# Computational Investigations and Control of Shock Interference +
## 3 Model Validation
### Results  
The computed static pressure along the top-wall centerline and side wall centerline is compared with the experimental results shown in [PERSON] et al. [22] in Figure 7. There are \begin{table}
\begin{tabular}{c c c} \hline  & **[PERSON] et al. [22]** & **Current Work** \\ \hline Dimensions & \(24\times 0.5\times 1\) [in] & \(0.6096\times 0.0127\times 0.0254\) [m] \\ \hline
**Mesh (Isolator)** & & \\ \hline Points & \(2000\times 160\times 208\)* & \\  & \(1000\times 80\times 104\) & \(1000\times 80\times 104\) \\ \hline Max. y+ & 1.0 & 1.0 \\ \hline Streamwise spacing in first half of isolator & 0.01 h & 0.02 h \\ \hline Streamwise spacing in second half of isolator & 0.01 h \(\rightarrow\) 0.025 h & 0.02 h \(\rightarrow\) 0.025 h \\ \hline Max. grid spacing in vertical and spanwise directions & 0.01 h & 0.02 h \\ \hline
**Solution Methodology** & & \\ \hline Numerics scheme & Incomplete LU & Incomplete LU \\ \hline CFL number & 100 & 100 \\ \hline Flux scheme & LDFSS & LDFSS \\ \hline Flow variable reconstruction scheme & MUSCL, \(k=\frac{1}{3}\) & MUSCL, \(k=\frac{1}{3}\) \\ \hline Flux limiter & Koren & Koren \\ \hline
**Model Specifications** & & \\ \hline Turbulence Model & [PERSON] 1998 & Wilcox 1998 \\ \hline Molecular and Turbulent Pr & 0.72, 0.9 & 0.72, 0.9 \\ \hline Viscosity model & McBride & Sutherland’s Law \\ \hline \end{tabular}  
* This mesh yielded similar results to the mesh that is half the size of this mesh.  
\end{table} 
Table 1: Numerical methods, mesh, and model specifications utilized for model validation. \begin{table}
\begin{tabular}{c c c} \hline  & **[PERSON] et al. [22]** & **Current Work** \\ \hline Total Temperature at Entry [K] & 292.91 & 297.90 \\ \hline Nozzle Plenum Pressure or Isentropic & & \\ Total Pressure [kPa] & 845.29 & 845.29 \\ \hline Isolator Entry Pressure [kPa] & 49.47 & 49.47 \\ \hline Isolator Back Pressure [kPa] & 304.51 & 304.51 \\ \hline Pressure Ratio & 0.360 & 0.360 \\ \hline \end{tabular}  
\end{table} 
Table 2: Flow variables. several metrics for comparing these two results, including: (1) location of the foot of the pseudo-shock-train, (2) length of the pseudo-shock-train, (3) maximum pressure rise across the isolator walls, and (4) number of oblique shocks formed in the pseudo-shock-train. An analysis of the computational results was performed for both centerlines. The shock location, max pressure rise, and shock-train length are displayed in Table 3. On the top wall, the shock location was 0.52 inches farther downstream in this work. This is approximately 2% of the total isolator length. The shock location on the side wall was 0.86 inches farther downstream in the current work. This is approximately 3.5% of the total isolator length. The maximum pressure rise and the number of oblique shocks on the top-wall centerline are equal between the two sets of results. To compare the pseudo-shock-train length, the computed results were translated so that the foot of the shock-train aligns with the measured data. This is shown in Figure 7, and consistency with the validation data is achieved. The side wall pressure has very good agreement with the validation case. The top-wall centerline static pressure distribution shows that the calculated shock-train has a similar structure to the validation data, but it is slightly longer. The slight differences can be attributed to two sources: first course could be the experimental error and uncertainty, which were not reported in the published data. Secondly, the elimination of the facility nozzle in front of the isolator results in a \begin{table}
\begin{tabular}{c c c} \hline \hline  & **[PERSON] et al.**[22] & **Current Work** \\ \hline Shock-train Length (top-wall centerline) & 8.62 inches & 10.00 inches \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantitative comparison between measured and computational results. Figure 7: Model validation with IDRL isolator—static pressure on side wall centerline (**left**) and top-wall centerline (**right**), [PERSON] et al. [22].