scholarly journals Time-dependent solutions for daily-periodic slope flows driven by surface energy budget

2021 ◽  
Author(s):  
Mattia Marchio ◽  
Sofia Farina ◽  
Dino Zardi
Keyword(s):  
Heat Flux ◽  
Surface Energy ◽  
Surface Temperature ◽  
Wind Velocity ◽  
Analytical Model ◽  
Slope Angle ◽  
Time Dependent ◽  
Fourier Series Expansion ◽  
Ambient Atmosphere ◽  
Slope Wind

<p>Diurnal wind systems generated from daytime heating and nighttime cooling of valleys and slopes are a very common feature over mountainous terrains. Despite their frequent occurrence and relevance for a variety of applications, ranging from pollutant transport to convection initiation, slope winds are far from being fully understood and still provide an open research topic.</p><p>A well-known steady-state analytical model <span>is the one</span> developed by Prandtl (1942). Then, a first time-dependent analytical model was proposed by F. Defant (1949) and later extended by Zardi and Serafin (2015). These models provide slope-normal profiles of temperature and along-slope wind velocity as a response to a sinusoidal forcing representing the surface temperature. The resulting profiles exhibit sinusoidal oscillations at every distance from the surface, although with different phase lags under different regimes, determined by different combinations of slope angle and stability of the unperturbed ambient atmosphere. As a consequence, they can not explain the observed differences between daytime upslope and nighttime downslope winds in terms of magnitude and height of the peak of wind velocity, as well as the different timing characterising nighttime, daytime, and the two reversal phases.</p><p>In the present work, the solutions derived in Zardi and Serafin (2015) are extended to include a more realistic daily-periodic surface forcing taking into account the daily evolution of the surface temperature computed on the basis of a surface energy <span>budget</span>. Incoming solar radiation is represented by means of a Fourier series expansion derived from well-established relationships taking into account latitude, day of the year, slope angle, exposition and other astronomical and atmospheric factors. Based on <span>these</span> expansions, suitable harmonic solutions are derived for the heat flux into the ground and sensible heat flux in the atmosphere, and hence for the daily evolution of slope-normal profiles of along-slope wind velocity and potential temperature.</p><p>References:</p><ul><li><span>Prandtl L. 1942. Führer durch die Strömungslehre, Chapter 5. Vieweg und Sohn: Braunschweig, Germany. </span>[English translation: Prandtl L. 1952. Mountain and valley winds in stratified air, in Essentials of Fluid Dynamics: 422–425. Hafner Publishing Company: New York, NY]</li> <li><span>Defant F. 1949. Zur Theorie der Hangwinde, nebst Bemerkungen zur Theorie der Berg- und Talwinde. </span>Arch. Meteorol. Geophys. Bioklimatol. A 1: 421–450</li> <li>Zardi D., Serafin S. 2015. An analytic solution for time‐periodic thermally driven slope flows. Q. J. R. Meteorol. Soc., 141, 1968–1974, https://doi.org/10.1002/qj.2485</li> </ul>

Transient Internal Forced Convection Under Arbitrary Time-Dependent Heat Flux

2013 ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
M. Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel’s integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict: i) fluid temperature distribution inside the tube ii) fluid bulk temperature and iii) the Nusselt number. A new definition, cyclic fully-developed Nusselt number, is introduced and it is shown that in the thermally fully-developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ANSYS to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

Intercomparison of Spatially Distributed Models for Predicting Surface Energy Flux Patterns during SMACEX

2005 ◽  
Vol 6 (6) ◽  
pp. 941-953 ◽  
Author(s):  
Wade T. Crow ◽  
Fuqin Li ◽  
William P. Kustas
Keyword(s):  
Remote Sensing ◽  
Heat Flux ◽  
Energy Balance ◽  
Surface Energy ◽  
Surface Temperature ◽  
Energy Flux ◽  
Land Surface ◽  
Sensible Heat Flux ◽  
Energy Fluxes ◽  
Spatially Distributed

Abstract The treatment of aerodynamic surface temperature in soil–vegetation–atmosphere transfer (SVAT) models can be used to classify approaches into two broad categories. The first category contains models utilizing remote sensing (RS) observations of surface radiometric temperature to estimate aerodynamic surface temperature and solve the terrestrial energy balance. The second category contains combined water and energy balance (WEB) approaches that simultaneously solve for surface temperature and energy fluxes based on observations of incoming radiation, precipitation, and micrometeorological variables. To date, few studies have focused on cross comparing model predictions from each category. Land surface and remote sensing datasets collected during the 2002 Soil Moisture–Atmosphere Coupling Experiment (SMACEX) provide an opportunity to evaluate and intercompare spatially distributed surface energy balance models. Intercomparison results presented here focus on the ability of a WEB-SVAT approach [the TOPmodel-based Land–Atmosphere Transfer Scheme (TOPLATS)] and an RS-SVAT approach [the Two-Source Energy Balance (TSEB) model] to accurately predict patterns of turbulent energy fluxes observed during SMACEX. During the experiment, TOPLATS and TSEB latent heat flux predictions match flux tower observations with root-mean-square (rms) accuracies of 67 and 63 W m−2, respectively. TSEB predictions of sensible heat flux are significantly more accurate with an rms accuracy of 22 versus 46 W m−2 for TOPLATS. The intercomparison of flux predictions from each model suggests that modeling errors for each approach are sufficiently independent and that opportunities exist for improving the performance of both models via data assimilation and model calibration techniques that integrate RS- and WEB-SVAT energy flux predictions.

scholarly journals An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes

2021 ◽  
Vol 11 (21) ◽  
pp. 10338
Author(s):  
Mohammed A. Hefni ◽  
Minghan Xu ◽  
Ferri Hassani ◽  
Seyed Ali Ghoreishi-Madiseh ◽  
Haitham M. Ahmed ◽  
...  
Keyword(s):  
Heat Flux ◽  
Energy Storage ◽  
Analytical Model ◽  
Thermal Performance ◽  
Closed Loop ◽  
Waste Heat ◽  
Analytical Framework ◽  
Thermal Design ◽  
Time Dependent ◽  
Borehole Wall

With the increasing engineering applications of geothermal borehole heat exchangers (BHEs), accurate and reliable mathematical models can help advance their thermal design and operations. In this study, an analytical model with a time-dependent heat flux boundary condition on the borehole wall is developed, capable of predicting the thermal performance of single, double, and multiple closed-loop BHEs, with an emphasis on solar- and waste-heat-assisted geothermal borehole systems (S-GBS and W-GBS) for energy storage. This analytical framework begins with a one-dimensional transient heat conduction problem subjected to a time-dependent heat flux for a single borehole. The single borehole scenario is then extended to multiple boreholes by exploiting lines of symmetry (or thermal superposition). A final expression of the temperature distribution along the center line is attained for single, double, and multiple boreholes, which is verified with a two-dimensional finite-element numerical model (less than 0.7% mean absolute deviation) and uses much lesser computational power and time. The analytical solution is also validated against a field-scale experiment from the literature regarding the borehole and ground temperatures at different time frames, with an absolute error below 6.3%. Further, the thermal performance of S-GBS and W-GBS is compared for a 3-by-3 borehole configuration using the analytical model to ensure its versatility in thermal energy storage. It is concluded that our proposed analytical framework can rapidly evaluate closed-loop geothermal BHEs, regardless of the numbers of boreholes and the type of the heat flux on the borehole wall.

Investigating the dynamics of thermally driven up-slope flows: analysis of data from measurements in the Inn Valley (Austria) and comparison with a simple model

2021 ◽  
Author(s):  
Mattia Marchio ◽  
Sofia Farina ◽  
Dino Zardi
Keyword(s):  
Surface Temperature ◽  
Prediction Models ◽  
Weather Prediction ◽  
Slope Angle ◽  
Turbulent Fluxes ◽  
Surface Energy Budget ◽  
Valley Wind ◽  
Slope Winds ◽  
Slope Wind ◽  
Slope Flow

<p><span>Diurnal wind systems typically develop in mountainous areas following the daytime heating and nighttime cooling of sloping surfaces. While down-slope winds have been extensively treated in the literature, up-slope winds have received much less attention. In particular, the physical mechanisms associated with the development of these winds, as well as the search for appropriate parameterization of turbulent fluxes of mass, momentum, and heat over slopes in numerical weather prediction models are still open research topics.</span></p><p><span>Here we present some preliminary results from the analysis of turbulence data (sonic wind speed, temperature, humidity, and turbulent fluxes) collected at two slope stations which are part of the i-Box initiative. The i-Box project (Rotach et al. 2017) aims at studying turbulent exchange processes in complex terrain areas. The experimental setup is composed of six stations disseminated in the surroundings of the alpine city of Innsbruck, in the Inn Valley. The two stations adopted for the present study are located at different points on the valley sidewalls, one with a slope angle of 27° (labelled NF27) and one with a slope angle of 10° (NF10). Both stations are located over slopes covered by alpine meadow and at an altitude of about 1000 m MSL (400 m above the valley floor). The station NF27 has two measurement points, 1.5 and 6.8 m AGL, while the station NF10 has one measurement point, at 6.2 m AGL.</span></p><p><span>The analysis shows that criteria proposed in the literature for the selection of valley-wind days may not apply for the identification of slope-wind days. Furthermore, from the analysis of second order moments, scaling relationships are derived for up-slope flow conditions. In addition, measurements representing the evolution of the up-slope flow structure from the early morning to the mid-afternoon are compared with an existing, simplified, analytical model, which provides the evolution of the vertical profiles of temperature and along-slope wind velocity as generated by a sinusoidal forcing representing the daily cycle of surface temperature. An improvement of the existing model, where the surface energy budget is considered as the boundary condition for the surface temperature, is also tested.</span></p>

Unsteady Laminar Forced-Convective Tube Flow Under Dynamic Time-Dependent Heat Flux

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
Mehdi Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Tube Flow ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow (SF) condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel's integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict (i) fluid temperature distribution inside the tube, (ii) fluid bulk temperature and (iii) the Nusselt number. A new definition, cyclic fully developed Nusselt number, is introduced and it is shown that in the thermally fully developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ansys fluent to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

scholarly journals Evaluation of the SPARSE Dual-Source Model for Predicting Water Stress and Evapotranspiration from Thermal Infrared Data over Multiple Crops and Climates

2018 ◽  
Vol 10 (11) ◽  
pp. 1806 ◽  
Author(s):  
Emilie Delogu ◽  
Gilles Boulet ◽  
Albert Olioso ◽  
Sébastien Garrigues ◽  
Aurore Brut ◽  
...  
Keyword(s):  
Heat Flux ◽  
Water Stress ◽  
Energy Balance ◽  
Surface Energy ◽  
Surface Temperature ◽  
Surface Energy Balance ◽  
Source Model ◽  
Vegetation Stress ◽  
Stress Levels ◽  
Dual Source

Using surface temperature as a signature of the surface energy balance is a way to quantify the spatial distribution of evapotranspiration and water stress. In this work, we used the new dual-source model named Soil Plant Atmosphere and Remote Sensing Evapotranspiration (SPARSE) based on the Two Sources Energy Balance (TSEB) model rationale which solves the surface energy balance equations for the soil and the canopy. SPARSE can be used (i) to retrieve soil and vegetation stress levels from known surface temperature and (ii) to predict transpiration, soil evaporation, and surface temperature for given stress levels. The main innovative feature of SPARSE is that it allows to bound each retrieved individual flux component (evaporation and transpiration) by its corresponding potential level deduced from running the model in prescribed potential conditions, i.e., a maximum limit if the surface water availability is not limiting. The main objective of the paper is to assess the SPARSE model predictions of water stress and evapotranspiration components for its two proposed versions (the “patch” and “layer” resistances network) over 20 in situ data sets encompassing distinct vegetation and climate. Over a large range of leaf area index values and for contrasting vegetation stress levels, SPARSE showed good retrieval performances of evapotranspiration and sensible heat fluxes. For cereals, the layer version provided better latent heat flux estimates than the patch version while both models showed similar performances for sparse crops and forest ecosystems. The bounded layer version of SPARSE provided the best estimates of latent heat flux over different sites and climates. Broad tendencies of observed and retrieved stress intensities were well reproduced with a reasonable difference obtained for most of the points located within a confidence interval of 0.2. The synchronous dynamics of observed and retrieved estimates underlined that the SPARSE retrieved water stress estimates from Thermal Infra-Red data were relevant tools for stress detection.

scholarly journals The role of aerodynamic resistance in thermal remote sensing-based evapotranspiration models

2021 ◽  
Author(s):  
Ivonne Trebs ◽  
Kaniska Mallick ◽  
Nishan Bhattarai ◽  
Mauro Sulis ◽  
James Cleverly ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Heat Flux ◽  
Energy Balance ◽  
Surface Energy ◽  
Surface Temperature ◽  
Surface Energy Balance ◽  
Aerodynamic Resistance ◽  
Atmospheric Stability ◽  
Semi Arid

<p>‘Aerodynamic resistance’ (hereafter r<sub>a</sub>) is a preeminent variable in the modelling of evapotranspiration (ET), and its accurate quantification plays a critical role in determining the performance and consistency of thermal remote sensing-based surface energy balance (SEB) models for estimating ET at local to regional scales. Atmospheric stability links r<sub>a</sub> with land surface temperature (LST) and the representation of their interactions in the SEB models determines the accuracy of ET estimates.</p><p>The present study investigates the influence of r<sub>a</sub> and its relation to LST uncertainties on the performance of three structurally different SEB models by combining nine OzFlux eddy covariance datasets from 2011 to 2019 from sites of different aridity in Australia with MODIS Terra and Aqua LST and leaf area index (LAI) products. Simulations of the latent heat flux (LE, energy equivalent of ET in W/m<sup>2</sup>) from the SPARSE (Soil Plant Atmosphere and Remote Sensing Evapotranspiration), SEBS (Surface Energy Balance System) and STIC (Surface Temperature Initiated Closure) models forced with MODIS LST, LAI, and in-situ meteorological datasets were evaluated using observed flux data across water-limited (semi-arid and arid) and radiation-limited (mesic) ecosystems.</p><p>Our results revealed that the three models tend to overestimate instantaneous LE in the water-limited shrubland, woodland and grassland ecosystems by up to 60% on average, which was caused by an underestimation of the sensible heat flux (H). LE overestimation was associated with discrepancies in r<sub>a</sub> retrievals under conditions of high atmospheric instability, during which errors in LST (expressed as the difference between MODIS LST and in-situ LST) apparently played a minor role. On the other hand, a positive bias in LST coincides with low r<sub>a</sub> and causes slight underestimation of LE at the water-limited sites. The impact of r<sub>a</sub> on the LE residual error was found to be of the same magnitude as the influence of errors in LST in the semi-arid ecosystems as indicated by variable importance in projection (VIP) coefficients from partial least squares regression above unity. In contrast, our results for mesic forest ecosystems indicated minor dependency on r<sub>a</sub> for modelling LE (VIP<0.4), which was due to a higher roughness length and lower LST resulting in dominance of mechanically generated turbulence, thereby diminishing the importance of atmospheric stability in the determination of r<sub>a</sub>.</p>

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