Sidewall Forcing Research Articles

Force Measurements and Computational Validation of a Transonic Wing-Tip Flow

A NACA 0012 wing tip was tested at Mach 0.75 and chord Reynolds number of 3 million at incidences from to 7 deg in a transonic Ludwieg tube. The Mach and Reynolds numbers are representative of full-scale rotorcraft blades. Because of the short test time of 0.1 s and high impulse loads, a dynamic calibration was applied to a conventional sidewall force balance to compensate for stress waves propagating within the force balance and test article. Numerical simulations of the entire test section were accomplished to provide data for comparison. The compensated, experimental lift and drag data compared well with the numerical results. This suggests that dynamic calibration improved the experimental data. This comparison demonstrates the feasibility of using complex models for calibrating short-duration wind tunnels in concert with numerical simulation.

Large-scale mean patterns in turbulent convection

Large-scale patterns, which are well-known from the spiral defect chaos (SDC) regime of thermal convection at Rayleigh numbers $\mathit{Ra}<10^{4}$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh–Bénard convection in extended cylindrical cells with an aspect ratio ${\it\Gamma}=50$ and $\mathit{Ra}>10^{5}$. They are revealed when the turbulent fields are averaged in time and turbulent fluctuations are thus removed. We apply the Boussinesq closure to estimate turbulent viscosities and diffusivities, respectively. The resulting turbulent Rayleigh number $\mathit{Ra}_{\ast }$, that describes the convection of the mean patterns, is indeed in the SDC range. The turbulent Prandtl numbers are smaller than one, with $0.2\leqslant \mathit{Pr}_{\ast }\leqslant 0.4$ for Prandtl numbers $0.7\leqslant \mathit{Pr}\leqslant 10$. Finally, we demonstrate that these mean flow patterns are robust to an additional finite-amplitude sidewall forcing when the level of turbulent fluctuations in the flow is sufficiently high.

Side pressure anomalies in 2D packings of frictionless spheres

The pressure in a dish filled with resting sand quickly saturates downward as a consequence of friction forces. This fact is often quoted to introduce granular material as a distinctive form of matter that exhibits behaviour rather different from that of ordinary liquids. One would expect that hydrostatics is fully recovered when friction is switched off. Here we demonstrate in a simple model system that even frictionless grains manifest unanticipated properties. First, wall induced layering in combination with a wedge effect leads to extremely large local pressures near the walls at the bottom of rectangular containers, and this feature does not vanish for diverging container width. Second, for monodisperse packings the average horizontal force is much weaker on the side walls than the hydrostatic value, but approaches the latter for increasing polydispersity. Third, the average sidewall force shows marked oscillations as a function of container width, which can be considered as a measure of wall-to-wall correlations.

Observation of spiral pattern and spiral defect chaos in dielectric barrier discharge in argon/air at atmospheric pressure

A rich variety of spiral patterns such as single-armed spiral, dipole spirals, target pattern, multiarmed spiral, and spiral defect chaos state have been observed in ac-driven atmospheric pressure gas discharge. The confined and free boundary conditions are defined by means of whether there is a sidewall in the discharge domain or not, respectively. In the free boundary condition, the spiral pattern arises when the stripe pattern undergoes core instability or notching instability. In the confined boundary condition, the spiral pattern is formed by sidewall forcing. The spiral drifts upward in the free boundary condition and meanders in the confined boundary condition. The topological charge of the spiral pattern can be changed when the spiral interacts with the dislocations. The spiral wavelength (average distance between two consecutive rolls) is a function of gas composition and decreases rapidly with increase of air concentration in discharge gas.

Wave-number selection by target patterns and sidewalls in Rayleigh-Bénard convection

We present experimental results for patterns of Rayleigh-Bénard convection in a cylindrical container with static sidewall forcing. The fluid used was methanol, with a Prandlt number sigma=7.17 , and the aspect ratio was Gamma identical withR/d approximately 19 ( R is the radius and d the thickness of the fluid layer). In the presence of a small heat input along the sidewall, a sudden jump of the temperature difference DeltaT from below to slightly above a critical value Delta T(c) produced a stable pattern of concentric rolls (a target pattern) with the central roll (the umbilicus) at the center of the cell. A quasistatic increase of epsilon identical withDeltaT/Delta T(c) -1 beyond epsilon(1,c) approximately 0.8 caused the umbilicus of the pattern to move off center. As observed by others, a further quasistatic increase of epsilon up to epsilon=15.6 caused a sequence of transitions at epsilon(i,b) ,i=1,...,8 , each associated with the loss of one convection roll at the umbilicus. Each loss of a roll was preceded by the displacement of the umbilicus away from the center of the cell. After each transition the umbilicus moved back toward but never quite reached the center. With decreasing epsilon new rolls formed at the umbilicus when epsilon was reduced below epsilon(i,a) < epsilon(i,b) . When decreasing epsilon , large umbilicus displacements did not occur. In addition to quantitative measurements of the umbilicus displacement, we determined and analyzed the entire wave-director field of each image. The wave numbers varied in the axial direction, with minima at the umbilicus and at the cell wall and a maximum at a radial position close to 2Gamma/3 . The wave numbers at the maximum showed hysteretic jumps at epsilon(i,b) and epsilon(i,a) , but on average agreed well with the theoretical predictions for the wave numbers selected in the far field of an infinitely extended target pattern. To our knowledge there is as yet no prediction for the wave number selected by the umbilicus itself, or by the cell wall of the finite experimental system.

Confined turbulent convection

New measurements of the Nusselt number have been made in turbulent thermal convection confined in a cylindrical container of aspect ratio unity. The apparatus is essentially the same as that used by Niemela et al. (2000), except that the height was halved. The measurement techniques were also identical but the mean temperature of the flow was held fixed for all Rayleigh numbers. The highest Rayleigh number was . Together with existing data, the new measurements are analysed with the purpose of understanding the relation between the Nusselt number and the Rayleigh number, when the latter is large. In particular, the roles played by Prandtl number, aspect ratio, mean wind, boundary layers, sidewalls, and non-Boussinesq effects are discussed. Nusselt numbers, measured at the highest Rayleigh numbers for which Boussinesq conditions hold and sidewall forcing is negligible, are shown to vary approximately as a 1/3-power of the Rayleigh number. Much of the complexity in interpreting experimental data appears to arise from aspects of the mean flow, including complex coupling of its dynamics to sidewall boundary conditions of the container. Despite the obvious practical difficulties, we conclude that the next generation of experiments will be considerably more useful if they focus on large aspect ratios.

Influence of constant and variable restraining force on springback of TRIP700 and stainless steel grades

Newly developed high strength steels (HSS) like dual phase (DP) and transformation induced plasticity (TRIP) grades as well as austenitic grades like AISI 304 and AISI 301 show superior strength compared to the microalloyed grades with the same formability (e.g. HSLA340). However, due to the multiphase microstructure and the austenite martensite transformation during forming, a higher springback will appear.In this paper the influence of different process parameters of six high strength steels on springback after stamping is investigated. The material properties were determined with uniaxial tensile tests. A modified Duncan Shabel test was used to draw U‐profiles with a controlled restraining force. To investigate different process parameters, constant restraining forces of 1 and 5kN and die radii of 3, 6, 9, and 12 mm were applied. In a second step, a shape set process was used. A constant restraining force of 1kN was used until a draw depth of 80 % was reached. Then the restraining was increased to 5.5 kN. The springback and the sidewall force were measured and analysed. An increased restraining force and a reduced die radius increases the sidewall force and reduces the springback. This resulted in a significant decrease in springback. The tests with variable restraining forces, also known as shape set process have shown that it combines a good formability with a reduced springback.

On the transient adjustment of a mid-latitude abyssal ocean basin with realistic geometry: the constant depth limit

The early stages in the adjustment of a mid-latitude abyssal basin with realistic geometry are studied using an inverted one and one-half layer model of the Eastern Mediterranean Sea as a natural test basin. The model is forced with a localized sidewall mass source and a compensating distributed mass sink. A flat bottom basin is investigated for comparison with existing theories on abyssal gyral spin-up, and as a precursor to a study with realistic topography. As in existing theories, the early adjustment is dominated by sub-inertial Kelvin and Rossby waves. Obstacles and the varying coastal geometry do not impede the passage of the Kelvin wave, though the circuit time of the main Kelvin wave signal is reduced by an aggregate 6% for the abyssal Eastern Mediterranean basin. The scattering of the Kelvin wave due to small-scale variations in the coastline is also shown not to be significant to the adjustment. The relatively short period of time needed to reach a statistical steady state is attributed to western boundary current formation in response to local Kelvin wave dynamics. Upon cessation of the sidewall forcing, sub-inertial motion controls the spin-down adjustment with basin-scale Rossby waves becoming the most pronounced feature of the flow. Two dynamical issues of particular interest emerge in these simulations: the retardation of Kelvin wave propagation around the abyssal basin and the roles of detrainment and sidewall forcing in the interior vorticity balance. An idealized simulation using an elliptical basin is used to illustrate that the mechanism for Kelvin wave retardation is a geometrically induced dispersion due to large-scale variations in the coastline. A dynamical analysis of the interior circulation shows that detrainment alone does not develop a Sverdrup response. Both the localized sidewall injection and the detrainment are needed to describe the interior dynamics, with both poleward and equatorward flows developing during the adjustment.

Hydraulically Drained Flows in Rotating Basins. Part II: Steady Flow

Abstract The slow, horizontal circulation in a deep, hydraulically drained basin is discussed within the context of reduced-gravity dynamics. The basin may have large topographic variations and is fed from above or from the sides by mass sources. Dissipation is provided by bottom friction. To the order of the appromixations made (weak forcing and dissipation), the nonlinear hydraulic control is found to influence only the mean level of the interface separating upper and lower layers, and not the horizontal circulation. For the case of forcing from above the interior basin flow is anticyclonic about closed geostrophic contours and feeds into diffusive boundary layers leading to the draining strait and sill. With sidewall forcing, the interior is motionless and flow is channeled directly to the strait in boundary layers. The latter may circle the basin cyclonically or anticyclonically depending on the source distribution, and a circulation integral is shown to predict the sense of the overall swirl velocity...

Nonlinear waves, patterns and spatio-temporal chaos in cellular neural networks

Spatio-temporal pattern formation occurring in discretely coupled nonlinear dynamical systems has been studied numerically. In this paper, we review the possibilities of using arrays of discretely coupled nonlinear electronic circuits to study these systems. Spiral wave initiation and Turing pattern formation are some of the examples. Sidewall forcing of Turing patterns is shown to be capable of driving the system into a perfect spatial organization, namely, a rhombic pattern, where no defects occur. The dynamics of the two layers supporting Turing and Hopf modes, respectively, is analysed as a function of the coupling strength between them. The competition between these two modes is shown to increase with the diffusion between layers. As well, the coexistence of low- and high-dimensional spatio-temporal chaos is shown to occur in one-dimensional arrays.

Sidewall forcing of hexagonal Turing patterns: rhombic patterns

Rhombic arrays were obtained by sidewall forcing during Turing pattern formation in numerical simulations. Locking between the frequency of forcing and the wave length between blobs was obtained in accordance with the Farey sequence. This locking appears as a perfect rhombic array oriented in the direction of the imposed forcing. For a constant forcing in duration and amplitude, the following scheme of bifurcation was observed: parallel stripes ↦ rhombic array ↦ domains of hexagons and rhombi separated by “penta-hepta” defects. Symmetry considerations based on a non-uniform stretching along the x-axis were used to describe these transitions. Unstable “varicose-vein” stripes were observed to evolve during the temporal evolution arrays.

SPATIOTEMPORAL STRUCTURES IN DISCRETELY-COUPLED ARRAYS OF NONLINEAR CIRCUITS: A REVIEW

Spatiotemporal pattern formation occurring in discretely-coupled nonlinear dynamical systems has been studied numerically. Reaction-diffusion systems can be viewed as an assembly of a large number of identical local subsystems which are coupled to each other by diffusion. Here, the local subsystems are defined by a system of nonlinear ordinary differential equations. While for continuous systems, the characteristic time scale corresponding to the diffusion is slower than that corresponding to the local subsystems, in discretely-coupled systems, both time scales can be of the same order of magnitude. Discrete systems can exhibit behaviors different from those exhibited by their equivalent continuous model: the wave propagation failure phenomenon occurring in nerve-pulse propagation due to transmission blockage is a case in point. In this case, it is found that the wave fails to propagate at or below some critical value of the coupling coefficient. Systems of coupled cells can be found to occur in the transformation and transport processes in living cells, tissues, neuron networks, physiological systems and ecosystems, as well as in all forms of chemical, biochemical reactors and combustion systems. In this paper, we review the possibilities of using arrays of discretely-coupled nonlinear electronic circuits to study these systems. The possibility of building large arrays of these circuits via VLSI technology makes this approach a unique tool for real time applications. Classical examples occurring in other continuous media, such as spiral wave initiation and propagation, and Turing pattern formation, are depicted here. Because of the discrete nature of our system, the influence of inhomogeneities arising from damaged cells, or from an anisotropic media, is analyzed for spiral wave propagation. Spiral wave initiation and vulnerability effects are considered and compared with their corresponding effects in continuous media. More complex spatiotemporal structures are also studied via three-dimensional arrays of discretely-coupled circuits. Straight and twisted scroll waves, as well as scroll ring waves, are shown to exist in these arrays, where their properties can be easily measured. Sidewall forcing of Turing patterns is shown to be capable of driving the system into a perfect spatial organization, namely, a rhombic pattern, where no defects occur. The dynamics of the two layers supporting Turing and Hopf modes, respectively, is analyzed as a function of the coupling strength between them. The competition between these two modes is shown to increase with the diffusion between layers.

Turing patterns in CNNs. III. Computer simulation results

For part II, see ibid., vol. 42, no. 10, pp. 612-26 (Oct. 1995). In this paper, various patterns obtained through computer simulations are presented. It is shown through simple examples that the four inequalities known as the Turing instability conditions are only necessary but not sufficient conditions for Turing patterns to exist. The influence of various parameters, initial conditions as well as sidewall forcing on the final patterns and the possibilities of eliminating defects are studied by means of computer simulations. The possibility of generating perfectly regular patterns or patterns with few defects through the application of small and short controlling signals at one boundary suggests the intriguing possibility of producing high-purity high-tech materials, such as crystals, which was not possible with current technology. In addition, novel applications in image processing, pattern recognition, and other areas can be expected. >

Stochastic influences on pattern formation in Rayleigh-Bénard convection: Ramping experiments.

We report on computer-enhanced shadowgraph flow-visualization and heat-flux measurements of pattern formation in convective flows in a thin fluid layer of depth {ital d} that is heated from below. Most of the experiments were conducted in a cylindrical container of radius {ital r} and aspect ratio {Gamma}=={ital r}/{ital d}=10. The temperature of the top plate of the container was held constant while the heat current through the fluid was linearly ramped in time, resulting in a temperature difference {Delta}{ital T} between the bottom and top plates. After initial transients ended, the reduced Rayleigh number {epsilon}=={Delta}{ital T}/{Delta}{ital T}{sub {ital c}}{minus}1, where {Delta}{ital T}{sub {ital c}} is the critical temperature difference for the onset of convection, increased linearly with ramp rate {beta} such that {epsilon}({ital t})={beta}{ital t}. When time was scaled by the vertical thermal diffusion time, our ramp rates were in the range 0.01{le}{beta}{le}0.30. When the sidewalls of the cell were made of conventional plastic materials, a concentric pattern of convection rolls was always induced by dynamic sidewall forcing. When sidewalls were made of a gel that had virtually the same thermal diffusivity as the fluid, pattern formation occurred independent of cell geometry. In the earliest stages the patterns were thenmore » composed of irregularly arranged cells and varied randomly between experimental runs. The same random cellular flow was also observed in samples of square horizontal cross section. The results demonstrate the importance of stochastic effects on pattern formation in this system. However, an explanation of the measured convective heat current in terms of theoretical models requires that the noise source in these models have an intensity that is four orders of magnitude larger than that of thermal noise.« less

Convective patterns in rotating binary mixtures.

A few-mode Lorenz-like model for convection in a rotating binary mixture confined between stress-free, impermeable boundaries is presented. It describes for positive separation ratios standing patterns of convective rolls in mutually perpendicular directions and the superposition of these rolls with the same wave number. The model is used to investigate the effect of slow rotation on convective patterns. In ideal systems squares are unstable, and the dynamical behavior immediately in the Rayleigh regime is chaotic. Side-wall forcing is incorporated by introducing a small inhomogeneity into the model. In the presence of side walls the chaotic behavior disappears, squares are stabilized close to onset, and rolls are stable in the Rayleigh regime with oscillations occurring in between. For Taylor numbers above a critical value, oscillations disappear and stable stationary patterns are possible over the whole range of Rayleigh numbers.

Pattern Formation and Wave-Number Selection by Rayleigh–Bénard Convection in a Cylindrical Container

We describe an apparatus and procedures for simultaneous heat transport measurements and computer enhanced shadowgraph flow-pattern imaging in a shallow horizontal layer of fluid heated from below. The heat transport measurements have a resolution of better than 0.1%, and the shadowgraph technique can detect the flow field for ϵ ≡ (R – Rc)/Rc as small as 10-2 (Rc is the critical value of the Rayleigh number R for onset of convection).The apparatus and procedures were used to study pattern and wave-number evolution in a cylindrical layer of water with radius-to-height ratio L = 7.5 and Prandtl number σ = 6.1. We found that dynamic sidewall forcing during the early thermal transients after a change in the heat current from a subcritical to a supercritical value establishes a cylindrical flow pattern. Once created, this pattern is stable in our apparatus over the wide range 0.16 ≲ ϵ ≲ 8 even after the transients have decayed.With changing ϵ, adjustment in the wave number k takes place discontinuously by hysteretic changes at the cell center in the number of convection roll pairs. When ϵ is increased, the discontinuous changes at the cell center are towards smaller k and are preceded by a continuous loss of cylindrical symmetry (the middle roll pair moves off center). The selected wave numbers coincide neither with the zig-zag instability of the infinite system, as once suggested, nor with a linear extrapolation to ϵ = 0(1) of the recent prediction to lowest order in ϵ of Manneville and Piquemal and of Cross. Comparison of the selected k with measurements by others reveals no dependence upon L and σ.For ϵ < 0.16, the cylindrical pattern is unstable and decays on a time scale much longer than a horizontal diffusion time to patterns of rolls which tend to be perpendicular to the sidewalls and which contain defects. Once formed, these latter patterns will persist at large values of ϵ. These patterns also undergo a wave-number adjustment process with hysteretic changes mediated mostly by focus singularities near the walls. In these cases, larger values of ϵ also tend to produce smaller values of k.

Computed tomography in the differential diagnosis of pelvic and extrapelvic disease

Displacement of various landmarks within the pelvis by enlarging mass lesions can be used advantageously to determine the nature and origin of a particular mass. The noncompliant pelvic osseous ring accentuates the effect of displacement by forcing the vector inwards. This usually results in cephalad extension of a pelvic process into the abdomen. Lesions originating in the sidewall force the neurovascular bundle medially while central lesions will displace these structures against the noncompliant osseous pelvis. The differentiation of supralevator from infralevator lesions by CT aids in planning the appropriate approach to a lesion preoperatively. The various peritoneal spaces can become enlarged by intraperitoneal abscesses, fluid collections or tumor. These processes will also displace sidewall structures laterally against the osseous rim. It is extremely rare for an intraperitoneal process to extend below the level of the mid-femoral head. Extraperitoneal disease arising out of the pelvis may involve areas caudad to the femoral heads as there is no peritoneum to limit the distal spread. The differentiation of intraperitoneal and large extraperitoneal masses arising out of the pelvis can be difficult. A mass which incorporates bowel loops suggests intraperitoneal disease, whereas one which abuts them smoothly suggests an extraperitoneal lesion.

Pattern Formation and Wave-Number Selection by Rayleigh–Bénard Convection in a Cylindrical Container

We describe an apparatus and procedures for simultaneous heat transport measurements and computer enhanced shadowgraph flow-pattern imaging in a shallow horizontal layer of fluid heated from below. The heat transport measurements have a resolution of better than 0.1%, and the shadowgraph technique can detect the flow field for ϵ ≡ (R-Rc)/Rc as small as 10-2 (Rc is the critical value of the Rayleigh number R for onset of convection).The apparatus and procedures were used to study pattern and wave-number evolution in a cylindrical layer of water with radius-to-height ratio L = 7.5 and Prandtl number σ = 6.1. We found that dynamic sidewall forcing during the early thermal transients after a change in the heat current from a subcritical to a supercritical value establishes a cylindrical flow pattern. Once created, this pattern is stable in our apparatus over the wide range 0.16 ≲ ϵ ≲ 8 even after the transients have decayed.With changing ϵ, adjustment in the wave number k takes place discontinuously by hysteretic changes at the cell center in the number of convection roll pairs. When ϵ is increased, the discontinuous changes at the cell center are towards smaller k and are preceded by a continuous loss of cylindrical symmetry (the middle roll pair moves off center). The selected wave numbers coincide neither with the zig-zag instability of the infinite system, as once suggested, nor with a linear extrapolation to ϵ = O(1) of the recent prediction to lowest order in ϵ of Manneville and Piquemal and of Cross. Comparison of the selected k with measurements by others reveals no dependence upon L and σ.For ϵ < 0.16, the cylindrical pattern is unstable and decays on a time scale much longer than a horizontal diffusion time to patterns of rolls which tend to be perpendicular to the sidewalls and which contain defects. Once formed, these latter patterns will persist at large values of ϵ. These patterns also undergo a wave-number adjustment process with hysteretic changes mediated mostly by focus singularities near the walls. In these cases, larger values of ϵ also tend to produce smaller values of k.