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NASA NTRS2000

Rotating Molten Metallic Drops and Related Phenomena: A New Approach to the Surface Tension Measurement

Molten aluminum and tin drops were levitated in a high vacuum by controlled electric fields, and they were systematically rotated by applying by a rotating magnetic field. When the evolution of the drop shape was measured as a function of rotation frequency, it agreed quantitatively well with the Brown and Scriven's theoretical prediction. The normalized rotation frequencies at the bifurcation point agreed with the predicted value 0.559, within 2%. An anomalous phenomenon which totally deviated from the prediction was observed in rotating molten tin drops when they were kept in a high rotation rate for several hours. No anomaly was observed in aluminum drops when they underwent similar condition. It was speculated that under the strong centrifugal force in the drop the tin isotopes must be separating. Since Al-27 is essentially the only naturally abundant isotope in the aluminum drops, the same anomaly is not expected. Based on the shape deformation of a rotating drop, an alternate approach to the surface tension measurement was verified. This new surface tension measurement technique was applied to a glassforming alloy, Zr(41.2)Ti(13.8)Cu(12.5)Ni(10.0)Be(22.5) in its highly viscous states. Also demonstrated in the paper was a use of a molten aluminum drop to verify the Busse's prediction of the influence of the drop rotation on the drop oscillation frequency.

Rhim, Won-Kyu↗

NASA NTRS1994

Design of a composite filter realizable on practical spatial light modulators

Hybrid optical correlator systems use two spatial light modulators (SLM's), one at the input plane and the other at the filter plane. Currently available SLM's such as the deformable mirror device (DMD) and liquid crystal television (LCTV) SLM's exhibit arbitrarily constrained operating characteristics. The pattern recognition filters designed with the assumption that the SLM's have ideal operating characteristic may not behave as expected when implemented on the DMD or LCTV SLM's. Therefore it is necessary to incorporate the SLM constraints in the design of the filters. In this report, an iterative method is developed for the design of an unconstrained minimum average correlation energy (MACE) filter. Then using this algorithm a new approach for the design of a SLM constrained distortion invariant filter in the presence of input SLM is developed. Two different optimization algorithms are used to maximize the objective function during filter synthesis, one based on the simplex method and the other based on the Hooke and Jeeves method. Also, the simulated annealing based filter design algorithm proposed by Khan and Rajan is refined and improved. The performance of the filter is evaluated in terms of its recognition/discrimination capabilities using computer simulations and the results are compared with a simulated annealing optimization based MACE filter. The filters are designed for different LCTV SLM's operating characteristics and the correlation responses are compared. The distortion tolerance and the false class image discrimination qualities of the filter are comparable to those of the simulated annealing based filter but the new filter design takes about 1/6 of the computer time taken by the simulated annealing filter design.

Rajan, P. K.↗

NASA NTRS2022

Design, Control, and Simulation of Tensegrity Based Kites

Due to lowering price and increased functionality, the future could bring in a huge number of UAVs flying in urban areas. In order to safely accommodate them, they should be fundamentally safe to fly. Unfortunately, current rigid designs could cause significant damage in case of a crash. To mitigate this problem, this report proposes constructing soft UAVs using tensegrity structures in order to mitigate the impact of collisions, effectively improving the safety of the vehicles and increasing public confidence in the use of UAVs. In this paradigm, the frame of the vehicle is designed using a tensegrity structure, a geometric structure composed of suspended elements of pure compression and pure tension, which during a collision can better absorb high stresses through elastic deformation. As a feasibility study we test this concept on an actuated tensegrity kite in a custom physics simulator, designed to simulate tensegrity structures with non-rigid rods, along with basic simulations of lift. Results show that this concept is feasible and that the kite can change orientation by actively changing the shape of the tensegrity structure.

Tensegrity↗

NASA NTRS2005

Stress Analysis of Composite Cylindrical Shells With an Elliptical Cutout

A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; nonuniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.

Nemeth, M. P.↗

NASA NTRS1993

Application of CFD Analysis to Design Support and Problem Resolution for ASRM and RSRM

The use of Navier-Stokes CFD codes to predict the internal flow field environment in a solid rocket motor is a very important analysis element during the design phase of a motor development program. These computational flow field solutions uncover a variety of potential problems associated with motor performance as well as suggesting solutions to these problems. CFD codes have also proven to be of great benefit in explaining problems associated with operational motors such as in the case of the pressure spike problem with the STS-54B flight motor. This paper presents results from analyses involving both motor design support and problem resolution. The issues discussed include the fluid dynamic/mechanical stress coupling at field joints relative to significant propellant deformations, the prediction of axial and radial pressure gradients in the motor associated with motor performance and propellant mechanical loading, the prediction of transition of the internal flow in the motor associated with erosive burning, the accumulation of slag at the field joints and in the submerged nozzle region, impingement of flow on the nozzle nose, and pressure gradients in the nozzle region of the motor. The analyses presented in this paper have been performed using a two-dimensional axisymmetric model. Fluent/BFC, a three dimensional Navier-Stokes flow field code, has been used to make the numerical calculations. This code utilizes a staggered grid formulation along with the SIMPLER numerical pressure-velocity coupling algorithm. Wall functions are used to represent the character of the viscous sub-layer flow, and an adjusted k-epsilon turbulence model especially configured for mass injection internal flows, is used to model the growth of turbulence in the motor port. Conclusions discussed in this paper consider flow field effects on the forward, center, and aft propellant grains except for the head end star grain region of the forward propellant segment. The field joints and the submerged nozzle are discussed as well. Conclusions relative to both the design evaluation of the ASRM and the RSRM scenarios explaining the pressure spikes were based on the flow field solutions presented in this paper.

Dill, Richard A.↗

NASA NTRS2007

Stress Analysis of Composite Cylindrical Shells with an Elliptical Cutout

A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; non-uniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.

Oterkus, E.↗

NASA NTRS1995

Microwave Resonator Measurements of Atmospheric Absorption Coefficients: A Preliminary Design Study

A preliminary design study examined the feasibility of using microwave resonator measurements to improve the accuracy of atmospheric absorption coefficients and refractivity between 18 and 35 GHz. Increased accuracies would improve the capability of water vapor radiometers to correct for radio signal delays caused by Earth's atmosphere. Calibration of delays incurred by radio signals traversing the atmosphere has applications to both deep space tracking and planetary radio science experiments. Currently, the Cassini gravity wave search requires 0.8-1.0% absorption coefficient accuracy. This study examined current atmospheric absorption models and estimated that current model accuracy ranges from 5% to 7%. The refractivity of water vapor is known to 1% accuracy, while the refractivity of many dry gases (oxygen, nitrogen, etc.) are known to better than 0.1%. Improvements to the current generation of models will require that both the functional form and absolute absorption of the water vapor spectrum be calibrated and validated. Several laboratory techniques for measuring atmospheric absorption and refractivity were investigated, including absorption cells, single and multimode rectangular cavity resonators, and Fabry-Perot resonators. Semi-confocal Fabry-Perot resonators were shown to provide the most cost-effective and accurate method of measuring atmospheric gas refractivity. The need for accurate environmental measurement and control was also addressed. A preliminary design for the environmental control and measurement system was developed to aid in identifying significant design issues. The analysis indicated that overall measurement accuracy will be limited by measurement errors and imprecise control of the gas sample's thermodynamic state, thermal expansion and vibration- induced deformation of the resonator structure, and electronic measurement error. The central problem is to identify systematic errors because random errors can be reduced by averaging. Calibrating the resonator measurements by checking the refractivity of dry gases which are known to better than 0.1% provides a method of controlling the systematic errors to 0.1%. The primary source of error in absorptivity and refractivity measurements is thus the ability to measure the concentration of water vapor in the resonator path. Over the whole thermodynamic range of interest the accuracy of water vapor measurement is 1.5%. However, over the range responsible for most of the radio delay (i.e. conditions in the bottom two kilometers of the atmosphere) the accuracy of water vapor measurements ranges from 0.5% to 1.0%. Therefore the precision of the resonator measurements could be held to 0.3% and the overall absolute accuracy of resonator-based absorption and refractivity measurements will range from 0.6% to 1.

Walter, Steven J.↗

NASA NTRS2015

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗

NASA NTRS2015

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

Impact↗

NASA NTRS1981

Unsteady environments and responses of the shuttle combined loads orbiter test

Both separate and combined wind tunnel and vibration shaker tests were conducted on two structural panels representative of the Shuttle orbiter in the NASA LaRC 8-foot transonic pressure tunnel (TPT) to determine the effects of combined loads on the thermal protection system (TPS). The primary objective of this test was to provide a combined full-scale load environment and realistic time history of the dynamic pressures, Mach numbers (through transonic), and dynamic structural responses of these panels. The panels were selected from orbiter locations where interactive load sources such as aerodynamic shock waves, turbulent boundary layers, strut-induced vorticity, and substrate deformation combined to provide high bonding loads between the TPS and the orbiter structure. The test panels for this program were highly instrumented with static and dynamic pressure gages, accelerometers, deflectometers, strain gages, Schileren and high-speed photography, and special instrumentation necessary to determine TPS/structure interface loads and tile motions. Two test specimens of each orbiter panel were utilized. Both were high-fidelity representations of the selected orbiter location. The first panel (calibration panel) for each test was utilized to calibrate the tunnel and shaker system as well as provide a data-gathering source for applied static and dynamic loads. The second panel (test panel) for each test was subjected to flight time exposures only so that TPS characteristics as a function of flight mission exposure could be determined. These tests were the last in a series that was suce6ssfully completed and necessary to certify the TPS prior to the first launching of the Shuttle.

P. H. Schuetz↗

NASA NTRS2001

Deriving the Coronal Magnetic Field Using Parametric Transformation Analysis

When plasma-beta greater than 1 then the gas pressure dominates over the magnetic pressure. This ratio as a function along the coronal magnetic field lines varies from beta greater than 1 in the photosphere at the base of the field lines, to beta much less than 1 in the mid-corona, to beta greater than 1 in the upper corona. Almost all magnetic field extrapolations do not or cannot take into account the full range of beta. They essentially assume beta much less than 1, since the full boundary conditions do not exist in the beta greater than 1 regions. We use a basic parametric representation of the magnetic field lines such that the field lines can be manipulated to match linear features in the EUV and SXR coronal images in a least squares sense. This research employs free-form deformation mathematics to generate the associated coronal magnetic field. In our research program, the complex magnetic field topology uses Parametric Transformation Analysis (PTA) which is a new and innovative method to describe the coronal fields that we are developing. In this technique the field lines can be viewed as being embedded in a plastic medium, the frozen-in-field-line concept. As the medium is deformed the field lines are similarly deformed. However the advantage of the PTA method is that the field line movement represents a transformation of one magnetic field solution into another magnetic field solution. When fully implemented, this method will allow the resulting magnetic field solution to fully match the magnetic field lines with EUV/SXR coronal loops by minimizing the differences in direction and dispersion of a collection of PTA magnetic field lines and observed field lines. The derived magnetic field will then allow beta greater than 1 regions to be included, the electric currents to be calculated, and the Lorentz force to be determined. The advantage of this technique is that the solution is: (1) independent of the upper and side boundary conditions, (2) allows non-vanishing magnetic forces, and (3) provides a global magnetic field solution, which contains high- and low-beta regimes and maximizes the similarity between the field lines structure and all the coronal images of the region. The coronal image analysis is crucial to the investigation and for the first time these images can be exploited to derive the coronal magnetic field in a well-posed mathematical formulation. This program is an outgrowth of an investigation in which an extrapolated potential field was required to be "inflated" in order to have the field lines match the Yohkoh/SXT images. The field lines were radially stretched resulting in a better match to the coronal loops of an active region. The PTA method of radial and non-radial deformations of field lines to provide a match to the EUV/SXR images will be presented.

Gary, G. Allen↗

NASA NTRS2004

Extracellular mass transport considerations for space flight research concerning suspended and adherent in vitro cell cultures

Conducting biological research in space requires consideration be given to isolating appropriate control parameters. For in vitro cell cultures, numerous environmental factors can adversely affect data interpretation. A biological response attributed to microgravity can, in theory, be explicitly correlated to a specific lack of weight or gravity-driven motion occurring to, within or around a cell. Weight can be broken down to include the formation of hydrostatic gradients, structural load (stress) or physical deformation (strain). Gravitationally induced motion within or near individual cells in a fluid includes sedimentation (or buoyancy) of the cell and associated shear forces, displacement of cytoskeleton or organelles, and factors associated with intra- or extracellular mass transport. Finally, and of particular importance for cell culture experiments, the collective effects of gravity must be considered for the overall system consisting of the cells, their environment and the device in which they are contained. This does not, however, rule out other confounding variables such as launch acceleration, on orbit vibration, transient acceleration impulses or radiation, which can be isolated using onboard centrifuges or vibration isolation techniques. A framework is offered for characterizing specific cause-and-effect relationships for gravity-dependent responses as a function of the above parameters.

Non-NASA Center↗

NASA NTRS1976

The lift force on a drop in unbounded plane Poiseuille flow

The lift force on a deformable liquid sphere moving in steady, plane Poiseuille-Stokes flow and subjected to an external body force is calculated. The results are obtained by seeking a solution to Stokes' equations for the motion of the liquids inside and outside the slightly perturbed sphere surface, as expansions valid for small values of the ratio of the Weber number to the Reynolds number. When the ratio of the drop and external fluid viscosities is small, the lift exerted on a neutrally buoyant drop is found to be approximately one-tenth of the magnitude of the force reported by Wohl and Rubinow acting on the same drop in unbounded Poiseuille flow in a tube. The resultant trajectory of the drop is calculated and displayed as a function of the external body force.

Wohl, P. R.↗

NASA NTRS1995

Dynamics of Vapour Bubbles in Nucleate Boiling: Evolution of Thermally Controlled Bubbles - 2

The previously developed dynamic theory of growth and detachment of vapour bubbles under conditions of nucleate pool boiling is applied to study motion and deformation of a bubble evolving at a single nucleation site. The bubble growth is presumed to be thermally controlled, and two components of heat transfer to the bubble are accounted of: the one from the bulk of surrounding liquid and the one due to heat conduction across a liquid microlayer formed underneath the bubble. Bubble evolution is governed by the buoyancy and an effective surface tension force, both the forces making the bubble centre of mass move away from the wall and, thus, assisting its detachment. Buoyancy-controlled and surface-tension-controlled regimes are considered separately in a meticulous way. The duration of the whole process of bubble evolution till detachment, the rate of growth, and the bubble departure size are found as functions of time and physical and operating parameters. Some repeatedly observed phenomena, such as an influence of gravity on the growth rate, are explained. Inferences of the model agree qualitatively with available experimental evidence, and conclusions pertaining to the dependence on gravity of the bubble radius at detachment and the whole time of the bubble development when being attached to the wall are confirmed quantitatively.

Buyevich, Yu A.↗

NASA NTRSDate not supplied

Multiscale Prediction of Yarn Pullout Failure Mode in Unreinforced Textile Fabrics

Unreinforced woven fabrics have been implemented in a variety of high performance applications, including body armor, deployable structures, and as the reinforcement material in composites. Multiscale modeling techniques have significantly improved the capabilities of simulation-based tools to capture fabric mechanics efficiently and accurately, but often lack in their prediction of failure and require pairing with finite element analysis (FEA) software, limiting their application to the design of ‘fit-for-purpose’ materials. NASA’s Multiscale Analysis Tool (NASMAT) is a standalone multiscale program that has been traditionally used in the analysis of reinforced composites materials. More recently, it has been amended to simulate unreinforced fabric behavior by allowing the geometric state of the tows to change with applied loading due to the lack of a reinforcement material, such as the matrix seen in composites. Previous work has shown the ability of NASMAT to capture nonlinear macroscale behavior by predicting geometric changes in the state of each subcell as a function of the applied loading and allowing each subcell in the analysis to rotate according to these predicted changes, as well as predict nonlinear behavior due to the fiber breakage failure mode. In this work, the capability of predicting the onset and propagation of failure in plain woven fabrics in NASMAT is presented for the yarn pullout failure mode, which occurs when a fabric is loaded at an off-axis angle relative to the warp of weft tow direction. Yarn pullout behavior is initiated by determining the applied load in which the shear resistance of the contact area between yarn families is overcome. When failure is initiated, yarn pullout is determined to have occurred when the applied displacement, calculated from global strain, exceeds the deformed position of a given contact points between yarn families, determined from pin-joint kinematics. Contact points where pullout has occurred contribute to a global damage parameter used to modify the homogenized stiffness of the fabric, resulting in nonlinear behavior observed at the macroscale. The off-axis loading behavior and yarn pullout failure theory have been developed and implemented into NASMAT such that users can simulate off-axis tensile behavior of fabrics in a single, standalone multiscale tool. Simulations are compared to uniaxial tensile tests at various off-axis angles to demonstrate the capability of the tool in its prediction of both the onset of failure at each off-axis angles and the stress-strain behavior as failure progresses.

Materials↗

NASA NTRS2003

Residual Strength Analyses of Monolithic Structures

Finite-element fracture simulation methodology predicts the residual strength of damaged aircraft structures. The methodology uses the critical crack-tip-opening-angle (CTOA) fracture criterion to characterize the fracture behavior of the material. The CTOA fracture criterion assumes that stable crack growth occurs when the crack-tip angle reaches a constant critical value. The use of the CTOA criterion requires an elastic- plastic, finite-element analysis. The critical CTOA value is determined by simulating fracture behavior in laboratory specimens, such as a compact specimen, to obtain the angle that best fits the observed test behavior. The critical CTOA value appears to be independent of loading, crack length, and in-plane dimensions. However, it is a function of material thickness and local crack-front constraint. Modeling the local constraint requires either a three-dimensional analysis or a two-dimensional analysis with an approximation to account for the constraint effects. In recent times as the aircraft industry is leaning towards monolithic structures with the intention of reducing part count and manufacturing cost, there has been a consistent effort at NASA Langley to extend critical CTOA based numerical methodology in the analysis of integrally-stiffened panels.In this regard, a series of fracture tests were conducted on both flat and curved aluminum alloy integrally-stiffened panels. These flat panels were subjected to uniaxial tension and during the test, applied load-crack extension, out-of-plane displacements and local deformations around the crack tip region were measured. Compact and middle-crack tension specimens were tested to determine the critical angle (wc) using three-dimensional code (ZIP3D) and the plane-strain core height (hJ using two-dimensional code (STAGS). These values were then used in the STAGS analysis to predict the fracture behavior of the integrally-stiffened panels. The analyses modeled stable tearing, buckling, and crack branching at the integral stiffener using different values of critical CTOA for different material thicknesses and orientation. Comparisons were made between measured and predicted load-crack extension, out-of-plane displacements and local deformations around the crack tip region. Simultaneously, three-dimensional capabilities to model crack branching and to monitor stable crack growth of multiple cracks in a large thick integrally-stiffened flat panels were implemented in three-dimensional finite element code (ZIP3D) and tested by analyzing the integrally-stiffened panels tested at Alcoa. The residual strength of the panels predicted from STAGS and ZP3D code compared very well with experimental data. In recent times, STAGS software has been updated with new features and now one can have combinations of solid and shell elements in the residual strength analysis of integrally-stiffened panels.

Forth, Scott↗

NASA NTRS2004

Residual Strength Characterization of a Curved Integrally-Stiffened Panel

Over the years, Finite-element fracture simulation methodology has been very well established at NASA Langley to predict the residual strength of damaged aircraft structures. This methodology has been experimentally verified at NASA Langley for structures ranging from laboratory coupons up to full-scale built-up structural components with single and multiple-site damage cracking. The methodology uses the critical crack-tip-opening-angle (CTOA) fracture criterion to characterize the fracture behavior of the material. The CTOA fracture criterion assumes that stable crack growth occurs when the crack-tip angle reaches a constant critical value. The use of the CTOA criterion requires an elastic-plastic, finite-element analysis. The critical CTOA value is determined by simulating fracture behavior in laboratory specimens, such as a compact specimen, to obtain the angle that best fits the observed test behavior. The critical CTOA value appears to be independent of loading, crack length, and in-plane dimensions. However, it is a function of material thickness and local crack-front constraint. Modeling the local constraint requires either a three-dimensional analysis or a two-dimensional analysis with an approximation to account for the constraint effects. In recent times as the aircraft industry is leaning towards monolithic structures with the intension of reducing part count and manufacturing cost, there has been a consistent effort at NASA Langley to extend critical CTOA based numerical methodology in the analysis of integrally-stiffened panels. In this regard, a series of fracture tests were conducted on curved aluminum-alloy integrally-stiffened panels. These curved panels were subjected to uniaxial tension and pressure loading. During the test, applied load-crack extension, out-of-plane displacements and local deformations around the crack tip region were measured. Compact and middle-crack tension specimens were tested to determine the critical angle (psi(sub c) using three-dimensional code (ZIP3D) and the plane-strain core height (h(sub c)) using two-dimensional code (STAGS).

Seshadri, B. R.↗

NASA NTRS2022

A Numerical Study of the Liquid Motion in Titan’s Subsurface Ocean

An ocean filled with liquid water lies beneath the icy surface of several Jovian and Saturnian moons. In such an ocean, the currents are driven by various phenomena such as the tidal forcing, the deformation of the ice shell lying at its top, the temperature gradient resulting from the surface and bottom heat fluxes…The flow induced by the first two forcings can be modelled by means of a 2D depth-averaged model, while the third one generates horizontal and vertical density variations whose effects can only be captured by a 3D baroclinic model. We study the tides of Titan’s subsurface ocean and the impact of the ice shell on the liquid motion by means of the Second-generation Louvain-la-Neuve Ice–ocean Model, SLIM (https://www.climate.be/slim). The impact of the ice shell lying at the top of the ocean is modelled by a surface friction term and surface pressure terms. The latter are a function of the difference between the ocean elevation and the vertical displacement of the shell and the time derivative of this difference. Because of Titan’s appreciable obliquity (0.306°), the tidal motion expected (and found) is similar to the Europa tidal scenario described by Tyler (2008): the surface elevation consists of two bulges rotating around Titan and the associated depth-averaged velocity field consists of two gyres, separated by an area of high speed flow, whose centre follows a sinusoidal path centred on the equator. The ice shell damps the surface motion, thus slowing down the flow, without significantly modifying the spatial patterns of these fields. The depth of the ocean and the mechanical characteristics of the ice shell being poorly constrained, a sensitivity analysis is conducted. The depth-averaged flow slows down when the depth is increased and a lag appears in the tidal phase but the tidal range remains similar. The ice shell mechanical characteristics influences both the elevation and depth-averaged velocity fields in terms of magnitude but does not modify the spatial patterns of these fields. The influence of the surface heat flux is studied by means of the 3D baroclinic version of SLIM. The heat flux derived from Titan’s topography by Kvorka et al. (2018) is used as surface boundary condition for the temperature equation while a uniform bottom heat flux is implemented. Its value is computed assuming that the heat budget of the ocean is at equilibrium. These boundary conditions cause density variations, which impact the hydrodynamics of the ocean. While the flow velocity induced by these variations is two orders of magnitude smaller than the tidal flow, its orientation is time-independent, hence impacting the orientation of the velocity field. Although the variations of ocean surface elevation and speed with respect to the shell mechanical properties can be larger than those induced by the surface heat flux, taking into account the latter results in large variations of the velocity field global patterns, which was not observed when modifying the shell mechanical properties. Future studies should therefore focus on modelling the surface and bottom heat fluxes while uncertainties about the mechanical characteristics of the shell can be tolerated.

Titan↗