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Integrated Aeromechanics with Three-Dimensional Solid-Multibody Structures

A full three-dimensional finite element-multibody structural dynamic solver is coupled to a three-dimensional Reynolds-averaged Navier-Stokes solver for the prediction of integrated aeromechanical stresses and strains on a rotor blade in forward flight. The objective is to lay the foundations of all major pieces of an integrated three-dimensional rotor dynamic analysis - from model construction to aeromechanical solution to stress/strain calculation. The primary focus is on the aeromechanical solution. Two types of three-dimensional CFD/CSD interfaces are constructed for this purpose with an emphasis on resolving errors from geometry mis-match so that initial-stage approximate structural geometries can also be effectively analyzed. A three-dimensional structural model is constructed as an approximation to a UH-60A-like fully articulated rotor. The aerodynamic model is identical to the UH-60A rotor. For preliminary validation measurements from a UH-60A high speed flight is used where CFD coupling is essential to capture the advancing side tip transonic effects. The key conclusion is that an integrated aeromechanical analysis is indeed possible with three-dimensional structural dynamics but requires a careful description of its geometry and discretization of its parts.

Three-Dimensional

Design and performance of a modularized NaI/Tl/ detector /The Crystal Ball prototype/

A prototype NaI(Tl) detector (the Cluster of 54) of spherical geometry subtending a solid angle of 7.5% of 4pi at its center, has recently been assembled and tested. This detector consists of 54 close-packed but optically isolated NaI(Tl) modules and the associated electronic circuitry. The Cluster of 54 is the predecessor of an almost complete spherical detector, the Crystal Ball, which will cover 94% of 4pi. The latter detector is now under construction and is especially designed for the study of gamma-rays produced in electron-positron collisions at colliding beam facilities. This article outlines the mechanical, optical, and electronic assembly of the prototype system.

Chan, Y.

Study of a Tricarbide Grooved Ring Fuel Element for Nuclear Thermal Propulsion

Deep space exploration, especially that of Mars, is on the horizon as the next big challenge for space exploration. Nuclear propulsion, through which high thrust and efficiency can be achieved, is a promising option for decreasing the cost and logistics of such a mission. Work on nu- clear thermal engines goes back to the days of the NERVA program. Currently, nuclear thermal propulsion is under development again in various forms to provide a superior propulsion system for deep space exploration. The authors have been working to develop a concept nuclear thermal engine that uses a grooved ring fuel element as an alternative to the traditional hexagonal rod design. The authors are also studying the use of carbide fuels. The concept was developed in order to increase surface area and heat transfer to the propellant. The use of carbides would also raise the operating temperature of the reactor. It is hoped that this could lead to a higher thrust to weight nuclear thermal engine. This paper describes the modeling of neutronics, heat transfer, and fluid dynamics of this alternative nuclear fuel element geometry. Fabrication experiments of grooved rings from carbide refractory metals are also presented along with material characterization and interactions with a hot hydrogen environment. Results of experiments and associated analysis are desired densities with some success in material distribution and reaching a solid solution. Future work is needed to improve distribution of material, minimize oxidation during the milling process, and de ne a fabrication process that will serve for constructing grooved ring fuel rods for large system tests.

Taylor, Brian

Blade Assessment for Ice Impact (BLASIM). User's manual, version 1.0

The Blade Assessment Ice Impact (BLASIM) computer code can analyze solid, hollow, composite, and super hybrid blades. The solid blade is made up of a single material where hollow, composite, and super hybrid blades are constructed with prescribed composite layup. The properties of a composite blade can be specified by inputting one of two options: (1) individual ply properties, or (2) fiber/matrix combinations. When the second option is selected, BLASIM utilizes ICAN (Integrated Composite ANalyzer) to generate the temperature/moisture dependent ply properties of the composite blade. Two types of geometry input can be given: airfoil coordinates or NASTRAN type finite element model. These features increase the flexibility of the program. The user's manual provides sample cases to facilitate efficient use of the code while gaining familiarity.

Reddy, E. S.

Experimental investigation of the flow field in the head-end star slot section of a solid rocket motor

A test program has been developed to investigate the complex flowfield in the head-end, star grain section of a solid rocket motor. Documentation of the flowfield pattern is to be obtained using both flow visualization techniques and quantitative methods, including static pressure measurements, heat transfer coefficient measurements, and hot-wire anemometry. A cold-flow, one-tenth-scale model based on the geometry of the Space Shuttle SRM head-end section and its single-port igniter, along with two models of a four-port igniter, have been constructed. The scale factor is derived from a scaling analysis which matches Reynolds number between the model and the full-scale flowfield in the star grain section. The NASA Marshall Space Flight Center 14 x 14 inch trisonic wind tunnel will be utilized for the cold flow tests. Since the work is still in progress, no results are included.

Ciucci, A.

Study of a Tricarbide Grooved Ring Fuel Element for Nuclear Thermal Propulsion

Deep space exploration, especially that of Mars, is on the horizon as the next big challenge for space exploration. Nuclear propulsion, through which high thrust and efficiency can be achieved, is a promising option for decreasing the cost and logistics of such a mission. Work on nuclear thermal engines goes back to the days of the NERVA program. Currently, nuclear thermal propulsion is under development again in various forms to provide a superior propulsion system for deep space exploration. The authors have been working to develop a concept nuclear thermal engine that uses a grooved ring fuel element as an alternative to the traditional hexagonal rod design. The authors are also studying the use of carbide fuels. The concept was developed in order to increase surface area and heat transfer to the propellant. The use of carbides would also raise the operating temperature of the reactor. It is hoped that this could lead to a higher thrust to weight nuclear thermal engine. This paper describes the modeling of neutronics, heat transfer, and fluid dynamics of this alternative nuclear fuel element geometry. Fabrication experiments of grooved rings from carbide refractory metals are also presented along with material characterization and interactions with a hot hydrogen environment. Results of experiments and associated analysis are discussed. The authors demonstrated success in reaching desired densities with some success in material distribution and reaching a solid solution. Future work is needed to improve distribution of material, minimize oxidation during the milling process, and define a fabrication process that will serve for constructing grooved ring fuel rods for large system tests.

Taylor, Brian

Ultra-Flexible Thermal Bus for Use in the Astro-H Adiabatic Demagnetization Refrigerator

The adiabatic demagnetization refrigerator (ADR) developed for the Astro-H Soft-X-ray Spectrometer (SXS) is a multi-stage solid-state cooler. It is capable of holding the SXS detector array at 0.050 K for greater than 24 hours with a recycle time of less than one hour. This quick recycle time relies upon high-conductivity thermal straps to couple the individual stages to a pair of heat switches without imposing a lateral load on the paramagnetic salt pills. To accomplish this we construct thermal straps using a technique of diffusion bonding together the ends of high-purity copper straps leaving the length between as individual foils. A thermal bus created this way has a thermal conductivity comparable to a solid strap of the equivalent thickness but with much-increased flexibility. The technique for selecting the base material, machining, cleaning, forming into final shape, and finally bonding together individual foils will be discussed along with examples of complete straps in various geometries.

Thermal Conductivity

Using SpaceClaimTD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractor's thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces/solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing/repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the "mark-up" of that geometry. These so-called "mark-ups" control how finite element (FE) meshes are to be generated through the "tagging" of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. "Domain-tags" were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine the objects each time as one would if using TDMesher. The use of SpaceClaim/TD Direct helps simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It also saves time and effort in the subsequent analysis.

Power Systems

Voxel Based Three-Dimensional Topology Optimization of Heat Exchanger Fins

Increasing interest in novel aircraft propulsion systems and potential for unwanted heat generation, or capture and reuse of waste heat, may require increasingly lightweight and high performing heat exchangers. Advances in manufacturing technologies have shown potential to create complex designs, but design tools need more flexibility. This study utilizes genetic algorithm-driven topology optimization to develop high performance heat exchanger fins for critical applications such as aerospace. The solid domain is generated using voxel representation where a voxel value of 1 indicates the solid domain and a voxel value of 0 refers to the fluid domain. The use of voxel representation somewhat matches the digitization of a model that is required to fabricate using additive manufacturing, and also allows for a highly unconstrained geometry. To test the topology optimization approach, a three-dimensional(3D)baseline offset strip fin geometry in steady laminar flow(Reynolds number = 215)with conjugate heat transfer(simultaneous solution of solid and fluid temperature fields)is optimized. New designs are generated using the genetic algorithm (GA) and sent to evaluation by the CFD software OpenFOAM; then the GA sorts and selects the reproduction pool for the following generation. This process is repeated for 60 generations. The study also investigates the effect off in material on the performance of the GA and the resulting designs. The results show that the optimal designs have overall performance improvement of 18% relative to the baseline. Additionally, a fin constructed of a lower conductivity material (such as an Inconel super alloy that might be necessary for waste heat recovery applications)results in lower overall performance improvement (11%)and optimal designs with higher pressure drop relative to their baseline, and relative to optimal designs produced using higher conductivity materials.

3D Optimization

Reconfigurable Cellular Composite Structures for Lighter than Air Vehicles with Scalable Size and Endurance

Engineered non-stochastic cellular materials show promising characteristics on the laboratory scale,with nearly ideal specific stiffness and strength scaling at ultralight mass density. These propertiessuggest performance benefits in any application with combined stiffness and mass constraints, suchas air vehicles. We investigate here the application of re-configurable cellular composite materialsand structures to lighter than air vehicles. We describe the properties and applicability of these materials,provide an example analysis of governing loading conditions associated with airships, showan example optimization method for navigating the design space, and describe how recent advancesin cellular material manufacturing and reconfiguration enable system performance benefits includingnew concepts of operation. Lastly, we propose lighter than air vehicles that are assembled andmaintained in-flight, eliminating structural compromises associated with transitional flight modesand ground handling.Engineered non-stochastic cellular material properties suggest performance benefits in lighter than air vehicles due tostiffness and mass constraints that are intrinsic to the airship design problem. Recent advances in cellular materialmanufacturing and reconfiguration enable system performance benefits including new concepts of operation, such aslighter than air vehicles that are assembled and maintained in-flight, eliminating structural compromises associatedwith transitional flight modes and ground handling. Existing engineered cellular materials display properties allowinglarge large scale airships design as monocoque cellular solids. Inevitable improvements in cellular material propertiesand manufacturing will improve feasibility even further. Given the suggestion that the two most significant technologygaps exist across all current airship projects are manufacturing and assembly processes and ground handling [7],a strategy that encompasses construction and maintenance in flight could provide critical rephrasing of the systemdesign problem through these new concepts of operation. Refactoring of traditional manufacturing, operation, andservice process constraints could extend to other domains in aerospace systems and manufacturing in general.In future work, the complexity of the design task would benefit from a form of optimization in order to find themost suitable geometry for a chosen application. For example, the Sequential Least SQuares Programming (SLSQP)function from within the SciPy Minimize library is a multiobjective constrained optimization method that has beenapplied to fixed wing aircraft design. [17] In this situation it would allow for several objective functions such as drag,bending stiffness, buoyancy and cost of transport to be incorporated into a composite objective function.

Copplestone, Grace

Recent Development in the CESE Method for the Solution of the Navier-Stokes Equations Using Unstructured Triangular or Tetrahedral Meshes With High Aspect Ratio

In the multidimensional CESE development, triangles and tetrahedra turn out to be the most natural building blocks for 2D and 3D spatial meshes. As such the CESE method is compatible with the simplest unstructured meshes and thus can be easily applied to solve problems with complex geometries. However, because the method uses space-time staggered stencils, solution decoupling may become a real nuisance in applications involving unstructured meshes. In this paper we will describe a simple and general remedy which, according to numerical experiments, has removed any possibility of solution decoupling. Moreover, in a real-world viscous flow simulation near a solid wall, one often encounters a case where a boundary with high curvature or sharp corner is surrounded by triangular/tetrahedral meshes of extremely high aspect ratio (up to 106). For such an extreme case, the spatial projection of a space-time compounded conservation element constructed using the original CESE design may become highly concave and thus its centroid (referred to as a spatial solution point) may lie far outside of the spatial projection. It could even be embedded beyond a solid wall boundary and causes serious numerical difficulties. In this paper we will also present a new procedure for constructing conservation elements and solution elements which effectively overcomes the difficulties associated with the original design. Another difficulty issue which was addressed more recently is the wellknown fact that accuracy of gradient computations involving triangular/tetrahedral grids deteriorates rapidly as the aspect ratio of grid cells increases. The root cause of this difficulty was clearly identified and several remedies to overcome it were found through a rigorous mathematical analysis. However, because of the length of the current paper and the complexity of mathematics involved, this new work will be presented in another paper.

Chang, Sin-Chung

Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.

Superalloy

Structural Analysis and Optimization of a Composite Fan Blade for Future Aircraft Engine

This report addresses the structural analysis and optimization of a composite fan blade sized for a large aircraft engine. An existing baseline solid metallic fan blade was used as a starting point to develop a hybrid honeycomb sandwich construction with a polymer matrix composite face sheet and honeycomb aluminum core replacing the original baseline solid metallic fan model made of titanium. The focus of this work is to design the sandwich composite blade with the optimum number of plies for the face sheet that will withstand the combined pressure and centrifugal loads while the constraints are satisfied and the baseline aerodynamic and geometric parameters are maintained. To satisfy the requirements, a sandwich construction for the blade is proposed with composite face sheets and a weak core made of honeycomb aluminum material. For aerodynamic considerations, the thickness of the core is optimized whereas the overall blade thickness is held fixed so as to not alter the original airfoil geometry. Weight is taken as the objective function to be minimized by varying the core thickness of the blade within specified upper and lower bounds. Constraints are imposed on radial displacement limitations and ply failure strength. From the optimum design, the minimum number of plies, which will not fail, is back-calculated. The ply lay-up of the blade is adjusted from the calculated number of plies and final structural analysis is performed. Analyses were carried out by utilizing the OpenMDAO Framework, developed at NASA Glenn Research Center combining optimization with structural assessment.

Coroneos, Rula M.

X-ray fluorescence surface contaminant analyzer: A feasibility study

The bonding of liner material to the inner metal surfaces of solid rocket booster cases is adversely affected by minute amounts of impurities on the metal surface. Suitable non-destructive methods currently used for detecting these surface contaminants do not provide the means of identifying their elemental composition. The feasibility of using isotopic source excited energy dispersive X-ray fluorescence as a possible technique for elemental analysis of such contaminants is investigated. A survey is made of the elemental compositions of both D-6ac steel, a common construction material for the booster cases, and Conoco HD-2 grease, a common surface contamination. Source and detector choices that maximize signal to noise ratio in a Recessed Source Geometry are made. A Monte Carlo simulation is then made of the optimized device incorporating the latest available X-ray constants at the energy of the chosen source to determine the device's response to a D-6ac steel surface contained with Conoco HD-2 grease.

Eldridge, Hudson B.

The implementation of the graphics of program EAGLE: A numerical grid generation code on NASA Langley SNS computer system

Program EAGLE (Eglin Arbitrary Geometry Implicit Euler) Numerical Grid Generation System is a composite (multi-block) algebraic or elliptic grid generation system designed to discretize the domain in and/or around any arbitrarily shaped three dimensional regions. This system combines a boundary conforming surface generation scheme and includes plotting routines designed to take full advantage of the DISSPLA Graphics Package (Version 9.0). Program EAGLE is written to compile and execute efficiently on any Cray machine with or without solid state disk (SSD) devices. Also, the code uses namelist inputs which are supported by all Cray machines using the FORTRAN compiler CFT77. The namelist inputs makes it easier for the user to understand the inputs and operation of Program EAGLE. EAGLE's numerical grid generator is constructed in the following form: main program, EGG (executive routine); subroutine SURFAC (surface generation routine); subroutine GRID (grid generation routine); and subroutine GRDPLOT (grid plotting routines). The EAGLE code was modified to use on the NASA-LaRC SNS computer (Cray 2S) system. During the modification a conversion program was developed for the output data of EAGLE's subroutine GRID to permit the data to be graphically displayed by IRIS workstations, using Plot3D. The code of program EAGLE was modified to make operational subroutine GRDPLOT (using DI-3000 Graphics Software Packages) on the NASA-LaRC SNS Computer System. How to implement graphically, the output data of subroutine GRID was determined on any NASA-LaRC graphics terminal that has access to the SNS Computer System DI-300 Graphics Software Packages. A Quick Reference User Guide was developed for the use of program EAGLE on the NASA-LaRC SNS Computer System. One or more application program(s) was illustrated using program EAGLE on the NASA LaRC SNS Computer System, with emphasis on graphics illustrations.

Houston, Johnny L.

Non-Reflecting Regions for Finite Difference Methods in Modeling of Elastic Wave Propagation in Plates

Solution of the wave equation using techniques such as finite difference or finite element methods can model elastic wave propagation in solids. This requires mapping the physical geometry into a computational domain whose size is governed by the size of the physical domain of interest and by the required resolution. This computational domain, in turn, dictates the computer memory requirements as well as the calculation time. Quite often, the physical region of interest is only a part of the whole physical body, and does not necessarily include all the physical boundaries. Reduction of the calculation domain requires positioning an artificial boundary or region where a physical boundary does not exist. It is important however that such a boundary, or region, will not affect the internal domain, i.e., it should not cause reflections that propagate back into the material. This paper concentrates on the issue of constructing such a boundary region.

Kishoni, Doron

Study of Magnetic Damping Effect on Convection and Solidification Under G-Jitter Conditions

As shown in space flight experiments, g-jitter is a critical issue affecting solidification processing of materials in microgravity. This study aims to provide, through extensive numerical simulations and ground based experiments, an assessment of the use of magnetic fields in combination with microgravity to reduce the g-jitter induced convective flows in space processing systems. Analytical solutions and 2-D and 3-D numerical models for g-jitter driven flows in simple solidification systems with and without the presence of an applied magnetic field have been developed and extensive analyses were carried out. A physical model was also constructed and PIV measurements compared reasonably well with predictions from numerical models. Some key points may be summarized as follows: (1) the amplitude of the oscillating velocity decreases at a rate inversely proportional to the g-jitter frequency and with an increase in the applied magnetic field; (2) the induced flow oscillates at approximately the same frequency as the affecting g-jitter, but out of a phase angle; (3) the phase angle is a complicated function of geometry, applied magnetic field, temperature gradient and frequency; (4) g-jitter driven flows exhibit a complex fluid flow pattern evolving in time; (5) the damping effect is more effective for low frequency flows; and (6) the applied magnetic field helps to reduce the variation of solutal distribution along the solid-liquid interface. Work in progress includes developing numerical models for solidification phenomena with the presence of both g-jitter and magnetic fields and developing a ground-based physical model to verify numerical predictions.

Li, Ben Q.

Comparing morphologies of drainage basins on Mars and Earth using integral-geometry and neural maps

We compare morphologies of drainage basins on Mars and Earth in order to confine the formation process of Martian valley networks. Basins on both planets are computationally extracted from digital topography. Integral-geometry methods are used to represent each basin by a circularity function that encapsulates its internal structure. The shape of such a function is an indicator of the style of fluvial erosion. We use the self-organizing map technique to construct a similarity graph for all basins. The graph reveals systematic differences between morphologies of basins on the two planets. This dichotomy indicates that terrestrial and Martian surfaces were eroded differently. We argue that morphologies of Martian basins are incompatible with runoff from sustained, homogeneous rainfall. Fluvial environments compatible with observed morphologies are discussed. We also construct a similarity graph based on the comparison of basins hypsometric curves to demonstrate that hypsometry is incapable of discriminating between terrestrial and Martian basins. INDEX TERMS: 1824 Hydrology: Geomorphology (1625); 1886 Hydrology: Weathering (1625); 5415 Planetology: Solid Surface Planets: Erosion and weathering; 6225 Planetology: Solar System Objects Mars. Citation: Stepinski, T. F., and S. Coradetti (2004), Comparing morphologies of drainage basins on Mars and Earth using integral-ge

Stepinski, T. F.