Optimum Shape Design for Multirow Turbomachinery Configurations Using a Discrete Adjoint Approach and an Efficient Radial Basis Function Deformation Scheme for Complex Multiblock Grids
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Bibliographic record
Abstract
This paper proposes a framework for fully automatic gradient-based constrained aerodynamic shape optimization in a multirow turbomachinery environment. The concept of adjoint-based gradient calculation is discussed and the development of the discrete adjoint equations for a turbomachinery Reynolds-averaged Navier–Stokes (RANS) solver, particularly the derivation of flow-consistent adjoint boundary conditions as well as the implementation of a discrete adjoint mixing-plane formulation, are described in detail. A parallelized, automatic grid perturbation scheme utilizing radial basis functions (RBFs), which is accurate and robust as well as able to handle highly resolved complex multiblock turbomachinery grid configurations, is developed and employed to calculate the gradient from the adjoint solution. The adjoint solver is validated by comparing its sensitivities with finite-difference gradients obtained from the flow solver. A sequential quadratic programming (SQP) algorithm is then utilized to determine an improved blade shape based on the gradient information from the objective functional and the constraints. The developed optimization method is used to redesign a single-stage transonic flow compressor in both inviscid and viscous flow. The design objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it