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Mathematical modeling and analysis of heat pipe start-up from the frozen state

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Jang, Jong Hoon

A second-order analytic analysis for frozen orbits

An analytical method for studying characteristics of frozen orbits using mean orbital elements is presented. By removing some of the approximations of Brouwer and Kosai (1959) and using the method of integration by parts, an analytic solution is obtained accurate to the second order in the sense of expansion of the perturbing potential of an aspherical approximation. The solution applies to orbits at and near the critical inclination as well as to frozen orbits and, of course, to unfrozen orbits. The analysis reveals that a frozen orbit can be interpreted as an orbit in which movements of the long-periodic part of the rate of change of periapsis cancels the secular part exactly at any time.

Tang, Charles C. H.

Some implications of the isotropic momentarily frozen assumptions for the SPAN-MAT program

Potential tests using turbulence velocity histories measured in the SPAN-MAT Program are outlined to determine validity of the homogeneous, momentarily frozen assumptions for the vertical turbulence velocity component and the homogeneous, isotropic, momentarily frozen assumptions for the horizontal turbulence velocity components. In addition, methods are reviewed for prediction of the crosscorrelation function between any two spatially separated turbulence velocity components using the homogeneous, isotropic, momentarily frozen assumptions and measurements of the transverse and longitudinal turbulence velocity components.

Mark, W. D.

Mathematical modeling and analysis of heat pipe start-up from the frozen state

The start-up process of a frozen heat pipe is described and a complete mathematical model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. The two-dimensional transient model for the wall and wick is coupled with the one-dimensional transient model for the vapor flow when vaporization and condensation occur at the interface. A parametric study is performed to examine the effect of the boundary specification at the surface of the outer wall on the successful start-up from the frozen state. For successful start-up, the boundary specification at the outer wall surface must melt the working substance in the condenser before dry-out takes place in the evaporator.

Jang, J. H.

Frozen start-up behavior of low-temperature heat pipes

Start-up and subsequent operation of a low-temperature heat pipe requires the liquid phase of the operating fluid to be continuously pumped back to the evaporator by the capillary action of the wick. If the pipe has been in an environment where ambient temperatures are below the freezing point of the working fluid prior to start-up, the frozen fluid in the condenser and adiabatic region scan prevent initial flow to the evaporator, causing dryout of the evaporator before all of the working fluid is in the liquid phase. This paper examines the time-dependent wall and vapor temperature profiles along the axial length of a low-temperature heat pipe during start-up from the frozen state, and freeze-out during a normal operation by applying a subfreezing temperature fluid through the condenser. In addition, the experimental transient frozen start-up wall temperature profile is compared with a two-dimensional numerical phase-change model. A successful start-up method using a pulsed power input is presented.

Faghri, Amir

Existence of frozen-in coordinate systems

The 'frozen-in' coordinate systems were first introduced in the works on 'reconnection' and 'magnetic barrier' theories (see review by M.l.Pudovkin and V.S.Semenov, Space Sci. Rev. 41,1 1985). The idea was to utilize the mathematical apparatus developed for 'general relativity' theory to simplify obtaining solutions to the ideal MHD equations set. Magnetic field (B), plasma velocity (v), and their vector product were used as coordinate vectors. But there exist no stationary solutions of ideal MHD set that satisfies the required boundary conditions at infinity (A.D.Chertkov, Solar Wind Seven Conf.,Pergamon Press,1992,165) having non-zero vector product of v and B where v and B originate from the same sphere. The existence of a solution is the hidden mine of the mentioned theories. The solution is constructed in the coordinate system, which is unknown and indeterminate before obtaining this solution. A substitution of the final solution must be done directly into the initial MHD set in order to check the method. One can demonstrate that 'solutions' of Petschek's problem, obtained by 'frozen-in' coordinate systems, does not satisfy just the 'frozen-in' equation, i.e. induction equation. It stems from the fact that Petschek's 're-connection' model, treated as a boundary problem, is over determined. This problem was incorrectly formulated.

Chertkov, A. D.

Heat Transfer to Surfaces of Finite Catalytic Activity in Frozen Dissociated Hypersonic Flow

The heat transfer due to catalytic recombination of a partially dissociated diatomic gas along the surfaces of two-dimensional and axisymmetric bodies with finite catalytic efficiencies is studied analytically. An integral method is employed resulting in simple yet relatively complete solutions for the particular configurations considered. A closed form solution is derived which enables one to calculate atom mass-fraction distribution, therefore catalytic heat transfer distribution, along the surface of a flat plate in frozen compressible flow with and without transpiration. Numerical calculations are made to determine the atom mass-fraction distribution along an axisymmetric conical body with spherical nose in frozen hypersonic compressible flow. A simple solution based on a local similarity concept is found to be in good agreement with these numerical calculations. The conditions are given for which the local similarity solution is expected to be satisfactory. The limitations on the practical application of the analysis to the flight of the blunt bodies in the atmosphere are discussed. The use of boundary-layer theory and the assumption of frozen flow restrict application of the analysis to altitudes between about 150,000 and 250,000 feet.

Chung, Paul M.

Frozen-Flux Modelling for Epochs 1915 and 1980

The frozen-flux hypothesis for the Earth's liquid core assumes that convective terms dominate diffusive terms in the induction equation governing the behaviour of the magnetic field at the surface of the core. While highly plausible on the basis of estimates of physical parameters, the hypothesis has been questioned. To study this hypothesis, we improve the method which tests the consistency of magnetic observations with the hypothesis by constructing simple, flux-conserving core-field models fitting the data at pairs of epochs. We introduce a new approach that fixes the patch configurations at each of the two epochs before inversion, so that each configuration is consistent with its respective data set but possesses the same patch topology. We expand upon the inversion algorithm, using quadratic programming to maintain the proper flux sign within patches; the modelling calculations are also extended to include data types that depend non-linearly on the model. Every test of a hypothesis depends on the characterization of the observational uncertainties; we undertake a thorough review of this question. For main-field models, the primary source of uncertainty comes from the crustal field. We base our analysis on statistical models of the crustal magnetization, adjusted to bring it into better conformity with our data set. The noise model permits us to take into account the correlations between the measurements and requires that a different weighting be given to horizontal and vertical components. It also indicates that the observations should be fit more closely than has been the practice heretofore. We apply the revised method to Magsat data from 1980 and survey and observatory data from 1915.5, two data sets believed to be particularly difficult to reconcile with the frozen-flux hypothesis. We compute a pair of simple, flux-conserving models that fit the averaged data from each epoch. We therefore conclude that present knowledge of the geomagnetic fields of 1980 and 1915.5 is consistent with the frozen-flux hypothesis.

OBrien, Michael S.

Impact melting of frozen oceans on the early Earth: implications for the origin of life

Without sufficient greenhouse gases in the atmosphere, the early Earth would have become a permanently frozen planet because the young Sun was less luminous than it is today. Several resolutions to this faint young Sun-frozen Earth paradox have been proposed, with an atmosphere rich in CO2 being the one generally favored. However, these models assume that there were no mechanisms for melting a once frozen ocean. Here we show that bolide impacts between about 3.6 and 4.0 billion years ago could have episodically melted an ice-covered early ocean. Thaw-freeze cycles associated with bolide impacts could have been important for the initiation of abiotic reactions that gave rise to the first living organisms.

NASA Discipline Exobiology

Preparation of a Frozen Regolith Simulant Bed for ISRU Component Testing in a Vacuum Chamber

In-Situ Resource Utilization (ISRU) systems and components have undergone extensive laboratory and field tests to expose hardware to relevant soil environments. The next step is to combine these soil environments with relevant pressure and temperature conditions. Previous testing has demonstrated how to incorporate large bins of unconsolidated lunar regolith into sufficiently sized vacuum chambers. In order to create appropriate depth dependent soil characteristics that are needed to test drilling operations for the lunar surface, the regolith simulant bed must by properly compacted and frozen. While small cryogenic simulant beds have been created for laboratory tests, this scale effort will allow testing of a full 1m drill which has been developed for a potential lunar prospector mission. Compacted bulk densities were measured at various moisture contents for GRC-3 and Chenobi regolith simulants. Vibrational compaction methods were compared with the previously used hammer compaction, or "Proctor", method. All testing was done per ASTM standard methods. A full 6.13 m3 simulant bed with 6 percent moisture by weight was prepared, compacted in layers, and frozen in a commercial freezer. Temperature and desiccation data was collected to determine logistics for preparation and transport of the simulant bed for thermal vacuum testing. Once in the vacuum facility, the simulant bed will be cryogenically frozen with liquid nitrogen. These cryogenic vacuum tests are underway, but results will not be included in this manuscript.

Klenhenz, Julie

Experimental Measurement of Frozen and Partially Melted Water Droplet Impact Dynamics

High-speed video of single frozen water droplets impacting a surface was acquired. The droplets diameter ranged from 0.4 mm to 0.9 mm and impacted at velocities ranging from 140 m/sec to 309 m/sec. The techniques used to freeze the droplets and launch the particles against the surfaces is described in this paper. High-speed video was used to quantify the ice accretion area to the surface for varying impact angles (30 deg, 45 deg, 60 deg), impacting velocities, and break-up angles. An oxygen /acetylene cross-flow flame used to ensure partial melting of the traveling frozen droplets is also discussed. A linear relationship between impact angle and ice accretion is identified for fully frozen particles. The slope of the relationship is affected by impact speed. Perpendicular impacts, i.e. 30 deg, exhibited small differences in ice accretion for varying velocities, while an increase of 60% in velocity from 161 m/sec to 259 m/sec, provided an increase on ice accretion area of 96% at an impact angle of 60 deg. The increase accretion area highlights the importance of impact angle and velocity on the ice accretion process of ice crystals. It was experimentally observed that partial melting was not required for ice accretion at the tested velocities when high impact angles were used (45 and 60 deg). Partially melted droplets doubled the ice accretion areas on the impacting surface when 0.0023 Joules were applied to the particle. The partially melted state of the droplets and a method to quantify the percentage increase in ice accretion area is also described in the paper.

Impact Dynamics

The Safe Removal of Frozen Air from the Annulus of an LH2 Storage Tank

Large Liquid Hydrogen (LH2) storage tanks are vital infrastructure for NASA. Eventually, air may leak into the evacuated and perlite filled annular region of these tanks. Although the vacuum level is monitored in this region, the extremely cold temperature causes all but the helium and neon constituents of air to freeze. A small, often unnoticeable pressure rise is the result. As the leak persists, the quantity of frozen air increases, as does the thermal conductivity of the insulation system. Consequently, a notable increase in commodity boil-off is often the first indicator of an air leak. Severe damage can result from normal draining of the tank. The warming air will sublimate which will cause a pressure rise in the annulus. When the pressure increases above the triple point, the frozen air will begin to melt and migrate downward. Collection of liquid air on the carbon steel outer shell may chill it below its ductility range, resulting in fracture. In order to avoid a structural failure, as described above, a method for the safe removal of frozen air is needed. A thermal model of the storage tank has been created using SINDA/FLUINT modeling software. Experimental work is progressing in an attempt to characterize the thermal conductivity of a perlite/frozen nitrogen mixture. A statistical mechanics model is being developed in parallel for comparison to experimental work. The thermal model will be updated using the experimental/statistical mechanical data, and used to simulate potential removal scenarios. This paper will address methodologies and analysis techniques for evaluation of two proposed air removal methods.

cryogenic insulation

Clustering Approach To Identifying Low Lunar Frozen Orbits In A High-Fidelity Model

Low lunar frozen orbits are of continued interest in the astrodynamics community for trajectory design and space domain awareness. This paper presents a data-driven approach to analyzing a wide variety of numerically-generated lunar trajectories in a 100 × 100 lunar gravity model with the point mass gravity of the Earth and Sun. First, clustering is used to extract a summary of these trajectories: within each cluster, trajectories possess a geometrically similar evolution of perilune but varying drift and lifetimes. Within some clusters, trajectories with a bounded perilune evolution are also identified to produce candidates for lunar frozen orbits of distinct geometries.

lunar frozen orbit gravity model data clustering

Transfers from TLI to Lunar Frozen Orbits with Applications to NASA’s CLPS & Artemis Programs

This paper will focus on trajectory transfers from trans-lunar injection (TLI) to lunar frozen orbits with applications to NASA’s Commercial Lunar Payload Services (CLPS) and Artemis Human Landing System (HLS) programs. For a CLPS application, the CS-3 mission is explored, which will deploy a communications relay satellite in lunar elliptical frozen orbit followed by landing a payload on the lunar farside during dawn. Given HLS will land a crew near the lunar south pole with lighting and timing requirements, the effect of varying the Earth-Moon transit duration to influence the approach direction upon landing will be explored.

lunar frozen orbits

Unidirectional amplification in the frozen mode regime enabled by a nonlinear defect

A stationary inflection point (SIP) is a spectral singularity of the Bloch dispersion relation ω(k) of a periodic structure where the first and the second derivatives of ω with respect to k vanish. An SIP is associated with a third-order exceptional point degeneracy in the spectrum of the unit-cell transfer matrix, where there is a collapse of one propagating and two evanescent Bloch modes. At the SIP frequency, the incident wave can be efficiently converted into the frozen mode with greatly enhanced amplitude and vanishing group velocity. This can be very attractive for applications, including light amplification. Due to its non-resonant nature, the frozen mode regime (FMR) has fundamental advantages over common cavity resonances. Furthermore, we propose, a novel, to the best of our knowledge, scheme for FMR-based unidirectional amplifiers by leveraging a tailored amplification/attenuation mechanism and a single nonlinear defect. The defect breaks the directional symmetry of the periodic structure and enables nonlinearity-related unidirectional amplification/attenuation in the vicinity of the SIP frequency. We demonstrate the robustness of the amplification mechanism to local impurities and parasitic nonlinearity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC

Thermodynamic and transport properties of frozen and reacting pH2-oH2 mixtures

Application of experimental state data and spectroscopic term values shows that the thermodynamic and transport properties of reacting pH2-oH2 mixtures are considerably different than those of chemically frozen pH2 at temperatures below 300 R. Calculated H-S data also show that radiation-induced pH2-oH2 equilibration at constant enthalpy produces a temperature drop of at least 28 R, corresponding to an ideal shaft work loss of 15% or more for a turbine operating downstream from the point of conversion. Aside from differences in thermodynamic and transport properties, frozen pH2-oH2 mixtures may differ from pure pH2 on a purely hydrodynamical basis.

Carter, H. G.