Favorable Pressure Gradient Research Articles

On the large-scale vortices in an L/D = 2.30 serpentine diffuser with internal bump

In this paper, the generation and spatial evolution of large-scale vortices in an ultra-compact serpentine diffuser (L/D = 2.30) featuring an integrated internal bump are experimentally and numerically investigated. Due to reduction of the local flow area caused by the internal bump, a favorable streamwise pressure gradient is induced first and then followed by an adverse one. Concurrently, a high-pressure region exists on the side of the diffuser as it contracts, yielding a sideward circumferential pressure gradient and then an inward one. Such circumferential pressure gradients divert the boundary layer on the windward side of the internal bump to the side and induce a spanwise U-shaped vortex on the leeward side, which constrains the development of flow separation in this region. The circumferential pressure gradients further induce two pairs of streamwise vortices located at the top and bottom of the diffuser, respectively. These vortex pairs entrain the low-energy fluids and transport them to the aerodynamic interface plane (AIP), resulting in two pairs of low-total-pressure regions and swirling flows. Moreover, in the experimentally studied range of the exit Mach number MAIP from 0.293 to 0.546, the distributions of low-total-pressure regions and swirl angles at the AIP exhibit a small variation, indicating that the internal flow field structures are insensitive to MAIP.

Aeroacoustics of a Square Finite-Wall-Mounted Cylinder in Pressure-Gradient Flows

An experimental investigation of the wake flow structures, surface pressure fluctuations, and noise production of a square finite-wall-mounted cylinder with an aspect ratio of 2.4 is presented. The cylinder was immersed in flows with favorable, near-zero, and adverse pressure gradients at a Reynolds number of 48,000, based on cylinder width. Far-field noise, unsteady surface pressure, and particle image velocimetry measurements were taken simultaneously using the open-jet pressure-gradient test rig in the UNSW Anechoic Wind Tunnel. Favorable and adverse pressure gradients were found to enhance and suppress the cylinder tonal noise, respectively. A favorable pressure gradient reduced the size of the recirculation region in the wake, which intensified the free-end downwash and suppressed the junction upwash. The intensities of the cylinder surface pressure fluctuations were slightly increased at the primary and secondary shedding Strouhal numbers (based on cylinder width) of approximately 0.1 and 0.2. Conversely, the recirculation region expanded under an adverse pressure gradient, with the downwash weakened and the upwash enhanced. The peaks in the surface pressure spectra were noticeably attenuated at the primary shedding Strouhal number and completely suppressed at the secondary Strouhal number. Wake flow structures correlated with the surface pressure fluctuations and far-field noise were identified to understand the enhancement or suppression mechanisms of the surface pressure fluctuations and the associated shedding regimes.

Distally Based Lymphatic Microsurgical Preventive Healing Approach-A Modification of the Classic Approach.

The treatment of breast cancer has seen great success in the recent decade. With longer survivorship, more attention is paid to function and aesthetics as integral treatment components. However, breast cancer-related lymphedema (BCRL) remains a significant complication. Immediate lymphatic reconstruction is an emerging technique to reduce the risk of BCRL, the Lymphatic Microsurgical Preventive Healing Approach (LYMPHA) being the most widely used approach. Despite promising results, it is often difficult to find suitably sized recipient venules and perform the microanastomoses between mismatched vessels deep in the axilla. Moreover, high axillary venous pressure gradients and potential damage from radiotherapy may affect the long-term patency of the anastomoses. From an ergonomic point of view, performing lymphaticovenular anastomosis in the deep axilla may be challenging for the microsurgeon. In response to these limitations, we modified the technique by moving the lymphatic reconstruction distally-terming it distally based LYMPHA (dLYMPHA). A total of 113 patients underwent mastectomy with axillary clearance in our institution from 2018 to 2021. Of these, 26 underwent subsequent dLYMPHA (Group 2), whereas 87 did not (Group 1). In total, 17.2% (15 patients) and 3.84% (1 patient) developed BCRL in Groups 1 and 2, respectively ( p = 0.018). Lymphatics and recipient venules suitable for anastomoses can be reliably found in the distal upper limb with better size match. A distal modification achieves a more favorable lymphaticovenular pressure gradient, vessel match, and ergonomics while ensuring a comparably low BCRL rate.

Modulation of the wake of a horizontal cylinder by pycnocline thickness in stratified flow

This study investigates the modulating effect of the pycnocline thickness in two-dimensional stratified flow on a cylinder. It encompasses three typical flow regimes identified by Boyer in experiments conducted within the Reynolds number range of Re = 260–2000. Quantitative control of the modulation effect of internal interface waves on the cylinder wake is achieved by varying the thickness of the pycnocline. Under appropriate thickness of the pycnocline, a multiple-centerline-structure can transition to isolated-mixed-structure flow regimes and Double-Eddy-Wavy-Wake flow regimes. Similar modulation patterns are also observed in isolated-mixed flow regimes. Normalized pressure distribution and velocity fields indicate that in low Reynolds number flow regimes (Re < 600), downstream isolated mixed regions generate dynamic pressure that periodically cascades upstream. This periodic reverse energy transfer provides favorable adverse pressure gradients, cyclically reducing the drag force on the cylinder. The cyclic period is, for the first time, classified into four stages: dynamic pressure storage stage, dynamic pressure transfer stage, dynamic pressure consumption stage, and dynamic pressure exhaustion stage. Despite the highly nonlinear modulation effect of internal interface waves in low Reynolds number conditions, the linear predictive theory of lee waves based on streamline equations remains instructive in predicting the trend of lee waves wavelength variation with pycnocline thickness. Drawing upon the modulation study results concerning the pycnocline thickness on lee waves, a regime map is constructed, illustrating the directional evolution of lee waves flow patterns based on variations in pycnocline thickness.

The boundary layer instability beneath internal solitary waves and its sensitivity to vortex wakes

We investigated the stability of the bottom boundary layer (BBL) beneath periodic internal solitary waves (ISWs) of depression over a flat bottom through two-dimensional direct numerical simulations. We explored the convective versus absolute/global nature of the BBL instability in response to changes in Reynolds number, and the sensitivity of the instability to seeding noise in the front of the ISW – spanning laboratory to geophysical scales. The BBL was laminar at $Re_{ISW}=90$ and convectively unstable at $Re_{ISW}=300$ . At laboratory-scale $Re_{ISW}=300$ , the convective wave packet was periodically amplified by each successive ISW, until vortex shedding occurred. The associated noise-amplification behaviour potentially explains the discrepancies of the critical $Re_{ISW}$ between the lock–release laboratory experiments and our Dubreil–Jacotin–Long-initialized numerical simulations as the result of the difference in background noise. Instability energy decreased under the front shoulder of the ISW, analogous to flow relaminarization under a favourable pressure gradient. At geophysical-scale $Re_{ISW}=900$ , the BBL was initially convectively unstable, and then the instability tracked with the ISW, appearing phenomenologically similar to a global instability. The simulated initial convective instability at both $Re_{ISW}=300$ and $Re_{ISW}=900$ is in agreement with local linear stability analysis which predicts that the instability group speed is always lower than the ISW celerity. Increased free stream perturbations in front of the ISW and larger $Re_{ISW}$ shift the location of vortex shedding (and enhanced bed shear stress) beneath the wave, closer to the ISW trough, thereby potentially changing the location of maximum sediment resuspension, in agreement with field observations at higher $Re_{ISW}$ .

Experimental investigation on the effects of complex pressure gradients on the film cooling effectiveness of a serpentine nozzle

Serpentine nozzles more easily deform and damage due to high-temperature airflow because of their multi-bend channel configuration. Therefore, film cooling technologies should be applied to serpentine nozzles. Complex pressure gradients in serpentine nozzles lead to different film cooling characteristics from combustion chambers, turbine blades, and other exhaust systems. This study experimentally investigated the effects of complex pressure gradients and film hole inclination angles on a serpentine nozzle’s film cooling effectiveness (FCE) using pressure-sensitive paint (PSP). The flow mechanisms were obtained via numerical simulations. The experimental nozzle design needs to consider the needs of PSP observations and the normal flow of serpentine nozzles. However, the complex structure of serpentine nozzles makes those increasingly difficult. The studied pressure gradients include the pressure gradient mutation (PGM), strong adverse pressure gradient (SAPG), weak adverse pressure gradient (WAPG), and favorable pressure gradient (FPG). The results show that complex pressure gradients change the coolant coverage and adhesion and may induce a recirculation zone in the SAPG region. This affects the development of the vortex construction and leads to different FCE distributions. The FCE under the effects of the PGM is the largest, followed by the SAPG, WAPG, and FPG. A larger inclination angle weakens the coolant adhesion but may enhance its downstream and lateral flow treads. This is coupled with the effects of complex pressure gradients, where larger inclination angles bring better film cooling effects in some cases. After accounting for the four blowing ratios, the area-averaged FCEs under the effects of the SAPG, WAPG, and FPG are 28.9 %, 42.8 %, and 52.3 % lower than that under the PGM, respectively. The area-averaged FCEs under the conditions α = 45° and 60° are 6.6 % and 10 % lower than that under α = 30°.

Implementation and validation of a generalized wall stress function

The generalized wall function by Shih et al. [Report No. M-1999-209398 (1999)], which accounts for non-equilibrium effects by the presence of favorable and adverse pressure gradients in turbulent flows, is addressed with the aim of performing high Reynolds number large-eddy simulations of the wall-bounded flow. The model uses a corrected law of the wall with a pressure gradient contribution to approximate the wall stress and applies to the entire viscous layer, buffer layer, and inertial region. A fully developed channel flow is first tested to validate the solver and model implementation, and then the wall function is assessed for the flow over a periodic hill. Wall-resolved simulations are in good agreement with reference results. A priori investigation with own experimental results corroborates the mathematical form of the model and suggests using different coefficients. The wall-modeled simulations show that the implemented wall model is able to improve the wall shear stress predictions compared to a standard equilibrium wall model. It corrects the underestimation of wall shear stresses by equilibrium models in the favorable pressure gradient region and the overestimation of wall shear stresses in the adverse pressure gradient region. The positions of the separation and reattachment points are also in good agreement with reference results. Furthermore, the prediction of the wall shear stress maximum in the favorable pressure gradient zone at the windward side of the hill is quite robust against coarsening the wall-normal grid spacing.

More General Wall Pressure Spectra Models: Combining Feature Engineering with Evolutionary Algorithms

This paper presents an improved mathematical expression for semi-empirical wall pressure spectra modeling based on gene expression programming (GEP). The main focus of this work is to obtain a model that applies to a wide range of cases in terms of parameters and the source of data. The dataset comprises flat plate and airfoil cases with adverse and favorable pressure gradients at various Reynolds numbers. First, a characterization of the dataset is performed to understand the low-dimensional distribution of parameters. Then, a feature importance study is conducted to choose the most suitable model input variables from the exhaustive list of nondimensional parameters. The GEP algorithm is modified to ensure that trained models adhere to the basic structure of previously published semi-empirical models. Following training on the diverse database, the new model is compared against existing, best-performing empirical models to quantify the performance improvements. The models are tested on cases with completely different configurations and parameter ranges, unseen during training, and maintain their superior performance. Finally, a comparison is made between models developed with GEP and neural networks in terms of their efficacy, complexity, and interpretability.

Challenges and perspective on the modelling of high-Re, incompressible, non-equilibrium, rough-wall boundary layers

The present paper gives an overview of the recent modelling activities under NATO-STO AVT-349, focussed on the understanding and modelling of boundary layers for incompressible, high-Reynolds-number flows subject to non-equilibrium conditions such as strong pressure gradients, three-dimensionality, and surface roughness and heterogeneity. For this, we consider simpler cases where the above flow conditions are present separately or in a reduced number of combinations. First, we focus on the effect of roughness on the outer flow and the problems associated to its characterisation and prediction, with a particular emphasis on the conditions necessary for outer-layer similarity to hold. We then focus on how the presence of adverse and favourable pressure gradients affects the effect of roughness, and to what extent the figures used to quantify it are still useful under such conditions. We also consider the effect of surface heterogeneity, the shortcomings when modelling it and how these can be addressed. We then focus on the effect on the outer layer of pressure gradients and non-equilibrium conditions, to what extent similarity holds in those conditions, and how RANS models perform for such flows, identifying routes for their improvement to handle pressure gradients and non-equilibrium. We also discuss the use of data-driven and machine-aided methods in closure models.

Evidence of quasiequilibrium in pressure-gradient turbulent boundary layers

Two sets of measurements utilizing hot-wire anemometry and oil-film interferometry for flat-plate turbulent boundary layers, exposed to various controlled adverse and favourable pressure gradients, are used to evaluate history effects of the imposed and varying free-stream gradients. The results are from the NDF wind tunnel at Illinois Tech (IIT) and the MTL wind tunnel at KTH, over the range $800 < Re_\tau < 22\,000$ (where $Re_{\tau }$ is the friction Reynolds number). The streamwise pressure-gradient parameter $\beta \equiv (-\ell /\tau _{w}) \cdot (\partial P_{e}/\partial x)$ varied between $-2 < \beta < 7$ , where $\ell$ is an outer length scale for boundary layers equivalent to the half-height of channel flow and the radius of pipe flow, and is estimated for each boundary-layer profile; note that $\tau_w$ is the wall-shear stress and $P_e$ is the free-stream static pressure. Extracting from each profile the three parameters of the overlap region, following the recent work of Monkewitz & Nagib (J. Fluid Mech., vol. 967, 2023, p. A15) that led to an overlap region of combined logarithmic and linear parts, we find minimum history effects in the overlap region. Thus, the overlap region in this range of pressure-gradient boundary layers appears to be in ‘quasiequilibrium’.

The multi-scale coupled model: a new framework capturing wind farm–atmosphere interaction and global blockage effects

Abstract. The growth in the number and size of wind energy projects in the last decade has revealed structural limitations in the current approach adopted by the wind industry to assess potential wind farm sites. These limitations are the result of neglecting the mutual interaction of large wind farms and the thermally stratified atmospheric boundary layer. While currently available analytical models are sufficiently accurate to conduct site assessments for isolated rotors or small wind turbine clusters, the wind farm's interaction with the atmosphere cannot be neglected for large-size arrays. Specifically, the wind farm displaces the boundary layer vertically, triggering atmospheric gravity waves that induce large-scale horizontal pressure gradients. These perturbations in pressure alter the velocity field at the turbine locations, ultimately affecting global wind farm power production. The implication of such dynamics can also produce an extended blockage region upstream of the first turbines and a favorable pressure gradient inside the wind farm. In this paper, we present the multi-scale coupled (MSC) model, a novel approach that allows the simultaneous prediction of micro-scale effects occurring at the wind turbine scale, such as individual wake interactions and rotor induction, and meso-scale phenomena occurring at the wind farm scale and larger, such as atmospheric gravity waves. This is achieved by evaluating wake models on a spatially heterogeneous background velocity field obtained from a reduced-order meso-scale model. Verification of the MSC model is performed against two large-eddy simulations (LESs) with similar average inflow velocity profiles and a different capping inversion strength, so that two distinct interfacial gravity wave regimes are produced, i.e. subcritical and supercritical. Interfacial waves can produce high blockage in the first case, as they are allowed to propagate upstream. On the other hand, in the supercritical regime their propagation speed is less than their advection velocity, and upstream blockage is only operated by internal waves. The MSC model not only proves to successfully capture both local induction and global blockage effects in the two analyzed regimes, but also captures the interaction between the wind farm and gravity waves, underestimating wind farm power by about only 2 % compared with the LES results. Conversely, wake models alone cannot distinguish between differences in thermal stratification, even if combined with a local induction model. Specifically, they are affected by a first-row overprediction bias that leads to an overestimation of the wind farm power by 13 % to 20 % for the modeled regimes.

Effects of bleed pressure on shock-wave/boundary-layer interactions in a transonic compressor stator with suction holes

Abstract This paper numerically investigated the influence of bleed pressure on the shock-wave/boundary-layer interaction in a transonic compressor stator with a row of suction holes. These suction holes are arranged on the suction surface in the spanwise direction. Six different bleed pressure ratios are studied at an inlet Mach number of 1.0. Results show that the reduction in the pressure loss increases as the bleed pressure decreases, and the maximum relative decline is 36.4 % when the flow loss caused by the suction flow path is taken into account. The bleeding of suction holes changes the shock wave structure, and the modified shock wave structure is three-dimensional. As the bleed pressure decreases, the tangential momentum of boundary layer increases. A strong spanwise variation in the boundary layer is observed downstream of the suction hole. Turning the flow direction and creating a favorable pressure gradient are key reasons for controlling boundary layer separation.

Design Of Tangentially Fired Pulverized Coal Burner Nozzle For Enhanced Erosion Resistance

Erosion-induced failure of pulverized coal burner nozzles (PCBN) presents a significant challenge in pulverized coal-based thermal power plants. Investigations have identified multiple causative factors leading to the accelerated degradation and consequent reduced lifespan of PCBN. These factors include the erosive impact of solid fuel particles carried at high velocities and angles, as well as the high-temperature conditions within the combustion zone. To mitigate erosion, strategies often revolve around enhancing material resistance or optimizing aerodynamic profiles to minimize drag forces. This study employs Computational Fluid Dynamics (CFD) via the CFX code to model and analyze the erosion dynamics within PCBN. By adjusting the geometry of the inner plates within the PCBN, simulations indicated a notable improvement in erosion resistance. The optimized design achieved this by expanding the flow area between the innermost bifurcated plates without altering their angle, leading to a more uniform flow distribution and favorable velocity and pressure gradients. These modifications have the potential not only to prolong nozzle life but also to contribute to more efficient combustion in tangentially fired furnaces.

Impact of Flow Unsteadiness on Turbine Airfoil Heat Transfer via Streaming

Abstract Thermal management of turbine airfoils is a critical design consideration, but the impact of unsteadiness on heat transfer of attached flow regions has received less attention in the literature. When turbine surfaces are subjected to unsteady zero-mean flow fluctuations, either naturally or artificially, the mean velocity around them is modified due to a nonlinear interaction of fluctuations, known as streaming. In this numerical study, we examine the effect of streaming on heat transfer and skin friction in a simplified model of the flow over a turbine blade. Both heat transfer and skin friction modifications were found to strongly depend on the amplitude and wave speed of the unsteady flow perturbations. Over a wide range of disturbance parameters, skin friction modification was negligible, but a significant effect on heat transfer due to streaming was identified. Moreover, the impact of favorable pressure gradients, which are typical for turbine airfoils, on the streaming phenomena was also considered, and it was found that flow regions of zero-pressure gradient produced the strongest amplification of heat transfer, although the effect of the pressure gradient varied with Strouhal number. Due to its significant effect on wall heat transfer, the streaming phenomenon should be taken into account during the design and measurement of the thermal properties of unsteady systems.

A streamline coordinate analysis of a turbulent boundary layer subject to pressure gradients and curvature on the windward side of a bump

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favourable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterised and compared with a lower-Reynolds-number flow over the same geometry. The momentum budgets are analysed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral-analysis-based approximations for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. The shear and wall-normal Reynolds stress profiles normalised by these approximations exhibit a better collapse compared with friction velocity and Zagarola–Smits normalisations in the strong favourable pressure gradient region and in the mild adverse pressure region that precedes it in this flow. Simplification of these Reynolds stress approximations along with results from the DNS are used to obtain semi-empirical approximations that are able to provide stress closure in terms of wall solution fields for the turbulent boundary layer under consideration.

Aerodynamic Performance of a Finite-Span Wing in a Time-Varying Freestream

The current study analyzes the dynamic response of a NACA 0015 finite-span wing to a time-varying freestream in an unsteady wind tunnel at a mean Reynolds number of 1.0×105. The aerodynamic response of the wing can be categorized based on the angle of attack and the degree of flow separation on the suction side of the wing. When the suction side is dominated by separated flow, either at low angles of attack with long laminar separation bubbles or at high, poststall, angles of attack, the lift is enhanced by the favorable pressure gradient during freestream acceleration and decremented by the adverse pressure gradient during freestream deceleration. In these cases, the sectional lift coefficient is shown to oscillate by as much as ±0.1 due to the unsteady pressure gradient. Comparatively, regions of attached flow on the wing surface remain largely unaffected by the time-varying conditions, regardless of the reduced frequency. Discrepancies between the measured lift and the estimated response from Isaacs’s theory demonstrate that the coupling between the viscous flow separation and the unsteady conditions dominates the unsteady aerodynamic response.

Vortex dynamics and boundary layer transition in flow around a rectangular cylinder with different aspect ratios at medium Reynolds number

The numerical investigation focuses on the flow patterns around a rectangular cylinder with three aspect ratios ( $L/D=5$ , $10$ , $15$ ) at a Reynolds number of $1000$ . The study delves into the dynamics of vortices, their associated frequencies, the evolution of the boundary layer and the decay of the wake. Kelvin–Helmholtz (KH) vortices originate from the leading edge (LE) shear layer and transform into hairpin vortices. Specifically, at $L/D=5$ , three KH vortices merge into a single LE vortex. However, at $L/D=10$ and $15$ , two KH vortices combine to form a LE vortex, with the rapid formation of hairpin vortex packets. A fractional harmonic arises due to feedback from the split LE shear layer moving upstream, triggering interaction with the reverse flow. Trailing edge (TE) vortices shed, creating a Kármán-like street in the wake. The intensity of wake oscillation at $L/D=5$ surpasses that in the other two cases. Boundary layer transition occurs after the saturation of disturbance energy for $L/D=10$ and $15$ , but not for $L/D=5$ . The low-frequency disturbances are selected to generate streaks inside the boundary layer. The TE vortex shedding induces the formation of a favourable pressure gradient, accelerating the flow and fostering boundary layer relaminarization. The self-similarity of the velocity defect is observed in all three wakes, accompanied by the decay of disturbance energy. Importantly, the decrease in the shedding frequency of LE (TE) vortices significantly contributes to the overall decay of disturbance energy. This comprehensive exploration provides insights into complex flow phenomena and their underlying dynamics.

Design Optimization of Blade Tip in Subsonic and Transonic Turbine Stages—Part II: Flow Physics and Augmented Aerothermal Integral Objective Function

Abstract In Part I, a companion paper of the two-part article, a subsonic turbine stage and a transonic one conditioned at the same Reynolds number, flow coefficient, loading coefficient and reaction, but two different exit Mach numbers are designed to provide a direct contrast between a high-subsonic and a transonic flow conditioning for rotor blade squealer tips. In this paper as Part II, further analyses are carried out to address the main issues of interest arising from Part I: first, to identify the driving flow physical mechanisms for the contrasting aerodynamic efficiency sensitivities of the two stages; second to seek a more suitable heat transfer objective function for the tip aerothermal design optimization, given the seemingly strong conflicts among those conventionally adopted heat transfer objective functions. Two counter-rotating tip vortical structures, the pressure side vortex (PSV) and the casing-driven cavity vortex (CCV), are shown to impact the aero-performance differently between the two stages. For the subsonic stage, the leakage flow is strongly affected by a stronger residual PSV at the squealer cavity exit. For the transonic stage however, the tip choking in limiting the over tip leakage (OTL) mass flow and favorable pressure gradient in a transonic flow over a separation bubble led to a much stronger and more persistent CCV and thus lower aero-effectiveness of squealer tip for the transonic stage. The two vortices also show major heat transfer signatures on the cavity surfaces by impingement. For the PSV, the impingement impact is mainly on the cavity floor. For the CCV, on the other hand, its impact is mainly on the inner side-wall of the suction side rim. The latter is found to be mainly responsible for the overall linear variations of the heat load with the squealer height. Again, the relative strength between PSV and CCV serves as an effective differentiator in the heat transfer performance. The stronger and more persistent CCV in the transonic stage results in a strong signature on a large portion of the suction side cavity inner sidewall, thus a much higher increment in heat transfer with the squealer height than that for the subsonic stage. In seeking to establish a more consistent heat transfer objective function for combined aerothermal design and optimization, a coolability weighted nonuniformity parameter is proposed to integrate the local heat transfer and the coolability. The proposed objective function is shown to lead to consistent Pareto fronts for the combined aerothermal performance sensitivities, particularly for the present cases with strong heat transfer nonuniformity which are particularly challenging to those conventional treatments as shown in Part I. The coolability-augmented objective function should thus serve as an enabler to help practical applications of blade tip aerothermal design optimizations.

Solute band transport in electroosmotic-pressure-driven flow of Carreau–Yasuda fluid over micropillar arrays

In this study, we numerically investigate the transport and dispersion characteristics of a neutral solute band in a fluid following generalized Carreau–Yasuda constitutive equations. The combined action of electroosmotic forcing and pressure gradient drives the flow through a microchannel embedded with micropillars. We analyze the band transport process by altering the flow-controlling parameters and fluid rheology. We observe an enhancement in band dispersion with increasing solute diffusivity. An augmentation in band dispersion is achieved using bluff micropillar designs compared to the streamlined micropillars. We also observe that the dispersion of solute band is less in shear-thickening fluids than in shear-thinning fluids. In a mixed electroosmotic-pressure-driven flow, the favorable pressure gradient conditions enhance the band dispersion phenomenon. Our results may prove valuable in understanding solute transport dynamics in non-Newtonian fluids, which has implications for lab-on-a-chip diagnostics and precise drug delivery.

The wind farm pressure field

Abstract. The disturbed atmospheric pressure near a wind farm arises from the turbine drag forces in combination with vertical confinement associated with atmospheric stability. These pressure gradients slow the wind upstream, deflect the air laterally, weaken the flow deceleration over the farm, and modify the farm wake recovery. Here, we describe the airflow and pressure disturbance near a wind farm under typical stability conditions and, alternatively, with the simplifying assumption of a rigid lid. The rigid lid case clarifies the cause of the pressure disturbance and its close relationship to wind farm drag. The key to understanding the rigid lid model is the proof that the pressure field p(x,y) is a harmonic function almost everywhere. It follows that the maximum and minimum pressure occur at the front and back edge of the farm. Over the farm, the favorable pressure gradient is constant and significantly offsets the turbine drag. Upwind and downwind of the farm, the pressure field is a dipole given by p(x,y)≈Axr-2, where the coefficient A is proportional to the total farm drag. Two derivations of this law are given. Field measurements of pressure can be used to find the coefficient A and thus to estimate total farm drag.