14 00 Dhr Speetjens

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14 00 Dhr Speetjens

  1. 1. Heat transfer made visible Michel Speetjens Energy Technology Laboratory Mechanical Engineering Department Outline • Physical setting • Fluid motion made visible • Some illustrative examples • Heat transfer made visible • Some illustrative examples • Conclusions and outlook May 2008 PAGE 1
  2. 2. • Physical setting • Fluid motion made visible • Some illustrative examples • Heat transfer made visible • Some illustrative examples • Conclusions and outlook May 2008 PAGE 2 Physical setting: laminar transport Laminar flow: Viscous flows: high ν • polymer/food processing • heat-transfer fluids • geophysical flows (magma, petroleum) Small-scale flows: low U,L • micro-fluidics • compact heat exchangers • physiological flows (lungs, blood) May 2008 PAGE 3
  3. 3. • Physical setting • Fluid motion made visible • Some illustrative examples • Heat transfer made visible • Some illustrative examples • Conclusions May 2008 PAGE 4 Fluid motion made visible Lagrangian approach: transport described by geometry of fluid paths Governing equations: • kinematic equation: • mass conservation: organises fluid paths into coherent structures May 2008 PAGE 5
  4. 4. • Physical setting • Fluid motion made visible • Some illustrative examples • Heat transfer made visible • Some illustrative examples • Conclusions May 2008 PAGE 6 Example: visualising 2D steady flows Steady flow: fluid paths streamlines: flow past object flow inside lid-driven cavity Organisation of streamlines into islands and/or open channels: • islands => confine and circulate fluid • channels => set up net throughflow basic geometrical building blocks of 2D steady flows May 2008 PAGE 7
  5. 5. Example: visualising 2D mixing Lid-driven cavity flow: simplification of industrial mixer/heat exchanger • flow forcing: time-periodic translation of sidewalls • parameter: period time T laminar flow (Re=1) May 2008 PAGE 8 Visualisation time-periodic fluid paths: Poincaré-sections: • release passive tracers in flow => “label” fluid parcels • “illuminate” tracers at t = 0,T,2T,… => “stroboscopic map” continuous flow Poincaré-section May 2008 PAGE 9
  6. 6. Time-periodic forcing: basics Visualising 2D mixing in lid-driven cavity by Poincaré-sections: steady transition to chaos with increasing T Organisation Poincaré-sections into islands and/or chaotic seas: • islands => poor mixing • chaotic regions => good mixing May 2008 PAGE 10 Time-periodic forcing: basics Organisation inside chaotic sea: manifolds: Manifolds: principal transport directions: • unstable: transport forward in time => asymptotic mixing pattern • stable: transport backward in time => origin of material May 2008 PAGE 11
  7. 7. • Physical setting • Fluid motion made visible • Some illustrative examples • Heat transfer made visible • Some illustrative examples • Conclusions May 2008 PAGE 12 Heat transfer made visible Heat transfer as the “motion” of a “fluid”: • fluid transport: Lagrangian representation: • thermal transport: - Eulerian representation: - Lagrangian representation: May 2008 PAGE 13
  8. 8. Fluid-motion representation of heat transfer: heat is transported along trajectories xT delineated by total heat flux Q in same way as fluid is transported along trajectories x delineated by fluid velocity u This admits: • heat-transfer visualisation by flow-visualisation methods • heat-transfer analysis with geometrical methods of laminar mixing based on organisation of trajectories into coherent structures • unified approach to fluid transport and heat transfer May 2008 PAGE 14 • Physical setting • Fluid motion made visible • Some illustrative examples • Heat transfer made visible • Some illustrative examples • Conclusions May 2008 PAGE 15
  9. 9. Example: 2D steady flows Cooling of hot object by cold uniform flow: fluid streamlines thermal streamlines Thermal streamlines: also organised into islands and/or open channels: • thermal island => confines and circulates heat • thermal channels => heat exchange object flow => “thermal path” basic geometrical building blocks of 2D steady heat transfer May 2008 PAGE 16 Example: 3D steady flows Cooling of 3D hot object by cold uniform flow: Example: 2D hot object … steady 3D thermal streamlines emanating from object => 3D thermal path May 2008 PAGE 17
  10. 10. Example: 2D transient behaviour Heat transfer in lid-driven cavity: transient to steady state Steady state: “high” Pe “low” Pe “moderate” Pe COLD HOT Thermal streamlines: same organisation as before: • thermal islands => confine and circulate heat • thermal path => fluid-wall heat exchange convection (higher Pe) promotes growth of islands May 2008 PAGE 18 lid-driven cavity revisited Transient (high Pe): evolution of T and instantaneous thermal streamlines: steady state Instantaneous thermal streamlines: • attaching to top wall => formation of steady-state thermal path • converging on instantanous stagnation points => formation of islands visualise formation of steady state May 2008 PAGE 19
  11. 11. Example: heat transfer versus mixing fluid Poincare-section thermal Poincaré-section Thermal Poincaré-section: • thermal path (gray curves) => only marginal difference with steady case • chaotic heat transfer (manifolds) => disintegration of thermal islands non-trivial connection mixing and (chaotic) heat transfer! May 2008 PAGE 20 • Physical setting • Fluid motion made visible • Some illustrative examples • Heat transfer made visible • Some illustrative examples • Conclusions May 2008 PAGE 21
  12. 12. Conclusions and outlook Heat transfer can be described as “motion” of “fluid”; this admits: • heat-transfer visualisation by flow-visualisation methods • heat-transfer analysis by geometrical methods from laminar mixing • unified approach to fluid transport and heat transfer Affords new insight: • isolation of heat transfer zones (thermal paths, …) • fundamental connection mixing and heat transfer • … Challenges: • further development of (unified) theoretical framework • application to realistic (industrial) configurations research in progress! May 2008 PAGE 22

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