3.1. Relationship between Wind Resistance and Experimental Capsule Radius
This study mainly focused on the wind resistance optimization of the CHIEF high-speed machine with a maximum acceleration of 1500 g. Therefore, the effect of the radius was investigated under the operating condition of an angular velocity of 57 rad/s, corresponding to 1500 g. This study considered a radius range of 4350–4650 mm. We simulated the torque resistance of an armature with various radii.
Figure 7 presents the relationship between the wind resistance torque, average sectional speed within the MRF motion reference system, and average effective viscosity across sections as they vary with the radius. A schematic of the section location is shown in the upper-left corner of
Figure 7.
Figure 7 shows that as the radius increases, the wind resistance exhibits an upward trend, with a maximum increase of approximately 19%. This finding agrees with the results obtained by Kutter [
5]. However, notably, Kutter attributed the increase in wind resistance to the growing mass of entrained air and the reduction in entrainment speed of the air as the radius expands, which leads to an increased relative velocity between the entrained air and the armature, thereby enhancing the wind resistance. Nevertheless, within the radius range of 4350–4650 mm, the simulation results did not lead to a reduction in the entrainment speed. We used the average sectional speed to visually represent the variation in the air entrainment speed, as indicated by the solid blue circles in
Figure 7. The average sectional speed remained at approximately 140 m/s, without any noticeable decline.
To analyze the reasons for the increase in the simulated wind resistance, the expression for windage power in
Table 1 was examined, revealing that only the dynamic viscosity appears in the formula. However, during high-speed rotational motion, turbulent shear stress cannot be neglected. The turbulent shear stress can be represented by Equation (14) [
22], as follows:
where
represents the eddy diffusivity coefficient and
denotes the turbulent mean velocity. Combining the turbulent shear stress with the laminar viscous shear stress results in an effective shear stress, as expressed in Equation (15), as follows:
In the equation, represents the effective dynamic viscosity, whereas denotes the dynamic viscosity. For high-Reynolds-number flows, in the viscous sublayer of the boundary layer, is significantly larger than , where laminar viscosity losses dominate. In contrast, outside the boundary layer in the turbulent region, is much greater than , where the viscous losses caused by turbulent shear stresses become dominant. Notably, is not a constant physical property but depends on spatial coordinates and is determined by the conditions of the flow field.
The wind resistance power was analyzed based on the Reynolds transport theorem. By employing tensor notations in Cartesian coordinates, the Reynolds transport equation can be given as follows [
22]:
where
E represents the total energy,
denotes the density,
represents the effective thermal conductivity,
is a constant, and
signifies viscous heating.
where
and
.
Under steady-state conditions, the wind resistance power should be entirely converted into viscous heat; therefore, studying the viscous heating term is equivalent to investigating wind resistance power.
For ease of studying the relationship between wind resistance power, effective viscosity, and velocity distribution, Equation (17) is transformed into Equation (18) using the ideal gas equation, as follows:
where
T,
P, and
R are the temperature, pressure, and gas constant, respectively. For fluids with constant density, the term
is zero.
Equation (18) clearly indicates that under conditions where changes in the temperature and pressure spatial distributions are negligible, the viscous heating term is solely related to the effective dynamic viscosity and spatial distribution of velocities. In our simulation, we observed that the spatial distribution of velocity near the armature did not exhibit significant variations. Thus, we focused on another influencing factor: the effective dynamic viscosity. To visualize the changes in the effective dynamic viscosity throughout space, we utilized the average sectional effective dynamic viscosity, as indicated by the yellow circles in
Figure 7. We noticed that the effective dynamic viscosity increased as the radius increased from 4350 to 4650 mm.
Figure 8a,b shows the sectional contour plots of the effective viscosity within the MRF rotating domain at radii of 4350 and 4650 mm, respectively. These figures reveal that when the radius increases, the effective dynamic viscosity within the wake region behind the armature increases significantly.
Based on the above analysis, we discovered that when the radius increases from 4350 to 4650 mm, the increase in wind resistance is not due to a decrease in the air entrainment speed or an increase in the relative velocity between the armature and entrained air but to an increase in the effective viscosity within the wake region.
3.2. Relationship between Wind Resistance and Height of the Experimental Capsule
To investigate the impact of the height of the experimental capsule on wind resistance, scenarios at an angular velocity of 57 rads/s and heights ranging from 1400 to 2200 mm were studied. In
Figure 9, the purple spheres represent the simulated wind resistance power at different heights. The figure reveals that wind resistance generally increases with increasing height, showing a maximum increase of approximately 34%. Compared to the influence of the radius, the effect of height on wind resistance is more pronounced. However, the influence of height on wind resistance did not increase linearly; we observed a notable increase in wind resistance when the height increased from 1600 to 1700 mm. Considering Equation (18), because the spatial distribution of the velocity undergoes relatively significant changes with an increase in height, it is not possible to directly analyze the cause of the increased wind resistance through the effective viscosity. Therefore, in this case, we utilized the Reynolds number to observe the changes in turbulence with increasing height. The yellow circles shown in
Figure 9 indicate the average vertical sectional Reynolds numbers obtained from the simulations at different heights. We found that the Reynolds number gradually increased with increasing height and that there was a notable spike in the Reynolds number when the height increased from 1600 to 1700 mm.
To analyze the causes of the changes in the Reynolds number, we present the local Reynolds number contour maps near the armature at different heights (
Figure 10).
Figure 10a shows the Reynolds number contour map at a height of 1400 mm; in the observation area, the Reynolds numbers between the armature and wall surface are small, represented by blue shades of color. When the height increased from 1600 to 1700 mm, as shown in
Figure 10b,c, in the observation areas, as the armature moves further away from the wall surface, the middle regions in the contour map rapidly change from blue to orange, indicating a rapid increase in the Reynolds numbers between the armature and wall surface. Finally, when the height increases from 1700 to 2000 mm, as illustrated in
Figure 10c,d, the orange regions continue to expand, and the Reynolds numbers between the armature and wall surface continue to increase in the observation areas.
These results demonstrate that the development of the Reynolds number is suppressed when the armature is close to the wall. As the armature moves away from the wall, the Reynolds number gradually increases, and a specific height range exists in which the Reynolds number rapidly increases. Similar phenomena have been widely reported in studies on the von Kármán vortex street phenomenon. For instance, de Oliveira et al. [
23] documented the aerodynamic behavior of a smooth circular cylinder near a fixed wall in a wind tunnel with a high-Reynolds-number flow and reported that as the cylinder approached the ground plane, the drag sharply decreased and then increased owing to the Venturi effect near the wall suppressing vortex shedding. The von Kármán vortex street phenomenon has not been previously reported in other supergravity centrifuge studies; therefore, to confirm its presence, we present vorticity cloud plots for a cylindrical cross-section with a radius R of 3500 mm in
Figure 11.
Figure 11a,b illustrates the vorticity cloud plot for the cylindrical cross-section at heights of 1400 and 2200 mm, respectively. Both figures exhibit vorticity in the wake region of the armature. When the wall is close to the armature, as shown in
Figure 11a, the high-vorticity region develops inadequately because of the influence of the wall. Conversely, when the wall is farther away from the armature, as shown in
Figure 11b, the high-vorticity region develops fully without being affected by the wall, and a longer wake region is observed.
Therefore, we conclude that the rapid decrease in torque resistance when the armature is close to the wall is also likely due to the Venturi effect near the wall, which inhibits the shedding of vortices, thereby suppressing the growth of the von Kármán vortex street and consequently reducing the wind resistance torque.
3.3. Relationship between Resistance Torque and Roughness Height
The roughness heights of the sidewalls, top and bottom walls, and armature also affect the torque resistance of the armature. To investigate the influence of the roughness height on the torque resistance, we simulated the torque resistance when the roughness heights of the sidewalls, top and bottom walls, and the armature varied at levels of 1 × 10
−6, 1 × 10
−5, 2.5 × 10
−5, 5 × 10
−5, and 1 × 10
−4 m, as shown in
Figure 12. The “Sidewall” subplot in
Figure 12 depicts the changes in the torque resistance under different roughness heights of the sidewall when the roughness heights of the top and bottom walls and the armature are fixed at 1 × 10
−5 m. The purple dots and yellow circles represent the torque resistance at an angular velocity of 57 and 40 rads/s, respectively. The graph shows that as the roughness height decreases, the torque resistance initially decreases and then stabilizes. At 57 rads/s, the torque resistance decreases by approximately 10.5%, whereas at 40 rads/s, it decreases by approximately 8%. Notably, the torque resistance does not necessarily decrease at lower roughness heights; instead, a critical roughness height exists. Below this threshold, the sidewall surface is effectively considered smooth, and torque resistance no longer decreases with decreasing roughness height. At an angular velocity of 57 rads/s, the critical roughness height is 1 × 10
−5 m, whereas at 40 rads/s, it is 2.5 × 10
−5 m. The critical roughness height is related to the angular velocity or rotational speed of the armature; higher speeds correspond to smaller critical roughness heights, a phenomenon that has also been verified by Avci and Karagoz [
24]. The “Top and bottom walls” subplot in
Figure 12 indicates a similar situation in which the torque resistance initially decreases and then stabilizes as the roughness height diminishes. At 57 rads/s, the resistance torque decreases by approximately 9.5%, whereas at 40 rads/s, it decreases by approximately 8.5%. Furthermore, a critical roughness height exists here as well, which decreases as the rotational speed increases. Consequently, when the rotational speed requirements for the supergravity centrifuge increase, to minimize the torque resistance as much as possible, the smoothness requirements of the sidewalls must be reduced, i.e., the roughness height must be reduced.
The “Rotating arm” subplot in
Figure 12 illustrates the variation in torque resistance under different roughness heights of the armature when the roughness heights of the top and bottom walls and sidewalls are fixed at 5 × 10
−5 m. The effect of the armature roughness height on the torque resistance is minimal compared with that of the roughness height of the sidewalls and top and bottom walls. At 57 rads/s, the torque resistance decreases by only 2.4%, and at 40 rads/s, it decreases by a mere 0.8%. This is primarily because, in the torque resistance components obtained from simulations, the shape (or pressure) component dominates the armature’s contribution, accounting for over 96% of the total resistance, whereas the friction (or viscous) component constitutes less than 4%. This partition of components is consistent with similar findings from a study by Achenbach [
25] on the resistance components of a streamlined cylindrical body, where they reported that the shape (or pressure) component accounted for over 98% of the resistance, whereas the friction component accounted for less than 2%. Clearly, the roughness height does not alter the shape (or pressure) of the resistance but only affects the friction component. Consequently, for the armature, the roughness height has a relatively minor impact on the torque resistance.
3.4. Relationship between Wind Resistance and Armature Geometry
In the analysis described in
Section 3.3, the shape (or pressure) component contributes predominantly to the torque resistance of the armature. Hence, the shape of the armature has a significant effect on the torque resistance. Given the impossibility of exhaustively examining every conceivable armature shape, we selected five typical armature geometries for comparative analysis, as shown in the accompanying figure. Here, Figure 14a represents the actual armature shape of the CHIEF device, Figure 14b depicts an armature with no chamfer treatment, Figure 14c shows an armature design with rounded fillet corners, Figure 14d presents an armature with chamfers at the edges, and Figure 14e shows an armature in a disc-shaped configuration.
Figure 13 shows the variation curves of torque resistance with angular velocity for the five aforementioned armature geometries. As shown in the figure, the torque resistances ranked from largest to smallest, corresponding to the armatures in the following order:
Figure 14b features an armature with no chamfers,
Figure 14a depicts the actual armature,
Figure 14c displays an armature with rounded fillets, and
Figure 14e presents a disc-shaped armature. Among these, the torque resistances under different angular velocities are relatively close for the armatures shown in
Figure 14a–c.
Figure 14d shows an armature with chamfers, which exhibits a notably reduced torque resistance with a maximum decrease of approximately 20% compared to the armature without chamfers, as shown in
Figure 14b. However, this armature design has the disadvantage of having a smaller volume. If used as an armature in a supergravity centrifuge, it would significantly reduce the space available for the experimental capsules. Finally,
Figure 14e indicates that the disc-shaped armature experienced the most significant reduction in torque resistance, with a maximum decrease of approximately 73% compared to the armature without chamfers in
Figure 14b. This substantial decrease is mainly because of the absence of pressure-induced resistance in the disc-shaped armature, which only incurs frictional resistance.
Figure 15 shows the vorticity cross-sectional contour plots of the flow field around different armature geometries at an angular velocity of 40 rads/s. The greater the vorticity, the larger the vortex losses within the flow field. In
Figure 15, colors closer to red indicate higher vorticity values, whereas colors closer to blue indicate the lowest vorticity values. Large vorticity regions are concentrated in the vicinity of the armature and its wake area. By observing the images in
Figure 15a–d, the high-vorticity regions gradually decrease. For a more direct comparison of the vorticity magnitudes among the different shapes, we calculated the volumetric average vorticity values. These values were found to be 263.8, 257.8, 235.7, and 129/s in
Figure 15a–d, respectively. In descending order, the volumetric average vorticity corresponds to armatures with no chamfers, armatures with rounded fillet corners, armatures with chamfers, and the disc-shaped armature, which aligns with the descending order of torque resistance. Thus, we conclude that different armature geometries result in varying vorticities in the surrounding flow field. The greater the vorticity, the larger the vortex losses, and hence, the larger the torque resistance. In comparison, the disc-shaped armature exhibits a much lower vorticity in its wake flow field.
To analyze the impact and contributions of different parts of the armature on the torque resistance, the armature was divided into four segments: end wall surface, sidewall surface, top wall surface, and bottom wall surface, as shown in
Figure 16a–d.
Figure 17 presents bar charts of the resistance contributions of different armature segments, with
Figure 17a–d representing the armatures without chamfers, armatures with rounded fillet corners, armatures with chamfers, and disc-shaped armatures, respectively. For non-disc-shaped armatures, according to
Figure 17a–c, the end portions contributed the largest proportion of the resistance, followed by the sidewall surfaces, with the contributions of both the top and bottom wall surfaces being negligible and not exceeding 1%. Among the end portions, the rounded fillet corner armature had the highest resistance share at (81 ± 1)%, followed by the armature with no chamfers at (71 ± 1)%, and the share of the chamfered armature with a head portion ranged from 57% to 60%. Regarding the contributions of the sidewall surface to the resistance for non-disc-shaped armatures, the chamfered armature tops the list with a resistance share of approximately (40 ± 1)%, followed by the armature with no chamfers, with a sidewall resistance share of around (28 ± 1)%, and the armature with rounded fillet corners, which has the smallest contribution with a sidewall resistance share of (18 ± 1)%. Because the disc-shaped armature lacks end portions, the sidewall surfaces account for approximately 50% of the resistance, whereas the top and bottom wall surfaces each contribute approximately 25% of the resistance.
In summary, we found that the disc-shaped armature dramatically reduces resistance because it lacks pressure–resistance components, possesses only frictional resistance, and exhibits a much smaller vorticity in the surrounding fluid flow. The resistance contribution from the sidewall segment of the disc-shaped armature is comparable to the combined contribution from the top and bottom wall segments. For the non-disc-shaped armatures, the ends of the armature contributed the most to the resistance, followed by the sidewalls, with the contributions from the top and bottom walls being incredibly small (less than 1%). The resistance contributions from different segments remained largely unchanged with variations in angular velocity. In the case of a disc-shaped arm under actual implementation, certain issues arise, such as difficulties in casting a solid arm of this shape while maintaining balance as well as challenges in casting and installation. However, we propose considering the use of a disc-shaped shell that simply envelops the existing arm configuration, with an access hatch atop the shell designed for disassembling the hypergravity experimental apparatus. With this approach, the primary concern would be the secure fixation of the shell itself. Therefore, we believe that the solution involving a hollow shell structure is practically feasible.