Responses to the 1st Reviewer
Responses to General Remarks:
Response 1.1: All sections of the paper were modified or re-written to address the reviewers’ comments and make the paper shorter and clearer. Section 4.3, Section 4.4, Appendix A (Iterative Convergence Error), and Appendix C (RAE2822 airfoil case) of the original manuscript have been dropped. Table 3, Table 5, Table 6, Table 10, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17, and Figure 18 of the original manuscript are not included in the revised manuscript. Two more figures (Figure 5 and Figure 6 of the new manuscript) were created to make the discussion of the discretization error clearer. The number of pages for the original manuscript was 71, whereas the current version has 55 pages.
Response 1.2: The title has been replaced with a more specific and suitable phrase that summarizes our work in this paper. With this study, we intend to (1) quantify the relative contribution and the importance of each source of uncertainty for design and show the level of scatter in results that a well informed CFD user may obtain (2) illustrate the interaction of numerical errors and physical modeling uncertainties, and (3) show that the complex flow fields with separated flow regions require highly refined grids to obtain solutions with acceptable level of accuracy. We believe that, with the achievement of the above goals, we will make a valuable and original contribution to the literature.
Response 1.3:Among many publications, the two most relevant references for the validation and the verification of the GASP code are:
1. Neel, R. E., Godfrey, A. G., and Slack, D. C. “Turbulence Model Validation in
GASP Version 4”, AIAA Paper 2003-3740, June 2003.
2. Brown, J. L. “Turbulence Model Validation for Hypersonic Flows”, AIAA Paper, 2002-3308, June 2002.
These references were obtained by consultation with the code authors. The first publication is given as Reference 6 and the second one asReference 7 in the revised manuscript. We refer to these publications in the third paragraph of Section 1 (Introduction): “…It should be noted that this is not a paper on validation or verification.Such studies have been conducted for the CFD code used here. (See Neel et al. [6] andBrown [7].) The experimental results are included only for reference and are not usedfor the code validation purpose…”
Response 1.4: All material (text, figures, and tables) related to the RAE2822 case has been dropped from the new manuscript.
Response 1.5:The following tables of the original manuscript are not included in the new version: Table 3,Table 5, Table 6, and Table 10. We also created two new figures (Figure 5 and Figure 6 in the new manuscript), which are similar to the one thatthe reviewer has plotted. These figures give a graphical representation of the discretization error results presented in Table 3 (new manuscript). In these figures, the discretization errors are added as error bars over the estimated exact value of nozzle efficiency for each turbulence model and the limiter at each grid level. The discussion that refers to these figures is given in the first paragraph of Section 4.1.5. We think that it may still be useful to keep Table 3 and Table 4as references for the numerical values in the new manuscript for interested readers.
Responses to Specific Remarks:
Response 1.6: This paper is neither on verification nor validation. The objective of the paper is given in the third paragraph of Section 1 (revised manuscript) and also indicated in Response 1.2.Since the uncertainties in the experimental measurements are not available, we have dropped the discussions which included comparison of the numerical results to the experiment. In the revised manuscript, the experimental results are included only for reference and are not used for the code validation purpose. In the third paragraph of Section 1 and second paragraph of Section 4, we have also emphasized the fact that this work is not a validation study.
Response 1.7: In accordance with the reviewer’s comment, the discussions that refer to the comparison of the numerical results with the experiment have been dropped from the new manuscript, since the uncertainties in the experimental measurements are not available. As also indicated in the previous response, the experimental wall pressure values are included in the graphs for reference only. We think that the second paragraph of Section 4 will help the reader to understand our approach to CFD simulation uncertainties, the validation issue, and the usage of the experimental data in this paper:
“In our studies on the transonic diffuser case, we have focused on five sources of the CFD simulation uncertainties: (1) iterative convergence error, (2) discretization error, (3) error in geometry representation, (4) turbulence model, and (5) change in the downstream boundary condition…….It should be noted that the current work is not a validation study. By studying uncertainty sources (3), (4), and (5), we would like to investigate the relative contribution and the importance of each source of uncertainty and show the level of scatter in results that a well informed CFD user may obtain in a design process. In a proper validation study, measurements from experiments should be compared to the numerical results to determine the accuracy of physical models, which requires detailed information about the uncertainties in measurements. For our test case, the experimental data may contain uncertainties originating from many factors such as geometric irregularities, difference between the actual Pe/P0i and its intended value, measurement errors, heat transfer to the fluid, etc. Since such uncertainties for the current experimental data set are not available, we will not compare our results with the experiment for the purpose of validation. The experimental results will be included for reference only.”
Response 1.8: The discussion about the iterative convergence, which was given in Appendix A of the original manuscript, is excluded in the revised manuscript to make the paper shorter. For a detailed analysis of the iterative convergence error in the transonic diffuser case, the reader has been directed to a VPI&SU report by Hosder et. al [21] . The “Results and Discussion” section has been re-written to give a more clear presentation and explanation of the results. In the “Results and Discussion”, we first focus on the “Discretization Error” (Section 4.1). In this section, the results are presented for each turbulence model and the limiter: Sp-Al/Van Albada (Section 4.1.1), Sp-Al/Min-Mod (Section 4.1.2), k-w/Van Albada (Section 4.1.3), k-w/Min-Mod (Section 4.1.4). Then the “General Remarks” on discretization errors are given in Section 4.1.5. Following Section 4.1, the uncertainties originating from geometry representation and the change in downstream boundary condition are given in Sections 4.2 and 4.3, respectively. These sections mainly describe the effects of geometric uncertainty and the downstream boundary condition on the flow-field. Since almost all the discussion for the geometric uncertainty and downstream boundary condition includes comparing the results of each code one to another, the results were not separated for each individual code. (Also note that the effect of the downstream boundary condition was studied only with the Sp-Al model and Van Albada’s limiter). In Section 4.4, we give relative comparisons of each source of uncertainty. This section also includes the relative uncertainty due to the selection of turbulence models. Since the numerical results are not compared to the experimental data in the revised manuscript, the evaluation with the orthogonal distance error (Section 4.3 of the original manuscript) and evaluation of the accuracy of turbulence models using the orthogonal distance error (Section 4.4 of the original manuscript) are not included in the revised text.
Response 1.9: As also indicated in the previous responses, we do not compare the numerical results with the experiment due to the lack of information on uncertainties in the experimental data. The discrepancy between the CFD results and the experimental wall pressure values near the throat may be due to the turbulence models used, since each model gives the shock at a different location. This is one of the common weaknesses of turbulence models in transonic flows. However, as the reviewer points out strongly in his remarks, we still need to know the experimental uncertainty to reach an accurate conclusion.
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