Adjoint-Based Constrained Aerodynamic Shape Optimization for Multistage Turbomachines
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Bibliographic record
Abstract
This paper develops the discrete adjoint equations for a turbomachinery Reynolds-averaged Navier–Stokes solver and proposes a framework for fully automatic gradient-based constrained aerodynamic shape optimization in a multistage turbomachinery environment. The systematic approach for the development of the discrete adjoint solver is discussed. Special emphasis is put on the development of the turbomachinery-specific features of the adjoint solver (that is, on the derivation of flow-consistent adjoint inlet and outlet boundary conditions) and, to allow for a concurrent rotor–stator optimization and stage coupling, on the development of an exact adjoint counterpart to the nonreflective, conservative mixing-plane formulation used in the flow solver. The adjoint solver is validated by comparing its sensitivities with finite difference gradients obtained from the flow solver. A sequential-quadratic programming algorithm is used to determine an improved blade shape based on the gradient information provided by the adjoint solution. Optimization within a sequential-quadratic programming framework avoids the time-consuming task to determine the weights of the individual constraints by including the constraints directly into the design problem. The functionality of the proposed optimization method is demonstrated by the redesign of two two-dimensional transonic compressor configurations. 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 | 0.000 | 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