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DOE OSTI2019

Validation of RELAP-7 for Forced Convective and Natural Circulation Reactor Flows

New reactor designs such as small modular reactors and newly proposed passive safety systems rely on natural circulation two-phase flow cooling of the reactor core under accident conditions. Without a pump to drive the flow, the circulation rate is a strong function of void fraction. Under these conditions where the flow rate, pressure drop, and heat transfer are all closely coupled through the mixture density, the accurate prediction of void fraction is pivotal. Furthermore, while these passive systems boast a more reliable cooling option, the sensitivity of the system to two-phase flow instabilities is more likely than in forced convective cooling and can result in dangerous density wave or flow excursion conditions. Improvement of one-dimensional system codes and further development of three-dimensional code capability are all important efforts in addressing these issues. The proposed work is a critical step towards providing confidence through validation of the capability of thermal-hydraulic tools to meet the emerging challenges in reactor simulation. Historically, system analysis codes develop a stiffness over time due to fine-tuning of adjustable code parameters that result in a reluctance or inability to adopt improved models. Therefore, a rigorous effort should be invested in preparation for RELAP-7 to identify required modeling improvements of constitutive relations and validation of the code applicability to the wide range of possible reactor flow conditions. Part of this validation involves the uncertainty quantification which is a critical step in the Code Scaling, Applicability, and Uncertainty (CSAU) methodology and Best-Estimate Plus Uncertainty (BEPU) licensing method. BEPU allows recovery of safety margins and potentially optimizing plant performance, resulting in economic benefit for the reactor operators. Beginning with the collection of past experimental data covering prototypic LWR conditions, this document reviews three critical datasets available for the validation of system codes. The experimental methods, procedures, facilities, instrumentation, and supplementary information are consolidated to aid the validation efforts of this work and future projects. These three datasets (824 conditions) are chosen due to their wide acceptance and demonstrated application for code validation. Two experimental datasets from the Nuclear Power Engineering Corporation (NUPEC) span prototypic conditions of Boiling Water Reactors (BWR) and Pressurized Water Reactors (PWR). These datasets are labeled as the BFBT (BWR Full-size Fine-mesh Bundle Test) and the PSBT (PWR Subchannel and Bundle Test) datasets respectively. The third dataset is taken in an internally heated annulus that is scaled based on a BWR subassembly and includes two-phase flows important to post-blowdown analysis. Together, the datasets consider the full range of pressure and mass flux expected in LWR forced convective flows from steady-state to long term cooling conditions. Recognizing the deficiency of available data under low-pressure, low-flow, a new natural circulation dataset consisting of 107 conditions is obtained. With system pressures ranging between 145 and 950 kPa, natural circulation is driven by a heat flux up to 275 kW/m2 in a 3 m long heated region of the annulus test section which is followed by a 2 m long unheated region before entering a condenser. Stable natural circulation flow rates in this facility were measured to be between 182 and 590 kg/m2-s. Pressure and temperature are measured at ten locations in the facility. In addition, measurements of void fraction, interfacial area concentration, and gas velocity are obtained at five axial locations in the annulus test section. The RELAP5-3D code demonstrates good accuracy for void fraction predictions in BFBT and PSBT benchmarks, but shows relatively large discrepancy in the annulus experiments at lower pressures. In two-phase natural circulation, large oscillations are observed in many system parameters during the simulation of 19 experiment cases which were conducted at low pressures, and the model shows good predictive performance with the remaining 88 experiment cases. However, some discrepancies in void fraction and temperature predictions are found which may require improved constitutive modeling under these low-pressure, low-flow condition. The quantified uncertainty in void fraction predictions in three forced convection benchmarks due to uncertainties in boundary conditions and geometries are relatively small, except for a few cases in the annulus experiment. The output uncertainty of the natural circulation model is quantified by considering the measurement error in boundary conditions, and it is shown that the output uncertainty ranges are relatively small for the range of conditions considered. Through this work, a clear pathway is provided for validation of RELAP7 once the code is available.

42 ENGINEERING↗

DOE OSTI2020

Hydrodynamic instabilities and heat transfer characteristics in the duct flow of a fluid in the supercritical thermodynamic regime

The behavior of fluids at supercritical thermodynamic conditions is inherently complex due to large variations in thermodynamic and transport properties. Recent numerical and experimental investigations illustrate ongoing interest for these fluids, especially supercritical CO 2 and supercritical water, for a variety of applications. For example, supercritical water reactors (SCWR) operate in this extreme condition of high-pressure and temperature, resulting in highly dynamic flow fields and unexpected heat transfer regimes. The potential heat transfer benefits in this regime are directly associated with the extreme variations in thermodynamic and transport properties, which occur at, and above, the critical point. This work characterizes the hydrodynamic instabilities that arise for fluids at supercritical thermodynamic conditions when buoyancy forces are significant. Two specific configurations are considered, a natural convection cavity flow, and a mixed convection, heated, horizontal channel flow. Natural convection flow in a cavity is a classical configuration with expected behavior below the critical point. This configuration aids in characterizing the effect of the variable properties in the supercritical thermodynamic regime. Further, limited studies in the existing literature have been conducted for low-Reynolds and intermediate-Rayleigh numbers, mixed-convection channel flows for supercritical water, which is the focus of the channel flow configuration. To investigate the thermally driven hydrodynamic instabilities in this regime, a high-order fully-implicit numerical method is used. Such strong variations in thermophysical properties (in particular, density) are difficult to simulate and an altogether compressible framework is needed. Therefore, the compressible Navier-Stokes equations are solved without any additional assumptions. The fully implicit, high-order in space and time, reconstructed discontinuous Galerkin method as implemented within the multi-physics code called ALE3D (Arbitrary Lagrangian and Eulerian in 2D and 3D), developed at Lawrence Livermore National Laboratory (LLNL), is used. This fully implicit, L-stable method accurately captures the compressible nature of the ow in the limit of very low Mach number. It has been widely accepted that above the critical point, only one phase is observed. However, recent research has indicated the existence of the distinct gas-like and liquid-like regions separated by the Widom line, the locus of the maxima of the specific heat. Along the Widom line, density decreases 6-fold, viscosity drops by a factor of 2, while specific heat spikes by an order of magnitude. These variations, specifically in density and viscosity, produce a thick pseudo-interface and flow dynamics behavior akin to film boiling. A pseudo-film at the heated wall of the cavity and the horizontal channel is observed where buoyancy forces induce mixing through the specific configurations. Further the local Rayleigh and Richardson numbers provide maps of the flow field and the buoyancy forces driving the microscopic mixing. In the first chapter, I describe a background of supercritical fluid and the various applications. The second chapter focuses on the mathematical model and numerical method used for simulations, where a description of the equation of state for supercritical water is described. The third chapter focuses on the natural convection cavity with a heated bottom wall. In this cavity a gas-like and a liquid-like flow within the supercritical thermodynamic regime are observed. The fourth chapter focuses on a forced convection, horizontal channel, distinguishing between the gas-like, liquid-like, and mixed flow regimes. Mixed convection flow, with the addition of gravitational forces in the horizontal channel show the influence of variable properties on the hydrodynamic development, heat transfer, and rising instabilities. The last chapter of this research focuses on characterizing the unstable hydrodynamics through time-averaging processes and analysis of the movement of energy through the developing plumes.

42 ENGINEERING↗

DOE OSTI2026

Oil Filled Flow Shield Performance Evaluation

When hydrophones are used to monitor underwater sound in areas with currents, like rivers or tidal channels, flow noise caused by turbulent flow past a hydrophone can mask low frequency acoustic signals of interest. Flow shields can reduce the impacts of flow noise on hydrophone data. A prior study conducted by PNNL compared three flow shield designs and determined that an oil-filled urethane shield performed better than other designs and was likely sufficiently robust for long-duration marine deployments. However, that study did not assess the high frequency performance of the oil-filled flow shield or conduct long-duration field testing. Further, the prototype flow shield was difficult to assemble. This report details the results of design refinement and testing to address these gaps. Design refinements resulted in a straightforward and repeatable assembly method. Field testing indicated that the flow shields reduce flow noise by over 20 dB below 50 Hz at flow speeds greater than 0.5 m/s and are proven to survive deployments more than 6 months long. Calibration of the same hydrophone with and without a flow shield installed indicated that the shields attenuate propagating sound by no more than 2 dB at frequencies below 30 kHz.

42 ENGINEERING↗

DOE OSTI2016

UV DRIVEN EVAPORATION OF CLOSE-IN PLANETS: ENERGY-LIMITED, RECOMBINATION-LIMITED, AND PHOTON-LIMITED FLOWS

We have investigated the evaporation of close-in exoplanets irradiated by ionizing photons. We find that the properties of the flow are controlled by the ratio of the recombination time to the flow timescale. When the recombination timescale is short compared to the flow timescale, the flow is in approximate local ionization equilibrium with a thin ionization front where the photon mean free path is short compared to the flow scale. In this “recombination-limited” flow the mass-loss scales roughly with the square root of the incident flux. When the recombination time is long compared to the flow timescale the ionization front becomes thick and encompasses the entire flow with the mass-loss rate scaling linearly with flux. If the planet's potential is deep, then the flow is approximately “energy-limited”; however, if the planet's potential is shallow, then we identify a new limiting mass-loss regime, which we term “photon-limited.” In this scenario, the mass-loss rate is purely limited by the incoming flux of ionizing photons. We have developed a new numerical approach that takes into account the frequency dependence of the incoming ionizing spectrum and performed a large suite of 1D simulations to characterize UV driven mass-loss around low-mass planets. We find that the flow is “recombination-limited” at high fluxes but becomes “energy-limited” at low fluxes; however, the transition is broad occurring over several orders of magnitude in flux. Finally, we point out that the transitions between the different flow types do not occur at a single flux value but depend on the planet's properties, with higher-mass planets becoming “energy-limited” at lower fluxes.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1976

A theoretical study of the acoustic impedance of orifices in the presence of a steady grazing flow

An analysis of the oscillatory fluid flow in the vicinity of a circular orifice with a steady grazing flow is presented. The study is similar to that of Hersh and Rogers but with the addition of the grazing flow. Starting from the momentum and continuity equations, a considerably simplified system of partial differential equations is developed with the assumption that the flow can be described by an oscillatory motion superimposed upon the known steady flow. The equations are seen to be linear in the region where the grazing flow effects are dominant, and a solution and the resulting orifice impedance are presented for this region. The nonlinearity appears to be unimportant for the usual conditions found in aircraft noise suppressors. Some preliminary conclusions of the study are that orifice resistance is directly proportional to grazing flow velocity (known previously from experimental data) and that the orifice inductive (mass reactance) end correction is not a function of grazing flow. This latter conclusion is contrary to the widely held notion that grazing flow removes the effect of the orifice inductive end correction. This conclusion also implies that the experimentally observed total inductance reduction with grazing flow might be in the flow within the orifice rather than in the end correction.

Rice, E. J.↗

NASA NTRS1976

Orifice resistance for ejection into a grazing flow

To explain the decrease in orifice resistance with the addition of grazing flow, the flow from an orifice was modeled by using an inviscid analysis which is valid when the orifice flow total pressure is nearly the same as the free stream grazing flow total pressure. For steady outflow from an orifice into a grazing flow, the orifice flow can enter the main grazing flow in an inviscid manner without generating large eddies to dissipate the kinetic energy of the jet. From the analysis, a simple closed-form solution was developed for the steady resistance for ejection from an orifice into a grazing-flow field. The calculated resistance compare favorably with data for a flow regime where the total pressure difference between the grazing flow and the orifice flow is small.

Baumeister, K. J.↗

NASA NTRS1984

Nonlinear aerodynamic effects on bodies in supersonic flow

The supersonic flow about generic bodies was analyzed to identify the elments of the nonlinear flow and to determine the influence of geometry and flow conditions on the magnitude of these nonlinearities. The nonlinear effects were attributed to separated-flow nonlinearities and attached-flow nonlinearities. The nonlinear attached-flow contribution was further broken down into large-disturbance effects and entropy effects. Conical, attached-flow bundaries were developed to illustrate the flow regimes where the nonlinear effects are significant, and the use of these boundaries for angle of attack and three-dimensional geometries was indicated. Normal-force and pressure comparisons showed that the large-disturbance and separated-flow effects were the dominant nonlinear effects at low supersonic Mach numbers and that the entropy effects were dominant for high supersonic Mach number flow. The magnitude of all the nonlinear effects increased with increasing angle of attack. A full-potential method, NCOREL, which includes an approximate entropy correction, was shown to provide accurate attached-flow pressure estimates from Mach 1.6 through 4.6.

Pittman, J. L.↗

NASA NTRS1985

Flow control in a diffusing S-Duct

Accurate measurements have been made of secondary flow in a 1.51 area ratio diffusing 30 deg - 30 deg S-Duct with circulair cross section. Turbulent flow was entering the duct at Mach number of 0.6, the boundary layer thickness at the duct entrance was ten percent of the duct inlet diameter. Through measurements made, local flow velocity vector as well as static and total pressures mapping of the flow at several stations were obtained. Strong secondary flow was measured in the first bend which continued into the second bend with new vorticity produced in there in the opposite direction. Surface oil flow visualization and wall pressures indicated a region of separated flow starting at theta approximately equal to 22 deg on the inside of the first bend up to theta approximately equal to 44 deg on the outside of the second bend. The flow separated in 'cyclone' form and never reattached in the duct. As a result of the secondary flow and the flow separation, significant total pressure distortion was observed at the exit of the duct. Using flow control devices the separation was eliminated while the exit distortion was improved.

Vakili, A. D.↗

NASA NTRS1986

Plume characteristics of single-stream and dual-flow conventional and inverted-profile nozzles at equal thrust

The plume velocity and temperature decay rates of single-stream, conventional dual-flow and inverted-profile dual-flow nozzles are compared at equal values of ideal thrust over a wide range of flow conditions. The comparisons are made in terms of constant velocity and temperature contour maps. The results show that both dual-flow nozzle types have much greater plume velocity and temperature decay rates than those of equivalent thrust single-stream nozzles when the respective secondary flows were at ambient temperature. With hot secondary flows, the inverted-profile dual-flow plumes decayed significantly faster than those of single-stream nozzles; however, the decay rates for the conventional dual-flow streams were about the same as those for the single-stream nozzles. Consequently, with hot secondary flows, the inverted-profile dual-flow plumes decayed much faster than the conventional dual-flow plumes at equal thrust.

Vonglahn, U. H.↗

NASA NTRS1986

Plume characteristics of single-stream and dual-flow conventional and inverted-profile nozzles at equal thrust

Von Glahn, U. H.↗

NASA NTRS1991

Crystallization during emplacement of lava flows

Thermal models of lava flows provide a way of estimating emplacement durations and eruption rates of planetary lava flows, which can help constrain magma ascent, rheology and composition. Most of the models that have been developed consider only the effects of cooling by radiation. However, heating due to crystallization can be a large component of the overall heat budget of a flow. Little is known about the amount of crystallization and latent heating during flow advance. Crystal size distribution (CSD) measurements were made to quantify and study the effects of crystallization in the 1984 Mauna Loa flow. For flows on Mars, we must assume that the amount of crystallization is similar to that in terrestrial flows and place minimum and maximum bounds on the latent heat effect. Unfortunately, as examples given here show, there can be anywhere from 0 to 60 percent crystallization during flow advance. To improve constraints for Martian flows, we need to search for correlations in terrestrial flows between flow morphology and the amount of crystallization during emplacement.

Crisp, J.↗

NASA NTRS1990

Numerical simulation of fluid flow and heat transfer in a thin liquid film over a stationary and rotating disk and comparison with experimental data

In the first section, improvements in the theoretical model and computational procedure for the prediction of film height and heat-transfer coefficient of the free surface flow of a radially-spreading thin liquid film adjacent to a flat horizontal surface of finite extent are presented. Flows in the presence and absence of gravity are considered. Theoretical results are compared to available experimental data with good agreement. In the presence of gravity, a hydraulic jump is present, isolating the flow into two regimes: supercritical upstream from the jump and subcritical downstream of it. In this situation, the effects of surface tension are important near the outer edge of the disk where the fluid experiences a free fall. A region of flow separation is present just downstream of the jump. In the absence of gravity, no hydraulic jump or separated flow region is present. The variation of the heat-transfer coefficient for flows in the presence and absence of gravity are also presented. In the second section, the results of a numerical simulation of the flow field and associated heat transfer coefficients are presented for the free surface flow of a thin liquid film adjacent to a horizontal rotating disk. The computation was performed for different flow rates and rotational velocities using a 3-D boundary-fitted coordinate system. Since the geometry of the free surface is unknown and dependent on flow rate, rate of rotation, and other parameters, an iterative procedure had to be used to ascertain its location. The computed film height agreed well with existing experimental measurements. The flow is found to be dominated by inertia near the entrance and close to the free surface and dominated by centrifugal force at larger radii and adjacent to the disk. The rotation enhances the heat transfer coefficient by a significant amount.

Faghri, Amir↗

NASA NTRS1992

In-flight flow visualization results from the X-29A aircraft at high angles of attack

Flow visualization techniques were used on the X-29A aircraft at high angles of attack to study the vortical flow off the forebody and the surface flow on the wing and tail. The forebody vortex system was studied because asymmetries in the vortex system were suspected of inducing uncommanded yawing moments at zero sideslip. Smoke enabled visualization of the vortex system and correlation of its orientation with flight yawing moment data. Good agreement was found between vortex system asymmetries and the occurrence of yawing moments. Surface flow on the forward-swept wing of the X-29A was studied using tufts and flow cones. As angle of attack increased, separated flow initiated at the root and spread outboard encompassing the full wing by 30 deg angle of attack. In general, the progression of the separated flow correlated well with subscale model lift data. Surface flow on the vertical tail was also studied using tufts and flow cones. As angle of attack increased, separated flow initiated at the root and spread upward. The area of separated flow on the vertical tail at angles of attack greater than 20 deg correlated well with the marked decrease in aircraft directional stability.

Delfrate, John H.↗

NASA NTRS1992

Study and development of an air conditioning system operating on a magnetic heat pump cycle (design and testing of flow directors)

This report describes the fabrication, design of flow director, fluid flow direction analysis and testing of flow director of a magnetic heat pump. The objectives of the project are: (1) to fabricate a demonstration magnetic heat pump prototype with flow directors installed; and (2) analysis and testing of flow director and to make sure working fluid loops flow through correct directions with minor mixing. The prototype was fabricated and tested at the Development Testing Laboratory of Kennedy Space Center. The magnetic heat pump uses rear earth metal plates rotate in and out of a magnetic field in a clear plastic housing with water flowing through the rotor plates to provide temperature lift. Obtaining the proper water flow direction has been a problem. Flow directors were installed as flow barriers between separating point of two parallel loops. Function of flow directors were proven to be excellent both analytically and experimentally.

Wang, Pao-Lien↗

NASA NTRS1992

In-Flight Flow Visualization Results From the X-29A Aircraft at High Angles of Attack

Flow visualization techniques were used on the X-29A aircraft at high angles of attack to study the vortical flow off the forebody and the surface flow on the wing and tail. The forebody vortex system was studied because asymmetries in the vortex system were suspected of inducing uncommanded yawing moments at zero sideslip. Smoke enabled visualization of the vortex system and correlation of its orientation with flight yawing moment data. Good agreement was found between vortex system asymmetries and the occurrence of yawing moments. Surface flow on the forward-swept wing of the X-29A was studied using tufts and flow cones. As angle of attack increased, separated flow initiated at the root and spread outboard encompassing the full wing by 30° angle of attack. In general, the progression of the separated flow correlated well with subscale model lift data. Surface flow on the vertical tail was also studied using tufts and flow cones. As angle of attack increased, separated flow initiated at the root and spread upward. The area of separated flow on the vertical tail at angles of attack ≥ 20° correlated well with the marked decrease in aircraft directional stability.

Flight Testing↗

NASA NTRS1994

Modification of the MML turbulence model for adverse pressure gradient flows

Computational fluid dynamics is being used increasingly to predict flows for aerospace propulsion applications, yet there is still a need for an easy to use, computationally inexpensive turbulence model capable of accurately predicting a wide range of turbulent flows. The Baldwin-Lomax model is the most widely used algebraic model, even though it has known difficulties calculating flows with strong adverse pressure gradients and large regions of separation. The modified mixing length model (MML) was developed specifically to handle the separation which occurs on airfoils and has given significantly better results than the Baldwin-Lomax model. The success of these calculations warrants further evaluation and development of MML. The objective of this work was to evaluate the performance of MML for zero and adverse pressure gradient flows, and modify it as needed. The Proteus Navier-Stokes code was used for this study and all results were compared with experimental data and with calculations made using the Baldwin-Lomax algebraic model, which is currently available in Proteus. The MML model was first evaluated for zero pressure gradient flow over a flat plate, then modified to produce the proper boundary layer growth. Additional modifications, based on experimental data for three adverse pressure gradient flows, were also implemented. The adapted model, called MMLPG (modified mixing length model for pressure gradient flows), was then evaluated for a typical propulsion flow problem, flow through a transonic diffuser. Three cases were examined: flow with no shock, a weak shock and a strong shock. The results of these calculations indicate that the objectives of this study have been met. Overall, MMLPG is capable of accurately predicting the adverse pressure gradient flows examined in this study, giving generally better agreement with experimental data than the Baldwin-Lomax model.

Conley, Julianne M.↗

NASA NTRS1993

A time-accurate finite volume method valid at all flow velocities

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Kim, S.-W.↗

NASA NTRS1994

Comparison of plate and asthenospheric flow models for the thermal evolution of oceanic lithosphere

Although seafloor depth and heat flow for young oceanic lithosphere can be descibed by modeling the lithosphere as the boundary layer of a cooling halfspace, a long standing question has been why data at older ages deviate from those expected for a halfspace. Two classes of models have been proposed for these deviations. In one, heat added from below 'flattens' depth and heat flow. In the other, asthenospheric flow beneath the lithosphere perturbs the depths. We compare recent versions of the model classes: the GDH1 thin-lithosphere plate model (Stein and Stein, 1992) and an asthenospehric flow model (Phipps Morgan and Smith, 1992). The plate model fits heat flow data better than the flow model for all cases considered, and topographic data in all but one case. The flow model significantly overpredicts depths for the North Atlantic, because the assumed asthenospheric flow in the plate motion direction would yield deepening for old ages rather than the observed flattening. Overall, the GDH1 global average model does better than this flow model, whose parameters were fit to specific plates. Moreover, the plate models fit to specific plates do better than the flow model. Plate models thus appear more useful than this flow model, suggesting that deviations from a cooling halfspace are largely thermal in origin.

Stein, Carol A.↗