The laminar boundary layer of a viscous incompressible fluid subject to a two-dimensional wall curvature is evaluated. It is well known that a curved surface induces streamwise pressure gradient as well as wall curvature driven pressure gradient. Under certain assumptions, a family of similarity solutions can be obtained under the influence of flow acceleration/deceleration, which is known as the Falkner-Skan similarity solutions. In this study, the effect of the wall normal pressure gradient is taken into consideration, and the
freestream flow parameters are adjusted for flow over a curved surface. Present results are obtained by numerical solution of a generalized Falkner-Skan equation governing similar solutions for flows over curved surfaces. The Falkner-Skan equations are solved by an RK4 shooting algorithm. Additionally, the transport of a passive scalar is incorporated in the present analysis at different Prandtl numbers. The objective of this paper is to use the curvilinear or axisymmetric boundary layer and energy equations to assess the effect of
Favorable, Adverse and Zero pressure gradient on the laminar momentum and thermal boundary layer development.
Major conclusions are summarized as follows: (i) as the pressure gradient β increases from negative values (APG) towards positive (FPG) values, the displacement (Δ∗) and momentum (θ∗) thickness tend to decrease no matter the curvature type, and, (ii) the normalized wall shear stress (i.e., f′′) exhibits a linear decreasing behavior as the wall curvature switches from concave (negative) to convex (positive) at a constant pressure gradient.
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Assessment of Turbulence Models over a Curved Hill Flow with Passive Scalar Transport
An incoming canonical spatially developing turbulent boundary layer (SDTBL) over a 2-D curved hill is numerically investigated via the Reynolds-averaged Navier–Stokes (RANS) equations plus two eddy-viscosity models: the K−ω SST (henceforth SST) and the Spalart–Allmaras (henceforth SA) turbulence models. A spatially evolving thermal boundary layer has also been included, assuming temperature as a passive scalar (Pr = 0.71) and a turbulent Prandtl number, Prt, of 0.90 for wall-normal turbulent heat flux modeling. The complex flow with a combined strong adverse/favorable streamline curvature-driven pressure gradient caused by concave/convex surface curvatures has been replicated from wind-tunnel experiments from the literature, and the measured velocity and pressure fields have been used for validation purposes (the thermal field was not experimentally measured). Furthermore, direct numerical simulation (DNS) databases from the literature were also employed for the incoming turbulent flow assessment. Concerning first-order statistics, the SA model demonstrated a better agreement with experiments where the turbulent boundary layer remained attached, for instance, in Cp, Cf, and Us predictions. Conversely, the SST model has shown a slightly better match with experiments over the flow separation zone (in terms of Cp and Cf) and in Us profiles just upstream of the bubble. The Reynolds analogy, based on the St/(Cf/2) ratio, holds in zero-pressure gradient (ZPG) zones; however, it is significantly deteriorated by the presence of streamline curvature-driven pressure gradient, particularly due to concave wall curvature or adverse-pressure gradient (APG). In terms of second-order statistics, the SST model has better captured the positively correlated characteristics of u′ and v′ or positive Reynolds shear stresses ( > 0) inside the recirculating zone. Very strong APG induced outer secondary peaks in and turbulence production as well as an evident negative slope on the constant shear layer.
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- NSF-PAR ID:
- 10407177
- Date Published:
- Journal Name:
- Energies
- Volume:
- 15
- Issue:
- 16
- ISSN:
- 1996-1073
- Page Range / eLocation ID:
- 6013
- 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/10.3390/en15166013
