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NASA NTRS2005

CFD Multiphysics Tool

The recent bold initiatives to expand the human presence in space require innovative approaches to the design of propulsion systems whose underlying technology is not yet mature. The space propulsion community has identified a number of candidate concepts. A short list includes solar sails, high-energy-density chemical propellants, electric and electromagnetic accelerators, solar-thermal and nuclear-thermal expanders. For each of these, the underlying physics are relatively well understood. One could easily cite authoritative texts, addressing both the governing equations, and practical solution methods for, e.g. electromagnetic fields, heat transfer, radiation, thermophysics, structural dynamics, particulate kinematics, nuclear energy, power conversion, and fluid dynamics. One could also easily cite scholarly works in which complete equation sets for any one of these physical processes have been accurately solved relative to complex engineered systems. The Advanced Concepts and Analysis Office (ACAO), Space Transportation Directorate, NASA Marshall Space Flight Center, has recently released the first alpha version of a set of computer utilities for performing the applicable physical analyses relative to candidate deep-space propulsion systems such as those listed above. PARSEC, Preliminary Analysis of Revolutionary in-Space Engineering Concepts, enables rapid iterative calculations using several physics tools developed in-house. A complete cycle of the entire tool set takes about twenty minutes. PARSEC is a level-zero/level-one design tool. For PARSEC s proof-of-concept, and preliminary design decision-making, assumptions that significantly simplify the governing equation sets are necessary. To proceed to level-two, one wishes to retain modeling of the underlying physics as close as practical to known applicable first principles. This report describes results of collaboration between ACAO, and Embry-Riddle Aeronautical University (ERAU), to begin building a set of level-two design tools for PARSEC. The "CFD Multiphysics Tool" will be the propulsive element of the tool set. The name acknowledges that space propulsion performance assessment is primarily a fluid mechanics problem. At the core of the CFD Multiphysics Tool is an open-source CFD code, HYP, under development at ERAU. ERAU is renowned for its undergraduate degree program in Aerospace Engineering the largest in the nation. The strength of the program is its applications-oriented curriculum, which culminates in one of three two-course Engineering Design sequences: Aerospace Propulsion, Spacecraft, or Aircraft. This same philosophy applies to the HYP Project, albeit with fluid physics modeling commensurate with graduate research. HYP s purpose, like the Multiphysics Tool s, is to enable calculations of real (three-dimensional; geometrically complex; intended for hardware development) applications of high speed and propulsive fluid flows.

Perrell, Eric R.↗

NASA NTRS1995

Advanced Methodology for Simulation of Complex Flows Using Structured Grid Systems

Detailed simulations of viscous flows in complicated geometries pose a significant challenge to current capabilities of Computational Fluid Dynamics (CFD). To enable routine application of CFD to this class of problems, advanced methodologies are required that employ (a) automated grid generation, (b) adaptivity, (c) accurate discretizations and efficient solvers, and (d) advanced software techniques. Each of these ingredients contributes to increased accuracy, efficiency (in terms of human effort and computer time), and/or reliability of CFD software. In the long run, methodologies employing structured grid systems will remain a viable choice for routine simulation of flows in complex geometries only if genuinely automatic grid generation techniques for structured grids can be developed and if adaptivity is employed more routinely. More research in both these areas is urgently needed.

Steinthorsson, Erlendur↗

DOE OSTI2020

Spectral Element Applications in Complex Nuclear Reactor Geometries: Tet-to-Hex Meshing

The spectral element code Nek5000 is an open-source, higher-order computational fluid dynamics code developed at Argonne National Laboratory. It is designed to solve incompressible Navier-Stokes equations, but it also has a low-Mach-number approximation feature available. Large eddy simulation is approached by explicit filtering of the velocity field (and other fields) to mimic the effect of dissipation due to the unresolved scale. The computational domain is decomposed into second-order hexahedral elements that conform to the boundaries. However, generating a high-quality pure-hexahedral mesh can be challenging for some problems. For simple geometries, traditional blocking methods can be used to decompose the domain into smaller blocks to generate a so-called structural mesh. A structural mesh can maintain good orthogonality but can have a highly skewed mesh to conform to the geometry, as well as unnecessary refinement in the far field. Moreover, for geometries with relative complexity, blocking the geometry becomes impossible. To address these issues, we adopted a let-to-hex strategy to generate a pure hexahedral mesh for Nek5000. First, we generate a pure tetrahedral mesh for the geometry; then we divide one tetrahedral element into four hexahedral elements. A pure tetrahedral mesh could be easily generated for complex geometries by using many current meshing codes. In this paper, we use the commercial codes ANSYS meshing and ANSYSICEM to generate the pure tetrahedral mesh and then convert it to a pure hexahedral mesh. Boundary layers are extruded in ANSYSICEM to maintain near-wall resolution.

ANSYS ICEM↗

DOE OSTI2018

Empirically assessing the potential release of rare earth elements from black shale under simulated hydraulic fracturing conditions

Rare earth elements (REEs) are economically important to modern society and the rapid growth of technologies dependent on REEs has placed considerable economic pressure on their sourcing. This study addresses whether REEs could be released as a byproduct of natural gas extraction from a series of experiments that were designed to simulate hydraulic fracturing of black shale under various pressure (25 and 27.5 MPa) and temperature (50, 90, 130 °C) conditions. The dissolved REEs in the reacted fluids displayed no propensity for the REEs to be released from black shale under high pressure and temperature conditions, a result that is consistent across the different types of fluids investigated. Overall, there was a net loss of REEs from the fluid. These changes in dissolved REEs were greatest at the moment the fluids first contacted the shale and before the high temperature and high pressure conditions were imposed, although the magnitude of these changes (10 -4 μg/g) were small compared to the magnitude of the total REE content present in the solid shale samples (10 2 μg/g). These results highlight the variability and complexity of hydraulic fracturing systems and indicate that REE may not serve as robust tracers for fracturing fluid-shale reactions. Additionally, the results suggest that significant quantities of REEs may not be byproducts of hydraulically fractured shales.

03 NATURAL GAS↗

DOE OSTI2018

Four equation k-omega based turbulence model with algebraic flux for supercritical flows

Hydrocarbon and nuclear fuels will contribute substantially to the growing global energy portfolio for some time to come. At the same time atmospheric carbon levels and economic concerns are increasingly shaping the power generation environment. Supercritical fluid technologies are being investigated to address both concerns. For example, direct fired supercritical CO 2 power cycles offer key advantages for carbon capture and thermal efficiency. Additionally, the supercritical water reactor Generation IV nuclear reactor allows higher power densities and more efficient operation than current pressurized or boiling water reactors. As these technologies are developed, a need exists for accurate, yet cost-effective modeling and simulation solutions to assist with design and safety calculations. Supercritical fluid properties are strongly dependent on temperature which results in a number of unique flow features. Among these features are the complex buoyancy and buoyancy-turbulence interaction behaviors exhibited by supercritical flows that are not found in liquid or gas flows. Therefore, standard turbulence models with current model coefficient values are not likely to be applicable to supercritical fluid flows. The subject of this paper is efficient modeling and simulation of supercritical flows to support nascent technologies growing to maturation and operational deployment. We present a framework for developing Reynolds-Averaged Navier-Stokes turbulence models specifically equipped for the challenges of supercritical flows. A novel formulation of the algebraic heat flux model of the buoyancy production of turbulence term is used with a traditional shear stress transport model. To produce a new turbulence model for supercritical channel flows, the empirical coefficients of the resulting four equation model were calculated from data previously published by other authors regarding upward supercritical flow through heated pipes. The presented SST k t - ω t approach was validated against heated tube experiments to show predictive capabilities in moderate flow conditions, where buoyancy effects are important but not dominating of inertial effects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2018

Modulating factors of hydrologic exchanges in a large-scale river reach: Insights from three-dimensional computational fluid dynamics simulations

Hyporheic exchange is a critical mechanism shaping hydrological and biogeochemical processes along a river corridor. Recent studies on quantifying the hyporheic exchange were mostly limited to local scales due to field inaccessibility, computational demand, and complexity of geomorphology and subsurface geology. Surface flow conditions and subsurface physical properties are well known factors on modulating the hyporheic exchange, but quantitative understanding of their impacts on the strength and direction of hyporheic exchanges at reach scales is absent. In this study, a high resolution computational fluid dynamics (CFD) model that couples surface and subsurface flow and transport is employed to simulate hyporheic exchanges in a 7-km long reach along the main-stem of the Columbia River. Assuming that the hyporheic exchange does not affect surface water flow conditions due to its negligible magnitude compared to the volume and velocity of river water, we developed a one-way coupled surface and subsurface water flow model using the commercial CFD software STAR-CCM+. The model integrates the Reynolds-averaged Navier-Stokes (RANS) equation solver with a realizable k-e two-layer turbulence model, a two-layer all y^+ wall treatment, and the volume of fluid (VOF) method, and is used to simulate hyporheic exchanges by tracking the free water-air interface as well as flow in the river and the subsurface porous media. The model is validated against measurements from acoustic Doppler current profiler (ADCP) in the stream water and hyporheic fluxes derived from a set of temperature profilers installed across the riverbed. The validated model is then employed to systematically investigate how hyporheic exchanges are influenced by surface water fluid dynamics strongly regulated by upstream dam operations, as well as subsurface structures (e.g. thickness of riverbed and subsurface formation layers) and hydrogeological properties (e.g. permeability). The results suggest that the thickness of riverbed alluvium layer is the dominant factor for reach-scale hyporheic exchanges, followed by the alluvium permeability, the depth of the underlying impermeable layer, and the assumption of hydrostatic pressure.

Bao, Jie↗

DOE OSTI2014

Innovative Grid-Based Vorticity-Velocity Solver for Analysis of Vorticity-Dominated Flows

Unsteady vorticity-dominated flows are prevalent in a wide variety of engineering applications and are particularly challenging to predict efficiently. Perhaps in no other application is this more apparent than rotorcraft, where prediction is complicated by a wide variety of interactional aerodynamics between strong vortical wakes shed from rotating components and various bodies and wings immersed in the flow. While conventional computational fluid dynamics methods are equipped with the modeling capabilities to support these flow behaviors, they are subject to significant numerical diffusion whose practical import is that high computational costs involving large grids, complex adaptation methods, and high interpolation orders are required to produce sufficiently accurate simulations and prevent the artificial diffusion of vortical structures. Hybrid computational fluid dynamics methods that couple a body-fitted solver to a vorticity–velocity method hold considerable promise in alleviating these costs while effectively preserving vorticity. However, several fundamental and long-standing issues identified with vorticity–velocity methods have precluded their wider adoption. Here, the four most prominent concerns are addressed: 1) maintaining a solenoidal vorticity field; 2) supporting a low-dissipation/dispersion scheme on a general multiresolution grid; 3) providing a consistent and efficient implementation of the viscous terms; and 4) properly including the unsteady pressure contributions.

42 ENGINEERING↗

DOE OSTI2022

Validation and parameterization of a novel physics-constrained neural dynamics model applied to turbulent fluid flow

We report, in fluid physics, data-driven models to enhance or accelerate time to solution are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In the context of reduced order models of high-dimensional time-dependent fluid systems, machine learning methods grant the benefit of automated learning from data, but the burden of a model lies on its reduced-order representation of both the fluid state and physical dynamics. In this work, we build a physics-constrained, data-driven reduced order model for Navier–Stokes equations to approximate spatiotemporal fluid dynamics in the canonical case of isotropic turbulence in a triply periodic box. The model design choices mimic numerical and physical constraints by, for example, implicitly enforcing the incompressibility constraint and utilizing continuous neural ordinary differential equations for tracking the evolution of the governing differential equation. We demonstrate this technique on a three-dimensional, moderate Reynolds number turbulent fluid flow. In assessing the statistical quality and characteristics of the machine-learned model through rigorous diagnostic tests, we find that our model is capable of reconstructing the dynamics of the flow over large integral timescales, favoring accuracy at the larger length scales. More significantly, comprehensive diagnostics suggest that physically interpretable model parameters, corresponding to the representations of the fluid state and dynamics, have attributable and quantifiable impact on the quality of the model predictions and computational complexity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1982

Analysis of volatile metabolites in biological fluids as indicators of prodromal disease condition

The volatile profile cannot be defined as a single class of substances, rather it is a broad spectrum of materials of different polarities characterized by having a boiling-point in the low to medium range (up to approximately 300 C) and the fact that the compounds are suitable for gas chromatography without derivatization. The organic volatile profiles are very complex mixtures of metabolic byproducts, intermediates, and terminal products of enzymatic degradations composed mainly of alcohols, ketones, aldehydes, pyrazines, sulfides, isothiocyanates, pyrroles, and furans. The concentration of organic volatiles in biological fluids covers a wide range with many important components present at trace levels. The complexity of the organic volatile fraction requires the use of capillary columns for their separation.

Zlatkis, A.↗

DOE OSTI2016

Model of non-stationary, inhomogeneous turbulence

Here, we compare results from a spectral model for non-stationary, inhomogeneous turbulence (Besnard et al. in Theor Comp Fluid Dyn 8:1–35, 1996) with direct numerical simulation (DNS) data of a shear-free mixing layer (SFML) (Tordella et al. in Phys Rev E 77:016309, 2008). The SFML is used as a test case in which the efficacy of the model closure for the physical-space transport of the fluid velocity field can be tested in a flow with inhomogeneity, without the additional complexity of mean-flow coupling. The model is able to capture certain features of the SFML quite well for intermediate to long times, including the evolution of the mixing-layer width and turbulent kinetic energy. At short-times, and for more sensitive statistics such as the generation of the velocity field anisotropy, the model is less accurate. We propose two possible causes for the discrepancies. The first is the local approximation to the pressure-transport and the second is the a priori spherical averaging used to reduce the dimensionality of the solution space of the model, from wavevector to wavenumber space. DNS data are then used to gauge the relative importance of both possible deficiencies in the model.

42 ENGINEERING↗

DOE OSTI2020

Magneto-structural and induction heating properties of MFe2O4 (M?=?Co, Mn, Zn) MNPs for magnetic particle hyperthermia application

The thermal decomposition approach was used for the synthesis of MFe2O4 magnetic nanoparticles (MNPs) by substituting M as Co, Mn, and Zn. The obtained MNPs were characterized for magneto-structural properties using X-Ray diffraction patterns, FTIR, Raman and Mossbauer spectroscopy techniques which confirm the formation of phase pure cubic spinel ferrite with space group Fd3m and five Raman active modes. The size, morphology, and compositional analysis was performed using HRTEM and EDX where the size of MNPs was found to be less than 10 nm that attains superparamagnetism. The magnetic hyperthermia performance of obtained MNPs was evaluated by induction heating experiments at magnetic field range 13.3 to 26.7 kAm-1. The specific absorption rate (SAR) and intrinsic loss power (ILP) values were determined at different magnetic fields within the human tolerable range and correlated with magneto-structural properties to evaluate its potential for possible magnetic particle hyperthermia therapy.

Magnetic nanoparticles, complex-decomposition, mag↗

DOE OSTI2017

Chapter 11: Concentrating Solar Power

This chapter summarizes the applications of the supercritical CO2 (sCO2) Brayton cycle in concentrating solar power (CSP) plants. The design and operation of CSP plants are reviewed to highlight the requirements for the power cycle and attributes that are advantageous for the solar-thermal application. The sCO2 Brayton cycle offers the potential of higher cycle efficiency versus superheated or supercritical steam cycles at temperatures relevant for CSP applications. In addition, Brayton cycle systems using sCO2 are anticipated to have smaller weight and volume, lower thermal mass, and less complex power blocks compared with Rankine cycles due to the higher density of the fluid and simpler cycle design. The simpler machinery and compact size of the sCO2 process may also reduce the installation, maintenance, and operation cost of the system. Power cycle capacities in the range of 10-150 MWe are anticipated for the CSP application. In this chapter, we explore sCO2 Brayton cycle configurations that have attributes that are desirable from the perspective of a CSP application, such as the ability to accommodate dry cooling and daily cycling, as well as integration with thermal energy storage.

14 SOLAR ENERGY↗

DOE OSTI2023

Fabric controls on fracture surface roughness of an architected rock material

Fluid flow through fractures is intimately linked to the fracture surfaces that define the void geometry through which fluids flow. Thus, an understanding of what controls fracture surface roughness is essential to the development of models for predicting fluid transport through fractured rock. The difficulty in predicting surface roughness arises from the complexity of rock which is inherently heterogeneous and nonuniform in composition, fabric, and structural components, even when samples are acquired from the same rock mass. Here, a benchmarked-simulation approach motivated from geo-architected 3D printed synthetic gypsum rocks is used to provide insight into the competing contributions from fabric and layering on fracture roughness formation. Simulation results from a discrete element model (Particle Flow Code, Itasca Consulting Group, Inc.) clearly indicate that the relative orientation between mineral layers and in-layer mineral fabric, and the variability in mineral bonding strengths determine whether anisotropic corrugated surfaces or isotropic surfaces are formed. Weak mineral layers oriented perpendicular to the applied load resulted in strong roughness anisotropy. Peak failure loads were found to vary up to 30% depending on the strength of the mineral fabric at the location of fracture initiation, which provides insight into the observed high variability in strength values of natural rock. The uniqueness of induced fracture roughness and peak failure load is intimately linked to layering, mineral fabric, and their distribution in the rock. These findings have important implications for any architected material fabricated through serial printing of layers with local compositional heterogeneity.

3D printed rock↗

DOE OSTI2026

Mesh-based multiphysics coupling acceleration for fusion neutronics through clustering for fusion blanket applications

Accurate modeling of particle transport within fusion blankets is essential for predicting performance metrics such as heat deposition and the tritium breeding ratio (TBR). However, high-fidelity coupling of thermal fluids from computational fluid dynamics (CFD) to neutronics simulations often incurs significant computational costs due to the complexity of surface intersection calculations in Monte Carlo codes. This paper presents an accelerated multiphysics coupling method for neutronics that utilizes hierarchical agglomerative clustering to map complex material property distributions to a neutronics model. Implemented within the fusion reactor design and assessment (FREDA) framework, the method leverages existing Python packages to automate the creation of clustered geometries for OpenMC. The approach is demonstrated on a sector model of an ARC-class tokamak with an immersion molten salt blanket, and an simple geometry with varying isotopic concentrations. Results show that the clustering method significantly reduces computational burden without compromising fidelity, providing a foundation for agile iteration of neutronics simulations involving multiple coupled material properties.

Bae, Jin Whan [ORNL] (ORCID:0000000326548907)↗

DOE OSTI2018

Modeling Host-Pathogen Interactions in the Context of the Microenvironment: Three-Dimensional Cell Culture Comes of Age

Tissues and organs provide the structural and biochemical landscapes upon which microbial pathogens and commensals function to regulate health and disease. While flat two-dimensional (2-D) monolayers composed of a single cell type have provided important insight into understanding host-pathogen interactions and infectious disease mechanisms, these reductionist models lack many essential features present in the native host microenvironment that are known to regulate infection, including three-dimensional (3-D) architecture, multicellular complexity, commensal microbiota, gas exchange and nutrient gradients, and physiologically relevant biomechanical forces (e.g., fluid shear, stretch, compression). Here, a major challenge in tissue engineering for infectious disease research is recreating this dynamic 3-D microenvironment (biological, chemical, and physical/mechanical) to more accurately model the initiation and progression of host-pathogen interactions in the laboratory. Here we review selected 3-D models of human intestinal mucosa, which represent a major portal of entry for infectious pathogens and an important niche for commensal microbiota. We highlight seminal studies that have used these models to interrogate host-pathogen interactions and infectious disease mechanisms, and we present this literature in the appropriate historical context. Models discussed include 3-D organotypic cultures engineered in the rotating wall vessel (RWV) bioreactor, extracellular matrix (ECM)-embedded/organoid models, and organ-on-a-chip (OAC) models. Collectively, these technologies provide a more physiologically relevant and predictive framework for investigating infectious disease mechanisms and antimicrobial therapies at the intersection of the host, microbe, and their local microenvironments.

3-D↗

DOE OSTI2016

CFD Analysis and Design of Detailed Target Configurations for an Accelerator-Driven Subcritical System

High-fidelity analysis has been utilized in the design of beam target options for an accelerator driven subcritical system. Designs featuring stacks of plates with square cross section have been investigated for both tungsten and uranium target materials. The presented work includes the first thermal-hydraulic simulations of the full, detailed target geometry. The innovative target cooling manifold design features many regions with complex flow features, including 90 bends and merging jets, which necessitate three-dimensional fluid simulations. These were performed using the commercial computational fluid dynamics code STAR-CCM+. Conjugate heat transfer was modeled between the plates, cladding, manifold structure, and fluid. Steady-state simulations were performed but lacked good residual convergence. Unsteady simulations were then performed, which converged well and demonstrated that flow instability existed in the lower portion of the manifold. It was established that the flow instability had little effect on the peak plate temperatures, which were well below the melting point. The estimated plate surface temperatures and target region pressure were shown to provide sufficient margin to subcooled boiling for standard operating conditions. This demonstrated the safety of both potential target configurations during normal operation.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Application of Modified Meshgraphnets for Subsurface Prediction during CO2 Sequestration

In the face of the increasingly dire consequences of anthropogenic climate change, capturing and storing carbon dioxide is paramount. However, several impediments exist to the safe and effective subsurface storage of CO2, such as cost of transport, identification of suitable sites for subsurface storage, and assessment of long-term risk from storage in subsurface aquifers. Accurate subsurface modeling is necessary to ensure that CO2 storage is both safe and effective. Still, such modeling has traditionally required either substantial time and computational power (numerical simulation) or a substantial amount of pre-existing data for training (machine learning models). Additionally, these models lack flexibility in dealing with both changes in discretization of the input data and generalizability beyond the data on which they are trained. In order to address these issues, this research applies graph neural networks (GNNs) to predict subsurface saturation and pressure during CO₂ injection in a model of the Illinois Basin-Decatur Project (IBDP). GNNs provide a flexible, intuitive method for representing and manipulating complex unstructured data, which is often found in many practical domain problems such as fluid flow and subsurface characterization. These unstructured grids are easily represented in GNNs by representing spatially-localized features such as permeability, porosity, saturation, and pressure as nodes in a graph and relationships between these properties as edges connecting these nodes. This research applies a specific GNN model called MeshGraphNets (MGN) to model the change in CO2 saturation and pressure over a 50-month time period (36 months of injection, 14 months post-injection). The MGN model leverages a message passing process that allows the network to learn both the spatial and temporal dynamics of this system simultaneously. Additionally, training on a limited dataset (64 realizations, 20 time points each) resulted in a high degree of accuracy in saturation prediction both within the same timeframe as the training (20 months, 0.039 average RMSE) and when projecting out to the end of injection (36 months, 0.053 average RMSE). Temporal predictions such as those generated by MGNs and other similar models are prone to accumulated error over time; in order to address this, a multi-step rollout (MSR) training process was applied to calculate training loss. This method mimics the forward prediction during inference by “rolling out” multiple time points in a single training step using the previous prediction as input to the MGN model. By calculating the loss several time steps forward from the current prediction, the model is forced to find a more stable state over time. Application of MSR to the MGN model resulted in an average 15% reduction in inference error over time during forward prediction. This study showcases the immense potential of GNNs as a game-changing methodology for predicting pressure and saturation evolution in CCS projects, ultimately paving the way for more sustainable and effective carbon storage solutions. Presentation prepared for the 2024 AiChE Annual Meeting, October 27 to November 1 2024, San Diego, CA.

Holcomb, Paul↗

NASA NTRS1978

A three-dimensional model of corotating streams in the solar wind. I - Theoretical foundations

The paper is concerned with the development of the theoretical and mathematical background pertinent to the study of steady, corotating solar wind structure in all three spatial dimensions. The dynamical evolution of the plasma in interplanetary space (defined as the region beyond roughly 35 Rs where the flow is supersonic) is approximately described by the nonlinear, single-fluid, polytropic magnetohydrodynamic or hydrodynamic equations. Efficient numerical techniques are outlined for solving this complex system of coupled, hyperbolic partial differential equations. The present formulation is inviscid and nonmagnetic, but the methods used allow for the potential inclusion of both features with only modest modifications. A simple, highly idealized hydrodynamic model stream is examined to illustrate the fundamental processes involved in the three-dimensional dynamics of stream evolution. It is found that spatial variations in the rotational stream interaction mechanism produce small nonradial flows on a global scale that lead to the transport of mass, energy, and momentum away from regions of relative compression and into regions of relative rarefaction. Comparison with simpler models demonstrates the essential nonlinear, multidimensional nature of the interplanetary dynamics.

Pizzo, V.↗