Favorable Pressure Gradient Research Articles

Double Wall Cooling of a Full-Coverage Effusion Plate With Main Flow Pressure Gradient, Including Internal Impingement Array Cooling

The present study provides new effusion cooling data for both the surfaces of the full-coverage effusion cooling plate. For the effusion-cooled surface, presented are spatially resolved distributions of surface adiabatic film cooling effectiveness and surface heat transfer coefficients (measured using transient techniques and infrared thermography). For the impingement-cooled surface, presented are spatially resolved distributions of surface Nusselt numbers (measured using steady-state liquid crystal thermography). To produce this cool-side augmentation, impingement jet arrays at different jet Reynolds numbers, from 2720 to 11,100, are employed. Experimental data are given for a sparse effusion hole array, with spanwise and streamwise impingement hole spacing such that coolant jet hole centerlines are located midway between individual effusion hole entrances. Considered are the initial effusion blowing ratios from 3.3 to 7.5, with subsonic, incompressible flow. The velocity of the freestream flow which is adjacent to the effusion-cooled boundary layer is increasing with streamwise distance, due to a favorable streamwise pressure gradient. Such variations are provided by a main flow passage contraction ratio CR of 4. Of particular interest are effects of impingement jet Reynolds number, effusion blowing ratio, and streamwise development. Also, included are comparisons of impingement jet array cooling results with: (i) results associated with crossflow supply cooling with CR = 1 and CR = 4 and (ii) results associated with impingement supply cooling with CR = 1, when the mainstream pressure gradient is near zero. Overall, the present results show that, for the same main flow Reynolds number, approximate initial blowing ratio, and streamwise location, significantly increased thermal protection is generally provided when the effusion coolant is provided by an array of impingement cooling jets, compared to a crossflow coolant supply.

Direct numerical simulation of a turbulent boundary layer with separation and reattachment over a range of Reynolds numbers

Direct numerical simulations (DNSs) are used to examine a turbulent boundary layer with large magnitudes of adverse and favourable pressure gradients, thus involving separation and reattachment. The present DNS datasets have been obtained from the simulations of a pressure-induced turbulent separation bubble (Abe 2017 J. Fluid Mech. 833 563–98). Three values of the inlet Reynolds number ( 600 and 900) are used. These magnitudes increase abruptly with pressure gradients; the maximum values are attained near reattachment (i.e. 2070 and 2915). Also used are the datasets with varying pressure gradient for a fixed inlet Reynolds number (). Particular attention is given to effects of Reynolds number and pressure gradient on the momentum transport. In particular, we examine the Reynolds shear stress () with the use of the transport equation, quadrant analysis and instantaneous fields and discuss how this quantity is generated in the present flow and is associated with mean streamwise velocity (). It is shown that the magnitude of increases in the APG and separated regions, while it decreases near top of the bubble due to the convex curvature when the bubble is large. For all three Reynolds numbers, the peaks are obtained in the outer region in which exhibits an inflection point. The similarity to a free shear flow in is convincing in the separated shear layer where the effect of the inlet Reynolds number (i.e. the active motion in an incoming boundary layer) is still observed in The maximum is attained after reattachment due to the convective nature of the present flow and depends essentially on the pressure gradient. It is also shown that large-scale structures of streamwise velocity fluctuation become more pronounced with moving downstream and contribute significantly to the momentum transport, which yield a large departure from the log law of mean streamwise velocity.

Actively Reduced Airfoil Drag by Transversal Surface Waves

The flow over a DRA2303 wing section at a Reynolds number of Re = 400,000 is actively controlled by spanwise traveling transversal surface waves. The actuated low-Mach number flow is investigated by a high-resolution large-eddy simulation. Approximately 74% of the solid surface on both sides of the wing section is deflected by a sinusoidal space- and time-dependent function in the wall-normal direction. The turbulence intensitites and wall-normal vorticity fluctuations are significantly reduced and a shift from one-dimensional turbulence to two-dimensional turbulence is observed. Besides a viscous drag reduction by 8.6% with a strong decrease of skin-friction in the favorable pressure gradient region and an overall drag decrease by 7.5%, a slight increase in lift is achieved for an external flow over a realistic geometry.

Numerical study of effect of pressure gradient on boundary-layer receptivity under localized wall blowing/suction

Boundary-layer receptivity is the initial stage of the laminar-turbulent transition process, and plays a key role in predicting and controlling the transition. The present researches indicate that the boundary-layer receptivity is affected not only by the different sorts of free-stream disturbances or the size, shape and position of the wall localized roughness and blowing/suction, but also by the pressure gradient. Therefore, the local receptivity under the interaction between the free-stream turbulence and localized wall blowing/suction in the pressure-gradient boundary layer is studied in the present work, thus revealing the effect of the pressure gradient on the receptive process and the group speeds of the excited T-S wave packets under the interaction of the free-stream turbulence with localized wall blowing/suction in the boundary layer. High-order finite difference scheme is utilized to discretize the incompressible perturbation Navier-Stokes equation. A modified fourth-order Runge-Kutta scheme is used for time integration. The compact difference scheme based on non-uniform meshes is applied to the spatial discretization. The convective term is discretized by the fifth-order upwind compact scheme. The pressure gradient term is discretized by the sixth-order symmetric compact scheme. The viscosity term is discretized by the fifth-order symmetric compact scheme. Besides, the pressure Poisson equation is solved by the fourth-order scheme on the non-uniform meshes. The favorable or adverse pressure gradient promotes or suppresses the receptivity triggered by the interaction between free-stream turbulence and blowing/suction. And the blowing always induces a stronger receptivity than the suction in the same intensity. The initial amplitude of the T-S wave and wave packet excited in the adverse-pressure-gradient boundary layer are two orders larger than those excited in the favorable-pressure-gradient boundary layer. It is analyzed in detail that the favorable and adverse pressure gradient play a promoting or suppressing role in the growth of the excited T-S wave. Then the influences of the pressure gradient on the amplitudes, growth rates, wave numbers, phase speeds and shape functions of the excited T-S waves are investigated. The intensive research on receptivity in the pressure-gradient boundary layers provides a reference for designing the turbine machinery blades in the practical engineering.

Properties of Turbulence Wedge Generated by a Single Roughness Element under Favorable Pressure Gradient

Properties of Turbulence Wedge Generated by a Single Roughness Element under Favorable Pressure Gradient

Laminarization of Flow with Heat Transfer in a Plane Channel with a Confuser

The process of laminarization of turbulent flow with heat transfer in a plane confuser with a constant constriction angle is numerically simulated. The effect of the favorable longitudinal pressure gradient on the flow and heat transfer parameters is shown. The results of the calculations are compared with the experimental data on the heat transfer. The value of the acceleration parameter, at which flow in the channel becomes fully laminar, is determined.

Structure in the outer layer of a turbulent boundary layer subjected to favorable pressure gradient

Structure in the outer layer of a turbulent boundary layer subjected to favorable pressure gradient

Application of WMLES to wall-bounded flows with pressure gradient

Two models, an algebraic WMLES and IDDES, were tested on their ability to predict wall-bounded flows with pressure gradient. A developed flow between two moving flat plates under an adjusted pressure gradient (Couette-Poiseulle flow) was used for testing. Within two considered test cases three types of boundary layers were examined: boundary layer with adverse pressure gradient (APG), boundary layer with favorable pressure gradient (FPG) and a wall-bounded flow with negligible skin-friction. It was shown that both models are capable of accurate prediction of the flow structure and mean parameters of boundary layers with APG and FPG and of frictionless wall-bounded flow. The difference between simulation results and DNS data is less than 7%.

Unsteady separated stagnation-point flow over a permeable surface

In this paper, we have investigated numerically the unsteady separated stagnation-point flow of an incompressible viscous fluid over a porous flat plate subjected to continuous suction or blowing. The analysis covers the complete range of the suction/blowing parameter d, including $$d = 0$$ and $$d \rightarrow \pm \infty $$ , in conjunction with the flow strength parameter $$a (> 0)$$ and the unsteadiness parameter $$\beta $$ . Two types of solutions, namely attached flow solution (AFS) and reverse flow solution (RFS), have been found for a negative value of $$\beta $$ . A novel result that emerges from our analysis is the characteristic features of the boundary layer flows which firmly depend on the sum values of $$(a + \beta )$$ in case of massive blowing $$(d \ll 0)$$ given at the wall. In fact, a negative value of $$(a + \beta )$$ opposes the flow like an adverse pressure gradient and the solution domain ends off with a RFS. On the other hand, a positive value of $$(a + \beta )$$ assists the flow like a favourable pressure gradient for which the solution continues with an AFS. An interesting result of this analysis is that after a certain negative value of $$(a + \beta )$$ , dependent on a and $$\beta $$ , the solution of this flow problem does not exist for blowing, and this trend persists even for suction $$(d>0)$$ . On the other hand, for large positive values of $$(a + \beta )$$ , the attached flow solution exists in case of both strong suction and massive blowing, whereas for small positive values of $$(a + \beta )$$ and especially in case of hard blowing, the solution of the governing boundary layer equation does not appear to have the boundary layer character. Furthermore, when $$(a + \beta ) = 0$$ , the velocity gradient at the wall is zero for both AFS and RFS flows, and ultimately, the governing boundary layer equation produces a trivial solution which does not satisfy the outer boundary condition.

Effect of submerged vegetation density on flow under favorable pressure gradient

Many species of flexible submerged vegetation are observed in natural streams in which the flow is rarely uniform. For better understanding the effect of flexible submerged vegetation density on the flow, experiments were conducted in the Hydraulics Laboratory of Isfahan University of Technology, Iran. Two runs with grassy artificial weeds with high and low density and one run without vegetation as a base case under favorable pressure gradient (FPG) flow were considered. Results showed the distributions of drag coefficient vary along vegetation strip. For both vegetation densities from bed to $$z/H = 0.6,$$ the velocity profile trend was like that in emergent vegetation. This result could be inferred from the low degree of vegetation submergence. The Reynolds shear stress showed a wavy distribution at both submerged vegetation densities under FPG flow. The maximum and minimum values of Reynolds shear stress were more in dense vegetation than in sparse one. In addition, results revealed turbulence intensity depend not only on FPG flow, but also on the vegetation density.

Corrugated Tabs for Enhanced Mixing of Supersonic Elliptic Jet

AbstractThe present study quantifies the mixing efficiency of triangular tabs with and without corrugation, in the presence of favorable and adverse pressure gradients. Measurements were carried ou...

FLOW BEHAVIOUR OF OIL BLOB THROUGH A CAPILLARY TUBE CONSTRICTION DURING PULSED INJECTION

A numerical simulation of flow of oil blob through a capillary tube constriction is presented. The simulation was run in a 2D axisymmetric model. Water is injected at the inlet to mobilize oil blob placed near the capillary tube constriction. Transient flow images were used to understand the flow evolution process. Results from the study show that pulsed injection effectively assisted to squeeze out the oil blob through the capillary tube constriction with shorter time compared to continuous injection. Pulsed injection reduced the time required for the first droplet to cross the capillary tube constriction by about 3 folds compared to continuous injection. In addition, the droplet that crossed the constriction is larger when the flow was pulsed. In both cases, there is a reverse flow in the opposite direction of the injection. However, the severity of the reverse flow is stronger in the case of continuous injection. Immediately downstream the constriction, there is an adverse pressure gradient zone during continuous injection which limits the mobility of droplet that crossed the constriction. However, in the case of pulsed injection, there is a favorable pressure gradient zone immediately downstream the constriction. This zone expedites mobility of droplets that cross the constriction by transporting them further downstream through suction effect. Apparently, pulsed injection eases off the adverse pressure gradient and allowed more volume of oil to pass through the constriction. Within about two periods of pulsation, 84% of original oil placed at the beginning crossed the constriction compared to only 35% in the case of continuous injection. Even though the same amount of water was injected in both cases, pulsed injection clearly altered the flow behavior. The observation from this study may be extended to more complex flows in order to tailor the method for certain specific applications, such as flow of residual oil through a reservoir.

Supersonic Jet Control by Tabs with Slanted Perforation

Abstract Control of Mach 1.8 circular jet with slanted perforated tabs is studied experimentally. Two sets of perforated tabs were used for this study. The perforation angles were 0° and 30° with respect to axis of the nozzle. The blockage areas of the tabs were 5 %. The mixing enhancements caused by these tabs were studied in the presence of adverse and favorable pressure gradients, corresponding to nozzle pressure ratio (NPR) of 4, 5.74 and 8. For Mach number 1.8, jet NPR 4 corresponds to 30 % adverse pressure gradients and NPR 8 corresponds to 39.37 % favorable pressure gradients. The pressure decay characteristics and shadowgraph images of perforated tabs at different NPR were compared. There is 45 % and 65 % reduction in jet core length were observed for the 0° and 30° perforated tabs respectively in both pitot and shadowgraph experiments in comparison to uncontrolled jet.

Impact of pure favorable pressure gradient on a supersonic flat-plate turbulent boundary layer

By employing the particle image velocimetry and Nanoparticle-based Planar Laser Scattering method, the impact of streamwise favorable pressure gradient on the mean and turbulent characteristics of a Mach 2.95 turbulent boundary layer is experimentally investigated. Through a careful arrangement of the experiment, the possible influence of streamline convex curvature is minimized to have a flat-plate streamwise favorable-pressure-gradient boundary layer. While the log law is found to be well preserved at all streamwise positions, the wake region is weakened by the pressure gradient. Different from the boundary layers formed over the convex wall and over the sudden expansion ramp, both principal strain rate and bulk dilatation in the near-wall region are found to be barely changed along the streamwise direction in the flat-plate favorable-pressure-gradient boundary layer. Because of this, the impact of the favorable pressure gradient on the near-wall turbulent fluctuation is also found to be insignificant, which differs from the supersonic convex boundary layer where the near-wall turbulence is found to be greatly suppressed.

Physics of unsteady thrust and flow generation by a flexible surface flapping in the absence of a free stream

Inspired by the flexible wings and fins of flying and swimming animals, we investigate the flow induced by the interaction between a flapping flexible surface and the surrounding fluid for the limiting case of Strouhal numberSt→∞(zero free-stream speed). The model selected for this purpose is a two-dimensional sinusoidally pitching rigid symmetric foil to which is attached at the trailing edge a thin chordwise flexible surface (along the chord line). The flow so generated is a coherent jet aligned along the foil centreline, containing a reverse Bénard–Kármán vortex street and delivering a corresponding unidirectional thrust. We analyse the flow and thrust generation process. The measured velocity field suggests that the flow and thrust generation mainly occurs during the phases when the trailing edge is near the centreline. Flexibility of the surface is important in accelerating the near-wake flow and in transferring momentum and energy to the fluid. We present a detailed account of when and where the momentum and energy are added to the fluid. This study shows that the deformations of the flexible surface are responsible for generating a favourable pressure gradient along the jet direction, and for the observed unsteady actuator disc-type action.

Shape optimization and experimental research of near space airship

Shape optimization has important effects on drag reduction of the near-space airship. This paper uses the Bezier curve to parameterize the hull of the airship. Based on multiple island genetic algorithms, the optimization platform combined with different programs is established, and a kind of low drag hull is obtained by optimization. Force measurement and flow observation wind tunnel test are used to research the aerodynamic characteristics of the ellipsoid hull and the optimized hull. Results show that, optimization mainly increases the volume ratio and the favorable pressure gradient region of the hull, therefore the surface area is reduced and transition position of the hull can be delayed. Compared with the LOTTE shape, transition position of the optimized shape moved backward by 13.78%, and the volume drag coefficient is reduced by 11.1%. It is known from the wind tunnel test that compared with the ellipsoid hull, transition position of the optimized shape moves backward obviously. Under the condition that the volume Reynolds number is 2.97 × 106, compared with the ellipsoid hull, volume drag coefficient of the optimized shape can reduce by 39.0%.

Wind turbine wakes over hills

Understanding and predicting the behaviour of wind turbine wake flows over hills is important for optimal design of wind-farm configurations on topography. In this study, we present an analytical modelling framework together with large-eddy simulation (LES) results to investigate turbine wakes over two-dimensional hills. The analytical model consists of two steps. In the first step, we deal with the effect of the pressure gradient on the wake evolution; and in the second step, we consider the effect of the hill-induced streamline distortion on the wake. This model enables us to obtain the wake recovery rate, the mean velocity and velocity deficit profiles and the wake trajectory in the presence of the hill. Moreover, we perform LES to test our model and also to obtain new complementary insight about such flows. Especially, we take advantage of the LES data to perform a special analysis of the behaviour of the wake on the leeward side of the hill. It is found that the mainly favourable pressure gradient on the windward side of the hill accelerates the wake recovery and the adverse pressure gradient on the leeward side decelerates it. The wake trajectory for a hill of the same height as the turbine’s hub height is found to closely follow the hill profile on the windward side, but it maintains an almost constant elevation (a horizontal line) downstream of the hilltop. The trajectory of the wake on the leeward side is also studied for a limiting case of an escarpment, and it is shown that an internal boundary layer forms on the plateau which leads to an upward displacement of the wake centre. Finally, a parametric study of the position of the turbine with respect to the hill is performed to further elucidate the effect of the hill-induced pressure gradient on the wind turbine wake recovery.

Numerical investigation of shock train unsteady movement in a mixing duct

Supersonic mixing layers and complex background waves exist in the mixing duct of the RBCC (Rocket-Based Combined Cycle) engine and supersonic-supersonic ejector. Different from the isolator with uniform incoming flow, the shock train in a mixing duct has special structures and motion characteristics. To study the characteristics of shock train forward movement in a mixing duct, a 2d unsteady numerical simulation was conducted. The results indicated that many unsteadiness factors existed in the background flow field such as the development of mixing layers, and multiple complex interactions. With backpressure linearly increasing over flow time, the shock train moved upstream in the process of which two forward movement patterns were found, namely slow pattern and jump pattern. Two patterns alternatively governed the whole forward movement, resulting in periodical changes of leading shock structures. The leading shocks were ‘stretched’ and ‘squeezed’ during the movement process, which was referred to as ‘spring’ characteristics in this research. Further analysis indicated that the characteristics of shock train movement were closely related to the background flow structure, or rather the surface pressure gradient. The shock train leading edges jumped forward in an adverse wall pressure gradient and crept forward in a favorable wall pressure gradient. The whole movement process consisted of 5 motion periods. In the 2nd motion period, speed of leading edges and wave-front Mach number varied, leading to the periodical changes of shock train structures. In the theoretical analysis, shock polar method was applied to clarify the intensity variation of reflection shocks in the shock train.

Aerodynamic characteristics of a rounded-corner square cylinder in shear flow at subcritical and supercritical Reynolds numbers

Shear-inflow effects on flows past a rounded-corner square cylinder is investigated when Reynolds number (Re) increases from subcritical regimes (Re=2.2×104) to supercritical regimes (Re=1.0×106), with a focus on the latter Re in this study. The dimensionless shear parameter K ranges from 0 to 1.0. Results show that shear inflows have different effects on the aerodynamic characteristics of the cylinder in two Re regimes, and generally shear effects are smaller when Re is in the supercritical region. Specifically, mean and r.m.s pressure distributions remain in the same shapes under all shear inflows tested at supercritical Re; however they witness strong dependency on K at subcritical Re. Moreover, the directions of mean lifts at supercritical Re are opposite to those at subcritical Re. Correspondingly, the mean flow patterns observed in the uniform flow are overall preserved in shear flows at the supercritical Re: the free stream flows along the cross section and separates from the trailing corners on both sides of the cylinder, despite of the existence of small-degree asymmetry in the near-wake. However, the flow patterns are significantly changed at the subcritical Re by the sufficiently high shear inflows: the shear layer in suspension tends to reattach on the side wall of the high-velocity side and eventually separates from the trailing edge while the other on the low-velocity side becomes farther from the side wall. It results in the near-wake forming along an axis rotated in the clockwise direction from the horizontal axis, being opposite to the anticlockwise direction at supercritical Re. The mechanism for Re effects is further explored. The preservation of overall flow pattern at supercritical Re even under the strong shear effects is suggested mainly due to the greater favorable pressure gradient and the induced greater velocity acceleration before flow separation on the low-velocity side.

Influence of plane boundary proximity on the Honji instability

This paper presents a numerical investigation of oscillatory flow around a circular cylinder that is placed in proximity to a plane boundary that is parallel to the cylinder axis. The onset and development of the Honji instability are studied over a range of Stokes numbers ($\unicode[STIX]{x1D6FD}$) and gap-to-diameter ratios ($e/D$) at a fixed Keulegan–Carpenter number ($KC=2$). Four flow regimes are identified in the ($e/D,\unicode[STIX]{x1D6FD}$)-plane: (I) featureless two-dimensional flow, (II) stable Honji vortex, (III) unstable Honji vortex and (IV) chaotic flow. As $e/D$ increases from $-0.5$ (embedment) to $1$, the critical Stokes number $\unicode[STIX]{x1D6FD}_{cr}$ for the onset of the Honji instability follows two side-by-side convex functions, peaking at the connection point of $e/D=0.125$ and reaching troughs at $e/D=0$ and 0.375. The Honji instability is always initiated on the gap side of the cylinder surface for $0.375\leqslant e/D\leqslant 2$ and occurs only on the top side for $-0.5\leqslant e/D<0.125$. The location for the initiation of the Honji instability switches from the gap side to the top side of the cylinder surface for $0.125<e/D<0.375$. No Honji instability is observed at $e/D=0.125$, where the flow three-dimensionality is developed through a different flow mechanism. Consistently, the three-dimensional kinetic energy of the flow, which represents a measure of the strength of flow three-dimensionality, varies with $e/D$ in a trend opposite to that of $\unicode[STIX]{x1D6FD}_{cr}$. Three physical mechanisms are identified as being responsible for the observed variation trend of $\unicode[STIX]{x1D6FD}_{cr}$ with $e/D$ and for various flow phenomena, which are the blockage effect induced by the geometry setting, the existence of the Stokes layer on the plane boundary and the favourable pressure gradient in the flow direction over the gap between the cylinder and the plane surface.