Assessment of Two Streamline Curvature Correction Methods for an Elliptic Blending Turbulence Model

Using two different methods, a previously developed elliptic blending model (the original <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>STT</mi><mrow><mo> </mo><mi>k</mi><mtext>-</mtext></mrow><mi>ω</mi><mtext>-</mtext><mi>φ</mi><mtext>-</mtext><mi>α</mi></mrow></semantics></math></inline-formula> model) is modified for sensitization to streamline curvature. One method involves modifying the dissipation term in the turbulent dissipation equation, while the other constructs a new formulation for the turbulent kinetic energy production term based on an explicit algebraic stress model. The capabilities of the proposed models are evaluated by applying them to three flows with curved surfaces; namely, the two-dimensional (2D) infinite serpentine passage flow, the 2D U-turn duct flow, and the 2D periodic hill flow. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>STT</mi><mrow><mo> </mo><mi>k</mi><mtext>-</mtext></mrow><mi>ω</mi></mrow></semantics></math></inline-formula> model with rotation and curvature correction (the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>STT</mi><mrow><mo> </mo><mi>k</mi><mtext>-</mtext></mrow><mi>ω</mi><mtext>-</mtext><mi>C</mi><mi>C</mi></mrow></semantics></math></inline-formula> model) is also used for comparison. The computed results are compared with the relevant direct numerical simulation, experimental, and large eddy simulation data from the literature. It is found that the two proposed models significantly improve upon the original <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>STT</mi><mrow><mo> </mo><mi>k</mi><mtext>-</mtext></mrow><mi>ω</mi><mtext>-</mtext><mi>φ</mi><mtext>-</mtext><mi>α</mi></mrow></semantics></math></inline-formula> model. Compared with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>STT</mi><mrow><mo> </mo><mi>k</mi><mtext>-</mtext></mrow><mi>ω</mi><mtext>-</mtext><mi>C</mi><mi>C</mi></mrow></semantics></math></inline-formula> model, the two proposed models produce better results in the 2D infinite serpentine passage flow and the 2D periodic hill flow. The proposed models are similarly competitive with the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>STT</mi><mrow><mo> </mo><mi>k</mi><mtext>-</mtext></mrow><mi>ω</mi><mtext>-</mtext><mi>C</mi><mi>C</mi></mrow></semantics></math></inline-formula> model in the 2D U-turn duct flow.