1. CH4 Alternative Altair fuel 0.0308 0.51 #Estimated values of achieved damping ratios of Apollo fuel slosh modes (with baffles) are on the order of 0.1-0.16%.30B. Computational Approach
2. In order to verify the validity of the Flow3D™ results, an independent anchoring exercise was performed, where Flow3D™ was used to model a simple tank configuration, for which the geometry, fill heights and experimentally obtained slosh frequencies were clearly defined and documented. In the experiment selected,32a 192-mm diameter tank was filled with water to various levels, ranging from 30 to 150 mm, and laterally excited to obtain frequency. This configuration was modeled in Flow3D™ and the process that was used to obtain the Altair tank slosh frequencies was repeated. The results are shown in Fig. 13. According to this exercise, Flow3D™ tends to overestimate the slosh frequencies by 7-14%. However, slosh test experience has shown that the specific methodology adopted for data reduction (i.e., excitation method, force vs. wave height trace, etc.) can affect the reported natural frequency by similar margins. This correlation, along with the favorable comparison with the Apollo-vintage methodology, is considered satisfactory confirmation of the accuracy of the Flow3DTMprediction. Other slosh parameters, such as damping ratio, pendulum length, slosh mass, etc., can also be obtained through CFD using a similar method, but work is required to experimentally validate the values of each.
3. As discussed in section VI.A.3, damping ratio of fuel slosh is a function of fuel tank geometry, longitudinal acceleration, and kinematic viscosity of the propellant. Estimated values of achieved damping ratios of Apollo fuel slosh modes are on the order of 0.1-0.16%.30Using available empirical formulae,24Altair GN&C team estimated the damping ratios of fuel slosh modes in a clean cylindrical tank (cf. Table 4). These estimates indicate that Altair fuel slosh damping ratios are even lower than those of Apollo's tanks. Baffles for the Altair's fuel tanks on both the ascent and descent modules will be needed. Baffles of various configurations add passive damping to the sloshing fuel. Damping ratios of 1-5% is achievable via baffles.35The obvious penalties of baffles are the weight increase and the manufacturability of tanks with baffles. Compartmentation of a tank will, in general, increase the slosh mode frequency. This is the case because, in general, slosh mode frequency is inversely proportional to the square-root of the tank characteristic dimension (cf. Eq. (6)). Again, there will be a weight penalty.
4. There is a general desire to select the TVC bandwidth as large as possible, not only to minimize maneuver errors (cf. Section IV.C) but also to keep both the spacecraft rate and the corresponding engine gimbal rate to within acceptable levels at ignition. Larger bandwidth will also help to bound the magnitude of the gimbal excursion angle at ignition (see Table 5, a representative engine gimbal excursion budget). The ratio of slosh mode frequency to BW of the Apollo TVC systems was ≈2.20That for the space shuttle TVC system was 1.94.21As depicted in Fig. 9, Altair's slosh mode frequencies vary over a range of 0.21-0.44 Hz from LOI to touchdown. Based on the general guideline of maintaining a 2:1 ratio between the fundamental slosh mode frequency and the TVC BW, the Altair GN&C team picked a placeholder TVC bandwidth of 0.12-0.15 Hz. This selection is comparable with the bandwidths used by Apollo, which was 0.13-0.18 Hz.20The TVC bandwidth of the space shuttle was 0.13 Hz.21Note that the selected TVC BW is also more than an order of magnitude lower than all other system dynamics and "flexibilities" including the engine gimbal actuator bandwidth, sensor bandwidth, structural frequency, the "tailwags-dog" spacecraft-engine interaction frequency,27,31,38andothers(seealsoFig.14).