How a mathematical fluid dynamics model (in most cases we solved and analysis through Navier Stokes equations and graphs) directly connect to physical models (experimental work) like mechanical ones are doing?
Hi,
The Navier Stokes equations are developed based on mathematical relationships (vector calculus and differential /integral equations) for analyzing dynamic behavior of a fluid in physical systems (environments) to a very high accuracy using the primitive variables, e.g. pressure, velocity, density and viscosity
These variables are considered fundamental to any fluid and its characteristics truly represent the actual system which change with varying boundary conditions according to complexity of physical model.
Though in experiment work, the conditions represent the same model, it may involve additional factors such as errors during measurement of physical quantities. Essentially there always exist some differences between computed solutions and experiment work or results to validate the model entities.
Hence, the whole idea behind the development of mathematical fluid dynamic model using N-S equations was to understand and investigate these scientific intricacies with more detail and clarity.
Regards
Integrating a mathematical fluid dynamics model with experimental data involves combining theoretical equations with real-world observations. Initially, a mathematical model is developed based on fundamental fluid dynamics principles, considering factors such as Navier-Stokes equations, continuity equations, and boundary conditions.
The model parameters are then calibrated and validated against experimental data. This involves adjusting the model's coefficients to best match the observed behavior in experiments. The calibration process fine-tunes the model's predictions, ensuring it accurately represents the physical phenomena under investigation.
Once calibrated, the model can be used to simulate scenarios beyond the experimental conditions, providing insights into the system's behavior under various circumstances. This integration allows researchers to extrapolate findings, optimize designs, or predict outcomes beyond the scope of the actual experiments.
It's crucial to note that the success of this integration depends on the accuracy of the mathematical model, the quality of experimental data, and the thoroughness of the calibration process. Continuous refinement and validation against new experimental data are essential to enhance the model's predictive capabilities and ensure its reliability in diverse scenarios.
Both experimental and numerical procedures are constrained by several htpotheses. Those constitute a model, you need to prescribe the math that fulfills the experinental model to have a congruent result.
if you have a more specific flow problem, the discussione could be more focused.
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