HX-1 Solid-State Hydrogen Turboelectric Cycle: Architecture, Loofah–CNT Fuel Modules, and Defensive Prior-Art Disclosure

HX-1 Solid-State Hydrogen Turboelectric Cycle Integration of Loofah–CNT Storage Modules and Cryogenic Cooling Antonios Valamontes Kapodistrian Academy of Science Defensive Publication and Prior-Art Disclosure Author: Antonios Valamontes Kapodistrian Academy of Science Date of Public Disclosure: November 26, 2025 This document is released as a formal defensive publication establishing worldwide prior art under USPTO, EPO, and WIPO rules. It is intended to place the HX-1 propulsion architecture, the loofah–CNT hydrogen modules, the cryogenic-sink topology, the thermal-material tensor network, and all derived mathematical operators into the public domain of knowledge for the sole purpose of preventing any third party from claiming patent rights over these inventions. Abstract Prior-Art Abstract. This disclosure describes the HX-1 Solid-State Hydrogen Turboelectric Cycle: a high-temperature Brayton system, a supercritical bottoming cycle, a dualmanifold hydrogen system (loofah–CNT modules + LH2cryogenic sink), a multifunctional thermal-material tensor network, and a DEP architecture powered exclusively by turboelectric conversion. This disclosure constitutes public prior art under USPTO/EPO/WIPO rules. Scientific Abstract. This article presents a unified concept specification for the HX1 Solid-State Hydrogen Turboelectric Cycle, a next-generation propulsion architecture for autonomous aircraft. The system combines a high-efficiency Brayton core, a compact bottoming cycle, distributed electric propulsion (DEP), and two complementary hydrogen subsystems: (i) modular 100 L loofah–CNT solid-state hydrogen storage vessels, and (ii) an optional small liquid-hydrogen (LH2) pod used purely as a cryogenic sink for cooling turbine blades, bottoming-cycle condensers, and power electronics. A multifunctional thermal material provides conformal, vibration-tolerant heat-transfer interfaces throughout the system. A mission-level hydrogen consumption and endurance model is derived, and key novelty claims are outlined. USPTO §102(a) Public Disclosure Statement This document is intentionally published to establish prior art under 35 U.S.C. §102(a), the European Patent Convention (EPC), and the WIPO Patent Cooperation Treaty (PCT). All concepts, claims, system architectures, diagrams, mathematical operators, and embodiments disclosed herein pertaining to the HX-1 Solid-State Hydrogen Turboelectric Cycle are hereby placed into the public domain as prior art upon the date of publication. 1 Zenodo Metadata (for archival deposition) Title: HX-1 Solid-State Hydrogen Turboelectric Cycle: Defensive Publication and Thermodynamic Architecture Author: Antonios Valamontes (Kapodistrian Academy of Science) ORCID: 0009-0008-5616-7746 Keywords: hydrogen propulsion, loofah–CNT storage, cryogenic sink, turboelectric cycle, distributed electric propulsion, thermodynamic prior art, defensive publication License: CC BY-NC 4.0 (recommended) or CC0 1.0 (if full dedication) Version: 1.0 Date: November 26, 2025 2 1 Introduction Future autonomous aircraft impose constraints on propulsion architectures expressible as a coupled optimization problem over thermodynamic state space T, structural configuration space S, and power–distribution manifold P. Let (T, p, h)∈ T denote temperature, pressure, and specific enthalpy, and let x∈ S encode geometric and material parameters. The admissible propulsion configurations are those for which the composite functional J[x, ϕ] = ZCηcore(T, p;x)+ηbottom(T, p;x)−∆ηloss(ϕ;x)dµ (1) achieves a local extremum on a connected configuration class C ⊂ S subject to the power–topology constraint ϕ∈ P. The HX–1 architecture corresponds to the subclass of solutions in which all mechanical work extracted from a high-temperature Brayton process and its bottoming-cycle extension is mapped into a high-voltage DC electrical manifold via a surjective power-flow operator Π : R→ P, ensuring that no direct mechanical thrust path remains. Formally, PDEP = Π(WBrayton +Wbottom),rank(Π) = 1,(2) where PDEP denotes electrical power supplied to the distributed electric propulsion (DEP) network. This restriction enforces a unidirectional mapping from thermal to electrical domains, enabling a variational decoupling between thermal-cycle optimization and aerodynamic force generation. A central structural input into (1) is the hydrogen supply manifold. Let ΩH2denote the admissible hydrogen state space consisting of pairs (p, T)∈[35,60]×[300,360] bar×K for which physisorption on CNT-decorated carbon matrices remains reversible. A modular 100 L loofah– CNT vessel is modeled as a composite storage operator A: ΩH2→R≥0,A(p, T)=mH2(p, T),(3) with mH2(p, T)≈1 kg per module over >103reversible adsorption–desorption cycles, and an energetic overhead bounded by 0<Edesorp ≤0.02 LHVH2,(4) characteristic of CNT-mediated physisorption [1, 2, 3]. The desorption dynamics are generated by a local temperature field T(y) inside the CNT sponge satisfying a controlled diffusion-type equation ∂tρH2=D∇2ρH2−κρH2−ρeq(T),(5) where Dis the effective diffusion coefficient on the loofah micro-lattice and κencodes the adsorption–desorption kinetics in the Langmuir-type equilibrium density ρeq(T). An auxiliary state space Ωcryo contains the thermodynamic variables of the optional LH2 pod, which furnishes a cold reservoir (Tcold ∼20 K) without contributing to the main hydrogen 3 inventory. The cryogenic subsystem enters (1) through a sink operator C:T × Ωcryo →R,C(Thot, Tcold) = −Tcold Thot ,(6) consistent with the Carnot-bound structure underlying the Brayton-cycle efficiency [4]. The LH2 pod remains decoupled from A, producing a two-manifold hydrogen architecture: a physisorptiondominated module array for fuel supply and an independent cryogenic manifold for thermal regulation. The multifunctional thermal material enters the configuration space Sas a tensor-valued constitutive map K(x) = kij(x) 0 0νij(x)!,(7) where kij governs anisotropic heat conduction and νij governs the vibrothermal compliance operator coupling thermal and elastic fields. Let Gbe the thermodynamic–structural graph whose nodes represent the Brayton core, bottoming-cycle condenser, hydrogen modules, cryogenic pod, inverter stages, and DEP actuators, and whose edges carry the conductive and elastic tensors induced by K. The thermal-material network enforces that for each oriented edge e∈E(G), qe=−Ke∇T, Fe=−∇·νeε,(8) with qethe heat flux, Fethe induced mechanical response, and εthe strain field. This joint governing structure yields a coherent thermodynamic network in which temperature gradients, vibrational spectra, and hydrogen delivery rates are determined by the coupled PDEs on G, consistent with modern formulations of thermoelastic coupling [5]. 2 HX-1 System Architecture Let Xdenote the configuration space of all admissible thermodynamic–electromechanical propulsion architectures. The HX–1 Solid-State Hydrogen Turboelectric Cycle corresponds to a distinguished submanifold MHX1 ⊂X,(9) characterized by a factorized power-transfer structure, a two-manifold hydrogen supply topology, and a conduction–compliance tensor network. The system decomposes into six operatorlevel subsystems, each treated as a node in an oriented hypergraph (V,E) with vertex set Vand thermodynamic edge set E. 1. Brayton Turbogenerator Core. Let ΓBdenote the Brayton-cycle flow manifold with state variables (T, p, s, h)∈ΓBand control parameters αcorresponding to compressor geometry, equivalence ratio, and turbine cooling schedule. Define the cycle operator B: ΓB×α→R,B(T, p, s, h;α) = Wnet,(10) with Wnet =I∂ΓB (hturb −hcomp)dγ, (11) 4 where the line integral is evaluated over the closed Brayton-cycle contour on the (s, T)- plane. The power turbine is represented by a mapping GHS :Wnet 7→ Pel (12) satisfying GHS surjective and ker(GHS)={0}, enforcing the absence of a mechanical thrust degree of freedom. 2. Bottoming Cycle. Let ΓSdenote the state space of a supercritical CO2or ORC working fluid. A compact bottoming cycle is modeled by an operator R: ΓS→R,R(ω)=WS,(13) with WSextracted from Brayton-stage exhaust subject to the constraint Tcond =Tcold +δT, δT > 0,(14) where the condenser temperature Tcond is dynamically coupled to the cryogenic pod or ambient radiative sinks. The secondary generator is given by a morphism GS:WS→P(2) el , forming a commutative diagram with GHS under the DC bus injection map (see item 6). 3. Hydrogen Subsystem A (Loofah–CNT Modules). Let Nmod ∈Ndenote the number of 100 L modules, and let each module correspond to a physisorption state element ωj∈ ΩH2. Define the aggregate storage functional Atot = Nmod X j=1 A(ωj),(15) with Aas in the introduction. The manifold structure is encoded by the direct product ΩA= Nmod Y j=1 ΩH2,(16) equipped with a desorption-flow operator D: ΩA×Θ→RNmod ,(17) where Θ denotes the heater-control space and Dgenerates the hydrogen mass-flow vector ˙ mH2feeding the combustor inlet boundary. 4. Hydrogen Subsystem B (Cryogenic Pod). Define Ωcryo as the thermodynamic manifold for LH2operating near 20 K. A dedicated cryogenic loop is generated by a sink operator C:T × Ωcryo →R,C(T, Tcold)=−Tcold T,(18) which enters the turbine cooling and condenser boundary conditions. No fuel-supply constraint couples Atot and Ωcryo, establishing a two-manifold hydrogen architecture. 5 5. Distributed Electric Propulsion (DEP). Let F={f1, . . . , fM}denote the set of ducted-fan actuators. Define the DEP network as a directed set of electromechanical maps Ek:R≥0→R3,Ek(P(k) el ) = Tk,(19) where Tkis the thrust vector for actuator fk. The collection E={E1,...,EM}forms a bundle over the DC bus power manifold PDC, with total thrust given by the fiber-wise sum Ttot = M M k=1 Tk.(20) 6. Thermal–Material Network. Let Gbe a weighted multigraph whose vertices correspond to the Brayton core, bottoming-cycle condenser, hydrogen modules, cryogenic pod, power-electronics stages, and DEP actuators. Each edge e∈E(G) carries a pair of tensor fields (kij(e), νij(e)), with kij the anisotropic conduction tensor and νij the vibrothermal compliance tensor. Thermal flux on each edge satisfies qe=−kij(e)∂jT, (21) while the mechanical counterpart satisfies Fe=−∂i(νij(e)εj),(22) with εjthe strain field and indices following the Einstein summation convention. This construction equips Gwith a coupled PDE structure consistent with thermoelastic formulations in continuum mechanics [5, 6]. Let Pgen ={Pel, P(2) el }denote the generator-output space. All mechanical work produced by the operators Band Ris mapped into the DC bus manifold PDC via the commutative diagram Wnet Pel PDC WSP(2) el PDC GHS Π ι GS Π ι (23) where ιdenotes the DC bus injection map and Π the total electrical power aggregation. The flight computer enforces a control law u(t)∈ U such that the composite thermodynamic state (T, p)∈ΓBremains in a neighborhood of the cycle optimum determined by δJ δα= 0,(24) evaluated along the trajectory generated by u(t). 6 3 Loofah–CNT Hydrogen Modules Let V100 denote the geometric configuration space of a 100 L loofah–CNT vessel. Each module is a composite-overwrapped pressure system with metallic liner L, internal CNT–carbon sponge domain ΩCNT, heater–sensor network H, and manifold set M. The total internal domain is the disjoint union Ωint = ΩCNT ⊔Ωmanifold ⊂ V100,(25) with dim(V100) = 3. Hydrogen is stored via physisorption on CNT-functionalized carbon matrices. Let ρ(x, t) denote the adsorbed mass density at x∈ΩCNT. The adsorption–desorption kinetics follow a Langmuir-type operator Lad generating a reaction–diffusion system ∂tρ=D∇2ρ−ka(T, p)ρ+kd(T)ρmax −ρ,(26) with Dan effective diffusion coefficient on the sponge micro-lattice, kathe adsorption coefficient, kdthe desorption frequency factor, and ρmax the saturation density. The temperature field satisfies the conduction equation cp(x)∂tT=∇ ·k(x)∇T+Qheater(x, t)−∆Had ∂tρ, (27) where cpis the local heat capacity, kthe anisotropic conductivity tensor of the CNT–carbon network, Qheater the heater power density, and ∆Had the adsorption enthalpy [1, 2, 3]. The internal microstructure imposes ∥∇T∥<5◦ C across ΩCNT under typical operating conditions (60–80◦C). The module operates within the admissible thermodynamic domain Ω(A) H2=(p, T)∈R2 +: 35 bar ≤p≤60 bar, Tamb ≤T≤80◦C.(28) Let mH2,mod(p, T) denote the deliverable hydrogen for a single module. The deliverable mass emerges from integrating (26) over ΩCNT: mH2,mod(p, T) = ZΩCNT ρ(x;p, T)d3x, (29) yielding mH2,mod(p, T)≈1 kg for (p, T)∈Ω(A) H2.(30) The desorption energy overhead is constrained by the thermodynamic inequality 0<Edesorp =ZΩCNT Qheater(x, t)d3x≤0.02 LHVH2,(31) with LHVH2= 33.3 kWh/kg. Define the structural operator S: ΩCNT →R3×3,(32) mapping the sponge geometry to an effective stiffness tensor describing the quasi-solid mechan7 ical behavior under flight loads. The absence of internal slosh follows from the constraint u(x)=0 ∀x∈ΩCNT,(33) where uis the fluid displacement field; the adsorbed hydrogen mass behaves as a stationary payload, advantageous for flight-dynamics stability. Heater and sensor networks form a feedback-controlled desorption system. Let θ(t) denote the heater control vector, and let I(t)∈RMbe the M-sensor measurement vector. A closed-loop control law θ(t) = KI(t),(34) with Ka bounded linear operator on the sensor space, generates a throttleable hydrogen massflow rate ˙mH2(t) = Z∂ΩCNT ρ(x, t)v·dA,(35) where vis the desorption-induced microflow velocity. For an aircraft carrying Nmod ∈Nmodules, the total deliverable mass is mH2,tot = Nmod X j=1 m(j) H2,mod ≈Nmod mH2,mod,(36) with cycle life exceeding 103cycles and capacity fade bounded by ∆mH2,mod mH2,mod <0.05,(37) consistent with the stability of CNT-based physisorption systems [3]. 4 Cryogenic Pod and Thermal-Material Integration Let Ωcryo denote the cryogenic domain containing the LH2reservoir, its boil-off region, and the primary heat-exchange interfaces. The state of the pod is represented by ξ= (TLH2, pLH2, hLH2)∈ Ωcryo, with TLH2≈20 K. A cryogenic circulation loop is modeled by a map C: Ωcryo × Sloop →ΓHX,(38) where Sloop encodes loop geometry and ΓHX is the space of heat-exchanger boundary conditions. The loop transports a mass-flow field ˙mcryo(s) along a path-parameter svia ∂sh(s) = q(s) ˙mcryo(s), q(s) = −kij(s)∂iT nj,(39) with qthe local heat flux, kij the anisotropic conductivity tensor, and njthe outward unit normal. The loop interfaces with four subsystems: turbine-blade cooling passages, bottoming-cycle condensers, generator and inverter cold plates, and DEP stator jackets. Let Bcool denote the turbine-blade cooling manifold. The enthalpy change of the cryogenic flow across this interface 8 satisfies ∆hblade =ZBcool kij ∂iT ˙mcryo njdA, (40) entering the cooled-turbine enthalpy balance hturb,out =hturb,in −∆hblade.(41) The reduction in blade-metal temperature modifies the admissible turbine-inlet temperature domain to Tadm hot = sup T:σth(T)≤σallow,(42) where σth is the thermally induced stress and σallow the material limit. For the bottoming cycle, the condenser boundary condition is imposed by a sink operator Scond : (Tcond, TLH2)7→ Tcond =TLH2+δT, δT > 0.(43) The real-cycle efficiency functional ηbottom(Tcond) satisfies ∂ηbottom ∂Tcond <0,(44) ensuring that coupling to the cryogenic pod drives a monotonic increase in secondary-cycle work. The thermal–material network Kis a piecewise-smooth tensor bundle over the airframe K:B → Sym2(R3)×Sym2(R3),K(x)=(kij(x), νij(x)),(45) assigning a conduction tensor kij and vibrothermal compliance tensor νij to each point xin the structural body B. At material interfaces—cold plates, condenser blocks, tank cradles, and cryogenic lines—the jump conditions kij ∂jT±= 0,νij εj±= 0,(46) ensure continuous heat flux and continuous thermomechanical traction across boundaries, suppressing thermal hotspots and eliminating micro-slip. The coupled thermal–elastic system obeys q=−kij ∂jT, (47) σij =Cijkl εkl −βij(T−T0),(48) where Cijkl is the stiffness tensor and βij the thermal expansion tensor. The temperature field satisfies ρcp∂tT=∇i(kij ∇jT)+Φsrc,(49) with Φsrc denoting localized heat sources from power electronics and stators. The cryogenic 9 5. Claim 5: Multifunctional thermal-material tensor network. The system of Claims 1–4 wherein the airframe is equipped with a multifunctional thermal material represented by a tensor bundle K:B → Sym2(R3)×Sym2(R3),K(x)=(kij(x), νij(x)),(85) with kij an anisotropic conduction tensor and νij a vibrothermal-compliance tensor. At each interface Σ ⊂ B the flux-matching jump conditions hold: kij∂jT±= 0,νijεj±= 0,(86) guaranteeing conformal heat-transfer contact, structural compliance, and vibration damping across loofah–CNT modules, cryogenic lines, cold plates, and condenser blocks. 6. Claim 6: Simultaneous increase of Tadm hot and reduction of Teff cold. The system of Claims 1–5 wherein the combined thermodynamic effect of the solid-state storage manifold and cryogenic sink yields the inequalities Tadm hot > T∗ hot, Teff cold < T∗ cold,(87) relative to any architecture lacking the (i) CNT–loofah desorption geometry and (ii) independent cryogenic manifold. As a consequence, the real-cycle efficiency functional ηreal = 1 −Teff cold Tadm hot −∆ηirr (88) satisfies: ηreal > η∗ real,(89) where η∗ real is the supremum achieved by any single-manifold hydrogen architecture. This is consistent with classical Brayton and exergy bounds [4]. 7. Claim 7: Mission-level modularity via discrete hydrogen operators. The system of Claims 1–6 wherein mission-level hydrogen sizing is determined by the discrete operator N:{Preq,i, ti, ηtot,i}7→Nmin mod =&1 mH2,mod X i∈S Preq,i ti ηtot,i LHVH2',(90) where mH2,mod ≈1 kg per module and LHVH2denotes hydrogen lower heating value. Thus the hydrogen supply is discretized as a combinatorial manifold of modules, enabling explicit mission-profile tuning. 16 8 Conclusion The HX-1 Solid-State Hydrogen Turboelectric Cycle integrates advanced materials, thermodynamic cycles, and distributed electric propulsion into a single architecture suitable for autonomous aircraft. Loofah–CNT hydrogen storage modules provide a safe, modular, and potentially carbon-negative fuel backbone, while a compact LH2pod and multifunctional thermal material manage entropy flows so that the engine operates near its theoretical efficiency ceiling. This combined approach offers a technically credible pathway to high-endurance, low-emission autonomous air mobility. Defensive Publication and Prior-Art Disclosure Author: Antonios Valamontes Kapodistrian Academy of Science Date of Public Disclosure: November 26, 2025 This document is released as a formal defensive publication establishing worldwide prior art under USPTO, EPO, and WIPO rules. It is intended to place the HX-1 propulsion architecture, the loofah–CNT hydrogen modules, the cryogenic-sink topology, the thermal-material tensor network, and all derived mathematical operators into the public domain of knowledge for the sole purpose of preventing any third party from claiming patent rights over these inventions. Integrity Verification The following SHA-256 hash corresponds to the final compiled PDF of this defensive publication at the moment of public release: [INSERT HASH HERE AFTER COMPILATION] License Notice This defensive publication is released under the Creative Commons Attribution–NonCommercial 4.0 International (CC BY-NC 4.0) license. Commercial use, manufacture, or patent refiling of the disclosed systems, architectures, or operators is expressly prohibited. Redistribution and academic use are permitted. How to Cite This Defensive Publication A. Valamontes, HX-1 Solid-State Hydrogen Turboelectric Cycle: Defensive Publication and Thermodynamic Architecture, Kapodistrian Academy of Science (2025). Public Disclosure: November 26, 2025. Available via Zenodo: [URL will be assigned after upload]. 17 References [1] S. Patchkovskii and J. S. Tse, “Thermodynamics of Hydrogen Physisorption in Nanoporous Materials,” Proc. Natl. Acad. Sci. USA,102, 10439–10444 (2005). doi:10.1073/pnas.0504324102 [2] F. Darkrim and D. Levesque, “Monte Carlo Simulations of Hydrogen Adsorption in Single-Walled Carbon Nanotubes,” J. Chem. Phys.,109(10), 4981–4984 (1999). doi:10.1063/1.478860 [3] L. Schlapbach and A. Z¨uttel, “Hydrogen-storage Materials for Mobile Applications,” Nature,414, 353–358 (2001). doi:10.1038/35104634 [4] A. Bejan, Advanced Engineering Thermodynamics, 4th ed., Wiley, Hoboken (2016). ISBN: 978-1118831994 [5] W. Nowacki, Thermoelasticity, Pergamon Press (1986). ISBN: 978-0080343743 [6] P. G. Ciarlet, Mathematical Elasticity, Vol. I: Three-Dimensional Elasticity, NorthHolland, Studies in Mathematics and its Applications, Vol. 20 (1988). ISBN: 9780444703391 18