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Scraped Surface Heat Exchangers

B Duffy A D Fitt M E-M Lee C P Please S K Wilson Mathematics. U Blomstedt, N Hall-Taylor, J Mathisson Industry. M J Baines D L Pyle K-H Sun Food Bioscience Mathematics. H Tewkesbury Technology Transfer. Scraped Surface Heat Exchangers. Overview of Current Research.

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Scraped Surface Heat Exchangers

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  1. B Duffy A D Fitt M E-M Lee C P Please S K Wilson Mathematics U Blomstedt, N Hall-Taylor, J Mathisson Industry M J Baines D L Pyle K-H Sun Food Bioscience Mathematics H Tewkesbury Technology Transfer Scraped Surface Heat Exchangers

  2. Overview of Current Research Problems in Fluid Dynamics and Heat Transfer: • Paradigm Problems • Channel flow • Thin cavity • Blade • Affects of wear near the tip • Stresses acting on Blade • 2D Flow • Cavity • Inter-connected chambers • 3D Flow

  3. Mathematical Considerations • Temperature dependant viscosity • Heat thinning • Non-Newtonian fluid • Power-law shear thinning • Viscous Dissipation • Conservation • Mass • Momentum • Energy

  4. y=H u2, p2, Q2 blade  Pivot h1 y u1, p1, Q1 h0 h2 y=0 x0 x U L Flow Around a Blade • Problem Formulation • Newtonian • Isothermal • Incompressible • Lubrication approximation

  5. Pressure conditions • Far-field entry pressure must be equal to the pressures above and below the leading blade tip • Far-field exit pressure must be equal to the pressures above and below the trailing blade tip • For the scraper to be in equilibrium, the moment about the pivot due to pressure must vanish • Blade Angle • Independent of viscosity and the speed of the moving lower boundary

  6. No solutions when the blade is pivoted near the trailing end • Extensions • Shear-Thinning • Periodic blade-arrays • “Naïve” contact problem has a singular force • Asperities in blade and machine-casing surfaces • Solid-fluid contact • Blade wear and geometry

  7. momentum energy Parallel Channel Flow • Unidirectional • Steady • Power-law fluid • Heat thinning • Viscous dissipation

  8. Linear Stability Analysis

  9. Thin Cavity Problem • Lubrication approach • Large Peclet • Small Brinkman • Newtonian • Neglect corner flow z y x

  10. Steady 2D Problem • FEM • Problems • Cavity • Annulus with blades • Extensions • 3D

  11. Streamlines for 2D Cross Section m=1.0 m=1.0 20% gap 60% gap m=0.33 m=0.33 20% gap 60% gap

  12. Isotherms 2D Cross Section m=1 Re=10 Br=0.3 b=0.05

  13. Isotherms for 3D Cavity Problem Re=2, Br=0.512, Pe=3200, W/U=1/8, m=1.0

  14. Summary • Blade flow • Lubrication approximation and contact problems • Blade geometry and wear • Paradigm problems • Stability problem for non-unique regimes in channel flows • Slender cavity problems for a number of small parameter regimes • Full two and three dimensional problems • Consolidate current findings • Numerical stability analysis

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