Fully resolved scalar transport for high Prandtl number flows using adaptive mesh refinement

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Abstract

In multiphase systems, boundary layers occur at fluid-fluid or fluid-solid interfaces. In a direct numerical simulation, the grid requirements are often dictated by the thickness of these boundary layers. Systems that are characterized by high Prandtl (or Schmidt number) exhibit temperature (or mass) boundary layers that are much thinner than the momentum boundary layers. In this paper, a hybrid computational approach is presented that uses a fixed Cartesian grid for the Navier-Stokes and continuity equations and an adaptive mesh for scalar transport, thus reducing the memory and CPU requirements tremendously while resolving all boundary layers. We describe the key aspects that need to be addressed in this hybrid approach, related to discretization, grid mapping, velocity interpolation along with detailed verification tests. Finally, the robustness and accuracy of our hybrid methodology is demonstrated for forced-convection heat transfer over stationary spherical particles at high Prandtl numbers.

Original languageEnglish
Article number100047
Number of pages18
JournalChemical Engineering Science: X
Volume4
DOIs
Publication statusPublished - 1 Nov 2019

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Prandtl number
Boundary layers
Fluids
Forced convection
Direct numerical simulation
Program processors
Interpolation
Momentum
Heat transfer
Data storage equipment
Temperature

Keywords

  • Adaptive mesh refinement
  • Boundary layers
  • High Prandtl number
  • High Schmidt number

Cite this

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title = "Fully resolved scalar transport for high Prandtl number flows using adaptive mesh refinement",
abstract = "In multiphase systems, boundary layers occur at fluid-fluid or fluid-solid interfaces. In a direct numerical simulation, the grid requirements are often dictated by the thickness of these boundary layers. Systems that are characterized by high Prandtl (or Schmidt number) exhibit temperature (or mass) boundary layers that are much thinner than the momentum boundary layers. In this paper, a hybrid computational approach is presented that uses a fixed Cartesian grid for the Navier-Stokes and continuity equations and an adaptive mesh for scalar transport, thus reducing the memory and CPU requirements tremendously while resolving all boundary layers. We describe the key aspects that need to be addressed in this hybrid approach, related to discretization, grid mapping, velocity interpolation along with detailed verification tests. Finally, the robustness and accuracy of our hybrid methodology is demonstrated for forced-convection heat transfer over stationary spherical particles at high Prandtl numbers.",
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AU - Panda, A.

AU - Peters, E.A.J.F.

AU - Baltussen, M.W.

AU - Kuipers, J.A.M.

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