Experimental tests to validate a new slender body theory in steady, incompressible Oseen flow.

提出的研究是基于一组实验，以测试一个新的细长体理论在稳定，不可压缩的Oseen流。新的理论已经发展了一系列的七个出版物的提议者在领先的数学科学同行-该理论是有用的，因为它使我们对细长物体在流体中运动时的升力是如何产生的有了基本的了解。这些想法可以进一步为船舶和潜艇操纵、导弹和火箭制导、低展弦比飞机的空气动力学以及海洋动物的流体动力学等领域的广泛流体问题而开发的。控制操纵细长体的最重要参数是由于流体绕体流动而使细长体以稳定的向前速度运动的升力或侧力。还有由于加速度和旋转而产生的附加贡献，这些贡献被包含在关于稳定结果的线性化中。流体的可压缩性也会影响结果，但是细长体上升力的变化还是比较小的，这种影响可以作为不可压缩结果的一个附加因素来处理。本文用半经验的艾伦和珀金斯粘性横流方法计算了细长体定常前飞时的升力。例如，美国空军（USAF）的计算机代码Missile DatCom就使用了这种方法。然而，这特别适用于圆形横截面的物体，而艾伦和帕金斯的方法很难推广到其他一般横截面的物体，其中一些已知能提供改进的操纵性能。一个例外是椭圆截面的细长体，对此，Jorgensen对艾伦和珀金斯的方法作了直接的推广。一个新的理论的提议者已经制定了这有两个优点超过艾伦和帕金斯的方法。第一，它在理论中加入了粘性贡献效应，而不是作为半经验的附加;第二，它很容易适用于一般横截面的细长体。这个理论是以Osen流动理论为基础的，但至今还没有专门进行实验来检验它。此外，现有的实验通过将升力系数划分在细长体的底部区域上来呈现结果的可变性。当基础面积非常小时，这尤其会在结果中引入不必要的可变性。通过在一定马赫数范围内进行试验，结果也产生了变化。不幸的是，这意味着现有的实验已经证明了新理论是否比艾伦和帕金斯的方法更准确或更不准确。这一提议为这一新理论提供了一个明确的实验检验。本文将评估一系列九个椭圆截面细长体在低速风洞中的升力。所有细长体都具有相同的半长轴半径，因此可以在同一基线上进行比较，然后绘制升力曲线斜率与椭圆度的关系图（见案例支持）。新理论预测这条线是完全直的，而Jorgensen对艾伦和Pekins的发展则预言这条线是弯曲的，并有一个明显的弓形。与艾伦和帕金斯方法的对比将根据实验结果与新理论预测的直线的接近程度来衡量，而不是与艾伦和帕金斯方法预测的弓形线的接近程度。

The proposed research is based upon a set of experiments to test a new slender body theory in steady, incompressible Oseen flow.The new theory has been developed over a series of seven publications by the proposer in the leading mathematical science peer-reviewed journals.The theory is useful because it gives us a fundamental understanding into how the lift on a slender body moving in a fluid is generated.These ideas can then be further developed for a wide-range of fluids problems in ship and submarine manoeuvring, missile and rocket guidance, aerodynamics for low aspect-ratio aeroplanes, and hydrodynamics for marine animals.The most significant parameter governing manoeuvring slender bodies is the lift, or side force, on the slender body moving at a steady forward speed due to the fluid flowing around the body. There are also additional contributions due to acceleration and rotation which are included by a linearisation about the steady result. Compressibility of the fluid also affects results, but again the changes in lift force on a slender body are relatively small and this effect can be treated as an additional factor to the incompressible result. The lift force on a slender body moving at steady forward speed is presently evaluated by using the semi-empirical Allen and Perkins viscous cross-flow approach. For example, the US Air Force's (USAF)'s computer code Missile DatCom uses this approach. However, this is geared particularly for bodies of circular cross-section, and the Allen and Perkins approach is difficult to extend for bodies of other general cross-section some of which are known to give improved manoeuvring performance. One exception is slender bodies with elliptical cross-section for which Jorgensen has provided a straightforward extension to the Allen and Perkins approach. A new theory by the proposer has been developed which has two advantages over the Allen and Perkins approach. First, it incorporates the viscous contributory effect within the theory rather than as a semi-empirical add-on. Second, it is easily adaptable to slender bodies with general cross-section.This theory is based upon Oseen flow theory, but as yet no experiments have been specifically performed to test it. Furthermore, existing experiments incorporate variability in the results by presenting them for the lift coefficient which divides over the base area of the slender body. This particularly incorporates unnecessary variability in the results when the base area is very small. Variability in the results has also been created by testing over a range of Mach numbers. Unfortunately, this has meant that existing experiments have proven inconclusive as to whether the new theory is more or less accurate than the Allen and Perkins approach. This proposal presents a definitive experimental test for this new theory. The lift of a series of nine slender bodies with elliptical cross-section placed in a low-speed wind tunnel will be evaluated. All the slender bodies will have the same semi-major axis radius, and so can be compared against the same base line.A graph of the lift curve slope against ellipticity is then plotted (see case for support).The new theory predicts this line to be perfectly straight, whereas the Jorgensen development to Allen and Pekins predicts the line to be curved with a significant bow.The test of the new theory and the comparison of it against the Allen and Perkins method will be measured against how closely experimental results fit the straight line predicted by the new theory as opposed to the bowed line predicted by the Allen and Perkins method.