Physics

Free-molecular aerodynamics

Rarefied-gas force and torque on every panel, summed over the vehicle, with the atmosphere rotating with the Earth. Two gas–surface interaction (GSI) models are available: Sentman (the default) and the Walker closed-form Cercignani–Lampis–Lord (CLL) fit.

Source: cpp/src/aero/sentman.cpp (panel sum + Sentman), cpp/src/aero/cll.cpp (Walker-CLL), called from Simulator::step every substep. Switch: aero.gsi in the physics YAML, or --gsi on the CLI.

Flow state

• corotating: true subtracts ω⊕ × r (ω⊕ = 7.2921150e-5 rad/s).
• v_wind is zero until you call Simulator.set_wind(w_N). MSIS has no winds, and no HWM model ships with the code.
• ρ, T and m̄ come from MSIS (see Atmosphere). The same (ρ, T, m̄, χ) is held within a substep and interpolated linearly across the step when atmosphere.interp is on.
• The gas velocity in body axes is v_B_gas = −C_BN v_rel. For each panel with outward normal n̂: \(\cos\theta=-\hat v\cdot\hat n\), with θ = 0 face-on.

Panel sum (common to both GSIs)

• The code stores \(C_\tau/\sin\theta\) and multiplies by the unnormalised \(\hat v+\cos\theta\,\hat n\), so an edge-on panel has no singularity.
• Wetted faces: every panel with \(s\cos\theta>-4\) is summed, back faces included. The erf/exp terms turn the lee-side flux off smoothly. For CLL the cut is per species (\(s_j\cos\theta\le -4\)).
• \(C_D=\mathbf F\cdot\hat v/(qA_\mathrm{ref})\), \(C_L=|\mathbf F_\perp|/(qA_\mathrm{ref})\). With one_sided_ref, A_ref is half of ΣA (a two-sided membrane counts once).
• Torque is about the body origin. Centroids are shifted by cp_offset_m in v8+ so the centre of pressure is offset from the CoM.
• There is no shadowing or shielding: panels do not block one another. This is exact for convex bodies and flat membranes. For concave assemblies it is an approximation.

Sentman (default)

Sentman (1961) diffuse re-emission with the Moe & Moe (2005) energy-flux accommodation closure (project item M-01). With \(\gamma=s\cos\theta\), \(Z=1+\mathrm{erf}\,\gamma\), \(E=e^{-\gamma^2}\):

• Parameters: aero.alpha_E (0.93), aero.T_w (300 K). They are global for the whole vehicle.
• Sentman is fully diffuse in direction. α_E only sets the re-emission energy, so there is no specular momentum.
• Numerical guard: for γ > 6, Z = 2 and E = 0 exactly (error ≤ 1e-15).
• Hyperthermal identity (tested): \(C_p\cos\theta+C_\tau\sin\theta\to2\cos\theta\) as s → ∞ with α_E = 1 and T_w = T_i.
• The \((1-\alpha_E)s^2/2\) term keeps only the directed incident energy. Including the thermal part (\(+(1-\alpha_E)\)) would change face-on C_p by ≈0.2 % at s = 8, which is negligible.

Walker–CLL (optional, gsi: cll)

Walker, Mehta & Koller (2014) fitted closed-form plate coefficients to CLL-kernel simulations, as transcribed in ADBSat (Sinpetru et al., arXiv:2104.05543, eqs. 9–15). The model has one fit per species and is not the exact kernel. With \(\Gamma_1=\gamma E/\sqrt\pi+\tfrac12(1+2\gamma^2)Z\) and \(\Gamma_2=E/\sqrt\pi+\gamma Z\):

• α_N = 1 switches to the Schaaf–Chambre branch (ADBSat eq. 9), which equals Sentman with α_E = 1.
• Species mix (eq. 15): \(C=\sum_j\chi_jm_jC_j/\sum_j\chi_jm_j\) over He, O, N₂, O₂, Ar, H, N, with a per-species speed ratio \(s_j\). MSIS anomalous O is folded into O, and NO is dropped. Without χ the model uses the atomic-O row and the mixture s.
• Walker fit rows β, γ, δ, ζ are in walker_fit(). He and H depend on the α_N band; Ar reuses the N₂ row.
• Parameters: aero.alpha_n (Walker α_N, normal energy accommodation), aero.alpha_t (σ_T, tangential momentum accommodation), aero.T_w. They are global for the vehicle.

How close is the Walker fit to the exact CLL kernel?

For this documentation pass I integrated the exact CLL kernel per plate with a scratch quadrature. The normal kernel is a Rice distribution, so its mean has a closed form in Bessel functions, and only the average over the incident Maxwellian needs a 1-D integral. No project code was changed. Atomic O, s = 8, T_w/T_i = 1/3, σ_T = 1:

The Walker fit is excellent face-on and at moderate incidence, but it drifts at grazing incidence as α_N → 1 (at 80° the fitted C_p even drops below the α_N = 1 value). On the whole 176-plate SolarCat the effect averages out to ≤ 0.3 % in C_D. The much larger lever is the accommodation values themselves (see the plan).

Drag baseline and energy terms

Each substep also evaluates coefficients_only with the flow along the vehicle's minimum-projected-area body axis (min_drag_axis). The result is cached until s changes by more than 2e-4 relative. That gives the counterfactual \(F_\mathrm{base}=C_{D,\mathrm{base}}\,q\,A_\mathrm{ref}\), and the plant integrates:

dE_drag and dE_lift split the aero part along and across \(\hat v_\mathrm{rel}\). These feed the RL reward (dE_vs_baseline).

Configuration

Standalone use

from arlamx_v2 import cpp
from arlamx_v2.geometry import load_geom
n, A, c = load_geom("data/SolarCat_v3_1pct_plates.geom")
out = cpp.spacecraft_aero(n, A, c, v_rel_B=[7600, 0, 0], rho=3e-12, T=900, m_bar=2.656e-26,
                          T_w=300, alpha_E=0.93, one_sided_ref=True,
                          gsi="cll", alpha_n=0.93, alpha_t=1.0, chi=[0, 1, 0, 0, 0, 0, 0])
out["F"], out["tau"], out["Cd"], out["Cl"], out["A_ref"]
cpp.sentman(theta, s, Tw_Ti, alpha_E)          # (Cp, Ctau) for one plate
cpp.cll(theta, s, Tw_Ti, alpha_n, alpha_t)      # (Cp, Ctau), atomic-O row

Validation

• tests/aero/test_sentman.py: hyperthermal identity (1e-3 at s = 8, 1e-8 at s = 80), α_E limits, face-on bands.
• tests/aero/test_cll.py: T-CLL-1 (α = 1 equals Sentman α_E = 1), T-CLL-4 (mixture differs from pure O), T-CLL-5 (unknown GSI throws). T-CLL-2/3 are specified in docs/CLL_TEST_SPEC.md but not yet written.
• tests/validation/verify_physics.py: independent scipy quadrature of the Sentman integrals.
• ACEnv/Reports/verify_sentman.md: audit record.

Limits

• One global (α, T_w) for all panels, with no per-material behaviour. See the plan.
• No shadowing or multiple reflection between panels (concave geometry).
• No surface-coverage (atomic-O adsorption) model, so α does not change with altitude or solar activity.
• Sentman is fully diffuse. Walker-CLL is a fit that is weakest at grazing incidence with α_N → 1.
• The onboard FP32 forecast uses a constant ballistic coefficient and an exponential atmosphere, not the panel model.

References

1. Sentman, L. H. (1961). Free molecule flow theory and its application to the determination of aerodynamic forces. LMSC-448514.
2. Moe, K. & Moe, M. M. (2005). Gas–surface interactions and satellite drag coefficients. Planet. Space Sci. 53, 793–801.
3. Cercignani, C. & Lampis, M. (1971). Kinetic models for gas–surface interactions. TTSP 1, 101–114; Lord, R. G. (1991) Phys. Fluids A 3, 706.
4. Walker, A., Mehta, P. & Koller, J. (2014). Drag coefficient model using the CLL GSI. J. Spacecraft Rockets 51(5), 1544–1563.
5. Sinpetru, L. et al. (2022). ADBSat. arXiv:2104.05543.
6. Doornbos, E. (2012). Thermospheric Density and Wind Determination from Satellite Dynamics. Springer.