Strong Favorable Pressure Gradient Research Articles

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.

Stability analyses of secondary instability and oblique breakdown in a supersonic boundary layer under the influence of pressure gradients

Studied here is how pressure gradients affect nonlinear transition processes in a supersonic flat-plate boundary layer. Linear stability analysis suggests that a favorable pressure gradient stabilizes the first-mode disturbances significantly, whereas an adverse pressure gradient destabilizes them. Nonlinear stability analysis indicates that the three nonlinear mechanisms of fundamental resonance, subharmonic resonance, and oblique breakdown can induce transition. Oblique breakdown causes the earliest transition, and subharmonic resonance is stronger than fundamental resonance. An adverse pressure gradient significantly destabilizes the primary modes and enhances the nonlinear transition mechanisms. However, a favorable pressure gradient affects the different nonlinear transition processes differently. A weak favorable pressure gradient completely suppresses the transition in fundamental resonance but just delays it slightly in subharmonic resonance. For oblique breakdown, a weak favorable pressure gradient delays the transition significantly, with two high-speed streaks observed clearly. In all cases, a strong favorable pressure gradient leads to a fully laminar flow.

Pressure gradient effect on flame–vortex interaction in lean premixed bluff body stabilized flames

This investigation considers the effect of axial pressure gradient on the dynamics of flame–vortex interaction for a lean premixed bluff body stabilized flame. Large eddy simulations (LESs) of four different combustor geometries generated through combustor wall adjustments that resulted in mild to strong pressure gradients are studied. A bluff body stabilized combustor for a propane/air flame is analyzed first. The results are compared with all available experimental data with the purpose of validating the LES methodology used in OpenFOAM and obtaining a base solution for the study of the pressure gradient effect on flame–vortex interaction. The role of the pressure gradient on flame structure, emission characteristics, vortex dynamics, and flame stability is presented. The mild favorable pressure gradient due to the decelerated flow in diffuser configurations influences flame–vortex dynamics by suppressing flame-induced vorticity sources, baroclinic torque and dilatation, and hence resulting in augmented hydrodynamic instabilities. The sustained hydrodynamic instabilities maintain the large flame wrinkles and sinusoidal flame mode in the wake region. The nourished near-lean blowoff dynamics also affect the emission characteristics, and the emission of species increases. However, the accelerated flow in the nozzle configuration amplifies the flame-induced vorticity sources that preserve the flame core, resulting in a more organized, symmetric, and stable flame. Ultimately, the combustion performance and operation envelope in the lean premixed flames can be increased by maintaining the flame stability and suppressing the limiting lean blowoff dynamics and emissions with the help of a strong favorable pressure gradient generated through adjusting the combustor geometry.

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.

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

Abstract

Reynolds shear stress modeling in turbulent boundary layers subject to very strong favorable pressure gradient

Recent numerical predictions of turbulent boundary layers subject to very strong Favorable Pressure Gradient (FPG) with high spatial/temporal resolution, i.e. Direct Numerical Simulation (DNS), have shown a meaningful weakening of the Reynolds shear stresses with a lengthy logarithmic behavior [1,2]. In the present study, assessment of the Shear Stress Transport and Spalart-Allmaras turbulence models (henceforth SST and SA, respectively) in Reynolds-averaged Navier-Stokes (RANS) simulations is performed. The main objective is to evaluate the ability of popular turbulence models in capturing the characteristic features present during the quasi-laminarization phenomenon in highly accelerating turbulent boundary layers. A favorable pressure gradient is prescribed by a top converging surface (sink flow) with an approximately constant acceleration parameter of K=4.0×10−6. Validation of RANS results is carried out by means of a large DNS dataset [1]. Generally speaking, the SA turbulence model has demonstrated the best compromise between accuracy and quick adaptation to the turbulent inflow conditions. Turbulence models properly captured the increasing trend of the freestream and friction velocity in highly accelerated flows; however, they fail to reproduce the decreasing behavior of the skin friction coefficient, which is typical in early stages of the quasi-laminarization process. Both models have shown deficient predictions of the decreasing and logarithmic behavior of Reynolds shear stresses as well as significantly overpredicted the production of Turbulent Kinetic Energy (TKE) in turbulent boundary layers subject to very strong FPG.

Turbulent wake behind a concave curved cylinder

We present a detailed study of the turbulent wake behind a quarter-ring curved cylinder at Reynolds number$Re=3900$(based on cylinder diameter and incoming flow velocity), by means of direct numerical simulation. The configuration is referred to as a concave curved cylinder with incoming flow aligned with the plane of curvature and towards the inner face of the cylinder. Wake flows behind this configuration are known to be complex, but have so far only been studied at low$Re$. This is the first direct numerical simulation investigation of the turbulent wake behind the concave configuration, from which we reveal new and interesting wake dynamics, and present in-depth physical interpretations. Similar to the low-$Re$cases, the turbulent wake behind a concave curved cylinder is a multi-regime and multi-frequency flow. However, in addition to the coexisting flow regimes reported at lower$Re$, we observe a new transitional flow regime at$Re=3900$. The flow field in this transitional regime is dominated not by von Kármán-type vortex shedding, but by periodic asymmetric helical vortices. Such vortex pairs exist also in some other wake flows, but are then non-periodic. Inspections reveal that the periodic motion of the asymmetric helical vortices is induced by vortex shedding in its neighbouring oblique shedding regime. The oblique shedding regime is in turn influenced by the transitional regime, resulting in a unified and remarkably low dominating frequency in both flow regimes. Owing to this synchronized frequency, the new wake dynamics in the transitional regime might easily be overlooked. In the near wake, two distinct peaks are observed in the time-averaged axial velocity distribution along the curved cylinder span, while only one peak was observed at lower$Re$. The presence of the additional peak is ascribed to a strong favourable base pressure gradient along the cylinder span. It is noteworthy that the axially directed base flow exceeded the incoming velocity behind a substantial part of the quarter-ring and even persisted upwards along the straight vertical extension. As a by-product of our study, we find that a straight vertical extension of 16 cylinder diameters is required in order to avoid any adverse effects from the upper boundary of the flow domain.

Separation mechanics of non-slender delta wings during streamwise gusts

The dynamic-stall behavior on a generalized non-slender delta wing subjected to streamwise gusts has been investigated experimentally. A 45∘ sweep, NACA0012 delta wing serves as the canonical shape. In lieu of varying inflow conditions, the model is accelerated in the streamwise direction from a chord-based Reynolds number of 300,000 to 450,000 through a ramp motion at incidence angles near maximum steady-state lift. Force augmentation both during and after the gust is shown to be dependent on the initial structure of separated leading edge shear layers, with strong sensitivity at an angle of attack of 30∘. It is shown that lift enhancement stems from initially separated flow near the wing apex reattaching during the gust. Surface pressure measurements show that the reattachment is driven by a strong favorable pressure gradient that is maintained after the gust ends. The equations governing near-wall vortex dynamics state that vorticity flux from the wall increases with favorable pressure gradients, indirectly predicting an increase in circulation near the wing surface during a streamwise gust. However, circulation obtained through Particle Image Velocimetry (PIV) on the z∕c=0.1, 0.3, and 0.5 spanwise sections does not support this prediction, rather showing that the circulation in the wake (near the wing surface) remains nearly constant throughout the gust. Overall, strong three-dimensional gradients dictate flow structure before and after the gust. Spanwise variation of flow structure is especially pronounced for the 30∘ angle of attack case, where each planar section exhibits unique separation behavior in response to the gust.

Structural Reynolds analogy in laminarescent boundary layers via DNS

Visualization of the thermal field in highly accelerated spatially developing turbulent boundary layers is carried out. Direct Numerical Simulation with high spatial/temporal resolution is performed in sink flow-type boundary layer by prescribing a passive scalar with a Prandtl number of 0.71. The range of the momentum thickness Reynolds number is approximately 320–432. The very strong Favorable Pressure Gradient (FPG) is imposed by a top converging shearless surface, which produces an approximately constant acceleration parameter of $$K = 4.0 \times 10^{-6}$$ . A precursor zone is prescribed upstream of the FPG region in order to generate accurate turbulent inflow information by means of the methodology proposed by Araya et al. (J Fluid Mech 670:518–605, 2011). While evident “signatures” of the very strong FPG have been identified in the velocity field, those “signatures” are much less evident in the temperature field causing a breakdown of the Reynolds analogy provoked by the streamwise pressure gradient (or source of dissimilarity between the momentum and thermal transport). A slow decrease in the thermal boundary layer thickness, $$\delta _T$$ , is observed in the FPG zone. Additionally, local maxima of absolute intensities of the thermal fluctuations $$t'_\mathrm{RMS}$$ exhibit nearly constant values (approx. 14% of $$T_{\infty }$$ ) along the composite domain. Conversely, absolute intensities of the streamwise ( $$u'_\mathrm{RMS}$$ ) show increases on their local maxima, with mild decreases in the transversal components of the velocity ( $$v'_\mathrm{RMS}$$ and $$w'_\mathrm{RMS}$$ ). Furthermore, profiles of cross-correlation $$ $$ at different streamwise stations depict a good collapsing level up to 4% of $$\delta$$ in the wall-normal direction, with peak values displacing farther from the wall in the FPG zone.

Visualization and assessment of turbulent coherent structures in laminarescent boundary layers

Direct numerical simulation (DNS) with high spatial/temporal resolution of spatially developing turbulent boundary layers subject to very strong favorable pressure gradient (FPG) has been performed. The sudden acceleration imposed on the flow provokes a significant attenuation of turbulent intensities (Araya et al. in J Fluid Mech 775:189–200, 2015), particularly due to the dominance of pressure forces over approximately frozen Reynolds stresses, Narasimha and Sreenivasan (Adv Appl Mech 19:221–309, 1979). In this article, visualization of the DNS velocity field is carried out in order to evaluate the effect of very strong FPG on elementary coherent structures, such as low- and high-speed streaks, sweeps and ejections, quasi-streamwise and horseshoe vortices, and large-scale motions. An important symbiosis between quasi-streamwise vortices and low-speed streaks (or regeneration cycle) has been observed in the FPG zone. The destabilizing shear layers upstream of vortex heads in strong accelerated flows appear as very thin zones developing in the buffer region ( $$20<y^+< 30$$ ). It seems that decaying $$uv'$$ in strong FPG flows (Araya et al. 2015) is principally due to the annihilation of sweeps, while ejections are responsible for the turbulence residual.

An Assessment of the Two-Layer Quasi-Laminar Theory of Relaminarization Through Recent High-Re Accelerated Turbulent Boundary Layer Experiments

The phenomenon of relaminarization is observed in many flow situations, including that of an initially turbulent boundary layer (TBL) subjected to strong favorable pressure gradients (FPG). As several experiments on relaminarizing flows have indicated, TBLs subjected to high pressure gradients do not follow the universal log-law, and (for this and other reasons) the prediction of boundary layer (BL) parameters using current turbulence models has not been successful. However, a quasi-laminar theory (QLT; proposed in 1973), based on a two-layer model to explain the later stages of relaminarization, showed good agreement with the experimental data available at that time. These data were mostly at relatively low Re and hence left the precise role of viscosity undefined. QLT, therefore, could not be assessed at high-Re. Recent experiments, however, have provided more comprehensive data and extended the Reynolds number range to nearly 5 × 103 in momentum thickness. These data provide a basis for a reassessment of QLT, which is revisited here with an improved predictive code. It is demonstrated that even for these high-Re flows subjected to high acceleration, QLT provides good agreement with experimental results, and therefore, has the potential to substitute for Reynolds-averaged Navier–Stokes (RANS) simulations in high FPG regions.

The logarithmic and power law behaviors of the accelerating, turbulent thermal boundary layer

Direct numerical simulation of spatially evolving thermal turbulent boundary layers with strong favorable pressure gradient (FPG) shows that the thermal fluctuation intensity, θ′+ and the Reynolds shear stress, u′v′¯+ exhibit a logarithmic behavior spanning the meso-layer (e.g., 50≤y+≤170). However, the mean thermal profile is not logarithmic even in the zero pressure gradient (ZPG) region; instead, it follows a power law. The maxima of u′2¯+ and v′θ′¯+ change little with the strength of acceleration, while v′+, w′+, and u′v′¯+ continue to decay in the flow direction. Furthermore, θ′+ and u′θ′¯+ surprisingly experience changes from constants in ZPG to sharp rises in the FPG region. Such behavior appears to be due to squashing of the streaks which decreases the streak flank angle below the critical value for “transient growth” generation of streamwise vortices, shutting down production [W. Schoppa and F. Hussain, “Coherent structure generation near-wall turbulence,” J. Fluid Mech. 453, 57–108 (2002)]. The streamwise vortices near the wall, although shrink because of stretching, simultaneously, also become weaker as the structures are progressively pushed farther down to the more viscous region near the wall. While the vortical structures decay rapidly in accelerating flows, the thermal field does not—nullifying the myth that both the thermal and velocity fields are similar.

The effect of contact line pinning favors the mass production of monodisperse microbubbles

A robust method for the generation of phospholipid-covered monodisperse microbubbles of diameters smaller than 10 μm at production rates larger than 105 Hz is presented here. We show that bubbles are periodically formed from the tip of a long and thin gas ligament stabilized thanks to both the strong favorable pressure gradient existing at the entrance region of a long rectangular PDMS–PDMS channel and to the pinning of the gas–liquid interface at a centered groove of several microns' width placed on one of its walls. Moreover, the long exit channel incorporated in our design favors the transport of phospholipid molecules toward the gas–liquid interface. Our experiments show that the resulting phospholipid shell inhibits both the diffusion of the gas in the surrounding liquid and the coalescence between contacting bubbles. These evidences indicate that the proposed method is suitable for the generation of monodisperse microbubbles for diagnosis or therapeutical applications.

Effects of compound angle on film cooling effectiveness with different streamwise pressure gradient and convex curvature

Streamwise pressure gradient and surface curvature are two important characteristics of turbine flow and compound angle film cooling is an efficient way to improve cooling performance. Compound angle film cooling effectiveness with those two effects was investigated using PSP technology. The corresponding numerical studies were validated and carried out to investigate the physical mechanism of the interaction between the coolant jet and the main flow. Compound angle increases film cooling effectiveness for high blowing ratios in the near hole region, but the stronger interaction between the jet and the main flow makes the coolant dissipate faster. On the flat surface, the favorable pressure gradient leads to a maximum of 50% increase of film cooling effectiveness compared with the adverse pressure gradient case. On the convex surface, the cooling jet is pushed to the wall by the radial pressure gradient in the free stream which makes film cooling effectiveness 20–50% higher than the flat wall case. The compound angle film cooling performance under strong favorable pressure gradient for the convex surface is quite different from the flat wall case and thus streamwise pressure gradient and surface curvature should be taken into consideration in gas turbine film cooling design.

Large Eddy Simulation of supersonic jet plumes from rectangular con-di nozzles

A Large Eddy Simulation investigation is described of a supersonic jet discharging from a rectangular convergent–divergent nozzle at a Nozzle Pressure Ratio typical of military aircraft propulsion. Accurate inlet conditions and an appropriate choice of sub-grid scale modelling, as well as appropriate mesh design, are essential for good LES predictions. The present work adopts an LES inlet condition generation method based on a rescaling/recycling method (R2M) and the Piomelli and Guerts SGS (PGSGS) model, which has the attractive feature of being independent of filter width (mesh size), but has not previously been used in combined boundary layer/free shear flow. Results show that the R2M technique was able to generate an unsteady, correlated 3D velocity field at the nozzle inlet plane which matched available experimental data and possessed physically consistent spatial and temporal correlations. Using an appropriately refined mesh, turbulence was sustained through the nozzle after experiencing strong favourable pressure gradient induced relaminarisation effects, enabling good prediction of the nozzle exit boundary layer state and hence the near field jet plume development. The PGSGS model was observed to improve predictions compared to the standard Smagorinsky SGS model.

Subgrid-scale modelling in relaminarizing flows

The reversion of a turbulent flow to a laminar or quasi-laminar state may take very different paths, depending on the cause of the relaminarization; modelling these flows is quite difficult. Large-eddy simulations (LES) may be quite effective as the large, momentum-carrying eddies are accurately resolved; the unresolved, subgrid-scale (SGS) stresses, however, may still play an important role. We report here the results of an a priori analysis of the behaviour of the SGS stresses in two relaminarizing flows: a plane channel subjected to spanwise rotation, and a boundary layer subjected to a strong favourable pressure gradient resulting in freestream acceleration. The a priori test results are accompanied by actual LES, which highlight the effect of grid resolution and modelling errors on the dynamics of the relaminarization. Dynamic SGS models predict the overall features of the relaminarization correctly, although some of the details are not captured. At the levels of grid refinement used, however, the SGS contribution to momentum transport is very small, and little difference is observed between the results obtained with the various models.

구심터빈의 노즐 내부 유동에 대한 시험 연구

Experimental study on the flow field inside the nozzle for radial turbine was performed. At design point, the pressure is high and the Mach number is low at the pressure side of the nozzle inlet semi-vaneless space as the flow turns through the nozzle vanes. As the flow accelerates through the nozzle passage to the throat the pressure level at the pressure and suction sides becomes similar. The flow continued accelerating from the throat to the inlet of turbine wheel and the pressure field became uniform in the circumferential direction in the vaneless space. In high expansion ratio condition, strong favorable pressure gradient band region occurred just after the throat in the semi-vaneless space in the circumferential direction and the pressure became uniform in the circumferential direction after this band. In low expansion ratio condition, core flow acceleration is dominant after the throat and this non-uniform pressure field reached to the inlet of turbine wheel.

Similarity analysis of favorable pressure gradient turbulent boundary layers with eventual quasilaminarization

Using similarity analysis, the scales and similarity constraints for a favorable pressure gradient (FPG) turbulent boundary layer with eventual quasilaminarization are obtained. In order to achieve equilibrium in the boundary layer, the pressure parameter Λ must be a constant; thus, a power relation between the boundary layer thickness δ and the free-stream velocity U∞ exists. Consequently, the power is given by the pressure parameter Λ as δ∼U∞−1/Λ. Through an analysis using the pressure parameter, two quadrants are found: quadrant I describes FPG turbulent flows and quadrant II corresponds to quasilaminar flows. Moreover, a horizontal line exists for zero pressure gradient flows. Different values of the pressure parameter are found for equilibrium FPG flows, contrary to the findings of Castillo and George [“Similarity analysis for turbulent boundary layer with pressure gradient: Outer flow,” AIAA J. 39, 41 (2001)]. In the case of strong FPG flows with quasilaminarization, the pressure parameter reaches a maximum value of 0.47. At this point, a sudden reduction in the skin friction of about 57% is observed and a redistribution of the Reynolds stresses throughout the boundary layer is achieved. The mean velocity deficit profiles are also found to be attenuated when scaled using the free-stream velocity U∞ or U∞δ∗/δ. For flows in quadrant II, a reduction in the outer flow of the ⟨u2⟩ component of the Reynolds stress is observed, whereas the ⟨v2⟩ and −⟨uv⟩ components nearly vanish impending quasilaminarization. Due to the presence of the ⟨u2⟩ component in the boundary layer, the flow never reaches a full laminar state and a more uniform redistribution of the component is observed as the skin friction decreases due to the imposed FPG. Furthermore, the shape of the profile remains the same until a quasilaminar state is reached, where the profile no longer shows high values of the stress on the proximity to the wall. In addition, the production term −⟨uv⟩dU/dy is nearly zero for flows in quadrant II. Also, the boundary layer parameters such as the shape factor H and the ratio of the displacement thickness to the boundary layer thickness, δ∗/δ, increase as the flow achieves a quasilaminar state.

An Experimental Study of Artificially-Generated Turbulent Spots Under Strong Favorable Pressure Gradients and Freestream Turbulence

This paper presents experimental results on the internal flow structure of turbulent spots, and examines the sensitivity of this structure to streamwise acceleration rate and freestream turbulence. Measurements were performed on a flat plate, with two levels of freestream acceleration rate and three levels of freestream turbulence. The turbulent spots were generated artificially at a fixed distance from the test-surface leading edge, and the development of the spot was documented through hotwire measurements at three streamwise locations. The measurements were performed at multiple spanwise locations to allow observation of the three-dimensional spatial structure of the turbulent spot and the temporal evolution of this structure. Analysis of the perturbation velocity and rms velocity fluctuations provides insight into the variations of the streaky streamwise-velocity structure within the turbulent spot, with a focus on the effects of freestream acceleration rate and turbulence level.

The influence of high free-stream turbulence and a favourable pressure gradient on an incompressible axisymmetric turbulent boundary layer

This experimental study investigates the effect of high free-stream turbulence intensity Tu δ ⩽ 13 % on a turbulent boundary layer in a strong favourable pressure gradient K = ( ν / u δ 2 ) ( d u δ / d x ) ⩽ 3.6 × 10 −6 . The Reynolds number Re δ 2 at the beginning of the favourable pressure gradient (FPG) is about 1200. The pressure gradient and the free-stream turbulence (FST) affect the development of the boundary layer, but the decay rate of Tu δ in the streamwise direction depends both on the magnitude of the initial level of Tu δ and on the pressure distribution. Therefore, two boundary layers were investigated in detail with the same pressure distribution but with different initial levels of FST. The investigation showed that only a high FST level reduced the relaminarization of the boundary layer which occurred without FST and less so at small FST. Extensive hot-wire and skin-friction measurements were made and the data comprise mean velocity profiles, Reynolds stresses, velocity correlations, integral length scales and power spectra for the streamwise velocity component.