0.475 0.474 0.521 3rd mode 0.562 0.555 0.552 0.551 0.660 Note: Compared with results of linear theory, the first mode differs by 1.7%. Differences may be related to limitations on the linear theory, with nonlinear theory closer to FEA values.

  22. For RigidTanks ANSYSResults Modeling approach is acceptable TheoreticalResults FlexibleTank Analysis

  23. Modal Analysis for Flexible Tanks • A total of 54 geometric variations, with and without roofs, were analyzed. • Tank/fluid variables were represented by three basic parameters: • Tank geometric aspect ratios, as represented by the tank height to radius (H/R) • Tank shell wall thickness ratio represented by the wall thickness to tank radius (ts/R) • Liquid depth ratio(h/R)

  24. 1st Natural Mode Shape – Full Tank

  25. 2nd Natural Mode Shape – Full Tank

  26. 3rd Natural Mode Shape – Full Tank

  27. 1st Natural Mode Shape - Partially Full Tank

  28. 2nd Natural Mode Shape – Partially Full Tank

  29. 3rd Natural Mode Shape – Partially Full Tank

  30. 1st Natural Mode Shape – Tall-Full Tank

  31. 1st Natural Mode Shape – Short-Full Tank

  32. 1st Natural Mode Shape – Tall-Partial-Full Tank

  33. 2nd Natural Mode Shape – Tall-Partial-Full Tank

  34. Modal Frequency Comparison

  35. Modal Frequency Comparison

  36. Modal Frequency Comparison

  37. Modal Frequency Comparison

  38. Modal Frequency Comparison

  39. Modal Frequency Comparison

  40. For FlexibleTanks Approximate“Cantilever-Beam”Results Acceptable ANSYSResults

  41. Earthquake Response Analyses (ANSYS Results)

  42. Earthquake Ground Input: El Centro N-S Adjusted 0.4g • Acceleration • Velocity • Displacement

  43. Pressure Time History (3 ft. from Base)

  44. Pressure distribution along wall at  = 0o and T=3.21 Sec.

  45. Compare with RigidTanksolutions: Pressure distribution along wall at  = 0o

  46. Courtesy U.C. Berkley

  47. Stress Time History Results • Hoop and Axial Stress Z=-21 ft at  = 0o • Hoop and Axial Stress Z=-21 ft at  = 180o

  48. Water Surface Displacement Time History  =180o  =0o

  49. Water Surface Profile at Time=5.09sec. (Maximum Water Surface Displacement = 33 inches)

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