Two-dimensional Flow Model Research Articles

Two-dimensional motion equations in water flow zone

The paper studies a two-dimensional water flow from a non-pressure rectangular or round pipe placed into a wide horizontal channel. To simplify the problem, the real three-dimensional flow is modeled as a two-dimensional zone by eliminating the liquid particles’ velocities and accelerations in the direction perpendicular to the flow zone. To describe the water flow motion law, L. Euler’s equations for the ideal fluid are used, taking into account the continuity equations and the Bernoulli equation. The two-dimensional flow models in the spreading zone with the adequacy degree sufficient for practice, describe the movement of water flows arising in the lower road drainage systems races, Liman irrigation systems, small bridges, water volley channels, various culverts and water-crossing facilities. The obtained dependences of the velocity distribution, depth and water flow geometry give an accuracy exceeding that known by the previously used methods both by the velocity values and by the boundary current lines geometry.

A new collision operator for lattice Boltzmann shallow water model: a convergence and stability study

This work presents a new lattice Boltzmann model for steady and unsteady two-dimensional shallow water flows. Compared to previous lattice Boltzmann based shallow water models, the proposed method uses a consistent characteristic speed in the pressure term and in the viscosity. To preserve the isotropy of viscosity, the relaxation rates for the different cumulants have to be decoupled. This is only possible by using multiple relaxation rates. The recovery of the correct viscosity is investigated by a convergence study based on the decay of a Taylor Green Vortex. Results from shallow water models using the proposed collision operator are then compared to those derived from standard BGK approach and from a continuous model.

Numerical analysis on the effects of a submerged bottom-mounted barrier in the head-on collision of two solitary waves

The collision of solitary waves is closely related to many physical problems. In this paper, the effects of a submerged bottom-mounted barrier in the head-on collision of two solitary waves are analyzed using a self-developed two-dimensional two-phase flow model. Advanced Adaptive Mesh Refinement (AMR) grid is adopted to reduce the computational cost. The free surface is captured with the Volume of Fraction (VOF) method combined with Piecewise Linear Interface Calculation (PLIC). The Immersed Boundary (IB) method is used to account for the existence of the barrier. Several benchmark problems including solitary wave propagation, head-on collision of two solitary waves, and solitary wave past a submerged barrier are considered to validate the accuracy of the model. Then the model is utilized to simulate the head-on collision of two solitary waves with the existence of a submerged bottom-mounted barrier. Both the symmetric (two waves with equal amplitudes) and asymmetric (two waves with unequal amplitudes) head-on collisions are investigated. The results with and without the barrier are compared and analyzed in detail. Special attention is paid to the variations of the wave amplitudes and the vortex sheddings.

On the governing equations for horizontal and vertical coupling of one- and two-dimensional open channel flow models

One-dimensional (1D) models of open-channel flow are efficient for simulating in-channel hydrodynamics over long reaches and time periods, but cannot accurately simulate overbank flows that require two-dimensional (2D) models. The derivation and discussion of the behaviour of the coupling terms for horizontal and vertical coupling of the governing equations of 1D and 2D flow are presented here for the first time. Transfer terms for mass and momentum are introduced. Also, for the first time, the quantification of these transfer terms for the case of an experimental meandering channel with overbank flow is presented. For both coupling methods and relatively high overbank flow depth, the advective momentum transfer exceeded the diffusive momentum transfer. The diffusive momentum transfer has similar magnitude between both coupling approaches. The advective momentum transfer was one order of magnitude higher for the horizontal-coupling approach than for the vertical-coupling approach.

Contrasting thinning patterns between lake- and land-terminating glaciers in the Bhutanese Himalaya

Abstract. Despite the importance of glacial lake development in ice dynamics and glacier thinning, in situ and satellite-based measurements from lake-terminating glaciers are sparse in the Bhutanese Himalaya, where a number of proglacial lakes exist. We acquired in situ and satellite-based observations across lake- and land-terminating debris-covered glaciers in the Lunana region, Bhutanese Himalaya. A repeated differential global positioning system survey reveals that thickness change of the debris-covered ablation area of the lake-terminating Lugge Glacier (-4.67±0.07 m a−1) is more than 3 times more negative than that of the land-terminating Thorthormi Glacier (-1.40±0.07 m a−1) for the 2004–2011 period. The surface flow velocities decrease down-glacier along Thorthormi Glacier, whereas they increase from the upper part of the ablation area to the terminus of Lugge Glacier. Numerical experiments using a two-dimensional ice flow model demonstrate that the rapid thinning of Lugge Glacier is driven by both a negative surface mass balance and dynamically induced ice thinning. However, the thinning of Thorthormi Glacier is minimised by a longitudinally compressive flow regime. Multiple supraglacial ponds on Thorthormi Glacier have been expanding since 2000 and have merged into a single proglacial lake, with the glacier terminus detaching from its terminal moraine in 2011. Numerical experiments suggest that the thinning of Thorthormi Glacier will accelerate with continued proglacial lake development.

Kinetic flux vector splitting scheme for solving non-reactive multi-component flows

This paper is about multi-component flow. There is no doubt that multi-component flow has a wide range of applications, specially in aerospace it plays a vital role during reentry of space ship into earth's atmosphere thats why it cannot be neglected for a proper vehicle design. In this paper one- and two-dimensional homogenous multi-component flow models are numerically investigated by using a high resolution splitting scheme and this scheme is known as Kinetic Flux Vector Splitting scheme. This scheme preserves positivity conditions and resolves shocks, rarefaction and contact discontinuity. The scheme is based on splitting of flux functions. Moreover Runge-Kutta time stepping technique with MUSCL-type initial reconstruction is used to guarantee higher order accurate solution. This work is first done by Qamar and Warnecke (2004) for the homogeneous multi-component flow equations using central scheme, here we investigate the same work using kinetic flux vector splitting scheme (KFVS) and compared the results with central scheme to verify the efficiency of studied scheme.

Enhancing the Flow Characteristics in a Branching Channel Based on a Two-Dimensional Depth-Averaged Flow Model

Natural rivers have many branching junctions. The flow in branching junctions is complex, owing to significant changes associated with flow dynamics and sediment transport that result in erosion and deposition problems. A branching channel of the Tigris River in Missan, Iraq, was selected for investigation of the scouring and deposition zones. A two-dimensional (2D) numerical model was used to simulate the hydro-morphodynamics in the branching channel, where hypothetical vanes as control structures were included at the junction to control the scouring and deposition zones. The simulation results suggest the most effective location, dimension, and angle of the introduced vanes. For the studied junction, controlling morphological features was achieved by introducing a single vane with an inclination angle of 90° on the flow direction of the Tigris River. The most effective location of the introduced vane was the location that caused considerable enhancement in the flow depth and velocity distribution.

Quantifying the restoration success of wood introductions to increase coho salmon winter habitat

Abstract. Large wood (LW) addition is often part of fish habitat restoration projects. However, there is limited information about the spatial–temporal variability in hydraulic changes after LW additions. We investigated reach-scale hydraulic changes triggered after the addition of LW that are relevant to juvenile coho salmon survival. We used Nays2DH, an unsteady two-dimensional flow model, to quantify the patterns and magnitudes of changes of stream velocity and shear stress in three alluvial gravel reaches. The study sites are located in low-gradient reaches draining 5 to 16 km2 in the Oregon Coast Range. Survivable habitat was characterized in terms of critical swim speed for juvenile coho and bed stability considering the critical shear stress required to mobilize the median bed particle size. Model predictions indicated that survivable habitat during bankfull conditions, measured as the area with velocity below the critical swim speed for juvenile coho, increased by 95 %–113 % after the LW restoration. Bed stability also increased between 86 % and 128 % considering the shear stress required to mobilize the median bed particle size. Model predictions indicated more habitat created in the larger site; however, considering that wood would move more frequently in this site there appears to be a trade-off between the timing and the resilience of restoration benefits. Overall, this study quantifies how the addition of LW potentially changes stream hydraulics to provide a net benefit to juvenile salmonid habitat. Our findings are applicable to stream restoration efforts throughout the Pacific Northwest.

Mapping geothermal heat flux using permafrost thickness constrained by airborne electromagnetic surveys on the western coast of Ross Island, Antarctica

ABSTRACTPermafrost is ubiquitous at high latitudes, and its thickness is controlled by important local factors like geothermal flux, ground surface temperature and thermal properties of the subsurface. We use airborne transient electromagnetic resistivity measurements to determine permafrost thickness on the coast of Ross Island, Antarctica, which contains the active volcano Mt Erebus. Here, resistivity data clearly distinguish resistive permafrost from the electrically conductive fluid-saturated materials underlying it. For our study, we define permafrost as frozen material with a resistivity > 100 Ω·m; more conductive material contains a significant fraction of water or (more likely) brine. We observe that permafrost is very thin near the coast and thickens within several hundred metres inland to reach depths that are typically within the range of 300–400 m. We attribute the sharp near-shore increase in permafrost thickness to lateral heat conduction from the relatively warm ocean, possibly combined with seawater infiltration into the near-shore permafrost. We validate this result with a two-dimensional heat flow model and conclude that away from the thermal influence of the ocean, the local geothermal gradient and heat flux are about 45 ± 5 °C/km and 90 ± 13 mW/m2, respectively. These values are in line with published estimates in the vicinity of Mt Erebus and within the actively extending Terror Rift, but do not reflect a strong heat flow anomaly from volcanic activity of Mt Erebus. Measurements made previously in the McMurdo Dry Valleys, on the other side of McMurdo Sound, tend to be a few dozens of mW/m2 lower, likely reflecting its different tectonic setting on the uplifted rift shoulder of Transantarctic Mountains. Our study demonstrates a new approach towards constraining geothermal flux in polar regions using airborne electromagnetic (AEM) data that can be relatively efficiently collected on regional scales where ice coverage does not exceed the penetration limits of the AEM device, which for the device used is ∼ 500 m under the favourable conditions in the study area.

Optimisation of tidal turbine array layouts whilst limiting their hydro-environmental impact

The economic viability of tidal energy projects will likely require large-scale deployment, with tens, or even hundreds, of turbines positioned in an array. There is limited published research available on the viability of large-scale deployments, which will depend on both the expected energy yield and potential adverse hydro-environmental impacts. This leads to the question of how best to position turbines in large-scale arrays for maximum energy capture with minimal associated hydro-environmental impacts. The primary aim of this research was the further development of an existing two-dimensional tidal flow model for optimising tidal turbine arrays relative to both power output and potential hydro-environmental impacts. Turbine impacts are simulated using a momentum sink approach and an optimisation algorithm was implemented, which determines an optimal array configuration for maximum energy capture, whilst employing spatial and environmental impact constraints. Application of the developed model to an idealised test case demonstrated that a staggered array is optimal, if one considers maximising power capture alone, while a fence layout was optimal, when considering both power output and associated impacts. In both the scenarios, the optimised configurations produced higher efficiencies than symmetrical inline arrays. To demonstrate the model’s applicability to a real tidal environment, it was applied to a case study site; the Shannon Estuary, along the West Coast of Ireland. To the authors’ knowledge, this is the first automated array optimisation model to incorporate hydro-environmental impact constraints with the aim of determining specific optimised array configurations with quantifiable efficiencies. The approach could be extremely useful for determining the economic viability of proposed arrays, enabling determination of ‘environmentally acceptable’ levels of tidal energy extraction, and thereby allowing the completion of realistic and accurate early stage cost–benefit analyses for tidal energy projects. The model is therefore, potentially, a very valuable tool for tidal energy researchers, developers and planners.

River Model Calibration Based on Design of Experiments Theory. A Case Study: Meta River, Colombia

Numerical models are important tools for analyzing and solving water resources problems; however, a model’s reliability heavily depends on its calibration. This paper presents a method based on Design of Experiments theory for calibrating numerical models of rivers by considering the interaction between different calibration parameters, identifying the most sensitive parameters and finding a value or a range of values for which the calibration parameters produces an adequate performance of the model in terms of accuracy. The method consists of a systematic process for assessing the qualitative and quantitative performance of a hydromorphological numeric model. A 75 km reach of the Meta River, in Colombia, was used as case study for validating the method. The modeling was conducted by using the software package MIKE-21C, a two-dimensional flow model. The calibration is assessed by means of an Overall Weighted Indicator, based on the coefficient of determination of the calibration parameters and within a range from 0 to 1. For the case study, the most significant calibration parameters were the sediment transport equation, the riverbed load factor and the suspended load factor. The optimal calibration produced an Overall Weighted Indicator equal to 0.857. The method can be applied to any type of morphological models.

A prediction method for the performance of a low-recoil gun with front nozzle

Abstract One of the greatest challenges in the design of a gun is to balance muzzle velocity and recoil, especially for guns on aircrafts and deployable vehicles. To resolve the conflict between gun power and recoil force, a concept of rarefaction wave gun (RAVEN) was proposed to significantly reduce the weapon recoil and the heat in barrel, while minimally reducing the muzzle velocity. The main principle of RAVEN is that the rarefaction wave will not reach the projectile base until the muzzle by delaying the venting time of an expansion nozzle at the breech. Developed on the RAVEN principle, the purpose of this paper is to provide an engineering method for predicting the performance of a low-recoil gun with front nozzle. First, a two-dimensional two-phase flow model of interior ballistic during the RAVEN firing cycle was established. Numerical simulation results were compared with the published data to validate the reliability and accuracy. Next, the effects of the vent opening times and locations were investigated to determine the influence rules on the performance of the RAVEN with front nozzle. Then according to the results above, simple nonlinear fitting formulas were provided to explain how the muzzle velocity and the recoil force change with the vent opening time and location. Finally, a better vent venting opening time corresponding to the vent location was proposed. The findings should make an important contribution to the field of engineering applications of the RAVEN.

Assessment of the Safe Isolation of Solid Radwaste in Subsurface Repositories

A calculation of the removal of radionuclides by groundwaters from a subsurface repository of solid low-level waste was performed. A two-dimensional model of the groundwater flow and advective-dispersive transport of radionuclides in a vertical section of a subsurface aquifer, along which radionuclide-contaminated groundwater moves from the repository to an open body of water, was studied. Data from many years of experimentation on the leaching of cemented low-level waste were used in the calculations. It was shown that the rocks of the aquifer effectively retain medium half-life radionuclides (60Co, 137Cs, 90Sr). An engineered barrier – a 0.7 m thick layer of consolidated bentonite clay – can secure the safety of a repository for long-lived transuranium radionuclides (235U, 239Pu) for 20000 years.

Two-dimensional two-fluid model for air-oil wavy flow in horizontal tube

This study concerns the development of a two-dimensional two-fluid model for wavy flows in horizontal tubes. To deal with the curved walls of the liquid and gas phases and the gas-liquid interface simultaneously, the bipolar coordinate system was used. Experiments on air-oil mixture flow in horizontal tubes with diameters of 20 and 40 mm were conducted to observe wavy flow patterns accompanying the two-dimensional (2D) and Kelvin-Helmholtz (KH) waves and to measure the pressure gradient under different flow conditions. Two different previous correlations for the interfacial friction factor were employed in the model for predicting the wavy flows with 2D and KH waves. Predictions of the model of the liquid film height, the average values of wall shear stresses of each phase, and the average interfacial shear stress were compared for different diameters and different superficial gas and liquid Reynolds numbers. Also presented are detailed predictions of the model for four different flow conditions, including the local values of interfacial shear stress, wall shear stress of the liquid phase, interfacial friction factor, liquid film height, and two-dimensional velocity distribution in the liquid phase at the cross-section of the tube.

Simple solutions for square and rectangular cofferdam seepage problems

Cofferdams are widely used temporary structures at construction sites. Two of the main parameters required in designing a cofferdam are the flow rate and exit hydraulic gradient at the bottom of the excavation. Commonly, these two parameters are evaluated by using two-dimensional (2D) ground water flow models. However, when the flow pattern is three-dimensional (3D), such as flow into the square or rectangular cofferdams, predictions by the 2D models underestimate the flow rate and exit gradients considerably. Therefore, it is necessary to incorporate the 3D flow effect through a correction factor. It is shown that treating a square cofferdam as a circular one of the same width or treating a rectangular cofferdam as a 2D double-walled cofferdam significantly underestimates the flow rate. In this study, simple expressions are developed and validated for accurately estimating the flow rate and exit hydraulic gradient values of square and rectangular cofferdams, based on hundreds of finite element simulations in both 2D and 3D. It is suggested that the expressions given in the Canadian foundation engineering manual be improved.

Study on the Assessment Method of the Impact on Hydrological Safety of Riverside Pit-Ponds along a Dike

Riverside pit-ponds are one of the hidden dangers of flood control project safety. At present, the safety evaluation of riverside pit-ponds is limited to the seepage and stable safety review of the dam, and the impact of the pit on the river flow is not considered. In this paper, a two-dimensional mathematical model of flow is established. Pressure correction method is used to solve the pressure-velocity coupling. Topographic cutting method is used to deal with the dynamic boundary problem. The model grid of the pit-ponds area is encrypted. The accuracy of the model in the analysis of river hydrodynamics is verified by an example. The model is applied to the evaluation of the impact of the pit-ponds on river flooding. Taking some riverside pit-ponds of the Yellow River as an example, the river water level, velocity, and flow in the present condition and the backfill condition are simulated by the model. The results show that the existence of these riverside pit-ponds only affects the hydrological features of regions around the pit-ponds, and the impact is too insignificant to threaten the hydrological safety. Through the hydrological safety assessment of the project, it is shown that the combination of the two-dimensional flow mathematical model with seepage, anti-sliding, and seismic safety review can comprehensively assess the hydrological safety of dike engineering.

Numerical simulation of sand transfer in wind storm using the Eulerian-Lagrangian two-phase flow model

In this paper a two-dimensional gas-solid flow model is used to investigate the sand particles carrying velocity of the Iran eastern desert area around the railway track as a case study. Reynolds-averaged Navier-Stokes (RANS) equations and Discrete Phase Method (DPM) are used to simulate the characteristic movement of sand particles in wind flow. A random sample is gathered from the sand near the railway in Iran deserts. The sample is classified based on weight and diameter according to AASHTOO T27 and sand distribution is determined. Using simulations, the carrying velocity of sand in each category in wind storm is determined. Finally, the sand distribution of the sample is imported to the model by the Rosin-Rummler dissipation model. The behavior of sand particles in storm considering wind blowing scheme of desert is studied parametrically. The results can be used for estimating the sand mitigation of a special desert and land desertification control around railway tracks.

Numerical and experimental study on the risk of paddy field damage due to river bank breach during serious floods

In Japan, paddy fields located adjacent to rivers are a familiar landscape in rural areas, and they are divided from rivers by soil banks. Soil banks are easily breached by overtopping in floods. Previously, although soil banks were often breached in many locations, inundation in paddy fields was not necessarily a serious disaster, but it was rather positively accepted as a nutrient supplier to paddy fields. In addition, bank breaches at several sites decreased the flood discharge in a river and disasters were distributed into smaller scales. Over time, land use has changed from paddy fields to residential areas where inundation is obviously a disaster, and thus, banks have been improved to be safer against higher flood stages than what they used to be. Recently, more severe rainfall due to climate change and subsequent flooding has happened, and more serious damage has been brought by limited bank failure. As a result, limited bank breaches occur as concentrated drastic events. The damage is brought about not only by inundation, but also and more seriously by sediment balance in paddy fields: overflow from a river brings a larger amount of sediments into paddy fields such that rice plants are buried by them; in other cases, soil suitable for rice paddies as well as rice plants themselves is washed away by rapid flow from the river forming deep scour holes. The above-mentioned phenomena can be understood by small-scale laboratory experiments and numerical analysis by applying a two-dimensional hydraulic model for depth-averaged flow with a proper sediment transport model for the whole river-bank-paddy area. By using an analytical model, several discussions become possible: For example, locations of retention ponds can be designed to avoid bank breaches accompanying scouring and sedimentation during severe floods.

Simulation of flow and soot particle distribution in wall-flow DPF based on lattice Boltzmann method

A two-dimensional mesoscopic gas-solid two-phase flow model has been developed to investigate the flow and soot loading in the micro-channel of diesel particulate filters. Soot particle size examined is in the range of 10 nm–1 µm. The flow is solved by an incompressible lattice Boltzmann model and the transport of solid particles is described by the cell automation probabilistic model. The lattice Boltzmann-cell automation probabilistic model (LB-CA model) is validated with the results of previous studies. The effects of different upstream velocities on the flow field in channels are investigated. The distribution and deposition of soot particles with different sizes in clean channels are simulated based on the LB-CA method and the LB-Lagrangian method respectively. The effects of deposited soot particles on flow field are evaluated in real soot particle capture process. The results show that the distributions of velocity field and pressure field in the channel are significantly affected by the upstream velocity. Compared with the effect of the particle size, the upstream velocity is more influential on the particle deposition distributions. The profiles of deposition distribution from the LB-CA method are in close agreement with those from the LB-Lagrangian method. The deposition distributions of particles with different diameters at the top of the porous wall are similar to the distributions of wall velocity along the channel length. Generally, the deposited soot particles increase the axial pressure and decrease the axial velocity in the inlet channel. The evolution trend of the areas where wall velocity undergoes changes is consistent with that of the solid nodes made of the captured soot particles.

Modelling and optimisation of water management in sloping coastal aquifers with seepage, extraction and recharge

We consider the management of sloping, long and thin, coastal aquifers. We first develop a simple mathematical model, based on Darcy flow for porous media, which gives the water table height, and the flow velocity as a function of the underground seepage rate, the recharge rates and the extraction rates, neglecting sea water intrusion. We then validate the model with recent data from the Germasogeia aquifer which caters for most of the water demand in the area of Limassol, Cyprus. The data is provided over a three-year period by the Cyprus Water Development Department (WDD), the governmental department managing the aquifer. Three different models of the recharge sources have been considered and it was found that Gaussian sources give the closest agreement with data. Furthermore, based on our model, we subsequently develop an optimised recharge strategy and identify the optimal recharge rates for a desired extracted water volume while the water table height is maintained at the acceptable level. We study several scenarios of practical interest and we find that we can achieve considerable water savings, compared to the current empirical strategy followed by WDD. Additionally, we model the transport of pollutants in the aquifer in the case of accidental leakage, using an advection-diffusion equation and the concentration is determined in the aquifer for an ongoing contamination and two pulsed contaminations (pulse duration 1 day and 30 days, respectively). We find that in the case of an undetected and unhindered contamination (worst case scenario) the aquifer would get polluted in about three years. Also, we find that double recharge rates flush the pollutant out of the aquifer faster. Finally, to incorporate the possibility of sea water intrusion, which can render aquifers unusable, we develop a new, transient two-dimensional model of groundwater flow based on the Darcy-Brinkman equations, and determine the position of the water table and the seawater-freshwater interface for conditions of drought, moderate rainfall and flooding. The validation of the new seawater intrusion modelling approach has been carried out via comparison with a widely-accepted code.