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英文论文代写 Thermal Counterflow Past A Cylinder

英文论文代写 Thermal Counterflow Past A Cylinder

Analyse the motion of vortex – antivortex pairs of four vortices downstream of the cylinder

该项目的下一个任务是看涡动时,有两个涡antivortex对这个时间,这意味着在上半平面和两涡在下半平面如图5.1所示的两涡:

图5.1:在盘势流点涡,两涡antivortex对下游(后)的磁盘。

在这种情况下Z11和Z12旋涡有负循环(顺时针)、Z21和z22旋涡有正循环(逆时针)现在方程共八(各两个涡)。固定点相同的情况在3节和MATLAB的M文件是由同样的想法之前,可以见附件1。一个例子,当λ= 1的图如图5.2所

图5.2:1:旋涡的涡Z11、Z12点轨迹、Z21和z22。2:Z11和Z12轨迹。3:对你和z22轨迹。

在这种情况下再从时间依赖的数字是不显示但将在最终报告中发现最初位于气缸尾部涡涡点所示,在一段时间保持接近其初始位置,随着非流通λ维中例2涡。从图5.2的另一个观察是,轨迹现在不只是一条线,移动,但正在做一个螺旋运动,同时旋转和移动

The next task of the project was to see how the vortices move when there are two vortex – antivortex pairs this time, that means two vortices at the upper half plane and two vortices at the lower half -plane as shown in figure 5.1 below:

Figure 5.1: Point vortices in the potential flow around the disk, two vortex – antivortex pairs downstream (at rear) of the disk.

At this case z11 and z12 vortices have negative circulation (clockwise) and z21 and z22 vortices have positive circulation (anticlockwise) and now the equations are eight in total (two for each vortex). The stationary points are the same as in the case in section 3 and the m – files in Matlab were made with the same idea as before and can be seen in Appendix 1. One example of the graphs when λ = 1 is shown below in figure 5.2

Figure 5.2: 1: Trajectories of the vortex points for vortices z11, z12, z21 and z22. 2: Trajectories of z11 and z12. 3: Trajectories of z21 and z22.

Again at this case the from the time – depended figures that are not shown here but will be shown in the final report it was observed that for vortices initially located at the rear of the cylinder, the period of time during the vortex points remain close to their initial locations increases with the non – dimensional circulation λ as in the case with two vortices. Another observation from figures 5.2 is that the trajectories now are not just a line and moving but are making a spiral motion, rotating and moving simultaneously.

Analyse the motion of vortex – antivortex pairs of four vortices downstream of the cylinder when there is no other flow

这一目标是看到旋涡的运动时,其他流动被删除,只留下一对相同的极性的涡流。这可以通过去除一些条款从拉格朗日运动方程。第一次尝试是从方程4.2中删除一个术语,例如。做这个术语是从strem2down删除。我所有的方程和一例为λ= 1是图如图6.1所示

图6.1:无流程案例1。旋涡的涡Z11、Z12点轨迹、Z21和z22。2:Z11和Z12轨迹。3:对你和z22轨迹。

在这种情况下,它预计将看到的旋涡的轨迹传播到一条直线,因为上半窗格中的涡流是负的,在下半平面的旋涡是积极的,他们不反对彼此。在图6.1中,这件事是观察,但不是在开始。要看到的旋涡时,有没有流动的正确的另一个术语被删除的拉格朗日方程的行为,这个术语是方程4.2的例子。的stream2down。M被修改和条款被删除和重命名为stream2downnf2 M(附录1)。运动的M文件和stationarypoints M文件是一样的小变化。下面的例图了不流动的情况下λ= 1图6.2

图6.1:无流程案例2。旋涡的涡Z11、Z12点轨迹、Z21和z22。2:Z11和Z12轨迹。3:对你和z22轨迹。

现在从图6.1可以清楚地看到什么是预期。的旋涡运动传播到直线(直线上的螺旋运动),因为上的旋涡是负的,较低的旋涡是积极的,不反对对方。由于上半平面上的涡旋具有相同的符号(负),它们围绕彼此旋转,在下半平面上的旋涡也有相同的符号(正),它们彼此旋转。

This objective was to see the motion of vortices when other flows are removed and leave just one pair of vortices of the same polarity. This can be done by removing some terms from the Lagrangian Motion Equations. The first attempt was to remove the term from equation 4.2 for example. To do this this term was removed from the Strem2down.m for all the equations and so one example of the graphs for λ = 1 that was made is shown below in figure 6.1.

Figure 6.1: NO FLOW case 1. Trajectories of the vortex points for vortices z11, z12, z21 and z22. 2: Trajectories of z11 and z12. 3: Trajectories of z21 and z22.

In this case it is expected to see the trajectories of the vortices to propagate to a straight line because the vortices in the upper half – pane are negative and the vortices in the lower half – plane are positive and they do not oppose each other. In figure 6.1 this thing is observed but not at the beginning. To see the behaviour of the vortices when there is no flow correct another term was removed from the Lagrangian equations, this term was of the equation 4.2 for example. The Stream2down.m was modified and both terms were removed and renamed to Stream2downnf2.m (Appendix 1). Motion m – file and stationarypoints m – file are the same as before with small changes. Below an example graph is presented about the no flow case for λ = 1 in figure 6.2.

Figure 6.1: NO FLOW case 2. Trajectories of the vortex points for vortices z11, z12, z21 and z22. 2: Trajectories of z11 and z12. 3: Trajectories of z21 and z22.

Now from figure 6.1 it can be seen clearly what was expected. The vortices motion propagates to straight line (spiral motion on a straight line) because the upper vortices are negative and the lower vortices are positive and do not oppose each other. Since the vortices on the upper half – plane have the same signs (negative) they rotate around each other and on the lower half – plane the vortices also have the same signs (positive) they rotate around each other.