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Density Models

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Book cover Recent Advances in Hydraulic Physical Modelling

Part of the book series: NATO ASI Series ((NSSE,volume 165))

Abstract

The term “density model” is defined here as a model of fluid motions in a gravitational field in which the variations of density within the field originate or influence the flow field. Strictly speaking»this applies to all free surface fluid motions, but in this case the emphasis is on motions involving fluid masses of the same state, and with relatively small density differences, (Δρ/ρ<<1). The term “stratified flow” is often used to designate the flow. Most of the cases of interest involve density differences (Δρ/ρ) of the order of 10-2 or less, although some cases, such as tailings plumes, oil slicks, and gas releases can involve Δρ/ρ>10-1.

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References

  1. Abraham G: Jet Diffusion in Stagnant Ambient Fluid. Delft Hydraulics Xab., Publ. No. 29, 1963.

    Google Scholar 

  2. Ackers P and Jaffrey L.J: The Applicability of Hydraulic Models to Pollution Studies. Proc. of Symposium on Mathematical and Estuarine Pollution”, Stevenage, UK 1972.

    Google Scholar 

  3. Ackers P: Modelling of Heated Water Discharges. Ch. 6, Engineering Aspects of Thermal Pollution, Parker and Krenkel (Ed.), Vanderbilt University Press, 1969.

    Google Scholar 

  4. Adams EE: Discussion of Reynolds Number Effects on Buoyant Surface Jets. ASCE, Journal of Hydraulic Engineering, Vol. III, No. 8, August 1985.

    Google Scholar 

  5. Adams EE and Cosier DJ: Density Exchange Flow Through a Slotted Curtain. Submitted to ASCE, Journal of Hydraulic Engineering, 1987.

    Google Scholar 

  6. Akiyama J and Stefan HG: Onset of Underflow in Slightly Diverging Channels. ASCE, Journal of Hydraulic Engineering, Vol. 113, No. 7, July 1987.

    Google Scholar 

  7. Babcock J, Ryan PJ, Tu SW and Wyman V: Diablo Canyon Project, University of California at Berkeley, Physical Model Study Quality Assurance Requirements. Pacific Gas and Electric Company, Department of Engineering Research, Report No. 420-DC-87.17, May, 1987.

    Google Scholar 

  8. Barr DIH: Densimetrie Exchange Flow in Rectangular Channels. Part 1: Definitions, Review, and Relevance to Model Design; Part II: Some Observations of the Structure of Lock Exchange Flow. La Houille Blanche 18(7): 739-766, 1963.

    Article  Google Scholar 

  9. Barr DIH: Part III, Large-Scale Experiments. La Houille Blanche 22(6): 619-632, 1967.

    Article  MathSciNet  Google Scholar 

  10. Bata GL: Recirculation of Cooling Water in Rivers and Canals. J. of Hydraulic Div., ASCE, Vol. 83, No. HY3, June 1957.

    Google Scholar 

  11. Britter RE and Linden PE: The Motion of a Front of a Gravity Current Travelling Down an Incline. Journal of Fluid Mechanics, Vol. 99, Part 3, 1980.

    Google Scholar 

  12. Bugler III TW and Tatinclaux JC: Scale Effects on Cooling Tower Model Studies. IIHR Report No. 168, IIHR, Univ. of Iowa, September 1974.

    Google Scholar 

  13. Carter HH: A Preliminary Report on the Characteristics of a Heated Jet Discharged Horizontally into a Transverse Current: Part I, Constant Depth. Technical Report No. 61, Chesapeake Bay Institute, Johns Hopkins University, Baltimore, November 1969.

    Google Scholar 

  14. Carter HH, Schiemer EW and Regier R: The Buoyant Surface Jet Discharging Normal to an Ambient Flow of Various Depths. Technical Report No. 81, Chesapeake Bay Institute, Johns Hopkins University, Baltimore, 1973.

    Google Scholar 

  15. Craya A: Theoretical Research on the Flow of Non-homogeneous Fluids. La Houille Blanche, January-February, 1949 y pp. 44-55.

    Google Scholar 

  16. Elder RA and Dougherty GB: Thermal Density Underflow Diversion, Kingston Steam Plant. Proc. ASCE, Vol. 84, No. HY2, April 1958.

    Google Scholar 

  17. Ellison TH and Turner JS: Turbulent Entrainment in Stratified Flows. Journal of Fluid Mechanics, Vol. 6, Part 3, 1959.

    Google Scholar 

  18. Fan LN: Turbulent Buoyant Jets into Stratified or Flowing Ambient Fluids. W.M. Keck Laboratory for Hydraulics and Water Resources, California Institute of Technology, Report No. KH-R-15, 1967.

    Google Scholar 

  19. Fay JA: Physical Processes in the Spread of Oil on a Water Surface. Proc. of Joint Conf. on Prevention and Control of Oil Spills, Washington, June 1971.

    Google Scholar 

  20. Farrell GJ and Stefan HG: Buoyancy Induced Plunging Flow into Reservoirs and Coastal Regions. Prepared for NSF, Proj. Report No. 241, St. Anthony Falls Hydraulic Laboratory, July 1986.

    Google Scholar 

  21. Fietz TR and Wood I: Three Dimensional Density Current. ASCE, Journal of Hydraulics Division, Nov., 1967.

    Google Scholar 

  22. Fisher HB and Holley ER: Analysis of the Use of Distorted Hydraulic Models for Dispersion Studies. Water Resources Research, Vol. 2, 1971.

    Google Scholar 

  23. Fisher HB, List EJ, Koh RCY, Imberger J and Brooks NH: Mixing in Inland and Coastal Waters. Academic Press, 1979.

    Google Scholar 

  24. Frazer W, Barr DIH and Smith AA: A Hydraulic Model Study of Heat Dissipation at Longannet Power Station. Proc. of Institution of Engineers, 39, Jan. 1988.

    Google Scholar 

  25. Gariel P: Experimental Research on the Flow on Non-homogeneous Fluids, LaHouille Blanche, January-February, 1949, pp. 56-64.

    Google Scholar 

  26. Gelhar LW, Wilson JL, Miller JS and Hamrick JM: Density Induced Mixing in Confined Aquifers. Massachusetts Institute of Technology, Parsons Laboratory Report No. 145, March 1972.

    Google Scholar 

  27. Harleman DRF: Stratified Flow. Handbook of Fluid Dynamics, Section 26, McGraw-Hill Book Company, 1961.

    Google Scholar 

  28. Harleman DRF and Elder RA: Withdrawal from Two Layer Stratified Flows. Proc. ASCE, HY 4, Vol. 91, July 1965.

    Google Scholar 

  29. Harleman DRF and Stolzenbach KD: Fluid Mechanics of Heat Disposal from Power Generation. Annual Review of Fluid Mechanics, Vol. 4, 1972.

    Google Scholar 

  30. Helfrich KR and Melville WK: On Long Non-Linear Internal Waves Over Slope-Shelf Topography. Journal of Fluid Mechanics, Vol. 167, 1986.

    Google Scholar 

  31. Huber WC and Harleman DRF: Laboratory and Analytical Studies of Thermal Stratification of Reservoirs. Massachusetts Institute of Technology, Department of Civil Engineering, Hydrodynamics Laboratory Technical Report No. 112, 1968.

    Google Scholar 

  32. Huber WC, Harleman DRF and Ryan PJ: Prediction of Internal and Outlet Temperatures in Stratified Reservoirs. Journal of ASCE, Hydraulics Division, April 1972.

    Google Scholar 

  33. Isaacson MS, Koh RCY and Bradas NH: Plume Dilution for Diffusers with Multiport Risers. Journal of Hydraulic Engineering, Vol. 109, No. 2, February 1983.

    Google Scholar 

  34. Ismail NM and Wiegel RL: Opposing Wave Effect on Momentum Jets Spreading Rate. Journal of Waterways, Port, Coastal and Ocean Engineering, Vol. 109, No. 4, November 1983.

    Google Scholar 

  35. Jain SC and Kennedy JF: Development and Verification of Laboratory Model Techniques for Prediction of Near-Field Behavior of Cooling Tower Plumes. IIHR Limited Distribution Report No. 60, IIHR, University of Iowa, June 1978.

    Google Scholar 

  36. Jain SC and Kennedy JF: Near Field Model Study of Mine Tailings Discharge Into a Fjord. Prepared for United States Borax & Chemical Corporation by Institute of Hydraulic Research, University of Iowa, September 1984.

    Google Scholar 

  37. Jain SC and Nikitopoulous C: Negatively Buoyant Methane Jet into Flowing Ambient Air. IIHR Limited Distribution Report No. 52, IIHR, University of Iowa, November 1977.

    Google Scholar 

  38. Jirka GH and Harleman DRF: The Mechanics of Submerged Multiport Diffusers for Buoyant Discharges in Shallow Water. R.M. Parsons Laboratory for Water Resources and Hydrodynamics, Department of Civil Engineering, Massachusetts Institute of Technology, Technical Report No. 169, 1973.

    Google Scholar 

  39. Jirka GH, Abraham G and Harleman DRF: An Assessment of Techniques for Hydrothermal Prediction. Massachusetts Institute of Technology, Parsons Laboratory Report No. 203, July 1975.

    Google Scholar 

  40. Jirka GH, Johnson RP and Sargent FE: Radial Source-Sink Flow into a Stratified Ocean. ASCE, Journal of Hydraulic Engineering, HY 12, December 1981.

    Google Scholar 

  41. Johnson TR, Farrell GJ, Ellis CR and Stefan HG: Negatively Buoyant Flow in a Diverging Channel, Part I: Flow Regimes and Part II: Flow Field Descriptions. Journal of Hydraulic Engineering, Vol. 113, No. 6, June 1987.

    Google Scholar 

  42. Kennedy JF and Diplas P: Laboratory Investigation of the Design and Operation of Pine Point Mines Salting Pond. IIHR Limited Distribution Report No. 143, IIHR, University of Iowa, August 1987.

    Google Scholar 

  43. Keulegan GH: Interfacial Stability and Mixing in Stratified Flows. Journal of Research of the National Bureau of Standards, Vol. 43, 1949.

    Google Scholar 

  44. Keulegan GH: Laminar Flow at the Interface of Two Liquids. National Bur. Standards (U.S.), Circ. 32, 3, 1944.

    MathSciNet  Google Scholar 

  45. Koh RCY and Brooks NH: Fluid Mechanics of Waste Water Disposal in the Ocean. Annual Review of Fluid Mechanics, No. 7, 1975.

    Google Scholar 

  46. Kuhlman JM: Reynolds Number Effects on Buoyant Surface Jets. Journal of Hydraulic Engineering, ASCE, Vol. 110, No. 6, June 1984.

    Google Scholar 

  47. Lawrence GA: Steady Flow Over an Obstacle. Journal of Hydraulic Engineering, ASCE, Vol. 113, No. 8, August 1987.

    Google Scholar 

  48. List EJ: Turbulent Jets and Plumes. Annual Review of Fluid Mechanics, Vol. 14, 1982.

    Google Scholar 

  49. Meroney RN: Wind Tunnel Experiments on Dense Gas Dispersion. Journal of Hazardous Materials, Vol. 6, 1982.

    Google Scholar 

  50. Meroney RN and Lohmeyer A: Prediction of Propane Cloud Dispersion by a Wind-Tunnel-Data Calibrated Box Model. Journal of Hazardous Materials, Vol. 8, 1984.

    Google Scholar 

  51. Meroney RN: Validation of Fluid Modelling Techniques for Assessing Hazards of Dense Gas Cloud Dispersion. Journal of Hazardous Materials, Vol. 15, 1987.

    Google Scholar 

  52. Meroney RH: Guidelines for Fluid Modelling of Liquified Natural Gas Cloud Dispersion, Vol. I — Instruction Guide and Vol. II — Technical Support Document. Prepared for Gas Research Institute, Chicago, Illinois, May 1986.

    Google Scholar 

  53. Melville WK and Helfrich KR: Transcritical Two-Layer Flow Over Topography. J. Fluid Mechanics, Vol. 178, 1987.

    Google Scholar 

  54. Nielsen JH: The Three Dimensional Steady Spread of a Density Current Down on Inclined Plane. Basic Research Report No. 22, Hydraulic Laboratory, Tech. University of Denmark, 1971.

    Google Scholar 

  55. Novak P and Cabelka J: Models in Hydraulic Engineering. Pitman Advanced Publishing Program, 1981.

    Google Scholar 

  56. O’Brien MP and Chemo J: Model Law for Motion of Salt Water Through Fresh. Trans., ASCE 99:576-609, 1934.

    Google Scholar 

  57. Rawn AM, Bowerman FR and Brooks NH: Diffusers for Disposal of Sewage in Sea Water. Trans., ASCE, Vol. 126, Part III, 1961.

    Google Scholar 

  58. Rigter BP: Density Induced Return Currents in Outlet Channels. Proc. ASCE, HY2, February 1970.

    Google Scholar 

  59. Roberts PJW: Dispersion of Buoyant Wastewater Discharged from Outfall Diffusers of Finite Length. KH-R-35, W.M. Keck Laboratory, California Institute of Technology, Pasadena, March 1977.

    Google Scholar 

  60. Roberts PJW, Snyder WH and Baumgartner DJ: Submerged Wastefield Formation by Ocean Outfalls. Submitted to ASCE Journal of Hydraulic Engineering, 1987.

    Google Scholar 

  61. Ryan PJ and Harleman DRF: Prediction of Annual Cycle of Temperature Changes in a Stratified Reservoir: Mathematical Model and User’s Manual. Technical Report No. 137, Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, March 1971.

    Google Scholar 

  62. Ryan PJ and Harleman DRF: Analytical and Experimental Study of Transient Cooling Pond Behavior. Technical Report No. 161, Ralph M. Parsons Laboratory for Hydrodynamics and Water Resources, Massachusetts Institute of Technology, February 1973.

    Google Scholar 

  63. Ryan PJ, Leonard MS, Jain SC and Elder RA: Instantaneous and Time Averaged Bottom Temperatures Induced by an Ocean Outfall. Proceedings of 17th Congress of the International Association of Hydraulic Research, Vol. 3, August 1977.

    Google Scholar 

  64. Ryan PJ: Behavior of Sediment Laden Plumes on Steep Slopes. Proceedings of ASCE Water Forum 1986 Conference, Long Beach, CA, August 1986.

    Google Scholar 

  65. Ryan PJ, Tu SW, Ismail N and Wiegel RL: Verification of a Physical Model of a Coastal Discharge. Proceedings of the National Conference in Hydraulic Engineering, Williamsburg, VA, August 1987.

    Google Scholar 

  66. Ryan PJ, Ismail N, Lou R, Tu SW and Wiege RL: Hydraulic Model Verification Tests for Units 1 and 2. Pacific Gas and Electric Company, Department of Engineering Research, Report 420-DC-87.15, April 1987.

    Google Scholar 

  67. Ryan PJ, Eiger S and Wiegel RL: Hydraulic Model Production Runs for Diablo Canyon Power Plant. Pacific Gas and Electric Co., Dept. of Engineering Research, Report No. 420-DC-88-1, March, 1988.

    Google Scholar 

  68. Schwüle F: Dense Chlorinated Solvents in Porous and Fractured Media — Model Experiments. English Language Edition, Lewis Publishers, 1988.

    Google Scholar 

  69. Sharp JJ: Hydraulic Modelling. Butterworths, 1981.

    Google Scholar 

  70. Simpson JE: Gravity Currents in the Laboratory, Atmosphere and Ocean. Annual Review of Fluid Mechanics, Vol. 14, 1982.

    Google Scholar 

  71. Snyder WH: Guideline for Fluid Modelling of Atmospheric Diffusion. EPA Report No. EPA-600/8/81/009, U.S. EPA., Research Triangle, N.C. 1981.

    Google Scholar 

  72. Stolzenbach KD and Adams EE: Aquatic Disposal of Brines from Geopressured Aquifers. Presented at 1981 International Gas Conference.

    Google Scholar 

  73. Stolzenbach KD and Harleman DRF: An Analytical and Experimental Investigation of Surface Discharges of Heated Water. R.M. Parsons Laboratory for Water Resources and Hydrodynamics, Department of Civil Engineering, Massachusetts Institute of Technology, Technical Report No. 135, 1971.

    Google Scholar 

  74. Stolzenbach KD and Harleman DRF: Physical Modelling of Heated Discharges. Ch. 10, Engineering Aspects of Heat Disposal from Power Generation, D.R.F. Harleman, (Ed), R.M. Parsons Laboratory, M.I.T. 1972.

    Google Scholar 

  75. Stommel H and Farmer HG: Control of Salinity in an Estuary by a Transition. Journal of Marine Research, Vol. 12, May 1953.

    Google Scholar 

  76. Sturm TW and Kennedy JF: Heat Loss from Sidearms of Cooling Lakes. ASCE, Journal of the Hydraulics Division, Vol. 106, No. HY5, May 1980.

    Google Scholar 

  77. Tong SS and Stolzenbach KD: Submerged Discharges of Dense Effluent. Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Technical Report No. 243, July 1979.

    Google Scholar 

  78. Wakeman TH and Hawkins ML: Bay/Delta Hydraulic Model — 30 Years of Service. ASCE Conference on Hydraulic Engineering, Colorado Springs, Colorado, August 1988.

    Google Scholar 

  79. Wright SJ: Mean Behavior of Buoyant Jets in a Crossflow. J. Hydr. Div., ASCE, HY5, May 1977.

    Google Scholar 

  80. Wright VG: Laboratory and Numerical Study of Mud and Debris Flow. Ph.D. Dissertation, Dept. of Civil Engineering, University of California, Davis, California, March 1987.

    Google Scholar 

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Authors and Affiliations

  1. Bechtel Civil, Inc., San Francisco, USA

    P. J. Ryan

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  1. P. J. Ryan
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Editors and Affiliations

  1. Department of Hydraulics, National Laboratory of Civil Engineering (LNEC), Lisbon, Portugal

    Rui Martins

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© 1989 Kluwer Academic Publishers

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Ryan, P.J. (1989). Density Models. In: Martins, R. (eds) Recent Advances in Hydraulic Physical Modelling. NATO ASI Series, vol 165. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2344-7_5

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  • DOI: https://doi.org/10.1007/978-94-009-2344-7_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7555-8

  • Online ISBN: 978-94-009-2344-7

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