The choice of leading-edge aspect ratio (AR) plays a crucial role when planning boundary layer wind tunnel tests on a flat plate. Poor selection of the leading-edge profile hampers effectiveness of the experiment and ...The choice of leading-edge aspect ratio (AR) plays a crucial role when planning boundary layer wind tunnel tests on a flat plate. Poor selection of the leading-edge profile hampers effectiveness of the experiment and increases testing costs associated with interchanging of leading edges to attain accurate results. Thus, the appropriate selection of the leading edge is a very crucial part of the wind tunnel experiment process. It is argued that the curvature of the leading edge and thus the AR is of paramount importance to achieve accurate results from the wind tunnel testing. In this project, seven different elliptical leading edges were tested, and their performance was compared with an ideal leading edge with zero thickness. Experiments and computation have been done for leading edges ranging from AR6 to AR20. Results were evaluated for boundary layer transition onset location, and it was found that AR20 has the least influence on the flow structure when compared to the ideal leading edge. A study of the flow structure at the stagnation point indicates an increase in adverse pressure gradient with an increase in the AR but also shows a decrease in the size of the stagnation region. The presence of a higher AR leading edge reduces the turbulent spot production rate, which is one of the primary causes of boundary layer transition. This paper presents a correlation that enables aerodynamicists to quantify the impact of the leading-edge AR on transition. A typical case is also presented to compare the relative performance of a wedge and the higher AR leading edge, which provides a choice between an elliptical or a wedge-shaped leading edge.展开更多
In this paper, we introduce a K Hölder p-adic derivative that can be applied to fractal curves with different Hölder exponent K. We will show that the Koch curve satisfies the Hölder conditi...In this paper, we introduce a K Hölder p-adic derivative that can be applied to fractal curves with different Hölder exponent K. We will show that the Koch curve satisfies the Hölder condition with exponent and has a 4-adic arithmetic-analytic representation. We will prove that the Koch curve has exact -Hölder 4-adic derivative.展开更多
In the past years, we established analytic expressions of various fractals and discussed Hölder derivatives of the expressions. Based on our earlier results, we will study the properties of harmonic functions on ...In the past years, we established analytic expressions of various fractals and discussed Hölder derivatives of the expressions. Based on our earlier results, we will study the properties of harmonic functions on a very important fractal, the Sierpinski gasket (SG). Our main result is that the harmonic function on SG satisfies a Hölder inequality of order α=ln35\ln2.展开更多
文摘The choice of leading-edge aspect ratio (AR) plays a crucial role when planning boundary layer wind tunnel tests on a flat plate. Poor selection of the leading-edge profile hampers effectiveness of the experiment and increases testing costs associated with interchanging of leading edges to attain accurate results. Thus, the appropriate selection of the leading edge is a very crucial part of the wind tunnel experiment process. It is argued that the curvature of the leading edge and thus the AR is of paramount importance to achieve accurate results from the wind tunnel testing. In this project, seven different elliptical leading edges were tested, and their performance was compared with an ideal leading edge with zero thickness. Experiments and computation have been done for leading edges ranging from AR6 to AR20. Results were evaluated for boundary layer transition onset location, and it was found that AR20 has the least influence on the flow structure when compared to the ideal leading edge. A study of the flow structure at the stagnation point indicates an increase in adverse pressure gradient with an increase in the AR but also shows a decrease in the size of the stagnation region. The presence of a higher AR leading edge reduces the turbulent spot production rate, which is one of the primary causes of boundary layer transition. This paper presents a correlation that enables aerodynamicists to quantify the impact of the leading-edge AR on transition. A typical case is also presented to compare the relative performance of a wedge and the higher AR leading edge, which provides a choice between an elliptical or a wedge-shaped leading edge.
文摘In this paper, we introduce a K Hölder p-adic derivative that can be applied to fractal curves with different Hölder exponent K. We will show that the Koch curve satisfies the Hölder condition with exponent and has a 4-adic arithmetic-analytic representation. We will prove that the Koch curve has exact -Hölder 4-adic derivative.
文摘In the past years, we established analytic expressions of various fractals and discussed Hölder derivatives of the expressions. Based on our earlier results, we will study the properties of harmonic functions on a very important fractal, the Sierpinski gasket (SG). Our main result is that the harmonic function on SG satisfies a Hölder inequality of order α=ln35\ln2.
