Favorable Pressure Gradient Research Articles

Micro-Vortex Generators on Transonic Convex-Corner Flow

A convex corner models the upper surface of a deflected flap and shock-induced boundary layer separation occurs at transonic speeds. This study uses micro-vortex generators (MVGs) for flow control. An array of MVGs (counter-rotating vane type, ramp type and co-rotating vane type) with a height of 20% of the thickness of the incoming boundary layer is installed upstream of a convex corner. The surface pressure distributions are similar regardless of the presence of MVGs. They show mild upstream expansion, a strong favorable pressure gradient near the corner’s apex and downstream compression. A corrugated surface oil flow pattern is observed in the presence of MVGs and there is an onset of compression moving downstream. The counter-rotating vane type MVGs produce a greater reduction in peak pressure fluctuations and the ramp type decreases the separation length. The presence of MVGs stabilizes the shock and shock oscillation is damped.

Excitation and Linear Instability of Stationary Modes in Falkner-Skan-Cooke Boundary Layer

Past studies showed that a micron-sized surface roughness may cause the generation of a significant ‎unstable, stationary wave in a crossflow boundary layer, and consequently promote or delay the laminar-‎turbulent transition. The crossflow boundary layer is usually driven by the favorable pressure gradient ‎which is produced by accelerated inviscid velocity. Hence, for a fixed sweep angle, the magnitude of ‎pressure gradient is the key parameter for the excitation and evolution of the stationary crossflow mode. ‎In order to study the effect of pressure gradient on the excitation and subsequent linear development of ‎stationary mode, a classical Falkner-Skan-Cooke boundary layer is introduced so that the magnitude of ‎pressure gradient can be easily parameterized by an acceleration coefficient. Numerical simulation is ‎performed to induce the stationary perturbation by chordwise-isolated, spanwise-periodic roughness at ‎the lower branch of neutral curve. Then the excited waves develop into Rayleigh modes in the ‎downstream region. The stationary modes with different spanwise wavenumbers in various favorable-‎pressure-gradient boundary layers are simulated and analysed to determine the effect of pressure ‎gradient. And the corresponding coupling coefficients are calculated to connect the initial amplitude and ‎the eigenmode of linear stability theory for implementing the existing prediction method of laminar-‎turbulent transition‎‎.

Turbulence Modeling in Hypersonic Turbulent Boundary Layers Subject to Convex Wall Curvature

Hypersonic boundary layers are crucial in aerospace applications such as hypersonic glide vehicles, rockets, and other advanced space vehicles. Hypersonic flows present unique transport phenomena, including nonnegligible flow compression/dilation, extra strain rates, and large momentum/thermal gradients. In this paper, the performance of three widely used turbulence models is compared, namely, the standard , the shear stress transport (SST) , and the Spalart–Allmaras (SA). Based on our turbulence modeling assessment plus the analysis of turbulent transport equation budgets over the experimental geometry from a previous study at a Mach number of 4.9, a moderate supremacy of SA over two equation models was found. To back our conclusions, previous experiments and direct numerical simulations at Mach numbers around 5 have been employed. Overall, the three considered models exhibited a consistent ability to predict first-order statistics both inside and outside the boundary layer. The SST variants were capable of describing the amplification of the constant shear layer induced by the presence of an adverse pressure gradient (APG). Furthermore, the SST model also replicated the second peak of turbulence production induced by the concave wall. There was a more aggressive distortion of the boundary layer by APG than by favorable pressure gradient (FPG) as compared with a zero pressure gradient (ZPG) boundary layer. A reasonable performance by Walz’s equation in the FPG region is also shown, whereas a notable lack of agreement is seen in the APG. Overall, one could argue for the SA model’s best compromise between accurate predictions, numerical stability, and mesh resolution insensitivity in the FPG and ZPG regions, particularly, in outer or integral boundary-layer parameters such as or . That being said, the two-equation models are far superior in terms of predicting near-wall parameters (such as or ) or their ability to accurately describe the physics of the hypersonic boundary layer for APG regions (for instance, outer-secondary peaks of turbulent kinetic energy production).

Direct numerical simulation of the two-dimensional speed bump flow at increasing Reynolds numbers

The Speed Bump flow model was designed by Boeing to provide a mildly three-dimensional flow with separation from a very smooth surface, strongly controlled by the turbulence. Experiments are conducted by several teams, as are simulations, over a range of Reynolds numbers. Direct Numerical Simulations (DNS) are not possible for the full 3D geometry of width L, leading several groups to conduct DNS over a two-dimensional geometry, in other words the cross-section of the full geometry, with periodic lateral conditions and a typical domain width of 0.04L. This does not allow precise comparisons with experiment, but code-to-code comparison is instructive. A shallow separation bubble is present, as intended. The domain width becomes marginal after reattachment, where the boundary layer is much thicker. The Reynolds number based on L has been 106, so far in the literature, which causes partial relaminarization and tends to defeat the purpose of testing turbulence models. Flow visualisation is clear on this. Here, we present results at the Reynolds number 106 and 1.4 × 106, and the higher value essentially eliminates relaminarization. Detailed results are shown, including studies of domain width, grid resolution, and numerical dissipation. The turbulence models give inaccurate results for skin friction, already in the intense favourable pressure gradient, which causes the formation of an internal boundary layer; the separation prediction on the other hand is reasonable. The wall curvature seems to play a role. The present results also provide trustworthy data to test Large-Eddy Simulation (LES), especially if using a Wall Model (WMLES). The comparisons will have a preliminary character until the results of the ongoing detailed experiments and of DNS at even higher Reynolds number and with a wider domain are available and carefully compared.

Slip hydrodynamics of combined electroosmotic and pressure driven flows of power law fluids through narrow confinements

Electroosmotic flows (EOF) in microfluidic devices can be greatly enhanced over superhydrophobic surfaces because the high shear rates within the electrical double layer can drive large slip velocities at the interface. Using the power law fluid model, we derive a novel formulation for the Helmholtz–Smoluchowski (HS) velocity and use it to examine the effect of slip on the hydrodynamics of a coupled pressure driven and EOF. Semi analytical relations for the velocity gradient are obtained for cases of a favourable pressure gradient but exact solutions of the velocity can be found only for certain power law indices. Cases of adverse pressure gradient and fractional power law indices are investigated using numerically using the Galerkin Finite Element Method. The validity of the semi analytical relations verified by comparison with the numerical method. The presence of velocity slip at the wall leads to an enhancement of the HS velocity that is most pronounced in shear thinning fluids. Adverse pressure gradients are observed to generate an inflection in the velocity profile and even a two-way flow for certain flow parameters. The strength of the adverse pressure gradient needed to setup a reverse flow at the channel centre reduces as the slip length is increased. The location of the point of inflection is found to depend on the channel height, pressure gradient, electric field, slip length, Debye length and non-Newtonian behaviour.

Local topography‐induced pressure gradient effects on the wake and power output of a model wind turbine

Wind-tunnel experiments were performed to study the effect of favorable and adverse constant pressure gradients (PG) from local changes in the topography right downwind of a model wind turbine. Particle image velocimetry was used to characterize the near and intermediate wake regions. We explored five scenarios, two favorable, two adverse PG, and a case with negligible PG. Results show that the PGs induce a wake deflection and modulate the wake. They imposed a relatively small impact on the turbulence kinetic energy and kinematic shear stress but a comparatively dominant effect on the bulk flow on the flow recovery. Based on this, a simple formulation is used to describe the impact of PG on the wake. We modeled the base flow through a linearized perturbation method; the wake is obtained by solving a simplified, integrated streamwise momentum equation. This approach reasonably estimated the flow profile and PG-induced power output variations.

Explicit Algebraic Reynolds-Stress Modeling of Pressure-Induced Separating Flows in the Presence of Sidewalls

AbstractReynolds-averaged Navier–Stokes (RANS) approach is used to simulate the steady-state of a family of pressure-induced turbulent separation bubbles in the presence of sidewalls. Different turbulence models are employed with a specific emphasis on the baseline explicit algebraic Reynolds stress model (BSL-EARSM) and the simulations are compared with experimental data. The separation and reattachment of a flat-plate turbulent boundary layer are generated through a combination of adverse and favorable pressure gradients (APG-FPG) by numerically reproducing the geometry of the wind-tunnel test section used for the experiments. Three cases are considered a large (LB) and a medium (MB) bubble presenting mean backflow, and a small bubble (SB) without mean-flow reversal. This is achieved by varying the streamwise position of the APG/FPG transition. Good agreement between the BSL-EARSM-computed solutions and the experimental results are obtained for wall-pressure and skin-friction distributions on the centerline plane of the test section as well as for the overall three-dimensional flow topology. However, both detachment and reattachment are predicted too early and the bubble length is slightly overestimated for cases LB and MB. For case LB, the streamwise Reynolds stress is estimated fairly well but its production is somewhat delayed. Normal and shear stresses are in good agreement with the experiments in the upstream part of the bubble but are significantly over-estimated in the reattachment region. The k−ω shear-stress transport (SST) model with the so-called reattachment modification performs better than the other tested linear-eddy-viscosity models but it is still unable to reproduce accurately the three-dimensional flow topology even for the “simplest” case SB. Overall, the results suggest that BSL-EARSM is the most suitable turbulence model for this flow configuration.

Direct numerical simulation of a turbulent boundary layer over a bump with strong pressure gradients

Abstract

On exactly self-similar turbulent boundary layers and single-layer scaling

Turbulent boundary layers are traditionally thought to obey two layer scaling. However, it was shown by Dixit and Ramesh [J. Fluid Mech. 615, 445–475 (2008)] that the so-called sink flow turbulent boundary layer obeys a Blasius-like scaling all through the boundary layer. We make this single layer scaling as an operational definition for perfectly equilibrium flow and derive equations for a general class of equilibrium flows with permeable walls allowing suction and blowing of fluid. Using the above definition, constraints required to be satisfied by such equilibrium turbulent boundary layers are derived and discussed in detail. Using direct numerical simulations (DNS), we demonstrate the existence of such turbulent boundary layers, and various properties of these boundary layers are studied in detail. In particular, it is shown that the mean velocity profiles and other turbulent statistics display excellent similarity, and various boundary layer parameters in such boundary layers vary systematically with the magnitude of blowing/suction parameter. By extension, it is also demonstrated by DNS that higher order moments (up to third order moments) also display streamwise self-similarity. We believe that this is an important result where self-similarity is demonstrated for the first time for higher moments of fluctuating velocity. The non-universality of the log-law coefficients in favorable pressure gradient flows is already known [S. A. Dixit and O. N. Ramesh, J. Fluid Mech. 615, 445–475 (2008) and Chauhan et al., in Proceedings of 11th EUROMECH European Turbulence Conference on Turbulence, Porto, Portugal (Springer Proceedings in Physics, 2007), pp. 239–241]. We demonstrate their non-universal nature in equilibrium boundary layers with suction and blowing using the present direct numerical simulations. Remarkably, the ratio of Reynolds shear stress (u′v′¯) to streamwise (u′2¯) and spanwise turbulent intensity (w′2¯) in these boundary layers is constant over the log-region in the mean velocity profile even though u′2¯, w′2¯, and u′v′¯ by themselves show variation with y+ in the log region, indicative of the absence of inactive motion in these flows. It is shown that the dominance of active motion and more importantly the absence of inactive motion leads to a universality of scaling that manifests as a single layer Blasius scaling with self-similarity in such flows. Equivalently, it could also be seen as a single layer scaling with all variables all through the boundary layer. This would mean that the friction velocity scales the entire boundary layer, which could be taken to suggest equivalence of attached eddies with the active component of motion.

Large-Eddy Simulation of Variable Speed Power Turbine Cascade With Inflow Turbulence

Abstract Numerical results are presented from the National Aeronautics and Space Administration (NASA) Glenn Research Center's in-house turbomachinery code Glenn-HT applied to the variable-speed power turbine (VSPT) experiment at the NASA Transonic Turbine Blade Cascade Facility. The main goal of this paper is to implement a digital filtering method to generate turbulence upstream and a subgrid model (localized dynamic k-equation model (LDKM)) in the framework of large-eddy simulation (LES) in order to investigate the effect of inflow turbulence on the transition seen in the VSPT experimental data at the cruise condition (incidence angle of 40 deg and Tu = 0.5%, 5%, 10%, and 15%). Although the boundary layer on the suction side and pressure side of the blades is initially laminar due to favorable pressure gradient, the laminar flow can transition to turbulent flow past a separation zone on the suction side or by natural or bypass transition. This process determines the total pressure losses in the wake. Therefore, it is desirable to develop a reliable prediction tool to accurately capture the transition mechanism in blade rows operated under the conditions of low Reynolds number and at a variety of freestream turbulence conditions. Our numerical studies reveal that the location of separation is rather insensitive to the level of Tu; however, the effect of increasing Tu seems to be in reducing the size and ultimately suppressing the separation bubble. In addition, we performed spectral analysis to identify the peak frequencies in the region where the separation bubble is formed, which provides valuable insights into the transition/separation mechanism.

Inertial Flow of Viscoelastic Second-Grade Fluid in a Ciliated Channel under a Magnetic Field and Darcy’s Resistance

This paper proposes a mathematical analysis of the inertial flow of an MHD second-grade non-Newtonian fluid in a ciliated channel. The two-dimensional flow is modelled under the effect of inertial forces, magnetic field and Darcy’s resistance, which make the system of partial differential equations highly non-linear. To solve the complex system of partial differential equations, the Homotopy Perturbation Method (HPM) is preferred. The HPM solutions for the velocity profile, stream function and pressure gradient are obtained using the software MATHEMATICA. The significances of the Reynolds number (due to inertial forces), Hartmann number (due to magnetic field), porosity parameter (due to Darcy’s resistance) and fluid parameters (related to the second-grade fluid) on the pressure gradient, stream function and velocity profile are discussed in detail. The pertinent parameters show that the horizontal velocity decays in the presence of a magnetic field, whereas it rises under the effect of inertial forces, Darcy’s resistance and fluid viscosity in the centre of the channel. This research indicates that, for the ciliary flow of a second-grade fluid, a favourable pressure gradient (negative pressure gradient) in the horizontal direction increases when applying a magnetic field, whereas it decreases due to the porous medium. This mathematical model can be helpful to observe ciliary activity under magnetic resonance imaging, when ciliary activity is abnormal.

Transition prediction and sensitivity analysis for a natural laminar flow wing glove flight experiment

Natural laminar flow technology can significantly reduce aircraft aerodynamic drag and has excellent technical appeal for transport aircraft development with high aerodynamic efficiency. Accurately and efficiently predicting the laminar-to-turbulent transition and revealing the maintenance mechanism of laminar flow in a transport aircraft’s flight environment are significant for developing natural laminar flow wings. In this research, we carry out natural laminar flow flight experiments with different Reynolds numbers and angles of attack. The critical N-factor is calibrated as 9.0 using flight experimental data and linear stability theory from a statistical perspective, which makes sure that the relative error of transition location is within 5%. We then implement a simplified eN transition prediction method with a similar accuracy compared with linear stability theory. We compute the sensitivity information for the simplified eN method with an adjoint-based method, using the automatic differentiation technique (ADjoint). The impact of Reynolds numbers and pressure distributions on TS waves is analyzed using the sensitivity information. Through the sensitivity analysis, we find that: favorable pressure gradients not only suppress the development of TS waves but also decrease their sensitivity to Reynolds numbers; there exist three special regions which are very sensitive to the pressure distribution, and the sensitivity decreases as the local favorable pressure gradient increases. The proposed sensitivity analysis method enables robust natural laminar flow wings design.

Adaptive-surrogate-based robust optimization of transonic natural laminar flow nacelle

Natural Laminar Flow (NLF) technology is very effective for reducing the skin friction drag of aircraft engine nacelle, but the aerodynamic performance of NLF nacelle is highly sensitive to uncertain working conditions. Therefore, it’s imperative to incorporate uncertainties into the design of NLF nacelle. In this study, for a robust optimization of NLF nacelle and for improving its efficiency, an adaptive-surrogate-based robust optimization strategy is established, which is an iterative optimization process where the surrogate model is updated to obtain the real Pareto front of multi-objective optimization problem. A case study is carried out to validate its feasibility and effectiveness. The results show that the optimization increases the favorable pressure gradient region and the volume ratio of the nacelle by increasing its lip radius and reducing its maximum diameter. And the aerodynamic robustness of the NLF nacelle is mainly determined by the lip radius, maximum diameter of nacelle and location of the maximum diameter. Compared to the initial nacelle, the optimized nacelle maintains a wide range of low drag and high laminar flow ratio in the disturbance space, which extends the average laminar flow region to 21.6% and facilitates a decrease of 1.98 counts in the average drag coefficient.

Balancing Laminar Extension and Wave Drag for Transonic Swept Wings

At a transonic condition, the design of a natural laminar flow (NLF) wing is challenging because the extension of the laminar flow needs to be finely balanced with the potential wave drag increase. To achieve this balance, it is proposed to unlock the wing sweep and introduce a three-dimensional (3-D) contour shock-control bump (SCB) in the optimization of the NLF infinite swept wing aiming at total drag reduction. A 3-D Reynolds-averaged Navier–Stokes flow solver is extended to incorporate laminar–turbulent transition prediction due to streamwise and crossflow instabilities. The flow solver is integrated in a gradient-based optimization framework. The transition criteria including streamwise and crossflow instabilities are coupled in the sensitivity calculation using a discrete-adjoint solver. Transonic design optimization of the sectional profile and wing sweep angle is first conducted at a Mach number of 0.78. The optimization managed to alleviate the shock wave, reducing the pressure drag while it failed to extend the laminar flow. Furthermore, a combined optimization of the wing with a parameterized SCB at the same condition is carried out. The optimized wing with the SCB features a long favorable pressure gradient region and a low-sweep angle, which allows for a large proportion of laminar flow without significant pressure drag. The shock wave is controlled by the 3-D bump, and the SCB has little effect on the upstream flow.

Periodic forcing of a large turbulent separation bubble

Abstract

On the influence of biomimetic shark skin in dynamic flow separation

The effect of shark skin on the boundary-layer separation process under dynamic conditions (maneuvers) has been studied experimentally. We use a foil covered with biomimetic shark skin to explore how this type of surface impacts boundary-layer dynamics in both steady and accelerating conditions. The effect of denticles is assessed via particle image velocimetry in the wake. It is shown that dynamic conditions and small-scale disturbances can mitigate boundary-layer separation through instantaneous modification of the local pressure-gradient distribution. For instance, the region of favourable pressure gradient can be extended by accelerating the foil. The acceleration results in a thinner separated shear layer on the foil surface when compared to the steady reference case. This remarkable difference indicates that local roughness (introduced through for instance biomimetic shark skin) may trigger an interaction with relatively large-scale structures in the boundary layer for effective boundary-layer control during unsteady propulsion and maneuvering.

Simulation of a turbulent flow subjected to favorable and adverse pressure gradients

This paper reports the results from a direct numerical simulation of an initially turbulent boundary layer passing over a wall-mounted “speed bump” geometry. The speed bump, represented in the form of a Gaussian distribution profile, generates a favorable pressure gradient region over the upstream half of the geometry, followed by an adverse pressure gradient over the downstream half. The boundary layer approaching the bump undergoes strong acceleration in the favorable pressure gradient region before experiencing incipient or very weak separation within the adverse pressure gradient region. These types of flows have proved to be particularly challenging to predict using lower-fidelity simulation tools based on various turbulence modeling approaches and warrant the use of the highest fidelity simulation techniques. The present direct numerical simulation is performed using a flow solver developed exclusively for graphics processing units. Simulation results are utilized to examine the key phenomena present in the flowfield, such as relaminarization/stabilization in the strong acceleration region succeeded by retransition to turbulence near the onset of adverse pressure gradient, incipient/weak separation and development of internal layers, where the sense of streamwise pressure gradient changes at the foot, apex and tail of the bump.

Global C∞ regularity of the steady Prandtl equation with favorable pressure gradient

In the case of favorable pressure gradient, Oleinik obtained the global-in-x solutions to the steady Prandtl equations with low regularity (see Oleinik and Samokhin [9], P.21, Theorem 2.1.1). Due to the degeneracy of the equation near the boundary, the question of higher regularity of Oleinik's solutions remains open. See the local-in-x higher regularity established by Guo and Iyer [5]. In this paper, we prove that Oleinik's solutions are smooth up to the boundary y=0 for any x>0, using further maximum principle techniques. Moreover, since Oleinik only assumed low regularity on the data prescribed at x=0, our result implies instant smoothness (in the steady case, x=0 is often considered as initial time).

Passive Control of Base Pressure: A Review

In the present world, passive control finds application in various areas like flow over blunt projectiles, missiles, supersonic parallel diffusers (for cruise correction), the engine of jets, static testbeds of rockets, the ports of internal combustion engines, vernier rockets, and single expansion ramp nozzle (SERN) rockets. In this review, various passive control techniques to control the base pressure and regulate the drag force are discussed. In the study, papers ranging from subsonic, sonic, and supersonic flow are discussed. Different types of passive control management techniques like cavity, ribs, dimple, static cylinder, spikes, etc., are discussed in this review article. This study found that the passive control device can control the base pressure, resulting in an enhancement in the base pressure and reducing the base drag. Also, passive control is very efficient whenever there is a favorable pressure gradient at the nozzle exit.

Hypersonic Oscillating Shock-Wave/Boundary-Layer Interaction on a Flat Plate

This work discusses the design, measurement, and simulation of an oscillating shock-wave/boundary-layer interaction on a flat plate at Mach 5.8 and . The shock generator is free to pitch and oscillates with a frequency of 42 Hz, resulting in a shock that varies in intensity and impingement point, with a maximum flow-deflection angle of approximately 10 deg. Transition appears to take place downstream of the separated region for both static (with a fixed flow-deflection angle) and dynamic experiments; however, heat-flux values are typically between laminar and turbulent solutions, thus suggesting that a complete transition to a fully turbulent boundary layer is delayed because of the favorable pressure gradient induced by the impinging expansion wave originating from trailing edge of the shock generator. Peak pressure is typically overpredicted by laminar simulations for large deflection angles. Starting from the reattachment point, heat-flux measurements show that the boundary layer gradually deviates from the laminar solution towards a fully turbulent boundary layer. Vortices are observed in the reattachment region, and their distribution is solely a function of the boundary-layer properties at the separation point. Transient effects induced by the shock motion result in a maximum bubble length variation of 30%. For the static cases, the separated region amplified disturbances with a frequency of approximately 200 Hz. In the dynamic experiment, harmonics induced by the pseudosinusoidal motion of the shock generator were measured everywhere on the plate.