Favorable Pressure Gradient Research Articles

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.

Spatial variability of the wave bottom boundary layer over movable rippled beds

[1] Observations of the spatially dependent velocity field over movable bed forms subjected to slightly skewed and asymmetric regular wave forcing were collected. The dynamics between the ripple elements is dominated by coherent vortices, characterized by the swirling strength, and evidenced in the temporal and spectral characterization. Within the boundary layer, spectral energy in the second harmonic (3f0) is amplified at the ripple slopes and is consistent with the location of the expected strongest pressure gradients. First-moment and second-moment velocity statistics were used to address the spatial variability of the intra-ripple hydrodynamics. Estimates of displacement and momentum thicknesses (δ* and δmom) are smaller than suggested by the higher harmonics, but consistently highlight areas of adverse and favorable pressure gradients. Shear stress and roughness estimates were inferred by fitting a logarithmic model to first-moment and second-moment statistics of the velocity field. The maximum Shields parameter was observed to peak at the stoss slope of asymmetric ripples during the strongest and shorter half-wave period (onshore). First-moment roughness estimates are similar in magnitude to bed load parameterizations provided by Li et al. (1997), and about a factor of 3 larger than second-moment estimates. Assessment of the vertical transfer of horizontal momentum derived using a Reynolds decomposition suggests that stresses inferred from the logarithmic law using first-moment velocity statistics appropriately reproduce the mean momentum transfer for the longer and weaker offshore half-wave period.

Frequency-domain prediction of broadband trailing edge noise from a blunt flat plate

The aim of this study is to develop an efficient methodology for frequency-domain prediction of broadband trailing edge noise from a blunt flat plate where non-zero pressure gradient may exist in its boundary layer. This is achieved in two ways: (i) by developing new models for point pressure spectra within the boundary layer over a flat plate, and (ii) by deriving a simple formula to approximate the effect of convective velocity on the radiated noise spectrum. Firstly, two types of point pressure spectra-required as input data to predict the trailing edge noise in the frequency domain-are used. One is determined using the semi-analytic (S-A) models based on the boundary-layer theory combined with existing empirical models. It is shown that the prediction using these models show good agreements with the measurements where zero-pressure gradient assumption is valid. However, the prediction show poor agreement with that obtained from large eddy simulation results where negative (favorable) pressure gradient is observed with the boundary layer. Based on boundary layer characteristics predicted using the large eddy simulations, new model for point wall pressure spectra is proposed to account for the effect of favorable pressure gradient over the blunt flat plate on the wall pressure spectra. Sound spectra that were predicted using these models are compared with measurements to validate the proposed prediction scheme. The advantage of the semi-analytic model is that it can be applied to problems at Reynolds numbers for which the empirical model is not available. In addition, it is expected that the current models can be applied to the cases where favorable pressure gradient exists in the boundary layer over a blunt flat plate. Secondly, in order to quantitatively analyze contributions of the pressure field within the turbulent boundary layer on the flat plate to trailing edge noise, total pressure over the surface of airfoil is decomposed into its two constituents: incident pressure generated in the boundary layer without a trailing edge and the pressure formed by the scattering of the incident pressure at the trailing edge. The predictions made using each of the incident and scattered pressures reveal that the convective velocity of turbulence in the boundary layer dominantly affects the radiated sound pressure spectrum, both in terms of the gross behavior of the overall acoustic pressure spectrum through the scattered pressure and in terms of the narrow band small fluctuations of the spectrum through the incident pressure. The interaction term between the incident and the scattered is defined and the incident is shown to contribute to the radiated acoustic pressure through the interaction term. Based on this finding, a simple model to effectively compute the effects of convection velocities of the turbulence on the radiated sound pressure spectrum is proposed. It is shown that the proposed method can effectively and accurately predict the broadband trailing edge noise from the plate with considering both the incident and the scattered contributions.

Unsteady separation and vortex shedding from a laminar separation bubble over a bluff body

Boundary layers are subject to favorable and adverse pressure gradients because of both the temporal and spatial components of the pressure gradient. The adverse pressure gradient may cause the flow to separate. In a closed loop unsteady tunnel we have studied the initiation of separation in unsteady flow past a constriction (bluff body) in a channel. We have proposed two important scalings for the time when boundary layer separates. One is based on the local pressure gradient and the other is a convective time scale based on boundary layer parameters. The flow visualization using a dye injection technique shows the flow structure past the body. Nondimensional shedding frequency (Strouhal number) is calculated based on boundary layer and momentum thicknesses. Strouhal number based on the momentum thickness shows a close agreement with that for flat plate and circular cylinder.

Investigation of Formation and Development of Stationary and Secondary Disturbances in the Favourable Pressure Gradient Area on the Swept Wing

In this work the combined technique of liquid-crystal thermography and thermoanemometry measurements is used to trace the stationary disturbance development from the moment of formation to the nonlinear stage transition. It has been shown that the pair of stationary vortices are formed after the cylindrical roughness element. These vortices modify a boundary layer and destabilize it. There is the area of maximal receptivity to the roughness location, which in the experiment was distant from the attachment line. If the stationary disturbance has enough magnitude in its core the secondary disturbances excite and lead to the laminar-turbulent transition. Secondary disturbances are sensitive to the acoustics and achieve the magnitude in hundred times higher than for the natural case

Effect of Pressure Gradient on Film Cooling From Holes Supplemented by Anti-Vortex Holes

An experimental test rig is constructed to study the effect of pressure gradient on different configurations of the anti-vortex film cooling technique. This technique depends on adding a pair of cylindrical anti-vortex holes branching out from the main cylindrical film cooling holes to mitigate the effect of kidney vortices that causes the jet to lift off. Four different values of velocity ratios (VR), (Coolant Jet Velocity/Main Stream Velocity) namely VR=0.5, 1.0, 1.5, and 2.0, are studied with three different positions of anti-vortex holes. A single row of 30o angled holes on a flat surface, under zero pressure gradient along the downstream test surface, is taken as a baseline case. The numerical study is carried out using FLUENT commercial code using the k-e model. The density ratio is taken in consideration. Numerical results are first compared with experimental values of temperatures and film cooling effectiveness and the comparisons verified the numerical model. Both of experimental and numerical studies show that the new technique improves the film cooling effectiveness.The numerical velocity vectors in the boundary layer region showed that the anti-vortex holes create reverse vortices against the main vortices that are created by the main hole. These reverse vortices help in keeping the coolant jet flow near the surface. The adverse pressure gradient decreases the film cooling effectiveness while the presence of favorable pressure gradient increases the film cooling effectiveness.

Response of a hypersonic turbulent boundary layer to favourable pressure gradients

AbstractThe role of streamline curvature-driven favourable pressure gradients in modifying the turbulence structure of a Mach 4.9, high-Reynolds-number (${\mathit{Re}}_{\theta } = 43\hspace{0.167em} 000$) boundary layer is examined. Three pressure gradient cases ($\beta = (\mathrm{d} p/ \mathrm{d} x)({\delta }^{\ast } / {\tau }_{w} )= 0. 07, - 0. 3$ and $- 1. 0$) are characterized via particle image velocimetry. The expected stabilizing trends in the Reynolds stresses are observed, with a sign reversal in the Reynolds shear stress in the outer part of the boundary layer for the strongest favourable pressure gradient considered. The increased transverse normal strain rate and reduced principal strain rate are the primary factors. Reynolds stress quadrant events are redistributed, such that the relative differences between the quadrant magnitudes decreases. Very little preferential quadrant mode selection is observed for the strongest pressure gradient considered. Two-point correlations suggest that the turbulent structures are reoriented to lean farther away from the wall, accompanied by a slight reduction in their characteristic size, consistent with previous flow visualization studies. This reorientation is more pronounced in the outer, dilatation-dominated region of the boundary layer, whereas the alteration in structure size is more pronounced nearer the wall, where the principal strain rates are larger. In addition, integration of a simplified form of a Reynolds stress transport closure model provided a framework to assess the role of the strain-rate field on the observed Reynolds shear stresses. Given the simple geometry, the present data provide a suitable test bed for Reynolds stress transport and large-eddy model development and validation.

Study of Underexpanded Sonic Jets by Numerical Simulation

This paper deals with the numerical simulation of sonic underexpanded axi-symmetric jets, issuing from a convergent nozzle, at different nozzle pressure ratios. The simulations have been carried out by solving the unsteady Reynolds Average Navier-Stokes (RANS) equations utilizing the realizable k-ε (epsilon) two equations turbulence model in the commercial software FLUENT (version 6.3.26). The flow is assumed to be axi-symmetric and turbulent. The computational domain included a convergent nozzle of length 50 mm and a rectangular domain of size 25 times the nozzle exit diameter (D) verses 4D, which have been modeled and meshed in GAMBIT (version 2.46). The grid consisted of 81020 cells, while gradient grid adaptions were performed later to pronounce the accuracy of the results and visualize the shock-cell structures. From the simulations, it is inferred that, for correctly expanded jets, the potential core extends upto 6D, where D is the exit diameter of the nozzle. For underexpanded jets, the shock-cell structures in the jet flow field were captured properly. A pattern of ‘shock-diamonds’ or shock-cells were observed in the flow at low NPR. The formation of shock-cell is found to change considerably and also its strength increases with increase in nozzle pressure ratio (NPR). From this study, it is clear that the effect of favorable pressure gradient in the underexpanded jet influences the jet characteristics significantly. At high NPRs, ‘Mach disc’ formation is observed in the flow field. The flow after the Mach disc becomes subsonic and regains energy from the surrounding fluid.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Energy dissipation in unsteady turbulent pipe flows caused by water hammer

Energy dissipation and turbulent kinetic energy production and its dissipation in unsteady turbulent pipe flows due to water hammer phenomena are numerically studied. For this purpose, the two-dimensional governing equations of water hammer are solved using the method of characteristics. A k–ω turbulence model which is accurate for two-dimensional boundary layers under adverse and favorable pressure gradients is applied. The numerical results are in good agreement with the experimental data. Through an order of magnitude analysis, two dimensionless parameters have been identified which can be used for the evaluation of viscous and turbulent shear stress terms. The influence of these non-dimensional parameters on pressure oscillations, wall-shear-stress, dissipation rate as well as profiles of velocity, turbulent production and dissipation are investigated. The non-dimensional parameter P, which represents time scale ratio of turbulence diffusion in the radial direction to the pressure wave speed, is used to study the structure and strength of turbulence. It is found that for the case of P≈1, for which the values of the non-dimensional groups are larger, the peaks of turbulence energy production and dissipation move rapidly away from the wall and turbulence structure is significantly changed. For the case of P≫1, for which the values of non-dimensional parameters are smaller, these variations are found to be small.

Wake-Induced Bypass Transition over a Flat Plate under Favorable and Adverse Pressure Gradients

The present study investigates wake-induced bypass transition of boundary layers on a flat plate subjected to favorable and adverse pressure gradients. The aim is to exploit unsteady effects in order to design an aft-loaded turbine blade without increasing the profile loss, as has been achieved for low pressure turbine blades. First of all, this fundamental study is to reveal the effect of the Strouhal number, which changed by using different numbers of wake generating bars. Detailed boundary layer measurements were conducted using two hot-wire probes. A passage-contouring device was employed to generate a pressure gradient on the test model, which was typical to that generated by an aft-loaded turbine blade. A spoked-wheel-type wake generator was used to create periodic wakes in front of the flat plate. It was found that the wake passage induces a significant change in the flow structure downstream of the flow acceleration region.

Laminar-Turbulent Transition of an Inlet Boundary Layer in a Circular Pipe Induced by Periodic Injection (Shape of Isolated Turbulent Patches and Their Growth)

The laminar-turbulent transition of a boundary layer induced by an injection of jet in the inlet region of a circular pipe was experimentally investigated. The jet was periodically injected radially from a small hole in the inlet region into the pipe flow. Axial velocity was measured by a hot-wire anemometer. The turbulence induced by the jet within the boundary layer developed into turbulent patches which then grew in the axial, circumferential and radial directions downstream. The shape of the patches shown by the intermittency factor in the diametrical plane was similar to the turbulent spot in the flat plate boundary layer. Their property became similar to the turbulent slug in the pipe flow developed downstream. The turbulent patches protruded from the boundary layer after they grew and reached the circumferential opposite side, although they stayed within the boundary layer as long as the shape was turbulent spot-like in the diametrical plane. The propagation velocity at the leading edge became faster than the bulk velocity, though it turned slower at the trailing edge. Therefore, the growth rate of its streamwise length varied downstream. The growth rate of the patches' circumferential length was smaller than that in the turbulent spot under zero pressure gradient and was almost the same as the spot under favorable pressure gradient.

0512 順圧力勾配下に発達する乱流境界層おけ壁法則(OS5-3 壁乱流:統計,構造,動力学の理解,OS5 壁乱流:統計,構造,動力学の理解)

0512 順圧力勾配下に発達する乱流境界層おけ壁法則(OS5-3 壁乱流:統計,構造,動力学の理解,OS5 壁乱流:統計,構造,動力学の理解)

J055033 平板翼面上を通過する周期的後流の速度計測に関する実験的研究(〔J055-03〕流体機械の研究開発におけるEFD/CFD(3))

The present study investigates wake-induced bypass transition of boundary layers on a flat plate subjected to favorable and adverse pressure gradients. The aim is to exploit unsteady effects in order to design a turbine blade without increasing the profile loss, as has been achieved for low pressure turbine blades. First of all, this fundamental study is to reveal the effect of wake passing frequency. Detailed boundary layer measurements were conducted using hot-wire probe. A passage-contouring device was employed to generate a pressure gradient on the test model, which was typical to that generated by an turbine blade. A wake generating squirrel cage was used to create periodic wakes in front of the flat plate. It was found that the wake passage induces a temporary turbulence promoting in the flow over a flat plate surface.

Truncated Triangular Tabs for Supersonic-Jet Control

An experimental investigation has been carried out to study the mixing-promoting efficiency of triangular tabs with sharp and truncated vertices. The mixing promotion caused by two identical triangular tabs, with sharp and truncated vertices, offering a geometrical blockage of 2.5% each, placed at the exit of a Mach 2 circular nozzle, was studied in the presence of adverse and marginally favorable pressure gradients. The pressure decay along the jet centerline and the pressure profiles along and normal to the tabs were measured. The waves present in the core of the uncontrolled and controlled jets were visualized with the shadowgraph technique. The nozzle-pressure ratio was varied from 4 to 8, in the step of one, covering overexpansion and marginally underexpansion levels at the nozzle exit. The results of the present study demonstrate the validity of the hypothesis that the triangular tabs shedding vortices of continuously varying sizes is a better mixing promoter than the rectangular tabs, of identical blockage, shedding vortices of uniform size. Furthermore, the truncated triangular tab is found to be a better mixing promoter than the triangular tab of sharp vertex. As high as 87% reduction in core length was achieved with truncated triangular tabs at nozzle-pressure ratio 8. The corresponding core-length reduction caused by triangular tabs with a sharp vertex and rectangular tabs are 83 and 25%, respectively.

On mixed electroosmotic-pressure driven flow and mass transport in microchannels

In this paper, we report the combined pressure-electroosmotically driven flow and species transport in micro/nano-channels. By performing a detailed numerical simulation based on the coupled Poisson, Nernst–Planck and incompressible Navier–Stokes equations (NP-model), we discuss the effects of imposed pressure gradient on the electrokinetic transport of electrolyte. The Reynolds number dependence of the mixed EOF is analyzed for both thin and overlapped EDL cases. Validity of the linear model based on the equilibrium Boltzmann distribution of ions and velocity governed by the linear superposition of Helmholtz–Smoluchowski velocity with the Poiseuille flow is examined by comparing with the non-linear NP-model. Both the models are found to be close when the EDL is sufficiently thin, but they differ when the bulk of the channel is not electrically neutral. Flow reversal and the suppression of electroosmotic flow are possible through regulating the imposed pressure field. At a sufficiently large value of the imposed pressure gradient the electrokinetic effect becomes negligible and flow resembles the fully developed Poiseuille flow. A similarity of the mixed EOF-pressure driven flow with the imposed pressure gradient, surface potential and imposed electric field is investigated. The mixed EOF characteristics is found to be strongly dependent on the electric double layer thickness. The advection effect dominates over the diffusion and electrophoretic migration in transport of charged species with favorable pressure gradient.

The Effects of Spatial Resolution in Turbulent Boundary Layers with Pressure Gradients

Single normal hot-wire measurements of the streamwise component of velocity were taken in boundary layer flows subjected to pressure gradients at matched friction Reynolds numbers Reτ ≈ 3000. To evaluate spatial resolution effects, the sensor lengths are varied in both adverse pressure gradient (APG) and favorable pressure gradient (FPG). A control boundary layer flow in zero pressure gradient ZPG is also presented. It is shown here that, when the sensor length is maintained a constant value, in a contant Reynolds number, the near-wall peak increases with (adverse) pressure gradient. Both increased contributions of the small- and especially large-scale features are attributed to the increased broadband turbulence intensities. The two-mode increase, one centreing in the near-wall region and the other one in the outer region, makes spatial resolution studies in boundary layer flow more complicated. The increased large-scale features in the near-wall region of an APG flow is similar to large-scales increase due to Reynolds number in ZPG flow. Additionally, there is also an increase of the small-scales in the near-wall region when the boundary layer is exposed to adverse pressure gradient (while the Reynolds number is constant). In order to collapse the near-wall peaks for APG, ZPG and FPG flows, the APG flow has to use the longest sensor and conversely, the FPG has to use the shortest sensor. This study recommends that the empirical prediction by Huthins et. al. (2009) to be reevaluated if pressure gradient flows were to be considered such that the magnitude of the near-wall peak is also a function of the adverse pressure gradient parameter.

Visualization of the structural response of a hypersonic turbulent boundary layer to convex curvature

The effects of convex curvature on the outer structure of a Mach 4.9 turbulent boundary layer (Reθ = 4.7 × 104) are investigated using condensate Rayleigh scattering and analyzed using spatial correlations, intermittency, and fractal theory. It is found that the post-expansion boundary layer structure morphology appears subtle, but certain features exhibit a more obvious response. The large-scale flow structures survive the initial expansion, appearing to maintain the same physical size. However, due to the nature of the expansion fan, a differential acceleration effect takes place across the flow structures, causing them to be reoriented, leaning farther away from the wall. The onset of intermittency moves closer towards the boundary layer edge and the region of intermittent flow decreases. It is likely that this reflects the less frequent penetration of outer irrotational fluid into the boundary layer, consistent with a boundary layer that is losing its ability to entrain freestream fluid. The fractal dimension of the turbulent/nonturbulent interface decreases with increasing favorable pressure gradient, indicating that the interface's irregularity decreases. Because fractal scale similarity does not encompass the largest scales, this suggests that the change in fractal dimension is due to the action of the smaller-scales, consistent with the idea that the small-scale flow structures are quenched during the expansion in response to bulk dilatation.

Optimized Laminar Axisymmetrical Nozzle Design Using a Numerically Validated Thwaites Method

This paper presents the Thwaites method as an accurate and efficient design tool for laminar, axisymmetrical nozzles. Based on historical developments, it is improved to describe internal flows with highly favorable pressure gradients in cylindrical coordinates. The calculation of the core flow velocity distribution based on the continuity equation is proposed as a replacement to other sophisticated numerical methods. A remarkably good agreement is obtained when comparing the results of the current Thwaites method against those of computational fluid dynamics (CFD) simulations, for which the integral boundary layer thicknesses are calculated with equations developed from first principles in the course of the work. This consistency among the results and the low time and resource costs of the Thwaites method confirm its applicability and usefulness as an engineering design and optimization tool.

Discrete linear local eigenmodes in a separating laminar boundary layer

AbstractThe evolution of two- and three-dimensional small-amplitude disturbances in the laminar part of a laminar separation bubble is investigated in detail. We apply a combination of local linear stability theory, results from different experimental measurement campaigns and direct numerical simulations to identify two different discrete eigenmodes in the laminar part of the bubble. A stable eigenmode, the outer mode, governs unsteady oscillations in the upstream part of the bubble. However, this perturbation is quickly overtaken by an unstable eigenmode, the inner mode, which eventually leads to transition of the detached shear layer. Such a behaviour is observed due to an acceleration region with a favourable pressure gradient preceding the adverse-pressure-gradient region. The flow is stable in the acceleration region, in which the outer mode is only moderately damped, while the inner mode is strongly damped. At the onset of instability for the unstable eigenmode upstream of separation, both viscous Tollmien–Schlichting and inviscid Kelvin–Helmholtz instability mechanisms contribute to amplification, while deeper inside the bubble only the inviscid mechanism is active. If the explicit forcing is moved to a region downstream of the favourable pressure gradient, only the unstable eigenmode appears. The same behaviour is found for two-dimensional and weakly oblique waves.