Large eddy simulation of mechanical mixing in anaerobic digesters

A comprehensive study of anaerobic digestion requires an advanced turbulence model technique to accurately predict mixing flow patterns because the digestion process that involves mass transfer between anaerobes and their substrates is primarily dependent on detailed information about the fine structure of turbulence in the digesters. This study presents a large eddy simulation (LES) of mechanical agitation of non-Newtonian fluids in anaerobic digesters, in which the sliding mesh method is used to characterize the impeller rotation. The three subgrid scale (SGS) models investigated are: (i) Smagorinsky-Lilly model, (ii) wall-adapting local eddy-viscosity model, and (iii) kinetic energy transport (KET) model. The simulation results show that the three SGS models produce very similar flow fields. A comparison of the simulated and measured axial velocities indicates that the LES profile shapes are in general agreement with the experimental data but they differ markedly in velocity magnitudes. A check of impeller power and flow numbers demonstrates that all the SGS models give excellent predictions, with the KET model performing the best. Moreover, the performance of six Reynolds-averaged Navier-Stokes turbulence models are assessed and compared with the LES results.     

Computational modeling and validation of human nasal airflow under various breathing conditions

The human nose serves vital physiological functions, including warming, filtration, humidification, and olfaction. These functions are based on transport phenomena that depend on nasal airflow patterns and turbulence. Accurate prediction of these airflow properties requires careful selection of computational fluid dynamics models and rigorous validation. The validation studies in the past have been limited by poor representations of the complex nasal geometry, lack of detailed airflow comparisons, and restricted ranges of flow rate. The objective of this study is to validate various numerical methods based on an anatomically accurate nasal model against published experimentally measured data under breathing flow rates from 180 to 1100 ml/s. The numerical results of velocity profiles and turbulence intensities were obtained using the laminar model, four widely used Reynolds-averaged Navier-Stokes (RANS) turbulence models (i.e., k-ε, standard k-ω, Shear Stress Transport k-ω, and Reynolds Stress Model), large eddy simulation (LES) model, and direct numerical simulation (DNS). It was found that, despite certain irregularity in the flow field, the laminar model achieved good agreement with experimental results under restful breathing condition (180 ml/s) and performed better than the RANS models. As the breathing flow rate increased, the RANS models achieved more accurate predictions but still performed worse than LES and DNS. As expected, LES and DNS can provide accurate predictions of the nasal airflow under all flow conditions but have an approximately 100-fold higher computational cost. Among all the RANS models tested, the standard k-ω model agrees most closely with the experimental values in terms of velocity profile and turbulence intensity.     

Turbulence Model Selection for Low Reynolds Number Flows

One of the major flow phenomena associated with low Reynolds number flow is the formation of separation bubbles on an airfoil’s surface. NACA4415 airfoil is commonly used in wind turbines and UAV applications. The stall characteristics are gradual compared to thin airfoils. The primary criterion set for this work is the capture of laminar separation bubble. Flow is simulated for a Reynolds number of 120,000. The numerical analysis carried out shows the advantages and disadvantages of a few turbulence models. The turbulence models tested were: one equation Spallart Allmars (S-A), two equation SST K-ω, three equation Intermittency (γ) SST, k-kl-ω and finally, the four equation transition γ-Re_θ SST. However, the variation in flow physics differs between these turbulence models. Procedure to establish the accuracy of the simulation, in accord with previous experimental results, has been discussed in detail.     

Comparison of LES of steady transitional flow in an idealized stenosed axisymmetric artery model with a RANS transitional model

In this study, two different turbulence methodologies are investigated to predict transitional flow in a 75% stenosed axisymmetric experimental arterial model and in a slightly modified version of the model with an eccentric stenosis. Large eddy simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) methods were applied; in the LES simulations eddy viscosity subgrid-scale models were employed (basic and dynamic Smagorinsky) while the RANS method involved the correlation-based transitional version of the hybrid k-ε/k-ω flow model. The RANS simulations used 410,000 and 820,000 element meshes for the axisymmetric and eccentric stenoses, respectively, with y(+) less than 2 viscous wall units for the boundary elements, while the LES used 1,200,000 elements with y(+) less than 1. Implicit filtering was used for LES, giving an overlap between the resolved and modeled eddies, ensuring accurate treatment of near wall turbulence structures. Flow analysis was carried out in terms of vorticity and eddy viscosity magnitudes, velocity, and turbulence intensity profiles and the results were compared both with established experimental data and with available direct numerical simulations (DNSs) from the literature. The simulation results demonstrated that the dynamic Smagorinsky LES and RANS transitional model predicted fairly comparable velocity and turbulence intensity profiles with the experimental data, although the dynamic Smagorinsky model gave the best overall agreement. The present study demonstrated the power of LES methods, although they were computationally more costly, and added further evidence of the promise of the RANS transition model used here, previously tested in pulsatile flow on a similar model. Both dynamic Smagorinsky LES and the RANS model captured the complex transition phenomena under physiological Reynolds numbers in steady flow, including separation and reattachment. In this respect, LES with dynamic Smagorinsky appeared more successful than DNS in replicating the axisymmetric experimental results, although inflow conditions, which are subject to caveats, may have differed. For the eccentric stenosis, LES with Smagorinsky coefficient of 0.13 gave the closest agreement with DNS despite the known shortcomings of fixed coefficients. The relaminarization as the flow escaped the influence of the stenosis was amply demonstrated in the simulations, graphically so in the case of LES.     

Turbulence detection in a stenosed artery bifurcation by numerical simulation of pulsatile blood flow using the low-Reynolds number turbulence model

The pulsatile blood flow in a partially blocked artery is significantly altered as the flow regime changes through the cardiac cycle. This paper reports on the application of a low-Reynolds turbulence model for computation of physiological pulsatile flow in a healthy and stenosed carotid artery bifurcation. The human carotid artery was chosen since it has received much attention because atherosclerotic lesions are frequently observed. The Wilcox low-Re k-omega turbulence model was used for the simulation since it has proven to be more accurate in describing transition from laminar to turbulent flow. Using the FIDAP finite element code a validation showed very good agreement between experimental and numerical results for a steady laminar to turbulent flow transition as reported in a previous publication by the same authors. Since no experimental or numerical results were available in the literature for a pulsatile and turbulent flow regime, a comparison between laminar and low-Re turbulent calculations was made to further validate the turbulence model. The results of this study showed a very good agreement for velocity profiles and wall shear stress values for this imposed pulsatile laminar flow regime. To explore further the medical aspect, the calculations showed that even in a healthy or non-stenosed artery, small instabilities could be found at least for a portion of the pulse cycle and in different sections. The 40% and 55% diameter reduction stenoses did not significantly change the turbulence characteristics. Further results showed that the presence of 75% stenoses changed the flow properties from laminar to turbulent flow for a good portion of the cardiac pulse. A full 3D simulation with this low-Re-turbulence model, coupled with Doppler ultrasound, can play a significant role in assessing the degree of stenosis for cardiac patients with mild conditions.     

Numerical modeling of pulsatile turbulent flow in stenotic vessels

Pulsatile turbulent flow in stenotic vessels has been numerically modeled using the Reynolds-averaged Navier-Stokes equation approach. The commercially available computational fluid dynamics code (CFD), FLUENT, has been used for these studies. Two different experiments were modeled involving pulsatile flow through axisymmetric stenoses. Four different turbulence models were employed to study their influence on the results. It was found that the low Reynolds number k-omega turbulence model was in much better agreement with previous experimental measurements than both the low and high Reynolds number versions of the RNG (renormalization-group theory) k-epsilon turbulence model and the standard k-epsilon model, with regard to predicting the mean flow distal to the stenosis including aspects of the vortex shedding process and the turbulent flow field. All models predicted a wall shear stress peak at the throat of the stenosis with minimum values observed distal to the stenosis where flow separation occurred.     

Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.     

Model studies of the flow in abdominal aortic aneurysms during resting and exercise conditions

Pulsatile flow in abdominal aortic aneurysm (AAA) models has been examined in order to understand the hemodynamics that may contribute to growth of an AAA. The model studies were conducted by experiments (flow visualization and laser Doppler velocimetry) and by numerical simulation using physiologically realistic resting and exercise flow conditions. We characterize the flow for two AAA model shapes and sizes emulating early AAA development through moderate AAA growth (mean and peak Reynolds numbers of 362<Re_mean<1053 and 3308<Re_peak<5696 with Womersley parameter 16.4<<21.2). The results of our investigation indicate that AAA flow can be divided into three flow regimes: (i) Attached flow over the entire cycle in small AAAs at resting conditions, (ii) vortex formation and translation in moderate size AAAs at resting conditions, and (iii) vortex formation, translation and turbulence in moderate size AAAs under exercise conditions. The second two regimes are classified in the medical literature as disturbed flow conditions that have been correlated with atherogenesis as well as thrombogenesis. Thus, AAA disturbed hemodynamics may be a contributing factor to AAA growth by accelerating the degeneration of the arterial wall. Our investigation also concluded that vortex development is considerably weaker in an asymmetric AAA. Furthermore, turbulence was not observed in the asymmetric model. Finally, our investigation suggests a new mode of transition to turbulence: vortex ring instability and bursting to turbulence. The transition process depends on a combination of the pulsatile flow conditions and the tube cross-sectional area change.     

Effects of vibration on steady flow downstream of a stenosis

A physical model was used to test the effects of vibrations on the position of transition to turbulence (zt) downstream of a constriction. Constrictions were inserted in a length of clear plastic (Tygon) tubing and vibrated. Water was the fluid medium and flow was visualized with India ink. The frequency and velocity of vibration were monitored. For a given constriction and flow velocity, there was a band of frequencies which caused zt to move upstream. This band corresponded to frequencies of flow disturbances as measured with a hot-film anemometer without vibration. Both flow-visualization and hot-film frequencies were correlated via a Strouhal number to the Reynolds number and contraction ratio of the flow. Values of zt decreased with increasing vibration amplitude. The critical Reynolds number for turbulence was also decreased by vibration. These results are of importance in the diagnosis of vascular disease and the design of physical models of stenotic flows.     

Flow in axisymmetrical glass model aneurysms

Experiments have been performed on the flow of water with a dye tracer in rigid glass models of axisymmetrical spherical aneurysms. Streamlines have been visualized, pressure drops over the surface of the bulbs have been measured, and a critical Reynolds number for the onset of turbulence in the aneurysms has been determined. Boundary layer separation and recirculating flow with closed streamlines was observed in all models for flow rates below those necessary for turbulence. Pressures on the aneurysm walls for both laminar and turbulent flow were found to be of the same order of magnitude as those immediately upstream and downstream with no large pressure differences over the bulb surfaces. An inviscid mathematical model of the flow field was developed and shown to give good agreement with experiment for high Reynolds number laminar flow. The use of a suitably defined critical Reynolds number as an aid in the decision to operate on fusiform aneurysms is noted, as well as the limitations imposed on the experimental and theoretical results by the neglect of flow periodicity and nonhomogeneity.     

Correction to: Characterization of anisotropic turbulence behavior in pulsatile blood flow

Turbulent-like hemodynamics with prominent cycle-to-cycle flow variations have received increased attention as a potential stimulus for cardiovascular diseases. These turbulent conditions are typically evaluated in a statistical sense from single scalars extracted from ensemble-averaged tensors (such as the Reynolds stress tensor), limiting the amount of information that can be used for physical interpretations and quality assessments of numerical models. In this study, barycentric anisotropy invariant mapping was used to demonstrate an efficient and comprehensive approach to characterize turbulence-related tensor fields in patient-specific cardiovascular flows, obtained from scale-resolving large eddy simulations. These techniques were also used to analyze some common modeling compromises as well as MRI turbulence measurements through an idealized constriction. The proposed method found explicit sites of elevated turbulence anisotropy, including a broad but time-varying spectrum of characteristics over the flow deceleration phase, which was different for both the steady inflow and Reynolds-averaged Navier–Stokes modeling assumptions. Qualitatively, the MRI results showed overall expected post-stenotic turbulence characteristics, however, also with apparent regions of unrealizable or conceivably physically unrealistic conditions, including the highest turbulence intensity ranges. These findings suggest that more detailed studies of MRI-measured turbulence fields are needed, which hopefully can be assisted by more comprehensive evaluation tools such as the once described herein.

     

Numerical simulation of a fully baffled biological reactor: the differential circumferential averaging mixing plane approach

A modified mixing plane approach for steady state simulation of flow field in fully baffled biological reactor is presented and discussed. Without requiring any experimental input, this approach of dividing the vessel into suitable number of connected and disconnected zones; solving steady state equation separately in each zone and then transferring information between them, provides a computationally less intensive alternative for simulating the flow in the whole vessel. Impeller used is the standard Rushton Turbine positioned at mid-height of the reactor and simulations are carried out using standard k-epsilon turbulence model implemented in CFD code FLUENT. Meshing is done using tetrahedral elements such that mesh size gradually increases from the center to the periphery. Most of the previous simulation works present only a few aspects of the flow field with scant importance to the energy balance in the tank and near tip turbulence. In this work, complete model prediction for velocity field and turbulence parameters (near tip and in the bulk region) are validated by comparison with experimental data. As compared to previous simulation works, the results predicted by this "Differential circumferential averaging mixing plane approach" show a better qualitative and quantitative agreement with the published experimental data. A distribution of energy dissipation in various zones of vessel is presented. Also a qualitative picture of flow field and stagnant zones inside the reactor is presented and discussed. Comparison of flow characteristics for different number of baffles shows that for the present dimension of the vessel, five baffles gives maximum enhanced mixing.     

CFD simulation of non-Newtonian fluid flow in anaerobic digesters

A general mathematical model that predicts the flow fields in a mixed-flow anaerobic digester was developed. In this model, the liquid manure was assumed to be a non-Newtonian fluid, and the flow governed by the continuity, momentum, and k-epsilon standard turbulence equations, and non-Newtonian power law model. The commercial computational fluid dynamics (CFD) software, Fluent, was applied to simulate the flow fields of lab-scale, scale-up, and pilot-scale anaerobic digesters. The simulation results were validated against the experimental data from literature. The flow patterns were qualitatively compared for Newtonian and non-Newtonian fluids flow in a lab-scale digester. Numerical simulations were performed to predict the flow fields in scale-up and pilot-scale anaerobic digesters with different water pump power inputs and different total solid concentration (TS) in the liquid manure. The optimal power inputs were determined for the pilot-scale anaerobic digester. Some measures for reducing dead and low velocity zones were proposed based upon the CFD simulation results.     

Pulsatile flow in fusiform models of abdoiminal aortic aneurysms: flow fields, velocity patterns and flow-induced wall stresses

As one important step in the investigation of the mechanical factors that lead to rupture of abdominal aortic aneurysms, flow fields and flow-induced wall stress distributions have been investigated in model aneurysms under pulsatile flow conditions simulating the in vivo aorta at rest. Vortex pattern emergence and evolution were evaluated, and conditions for flow stability were delineated. Systolic flow was found to be forward-directed throughout the bulge in all the models, regardless of size. Vortices appeared in the bulge initially during deceleration from systole, then expanded during the retrograde flow phase. The complexity of the vortex field depended strongly on bulge diameter In every model, the maximum shear stress occurred at peak systole at the distal bulge end, with the greatest shear stress developing in a model corresponding to a 4.3 cm AAA in vivo. Although the smallest models exhibited stable flow throughout the cycle, flow in the larger models became increasingly unstable as bulge size increased, with strong amplification of instability in the distal half of the bulge. These data suggest that larger aneurysms in vivo may be subject to more frequent and intense turbulence than smaller aneurysms. Concomitantly, increased turbulence may contribute significantly to wall stress magnitude and thereby to risk of rupture.     

Importance of flow division on transition to turbulence within an arteriovenous graft

Transitional blood flow in an arteriovenous graft under various conditions of flow division was examined through direct numerical simulation. This junction consists of an inlet vessel (prosthetic graft) connected to a host vessel (vein) at an acute angle (21.6 degrees ). Inlet Reynolds numbers, based on mean velocity and graft inlet diameter, ranged from 800 to 1400. Various flow divisions between the two ends of the host vessel (i.e., the proximal venous segment, PVS, and distal venous segment, DVS) were considered (PVS:DVS ratios of 100:0, 85:15, 70:30 and 115:(15)). The numerical technique employed the spectral element method which is a high-order discretization ideally suited to the simulation of transitional flows in complex domains. High velocity and pressure fluctuations were observed for the PVS:DVS=70:30 and 85:15 cases and absent from the 100:0 and 115:(15) cases; the results indicate the importance of flow division on the development of turbulence in this junction. Transition to turbulence was observed at Reynolds numbers as low as 1000 and 800 under flow divisions of 85:15 and 70:30, respectively, significantly lower than the critical value of 2100. The frequency spectra of velocity fluctuations indicated a significant intensity within the frequency range of approximately 300Hz downstream of the junction. An adverse pressure gradient developed in the PVS when graft inflow divided into opposite directions in the junction. This pressure gradient had a destabilizing effect on the flow and enhanced transition to turbulence in the PVS. These findings suggest that measurements of in vivo flow rates at the inlet and outlets are critical for the accurate prediction of arteriovenous hemodynamics. A potential clinical application of these results might be to close off the DVS during graft construction to ensure a 100:0 flow division.     

Laboratory studies of predator-prey encounters in turbulent environments: effects of changes in orientation and field of view

Small polystyrene particles were used to represent aquatic micro-organismson millimeter scales, assuming small or negligible self-inducedmotions. A large number of such particles were released in turbulentflows that were generated in a controlled laboratory experiment,where the turbulence parameters were reproducible and couldbe kept constant over extended times. These polystyrene particlesare tracked by video techniques. The available database allowsestimates of the equivalents of planktonic contact rates inthe turbulent flow. The results are expressed in terms of averageprey fluxes. Scaling laws for the average contact rates fordifferent turbulence intensities and for varying ranges of interceptionof the predators and also for different forms of the fieldsof view were analyzed, using two models for the orientationwith respect to the flow. Irrespective of orientation and shapeof the volume of interception, the scaling with the turbulenceintensity is weak, while the variations with the range of perceptionare significant. The scaling laws obtained by this procedurehave universal validity, and they are applicable also for conditionsin nature. The sole restriction is that the range of predatorperception is within the universal subrange.     

Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm

In experiments turbulence has previously been shown to occur in intracranial aneurysms. The effects of turbulence induced oscillatory wall stresses could be of great importance in understanding aneurysm rupture. To investigate the effects of turbulence on blood flow in an intracranial aneurysm, we performed a high resolution computational fluid dynamics (CFD) simulation in a patient specific middle cerebral artery (MCA) aneurysm using a realistic, pulsatile inflow velocity. The flow showed transition to turbulence just after peak systole, before relaminarization occurred during diastole. The turbulent structures greatly affected both the frequency of change of wall shear stress (WSS) direction and WSS magnitude, which reached a maximum value of 41.5Pa. The recorded frequencies were predominantly in the range of 1-500Hz. The current study confirms, through properly resolved CFD simulations that turbulence can occur in intracranial aneurysms.     

The effect of inlet flow profile and nozzle diameter on drug delivery to the maxillary sinus

In this paper, the effect of the turbulence and swirling of the inlet flow and the diameter of the nozzle on the flow characteristics and the particles' transport/deposition patterns in a realistic combination of the nasal cavity (NC) and the maxillary sinus (MS) were examined. A computational fluid dynamics (CFD) model was developed in ANSYS® Fluent using a hybrid Reynolds averaged Navier–Stokes–large-eddy simulation algorithm. For the validation of the CFD model, the pressure distribution in the NC was compared with the experimental data available in the literature. An Eulerian–Lagrangian approach was employed for the prediction of the particle trajectories using a discrete phase model. Different inlet flow conditions were investigated, with turbulence intensities of 0.15 and 0.3, and swirl numbers of 0.6 and 0.9 applied to the inlet flow at a flow rate of 7 L/min. Monodispersed particles with a diameter of 5 µm were released into the nostril for various nozzle diameters. The results demonstrate that the nasal valve plays a key role in nasal resistance, which damps the turbulence and swirl intensities of the inlet flow. Moreover, it was found that the effect of turbulence at the inlet of the NC on drug delivery to the MS is negligible. It was also demonstrated that increasing the flow swirl at the inlet and decreasing the nozzle diameter improves the total particle deposition more than threefold due to the generation of the centrifugal force, which acts on the particles in the nostril and vestibule. The results also suggest that the drug delivery efficiency to the MS can be increased by using a swirling flow with a moderate swirl number of 0.6. It was found that decreasing the nozzle diameter can increase drug delivery to the proximity of the ostium in the middle meatus by more than 45%, which subsequently increases the drug delivery to the MS. The results can help engineers design a nebulizer to improve the efficiency of drug delivery to the maxillary sinuses.

     

街道峡谷绿化带设置对空气流场及污染分布的影响模拟研究

合理设置道路绿化带能够改变街道空气流场进而改善空气质量。利用风洞试验结合数值模型的方法测试了树冠形状和绿化带位置对街道峡谷的风场影响。在数值模型中,采用针对植物模型不同高度赋予不同叶面积密度(leaf area density,LAD)值的新方法近似模拟不同树冠形状的植物,通过输入污染源数据,得到风场及污染物浓度数据结果;与风洞试验结果进行对比,验证了其有效性;进而,利用数值模型分析了不同绿化带设置下街道峡谷内行人的污染暴露特征,结果表明绿化带位置及树冠形状影响街道峡谷中的涡流结构,形成复杂的细小湍流,从而影响街道峡谷中的风环境和污染物分布。阔叶树冠和位于街道峡谷中央的绿化带位置有利于降低行人污染暴露风险。未来研究中,通过增加风洞试验布点、考虑热力作用及气象因子的影响,或许可以提供更加详细的改善街道峡谷微环境的绿化带布局,为城市大气环境管理和绿地系统建设提供科学依据。     

Validating CFD predictions of respiratory aerosol deposition: effects of upstream transition and turbulence

A number of computational fluid dynamics (CFD) studies have explored local deposition patterns of inhaled aerosols in the respiratory tract. These studies have highlighted the effects of multiple physiologic, geometric, and particle characteristics on deposition. However, very few studies have reported local or sub-branch quantitative comparisons to in vitro particle deposition data. The objective of this study is to numerically investigate the effects of transition and turbulence on highly localized particle deposition in a respiratory double bifurcation model in order to quantitatively validate CFD results. To perform the validations, local comparisons have been made to a specific in vitro case study of 10 microm particles depositing in a model of respiratory generations G3-G5. To achieve this objective, two geometric cases have been considered. The first case includes only the double bifurcation model. The second case includes a portion of the experimental particle delivery geometry, where transitional flow is expected. To evaluate the effectiveness of two-equation turbulence models in this system, the flow field solutions have been computed using laminar, standard k-omega, and low Reynolds number (LRN) k-omega approximations. Results indicate that even though the Reynolds number remained below the critical limit required for full turbulence, transition and turbulence have a significant impact on the flow field and local particle deposition patterns. For the experimental case considered, turbulence impacted the local deposition of 10 microm particles primarily by influencing the initial velocity and particle profiles. As such, both the laminar and LRN k-omega flow models provided good local quantitative matches to the in vitro deposition data, provided that the correct initial particle profile was specified. Implications of this study include the need for local quantitative validations of particle deposition results, the importance of correct inlet conditions, and the need to consider upstream effects in experimental and computational studies of the respiratory tract. Applications of these results to realistic respiratory geometries will require consideration on upstream flow conditions in the lung, transient flow, and intermittent turbulent structures.