## 4 Determination of the Range of the High-Pressure Area at the Corner  
The formation of high pressure at the corner has been studied previously but further study into the range of high-pressure areas is also crucial to understanding the convergence effect of shock waves at the corners. Therefore, the pressure peaks at each measurement point in Figure 3 were recorded and pressure contour maps were plotted. Figure 13 shows the pressure contour map when \(b\) = 500 mm, \(W\) = 100 g, and K = 2, 3, 4, and 5.  
Figure 11: Changes in the pressure and pressure ratio at two lateral points with K when b = 500 mm and W = 100 g.  
Figure 12: Distribution of peak pressure in the corner area at different values of K.  
Figure 13 shows that as K increases, the high-pressure area at the corner gradually widens with little change in height. In addition, the high-pressure area gradually moves towards the center of the surface of wall B and is no longer noticeable at the corner but a high-pressure area is formed at the center of the B wall surface. Figure 13 also shows that when K > 3, the high-pressure area at the corner is not apparent; thus, the K range from 1 to 3 will be discussed next. The high-pressure areas at the corners are individually intercepted along the boundary line, as shown in Figure 14, where the numerical relationship between the size of the area boundary and the value of b is indicated.  
Figure 14 clearly shows that the high-pressure area appears triangular when K is small and as isosceles triangles when K = 1. As K increases, the shape of the high-pressure area gradually approximates to a rectangular form; this result is consistent with the high-pressure area formation rule at the corner that has already been discussed. The high-pressure area gradually widens primarily as the Mach-reflected wavefront formed at the surface of wall A widens. The relationship between the range of areas obtained in Figure 14 was represented in a coordinate system with the height and width of the corner high-pressure area a\({}_{p}\) and b\({}_{p}\), respectively. Figure 15 shows the data points in the coordinate system with K, with a\({}_{p}\)/b and b\({}_{p}\)/b as the horizontal and vertical coordinates, respectively.  
Figure 13: Pressure contour distribution diagram in the corner area.  
The polynomial fit performed on the data points in Figure 15 shows that b\({}_{p}\)/b increases linearly as K increases. Equation (3) gives the functional relationship between b\({}_{p}\)/b and K based on the polynomial fit.  
\[\mathrm{b}_{p}/\mathrm{b}=-0.17673+0.26709\mathrm{K} \tag{3}\]  
Figure 14: Change of the high-pressure area at the corners with the value of K.  
Figure 15: Relationship between the size of the high-pressure area and K.  
The functional relationship between \(\text{a}_{p}/\text{b}\) and K is also polynomial, as shown by Equation (4):  
\[\text{a}_{p}/\text{b}=0.02015\text{K}^{3}-0.15693\text{K}^{2}+0.42428\text{K}-0.2 0127 \tag{4}\]  
As the fitted data points were obtained under the conditions b = 500 mm and W = 100 g, simulations were conducted considering the generality of the functional relationship given by Equations (3) and (4). Two sets of data points were obtained at b = 500 mm and W = 200 g, and b = 1000 mm and W = 1000 g, as represented in Figure 15. Both data sets satisfy the functional relationship obtained and show that K is the main factor influencing the range of high-pressure areas.