Variable Gravity Research Articles

Choices for temporal gravity field modeling for precision orbit determination of CryoSat-2

In this paper we review the precision orbit determination (POD) performance of the CryoSat-2 mission where we used all tracking data between June-2010 and Jan-2023; with station and beacon coordinates provided in the ITRF2020 reference system, we use a mean gravity model, and we use spacecraft specific models for modeling drag and radiation pressure. To model time variable gravity (TVG) we distinguish between two components, there is a short term oceanic and atmospheric part for which we use the AOD1B model; for the longer term part we employ GRACE and GRACE-FO monthly potential coefficient solutions. Our experience is that adding TVG information is not necessarily successful during POD, and that attention must be paid to the proper processing of the GRACE and GRACE-FO data. To demonstrate this property we define four runs where we gradually implement TVG information. An evaluation criterion is the level of POD tracking residuals, the level of the empirical accelerations, and a comparison to precision orbit ephemeris provided by the Centre National d’Etudes Spatiales (CNES). Unexplained empirical accelerations found during POD are on the level of 3 nm/s2 for the along-track component and 13 nm/s2 for the cross-track component. The laser residuals converge at approximately 1.02 cm and the Doppler residuals are on the level of 0.406 mm/s, the radial orbit difference to the CNES POE-F (Precision Orbit Ephemeris version F) orbits narrows to 6.5 mm. Tracking residuals are not evenly distributed for DORIS (Doppler Orbitography and Radiopositioning Integrated by Satellite) beacons, the South Atlantic Anomaly effect is for instance clearly visible in the first empirical orthogonal function EOF mode of monthly binned DORIS residuals. After consideration of all possible TVG approaches our conclusion is that 3 hourly AOD1B model fields result in a small but visible improvement. The addition of TVG from GRACE and GRACE-FO is implemented in two different ways from which we can select a version that does lead to a reduction in the Doppler tracking residuals and which does reduce the level of solved for empirical accelerations.

Variable gravity effects on penetrative porous convection

The effect of variable gravity on the onset of penetrative convection in a horizontal fluid-saturated porous layer is studied, performing the linear instability analysis and the nonlinear stability analysis (via the weighted energy method) of the thermal conduction solution. The linear and nonlinear critical Rayleigh numbers for the onset of penetrative porous convection are determined and their behaviour with respect to the fundamental physical parameters of the model is studied. In particular, we found that there exists a region of subcritical instabilities and that the increase of the upper bounding plane temperature and the decrease of gravity have a stabilizing effect on the onset of convection.

The role of local thermal non-equilibrium on the instability analysis in the presence of variable gravity field with throughflow

The influence of variable gravity on the stability analysis has been investigated in a horizontal porous region with throughflow under a local thermal non-equilibrium (LTNE) situation. Flow inside the porous region is considered to be followed by the Darcy model. Also, the linear varying gravity field with height and nonlinear (parabolic, cubic, and exponential) changing gravity field depth have been considered to address the investigation. The obtained eigenvalue problem for the perturbed state is solved via bvp4c technique in MATLAB. Finally, we investigated the convective boundaries of the system due to the governing parameters, such as gravity variation parameter (λ), porosity-modified conductivity ratio (γ), interphase heat transfer parameter (H), and throughflow parameter (Q). The outcomes assure that the interphase heat transfer parameter has a significant impact on the breakdown of the convection inside of its intermediate range, while the local thermal equilibrium (LTE) state occurred when H converges both the limiting cases, i.e. H→0 and H→∞. It has also been observed that the gravity variation parameter and throughflow parameter have a stabilizing effect, whereas the porosity-modified conductivity ratio destabilizes the flow. Further, it is distinguished that the instability boundaries are unchanged by H when γ≥10. In addition, the flow field is more delayed for exponential changing gravity field, whereas more advanced for cubic varying gravity field.

CFD Modeling of Bidirectional PMDs Inside Cryogenic Propellant Tanks Onboard Parabolic Flights

Future cryogenic propulsion systems will require efficient methods for transferring cryogenic propellants from a depot storage tank to a customer receiver tank to minimize costs and maximize reusability. The Reduced Gravity Cryogenic Transfer Project is currently developing advanced cryogenic fluid management technology and developing and validating new numerical models for three phases of transfer: line chill down, tank chill down, and tank fill. Additionally, multiple liquid nitrogen (LN2) parabolic flight transfer rigs are being designed by universities and NASA to investigate the gravitational sensitivities that exist in these three technologies. To maximize the collection of low-g data during flights, it is required to extract as much LN2 as possible from the supply tank, despite variable gravity levels. The purpose of this study is to present computational fluid dynamics volume of fluid simulations of LN2 behavior in the supply tank onboard parabolic flights to validate the optimal design of a bidirectional propellant management device (PMD) using the commercial software FLOW-3D. A parametric study was conducted on the effects of gravity level, fill level, pore size, open area, thickness, and type of baffle on PMD performance. Based on the results, the designed PMD exceeded the targeted expulsion efficiency.

Accounting for the instability of a liquid flow front through a porous medium under conditions of low gravity and in the presence of chemical interactions between the phases

Safe operation of orbital platforms relies heavily on stability of fluid flows in microgravity, which are strongly affected by capillary forces. The paper considers multiphase fluid seepage through a porous medium. Questions of instability of the interface between liquids are discussed. The effect of capillary instability is shown, which was revealed during the processing of experimental data on the imbibition of a porous structure in microgravity conditions during parabolic flights. A mathematical model is proposed to describe the process of multiple imbibition of a porous medium under conditions of variable gravity. The model takes into account hysteresis, various models of capillary pressure are used during imbibition and drainage. The paper also considers a method for modeling the instability by transforming the constitutive equations. The method allows modeling additional blurring of the imbibition front. The results of modeling based on this method for capillary imbibition of a porous medium under microgravity conditions, as well as for the case when chemical interactions occur between flowing fluids, are considered.

Effect of variable gravity on thermal convection in Jeffrey nanofluid: Darcy-Brinkman model

The subject under consideration in this research has various geophysical and astrophysical applications. Specifically, we investigate the impact of variable gravity on the onset of thermal instability within a layer of Jeffrey nanofluid confined in a Darcy-Brinkman porous medium. The solution of the fluid layer, which is positioned between two free-free boundaries, is determined using a linear stability analysis employing the normal mode technique. The Rayleigh number on the onset of convection is derived by using the Galerkin method. For stationary convection, the effects of different variable gravity parameters on the Jeffrey parameter, Darcy-Brinkman number, Lewis number, moderated diffusivity ratio, porosity of porous media and nanoparticle Rayleigh number are analyzed and presented graphically. The choices of using Jeffrey nanofluid as the base fluid for the study add novelty. Non-Newtonian fluids encompass a diverse range of substances, such as engine oils, oil extraction, wallpaper paste, and various biological liquids like blood etc.

Numerical investigation of natural circulation loop with supercritical CO2 on the thermal control system of micro spacecrafts

Aiming at the heat dissipation problem under the strict constraints of mass, volume, and power consumption in micro spacecrafts, the feasibility of applying a natural circulation loop (NCL) to the thermal control system is performed for the CubeSats (Cube satellites) of orbiting operations or the micro-rovers of extraterrestrial explorations. A 3-dimensional NCL model under variable gravity conditions corresponding the environment of aerospace is established, and the supercritical CO2 as the coolant. The heat transfer and thermal performance of NCL under gravity range of 10−6 g to 10 g are analyzed numerically, including the Earth orbit, the surface of the Moon and the Mars etc. The calculation results present that the gravity has a great influence on the flow circulation characteristics and thermal performance of the NCL. The applicability of employing NCL on the thermal control system of micro spacecrafts is validated with the gravity no less than 0.05 g. It is worth noting that, by designing the range of temperature from inlet to outlet of the heated tube covering the large specific heat region, the superior thermal performance can be obtained on account of the strong heat-carrying capacity of supercritical fluid, even under the low gravity with a small mass flow rate. Finally, a flow correlation is proposed considering the effect of gravity, flow regime, buoyancy force, and geometric factors, which is suitable on the NCL in the thermal control system of micro spacecrafts, and the R2 is 99.77%.

Detection of time variable gravity signals using terrestrial clock networks

The relativistic redshift between two earth-bound clocks can be interpreted in terms of gravity potential variation between the clock locations. A clock with a fractional frequency uncertainty of 10-18 is sensitive to a gravity potential variation of 0.1 m2/s2 or a height difference of 1 cm. Case studies for four regions affected by different mass change processes - Himalaya, Amazon, Greenland, and Fennoscandia - have been carried out. As the clocks rest on the deformable Earth’s surface, clock observations do not only include potential variations due to mass changes but also associated variations due to the vertical deformation of the land. For the simulations, vertical displacements were derived from real GNSS (Global Navigation Satellite Systems) measurements, and mass variations were computed from GRACE (Gravity Recovery And Climate Experiment) solutions. In the Himalayan region, seasonal variations with a maximum range of -0.20.2 m2/s2 were obtained. There, early and long-lasting precipitation patterns in North-East India and the gradual spreading towards the West can be observed by a dedicated clock network. For the Amazon region, seasonal variations with a maximum range of -0.50.5 m2/s2 observed by clocks also reveals the Amazon’s seasonal properties of annual rainfall variability at the North and South of the equator. The rainy season in the North of the equator is during the summer season from June to August, but from November to April in the South of the equator. The long-term trend of the ice mass loss in Greenland between 2004 and 2015 causes signals of potential variations of 1 m2/s2 that again can clearly be observed by clock measurements. Especially, the higher rates of mass variations in the west and south parts of Greenland can well be observed. The land uplift pattern of Fennoscandia due to the GIA (Glacial Isostatic Adjustment) can also be detected using optical clocks, however, the vertical deformations dominate the signal and not the mass changes. These examples illustrate that terrestrial clock networks can be used in the future as a modern tool for detecting various time-variable gravity signals for understanding the regional/local patterns of the variations and for providing complementary information to other geodetic techniques.

Continental and island arc segmentation: Implications for retro‐arc and pro‐arc foreland basin and backarc basin geometries and sediment distributions

AbstractSegmented magmatic arcs create arc‐parallel variable loads and influence associated foreland basins through flexural isostasy along strike, in addition to standard subduction‐perpendicular foredeep/forebulge/backbulge models. Segmentation occurs in both continental and island arcs (Aleutians, Calabria, Japan, Kuril/Kamchatka, Lesser Antilles, Solomon Islands and Sumatra/Java). Some segments have variable gravity anomalies and elastic thicknesses (Te). In standard theory, the load created by an orogenic belt/magmatic arc depresses the lithosphere modelled as a thin elastic plate floating on a fluid mantle substrate, leading to an arc‐perpendicular foredeep, forebulge and backbulge. Arc‐parallel topographic and gravitational features should influence loading along strike in a similar way, resulting in a checkerboard pattern of foredeeps, forebulges and backbulges in both pro‐arc and retro‐arc foreland basins. This pattern exercises profound controls on sediment and facies distribution in a here‐to‐fore un‐envisaged manner, with implications for resource exploration in foreland basins.

Thermal instability of rotating Jeffrey nanofluids in porous media with variable gravity

It is investigated how changes in gravity affect the thermal instability rotating Jeffrey nanofluids in porous media. Along with the Galerkin method and normal mode approach, the Darcy model is used. The distinct variable gravity parameters taken in this paper are: h(z)=z2-2z, h(z)=-z2, h(z)=-z and h(z)=z and their effects on the Jeffrey parameter, Taylor number, moderated diffusivity ratio, porosity of porous media, Lewis number and nanoparticle Rayleigh number on stationary convection have been scrutinized and graphically shown. Our finding demonstrates that varying gravity parameter h(z)=z2-2z has more stabilising impact on stationary convection. We have also discovered the necessary condition for overstability in the instance of oscillatory convection for this problem.

Effect of variable gravity field on the onset of convection in a Brinkman porous medium under convective boundary conditions

The effect of variable gravity on the onset of convection in a horizontal porous layer has been analyzed due to external heating. The third kind of thermal boundary conditions is considered on both the boundaries which are connected by Biot numbers B0 and B1. Also, the Brinkman model has been employed in the momentum equation. Further, linear and quadratic varying downward gravity fields depending on height have been taken to investigate the above observation. The bvp4c scheme is used in MATLAB to solve the eigenvalue problem for neutral stability mode. It is observed that the system's stability increases monotonically due to the rising effect of gravity variation parameter, Darcy number, and Biot numbers. Further, the onset of convection has been discussed for the two limiting cases of external heating on the boundaries where one boundary is associated with constant heat flux while another one is associated with an isothermal state. Finally, it is observed that the convection comes earlier for quadratic varying gravity field compared to linear varying gravity field when the external heat supplies from one boundary or both boundaries.

Thermal instability analysis in magneto-hybrid nanofluid layer between rough surfaces with variable gravity and space-dependent heat source

The onset of thermal instability with hybrid nanoparticles Al2O3–Cu in nanofluid is investigated with the combined effects of variable gravity, variable heat source and Lorentz force in a porous medium. Its applications are in many areas like chemical engineering, geophysics, astrophysics, etc. Based on literature, many gravity variations are assumed in the present analysis, along with a space-dependent heat source/sink parameter that varies along the width of the channel. The finite difference-based Lobatto IIIa method has been applied to solve the system under no nanoparticle flux and rough boundary conditions, and approximate analytical results are generated for some special cases. The roughness parameters ([Formula: see text]), Darcy number (Da), gravity variation function ([Formula: see text]), and Chandrasekhar number (Q) delay the onset of convection and thus stabilize the system. It is also observed that an increase in the Lewis number Le, power index in variable heat source, and the nanoparticle Rayleigh concentration number Rn decreases the critical Rayleigh number [Formula: see text] which destabilizes the system, and increases the critical wave number, which enlarges the convection cell size. In the case of exponential variation ([Formula: see text]) in the gravity variation parameter, the system becomes stabilized due to a delay in the onset of convection. In addition, we have considered multilayer perceptron-artificial neural network (MLP-ANN) computation to predict the critical Rayleigh number as per function of important controlling parameters. The data set of 625 observations is chosen keeping 70% for testing, 15% for training and 15% for validation using efficient Levenberg−Marquardt back propagation algorithm with optimal accuracy measures i.e., root mean square deviation (RMSE), root mean relative error (RMRE) and [Formula: see text] (coefficient of determination). Finally, the regression plots are drawn that correlate, target and output data.

Nonlinear instability analysis of internally heated convection in a porous layer with the impact of magnetic field and variable gravity

AbstractThe impact of the magnetic field, heat source, and variable gravity field on the stability of convective phenomena in a porous layer are investigated numerically. Three types of gravity variations, such as linear, parabolic, and cubic functions are considered. For linear and nonlinear theories, the method of normal modes has been employed to solve governing dimensionless equations. It is found that the onset of convection is delayed by increasing the Hartmann number and gravity variation parameter and enhancement of the internal heat source makes the system stable. The subcritical instability region increases as the Hartmann number and gravity variation parameter increase.

Study on the Self-Pressurization Laws of Cryogenic Liquid Krypton Tank for the Electric Propulsion System

To meet the application requirements of zero boil-off storage of cryogenic liquid krypton propellant in the process of completing deep space exploration missions by electric propulsion system, it is important to study the thermodynamic changes in cryogenic liquid krypton tanks under different environments. The gas phase and liquid phase material model of krypton working fluid, the gas-liquid phase change model at the interface layers, and the heat transfer process between the wall and the internal fluid are established by ANSYS-Fluent. The energy source term, gas phase, liquid phase mass source term, and phase change saturation temperature in the liquid krypton cryogenic tank are defined. This paper’s three influencing factors of gravity, initial liquid filling rate, and wall heat leakage are simulated and analysed. The results show that: (1) The self-pressurization rate significantly rises as the wall heat flux rises, and the gas-liquid interface drops less quickly. The pressure and temperature in the tank are also increasing at the same liquid level. (2) In the normal gravity environment, the bigger the filling rate, the lower the corresponding self-pressurization rate. (3) In the process of variable gravity, the gas pressurization rate in the cryogenic liquid krypton tank falls with the decrease of gravity.

Geodetic residual time series: A combined series by minimization of their internal noise level

This study aims to assess the hydrological effects of polar motion calculated from different combinations of geophysical excitations at decadal, seasonal, and non-seasonal periods. The geodetic residuals GAO, being a difference between observed geodetic excitation function of polar motion Geodetic Angular Momentum (GAM) and atmospheric (Atmospheric Angular Momentum—AAM) plus oceanic excitation functions (Oceanic Angular Momentum—OAM), are compared. Estimating hydrological effects on Earth’s rotation differs significantly, especially when using various oceanic models. Up to now, studies of geophysical excitations of polar motion containing AAM, OAM, and hydrological angular momentum (HAM) have not achieved entire agreement between geophysical (sum of AAM, OAM, and HAM obtained from the models) and geodetic excitation. Many geophysical models of the atmosphere, oceans, and land hydrology can be used to compute polar motion excitation. However, these models are very complex and still have uncertainties in the process descriptions, parametrization, and forcing. This work aims to show differences between various GAO solutions calculated from different mass and motion terms of various AAM and OAM models. Justifying to use one combination of GAO to estimate geodetic residuals is comparing those time series to hydrological excitations computed from Gravity Recovery and Climate Experiment (GRACE) data and the Land Surface Discharge Model (LSDM) model. Especially the quality of each geodetic residual time series is determined by estimating their noise level using a generalized formulation of the “three-cornered hat method” (3CH). This study presents a combined series of geodetic residuals GAO in polar motion (PM), wherein the internal noise level is shortened to a minimum by using the 3CH method. The combined GAO time series are compared with results obtained from the GRACE/GRACE Follow-On (GRACE-FO) solution provided by International Combination Service for Time variable Gravity Fields (COST-G) and the single solution elaborated by the Center for Space Research (CSR) and from the HAM LSDM hydrological model. The results show that higher consistency between GAO and HAM excitations can be achieved by minimizing the internal noise level in the GAO combined excitation series using the 3CH method, especially for the overall broadband and seasonal oscillations. For seasonal spectral bands, an agreement between combined GAO and the best-correlated series of GRACE CSR achieve correlations as high as 0.97 and 0.83 for the χ1 and χ2 equatorial components of PM excitation, respectively. This study’s combined geodetic residual time series slightly improved consistency between observed geodetic polar motion excitations and geophysical ones.

"Thermosolutal Instability of Couple Stress Rivlin Ericksen Ferromagnetic Fluid with Rotation, Magnetic and Variable Gravity Field in Porous Medium"

"Thermosolutal Instability of Couple Stress Rivlin Ericksen Ferromagnetic Fluid with Rotation, Magnetic and Variable Gravity Field in Porous Medium"

The study of internal heat and variable gravity field on the onset of convection in a sparsely packed porous medium

The qualitative influence of internal heat and variable gravity field on the onset of convection in a sparsely packed porous layer with horizontal fluid-saturated are investigated. Linear stability analysis is performed using the normal mode technique. The dimensionless governing equations with four cases of gravity field variation: (1) [Formula: see text], (2) [Formula: see text], (3) [Formula: see text], and (4) [Formula: see text] are solved using bvp4c in MATLAB R2020a and the corresponding eigenvalue problem is calculated for three types of boundaries, namely free-free, rigid-free, and rigid-rigid, respectively. The effect of an internal heat parameter [Formula: see text], Darcy number [Formula: see text], and gravity variation parameter [Formula: see text] for the stability of the system is investigated graphically. The critical value of the Rayleigh number and corresponding wavenumber are calculated for other fixed parameters. It is observed that internal heat parameters enhance the onset of convection, whereas the gravity variation parameter delays the same. It is also observed that the system becomes more stable for the exponential variable gravity function and less stable for the cubic variable gravity function.

Thermosolutal Instability of Couple Stress Rivlin Ericksen Ferromagnetic Fluid with Rotation, Magnetic and Variable Gravity Field in Porous Medium

In this paper thermosolutal instability of a couple stress Rivlin-Ericksen ferromagnetic fluid layerwith rotation, magnetic and variable gravity field in porous medium is studied. Using normalmode analysis technique the dispersion relation has been obtained and solved analytically. Forstationary convention, it is found that couple stress, magnetic field and permeability of mediumhave stabilizing effect on thermal instability under certain conditions. Rotation has stabilizingeffect if λ> 0 and destabilizing effect if λ< 0. Solute gradients has stabilizing effect either λ >0 or λ < 0. The presence of solute gradient, viscoelastic parameter, rotation and magnetic fieldintroduces oscillatory modes, stability in the system and principle of exchange of stability is notsatisfied if λ < 0 and system may be stable or unstable if λ > 0.

The Effect of Variable Gravity and Chemical Reaction on Double Diffusive Convection in a Sparsely Packed Porous Layer

The Effect of Variable Gravity and Chemical Reaction on Double Diffusive Convection in a Sparsely Packed Porous Layer

A novel energy-efficient actuator integrated with compact variable gravity compensation module

• Modularized CVGCm by 3D shape design and improved its performance. • Novel energy-efficient actuator that can compensate for the gravitational torque. • Power estimation model of the VGCA based on the Lagrangian method is presented. • Reduced rate of current and power in static and dynamic motion is 63.1 % and 64.0 %, respectively. This paper proposes a new type of energy-efficient actuator called variable gravity compensation module integrated actuator (VGCA). VGCA improves the energy efficiency by compensating the gravitational torque at the target joint. Additionally, the variability of compensation torque can further improve the energy efficiency by dealing with the variation of payload, which is required in many robotic applications. As a core part of the VGCA, a compact variable gravity compensation module, called CVGCm , is a cylindrical compact modular unit based on the cam and variable pivot of the lever mechanism. By the theoretically designed cam and lever profiles, the CVGCm can generate a non-linear compensation torque and energy-free variability. First, the functional principles of CVGCm and VGCA are explained. Next, implementation detail and manufacturing of VGCA are introduced. Subsequently, the power estimation model of the actuator is explained based on the Lagrangian method. The experimental results showed that the CVGCm achieved a rapid change of the compensation torque in the compact module. Furthermore, compared to the actuator without CVGCm, VGCA showed a 63.1% reduction of current in static motion and a 64.0% reduction of power in dynamic motion.