Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

Abstract

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1 $$\times$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>×</mml:mo></mml:math> 10 $$^{5}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>5</mml:mn></mml:msup></mml:math> $$\le$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>≤</mml:mo></mml:math> Re $$_{D}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow/><mml:mi>D</mml:mi></mml:msub></mml:math> $$\le$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>≤</mml:mo></mml:math> 1 $$\times$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>×</mml:mo></mml:math> 10 $$^{7}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>7</mml:mn></mml:msup></mml:math> . For the smooth prism with $$k_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>k</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> / D = 4 $$\times$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>×</mml:mo></mml:math> 10 $$^{-5}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mrow><mml:mo>-</mml:mo><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:math> , tests were performed at three angles of incidence, i.e. $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> = 0 $$^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mo>∘</mml:mo></mml:msup></mml:math> , −22.5 $$^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mo>∘</mml:mo></mml:msup></mml:math> and −45 $$^{\circ }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mo>∘</mml:mo></mml:msup></mml:math> , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>k</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math> / D = 1 $$\times$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>×</mml:mo></mml:math> 10 $$^{-3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mrow><mml:mo>-</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math> . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>O</mml:mi></mml:math> (10 $$^{7}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow/><mml:mn>7</mml:mn></mml:msup></mml:math> ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

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