A Flat Plate Skin Friction Correlation Including Transition

Many existing boundary layer models treat transition as a rapid switch from laminar to turbulent flow, with correlations defining properties in each respective region. Natural transition, however, is not always a very spanwise uniform process, with the onset of transition varying somewhat between different streamwise paths of fluid flow. Thus, a spanwise average of natural transition can result in a more gradual, extended transition region than many existing models predict. Modern applications, such as aircraft wings and fuselages, are extremely streamlined and smooth, allowing for natural transition to occur rather than flow tripping to turbulent near the leading edge. Under these conditions, a skin friction model that takes this extended transition region into account provides a more accurate model compared to those which incorporate a rapid transition from laminar to turbulent flow. Lienhard’s recent publication 1 presents a new rationale for modeling the extent of the transition region on a smooth flat plate developed from re-analysis of existing heat transfer data. This correlation accounts for the extended natural transition region corresponding to a spanwise average of values. The primary objective of this thesis was to reinterpret Lienhard’s heat transfer correlation to solve for skin friction coefficient, then compare this correlation to available experimental data and higher order boundary layer models. After reinterpreting Lienhard’s correlation using the Reynolds analogy, it produced a gradual, extended transition region for skin friction coefficient. The reinterpreted correlation had excellent agreement with experimental data corresponding to a spanwise average of flow with natural transition. Tripped transitional values and data taken along a streamwise path of fluid resulted in a more rapid transition from laminar to turbulent flow. Both an integral boundary layer model and a Reynolds-averaged Navier-Stokes boundary layer model were used to validate the reinterpreted Lienhard correlation. Both of these models produced transition curves steeper than the reinterpreted Lienhard curve. These existing boundary layer models do not take into account the gradual transition region that natural transition may produce when looking at a spanwise average of values. With a focus on spanwise averaged values, such as overall drag over a streamlined surface, existing sophisticated boundary layer models may not accurately predict the behavior produced. The reinterpreted Lienhard correlation provides a new representation of skin friction coefficient throughout the boundary layer that takes into account the extended transition region that may occur when it is desired to model a spanwise average of fluid flow. 1Lienhard, J. Heat transfer in flat-plate boundary layers: A correlation for laminar, transitional, and turbulent flow. ASME Journal of Heat Transfer, 142, 2020