Porous Media Approach Research Articles

CFD simulation of heating greenhouse using a perforated polyethylene ducts

The location and the power of the heating devices determines in a large extend the flow and temperature patterns inside the greenhouse. The aim of this paper is to analyse the internal convective flows generated in a closed cultivated tunnel greenhouse. Numerical model of greenhouse, which has a size of (20 × 8 × 4.1) m, installing ducting system was evaluated with CFD simulation model (commercially available computational fluid dynamics CFD code CFX-13). The greenhouse was heated by hot air, distributed via clear perforated polyethylene ducts. The standard k-e model was adopted to describe the turbulent transport. The dynamics' effects of the crop were simulated using the equivalent porous medium approach proposed by Darcy and reorganised by Forshheimer equation. The results are shown in the form of pressure, velocity and temperature contours. Better visualisation of the distribution of these parameters was obtained in order to homogenise the greenhouse climate. The pressure contours along he three perforated ducts show that the discharge through holes is not uniform because of the static pressure difference between upstream and downstream of the hole, as well as the angle and discharge coefficient variation of each hole.

Linking hydraulic traits to tropical forest function in a size-structured and trait-driven model (TFS v.1-Hydro)

Abstract. Forest ecosystem models based on heuristic water stress functions poorly predict tropical forest response to drought partly because they do not capture the diversity of hydraulic traits (including variation in tree size) observed in tropical forests. We developed a continuous porous media approach to modeling plant hydraulics in which all parameters of the constitutive equations are biologically interpretable and measurable plant hydraulic traits (e.g., turgor loss point πtlp, bulk elastic modulus ε, hydraulic capacitance Cft, xylem hydraulic conductivity ks,max, water potential at 50 % loss of conductivity for both xylem (P50,x) and stomata (P50,gs), and the leaf : sapwood area ratio Al : As). We embedded this plant hydraulics model within a trait forest simulator (TFS) that models light environments of individual trees and their upper boundary conditions (transpiration), as well as providing a means for parameterizing variation in hydraulic traits among individuals. We synthesized literature and existing databases to parameterize all hydraulic traits as a function of stem and leaf traits, including wood density (WD), leaf mass per area (LMA), and photosynthetic capacity (Amax), and evaluated the coupled model (called TFS v.1-Hydro) predictions, against observed diurnal and seasonal variability in stem and leaf water potential as well as stand-scaled sap flux. Our hydraulic trait synthesis revealed coordination among leaf and xylem hydraulic traits and statistically significant relationships of most hydraulic traits with more easily measured plant traits. Using the most informative empirical trait–trait relationships derived from this synthesis, TFS v.1-Hydro successfully captured individual variation in leaf and stem water potential due to increasing tree size and light environment, with model representation of hydraulic architecture and plant traits exerting primary and secondary controls, respectively, on the fidelity of model predictions. The plant hydraulics model made substantial improvements to simulations of total ecosystem transpiration. Remaining uncertainties and limitations of the trait paradigm for plant hydraulics modeling are highlighted.

Hydrogeological study and numerical model of the Suio-Castelforte hydrothermal area (central Italy)

A numerical simulation has been performed through the natural geothermal system of Suio-Castelforte (LT) in order to investigate the hydothermal area and assess its geothermal potentiality. Starting from geological and hydrogeological data a 2D conceptual model has been built. For numerical purpose, the latter idealizes and simplifies the natural system. The area has been affected by a temperature gradient, from low to medium enthalpy, related to the Quaternary volcanism. By a FEM (Finite Element Model) method, using the COMSOL MULTIPHYSICS® software, a homogeneous and isotrope media have been assumed, simulating the groundwater flow and simultaneous heat transfer. Using the porous media approach, Darcy and heat transfer laws have been applied in steady-state conditions. The results have been compared with the collected data and bibliography.

Flow through a filter plate backed by a packed bed of spheres

In this paper we perform direct numerical simulation (DNS) on the problem of fluid flow through a filter plate backed by a packed bed of spheres, resembling a cake layer on top of a membrane. For both the complete problem, and its single components (the filter plate and a bed of spheres of finite height) we have observed three flow regimes, depending on the Reynolds number. In each regime the flow resistance is showing a different scaling with the Reynolds number. In the Stokes flow regime the total flow resistance can be decomposed in linear independent components. The interior flows inside the filter holes and inside the packed bed follow the same correlations as hold for the single component. However, at the transition zone between filter plate and packed bed, there is a diverging flow in the first row of the packed bed, whose contribution in the flow resistance scales with the fractional hole to the power −1.5. Similar scaling exponent has been found earlier for the viscous-inertial regime with Reynolds numbers larger than 10, which has been modelled using the porous medium approach. Our findings suggest that also in the Stokes flow and the weakly flow regime the problem can also be solved with the same porous medium approach using the Navier-Stokes equation having Darcy–Brinkman terms incorporated. This investigation provides a good basis for developing more accurate analytical models for the flow resistance of membrane filters with a cake layer on top.

Investigation of natural convection in Miniature Neutron Source Reactor of Isfahan by applying the porous media approach

The small and complex core of Isfahan Miniature Neutron Source Reactor (MNSR) in addition to its large tank makes a parametric study of natural convection difficult to perform in aspects of time and computational resources. In this study, in order to overcome this obstacle the porous media approximation has been used. This numerical technique includes two steps, (a) calculation of porous media variables such as porosity and pressure drops in the core region, (b) simulation of natural convection in the reactor tank by assuming the core region as a porous medium. Simulation has been carried out with ANSYS FLUENT® Academic Research, Release 16.2. The core porous medium resistance factors have been estimated to be, Dij=1850 [1/m] and Cij=415 [1/m2]. Natural Convection simulation with Boussinesq approximation and variable property assumption have been performed. The experimental data and nuclear codes available in the literature, have verified the method. The average temperature difference between the experimental data and this study results was less than 0.5°C and 2.0°C for property variable technique and Boussinesq approximation, respectively. Temperature distribution and flow pattern in the entire reactor have been obtained. Results have shown that the temperature difference between core outlet and inlet is about 18°C and in this situation flow rate is about 0.004kg/s. A full parametric study could be the topic of future investigations.

Evolution of fluid flow and heat distribution over geological time scales at the margin of unconfined and confined carbonate sequences - A numerical investigation based on the Buda Thermal Karst analogue

Hydrogeological processes acting at the margins of confined and unconfined thick carbonate sequences are particularly interesting due to a complex system evolution including partial uplift of fully confined carbonate systems and subsequent erosion of cover layers. We provide insights into this evolution by simulating coupled density-dependent fluid flow and heat transport based on the Buda Thermal Karst (BTK) system (Hungary) in a 2D vertical plane. Applying an equivalent porous medium (EPM) approach using the Heatflow-Smoker finite element model, scenario modelling of three evolutionary steps was carried out between the fully-confined carbonate stage through to partly and completely unconfined conditions over the western ridge. The numerical simulations were used to derive the main evolutionary characteristics of groundwater flow and heat transport patterns for the unconfined and confined parts of the hydrogeologic system. The initial fully-confined state led to the development of thermal convection cells due to the insulating role of the low-permeability confining layer, which facilitates buoyancy-driven flow by restricting the dissipation of heat. Over geological time, these cells were gradually overprinted by gravity-driven flow and thermal advection due to uplift of the west ridge. The limited thickness of the cover allowed sufficient water infiltration into the system, which led to increased cooling. Further uplifting led to a prevalence of gravity-driven groundwater flow. The results highlight the critical role of confining formations on flow patterns, and their effect on heat distribution and dissipation over geological time scales. The results have important implications for heat accumulation as well as for the development of a deep geothermal energy potential in confined carbonates.

Porous media approach for RANS simulation of compound open-channel flows with submerged vegetated floodplains

The main goal of this study is the 3D numerical simulation of river flows with submerged vegetated floodplains. Since, vegetation layers are usually dense and present a large spatial heterogeneity they are here represented as a porous media. Standard semi-empirical relations drawn for porous beds packed with non-spherical particles are used to estimate the porous media parameters based on the averaged geometry of the vegetation elements. Thus, eliminating the uncertainty arising from a bulk drag coefficient approach and allowing the use of a coarser mesh. The free flow is described by Reynolds-averaged Navier–Stokes (RANS) equations, whereas the porous media flow is described by the volumetric-average of RANS equations. The volume-of-fluid method and an anisotropic explicit algebraic Reynolds stress model are used for free-surface and turbulence closure, respectively. The simulation approach is validated against results by other authors featuring vegetated flows in horizontal and rectangular open-channel. The computed results show that the time-averaged streamwise velocity and Reynolds shear stress vertical profiles are properly simulated. The validated approach was applied to simulate compound open-channel flows with submerged vegetated floodplains and compared with data obtained in an experimental facility. The results show that the proposed porous media approach is adequate to simulate flows with submerged vegetation on the floodplains.

Preliminary study for a PWR steam generator with CUPID/MARS multi-scale thermal-hydraulics simulation

For the thermal hydraulics analysis of nuclear reactor components of LWRs (Light Water Reactors) such as reactor vessel, steam generator, containment, a multi-dimensional two-phase flow code, named CUPID, has been being developed. The CUPID code pursues a capability of multi-physics and multi-scale thermal hydraulics analysis. In the present study, multi-scale simulation was performed by coupling with system-scale code, MARS. The coupled code was assessed to visualize the flow behavior of the steam generator of the Advanced Power Reactor (APR1400). The primary side of the steam generator and remaining Reactor Coolant System (RCS) is modeled by MARS and secondary side is by CUPID. For the secondary side simulation by the CUPID part, a porous media approach was adopted to two-fluid model and conductor model to simplify the complicated geometry of the steam generator. In order to obtain a porosity of a given computing cell, a special algorithm was employed to directly calculate volume ratio by mapping the 3D CAD file onto the grid system. Besides, the proper constitutive relationships for U-tubes are considered further. To treat the complex thermo-hydraulic phenomena on the shell side of a steam generator, a set of constitutive models available in the literature for a two-phase flow map, interfacial heat and mass transfer, interfacial drag, wall friction, wall heating, and heat partitioning in flows over tube bundles were applied to close the numerical model. This paper presents the description of the coupling method, porous media approach to simplify the steam generator, and the simulation results using the coupled code.

Unsteady void measurements within debris beds using high speed X-ray tomography

Two-phase flow and boiling within debris beds representing a destroyed reactor core after a severe accident with core fragmentation can be simulated by using the porous media approach. In this approach, a local pressure drop and the heat transfer between the solid debris particles and the two-phase flow is modelled with the help flow-pattern maps, in which the boundaries between bubbly, slug, and annular flow are assumed. In order to support further understanding of these flows we have developed a very fast X-ray measurement device to visualize the 3D-void distribution within particle beds or porous media, which are otherwise un-accessible internally. The experimental setup uses a scanned electron beam directed in circles on a tungsten target to generate the X-rays. The particle bed, which has a diameter of 70mm, is located between this target and a field of 256 X-ray detectors, which are arranged on a circle concentric to the target. The void distribution is reconstructed numerically from the attenuation of signals, which penetrates the particle bed and the two-phase flow inside. A 3D frame rate of up to 1000Hz can be reached. The spatial resolution is such that bubbles with a diameter>1.7mm can be detected. We have investigated two-phase flows air/water through beds of packed plastic spheres (diameter between 3 and 15mm) as well as through plastic beds, which were manufactured using a ‘3D-plotter’. Flow patterns can be individually determined on the basis of empirical criteria. It is confirmed, that the transition between slug and annular flow depends on the air mass flux, but the particle diameter must be considered as an additional parameter.

Seawater intrusion in karstic, coastal aquifers: Current challenges and future scenarios in the Taranto area (southern Italy)

Mediterranean areas are characterized by complex hydrogeological systems, where management of freshwater resources, mostly stored in karstic, coastal aquifers, is necessary and requires the application of numerical tools to detect and prevent deterioration of groundwater, mostly caused by overexploitation.In the Taranto area (southern Italy), the deep, karstic aquifer is the only source of freshwater and satisfies the main human activities. Preserving quantity and quality of this system through management policies is so necessary and such task can be addressed through modeling tools which take into account human impacts and the effects of climate changes.A variable-density flow model was developed with SEAWAT to depict the “current” status of the saltwater intrusion, namely the status simulated over an average hydrogeological year. Considering the goals of this analysis and the scale at which the model was built, the equivalent porous medium approach was adopted to represent the deep aquifer.The effects that different flow boundary conditions along the coast have on the transport model were assessed. Furthermore, salinity stratification occurs within a strip spreading between 4km and 7km from the coast in the deep aquifer. The model predicts a similar phenomenon for some submarine freshwater springs and modeling outcomes were positively compared with measurements found in the literature.Two scenarios were simulated to assess the effects of decreased rainfall and increased pumping on saline intrusion. Major differences in the concentration field with respect to the “current” status were found where the hydraulic conductivity of the deep aquifer is higher and such differences are higher when Dirichlet flow boundary conditions are assigned. Furthermore, the Dirichlet boundary condition along the coast for transport modeling influences the concentration field in different scenarios at shallow depths; as such, concentration values simulated under stressed conditions are lower than those simulated under undisturbed conditions.

Computational fluid dynamics of cerebral aneurysm coiling using high-resolution and high-energy synchrotron X-ray microtomography: comparison with the homogeneous porous medium approach

BackgroundComputational modeling of intracranial aneurysms provides insights into the influence of hemodynamics on aneurysm growth, rupture, and treatment outcome. Standard modeling of coiled aneurysms simplifies the complex geometry of the...

Modeling of heat transfer in a vascular tissue-like medium during an interstitial hyperthermia process

This paper aims to evaluate the role of small vessels in heat transfer mechanisms of a tissue-like medium during local intensive heating processes, for example, an interstitial hyperthermia treatment. To this purpose, a cylindrical tissue with two co- and counter-current vascular networks and a central heat source is introduced. Next, the energy equations of tissue, supply fluid (arterial blood), and return fluid (venous blood) are derived using porous media approach. Then, a 2D computer code is developed to predict the temperature of blood (fluid phase) and tissue (solid phase) by conventional volume averaging method and a more realistic solution method. In latter method, despite the volume averaging the blood of interconnect capillaries is separated from the arterial and venous blood phases. It is found that in addition to blood perfusion rate, the arrangement of vascular network has considerable effects on the pattern and amount of the achieved temperature. In contrast to counter-current network, the co-current network of vessels leads to considerable asymmetric pattern of temperature contours and relocation of heat affected zone along the blood flow direction. However this relocation can be prevented by changing the site of hyperthermia heat source. The results show that the cooling effect of co-current blood vessels during of interstitial heating is more efficient. Despite much anatomical dissimilarities, these findings can be useful in designing of protocols for hyperthermia cancer treatment of living tissue.

Numerical long-term assessment of managed aquifer recharge from a reservoir into a karst aquifer in Jordan

In semi-arid regions with high seasonal variability of water availability, adaptive management strategies and technical measures are required to ensure the sustainable use of water resources. In this study, managed recharge of storm water into a karst aquifer and the water level fluctuations related to pumping in a nearby wellfield were simulated at Wadi Wala, Jordan. We used a numerical equivalent porous medium (EPM) approach with specific adaptations to account for the heterogeneity and anisotropy of the karst aquifer. The model domain was vertically projected along the wadi course, resulting in a 2-dimensional model, and subdivided into hydraulic zones representing the karst-specific flow pattern of fast flow and slow depletion. Results show satisfying agreement of measured and simulated groundwater tables from 2002 to 2012 and predict a lowering of the average groundwater table until 2022 of around 2.7m in the immediate surroundings of the reservoir and an increased depletion towards the wellfield, mainly caused by sedimentation in the reservoir and an associated decrease in infiltration. Abstraction at the wellfield changed considerably over the regarded time period and strongly influences the groundwater fluctuations, which shows the need of improved pumping management and monitoring. The results can serve as a basis for decision makers regarding an optimization of water management at the reservoir and wellfield. Furthermore, the presented numerical approach can be transferred to karst regions with similar physio-geographical conditions to assess managed aquifer recharge.

Numerical investigation of the spatial scale and time dependency of tile drainage contribution to stream flow

Summary Tile drainage systems are pervasive in the Central U.S., significantly altering the hydrologic system. The purpose of this study was to assess the effects of tile drainage systems on streamflow. A physically based coupled hydrologic model was applied to a 45 km 2 agricultural Iowa watershed. Tile drainage was incorporated though an equivalent porous medium approach, calibrated though numerical experimentation. Experimental results indicated that a significant increase in hydraulic conductivity of the equivalent medium layer was needed to achieve agreement in total outflow with an explicit numerical representation of a tiled system. Watershed scale analysis derived the tile drainage contribution to stream flow ( Q T / Q ) from a numerical tracer driven analysis of instream surface water. During precipitation events tile drainage represented 30% of stream flow, whereas during intervals between precipitations events, 61% of stream flow originated from the tile system. A division of event and non-event periods produced strong correlations between Q T / Q and drainage area, positive for events, and negative for non-events. The addition of precipitation into the system acted to saturate near surface soils, increase lateral soil water movement, and dilute the relatively stable instream tile flow. Increased intensity precipitation translated the Q T / Q relationship downward in a consistent manner. In non-event durations, flat upland areas contributed large contributions of tile flow, diluted by larger groundwater (non-tile) contribution to stream flow in the downstream steeper portion of the watershed. Study results provide new insights on the spatiotemporal response of tile drainage to precipitation and contributions of tile drainage to streamflow at a watershed scale, with results having important implications for nitrate transport.

Improved regional groundwater flow modeling using drainage features: a case study of the central northern karst aquifer system of Puerto Rico (USA).

In northern Puerto Rico (USA), subsurface conduit networks with unknown characteristics, and surface features such as springs, rivers, lagoons and wetlands, drain the coastal karst aquifers. In this study, drain lines connecting sinkholes and springs are used to improve the developed regional model by simulating the drainage effects of conduit networks. Implemented in an equivalent porous media (EPM) approach, the model with drains is able to roughly reproduce the spring discharge hydrographs in response to rainfall. Hydraulic conductivities are found to be scale dependent and significantly increase with higher test radius, indicating scale dependency of the EPM approach. Similar to other karst regions in the world, hydraulic gradients are steeper where the transmissivity is lower approaching the coastline. This study enhances current understanding of the complex flow patterns in karst aquifers and suggests that using a drainage feature improves modeling results where available data on conduit characteristics are minimal.

Correlations and optimization of a heat exchanger with offset fins by genetic algorithm combining orthogonal design

In this paper, the study is focused on a double flow plate-fin heat exchanger (PFHE) which heat transfer element is staggered offset fin, and heat transfer model and the energy equations for the structure have been established, seven geometric parameters such as the fin height, fin length and fin wrinkling angle are taken as the decision variables for optimization. A genetic algorithm (GA) combined with orthogonal design is used to search for the optimal overall structure and the correlations about the fin heat transfer factor j and the friction factor f. The maximum total heat transfer rate and the minimum total pressure drop are taken as objective functions in the GA, respectively. Performance of the optimized structure is evaluated and correspondingly the heat transfer and hydrodynamic characteristics of the full-size PFHE are calculated by using a porous media approach. Numerical results show that the total heat transfer rate of the optimized structure is improved about 6.2% comparing with the original design, the total pressure drop decreases by about 40% and the volume can reduce about 2.7%.

Hydrodynamic modelling and characterisation of a shallow fluvial lake: a study on the Superior Lake of Mantua

This paper presents a numerical modelling framework developed to simulate circulations and to generally characterise the hydrodynamics of the Superior Lake of Mantua, a shallow fluvial lake in Northern Italy. Such eutrophied basin is characterised by low winds, reduced discharges during the summer and by the presence of large lotus flower (<em>Nelumbo</em> <em>nucifera</em>) meadows, all contributing to water stagnation. A hydrodynamic numerical model was built to understand how physical drivers shape basic circulation dynamics, selecting appropriate methodologies for the lake. These include a 3D code to reproduce the interaction between wind and through-flowing current, a fetch-dependent wind stress model, a porous media approach for canopy flow resistance and the consideration of wave-current interaction. The model allowed to estimate the circulation modes and water residence time distributions under identified typical ordinary, storm and drought conditions, the hydrodynamic influence of the newly-opened secondary outlet of the lake, the surface wave parameters, their influence on circulations and the bottom stress they originate, and the adaptation time scales of circulations to storm events. Some probable effects of the obtained hydrodynamic characteristics of the Superior Lake of Mantua on its biochemical processes are also introduced.

Simulation and experimental investigation of the wavy fin-and-tube intercooler

In this paper, flow and heat transfer characteristics in the fin-and-tube intercooler were numerically investigated using the FLUENT software by adopting the porous medium approach, which could obtain the distributions, including temperature, pressure and non-uniform, etc. The effects of the air flow rate on the resistance characteristic and the heat transfer performance were analyzed. The simulation results show that the pressure drop and the heat transfer capacity increase with the increase of air flow rate. Simultaneously, the coolant distribution is uniform in the header with the maximum error within±10%. Two kinds of coolant flow schemes have an important influence on heat transfer. Those results also confirm that the higher the heat transfer rate, the lower the inlet coolant temperature is. Finally, comparison results show that the numerical results based on the heat transfer model in porous medium agree well with the measured data based on the engine bench test. The conclusions of this paper are of great significance in the improvement of fin-and-tube intercooler.

Groundwater flow dynamics of weathered hard-rock aquifers under climate-change conditions: an illustrative example of numerical modeling through the equivalent porous media approach in the north-western Pyrenees (France)

A numerical groundwater model of the weathered crystalline aquifer of Ursuya (a major water source for the north-western Pyrenees region, south-western France) has been computed based on monitoring of hydrological, hydrodynamic and meteorological parameters over 3 years. The equivalent porous media model was used to simulate groundwater flow in the different layers of the weathered profile: from surface to depth, the weathered layer (5 · 10−8 ≤ K ≤ 5 · 10−7 m s−1), the transition layer (7 · 10−8 ≤ K ≤ 1 · 10−5 m s−1, the highest values being along major discontinuities), two fissured layers (3.5 · 10−8 ≤ K ≤ 5 · 10−4 m s−1, depending on weathering profile conditions and on the existence of active fractures), and the hard-rock basement simulated with a negligible hydraulic conductivity (K = 1 10 −9 ). Hydrodynamic properties of these five calculation layers demonstrate both the impact of the weathering degree and of the discontinuities on the groundwater flow. The great agreement between simulated and observed hydraulic conditions allowed for validation of the methodology and its proposed use for application on analogous aquifers. With the aim of long-term management of this strategic aquifer, the model was then used to evaluate the impact of climate change on the groundwater resource. The simulations performed according to the most pessimistic climatic scenario until 2050 show a low sensitivity of the aquifer. The decreasing trend of the natural discharge is estimated at about −360 m3 y−1 for recharge decreasing at about −5.6 mm y−1 (0.8 % of annual recharge).

Drought impacts on the fresh water potential of a karst aquifer in Crete, Greece

Malia’s coastal aquifer supplies water for domestic and irrigation purposes most of northern part of Heraklion prefecture (central Crete). The extensive exploitation of groundwater since the late 1960s has resulted in a continual decline in groundwater level and significant degradation in groundwater quality, due to salinity intrusion in the coastal aquifer. Moreover, the aquifer will likely to experience impacts of climate-driven recharge changes in the coming years, with adverse consequences for water supply in the region. A regional groundwater flow model was developed to simulate the existing hydrogeological system, and to evaluate the effects of combined impacts of groundwater exploitation and climate variability in future. The investigation results suggest that the equivalent porous medium (EPM) approach appears reasonable for the karst aquifers on a regional scale, as it is capable to simulate the groundwater flow and the spreading of chloride concentration with sufficient accuracy. However, locally the transport of saline water may depend primarily on the karst conduit network rather than matrix permeability; therefore the point information must be evaluated and not taken as undisputed. Furthermore, the study provides a valuable guidance on predicting the seawater intrusion in aquifers under similar hydrogeological conditions; and offers a considerable issue in management of the groundwater quality deterioration.