Wake Region Research Articles

Dynamics of elevated dodecane jets in crossflow at supercritical pressure

In advanced aero-engines, kerosene is often transversely injected into the combustor at supercritical pressure, where the shorter jet penetration depth may result in poor mixing and the local hot spots near the combustor wall. Elevating the jet nozzle is proposed to remedy these issues, where the flowfield complexity increases as a result of the intricate interactions among the jet, crossflow, and stack wake. The distinct flow dynamics of elevated dodecane jets in crossflow (EJICF) at supercritical pressure are numerically investigated using large eddy simulation. The effects of various parameters, including ambient pressure, elevation stack thickness, and stack height are studied. The results reveal that, the jet-wake recirculation bubble is prominently evident at low supercritical pressure, attributed to the strong real-fluid effect resulting from significant density stratification in the jet's upstream shear layer. Analysis of streamline patterns and vorticity budgets underscores the role of the real-fluid effect in delaying the shift of the flow pattern from the transitional regime to the jet-dominated regime. Increasing stack thickness mitigates the impact of jet upshear effects and has the potential to eliminate the lock-in phenomena between jet wake and stack wake. A reduction in stack height leads to the diminishment of the stack wake vortex shedding. In contrast to conventional JICF, the EJICF configuration exhibits a heightened tendency for recirculation bubble formation in the jet wake region. An analysis of spatial mixing deficiencies demonstrates that incorporating an elevation stack with proper thickness and height can dramatically improve the jet-crossflow mixing efficiency.

The groove effect on wake characteristics of rotating cylinders

In the present study, active and passive flow control methods have been implemented to investigate their effects on the wake flow structures of a circular cylinder. Grooves having circular, rectangular, and triangular cross sections have been applied to the cylinders exposed to the rotation rates, α, from 0 to 0.79. The experiments have been conducted by particle image velocimetry at a Reynolds number of Re = 5 × 103. The contour graphics of time-averaged results have been presented. Moreover, the variations in velocity profiles have also been depicted. The experimental results revealed significant variations for flow patterns, wake structures, and turbulence parameters due to the effects of both groove geometries and rotational motion. In the stationary cases, for turbulence intensity, the circular grooved cylinder exhibited a 15% increase, while the triangular grooved cylinder showed a slightly higher increase of around 20% compared to that of the bare cylinder (BC). Conversely, in non-stationary cases, the rectangular grooved cylinder displayed the most prominent reduction in turbulence intensity, decreasing by approximately 10% compared to that of the BC. The groove type has considerably affected the flow structures of the wake regions, especially for the lower rotation rates.

Research on three-dimensional wake model of horizontal axis wind turbine based on Weibull function

In wind turbine wake models, Gaussian models depend on multidimensional integration to ascertain the distribution of wake velocity deficits. These integrations, which often involve complex boundary conditions, significantly enhance the complexity of mathematical computations. Due to the difficulty of obtaining analytical solutions, numerical integration methods such as Monte Carlo or other numerical integration techniques are commonly employed. This study presents a three-dimensional wake model (3DJW) for horizontal axis wind turbines, utilizing the Weibull function to simplify wake deficit characterization instead of traditional Gaussian distribution methods. The 3DJW model considers wind shear effects and mass conservation laws to enhance predictions of vertical wake velocities. By integrating incoming wind conditions and turbine parameters, the model efficiently computes downstream wake velocities, improving computational efficiency. To enhance predictions in the ultra-far wake region, an improved three-dimensional Weibull wake model is proposed using the exponential fitting method. Validation through wind tunnel experiments and wind farm data demonstrates the model's accuracy in predicting wake deficits at the hub height, with relative errors in horizontal and vertical profiles mostly within 5% and 3%, respectively. The proposed model enables accurate and rapid calculation of wake velocities at any spatial location downstream, facilitating enhanced energy utilization and reduced costs.

Statistical Study of the Sub-ion-scale Magnetic Holes in the Lunar Space Environment

Sub-ion-scale magnetic holes play a significant role in electron transportation and energy dissipation. In the upstream region of the terrestrial bow shock, they are expected to originate from the upstream solar wind as well as the foreshock. The Moon can move into the solar wind; whether it can affect the observation of the sub-ion-scale magnetic holes is unclear. Here, we statistically investigate 268 sub-ion-scale magnetic holes in the lunar space environment based on observations of the Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon’s Interaction with the Sun mission. The median duration of these magnetic holes is ∼0.31 s, and the median size of their cross sections is ∼0.5 ρ i or ∼38.9 ρ e. We regard an isolated or a train of magnetic holes as an event; thus, these magnetic holes belong to 207 events. The data at X SSE < 0 and |Y SSE| < 2 R M (lunar radii) account for ∼21.7% of all observed data, but ∼89.4% of the events are observed in this region, suggesting that they are more likely to occur in the lunar wake. Furthermore, their occurrence rates in the lunar wake are much larger in the region close to its boundary than in other wake regions. And the occurrence rates in the lunar wake near the boundary at X SSE > −3 R M are larger in the dawnside than that in the duskside. These observations suggest that the region in the lunar wake close to its boundary is a possible source of sub-ion-scale magnetic holes.

Thermal and energy performance characteristics of spiral-wing pin-fin heatsinks for liquid cooling of electronic devices in electric vehicles

Insulated gate bipolar transistors (IGBTs) are crucial components of electric vehicles (EVs) that regulate power. Liquid cooling has emerged as a cooling solution for high-power IGBTs in EVs. Although several pin-fin heatsinks (PFHs) have been developed to enhance cooling performance, comprehensive research on PFHs for IGBTs under liquid-cooling conditions is limited. This study investigated the cooling performance improvement of spiral-wing pin-fin heatsinks (SWPFHs) against conventional PFHs under liquid-cooling conditions. Using the developed simulation model, the optimal design of the SWPFH was determined to achieve the maximum Webb efficiency, which indicates the heat transfer capacity at the same power consumption. Furthermore, the heat transfer performance of the optimized SWPFH was compared with those of conventional PFHs with circular, square, and hexagonal pin-fin heatsinks under practical Reynolds numbers. The optimized SWPFH exhibited the lowest maximum temperature and standard temperature deviation among the conventional PFHs. The Webb efficiency of the optimized SWPFH was 21.9% higher on average than that of the conventional circular pin-fin heatsink (CPFH) owing to the enhanced mixing effects with the reduced wake region. Overall, the use of SWPFH for cooling IGBTs in EVs is recommended to improve the thermal performance of the CPFH under the same pumping power.

Experimental study on the periodicity of wake flow of a vertical staggered wind turbine fleet

To optimize wind farm layout and micro-siting, this study analyzes the impact of different numbers of small wind turbines on the wake region of a large wind turbine at varying yaw angles. It also explores the periodic characteristics of wind speed signals at different time scales. The study involves one large and nine scaled-down small wind turbines in a 3 × 3 arrangement to simulate real-world interactions. The results reveal that increasing small turbine numbers significantly amplify wake deficits downstream, intensifying periodic oscillations, providing crucial theoretical support for wind farm design optimization. These findings contribute to understanding complex wind turbine dynamics in wind farms and supporting future efficient and sustainable designs.

Analysis of wake and power fluctuation of a tidal current turbine under variable wave periods

In the Marine environment, waves and turbulence usually coexist, affecting the operation performance of the tidal current energy turbine. This paper conducts experiments on a scaled tidal stream turbine to study the wave period effect on the wake and power characteristics. Under a wave-current environment, the wake is found to display Gaussian distribution. Within the 4 times diameter downstream range (4D), the turbulence is significant, and both the wake velocity loss and fluctuation increase first and then decrease with wave period. After 6D, the flow field gradually recovers to the inflow level. The wave period affects the transversal turbulence, more in the near than far wake region, as the significant turbulence intensities at the hub and blade tips gradually merge and become consistent after 6D. The wave period affects little the power coefficient CP owing to the sinusoidal inflow velocity nature. However, the amplitude of the phase average power increases first and then decreases with the wave period. By contrast, the phase average power fluctuations are sensitive to cycle changes only within the low TSR interval; they decrease sharply with TSR. In addition, the energy distribution of power fluctuation in the wave flow coupling environment is mainly concentrated at the sum and difference, and as well multiples, of the rotational and wave frequency. The wave and its multiples energy distribution increases and then decreases with the wave period.

A numerical study of rainfall effects on wind turbine wakes

Rainfall has significant impacts on the operations of wind turbines due to erosion of turbine blades and alterations in aerodynamic performance of wind turbines. However, little is understood in the influences of rainfall on wind turbine wakes. In this study, large-eddy simulation (LES) coupled with actuator-disk model with rotation (ADM-R) is used to investigate impacts of rainfall on wind turbine wakes. A double Euler method is employed in ADM-R to simulate the rainfall injection. The results of the model indicate that rainfall reduces wind speed in the sweep area and increases wind speed in the outer region of the top tip level by 2.1 %. Furthermore, rainfall reduces turbulence intensity in the near wake and outer wake region of the top tip (up to 2.0 %), with the influence extending up to 10 d (diameters of the wind turbine) in the downstream. These changes have a positive correlation with the rainfall intensity and an inverse correlation with the wind speed. The mean kinetic energy (MKE) and turbulent kinetic energy (TKE) budget analysis reveals that (1) the turbulent radial transport variation of MKE is the primary reason for the rainfall-induced wind speed change; (2) the change in shear production of TKE is responsible for the rainfall-induced turbulent intensity change; (3) the rainfall-induced Reynolds stress −u′w′‾ is the dominant factor of this dynamics.

Reynolds number sensitivity of the vortex dynamics around a long-span rail-cum-road bridge girder with three separated boxes

The novel separated three-box girder is gradually adopted for very long-span cable-stayed bridges due to its excellent flutter stability. Due to its special design of cross section, it exhibits notable Reynolds number effects in the flow patterns and vortex dynamics when subject to incoming flow. To explore its Reynolds number sensitivity, this paper performs a three-dimensional large eddy simulation (LES) on the flow around a static long-span rail-cum-road bridge girder with three separated boxes at different Reynolds numbers. The overall centre height H of the bridge model is chosen as the characteristic length, and the investigated Reynolds number regime falls into the regime of 1e2≤Re≤2.8e4. Through the analysis of the flow characteristics of three distinct regions in the flow field(the windward leading edge region, the gap region and the wake region), a successive transition of the wake flow, gap flow, and leading edge shear flow is observed with increasing Reynolds number. The surrounding flow patterns are divided by different Reynolds number regimes as: laminar separation at the trailing edge (Re<5e2); simultaneous instability of the gap shear layer and the wake (5e2≤Re<1e3); restabilisation of the upstream gap shear layer (1e3≤Re<3e3); secondary instability of the upstream gap shear layer and transition of the wake (3e3≤Re<8e3); transition of the separated shear layer at the leading edge (8e3≤Re≤2.8e4). This paper reveals in detail the complex vortex dynamics in the surrounding flow field of the special cross section with three separated boxes.

Further improvements to the double-Gaussian wake model

In onshore wind farms, the turbine-to-turbine distance can be in the order of three diameters or less. In these circumstances, traditional wake models, developed for the far wake region, lose accuracy. The double-Gaussian wake model is an approach to extend algebraic wake modelling to the near wake region, where the wake is not yet self-similar. In this work, the double-Gaussian wake model is advanced by performing large eddy simulations of a reference wind turbine and a scaled wind turbine model to investigate how the thrust coefficient and the turbulence intensity influence the near wake and wake recovery. Results show that in the near wake the maximum velocity deficits move towards the outer part of the rotor with an increasing thrust coefficient. Thus, a thrust coefficient dependent position of the double-Gaussian peaks is proposed. In addition, a wake expansion function including turbulence intensity and thrust coefficient is tuned. The new model proves to be capable of predicting the wake of different turbine models under various ambient conditions and operational states.

A simple RANS closure for wind-farms under neutral atmospheric conditions: Preliminary findings

Accurately predicting wind turbine wake effects is essential for optimizing wind-farm performance and minimizing maintenance costs. This study explores the applicability of the Sparse Regression of Turbulent Stress Anisotropy (SpaRTA) framework to develop a simple yet robust Reynolds-averaged Navier-Stokes (RANS) model for wake prediction in wind energy contexts. The framework introduces two correction terms into two-equation models, with k − ε model being utilized in the current study. One correction term resembles the residual of the Turbulent Kinetic Energy (TKE) equation, and the other corrects the deviatoric part of the Reynolds Stress Tensor (RST). The terms are calculated from high-fidelity measurement or simulation data, and symbolic regression is used to determine the model for these terms.In this study, Large Eddy Simulation (LES) data from a single turbine is used as the training dataset, and a sample pre-selection process is employed to discover a correction model efficiently. The derived model incorporates two terms based on Pope’s basis tensors and their invariants. The expression of the obtained model shows that it functions as a modification to the constant Cµ in the k − ε model. The model is evaluated by comparing its predicted velocity and TKE fields with the LES data used for the training. The model showed satisfactory performance in predicting both fields. Additionally, its generalizability is evaluated by testing it against a more complex six-turbine unseen case. The results indicate that the model effectively captures the velocity field and power output, but it tends to overpredict TKE, especially in the wake region.

The effect of nacelle-to-rotor size on the wake of a miniature wind turbine

Wind tunnel experiments are performed to investigate the effect of nacelle-to-rotor size on the wake of a wind turbine under different Reynolds numbers. Four different turbine configurations are tested, which vary in the rotor diameter and nacelle length and diameter. The near wake region is observed to be significantly affected by the nacelle-to-rotor size of the turbine. The difference in the averaged streamwise velocity and streamwise turbulence intensity is affected more by the change in the rotor diameter than by the change in the nacelle diameter. This is likely due to the change in the nacelle length to rotor diameter ratio, and the change in the distance between the ground and rotor lower tip. The differences in the near wake characteristics are reduced by the increase in the Reynolds number. The onset of the far wake is unaffected by the nacelle-to-rotor size, and consequently, the far wake modeling can be performed with good accuracy using existing analytical models. The power coefficient values show an improvement with the increase in the Reynolds number due to the higher efficiency of the rotor and motor.

Transient numerical simulation to investigate pressure fluctuation spectrum and deficit in the near wake of a horizontal axis wind turbine

Wind energy becomes one of the promised solutions as alternatives of using fossil power energy in the upcoming decades. As pressure fluctuation and flow deficit in the near wake play a crucial role in predicting the turbine performance, the novelty in the current study focuses on a three dimensional (3 D) transient numerical simulation to investigate near wake characteristics of NREL phase IV wind turbine. Pressure fluctuation spectrum and wake deficit at four sections downstream the turbine are the main parameters studied as well as the flow streams and iso-surface characteristics. The mentioned parameters are studied at four sections: (0.25 D), (0.5 D), (0.75 D), and (1 D) of turbine diameter. The obtained results are compared with corresponding data from the NREL Phase IV experiments for validation purposes. Results show that the highest-pressure fluctuation spectrum would be at the nearest wake region, and, then it decreases periodically. Hub pressure spectrum density is much lower than that density for the turbine blade. The wake deficit profile shows that the deficit is developing with time at a rate equal to (0.115 rate per sec). In addition, it was found that the wake is recovered just (1 d) of the hub diameter while the blade wake deficit becomes the dominant after (0.75 D) of turbine diameter to cover the whole wake region. It was also found that the downstream distances should be extended more to resolve the whole wake recovery. The comparison with the tests measurements shows agreement between both the numerical and experimental works such that the error doesn't pass 4.3 %.

Variations of the shock and secondary flow structure in a transonic compressor cascade with outlet back pressure

The effects of back pressure on the transonic cascade operating state are crucial and can determine the structure of internal shock waves and secondary flows. In this paper, numerical methods validated by experiments were employed to investigate the evolution mechanisms of the inlet flow field, shock structure, secondary flow structure, and cascade performance under different back pressures. Analysis revealed that transonic cascade exhibited unique incidence characteristics in the inlet flow field under both subsonic and supersonic regimes, although these two regimes involved different physical mechanisms. The results revealed that the operating state of the transonic compressor cascade under the unique incidence condition was influenced by the outlet back pressure, and there existed a critical static pressure ratio. The critical static pressure ratio shifted from 1.61 for two-dimensional flow to 1.37 for three-dimensional (3D) flow at M1 = 1.1, due to the corner separation and the characteristics of 3D shocks. The 3D shock structure exhibited a non-uniform distribution along the spanwise direction due to the influence of back pressure and the separated boundary layer. The vortex structures analysis revealed that the secondary flow structure on the sidewalls of the transonic compressor cascade was primarily dominated by corner vortices, whose formation mechanism was related to the interaction between the shock wave and the sidewall boundary layer. Additionally, this interaction also led to the formation of detached shock and lip shock vortex structures. Finally, loss analysis indicated that the wake region of the transonic cascade primarily includes six types of loss, and the total loss of the cascade decreased with the rise in back pressure.

Active Cluster Wake Mixing

In recent years, the relevance of the interaction between neighboring wind farms has grown steadily. As one farm extracts energy from the wind, a downstream one can systematically experience lower wind speeds which threatens the economic viability of the farm. Significant progress has been made in understanding these farm-farm wake interactions, but we still lack methodologies to mitigate their undesired effects. In this study, we introduce Active Cluster Wake Mixing (ACWM). This novel method aims to accelerate the recovery of the cluster wake using dynamic control actions: By exciting the thrust of the individual turbines depending on their relative location, we generate non-uniform patterns of energy extraction. Phase offsets between the individual excitation signals propagate these regions through the wind farm. This results in large-scale velocity gradients inside the farm, which also affect the flow in the cluster wake region. An in-depth exploration and optimization of ACWM requires significant computational effort. Therefore, we compare three different wind farm modeling approaches in Large Eddy Simulations (LES) that differ in their computational costs regarding their suitability for further exploration of ACWM. For this purpose, we use an unoptimized ACWM scheme with two different excitation frequencies. For the first time ever we successfully show that ACWM manipulates the flow inside the wind farm with favorable effects on the wake velocity. We also demonstrate that the modeling of cluster wakes is challenging and has a significant effect on the potential gain.

Numerical investigation of the vortical structures in the near wake of a model wind turbine

It is well known that the vortex system in a horizontal axis wind turbine wake is highly relevant in terms of fatigue loads and performance of wind turbines located in the wake of other wind turbines. The breakdown process of tip vortices particularly influences the mixing process of the low-speed wake region with the undisturbed flow outside the wake. As a collaboration with the Technische Universität Berlin (TUB), a major goal in a joint research is to study the effects involved in tip vortex breakdown. TUB designed a model turbine that will be towed through a large water tank to analyse and to control the tip vortex decay. To accommodate the measurement equipment, the ratio of blade length to nacelle length is unconventionally small, leading to uncertainty regarding the effect on the breakdown of the tip vortex. Due to the dimensions of the model wind turbine the root vortex system and the nacelle wake are not comparable to former studies and should therefore be investigated in detail. To do so computational fluid dynamics, in particular delayed detached eddy simulations, are conducted for the model turbine with the compressible flow solver FLOWer and the two-equation Menter-SST turbulence model. Two simulations are conducted with and without the nacelle. The results indicate that the root vortices propagate downstream and interact with each other. Additionally, these vortical structures are also influenced by the geometry of the turbine nacelle which causes faster decay of the root vortices compared to a configuration without the nacelle. However, the root vortex breakdown does not influence the tip vortices as the turbulent intensity matches for the area where tip vortices are present. In short, this investigation shows that the influence of the nacelle geometry and root vortex system on the tip vortices is negligible. Thus, the model wind turbine designed by TUB is suitable for the investigation of tip vortices.

Vortex-induced noise suppression of a cylinder with blowing through porous media

To mitigate vortex shedding for flow and noise control of a circular cylinder, an experimental approach combining air blowing and porous coating was implemented simultaneously as a hybrid method. Localized air blowing was symmetrically applied through structured porous media at four angles, corresponding to different regions of the flow field: boundary layers, shear layers on the cylinder, separated shear layers, and the cylinder's base. The study involved synchronizing near-field pressure fluctuation and far-field noise measurements with flow field measurements obtained via particle image velocimetry. Near-field pressure measurements were taken around the cylinder's circumference using a remote sensing method. This comprehensive investigation revealed that vortex shedding primarily induced pressure fluctuations at the cylinder's shoulders, resulting in the propagation of acoustic waves to the far field. The hybrid method, alongside the separate application of porous coating and local blowing, showcased substantial efficacy in mitigating near-field pressure, consequently leading to a reduction in far-field noise. These techniques achieved this by strategically shifting the vortex formation region further downstream and expanding the wake region compared to the baseline. Notably, the hybrid method, particularly when local blowing was applied at the base of the porous coated cylinder, exhibited a significantly enhanced impact in this regard, resembling the behavior observed with the individual application of porous coating.

Tip shape effects on the axial-flow-induced vibration of a cantilever rod

The influence of tip shape on flow-induced vibration of a cantilever rod subjected to axial water flow is experimentally investigated, through optical tracking of the rod movement and mapping of the instantaneous flow field around the rod tip. The experimental setup consists of a vertical cantilever rod housed within a tube. The rod tip shapes considered in this study include a blunt tip and cones with height-to-diameter ratios of 0.5, 1, and 2. The experiments were conducted across a Reynolds number range between 20k to 100k in both clamped-free and free-clamped configurations, representing opposite flow directions. The rod tip motion was captured using fast video image tracking, whereas the flow field near the rod tip was obtained using particle image velocimetry (PIV). The rod vibration dynamics exhibited a primarily fuzzy period-1 behavior, characterized by a periodic motion with a chaotic component. Flutter-like oscillation and buckling were also observed at higher Reynolds numbers, depending on the flow direction. The mechanisms of fluid-structure interaction involved turbulent buffeting and movement-induced excitations. Unsteady flow separation around the rod tip was identified as a further contributing mechanism to flow excitation. In the clamped-free configuration, unsteady flow separation was more pronounced for the cone tips due to the increased rod surface area in the wake region, leading to larger vibration amplitude. In the free-clamped configuration, flow separation effects were more prominent for the blunt tip, as the streamlined cone shapes were less prone to flow separations. Overall, the rod with a blunt tip resulted in smaller displacement in the clamped-free configuration, while the rods with cone tips led to smaller displacement in the free-clamped configuration.

Nature-Inspired Wind Farm Layout Optimization: Harnessing Smart Patterns for Sustainable Energy

This research investigates the transformative realm of wind farm layout optimization, with a specific focus on harnessing the efficiency of bio-inspired patterns. The positioning of wind turbine is play a vital role in the maximizing the energy output of a wind farm. If a wind turbine is placed in the wake region of the upstream turbine, the energy produced by the downstream turbine is reduced. Hence, it is imperative to place turbines in such a way that effect of the wake is minimum on a performance of turbines. The conventional grid-based approaches, commonly employed in wind farm layouts, face limitations in capturing the inherent complexity of wind flow dynamics, especially in varied terrains. In contrast, bio-inspired layouts, inspired by patterns observed in natural ecosystem, offer the promising results over the conventional Grid based approach. Our investigation involves the development and implementation of a novel bio-inspired wind farm layout positioning pattern. In the proposed approach, various nature inspired pattern like honeycomb and sunflower seeds pattern is explored for the turbine positioning. Further, the modeling of wind behavior includes both uniform wind speeds and variable wind speeds originating from all directions. The modified passing vehicle search (mPVS) optimization algorithm is used for optimizing the wind turbine placement. The results are obtained for the different wind scenario and compare it with the available results in the literature. The anticipated outcomes of this research include a deeper understanding of the potential benefits and challenges associated with bio-inspired wind farm layouts. The findings aim to contribute valuable insights into optimizing wind turbine placements, maximizing energy capture, and fostering sustainable practices in the wind energy sector. Results shows that the turbine positioning in the proposed bio-inspired pattern produce the higher power output (6%) compared to the conventional grid based approach. Hence, it can be concluded that the approach present in this study can assist wind farm designers and developers in optimally placing turbines for better performance.

Adaptive mesh refinement (AMR) criteria comparison for the DrivAer model

Aerodynamics is one of the main areas of development in vehicle design. One of the most efficient ways of testing the aerodynamic design of a vehicle is to use Computational Fluid Dynamics (CFD), which allows for faster and more accurate aerodynamic simulations, which in turn helps increase the fuel economy and electric vehicle's range. Resource optimization is one of the most important aspects of CFD, and one of its main aspects is the spatial discretization of the fluid domain. This study discusses the use of Adaptive Mesh Refinement (AMR) for the aerodynamic design of private vehicles. This paper compares the results obtained with the use of AMR based on different fluid dynamic criteria for the DrivAer model and correlates the results with experimental data and computational results provided by various authors in previous publications. Four different optimization functions are defined and compared. The results for the drag coefficient, pressure coefficient, and total pressure wake have been correlated, showing great accuracy. This study has proven that the use of AMR highly optimizes computational resources by optimizing the mesh in the desired areas, thereby reducing the number of cells needed elsewhere. The use of these criteria has proven useful for drag coefficient prediction simulations because these criteria make use of the AMR to optimize the wake region.