Adverse Pressure Gradient Research Articles

Scaling of self-similar turbulent boundary layers under adverse pressure gradient

We present a theoretical and numerical study of the self-similarity turbulent boundary layers (SSTBLs) under adverse pressure gradient. Two relations are emphasized in theoretical extension. The first one explains the necessary relation to establish the same TBL with different choices of scaling, called coordinate transformation relation. The second relation is the equivalent requirement on the outer scaling of the mean velocity profile, named as scaling equivalence relation. Numerical verification is implemented with a set of ideal SSTBL velocity profiles that exhibit no Reynolds number effect by numerically solving the generalized governing equations of SSTBL under specified external conditions and self-similar scalings. Existing scalings in literature and two presently designed scalings are examined based on self-similar requirement to show their fulfillment of the two relations. Large-eddy simulations (LESs) of SSTBL are performed by directly specifying the pressure gradient parameter β corresponding to different scalings. We show once the coordinate transformation relation is satisfied, the similar fully developed SSTBL can be settled with different scalings. Further detailed quantitative analysis confirms the validity of the two conditions. Two velocity profile models of SSTBL are evaluated with LES results. The former is based on the numerical solution of the SSTBL equations, and the latter is based on the similarity between the outer region of TBL and the laminar boundary layer. Both models work reasonably well for present LES.

Mean-flow structures of the turbulent boundary layers bounding a two-dimensional separation bubble

Understanding the mean-flow structures of a separated turbulent boundary layer (TBL) is crucial for turbulence modeling. This study investigates the spatial scaling properties of the total shear stress and mixing length in the TBLs bounding a two-dimensional (2D) separation bubble, aiming to derive analytical descriptions for the entire mean-velocity profiles of the TBLs. For the adverse pressure gradient (APG) TBL upstream of the separation bubble, the total shear stress possesses a two-layer structure with an inner layer adhering to a linear law and an outer layer conforming to a defect power law. In contrast, the mixing length profile consists of four layers, namely the viscous sublayer, the buffer layer, the overlap layer, and the wake region. Each of the layers exhibits a power law or a defect power law relationship with the spatial coordinate normal to the wall. In the four-layer structure, three parameters are sensitive to the variation of the APG: the buffer-layer thickness, the relative magnitude of the mixing length at the boundary layer edge, and a defect power law exponent quantifying the extent of the wake region. For the reattached TBL downstream of the separation bubble, the total shear stress consists of two parts. One part is induced by the pressure gradient and retains the two-layer structure, while the other, engendered by the intense turbulence advected from the separated shear layer, exhibits a dual-power-law distribution. The advected turbulence also significantly alters the four-layer structure of the mixing length, resulting in an augmented buffer layer, a diminished overlap layer, and a wake region that mimics a turbulent mixing layer. Via a dilation ansatz to describe the scaling transition between adjacent layers, the study formulates the complete profiles of the total shear stress and mixing length. The formulation leads to the derivation of novel analytical expressions for the entire mean-velocity profiles of the TBLs. The expressions are in precise accord with the direct numerical simulations of an incompressible 2D separation-bubble flow and a 2D impinging shock wave/TBL interaction. The elucidation of the mean-flow structures through this study is anticipated to facilitate the analysis of turbulence models, thereby enhancing their performance in simulating separated TBLs. The construction of the mean-flow descriptions by inspecting the spatial scaling properties of turbulence paves a promising way for theoretical exploration of complex nonequilibrium TBLs.

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.

Impact of the expansion ratio on the properties of hydrogen recirculation ejectors

Exploring the development characteristics and influencing factors of the mixing layer (ML) inside the hydrogen recirculation ejector is of great importance for enhancing the recirculation properties of the ejector and promoting green and sustainable energy development. However, the evolution of ML in the ejector and the transport and diffusion characteristics of the fluid are problematic, in particular, the influence of the expansion ratio on the properties of the ejector is unclear. Therefore, in this study, a CFD numerical model of an ejector was established to simulate the flow of fluids in the ejector. The evolution of ML was elucidated, and the interaction mechanism between the mixing and the recirculation performance of the ejector was revealed. The findings showed that the velocity difference is a significant driving force for the development of ML, and the formation of an adverse pressure gradient contributes to the diffusion of hydrogen and the rapid development of ML. The development process of ML in the ejector can be divided into three stages under the interaction of the velocity difference and the convective Mach number: the rapid growth stage, the slow growth stage, and the exponential growth stage. By studying the evolution of ML at different expansion ratios, it was found that there exists a critical expansion ratio for the ejector, which results in the largest of the non-mixing length ratio and the effective mixing thickness, the strongest relative mass transfer capability of the entrained flow, the fullest development of ML, and the optimal hydrogen recirculation performance.

Transpiration-induced convective heat transfer in ternary hybrid nanofluid flow due to dual stretching on wedge: Reverse flow analysis

Boundary layer separation is a common challenge in fluid dynamics, where flow separates from a surface due to adverse pressure gradients. Transpiration, the injection or suction of fluid through a surface, is a technique used to mitigate this issue. This study investigates transpiration’s effects on boundary layer separation over a stretching wedge conveying ternary hybrid nanoparticles, which is crucial for optimizing various engineering systems. The study establishes a mathematical model incorporating transpiration, dual stretching, viscous dissipation, and nanoparticle volume fractions. The model is reduced to ordinary differential equations using similarity transformations and then solved numerically with MATLAB’s bvp4c package. Here, the convective heat transfer increases with suction and decreases with blowing due to changes in boundary layer thickness. This insight provides valuable information for engineers seeking to control temperature gradients in their systems. Moreover, the study highlights transpiration’s efficacy in mitigating boundary layer separation induced by adverse pressure gradients. Furthermore, flow enhancement with blowing depends on specific conditions, such as the value of the blowing parameter, highlighting its nuanced influence.

Influence of Time-Varying Freestream Conditions on the Dynamics of Unsteady Boundary-Layer Separation

Unsteady flow separation of a turbulent boundary layer under dynamic pressure gradients is investigated using the Large-Eddy Simulation technique. The unsteadiness is introduced by prescribing an oscillating freestream vertical-velocity profile at the top boundary of the domain. Although previous studies, including Ambrogi et al. (Journal of Fluid Mechanics, Vol. 945, Aug. 2022, p. A10) and Ambrogi et al. (Journal of Fluid Mechanics, Vol. 972, Oct. 2023, p. A36), focused on the kinematics of the flow and the effects of the oscillation frequency on flow separation, the goal of this paper is to analyze the effects of three time-varying freestream-forcing profiles while the oscillation frequency is kept the same for all Cases. Whereas in Case A the freestream-velocity profile changes from suction–blowing to blowing–suction in a complete cycle, Cases B and C are both suction–blowing only and the strength of the adverse pressure gradient is modulated in time. Moreover, the boundary layer in Case B never approaches a zero-pressure gradient condition. A closed separation bubble is formed for all Cases; however, its dimensions change depending on the far-field forcing. The time evolution of turbulent kinetic energy (TKE) reveals an advection mechanism of turbulent structures out of the domain for all Cases. Whereas in Case A and C the high-TKE region, generated in the separated shear layer, is washed out of the domain as a rigid body, in Case B the separation bubble remains present and the advection mechanism of TKE is characterized by a breathing pattern.

Spatial Averaging Effects in Adverse Pressure Gradient Turbulent Boundary Layers

Spatial Averaging Effects in Adverse Pressure Gradient Turbulent Boundary Layers

A Computational Analysis of Turbocharger Compressor Flow Field with a Focus on Impeller Stall

Understanding the flow instabilities encountered by the turbocharger compressor is an important step toward improving its overall design for performance and efficiency. While an experimental study using Particle Image Velocimetry was previously conducted to examine the flow field at the inlet of the turbocharger compressor, the present work complements that effort by analyzing the flow structures leading to stall instability within the same impeller. Experimentally validated three-dimensional computational fluid dynamics predictions are carried out at three discrete mass flow rates, including 77 g/s (stable, maximum flow condition), 57 g/s (near peak efficiency), and 30 g/s (with strong reverse flow from the impeller) at a fixed rotational speed of 80,000 rpm. Large stationary stall cells were observed deep within the impeller at 30 g/s, occupying a significant portion of the blade passage near the shroud between the suction surface of the main blades and the pressure surface of the splitter blades. These stall cells are mainly created when a substantial portion of the inlet core flow is unable to follow the impeller’s axial to radial bend against the adverse pressure gradient and becomes entrained by the reverse flow and the tip leakage flow, giving rise to a region of low-momentum fluid in its wake. This phenomenon was observed to a lesser extent at 57 g/s and was completely absent at 77 g/s. On the other hand, the inducer rotating stall was found to be most dominant at 57 g/s. The entrainment of the tip leakage flow by the core flow moving into the impeller, leading to the generation of an unstable, wavy shear layer at the inducer plane, was instrumental in the generation of rotating stall. The present analyses provide a detailed characterization of both stationary and rotating stall cells and demonstrate the physics behind their formation, as well as their effect on compressor efficiency. The study also characterizes the entropy generation within the impeller under different operating conditions. While at 77 g/s, the entropy generation is mostly concentrated near the shroud of the impeller with the core flow being almost isentropic, at 30 g/s, there is a significant increase in the area within the blade passage that shows elevated entropy production. The tip leakage flow, its interaction with the blades and the core forward flow, and the reverse flow within the impeller are found to be the major sources of irreversibilities.

Assessment of Wall Modeling With Adverse Pressure Gradient for High Reynolds Number Separated Flows

Assessment of Wall Modeling With Adverse Pressure Gradient for High Reynolds Number Separated Flows

The Mechanism of Air Blocking in the Impeller of Multiphase Pump

The exploitation and transportation of deep-sea and remote oil and gas fields have risen to become important components of national energy strategies. The gas–liquid separation and gas blocking caused by the large density difference between the gas and liquid phases are the primary influencing factors for the safe and reliable operation of gas–liquid mixed transportation pump systems. This paper takes the independently designed single-stage helical axial-flow mixed transportation pump compression unit as the research object. Through numerical simulation, the internal flow of the mixed transportation pump is numerically calculated to study the aggregation and conglomeration of small gas clusters in the flow passage hub caused by gas–liquid phase separation, influenced by the shear flow of phase separation, forming axial vortices at the outlet where gas clusters gather in the flow passage. The work performed by the impeller on the gas clusters is insufficient to overcome the adverse pressure gradient formed at the outlet of the flow passage due to the gathering of the liquid phase in adjacent flow passages, resulting in the phenomenon of gas blocking, with vortex gas clusters lingering near the hub wall of the flow passage.

Volumetric Reconstruction Of Stagnated Wake Structures In Adverse Pressure Gradient

To gather insights about turbulent structures of a wake in adverse pressure gradient, a wind tunnel model is investigated with PIV methods. A flat plate of L = 1.058 m at zero angle of attack is placed in the MUB wind tunnel at TU Braunschweig. The wake convects downstream into a carefully designed diffuser, where it undergoes a pressure increase of ∆c p = +0.6. Wakes, with the common example of a cylinder shedding van-Karman vortices, are generally prone to instability. The wake instability of the sharp-edged plate is attenuated by the adverse pressure gradient, manifesting in large coherent structures that carry up to 37 % of the turbulent kinetic energy. While the primary shedding motion is effectively a quasi-2D motion, a secondary mode of is also observed: Over the span S = 1.3 m of the wake, it organizes in three distinct cells. Their motion is similar to "owl-eyes", that are known to appear on separated flow over smooth 2D bodies. The presence of these modes reduces the average flow velocity in the wake centre up to stagnation in the mean sense. Because stagnation and shedding does occur far away from any solid surfaces, this test case offers excellent observability of the phenomenon with PIV methods. RANS results of this setup cannot predict the flow stagnation accurately. Because the shedding frequency is low compared to freestream velocity, scale and time resolving IDDES results need to run many convective time units until the observed instability develops. While the original goal of observing small scale turbulent wake structures is compromised by the large shedding modes, the observation gives an insight on wake-bursting phenomena that occur on multi-element high-lift devices. The mode shedding and consequent wake stagnation is sensitive to the Reynolds-number (Re = [1.6 ... 3.2] · 10 6 ) as well as to the initial boundary layer thickness of the flat plate.

Validating Volumetric Measurements Using Helium-Filled Soap Bubbles in a Turbulent Boundary Layer And Wake Of An Axisymmetric Body Of Revolution

This study focuses on the validation of a volumetric measurement technique to characterize the turbulent boundary layers (TBL) and wake of a slender axisymmetric body. Specifically, Lagrangian Particle Tracking (LPT) was employed to analyse a TBL subjected to an adverse pressure gradient (APG) and transverse curvature at the tail of an axisymmetric body, with a Reynolds number based on model length of 3.95×10 6 . For the LPT method, a seeding rake with 100 nozzles was used to disperse helium-filled soap bubbles (HFSB), which served as tracers. These tracers were illuminated by high-powered LED arrays, allowing their motion to be captured by three high-speed cameras at acquisition rates up to 20 kHz. A key aspect of this research was using shadowgraphy to measure the diameter of the bubbles exiting the nozzles and obtaining their statistical variations across the various nozzles in the seeding rake. The study identified that the diameter of bubbles averaged 0.45 mm, indicating a state of near-neutral buoyancy. The LPT results were then obtained using the shake-the-box (STB) tracking alogirthm, while ensemble bin-averaging of the scattered particle tracks was used to obtain turbulence statistics on a regular grid. To validate the LPT results, comparisons were made with time-resolved 2D Particle Image Velocimetry (TR-PIV) and highly resolved hot-wire anemometry. This comparative analysis revealed good agreement of the mean profiles across the methodologies, highlighting the robustness and accuracy of the LPT technique. While the turbulence levels in the outer layer were well captured by the LPT, some discrepancies were observed near the wall in both PIV and LPT data, indicating limitations in capturing small-scale phenomena. The implications of these findings, particularly in understanding the complex 3D flow effects of such TBLs and the resulting wake flow field are discussed.

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°.

Hot-wire spatial resolution issues in adverse pressure gradient turbulent boundary layers

The effect of a finite length of hot-wire probe sensor length on the measured streamwise velocity fluctuations is well understood in canonical wall-bounded flow, where the small-scale energy has been found to be universal and invariant with Reynolds number. A straightforward application of that assumption to non-canonical flows such as strong adverse pressure gradient (APG) flows has, however, been hampered since the effect of Re and APG could not conclusively be studied separately due to the lack of data with a clear scale separation. The present experimental investigation at Reτ≈4000 in weak, moderate and strong APGs with different wire length shows that spatial averaging effects are not only limited to the inner layer. A note of caution is hence warranted for measurements that seemingly try to take the bias effect of spatial attenuation into account by performing measurements with albeit long but fixed viscous-scaled wire length.

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.

Investigating the mechanism of flow of transonic compact crossover tandem diffuser

Dealing with high transonic airflow at the outlet of a mixed-flow impeller is a challenging issue in research on the design of efficient and compact diffusers. A low aspect ratio and an adverse pressure gradient in the passage of the diffuser can lead to flow separation on the hub side of the bend and the suction side of the aft blade. Tandem blading can be used to attain flow control through an appropriate relative circumferential tandem position (λ). However, a comprehensive understanding of flow in a compact crossover tandem diffuser (CTD) requires further investigation. This study provides a detailed analysis of the mechanism of flow in a compact crossover baseline tandem diffuser (CBTD) as well as the influence of different values of λ on the structure of flow of the CTD. The findings show that the CBTD can suppress secondary flow separation on the hub side of the bend by reasonably distributing the radial load. We also found that a value of λ of 75% can delay the point of separation on the suction side of the aft blade over a wide range of spans, where this inhibits the corner separation vortex and improves the structure of flow and performance of the diffuser. We also preliminarily explore the impacts of excitation of full-span jet intensities with different values of λ on the corner separation vortex on the suction side of the aft blade and offer guidance for the design of a compact and efficient CTD.

Aerodynamic design of supersonic compressor cascade and vorticity dynamic diagnosis of flow field structure

High-load counter-rotating compressor plays a crucial role in reducing the axial length and weight of the compressor and increasing the thrust-to-weight ratio of the aero-engine. However, the boundary layer flow separation induced by shock waves in the channel of high adverse pressure gradient also brings more aerodynamic losses. This paper proposed a supersonic compressor cascade modeling method based on the unique inlet angle theory and the superimposing thickness on the suction surface method. It carried out aerodynamic optimization design of cascade with inlet Mach number of 1.85 combined with numerical optimization technology, vorticity dynamics diagnosis, and planar cascade experiment. The results show that multiple shock wave combination pressurization can be realized in the supersonic cascade channel. At the design point, the static pressure ratio is 3.285, and the total pressure recovery coefficient reaches 86.82%, and the experimental results of planar cascade also verify the correctness of the simulation method. In addition, the correlation laws between the distribution of the vorticity dynamic parameter, shock wave structure, and aerodynamic performance of cascade were analyzed by the vorticity dynamic flow field diagnosis method, which provides a beneficial reference for the subsequent compressor design.

A developed transition simulation model for turbulent plane jet impingement heat transfer

Jet impingement has been widely used due to its high heat transfer rate, but numerical simulation of this flow is highly challenging because of complex flow phenomena. In this paper, a turbulence model based on the physics of jet impingement is developed using the shear stress transport (SST) four-equation transition model and the SST with cross-diffusion correction (SSTCD) model. The proposed method is evaluated for plane jet impingement under various nozzle-plate spacings (2.6, 4 and 6) and different Reynolds numbers ranging from 10,200 to 20,000 in terms of heat transfer and flow fields. The results show that the developed model has the ability to capture the second peak of heat transfer and skin friction at low nozzle-plate spacing. Even at high nozzle-plate spacing, this approach also gives accurate trends for the above two features. However, without the cross-diffusion correction, the transition model provides too high energy and low velocity peaks. With the developed model in hand, the effects of pressure gradient on heat transfer and skin friction coefficient are further investigated. It is found that when the adverse pressure gradient becomes strong, the position of the secondary peak of skin friction occurs earlier than that of the secondary peak of heat transfer rate. Conversely, if the adverse pressure gradient disappears, the positions of these features coincide.

Understanding Low-Speed Streaks and Their Function and Control through Movable Shark Scales Acting as a Passive Separation Control Mechanism.

The passive bristling mechanism of the scales on the shortfin mako shark (Isurus oxyrinchus) is hypothesized to play a crucial role in controlling flow separation. In the hypothesized mechanism, the scales are triggered in response to patches of reversed flow at the onset of separation occurring in the low-speed streaks that form in a turbulent boundary layer. The two goals of this investigation were as follows: (1) to measure the reversing flow occurring within the low-speed streaks in a separating turbulent boundary layer; (2) to understand the passive flow control mechanism of movable shark skin scales that inhibit reversing flow within the low-speed streaks. Experiments were conducted using digital particle image velocimetry (DPIV). DPIV was used to analyze the flow in a turbulent boundary layer subjected to an adverse pressure gradient formation over both a smooth flat plate and a flat plate on which shark skin specimens were affixed. The experimental analysis of the flow over the smooth flat plate corroborated the findings of previous direct numerical simulation studies, which indicated that the average spanwise spacing of the low-speed streaks increases in the presence of adverse pressure gradients upstream of the point of separation. However, the characteristics of the flow over the shark skin specimen more closely resemble that of a zero-pressure gradient turbulent boundary layer. A comparative analysis of the width and velocity of the reversed streaks between flat plate and shark skin cases reveals that the mean spanwise spacing decreases, and thus, the number of streaks increases over the shark skin. Additionally, the reversed streaks observed over shark scales are thinner and the highest negative velocity within the streaks falls within the range required to bristle the scales.

Experimental study on flow field and combustion characteristics of V-gutter and integrated flameholders

Abstract To optimize the integrated flameholder, PIV was used to study flow fields of V-gutter and integrated flameholder under both non-reacting and reacting conditions. PLIF, high-speed cameras, and TDLAS were adopted to capture OH distribution, flame structure, and temperature distribution. Comparative analysis of flow fields, combustion characteristics and flame stabilization mechanisms were analyzed. Results show that heat release increases adverse pressure gradient, which can enlarge the recirculation zone size and recirculation rate compared to non-reacting flow field. The flames of both flameholders exhibit symmetrical structures distributed near the shear layers. The blockage ratio dominates the non-reacting flow field, while the expansion angle dominates the reacting flow field, which can further increase the adverse pressure gradient under reacting condition. The V-gutter flameholder demonstrates better fuel/air mixing and larger recirculation than the integrated flameholder. The combustion performance of the integrated flameholder is inferior to the V-gutter flameholder, albeit with better flow resistance properties.