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NASA NTRS1982

Advanced Strain-Isolation-Pad Material with Bonded Fibrous Construction

The feasibility of utilizing air lay and liquid lay felt deposition techniques to fabricate strain isolation pad (SIP) materials for the Space Shuttle Orbiter was demonstrated. These materials were developed as candidate replacements for the present needled felt SIP used between the ceramic tiles and the aluminum skin on the undersurface of the Orbiter. The SIP materials that were developed consisted of high temperature aramid fibers deposited by controlled fluid (air or liquid) carriers to form low density unbonded felts. The deposited felts were then bonded at the fiber intersections with a small amount of high temperature polyimide resin. This type of bonded felt construction can potentially eliminate two of the problems associated with the present SIP, viz., transmittal of localized stresses into the tiles and load history dependent mechanical response. However, further work is needed to achieve adequate through thickness tensile strength in the bonded felts.

Seibold, R. W.↗

NASA NTRS2004

Thermal Performance of a Multi-Evaporator Loop Heat Pipe with Thermal Masses and Thermoelectric Coolers

This paper describes thermal performance of a loop heat pipe (LHP) with two evaporators and two condensers in ambient testing. Each evaporator has an outer diameter of 15mm and a length of 76mm, and has an integral compensation chamber (CC). An aluminum mass of 500 grams is attached to each evaporator to simulate the instrument mass. A thermoelectric cooler (TEC) is installed on each CC to provide heating as well as cooling for CC temperature control. A flow regulator is installed in the condenser section to prevent vapor from going back to the evaporators in the event that one of the condensers is fully utilized. Ammonia was used as the working fluid. Tests conducted included start-up, power cycle, heat load sharing, sink temperature cycle, operating temperature control with TECs, and capillary limit tests. Experimental data showed that the loop could start with a heat load of less than 10W even with added thermal masses. The loop operated stably with even and uneven evaporator heat loads, and even and uneven condenser sink temperatures. The operating temperature could be controlled within +/- 0.5K of the set point temperature using either or both TECs, and the required TEC control heater power was less than 2W under most test conditions. Heat load sharing between the two evaporators was also successfully demonstrated. The loop had a heat transport capability of 120W to 140W, and could recover from a dry-out when the heat load was reduced. The 500-gram aluminum mass on each evaporator had a negligible effect on the loop operation. Existing LHPs servicing orbiting spacecraft have a single evaporator with an outer diameter of about 25mm. Important performance characteristics demonstrated by this LHP included: 1) Operation of an LHP with 15mm diameter evaporators; 2) Robustness and reliability of an LHP with multiple evaporators and multiple condensers under various test conditions; 3) Heat load sharing among LHP evaporators; 4) Effectiveness of TECs in controlling the LHP operating temperature; and 5 ) Effectiveness of the flow regulator in preventing vapor from going back the evaporators.

Ku, Jen-Tung↗

NASA NTRS2004

Thermal performance of a multi-evaporator loop heat pipe with thermal masses and thermal electrical coolers

This paper describes thermal performance of a loop heat pipe (LHP) with two evaporators and two condensers in ambient testing. Each evaporator has an outer diameter of 15mm and a length of 76mm, and has an integral compensation chamber (CC). An aluminum mass of 500 grams is attached to each evaporator to simulate the instrument mass. A thermal electric cooler (TEC) is installed on each CC to provide heating as well as cooling for CC temperature control. A flow regulator is installed in the condenser section to prevent vapor from going back to the evaporators in the event that one of condenser is fully utilized. Ammonia was used ad the working fluid. Tests conducted included start-up, power cycle, heat load sharing, sink temperature cycle, operating temperature control with TECs, and capillary limit tests. Experimental data showed that the loop could start with a heat load of less than 1OW even with added thermal masses. The loop operated stably with even and uneven evaporator heat loads, and even and uneven condenser sink temperatures. The operating temperature could be controlled within +/-0.5K of the set point temperature using either or both TECs, and the required TEC control heater power was less than 2W under most test conditions. Heat load sharing between the two evaporators was also successfully demonstrated. The loop had a heat transport capability of 120W to 140W, and could recover from a dry-out when the heat load was reduced. The 500-gram aluminum mass on each evaporator had a negligible effect on the loop operation. Existing LHPs servicing the orbiting spacecraft have a single evaporator with an outer diameter of about 25mm. Important performance characteristics demonstrated by this LHP included: 1) Operation of an LHP with 15mm diameter evaporators; 2) Robustness and reliability of an LHP with multiple evaporators and multiple condensers under various test conditions; 3) Heat load sharing among LHP evaporators; 4) Effectiveness of TECs in controlling the LHP operating temperature; and 5) Effectiveness of the flow regulator in preventing vapor from going back the evaporators.

loop heat pipes↗

NASA NTRS2011

Analysis of Exhaust Plume Effects on Sonic Boom for a 59-Degree Wing Body Model

Reducing or eliminating the operational restrictions of supersonic aircraft over populated areas has led to extensive research at NASA. Restrictions are due to the disturbance of the sonic boom, caused by the coalescence of shock waves formed off the aircraft. Recent work has been performed to reduce the magnitude of the sonic boom N-wave generated by airplane components with focus on shock waves caused by the exhaust nozzle plume. Previous Computational Fluid Dynamics (CFD) analyses showed how the shock wave formed at the nozzle lip interacted with the nozzle boat-tail expansion wave. The nozzle lip shock moved with increasing nozzle pressure ratio (NPR) and reduced the nozzle boat-tail expansion. Lip shock movement caused a favorable change in the observed pressure signature. These results were applied to a simplified supersonic vehicle geometry with no inlets and no tail, in which the goal was to demonstrate how under-expanded nozzle operation reduced the sonic boom signature by twelve percent. A secondary goal was to demonstrate the use of the Cart3D inviscid code for off-body pressure signatures including the nozzle plume effect.

Castner, Raymond S.↗

NASA NTRS2011

A Generalized Framework for Constrained Design Optimization of General Supersonic Configurations Using Adjoint Based Sensitivity Derivatives

The Aeronautics Research Mission Directorate (ARMD) sent out an NASA Research Announcement (NRA) for proposals soliciting research and technical development. The proposed research program was aimed at addressing the desired milestones and outcomes of ROA (ROA-2006) Subtopic A.4.1.1 Advanced Computational Methods. The second milestone, SUP.1.06.02 Robust, validated mesh adaptation and error quantification for near field Computational Fluid Dynamics (CFD), was addressed by the proposed research. Additional research utilizing the direct links to geometry through a CAD interface enabled by this work will allow for geometric constraints to be applied and address the final milestone, SUP2.07.06 Constrained low-drag supersonic aerodynamic design capability. The original product of the proposed research program was an integrated system of tools that can be used for the mesh mechanics required for rapid high fidelity analysis and for design of supersonic cruise vehicles. These Euler and Navier-Stokes volume grid manipulation tools were proposed to efficiently use parallel processing. The mesh adaptation provides a systematic approach for achieving demonstrated levels of accuracy in the solutions. NASA chose to fund only the mesh generation/adaptation portion of the proposal. So this report describes the completion of the proposed tasks for mesh creation, manipulation and adaptation as it pertains to sonic boom prediction of supersonic configurations.

Karman, Steve L., Jr.↗

NASA NTRS2019

Investigation of Transient Gas Phase Column Density Due to Droplet Evaporation

A NASA robotic refueling mission experiment on board the International Space Station (ISS) was designed to repeatedly transfer simulated cryogenic propellant between two dewars. After each metered transfer, the cryogen was to be vented overboard via sublimation or evaporation. ISS payload providers must conduct analyses to demonstrate that any planned gaseous venting generate no more than a certain level of material that may interfere with optical measurements from other payloads that may be located nearby. This requirement is expressed in terms of a maximum column number density (CND). For the experiment under consideration, fluid droplets likely would accompany any such vapor. Earlier related studies led to development of analytical expressions for column density along general paths for a number of practical cases under steady conditions, including droplet evaporation. These expressions are not appropriate for rapid evaporation of small droplets however, since the droplets cannot sustain mass flow rates consistent with steady conditions. In this work, analytical expressions are developed for estimating column density near a rapidly evaporating droplet along general paths. The influence for instantaneous evaporation is created first as a limiting case, where it is found the peak value occurs at the time it takes a wave of vapor to reach the closest point along the optical path traveling at its most probable thermal speed. Next, the case for finite-period evaporation is evaluated for constant conditions. Compared to the instantaneous case, peak column density occurs shortly after droplet extinction, but at a lower intensity. A new mathematical function is discovered that solves the integrals associated with this case. Finally, ways to account for droplet motion and changes in evaporation rate with size and temperature are discussed in this framework.

Woronowicz, M. S.↗

DOE OSTI2022

Data-driven modeling of coarse mesh turbulence for reactor transient analysis using convolutional recurrent neural networks

Advanced nuclear reactors often exhibit complex thermal-fluid phenomena during transients. To accurately capture such phenomena, a coarse-mesh three-dimensional (3-D) modeling capability is desired for modern nuclear-system code. In the coarse-mesh 3-D modeling of advanced-reactor transients that involve flow and heat transfer, accurately predicting the turbulent viscosity is a challenging task that requires an accurate and computationally efficient model to capture the unresolved fine-scale turbulence. In this work, we propose a data-driven coarse-mesh turbulence model based on local flow features for the transient analysis of thermal mixing and stratification in a sodium-cooled fast reactor. The model has a coarse mesh setup to ensure computational efficiency, while it is trained by fine-mesh computational fluid dynamics (CFD) data to ensure accuracy. A novel neural network architecture, combining a densely connected convolutional network and a long-short-term-memory network, is developed that can efficiently learn from the spatial temporal CFD transient simulation results. The neural network model was trained and optimized on a loss-of flow transient and demonstrated high accuracy in predicting the turbulent viscosity field during the whole transient. The trained model's generalization capability was also investigated on two other transients with different inlet conditions. The study demonstrates the potential of applying the proposed data-driven approach to support the coarse-mesh multi-dimensional modeling of advanced reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS1998

Mir Glovebox Facility

The Glovebox Facility on Mir was developed by the Marshall Space Flight Center for use on the space shuttle middeck and modified slightly for use on the Mir Space Station. Its design is based on a similar facility provided by the European Space Agency for use on Spacelab and flown on the USML-I and 2 missions. Its purpose is to provide a work space for experiments which is isolated from the manned environment while allowing a high degree of access to the experiment apparatus. It also provides experiment power, lighting, and data acquisition. This facility has successfully supported 7 experiments representing the fluid physics and combustion disciplines during NASA increments 2 - 5. During over 400 hours of operation, only 3 minor facility anomalies were encountered, none of which prevented science operations or resulted in hazardous conditions. No in-flight maintenance has been required through increment 5. Crew comments have been generally favorable, stressing the usefulness, reliability and ease of use of the facility. The success of the glovebox to date demonstrates the value of this type of multi-use facility in a space station environment.

Kroes, Roger L.↗

NASA NTRS2014

Advances in Spacecraft Brine Water Recovery: Development of a Radial Vaned Capillary Drying Tray

Technology improvements in the recovery of water from brine are critical to establishing closed-loop water recovery systems, enabling long-duration missions, and achieving a sustained human presence in space. A genre of 'in-place drying' brine water recovery concepts, collectively referred to herein as Brine Residual In-Containment, are under development. These brine water recovery concepts aim to increase the overall robustness and reliability of the brine recovery process by performing drying inside the container used for final disposal of the solid residual waste. Implementation of in-place drying techniques have been demonstrated for applications where gravity is present and phase separation occurs naturally by buoyancy-induced effects. In this work, a microgravity-compatible analogue of the gravity-driven phase separation process is considered by exploiting capillarity in the form of surface wetting, surface tension, and container geometry. The proposed design consists of a series of planar radial vanes aligned about a central slotted core. Preliminary testing of the fundamental geometry in a reduced gravity environment has shown the device to spontaneously fill and saturate rapidly, thereby creating a free surface from which evaporation and phase separation can occur similar to a terrestrial-like 'cylindrical pool' of fluid. Mathematical modeling and analysis of the design suggest predictable rates of filling and stability of fluid containment as a function of relevant system dimensions; e.g., number of vanes, vane length, width, and thickness. A description of the proposed capillary design solution is presented along with preliminary results from testing, modeling, and analysis of the system.

Callahan, Michael R.↗

DOE OSTI2020

Hybrid nanocapsules for in situ TEM imaging of gas evolution reactions in confined liquids

Liquid cell transmission electron microscopy (TEM) enables the direct observation of dynamic physical and chemical processes in liquids at the nanoscale. Quantitative investigations into reactions with fast kinetics and/or multiple reagents will benefit from further advances in liquid cell design that facilitate rapid in situ mixing and precise control over reagent volumes and concentrations. This work reports the development of inorganic–organic nanocapsules for high-resolution TEM imaging of nanoscale reactions in liquids with well-defined zeptoliter volumes. These hybrid nanocapsules, with 48 nm average diameter, consist of a thin layer of gold coating a lipid vesicle. As a model reaction, the nucleation, growth, and diffusion of nanobubbles generated by the radiolysis of water is investigated inside the nanocapsules. When the nanobubbles are sufficiently small (10–25 nm diameter), they are mobile in the nanocapsules, but their movement deviates from Brownian motion, which may result from geometric confinement by the nanocapsules. Gases and fluids can be transported between two nanocapsules when they fuse, demonstrating in situ mixing without using complex microfluidic schemes. The ability to synthesize nanocapsules with controlled sizes and to monitor dynamics simultaneously inside multiple nanocapsules provides opportunities to investigate nanoscale processes such as single nanoparticle synthesis in confined volumes and biological processes such as biomineralization and membrane dynamics.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A Novel Approach for Bounding the Stress Experienced by the Core of Utility-Scale Printed Circuit Heat Exchangers Under Thermohydraulic Loads

Printed circuit heat exchangers (PCHEs) have rapidly gained popularity since being introduced nearly three decades ago, and they are currently widely deployed in the petrochemical and aviation industry. Their compactness, thermohydraulic efficiency, inherent suitability for high temperature/pressure fluids containment, and demonstrated durability are some of the reasons the nuclear industry is seeking to adopt this technology as well. However, the relatively strict nuclear-related regulatory design code, especially when classified as critical to the safety of the reactors, is posing challenges to adopting the technology. From stress analysis point of view, one undesirable feature of PCHEs is their geometrical complexity, which is implied by their multilength-scale features. As a result, a full-scale model of a utility-scale exchanger cannot simply be solved on a computer because meshing such components results in a vast number of degrees-of-freedom. Here, this work seeks to address the challenge of stress analyses to PCHEs by presenting a method to simplify the geometry of PCHE designs. The models proposed by this work can be practically analyzed on a standard computer and provide a path for implementing ASME design rules. The analyses presented herein are divided into five separate investigations. Each is carried out to incrementally simplify the analyzed model by addressing features such as the shapes of the flow passages, the complex distribution of stress in large components, the three-dimensionality of the stress and strain, the thermal stresses caused by thermohydraulic operation observed experimentally and more.

42 ENGINEERING↗

DOE OSTI2021

NRAP-Open-IAM: Open Wellbore Component (V.2.0)

The Open Wellbore component of NRAP-Open-IAM is applicable to the calculation of Area of Review at a carbon storage site and fast estimation of dense gas dispersion from multiple continuous CO 2 surface leakage sources for risk assessment. The Open Wellbore Component of NRAP-Open-IAM is a lookup table model based on the drift-flux approach. The National Research Assessment Partnership’s second-generation integrated assessment model, NRAP-Open-IAM, is open-source software written in Python for use in performance and quantitative risk assessment of geologic carbon storage (GCS) systems. The look-up table for open well leakage is an updated version the previous model which provides finer resolution of reservoir depth and more accurate fluid properties than the previous open well look-up table, especially in calculating the gas (CO 2 -rich) phase properties. The component model input parameters include the reservoir transmissivity, aquifer transmissivity, brine salinity, well radius, and well top and bottom depths. The reservoir transmissivity and brine salinity were set to values consistent with the reservoir component, and the well top and bottom depths varied with location. The possible outputs from the Open Wellbore component are leakage rates of CO 2 and brine to either an aquifer or atmosphere, depending on the depth of the well top. Several python test scripts are presented that demonstrate that the Open Wellbore component works correctly. Use of the open wellbore model in NRAP-Open-IAM may result in a large CO 2 leakage rates, comparable to the leakage rates of CO 2 blow out.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

CFD Benchmark of Pressure Drop in a 61-Pin Wire-Wrapped Assembly with Blocked Channels Using NekRS

Thermal hydraulic behaviors of wire-wrapped rod bundles continue to be a subject of intense research. One of the leading next-generation designs, the sodium fast reactor, relies on a hexagonal assembly of wire-wrapped fuel pins. The issue of potential channel blockage has been raised as a safety concern due to the tightly packed arrangement of the fuel pins. This has led to several recent experimental and computational studies working to quantify the potential impact on the fluid flow and heat transfer behaviors of such blockages. The objective of the present study is to benchmark the high-fidelity NekRS CFD solver in predicting pressure drop for large blockages against available experimental data. A 61-pin wire-wrapped fuel assembly with two flow blockage configurations has been simulated and investigated at various low to moderate Reynolds numbers. The NekRS solver has been shown to yield exponentially decreasing spatial discretization errors with increasing polynomial order. All simulated results agreed well with measured data, which indicates that the overall methodology is adequate and consistent. The results of this benchmark study demonstrate the accuracy of NekRS for sodium fast reactor hydrodynamic simulations, increasing the confidence in its use for design, licensing, and analysis activities.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2020

Evaluation of a Robust, In-Situ Surface Treatment for Pipeline Solids Deposition Mitigation in Flowing Systems

Abstract The formation/precipitation and deposition of pipeline solids, such as gas hydrates, asphaltenes, and waxes have long plagued production fields. Given the vast differences in chemistries of these solids, any current prevention or mitigation strategy, particularly for cases where multiple issues are a concern, is likely to involve an extensive assortment of undefined chemical additives that are both costly and add complexity to the system. Surface treatments (coatings), on the other hand, present a relatively new viable option for management strategies. A chemically and physically robust surface treatment with the ability to address deposition issues for multiple pipeline solids could not only decrease the operating expenditures for a field through material cost savings and obviation of downstream separation, but could also simplify produced fluids by eliminating additional chemicals from the mixture. The purpose of this study is to explore the feasibility of a particular surface treatment as part of a solids management strategy. This work utilizes an omniphobic surface treatment to probe its effects on gas hydrate, asphaltene, and wax deposition. Specifically, high pressure rocking cells are employed to study gas hydrate nucleation and deposition. A bench-scale flowloop filled with crude oil and heptane is used to quantify the deposition of crude oil and asphaltenes after a set time period. Lastly, a mechanical shear device measures the adhesion force of wax deposits on untreated/treated surfaces. The gas hydrate rocking cell tests demonstrate an increase in induction time and occasional elimination of hydrate nucleation with the surface treatment. Moreover, the same apparatus indicates that the critical shear to avoid hydrate deposition may be lowered in the presence of the surface treatment compared to untreated pristine carbon steel coupons. A custom-built asphaltene flowloop then establishes that this surface treatment is effective in dramatically reducing the deposition of the aliphatic components of a crude oil, with a moderate reduction in the asphaltene fraction. Finally, mechanical adhesion force measurements for solidified paraffin wax display trends in agreement with the asphaltene results. The surface treatment on both pristine and corroded surfaces is able to reduce the adhesion of wax deposits to values below a pristine, untreated surface.

03 NATURAL GAS↗

NASA NTRS1996

Aerodynamic Influence Coefficient Computations Using Euler/Navier-Stokes Equations on Parallel Computers

Modem design requirements for an aircraft push current technologies used in the design process to their limit or sometimes require more advanced technologies to meet the requirement. New design requirements always demand to improve the operational performance. Accurate prediction of aerodynamic coefficients is essential to improve the performance. For example, in the design of an advanced subsonic civil transport, since the fluid flow at transonic regime shows strong nonlinearities, high fidelity equations, such as the Euler or Navier-Stokes equations predict flow characteristics more accurately than the linear aerodynamics, which are widely used in the current design process However, high fidelity flow equations are computationally expensive and require an order of magnitude longer time to obtain aerodynamic coefficients required in the design. Parallel computing is one possibility to cut down the computational turn-around time in using high fidelity equations so that high fidelity equations would be incorporated into the design process. By doing so, high fidelity equations would be used in the routine design process. This work will demonstrate the feasibility of using high fidelity flow equations in a design process by computing aerodynamic influence coefficients of a wing-body-empennage configuration on a multiple-instruction, multiple-data parallel computer.

Byun, Chansup↗

DOE OSTI2024

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Theory of capillary tension and interfacial dynamics of motility-induced phases

The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the past decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces arbitrarily far from equilibrium. In this work, beginning from microscopic particle dynamics that break time-reversal symmetry, we derive the linear interfacial dynamics of coexisting motility-induced phases. Doing so allows us to identify the athermal energy scale that excites interfacial fluctuations and the nonequilibrium surface tension that resists these excitations. Our theory identifies that, in contrast to equilibrium fluids, this active surface tension contains contributions arising from nonconservative forces which act to suppress interfacial fluctuations and, crucially, is distinct from the mechanical surface tension of Kirkwood and Buff. Here we find that the interfacial stiffness scales linearly with the intrinsic persistence length of the constituent active particle trajectories, in agreement with simulation data. We demonstrate that at wavelengths much larger than the persistence length, the interface obeys surface-area minimizing Boltzmann statistics with our derived nonequilibrium interfacial stiffness playing a role identical to that of equilibrium systems.

36 MATERIALS SCIENCE↗

NASA NTRS1995

On the spatial distribution of magnetic fields on the solar surface

Recent measurements of solar surface magnetic fields suggest that the spatial distribution of these fields is fractal. In order to understand the physical basis for such geometric complexity, we study here the advection of magnetic flux tubes relatively simple random motions on the surface of a fluid and investigate the spatial statistics of the resulting surface field. While this study does not directly address the question of why solar surface fields have the observed spatial structure, it is designed to build our intuition about how surface flows lead to complex spatial structuring of magnetic fields. As part of our study, we discuss the various methods by which one can describe the spatial distribution of the surface magnetic flux and relate them mathematically; this turns out to be a crucial point of our work since, as we show, a number of previous analyses have misinterpreted the analysis procedures for determining fractal dimensions. Our principal result is the explicit demonstration that simple random flows lead to magnetic flux spatial distributions with a multifractal dimension spectrum. Furthermore, we demonstrate that this magnetic spatial structure is generic, i.e., is characteristic of a very large class of random flows.

Tao, L.↗