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Let say you have an object made of simple objects (figA1). You know the drag coefficients of simpler objects (here spheres and rods, figB1). Is there a way to estimating the drag coefficients of the complex object in term of simpler objects? If it help, I am only interested in very small Reynolds number (Re<10^-3) regime and even an approximation is fine. Any suggestion and method is helpful. Please do cite appropriate references.

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  • $\begingroup$ What figure? combining drag is more than adding the numbers. $\endgroup$
    – Solar Mike
    Jan 13 at 11:45
  • $\begingroup$ @SolarMike For figure refer to the hyperlink with 1. Yes, of course I know that combining drag is more than adding the numbers, thats why the questions. If some method exist to approximate the collective drag, instead of numerically solving the Navier-Stokes! Does this make sense. $\endgroup$
    – D Dum
    Jan 13 at 11:51
  • $\begingroup$ It should be obvious from the examples you have provided that it is not possible to predict. $\endgroup$
    – NMech
    Jan 13 at 12:11
  • $\begingroup$ @NMech May I ask how it is 'obvious' for you that it is not possible! $\endgroup$
    – D Dum
    Jan 13 at 12:19
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    $\begingroup$ @ddum If you place the two objects next to each other an d behind each other at different angles the values will change. Even a single object at different angles is needs numerical methods to "estimate" the drag and lift. $\endgroup$
    – NMech
    Jan 13 at 13:27

1 Answer 1

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At such very low Reynolds numbers, skin friction drag will (Landau and Lifshitz, 1987, Fluid mechanics, Butterworth-Heinemann, section 45) dominate over pressure drag (this is despite the sharp edges at the ends of the rods making this shape pretty thoroughly optimized to maximize the pressure drag coefficient at any given Reynolds number). The low Reynolds number will also mean (ibid., section 41) that the boundary layer stays laminar all the way over the surfaces. Therefore, for a Reynolds number $\textit{Re}$ and drag coefficient $C_{\textrm{D}}$ defined using the free stream velocity over the surfaces as velocity scale and the path length the fluid follows over the surfaces as length scale, one would (ibid., equation 39.16) expect $$C_{\textrm{D}} = \frac{1.328}{\sqrt{\textit{Re}}}$$

However, since both the drag coefficient and the Reynolds number here are defined with respect to the free stream velocity over the surfaces, not the far-field velocity, you'll have to analyse the form of potential flow around this shape to find out that free stream velocity, and you may still end up having to solve Laplace's equation numerically.

I'd also suggest that the best way to be really confident of the relationship between $C_{\textrm{D}}$ and $\textit{Re}$ in this case would be through a scale model experiment, not through any kind of theoretical or numerical analysis.

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