Fluid dynamics are studied in 3 different ways: analytically, numerically and experimentally. Analytical calculations are useful or “order of magnitude” estimations. We gain insight in the relevant system parameters by doing so, we can calculate the approximate pressure drop, or we can determine whether a flow is laminar or turbulent. Furthermore, a solid understanding of the mathematical description of a flow is pivotal to correctly interpret experiments or simulations. To calculate a flow profile with a sum by hand, however, is only possible for the most simplified class of problems, such as a steady laminar pipe flow. Transient flows, turbulent flows, or flows in more complex geometries cannot be calculated similarly by analytical means.
Traditionally, if analytical calculations were not sufficient, we relied on experimental investigations. Experiments provide an enormous understanding of the dynamics of a flow. We can visualize a flow by adding smoke of dye. And we can quantify a flow with velocity-, temperature- and pressure measurements. Earlier most of these measurements were “intrusive” – a probe was directly put in a flow. Over the last 2 decades, we switched to optical methods, such as Particle Image Velocimetry (PIV), Particle Tracking Velocimetry (PTV) and Laser Doppler Anemometry (LDA). Here, the flow is illuminated with a laser, whose light is reflected by added tracer particles. The velocity is measured by the redshift (LDA), or by making two photos, which are correlated (PIV, PTV).
Experiments have their limitations, however. Experiments are relatively costly, both in equipment as in manpower. Making good experimental setups and performing multiple iterations are very time-consuming.
Only relatively recently, computer simulations became popular for industrial applications. Earlier, numerical simulations were only performed by universities and specialized companies such as Boeing and NASA. In the nineties, user-friendly commercial codes were introduced, which enabled the use of numerical simulations for a larger group of companies.
In numerical simulations, the underlying mathematical flow equations (the Navier-Stokes equations) are calculated numerically and solved at discrete points. This technique is commonly referred to as computational fluid dynamics (CFD). The Navier-Stokes equations are often simplified to the Reynolds-averaged Navier-Stokes equations. By doing so, the turbulence properties are averaged in time. As shown in the figure, a geometry is split up in tiny volumes. The conservation laws of mass, momentum, and energy are applied to these volumes. Resultantly, the entire mesh is analyzed and we obtain the numerical solution.
In the translation from a real flow to the numerical solution, we have to simplify the flow. Usually, we simplify the geometry to ease the meshing, and the turbulence properties are modeled in a simplified way. Consequently, some people are skeptical about the benefits of numerical simulations.
However, simulations have a number of significant advantages over experiments. Firstly: numerical simulations are faster and cheaper than experiments. Secondly: iterating is easier. A different geometry, a different fluid, a larger velocity of volume flux: all are parameters which can be varied. In this way, a design process is simplified and faster. Thirdly: in experiments, we mostly measure a single important parameter, such as the pressure drop. In simulations, all flow data is available. We can visualize the flow with velocity vectors, movies, contour plots and streamlines. Therefore, we gain more insight of the flow, and better understand its problematic areas.
Will simulations completely replace experiments? No, probably not. Experiments always result in valuable insight without any simplifications. And in more specific research areas, experimental validations for the numerical simulations are often needed due to the complexity of the flow. In this way, experiments, numerical simulations and analytical methods all give a different way of understanding a flow. In that sense, they are completely complementary and will remain like that for the time being.