Good Question, and one that is quite difficult to answer, at least beyond the theoretical level. I'm an experimentalist at heart and have been long interested in the effects Reynolds Number has on predicting aerodynamic performance of bluff bodies. Since practical solutions often limit the ability to test subjects at the actual size or environment, it is necessary to develop scale test or simulation models to answer performance questions. Both of those methods fall short of predicting the correct turbulence length scale in the transition from laminar to turbulent. They also struggle with predicting the shear layer in an outdoor or wind tunnel environment.

You mentioned immersed bodies in your question so if that is to mean something in a body of water, this case could be scaled up to study the effect of different variables in a wind tunnel environment. In reduce scale testing the possibility exist to have very high local Mach numbers or local Reynolds Numbers that cause unwanted inaccuracies to the forces acting on the system. However, predicting performance of a scaled-up model in a wind tunnel to achieve the Reynolds Number seen in water could prove to have very small errors from these local Reynolds and Mach numbers.

I know this isn't a direct answer to your question but there was not enough information about the application to focus on the specific scenario. I'm happy to discuss further with you, or perhaps another member with more knowledge on the matter can chime in,

kind regards

Reynolds number is not univocally defined, there are several choice of lenght and velocity producing different values. Sometimes, the Re number is actually a function depending on distance.

Thus, depending on the flow problem, a suitable physical assumption based on a value is acceptable provided that the choice of the characteristic scales is such to get normalized (not only non-dimensional) the equations.

Note that the Re number is also a ratio between characteristic time scales of the problem.

Desta,

What is your question?

Engineers consider these factors in designing systems like pipes, aircraft wings, or heat exchangers, aiming to optimize efficiency and performance based on the desired flow regime.

Thousands of text books explain the use of Re in laminar to turbulent flow transition: what aspect are you looking at? Hae you looked at the literature?

At low Reynolds numbers, flow is laminar and well-ordered, while at high Reynolds numbers, there is increased chaos and mixing. As a result, the flow becomes turbulent.

I hope you find it useful. I may have misunderstood you, but Reynolds's number doesn't influence anything. Re describes and defines the situation with the single, nondimensional number only. Forces are of interest to you because they play a central role and control reality.

The Reynolds number is a dimensionless parameter that plays a crucial role in determining the flow regime around immersed bodies. It is defined as the ratio of inertial forces to viscous forces in a fluid flow and is expressed as:

\text{Re} = \frac{\rho \cdot V \cdot L}{\mu}Re=μρ⋅V⋅L​

Where:

• \text{Re}Re is the Reynolds number,
• \rhoρ is the fluid density,
• VV is the velocity of the fluid relative to the object,
• LL is a characteristic length (e.g., diameter for a pipe or chord length for an airfoil),
• \muμ is the dynamic viscosity of the fluid.

The Reynolds number is a dimensionless quantity, and its value provides insights into the flow regime:

There is some misconception about the role of the Re number.

For example, let me consider the wall bounded turbulence. There is no specific value for the Re number, indeed y+ represents a local Re number and you can see that, depending on its local value, laminar, transitional and fully developed conditions coexist.

There is a concept called "turbulence management" in fluid flow that determine when we need turbulence and when we should avoid it. It all depends on what kind fluid flow (e.g. internal or external), or which kind of immersed body ( e.g. bluff or streamlined body) are focused on. For all such cases Reynolds number is crucial and important parameter to be considered. Because this non-dimensional number tells you whether the flow is laminar or turbulent.