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At least 19 records

Dependence of Convective Heat Flux Calculations on Roughness Lengths

The zero plane displacement height (d) and aerodynamic roughness length (z0) can be determined separately for momentum, heat, and humidity by using a procedure based on the Levenberg-Marquardt method for solving non-linear equations. This procedure is used to analyze profile data previously collected by Lo (1977) in a forested area in Canada and by Morgan et al (1971) on a field at the University of California at Davis (UCD) in the United States. The UCD data base is used to show the effects of allowing for different roughness lengths (zom,z0h,z0q) in calculating sensible and latent heat flux densities from bulk transfer coefficients.

Convective Heat

Reynolds shear stress and heat flux calculations in a fully developed turbulent duct flow

The use of a modified form of the Van Driest mixing length for a fully developed turbulent channel flow leads to mean velocity and Reynolds stress distributions that are in close agreement with data obtained either from experiments or direct numerical simulations. The calculations are then extended to a nonisothermal flow by assuming a constant turbulent Prandtl number, the value of which depends on the molecular Prandtl number. Calculated distributions of mean temperature and lateral heat flux are in reasonable agreement with the simulations. The extension of the calculations to higher Reynolds numbers provides some idea of the Reynolds number required for scaling on wall variables to apply in the inner region of the flow.

Antonia, R. A.

Eddy Covariance Theory: A Review

Eddy covariance (EC), the gold standard for measuring ecosystem scale gas and heat exchanges, has transformed our understanding of the breathing of the biosphere, and thus global change biology. Despite numerous methodological improvements and insights gained from the technique, the community faces persistent challenges that have been present since the first EC measurements. Here, we review the theoretical developments underpinning EC. We present theoretical developments in four important areas that have relevance to EC measurements of the net ecosystem exchanges (NEE) of gases and heat from a single tower: (i) measuring the total vertical flux density, (ii) flux attenuation, (iii) coordinate rotations, and (iv) energy balance closure. Persistent problems with EC measurements, such as the inability to close the energy budget, led us to identify two priorities for revisiting the theory underlying: (i) sensible heat flux calculations, and (ii) constraining the mean vertical wind velocity. We present a framework for improved calculation of sensible heat flux derived from first principles of fluid mechanics and thermodynamics that considers coupled heat and mass transfer so that conservation of both is obeyed. These refinements are motivated by the need for unbiased measurements of energy and mass transfer between the land surface and atmosphere for ecosystem research and to validate satellite observations and land surface models.

ecosystem fluxes

Observations of Recent Arctic Sea Ice Volume Loss and Its Impact on Ocean-Atmosphere Energy Exchange and Ice Production

Using recently developed techniques we estimate snow and sea ice thickness distributions for the Arctic basin through the combination of freeboard data from the Ice, Cloud, and land Elevation Satellite (ICESat) and a snow depth model. These data are used with meteorological data and a thermodynamic sea ice model to calculate ocean-atmosphere heat exchange and ice volume production during the 2003-2008 fall and winter seasons. The calculated heat fluxes and ice growth rates are in agreement with previous observations over multiyear ice. In this study, we calculate heat fluxes and ice growth rates for the full distribution of ice thicknesses covering the Arctic basin and determine the impact of ice thickness change on the calculated values. Thinning of the sea ice is observed which greatly increases the 2005-2007 fall period ocean-atmosphere heat fluxes compared to those observed in 2003. Although there was also a decline in sea ice thickness for the winter periods, the winter time heat flux was found to be less impacted by the observed changes in ice thickness. A large increase in the net Arctic ocean-atmosphere heat output is also observed in the fall periods due to changes in the areal coverage of sea ice. The anomalously low sea ice coverage in 2007 led to a net ocean-atmosphere heat output approximately 3 times greater than was observed in previous years and suggests that sea ice losses are now playing a role in increasing surface air temperatures in the Arctic.

Kurtz, N. T.

Mass, heat and freshwater fluxes in the South Indian Ocean

Six hydrographic sections were used to examine the circulation and property fluxes in the South Indian Ocean from 10 to 32 deg S. The calculations were made by applying an inverse method to the data. In the interior of the South Indian Ocean, the geostrophic flow is generally northward. At 18 deg S, the northward interior mass flux is balanced by the southward Ekman mass flux at the surface, whereas at 32 deg S the northward interior mass flux is balanced by the southward mass flux of the Agulhas Current. There is a weak, southward mass flux of 6 x 10 to the 9th kg/s in the Mozambique Channel. The rate of water exchange between the Pacific Ocean and the Indian Ocean is dependent on the choice of the initial reference level used in the inverse calculation. The choice of 1500 m, the depth of the deep oxygen minimum, has led to a flux of water from the Pacific Ocean to the Indian Ocean at a rate of 6.6 x 10 to the 9th kg/s. Heat flux calculations indicate that the Indian Ocean is exporting heat to the rest of the world's oceans at a rate of -0.69 x 10 to the 15th W at 18 deg S and -0.25 x 10 to the 15th W at 32 deg S (negative values being southward).

Fu, Lee-Lueng

Estimation of Sea Ice Thickness Distributions through the Combination of Snow Depth and Satellite Laser Altimetry Data

Combinations of sea ice freeboard and snow depth measurements from satellite data have the potential to provide a means to derive global sea ice thickness values. However, large differences in spatial coverage and resolution between the measurements lead to uncertainties when combining the data. High resolution airborne laser altimeter retrievals of snow-ice freeboard and passive microwave retrievals of snow depth taken in March 2006 provide insight into the spatial variability of these quantities as well as optimal methods for combining high resolution satellite altimeter measurements with low resolution snow depth data. The aircraft measurements show a relationship between freeboard and snow depth for thin ice allowing the development of a method for estimating sea ice thickness from satellite laser altimetry data at their full spatial resolution. This method is used to estimate snow and ice thicknesses for the Arctic basin through the combination of freeboard data from ICESat, snow depth data over first-year ice from AMSR-E, and snow depth over multiyear ice from climatological data. Due to the non-linear dependence of heat flux on ice thickness, the impact on heat flux calculations when maintaining the full resolution of the ICESat data for ice thickness estimates is explored for typical winter conditions. Calculations of the basin-wide mean heat flux and ice growth rate using snow and ice thickness values at the 70 m spatial resolution of ICESat are found to be approximately one-third higher than those calculated from 25 km mean ice thickness values.

Kurtz, Nathan T.

3D modeling of n = 1 RMP driven heat fluxes on the SPARC tokamak PFCs using HEAT

3D heat flux calculations at the lower outer divertor plate of SPARC using the HEAT code show that 3D fields generated from error field correction coils can lead to enhanced peak heat fluxes up to 15 times larger compared to the axisymmetric case. Previously employed to simulate axisymmetric heat flux on 3D plasma facing components, the HEAT code can now predict 3D heat flux generated by non-axisymmetric plasmas. This is achieved via a new HEAT module which leverages the 3D field line tracing capabilities of MAFOT starting from an M3D-C1 (MHD resistive code) perturbed equilibria. The resulting heat flux is assigned using the magnetic footprint and the heat flux layer model, an extension of the 2D heat flux model also known as the Eich, to 3D non-axisymmetric plasmas. For SPARC, the new capabilities of HEAT are used to calculate the 3D heat loads resulting from n = 1 perturbation fields (with n indicating the toroidal periodicity) applied through a toroidal array of six picture frame coils with different amplitude. The comparison with the unperturbed case shows significant changes in shape and intensity of the heat flux profile. The results show that the application of n = 1 3D field leads to a localized enhancement of the heat flux peak, influenced by the wetted area impacted by the magnetic footprint, and the appearance of a secondary heat flux peak, whose intensity depends on amplitude of the applied 3D field and toroidal location.

3D heat flux

Higher-Order Finite Elements for Computing Thermal Radiation

Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other unrealistic physical conditions are assumed. Instead, the equations of radiative heat transfer are integrated numerically over the parent finite elements by use of a computationally efficient Gaussian integration scheme.

Gould, Dana C.

Steady-State and Frequency Response of a Thin-Film Heat Flux Gauge

A new and simpler design of thin-film heat flux gauge has been developed for use In high-heat-flux environments. Heat flux gauges of the same design were fabricated on three different substrates and tested. The heat flux gauge comprises a thermopile and a thermocouple junction, which measures the surface temperature. The thermopile has 40 pairs of S-type thermocouples and is covered by two thermal resistance layers. Calibration and testing of these gauges were first carried out in an arc-lamp calibration facility. Sensitivity of the gauge was discussed in terms of the relative conductivity and surface temperature. The heat flux calculated from the gauge output was In good agreement with the precalibrated standard sensor. The steady-state and the transient response characteristics of the heat flux gauge were also investigated using a carbon dioxide pulse laser as a heat source. The dynamic frequency response was evaluated in terms of the nondimensional amplitude ratio with respect to the frequency spectrum of a chopped laser bcam. The frequency response of the gauge was determined to be about 3 kHz. The temperature profiles in the thin-film heat flux gauge were obtained numerically in steady-state conditions using FLUENT and compared with the experimental results.

Fralick, Gustave C.

Heat Flux Sensor Calibrator

The heat flux to space shuttle main engine (SSME) turbopump turbine blades may be as high as 10 to the 7th power. The heat flux causes thermal transients that are of the order of 1 sec as temperature varies from perhaps 1500 K to 100 K. It is suspected that these transients cause durability problems in the turbine blades. To quantitatively evaluate the effect of these transients, heat flux sensors or gauges were developed to obtain data to verify analytical models. The objective is to design and fabricate a system for steady state and transient calibration and durability testing of heat flux sensors for use in SSME turbine blades. The calibrator consists of: (1) the arc lamp, (2) a high speed positioning table for placing standard and special heat flux sensors in the incident beam of radiant heat flux, (3) provision for cooling the blade and special sensors inserted in the blade, (4) a computer for controlling the positioning table, storing electrical output values from sensors, and calculating heat flux from these values, and (5) a pyrometer for measuring sensor surface temperatures.

Liebert, C. H.

RTE: A computer code for Rocket Thermal Evaluation

The numerical model for a rocket thermal analysis code (RTE) is discussed. RTE is a comprehensive thermal analysis code for thermal analysis of regeneratively cooled rocket engines. The input to the code consists of the composition of fuel/oxidant mixture and flow rates, chamber pressure, coolant temperature and pressure. dimensions of the engine, materials and the number of nodes in different parts of the engine. The code allows for temperature variation in axial, radial and circumferential directions. By implementing an iterative scheme, it provides nodal temperature distribution, rates of heat transfer, hot gas and coolant thermal and transport properties. The fuel/oxidant mixture ratio can be varied along the thrust chamber. This feature allows the user to incorporate a non-equilibrium model or an energy release model for the hot-gas-side. The user has the option of bypassing the hot-gas-side calculations and directly inputting the gas-side fluxes. This feature is used to link RTE to a boundary layer module for the hot-gas-side heat flux calculations.

Naraghi, Mohammad H. N.

An Experimental Study of a Radially Arranged Thin Film Heat Flux Gauge

A new thin-film heat-flux gauge was designed and fabricated on three different substrate materials. Forty pairs of Pt-Pt/10% Rh thermocouple junctions were deposited in a circular pattern on the same plane of the substrate. Over the thermocouples, 5 and 10 micron thick thermal resistance layers were deposited to create a temperature gradient across those layers. Calibration and testing of these gauges were carried out in an arc-lamp calibration facility. The heat flux calculated from the gauge output is in good agreement with the value obtained from the pre-calibrated standard sensor. A CO2 laser was also used to test the steady-state and dynamic responses of the heat-flux gauge. During the steady-state test, the time constant for the heating period was 30 s. The frequency response of the heat-flux gauge was measured in the frequency domain using a CO2 laser and a chopper. The responses from an infrared detector and the heat-flux gauge were measured simultaneously and compared. It was found that the thin-film heat-flux gauge has a dynamic frequency response of 3 kHz.

Cho, Christoper S. K.

Sea ice-atmosphere interaction: Application of multispectral satellite data in polar surface energy flux estimates

The application of multi-spectral satellite data to estimate polar surface energy fluxes is addressed. To what accuracy and over which geographic areas large scale energy budgets can be estimated are investigated based upon a combination of available remote sensing and climatological data sets. The general approach was to: (1) formulate parameterization schemes for the appropriate sea ice energy budget terms based upon the remotely sensed and/or in-situ data sets; (2) conduct sensitivity analyses using as input both natural variability (observed data in regional case studies) and theoretical variability based upon energy flux model concepts; (3) assess the applicability of these parameterization schemes to both regional and basin wide energy balance estimates using remote sensing data sets; and (4) assemble multi-spectral, multi-sensor data sets for at least two regions of the Arctic Basin and possibly one region of the Antarctic. The type of data needed for a basin-wide assessment is described and the temporal coverage of these data sets are determined by data availability and need as defined by parameterization scheme. The titles of the subjects are as follows: (1) Heat flux calculations from SSM/I and LANDSAT data in the Bering Sea; (2) Energy flux estimation using passive microwave data; (3) Fetch and stability sensitivity estimates of turbulent heat flux; and (4) Surface temperature algorithm.

Steffen, K.

CFD Predictions of Boiling Regime Transitions during Line Chilldown validated against a 1G LN2 Experiment

Introduction Before filling a propellant tank on the ground or in Space, the transfer line between the donor and receiver tanks must be cooled down preferably by sacrificing a minimum amount of the cryogenic fluid. The cryogenic line chill-down process involves a transition between different flow boiling regimes, namely, film boiling, transition film boiling, and nucleate boiling which are complex and may be quite gravity-dependent. Capturing these boiling phenomena and predicting the transition between them in a CFD framework is new and challenging both for 1g and microgravity applications. Materials & Methods The present work addresses this challenge by employing a two-phase Eulerian approach in the context of a homogeneous fluid mixture together with the Lee phase change model to capture the film boiling regime of the chill-down process using ANSYS Fluent®. The nucleate boiling regime is predicted by incorporating an in-house developed sub-grid model that accounts for bubble nucleation, bubble growth, bubble departure diameter, and their shedding frequency. The sub-grid model is encoded and implemented into Fluent via a user-defined function for the wall-fluid heat flux calculations. The mathematical formulation and numerical implementation of the CFD model are described in detail. The coupled CFD-Subgrid model is validated against published experimental data for liquid nitrogen chill-down of a heated stainless-steel pipe in 1g. Results Numerical simulation results show good agreements between the CFD predictions of the wall temperature evolution, rewetting temperature, and transition between film and nucleate boiling, with the experimental measurements published by Darr et al [2] for several different LN2 flowrates in the vertical pipe orientation. The CFD predictions for the wall temperature distribution indicate a rapid quenching of the wall at two upstream and downstream temperature sensing locations as compared to the experimental measurement. The only tuning parameter in the CFD model is the Lee mass transfer coefficient. The CFD Model predicts the Liedenfrost rewetting temperature in close agreement with the experiment. This marks a transition between stable and transitionary flow boiling regimes. The CFD-predicted boiling curve for the downstream sensor location is also compared against its experimental counterpart and indicates that the model is able to predict all the key temperature and heat flux parameters during the transitions from stable to transitionary film boiling to nucleate boiling in close agreement with the experiment. A sequence of predicted volume fraction, and temperature contours depicting these transitions will be presented.

Evaporation Condensation

Liquid hydrogen and liquid oxygen feedline passive recirculation analysis

The primary goal of the National Launch System (NLS) program was to design an operationally efficient, highly reliable vehicle with minimal recurring launch costs. To achieve this goal, trade studies of key main propulsion subsystems were performed to specify vehicle design requirements. These requirements include the use of passive recirculation to thermally condition the liquid hydrogen (LH2) and liquid oxygen (LO2) propellant feed systems and Space Transportation Main Engine (STME) fuel pumps. Rockwell International (RI) proposed a joint independent research and development (JIRAD) program with Marshall Space Flight Center (MSFC) to study the LH2 feed system passive recirculation concept. The testing was started in July 1992 and completed in November 1992. Vertical and sloped feedline designs were used. An engine simulator was attached at the bottom of the feedline. This simulator had strip heaters that were set to equal the corresponding heat input from different engines. A computer program is currently being used to analyze the passive recirculation concept in the LH2 vertical feedline tests. Four tests, where the heater setting is the independent variable, were chosen. While the JIRAD with RI was underway, General Dynamics Space Systems (GDSS) proposed a JIRAD with MSFC to explore passive recirculation in the LO2 feed system. Liquid nitrogen (LN2) is being used instead of LO2 for safety and economic concerns. To date, three sets of calibration tests have been completed on the sloped LN2 test article. The environmental heat was calculated from the calibration tests in which the strip heaters were turned off. During the LH2 testing, the environmental heat was assumed to be constant. Therefore, the total heat was equal to the environmental heat flux plus the heater input. However, the first two sets of LN2 calibration tests have shown that the environmental heat flux varies with heater input. A Systems Improved Numerical Differencing Analyzer and Fluid Integrator (SINDA/FLUINT) model is currently being built to determine if this variation in environmental heat is due to a change in the wall temperature. During the third set of calibration tests, a faulty reference junction was found. Based on this anomaly with the reference junction, the heat flux calculations from the first two calibration sets are now considered questionable.

Holt, Kimberly Ann

Predictions of Line Chilldown Boiling Regime Transitions by a Coupled CFD-Sub-Grid Boiling Model Validated against 1G LN2 Experiments

Propellant storage and transfer during future long-duration missions will involve fuel depot operations in which a donor depot tank is used to fill a receiver spacecraft tank with a cryogenic propellant. Prior to the on-Orbit filling operation both the receiver tank and the transfer line must be cooled. The line chilldown process involves transition between boiling regimes in microgravity that will be quite different from their 1g ground-based counterparts. Since the cryogenic propellant itself will be used to perform the chilldown process, the time constants to cool the wall and the amount of fuel that will be used become important design considerations. In this light, the focus of the present work is to capture the flow boiling characteristics of a cryogenic fluid, namely, liquid nitrogen, during the chill-down of a transfer line using CFD modelling and simulations. The cryogenic chill-down process involves different flow boiling regimes: film boiling, transition boiling and nucleate boiling. The prediction of transition between these regimes in a CFD framework is new and challenging. The present work addresses this challenge by employing a volume-of-fluid (VOF) based methodology with Lee phase change model to predict the film boiling regime of the chill-down process in ANSYS Fluent®. The transition and nucleate boiling regimes are predicted by incorporating a sub-grid model that accounts for bubble nucleation, growth, shedding frequency, and departure diameter. The sub-grid model is implemented into Fluent via a user-defined function for wall-fluid heat flux calculations. The sub-grid model is similar in formulation to the well-known Rensselaer Polytechnic Institute (RPI) boiling model. The CFD model is validated against published experimental data for liquid nitrogen chill-down of a heated stainless-steel pipe in 1g. Predicted results shows good agreement of wall temperature, rewetting temperature, and transition between film and nucleate boiling with the experimental measurements for several different LN2 flowrates in the vertical orientation. The strengths and weaknesses of this modeling approach are presented and discussed.

Cryogenic Fluid Management

Urban weather modeling using WRF: linking physical assumptions, code implementation, and observational needs

The Weather Research and Forecasting (WRF) model includes urban schemes that simulate the influence of urban surfaces on the atmosphere using parameterizations for flux, and radiative exchanges. Three core schemes – the Bulk urban parameterization, Single-Layer Urban Canopy Model (SLUCM), and Multi-Layer Urban Canopy Model (MLUCM) – represent increasing levels of complexity. Although the parameterizations within these urban schemes are described in the literature, their specific implementation remains poorly documented, thus slowing down model development efforts. This manuscript provides a roadmap to the three urban schemes in WRF version 4.5.2, presenting equations using the same symbols as in the model code, along with references to code lines, and including graphics and explanations that connect the code to its physical foundations. Our thorough review of the urban parameterizations implemented in WRF version 4.5.2 highlighted a handful of parameters that may introduce discontinuities in simulations: (i) in the SLUCM, a 1 mm h −1 rain rate threshold is employed to switch between two minimum moisture availability parameterizations, thus impacting latent heat flux calculations; (ii) in the SLUCM a threshold is used to partition shortwave radiation into direct and diffuse components; (iii) in all three urban schemes, the bulk Richardson number is employed to select the similarity function, which influences the vertical distribution of heat and momentum. We also identified a highly simplified treatment of the radiative balance on roof surfaces. The implications of these simplifications can be assessed through targeted observations across relevant conditions, including varying precipitation rates, cloud cover, and transitions between stability regimes. Furthermore, the widespread application of the Monin-Obukhov similarity theory in these urban schemes warrants model evaluation under highly stable and unstable conditions and in heterogeneous urban settings with variable land cover and building heights on scales finer than model resolution. To address these challenges, we offer guidance on observational strategies, emphasizing the need for multi-parametric measurements to capture potential compensating biases and multi-height measurements that align with the levels where quantities are diagnostic and prognosed in the model (i.e., the lowest atmospheric level of the WRF model). Finally, our inspection of the code revealed implementation bugs that have now been corrected in WRF versions 4.6.0 and 4.6.1. Sensitivity tests over the Atlanta urban area show that these corrections affect surface temperatures, underscoring the importance of performing rigorous documentation and verification of the implementation of parameterizations in model code.

54 ENVIRONMENTAL SCIENCES