In this paper we want to describe the generation of random surfaces. They are used to create rough microstructures in heat exchangers. Thus the potential exchange area can be maximized to gain a more efficient heat exchange. In our examples the microstructure is established on a macrostructure, which is based on fractal curves and divides two fluids. As such the microstructure is only one factor to gain an efficient heat transition. The other is the fractal-like macrostructure.
The microstructure is generated with random processes. These are self-similar Gaussian processes, the so-called fractional Brownian motions. Our random variables X_i~N(0,σ), i=1,…,N, are independent and identically distributed. The roughness of our surface is measured with the Hurst exponent D∈(0,1). A small value for D results in a rougher surface.
Figure 1: A randomly generated surfaces with N=1024, H=0.3, σ=0.1 on the unit disc.
In figure 1 we present a possible random surface. For this a grid of random variables is generated and connected with continuous lines. It can be easily seen that a huge local difference in the values results in great prongs. With respect to typical processes in additive manufacturing these prongs cause some issues. One obvious problem is the conflict with the resolution of the additive manufacturing process.
Like sketched above, we want to morph these random surfaces onto a macrostructure. The prongs now cause another problem: the offset areas. The thickness of a prong (as the difference between the upper and the lower layer) is not uniform. We show some ways to weaken or solve this problem to get nearly equidistant layers.
Figure 2: The typical offset problem. The distance between the upper and lower layer (black) is not globally uniform. The way to the peak (blue) is longer than the way to the orthogonal (next) points in red.
We can bound the maximum distance between the two layers by a constant, depending or not-depending on the minimal layer thickness in the 3-D printing process. Another way is to cut the prong at some point. The approaches are presented in the paper. They raise some theoretical problems of random surfaces. We will show how these problems can be solved and how these surfaces can be used efficiently in additive manufacturing.
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