This paper focuses on the laminar boundary layer startup process (momentum and thermal) in incompressible flows.
The unsteady boundary layer equations can be solved via similarity analysis by normalizing the stream-wise (x), wall-normal (y) and time (t) coordinates by a variable η and τ, respectively. The resulting ODEs are solved by a finite difference explicit algorithm. This can be done for two cases: flat plate flow where the change in pressure are zero (Blasius solution) and wedge or Falkner-Skan flow where the changes in pressure can be favorable (FPG) or adverse (APG). In addition, transient passive scalar transport is examined by setting several Prandtl numbers in the governing equation at two different wall thermal conditions: isothermal and isoflux. Numerical solutions for the transient evolution of the momentum and thermal boundary layer profiles are compared with analytical approximations for both small times (unsteady flow) and large (steady-state flow) times.
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On the Kármán momentum-integral approach and the Pohlhausen paradox: Extension to a cylinder in crossflow with a potential farfield motion
In this work, the Kármán–Pohlhausen (KP) momentum-integral approach based on optimized fourth-order (MX4) polynomial approximations of the velocity and temperature profiles is applied to a classical benchmark problem, namely, that of a cylinder in crossflow with a variable pressure gradient. This enables us to extract closed-form expressions for both hydrodynamic and thermal boundary-layer parameters and then compare the newly found solutions to their counterparts obtained using Pohlhausen's cubic (KP3) and quartic (KP4) polynomials. As usual, the farfield around the cylinder is modeled using potential flow theory and the momentum-integral analysis is paired with Walz's empirical expression for the momentum thickness, which is based on a wide collection of experiments. This procedure permits retrieving explicit relations for the pressure-sensitive KP3, KP4, and MX4 velocity profiles across the boundary layer; one also obtains accurate approximations for the pressure distribution around the cylinder as well as an improved prediction of the separation point, namely, to within 0.87% of the actual location. In this process, refined estimates are produced for several characteristic parameters whose distributions are found to be in favorable agreement with experimental measurements and numerical simulations. These include the disturbance, momentum, and displacement thicknesses as well as the skin friction, pressure, and total drag coefficients. Finally, the thermal analysis is undertaken using both isothermal and isoflux boundary conditions. For each of these cases, closed-form analytical solutions are obtained for the local Nusselt number distribution around the cylinder, and these distributions are found to exhibit noticeably reduced errors relative to their classical values.
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- Award ID(s):
- 1761675
- PAR ID:
- 10340984
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 34
- Issue:
- 6
- ISSN:
- 1070-6631
- Page Range / eLocation ID:
- 063107
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0096780
