Numerical simulation of flow field in a Laval nozzle based on one-dimensional Euler equation
Bibliographic record
Abstract
Abstract Numerical simulation refers to a computer research method which runs calculation based on a specific mathematical model to simulate actual physical processes. It is a powerful tool to analyse complex engineering problems. In this paper, a numerical method for solving the steady one-dimensional Euler equations using a two-step second-order difference scheme is developed. The method is implemented by a Python code. The method is applied to numerical simulation of flows in a Laval nozzle and used to investigate the influence of shapes of Laval nozzle. It is found that the physical quantities of the nozzle flow show a positive correlation trend with different throat positions. In terms of the temperature, density, and pressure, they increase during the initial evolutions, then reach the maximum point and produce significant fluctuations, indicating the flow flows into the transonic stage. Subsequently, those physical properties gradually tend to a stable value during the supersonic stage. Moreover, it is observed that the closer the throat is to the exit, the lower the Mach number at which it eventually stabilizes. Finally, a suggestion about the best shape of the nozzle which can realize the max efficiency is concluded. Despite using an inviscid flow model, the steady pressures are quite satisfactorily predicted over the range of frequencies studied.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".