University:
Boston University
Course:
MET CS 201 | Introduction to Programming
Academic year:

2022
Views:

55

Pages:

11
Author:

Kasazami2c24

FIGURES The first three figures have been made with PowerPoint. The fourth figure is from an existing MATLAB code mentioned in the report section 1. All the figures with plots have been elaborated with Python 2.7. Figure 1: Cartoon of a 3D shock tube with rectangular cross section. The pipe is colored in two different regions to show the difference between the initial conditions: the red half has higher pressure, density and temperature, the blue region has lower pressure, density and temperature. The triad of vectors shows the orientation of the axes. Figure 2: Geometry of the shock tube used in the project. The pipe is 10 m long, 2 m high and 0.2 m thick. The width of the tube (in the z direction) is smaller compared to the other two to simulate a 2D case rather than a 3D tube. The triad of vectors shows the orientation of the axes. Figure 3: Vertex of the shock tube that identify the boundary walls. The boundary active walls are defined by the vertex 0473, 1562, 0154 and 3763. The walls 4765 and 0123 are empty walls since the case analyzed is a 2D case. Only the x and y directions are refined by a specific number of cells (20x20, 30x30, 50x50, 100x100, 300x300 and 400x400). The triad of vectors shows the orientation of the axes. Figure 4: Analytical 1D solution of the shock tube problem from the MATLAB code here: http:// www.mathworks.com/matlabcentral/fileexchange/46311-sod-shock-tube-problem-solver. The initial conditions have null speed along the x axis, pressure of 1 Pa in the first half and 0.1 Pa in the second half and density of 1.000 kg/m3 in the first half and 0.125 kg/m3 in the second half. Figure 5: Cartoon of the contiguous polyhedral finite volumes in the solver rhoCentralFoam. P and N are −−→ → − − → indicative of the centroid of each cell. f is the neighbouring face and the vector df N , d and Sf indicate respectively distances and the surface f normal unit vector. Adapted figure from Greenshields et al. 2010. Figure 6: Line cut along the x axis between -5 and 5 m for the 20x20 case, sampled at 500 points. The different color lines represent the solutions at different times as indicated by the legend. From the top to the bottom plot, I display pressure, temperature, speed along x and density as a function of x. Figure 7: Line cut along the x axis between -5 and 5 m for the 30x30 grid resolution case, sampled at 500 points. The different color lines represent the solutions at different times as indicated by the legend. From the top to the bottom plot, I display pressure, temperature, speed along x and density as a function of x. Figure 8: Line cut along the x axis between -5 and 5 m for the 50x50 grid resolution case, sampled at 500 points. The different color lines represent the solutions at different times as indicated by the legend. From the top to the bottom plot, I display pressure, temperature, speed along x and density as a function of x. Figure 9: Line cut along the x axis between -5 and 5 m for the 100x100 grid resolution case, sampled at 500 points. The different color lines represent the solutions at different times as indicated by the legend. From the top to the bottom plot, I display pressure, temperature, speed along x and density as a function of x. Figure 10: Line cut along the x axis between -5 and 5 m for the 300x300 grid resolution case, sampled at 500 points. The different color lines represent the solutions at different times as indicated by the legend. From the top to the bottom plot, I display pressure, temperature, speed along x and density as a function of x. Figure 11: Line cut along the x axis between -5 and 5 m for the 400x400 grid resolution case, sampled at 500 points. The different color lines represent the solutions at different times as indicated by the legend. From the top to the bottom plot, I display pressure, temperature, speed along x and density as a function of x. Figure 12: Line cut along the x axis between -5 and 5 m at 4 ms, sampled at 500 points. The different color lines represent the solutions at resolutions as indicated by the legend. From the top to the bottom plot, I display pressure, temperature, speed along x and density as a function of x. Figure 13: Slice cut of the xy plane at 4 ms between -5 and 5 m in the x direction and at y=0 m. The interpolation is turned on so the number of points is 300x300, like the resolution. From the top to the bottom plot, I display pressure, temperature, speed along x and density as a function of the coordinates x and y. The colors are indicative of the actual value of the physical property plotted. Figure 14: Comparison between the OpenFOAM simulation in the 300x300x1 grid resolution and the 2-step scheme by MacCormack, coded in Python 2.7 during the CFD course. The simulations have the same spacial and temporal resolutions, and are both run for 4 ms. The MacCormack scheme has an artificial viscosity term added to avoid oscillations at the discontinuities boundaries.