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Approximation models for drag and heat flux of random tumbling objects in the transitional regime

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Abstract

A Direct Simulation Monte Carlo (DSMC) code is presented with its validation and its applications. The code uses a cut-cell approach combined with an on-the-fly Cartesian grid adaptation. The simulation is distributed using the MPI protocol and can rebalance the computation loads through the simulation. Validation of the code is demonstrated. Over 3400 simulations are carried out on 105 geometries in order to compute the random tumbling drag and heat rate in the transitional regime. The simulation setup to obtain reliable DSMC results in an automated way is outlined. Simulation results are compared with an approximation model. In order to compute the dimensionless random tumbling coefficients characterizing both the drag force and the heat rate, the random tumbling average of the projected shape is selected as a reference surface. A formulation that can be applied to various topologies of objects is used as a basis for the characteristic length used to define the average Knudsen number and for the equivalent radius used in the approximation model that computes the heat rate. For the 105 cones and cone-segments investigated, parameters can be selected such that the average difference between the approximation model and the DSMC results are below 1% for both drag and heat rate.

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Acknowledgements

The development of the DSMC solver has been done thanks to "Wet Bevordering Speur and Ontwikkelingswerk" program from the Netherlands in 2014 and 2015. Part of the work on the determination of the reference quantities has been financed under contract n\(^\circ\) 170,990 from the "Centre national d’études spatiales".

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  1. R.Tech Engineering B.V., Baarsjesweg 243, 1058AA, Amsterdam, The Netherlands

    Pierre Van Hauwaert

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Correspondence to Pierre Van Hauwaert.

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Appendix: Additional figures and tables

Appendix: Additional figures and tables

See below Tables 5, 6 and 7; Figs 24, 25, 26, 27 and 28.

Table 5 Species parameters. Viscosities are given for a reference temperature \(T_{ref}=273\) K
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Table 6 Free-stream conditions and wall temperature
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Table 7 Weight for axisymmetric configuration as a function of the angle of attack
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Fig. 24
figure 24

Variation in shape factor and drag coefficient due to the number of simulation particles and the time step

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Fig. 25
figure 25

Drag coefficient as a function of the Knudsen number, including geometry labels. DSMC data is represented by points and approximation models are represented by lines

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Fig. 26
figure 26

St number as a function of the Knudsen number, including geometry labels. DSMC data is represented by points and approximation models are represented by lines

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Fig. 27
figure 27

Drawing of cones

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Fig. 28
figure 28

Drawing of cone-segments

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Van Hauwaert, P. Approximation models for drag and heat flux of random tumbling objects in the transitional regime. CEAS Space J 15, 895–921 (2023). https://doi.org/10.1007/s12567-023-00492-1

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