Exit Boundary Conditions Research Articles

An Optimal Numerical Strategy for Intake in Crosswind Conditions

Abstract Crosswind can reduce the operability of an aeroengine significantly at static or near static operating conditions. Computational fluid dynamics predictions of the flow at crosswind conditions will play an important part in future designs, however, accurate numerical predictions of the flow within the intake remain challenging even for simulations of cases with intake only. The main objective of this paper is to demonstrate the importance of numerical setup and to determine an optimal computational model for crosswind investigations that can be used by other researchers. By considering the flow to be inherently unsteady, the influence of inlet and exit boundary conditions, and grid sensitivity is studied by using unsteady Reynolds-average Navier–Stokes (URANS) simulations. Numerical predictions of the time-averaged intake pressure recovery (IPR) and the motion of the vortex on the ground are compared against the existing experimental data. The results show that for an intake under crosswind, the ground vortex that forms under the intake and the in-duct separation, when present, exhibit unsteady behavior that become stronger as the crosswind velocity is increased. The steady-state simulation is only representative at lower crosswinds. The intake flow separation and ground vortex predictions are influenced by the inlet boundary layer profiles. Moreover, acoustic reflection was observed at the intake exit boundary which propagates upstream, creating artificial unsteady frequencies in IPR. The reflection is generated from the use of uniform boundary conditions at the intake exit and is not dissipated in the grid due to the long wavelength; this can be mitigated by using a choked nozzle at the intake exit. Acoustic reflection was also observed at the far-field exit boundary. These reflections are caused from interaction of trailing vortex and far-field boundary.

Theoretical and numerical study of contaminant transport in clayey barriers using a revised numerical model considering the dependency of membrane efficiency and hydraulic conductivity on solute concentration

Solid waste is often buried in landfills isolated with a bentonite-based clay barrier to guarantee the high quality of groundwater. As the efficiency of clay barriers is highly dependent on solute concentration, this study aims to modify membrane efficiency, effective diffusion, and hydraulic conductivity of bentonite-based clayey barriers exposed to saline environments for numerical investigation of solute transport in such barriers. Therefore, the theoretical equations were modified as a function of solute concentration instead of constant values. First, a model was extended for membrane efficiency as a function of void ratio and solute concentration. Second, an apparent tortuosity model was developed as a function of porosity and membrane efficiency to adjust the effective diffusion coefficient. Moreover, a recently developed semi-empirical solute-dependent hydraulic conductivity model was employed, which is dependent on solute concentration, liquid limit, and void ratio of the clayey barrier. Afterward, four approaches for applying these coefficients were defined as either “variable” or “constant” functions in ten numerical scenarios using COMSOL Multiphysics. The results reveal that “variable” membrane efficiency affects the outcomes in lower concentrations, while “variable” hydraulic conductivity is more influential in the domain of higher concentrations. Although all approaches converge to the same ultimate distribution of solute concentration using the Neumann exit boundary condition, the choice of different approaches clearly affects the ultimate state for the Dirichlet exit boundary condition. As the thickness of the barrier increases, the ultimate state is reached later, and choosing the approach to apply coefficients is more influential. Decreasing the hydraulic gradient postpones the solute breakthrough in the barrier, and picking the variable coefficients is more crucial in higher hydraulic gradients.

An analytic solution for Counter-Current spontaneous imbibition in porous media by the perturbation method

Following primary production of hydrocarbon from naturally fractured reservoirs, secondary recovery by waterflooding relies on Spontaneous Imbibition (SI) as the primary mechanism for oil expulsion to the fracture network, where it can be easily transported to neighboring production wells. Thus, a more complete understanding of this phenomenon is warranted and essential for process improvement. The imbibition process, taking advantage of inherent preferential affinity for water contact over oil of high energy solids, is the rate determining step in recovery and can proceed in either co-current or counter-current fashion, depending upon entrance and exit boundary conditions. Due to the prominence of linear flow normal to extensive planar fracture faces, the phenomena can be largely described as one-dimensional displacement. In this study, the nonlinear one-dimensional diffusivity equation, derived by combining Darcy’s law for both wetting and non-wetting phases with the mass conservation equation, is solved for counter-current spontaneous imbibition using a direct regular perturbation scheme. Saturation and phase pressure profiles in time and space were found to agree with literature solutions. In its analytic formulation, the method constitutes a simpler, more accurate, and more direct way to compute spontaneous imbibition performance than previously available. We claim generality with regard to functional forms for relative permeability and capillary pressure and applicability over the entire range of wettability, provided these effects are reflected in the parameterization of capillary pressure and saturation normalization. In particular, the present method avoids the difficulty in solving nonlinear integral equations. Instead, we reduce computations to a set of simple numerical integrations of the diffusion coefficient. Such a streamlined solution method can more easily provide a compute engine for inverse modeling or optimization schemes to recovery rock and fluid properties from displacement experiments. The solution method is benchmarked against oil–water and air–water solutions by alternative techniques and experimental data. The case of spontaneous imbibition into dry diatomite represents extreme contrast in phase mobility and a rigorous test of the perturbation method as an easier and more direct way to model 1D SI. Following method construction and benchmarking of the new streamlined countercurrent spontaneous imbibition solution method, a subsequent parametric study contributes to a greater understanding of controlling factors in fracture-matrix exchange in porous media.

Numerical Simulation on Air-Liquid Transient Flow and Regression Model on Air-Liquid Ratio of Air Induction Nozzle

Air induction nozzle (AIN) has a special Venturi structure that has been widely used in the field of reducing the probability of drift of pesticide droplets and realizing precise application. The present research mainly adopts the method of comparative test and analyzes the difference between AIN and standard fan nozzle. However, the research on internal flow characteristics and air–liquid ratio (ALR) of AIN is very limited. In order to detect the air-liquid transient flow distribution and the influence of the geometric parameter structure of Venturi on the air–liquid ratio in the air induction nozzle, numerical simulation and air-liquid ratio prediction model of AIN combined with TD (Turbo Drop series) type Venturi tubes and ST110 (standard nozzle series) type fan nozzles are used. Based on the VOF (volume of fluid) model and Realizable k-ε turbulence control method, the TD-ST combined AIN is simulated numerically using open input and exit boundary conditions. The results show that the transient flow characteristic of the combined AIN is determined by the geometric structure of the Venturi tube, and the internal velocity and pressure change significantly at the Venturi angle. Under the same ST110 fan nozzle, the size of the larger TD Venturi tube will decrease the air phase content in the air–liquid flow. TD03-ST06 combined AIN has a maximum volume flow of 0.0092 (L/min) under 0.6 MPa. The air–liquid ratio regression model is established by designing the intake volume measurement system. According to this model, the influence law of tube size and spray parameters on the air–liquid ratio can be clarified. After variance analysis, it is proved that this model is suitable for air–liquid ratio prediction of TD-ST combined AIN. This study clarifies the air–liquid coupling law inside AIN and provides some reference for the quantitative analysis of the relationship between the geometric parameters, spray parameters, and the air–liquid ratio.

Effect of Outlet Boundary Condition on the Acoustic Modeshape and Flame Dynamics of a Partially Premixed Swirl Stabilized Combustor

Abstract Industrial gas turbines commonly use lean premixed swirl stabilized combustors that are prone to thermo-acoustic instabilities. Combustor testing involves several steps ranging from atmospheric to high-pressure conditions. An open outlet boundary condition is maintained for atmospheric tests commonly, whereas high-pressure testing involves complex exit boundary conditions, which change the reflection coefficient and can affect the nature of instability. Current work aims at studying how the change in outlet boundary affects the nature of instability due to changes in the exit reflection coefficient and acoustic mode shape inside the combustor. A laboratory-scale industrial swirl burner that uses partially premixed methane and air at atmospheric conditions is analyzed for this purpose. A constant area contraction ratio of 6.5:1 is maintained at the exit of the combustor while varying the inlet Reynolds number at a constant global equivalence ratio. Flame dynamics based on conditional phase averaged OH* chemiluminescence images and spatial Rayleigh index maps were used to compare different flow rate and exit boundary cases. The outlet contraction affects both the frequency and amplitude of the dominant thermoacoustic mode. The orifice plate at the exit reduces the outlet reflection coefficient leading to a change in acoustic mode shape inside the combustor. Overall, the instability amplitude is reduced considerably for cases with an orifice plates at the exit boundary compared to open exit boundary cases. The results show the importance of defining outlet boundary conditions as a parameter in combustion instability studies. Care should be taken while comparing and interpreting results from different facilities where outlet boundary condition is different.

Extension of the boundary integral method for different boundary conditions in steady-state Stokes flows

PurposeThe boundary integral method (BIM) provides unparalleled computational efficiency for solving problems wherever it is applicable. For Stokes flows, the BIM in its current form can only be applied to a limited class of problems that generally comprises boundaries with either specified velocity or stress. This study aims to radically extend the applicability by developing a general method within the BIM framework that can handle periodic, symmetry, zero normal-velocity gradient and the specified pressure boundary conditions. This study is limited in scope to steady-state flows.Design/methodology/approachThe proposed method introduces a set of points near the boundary for the symmetry, zero normal-velocity gradient and specified pressure boundary conditions. The formulation for the first two boundary conditions use a spatial discretization procedure within the BIM framework to arrive at a set of equations for the unknowns. The specified pressure boundary condition warrants the decomposition of the unknown traction term into simpler components before the discretization procedure can be executed. Though the new methodology is illustrated in detail for two-dimensional rectangular domains, it can be generalized to more complex three-dimensional cases. This will be the subject for future investigations.FindingsThe current endeavor has successfully demonstrated the incorporation of the above boundary conditions through simple Stokes flow problems like plane channel flow, flow through ribbed duct and plane wall jet. The predicted results matched adequately with either analytical solutions or with available literature data.Originality/valueTo the best of the author’s knowledge, this is the first time that the exit boundary conditions like zero normal-velocity gradient and specified pressure have been formulated within the BIM for Stokes flows. These boundary conditions are extremely powerful and the current research initiative has the potential to dramatically increase the range of applicability of the BIM for Stokes flow simulations.

PERSONALIZED FLOW DIVISION METHOD BASED ON THE LEFT-RIGHT CORONARY CROSS-SECTIONAL AREA

This paper proposes a personalized method to estimate blood flow distribution based on the cross-sectional area of the left-right coronary artery openings. According to the cross-sectional area of the left-right coronary artery in 30 cases, a personalized flow distribution model was derived. A 0D/3D geometric multiscale model was used for the numerical simulation of FFR. To evaluate the accuracy of the cross-sectional area method, invasive FFR was used as the standard. The diagnostic efficiency of the proposed method was verified through the simulation results of the volume and the fixed ratio methods. The flow of the left-right coronary artery was proportional to the 3/4 power of the cross-sectional area. The 95% LOA between the cross-sectional area method, volume method, fixed ratio method and FFR were [Formula: see text]0.06 ([[Formula: see text]0.22, 0.10]), [Formula: see text]0.03 ([[Formula: see text]0.35, 0.28]), and [Formula: see text]0.05 ([[Formula: see text]0.30, 0.20]), the accuracy values were 94.44%, 77.78%, and 77.78%, respectively. Flow distribution based on the cross-sectional area represents the supply and demand relationship of the myocardium. The flow of the left-right coronary arteries is proportional to the 3/4 exponent of the cross-sectional area, which affects the accuracy of FFRCT by affecting the exit boundary conditions of the 0D/3D model.

Impact of coronary bifurcated vessels flow-diameter scaling laws on fractional flow reserve based on computed tomography images (FFRCT).

To explore the influence of the blood flow-diameter scaling laws of $ \mathrm{Q}\mathrm{\alpha }{\mathrm{D}}^{3} $, $ \mathrm{Q}\mathrm{\alpha }{\mathrm{D}}^{2.7} $ and $ \text{Q}\alpha \text{D}{}^{7}\!\!\diagup\!\!{}_{3}\; $ on the numerical simulation of fraction flow reserve based on CTA images and to find the optimal exponents. 1) 26 patients with coronary artery disease were screened according to the inclusion criteria; 2) Microcirculation resistance (Rm) was calculated under the 3, 2.7 and 7/3 power of the flow-diameter scaling law, which were recorded as 3Rm, 2.7Rm and 7/3Rm, respectively; 3) 3Rm, 2.7Rm and 7/3Rm were used as exit boundary conditions to simulate FFRCT, quoted as 3FFRCT, 2.7FFRCT and 7/3FFRCT, respectively; 4) The correlation and diagnostic performance between three kinds of FFRCT and FFR were analyzed. The p-values of comparing 3Rm, 2.7Rm and 7/3Rm with FFR were 0.004, 0.005 and 0.010, respectively; the r value between 7/3FFRCT and FFR (0.96) was better than that of 3FFRCT (0.95) and 2.7FFRCT (0.95); the 95% LoA between 7/3FFRCT and FFR (-0.08~0.11) was smaller than that of 3FFRCT (-0.10~0.12) and 2.7FFRCT (-0.09~0.11); the AUC and accuracy of 7/3FFRCT [0.962 (0.805-0.999), 96.15%] were the same as those of 2.7FFRCT [0.962 (0.805-0.999), 96.15%] and better than those of 3FFRCT [0.944 (0.777-0.996), 92.3%]. The prediction threshold of 7/3FFRCT (0.791) was closer to 0.8 than that of 3FFRCT (0.816) and 2.7FFRCT (0.787). The blood flow-diameter scaling law affects the FFRCT simulation by influencing the exit boundary condition Rm of the calculation. With $ Q\alpha D{}^{7}\!\!\diagup\!\!{}_{3}\; $, FFRCT had the highest diagnostic performance. The blood flow-diameter scaling law provides theoretical support for the blood flow distribution in the bifurcated vessel and improves the FFRCT model.

Modeling Vapor Migration for Estimating the Time to Reach Steady State Conditions

AbstractThe design and planning of soil vapor sampling for vapor intrusion assessment require an estimate of the time for vapor migration from the contamination source to reach steady state prior to vapor sampling and analysis for volatile organic compounds (VOCs). This study presents the model derivation, analytical solutions, as well as the assumptions and limitations of a one‐dimensional VOC vapor transport model based on diffusion in porous media and equilibrium partitioning of VOCs in solid, aqueous, and vapor phases. The model assumes a finite domain with boundary conditions that represent the scenarios of vapor migration in the real environment. The derivation of the conceptual model is presented along with its practical use and implications as illustrated through case examples. Consideration of the upper (or exit) boundary condition along with the distance between the source and the applicable boundary, rather than the distance from the source to the measurement point, are shown to be critical in the time estimates as compared to an expression typically used and cited in guidance documents. The study reveals the importance of defining a conceptual model and relevant boundaries in assessing near steady state conditions, and suggests a tiered approach in refining the estimate with increasing level of effort for practical applications in vapor assessment.

An analytical model for one-dimensional diffusion of degradable contaminant through a composite geomembrane cut-off wall

A one-dimensional analytical model is proposed to analyze contaminant diffusion through a composite geomembrane cut-off wall (CGCW) composed of a geomembrane (GMB) and a bentonite cut-off wall (BCW). The model considers degradation process of contaminant and time-dependent inlet boundary condition which are common in engineering practices. Moreover, two limiting scenarios of the exit boundary condition (EBC) of CGCW for field conditions are taken into account, including the flushing and non-advective semi-infinite aquifer EBCs. The influence of boundary conditions and performance of CGCW are comprehensively investigated. The results show that the upper and lower limits of the mass flux of the exit face of CGCW can be obtained by the models with flushing EBC and the model with non-advective semi-infinite aquifer EBC, respectively. In addition, degradation has substantial influence on the contaminant migration, and smaller half-life in BCW results in smaller contaminant leakage. The performance of CGCW can be improved by embedding GMB at a proper location which is related to the type of contaminant and EBC. Furthermore, thickening HDPE GMB or adopting a coextruded EVOH GMB is efficient to improve the performance of CGCW. The present model can be used as an applicable tool for rational design of CGCW.

The effect of hydrogen addition on the amplitude and harmonic response of azimuthal instabilities in a pressurized annular combustor

The present work introduces an annular combustion chamber operated at intermediate pressures. The combustor is operated with CH4-H2 blends leading to a variety of azimuthal combustion instabilities. The influence of the hydrogen content, the air mass flow rate and the equivalence ratio on the instabilities is investigated over a wide range of operating conditions with mean chamber pressures from 1.5 to 3.3 bar. This leads to a range of exit boundary conditions, from partially to fully reflecting. It is found that pure methane and methane-hydrogen mixtures with low hydrogen contents result in stable combustion. However, when the hydrogen content reaches 25% by volume high-amplitude instabilities are excited, which exhibit higher order harmonics with significant pressure amplitude contributions. Such harmonic response was not previously observed in atmospheric annular combustors. The amplitudes decrease slightly when the H2 content is increased further. The harmonic response is found to be amplitude dependent with fewer significant harmonic contributions occurring at low-amplitudes and a cut-on amplitude of the fundamental mode at which higher harmonics become significant. The interaction between the harmonic components of the pressure amplitudes is shown to follow a quadratic relationship. The modal response was analyzed and it was found that all high-amplitude instabilities feature clockwise spinning modes whereas lower-amplitude instabilities feature counter clockwise spinning modes. Finally, a low- and high-amplitude case were investigated in detail and phase-averaged images are discussed. The low-amplitude instabilities result in flame dynamics similar to those observed in atmospheric combustors previously whereas the high-amplitude instabilities exhibit large oscillations in the flame height and intensity. A characterization of the boundary conditions is also provided for numerical simulations which includes temperature measurements, acoustic characterization and cold flow velocity profiles.

A one-dimensional semi-implicit finite volume modeling of non-inertia wave through rockfill dams

Abstract For hydraulic routing through coarse rockfill dams, there is still debate on whether the inertia terms might be neglected as a result of the drag force generated by the rock materials. In this study, a one-dimensional unsteady model for flow-through rockfill dams is built. For this purpose, inertia terms of Saint–Venant equations are disregarded. A semi-implicit scheme adopted for linearizing the nonlinear friction term within the time integration satisfies the Courant–Friedrich–Lewy stability criterion. The most challenging issue in the modeling of flows through rockfill dams is the appropriate definition of boundary conditions at the dam's exit zone. In addition to the analysis of different exit boundary conditions proposed in the literature, a Neumann-type boundary condition suitable for the non-inertia wave equation is also employed to estimate the exit boundary condition. This procedure is basically in appreciation of the nonlinear behavior of the water surface closer to the exit boundary. Due to the existence of the sloping edges in the trapezoidal-shaped dam, an effective length is considered for the solution domain. Finally, the model is compared with observed data and a dynamic wave model. A very good match is observed, which builds confidence in the presented modeling approach.

Sensitivity Analysis of Bluff-Body Stabilized Premixed Flame Large-Eddy Simulations

Bluff-body stabilized turbulent premixed flames represent a challenging canonical configuration for computational simulation and validation. Past simulation results from many research groups on the same bluff-body flame test case demonstrate significant variation that is neither fully understood nor quantified. To identify potential sources of this variation, three categories of sensitivities are assessed for a stable combustion bluff-body flame test case: exit boundary conditions, turbulent combustion closure models, and grid resolution. Comparisons with experimental data are presented, and an analysis of the causes of the discrepancies is informed by the sensitivity analysis. Specifically, low grid sensitivities at the finest resolution indicate that notable discrepancies with the experiment are likely due to model or boundary condition errors. All three categories of sensitivities are identified as significant, and the dominant source of variation in the results depends on the resolution and flow variable of interest. In spite of a lack of thermoacoustic oscillations, exit boundary condition effects are shown to be substantial, and errors in velocity statistics are minimized by extending the computational domain into the exhaust region.

Abstract 122: Reliability Analysis for Image-based Non-invasive Pressure Quantification in Aortorenal Artery Systems

Non-invasive quantification of fractional flow reserve (FFR) based on CT angiography has great potential to replace invasive catheterization for quantifying the amount of ischemia caused by a specific arterial stenosis (AS), promising for lower medical cost and better patient care. In clinical practice, the reliability of quantifying the 4-D approximate pressure (p a ) and distal pressure (p d ) across an AS is critical since FFR=p d /p a by definition. The objective of this work is to assess the effects of uncertainties (empiricalness) in the 3-element Windkessel model (WK3) used as exit boundary conditions (BC) on the quantification of p d and p a in aortorenal artery systems. A developed and validated in-house software ( InVascular , see Fig. 1(a)), featured with revolutionarily fast speed for image-based computational hemodynamics, is used for the uncertainty quantification analysis. Fifteen total aortic and renal arteries were studies in five male patients aged 64 to 83. In each case, the effects of the uncertainty on the 4-D pressure quantification are assessed using the First Order Second Moment method. We conduct analyses where the input variables are normally distributed with their coefficients of variation being 3%. Figure 1(b) shows the effects of uncertainty on the systolic pressure (SP) with their means, standard deviations, and 95% confident intervals. The results indicate that the uncertainty (measured by standard deviation) in SP in the aorta is higher than that in the renal arteries. The uncertainty is minimal for the severe stenosis (in red), implying more reliable noninvasive pressure quantification in stenosed arteries.

Numerical investigation of surge prediction in a transonic axial compressor with a hybrid BDF/Harmonic Balance Method

This paper aims at evaluating an efficient combination of a hybrid Backward Difference Formula/Harmonic Balance Method and the necessary time dependent exit boundary condition for the prediction of the performance line and ultimately surge line in a transonic one stage axial compressor (Stage 35) designed and measured at NASA Glenn Research Center. The agreement of the total pressure ratio, total temperature ratio as well as the efficiency curve with the experimental findings are encouraging. The results of the proposed methodology compare very well with the URANS predictions of Herrick et al. albeit the calculation is more efficient. While the prediction of the performance line in the stabile regime can be predicted by the classical Harmonic Balance Method (HBM), the investigation of strong off-design conditions, a quasi-periodic extension of the HBM is necessary. In addition, the mass flow rate and the exit pressure are no longer constant in time in this flow field an appropriate boundary condition is required for the successful simulation of this flows. Using this features the prediction of the surge behavior has been computed and a realistic flow pattern has been obtained. The computational time extents over more than 50 revolutions in order to capture the surge frequency of the compressor.

Instability modes on a solid-body-rotation flow in a finite-length pipe

Numerical solutions of the incompressible Navier-Stokes equations are obtained to study the time evolution of both axisymmetric and three-dimensional perturbations to a base solid-body-rotation flow in a finite-length pipe with non-periodic boundary conditions imposed at the pipe inlet and outlet. It is found that for a given Reynolds number there exists a critical swirl number beyond which the initial perturbations grow, in contrast to the solid-body rotation flow in an infinitely-long pipe or a finite-length pipe with periodic inlet and exit boundary conditions for which the classical Kelvin analysis and Rayleigh stability criterion affirm neutrally stable for all levels of swirl. This paper uncovers for the first time the detailed evolution of the perturbations in both the axisymmetric and three-dimensional situations. The computations reveal a linear growth stage of the perturbations with a constant growth rate after a brief initial period of decay of the imposed initial perturbations. The fastest growing axisymmetric and three-dimensional instability modes and the associated growth rates are identified numerically for the first time. The computations show that the critical swirl number increases and the growth rate of instability decreases at the same swirl number with decreasing Reynolds number. The growth rate of the axisymmetric mode at high Reynolds number agrees well with previous stability theory for inviscid flow. More importantly, three-dimensional simulations uncover that the most unstable mode is the spiral type m = 1 mode, which appears at a lower critical swirl number than that for the onset of the axisymmetric mode. This spiral mode grows faster than the unstable axisymmetric mode at the same swirl. Moreover, the computations reveal that after the linear growing stage of the perturbation the flow continues to evolve nonlinearly to a saturated axisymmetric vortex breakdown state.

An analytical model for solute transport in an infiltration tracer test in soil with a shallow groundwater table

Summary It is recommended that an in-situ infiltration tracer test is considered for simultaneously determining the longitudinal and transverse dispersion coefficients in soil. Analytical solutions have been derived for two-dimensional advective–dispersive transport in a radial geometry in the literature which can be used for interpreting the result of such a tracer test. However, these solutions were developed for a transport domain with an unbounded-radial extent and an infinite thickness of vadose zone which might not be realistically manifested in the actual solute transport during a field infiltration tracer test. Especially, the assumption of infinite thickness of vadose zone should be invalid for infiltration tracer tests conducted in soil with a shallow groundwater table. This paper describes an analytical model for interpreting the results of an infiltration tracer test based on improving the transport domain with a bounded-radial extent and a finite thickness of vadose zone. The analytical model is obtained with the successive application of appropriate integral transforms and their corresponding inverse transforms. A comparison of the newly derived analytical solution against the previous analytical solutions in which two distinct sets of radial extent and thickness of vadose zone are considered is conducted to determine the influence of the radial and exit boundary conditions on the solute transport. The results shows that both the radial and exit boundary conditions substantially affect the trailing segment of the breakthrough curves for a soil medium with large dispersion coefficients. Previous solutions derived for a transport domain with an unbounded-radial and an infinite thickness of vadose zone boundary conditions give lower concentration predictions compared with the proposed solution at late times. Moreover, the differences between two solutions are amplified when the observation positions are near the groundwater table. In addition, we compare our solution against the approximate solutions that derived from the previous analytical solution and has been suggested to serve as fast tools for simultaneously estimating the longitudinal and transverse dispersion coefficients. The results indicate that the approximate solutions offer predictions that are markedly distinct from our solution for the entire range of dispersion coefficient values. Thus, it is not appropriate to use the approximate solution for interpreting the results of an infiltration tracer test.

Performance assessment of various fan ribs inside a centrifugal blower

This study aims towards the development of an optimised design of a centrifugal blower consisting of various fan ribs, based on performance assessments following changes in the shape of its internal components. Various components, such as the external cases and the rotating fan ribs placed in a variety of operating conditions, are evaluated numerically and experimentally. Evaluation is based on performance parameters, including the inlet and outlet pressures, flow rate, torque, and power of the centrifugal fan. The numerical analysis suggests that the combination of the multiple rotating frame method and the standard k-ε turbulence model was appropriate for simulation of the internal flow characteristics and for power prediction. The numerical results were compared with tests under carefully designed experimental conditions. Based on the results and depending on the exit shape of the fan, the flow rate gradually increased to a value 7% higher than the existing model. The experimental and the numerical calculation results were in good agreement, particularly at the exit boundary condition at atmospheric pressure. In addition, among the four different impellers studied, the fan type with forward-curved fan ribs was associated with the best performance, reaching a maximum flow rate of 2.2 m3/min and a torque of 0.09N⋅m.

Discrete Artificial Boundary Conditions for the Lattice Boltzmann Method in 2D

To conne a spatial domain to a smaller computational domain, one needs articial bound- aries. This work considers the lattice Boltzmann method and deals with boundary conditions for these open boundaries. Ideally, such a condition does not interact with the uid at all. We present novel two-dimensional discrete articial boundary conditions to pursue that goal and we discuss four dier- ent versions. This type of condition is formulated on the discrete lattice Boltzmann level and does not require a PDE formulation of the uid. We set a special focus on the D2Q9 model. Our numeri- cal results compare the novel discrete articial boundary conditions to simulations using the existing non-reecting characteristic boundary condition and an exit boundary condition.

Downstream-Conditioned Maximum Entropy Method for Exit Boundary Conditions in the Lattice Boltzmann Method

A method for modeling outflow boundary conditions in the lattice Boltzmann method (LBM) based on the maximization of the local entropy is presented. The maximization procedure is constrained by macroscopic values and downstream components. The method is applied to fully developed boundary conditions of the Navier-Stokes equations in rectangular channels. Comparisons are made with other alternative methods. In addition, the new downstream-conditioned entropy is studied and it was found that there is a correlation with the velocity gradient during the flow development.