Transverse Curvature Effects Research Articles

Unsteady Mixed Convection From a Moving Vertical Slender Cylinder

A general analysis has been developed to study flow and heat transfer characteristics of an unsteady laminar mixed convection on a continuously moving vertical slender cylinder with surface mass transfer, where the slender cylinder is inline with the flow. The unsteadiness is introduced by the time-dependent velocity of the slender cylinder as well as that of the free stream. The calculations of momentum and heat transfer on slender cylinders considered the transverse curvature effect, especially in applications such as wire and fiber drawing, where accurate predictions are required. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation, and the resulting system of nonlinear coupled partial differential equations is then solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Numerical results are presented for the skin friction coefficient and Nusselt number. The effects of various parameters on the velocity and temperature profiles are also reported here.

Direct numerical simulation of turbulent flow in elliptical ducts

Direct numerical simulation (DNS) of fully developed turbulent flow in elliptical ducts is performed. The mean cross-stream secondary flows exhibited by two counter-rotating vortices which are symmetrical about the major ellipse's axis are examined. The mean flow characteristics and turbulence statistics are obtained. The variation of the statistical quantities such as the Reynolds stresses and turbulence intensities along the minor axis of the elliptical cross-section are found to be similar to plane channel data. The turbulent statistics along the major axis are found to be inhibited by the secondary flow transferring high-momentum fluid from the duct's centre towards the wall. The instantaneous velocity fields in the near-wall region reveal structures similar to the ‘streaks’ except in the vicinity of the major axis endpoints where significant reduction of the turbulent activity due to the wall transverse curvature effect is found.

Large eddy simulation of turbulent concentric annular channel flows

AbstractFully developed turbulent concentric annular channel flow has been investigated numerically by use of large eddy simulation (LES) technique coupled with a localized one‐equation dynamic subgrid‐scale (SGS) model. The objective of this study is to deal with the behaviour of turbulent flow near the inner and outer walls of the concentric annular channel and to examine the effectiveness of LES technique for predicting the turbulent flow influenced by the transverse curvature effect. The computations are performed for the Reynolds number Reτ=180, 395 and 640, based on an averaged friction velocity and the annular channel width with the inner and outer cylinder radius being Ri=1 and Ro=2. To validate the present approach, calculated results for turbulent pipe flow and concentric annular channel flow are compared with available experimental data and direct numerical simulation results, which confirms that the present approach can be used to study turbulent concentric annular channel flow satisfactorily. To elucidate turbulence characteristics in the concentric annular channel, some typical quantities, including the resolved velocity, turbulence intensity, turbulent eddy viscosity, SGS kinetic energy, SGS dissipation rate, Reynolds stress budgets, and turbulence structures based on the velocity fluctuations, are analysed. Copyright © 2004 John Wiley & Sons, Ltd.

Direct numerical simulation of turbulent concentric annular pipe flow: Part 2: Heat transfer

A direct numerical simulation is performed for turbulent heat transfer in a concentric annulus at Re D h =8900 and Pr=0.71 for two radius ratios ( R 1/ R 2=0.1 and 0.5) and wall heat flux ratio q ∗=1.0 . Main emphasis is placed on the transverse curvature effect on near-wall turbulent thermal structures. Near-wall turbulent thermal structures close to the inner and outer walls are scrutinized by computing the lower-order statistics. The fluctuating temperature variance and turbulent heat flux budgets are illustrated to confirm the results of the lower-order statistics. Probability density functions of the splat/anti-splat process are investigated to analyze the transverse curvature effect on the strong relationship between sweep and splat events. The present numerical results show that the turbulent thermal structures near the outer wall are more activated than those near the inner wall, which may be attributed to the different vortex regeneration processes between the inner and outer walls.

Effects of the Transverse Curvature on the Statistics of Fully Developed Turbulent Flow in an Annular Pipe

Effects of the Transverse Curvature on the Statistics of Fully Developed Turbulent Flow in an Annular Pipe

Direct numerical simulation of turbulent concentric annular pipe flow: Part 1: Flow field

A direct numerical simulation is performed for a turbulent concentric annular pipe flow at Re D h =8900 for two radius ratios ( R 1/ R 2=0.1 and 0.5). Main emphasis is placed on the transverse curvature effect on near-wall turbulent structures. Near-wall turbulent structures close to the inner and outer walls are scrutinized by computing the lower-order and higher-order statistics. The Reynolds stress budgets are illustrated to confirm the results of the lower-order statistics. A quadrant analysis of the Reynolds shear stress is explored to develop a sufficiently complete picture of the contribution of flow events to turbulence production (consumption). Probability density functions of the inclination angles of the projected vorticity vectors are investigated to analyze the transverse curvature effects on the orientation of the vorticity field. The present numerical results show that the turbulent structures near the outer wall are more activated than those near the inner wall, which may be attributed to the different vortex regeneration processes between the inner and outer walls.

Fluid-loaded elastic plate with mean flow: point forcing and three-dimensional effects

The unsteady behaviour of an infinitely long fluid-loaded elastic plate subject to a single-frequency line forcing in the presence of a uniform mean flow is known to exhibit a number of interesting phenomena. These include the onset of absolute instability for non-dimensional flow speeds U in excess of some critical speed Uc, and various interesting propagation effects when U < Uc. In the latter respect Crighton & Oswell (1991) have shown that over a particular frequency range there exists an anomalous neutral mode with group velocity directed towards the driver, in violation of the usual Lighthill outgoing radiation condition. Similar results have been found by Peake (1997) when transverse curvature effects are included. In this paper we seek to extend these results and consider the substantially harder problem of a fluid-loaded elastic plate with uniform mean flow which is subject to a point forcing, thereby resulting in a two-dimensional structural problem. A systematic method for determining the absolute instability threshold is developed, and it is shown that the flow is absolutely unstable for flow speeds U > Uc, where Uc is the one-dimensional value found by Crighton & Oswell. At flow speeds U < Uc the flow is marginally stable and convective growth is found to occur downstream of the driver, over a particular frequency range depending on the transverse Fourier wavenumber ky, within a wedge-shaped region. Outside this wedge-shaped region there is only neutral mode behaviour. Asymptotic forms are found for the dominant large-distance causal flexion response downstream of the driver inside and outside the wedge region, and the appropriate critical angle for the wedge region is identified. Within the convective instability wedge the flexion and critical angle take two different forms depending on whether the frequency ω is greater or less than U2/√5. In addition to this interesting behaviour, the flow also exhibits the usual anomalous neutral mode behaviour and, as with Peake's problem, we also find an extra stability (hoop) resulting in neutral mode behaviour over a small frequency range. Asymptotic forms are also found for the threshold frequencies which divide up the various regions of stability of the system (neutral, neutral anomalous, convectively unstable), as a function of ky, and are compared with the results of both Crighton & Oswell and Peake.

Transverse curvature effects in turbulent boundary layer

The effect of transverse surface curvature on the turbulent boundary layer is reviewed by recourse to experiments on axial flow along a circular cylinder. Three flow regimes are identified depending on values of the two controlling parameters, namely, the Reynolds number and the ratio of the boundary layer thickness to cylinder radius. The boundary layer flow resembles a wake when both parameters are large. As expected, the effect of curvature is small when the Reynolds number is large and the boundary layer is thin. When the boundary layer is thick and the Reynolds number is small, which is typical of laboratory investigations, the effect of transverse curvature is felt throughout the boundary layer with evidence for relaminarization at the low Reynolds numbers. This review describes the experimental evidence and points out gaps that remain.

Low Reynolds number axisymmetric turbulent boundary layer on a cylinder

In the present study, an axisymmetric turbulent boundary layer growing on a cylinder is investigated experimentally using hot wire anemometry. The combined effects of transverse curvature as well as low Reynolds number on the mean and turbulent flow quantities are studied. The measurements include the mean velocity, turbulence intensity, skewness and flatness factors in addition to wall shear stress. The results are presented separately for the near wall region and the outer region using dimensionless parameters suitable for each case. They are also compared with the results available in the open literature. The present investigation revealed that the mean velocity in near wall region is similar to other simple turbulent flows (flat plate boundary layer, pipe and channel flows); but it differs in the logarithmic and outer regions. Further, for dimensionless moments of higher orders, such as skewness and flatness factors, the main effects of the low Reynolds number and the transverse curvature are present in the near wall region as well as the outer region.

Some simple solutions for buckling loads of thin and moderately thick cylindrical shells and panels made of laminated composite material

The objective of the present paper is to present a simple analytical solution for computing bifurcation buckling loads of thin and moderately thick orthotropic cylindrical shells and panels subjected to axial compression and normal pressure. That solution • — does not necessarily make use of the simplifying assumptions of shallow shell theory, and • — takes the flexibility with respect to transverse shear loads into account, which is supposed to be relatively high with laminated composite structures. The analysis is based on the governing nonlinear equations and boundary conditions of deep and shallow shell theory. They are linearised to yield the differential equations for bifurcation buckling. The linearised set admits a single-term analytical solution when the cylinder ends or panel edges are simply supported. It reduces the task to a small size (3∗3) algebraic eigenvalue problem that can be solved by standard methods. A computer program BOSCAP (Buckling of Orthotropic Shear-flexible Cylinders And Panels) is developed based on the above mentioned formulation which is very quick and easy to use during design trials or in automated optimization. A series of numerical examples is presented to demonstrate effects of transverse shear flexibility and curvature. Good agreement with some test results is shown.

Effect of transverse convex curvature on heat transfer from heated cylinders with axisymmetric backward-facing steps

Effect of transverse convex curvature on heat transfer from heated cylinders with axisymmetric backward-facing steps

Comparison of four turbulence models for wall-bounded flows affected by transverse curvature

In many engineering applications, such as flow along ships, missiles, aircrafts, torpedoes, and underwater towed cables, and during fabrication of glass and polymer fibers, the boundary-layer thickness $\delta$ can be of the order of or greater than the body radius and thus the transverse curvature effects become important, i.e., the boundary layers are thick. The objective of the present work is to check the applicability of four eddy-viscosity-based turbulence models for two configurations of flows affected by transverse curvature: (1) the zero pressure-gradient boundary layer developing on the surface of a circular cylinder of radius a aligned with the flow and (2) the axial fully developed flow between concentric cylinders. For turbulent flow, two parameters $a^+$ and $\delta /a$ can be used to represent the effects of transverse curvature in the inner and the outer parts of flow, respectively; $a^+=au_t / v$. (For the second flow type, $\delta$ denotes the radial location of zero shear stress from the inner cylinder surface of radius a).

Wall pressure and coherent structures in a turbulent boundary layer on a cylinder in axial flow

Measurements of wall pressure and streamwise velocity fluctuations in a turbulent boundary layer on a cylinder in an axial air flow (δ/a = 5.04, Reθ = 2870) have been used to investigate the turbulent flow structures in the cylindrical boundary layer that contribute to the fluctuating pressure at the wall in an effort to deduce the effect of transverse curvature on the structure of boundary layer turbulence. Wall pressure was measured at a single location with a subminiature electret condenser microphone, and the velocity was measured throughout a large volume of the boundary layer with a hotwire probe. Auto- and cross-spectral densities, cross-correlations, and conditional sampling of the pressure and streamwise velocity indicate that two primary groups of flow disturbances contribute to the fluctuating pressure at the wall: (i) low-frequency large-scale structures with dynamical significance across the entire boundary layer that are consistent with a pair of large-scale spanwise-oriented counter-rotating vortices and (ii) higher frequency small-scale disturbances concentrated close to the wall that are associated with the burst-sweep cycle and are responsible for the short-duration large-amplitude wall pressure fluctuations. A bidirectional relationship was found to exist between both positive and negative pressure peaks and the temporal derivative of u near the wall. Because the frequency of the large-scale disturbance observed across the boundary layer is consistent with the bursting frequency deduced from the average time between bursts, the burst-sweep cycle appears to be linked to the outer motion. A stretching of the large-scale structures very near the wall, as suggested by space-time correlation convection velocity results, may provide the coupling mechanism. Since the high-frequency disturbance observed near the wall is consistent with the characteristic frequency deduced from the average duration of bursting events, the bursting process provides the two characteristic time scales responsible for the bimodal distribution of energy near the wall. Because many of the observed structural features of the cylindrical boundary layer are similar to those observed in flat-plate turbulent boundary layers, transverse curvature appears to have little effect on the fundamental turbulent structure of the boundary layer for the moderate transverse curvature ratio used in this investigation. From differences that exist between the turbulence intensity, skewness, and spectra of the streamwise velocity, however, it appears that transverse curvature may enhance (i.e. energize) the large-scale motion owing to the reduced constraint imposed on the flow by the smaller cylindrical wall.

Effects of convex transverse curvature on wall-bounded turbulence. Part 1. The velocity and vorticity

Convex transverse curvature effects in wall-bounded turbulent flows are significant if the boundary-layer thickness is large compared to the radius of curvature (large γ = δ/a). The curvature affects the inner part of the flow if a+, the cylinder radius in wall units, is small.Two direct numerical simulations of a model problem approximating axial flow boundary layers on long cylinders were performed for γ = 5 (a+ ≈ 43) and γ = 11 (a+ ≈ 21). Statistical and structural data were extracted from the computed flow fields. The effects of the transverse curvature were identified by comparing the present results with those of the plane channel simulation of Kim, Moin & Moser (1987), performed at a similar Reynolds number. As the curvature increases, the skin friction increases, the slope of the logarithmic region decreases and turbulence intensities are reduced. Several turbulence statistics are found to scale with a curvature dependent velocity scale derived from the mean momentum equation. Near the wall, the flow is more anisotropic than in the plane channel with a larger percentage of the turbulent kinetic energy resulting from the streamwise velocity fluctuations. As the curvature increases, regions of strong normal vorticity develop near the wall.

Effects of convex transverse curvature on wall-bounded turbulence. Part 2. The pressure fluctuations

The effects of convex transverse curvature on the wall pressure fluctuations were studied through direct numerical simulations. The flow regime of interest is characterized by large ratio of the shear-layer thickness to the radius of curvature (γ = δ/a) and by small a+, the radius of curvature in wall units. Two direct numerical simulations of a model problem approximating axial flow boundary layers on long cylinders were performed for γ = 5 (a+ ≈ 43) and γ = 11 (a+ ≈ 21). The space-time characteristics of the wall pressure fluctuations of the plane channel flow simulation of Kim, Moin & Moser (1987), which were studied by Choi & Moin (1990) are used to assess the effects of curvature.As the curvature increases the root-mean-square (r.m.s.) pressure fluctuations decrease and the ratio of the streamwise to spanwise lengthscales of the wall pressure fluctuations increases. Fractional contributions from various layers in the flow to the wall r.m.s. pressure fluctuations are marginally affected by the curvature. Curvature-dependent timescales and lengthscales are identified that collapse the high-frequency range of the wall pressure temporal spectra and the high wave-number range of the wall pressure streamwise spectra of flows with different curvatures. Taylor's hypothesis holds for the wall pressure fluctuations with a lower convection velocity than in the planar case.

An analysis on effect of transverse convex curvature on turbulent flow and heat transfer

An analysis based on a model of modified mixing length by Hornby, Mistry und Barrow [1] was made on the effect of transverse convex curvature in turbulent boundary layer for incompressible axial flows along circular cylinders. The deviation of various turbulent flow and heat transfer properties from those of flat plates is presented.

Resonances of a finite elastic cylinder with hemispherical endcaps

Experiments on ultrasonic backscattering from submerged elastic cylinders with hemispherical endcaps have been carried out for solid steel cylinders at Catholic University, for solid tungsten carbide cylinders at the University of Le Havre, and for hollow air-filled steel cylindrical shells at DTRC and Le Havre. The experimental results will be presented, and will be theoretically interpreted by the method of phase matching, taking into account the dispersion of the wave speed of the surface waves propagating axially along the cylinder (guided waves). Use of these explicit dispersion formulas, rather than their high-frequency constant limits as they have been employed previously (thereby neglecting transverse curvature effects) is shown to be very important in the correct identification of the resonance peaks.

Numerical studies of transverse curvature effects on transonic flow stability

A numerical study of transverse curvature effects on compressible flow temporal stability for transonic to low supersonic Mach numbers is presented for axisymmetric modes. The mean flows studied include a similar boundary-layer profile and a nonsimilar axisymmetric boundary-layer solution. The effect of neglecting curvature in the mean flow produces only small quantitative changes in the disturbance growth rate. For transonic Mach numbers (1–1.4) and aerodynamically relevant Reynolds numbers (5000–10 000 based on displacement thickness), the maximum growth rate is found to increase with curvature—the maximum occurring at a nondimensional radius (based on displacement thickness) between 30 and 100.

Effect of transverse curvature on the stability of compressible boundary layers

Linear stability theory is used to determine the effect of transverse curvature on the estimated location of the onset of transition for supersonic boundary layers. Results have been obtained for Mach 5 and Mach 1.25 boundary layers formed over cylinders and sharp cones. As transverse curvature increases, the growth rates for the first mode (asymmetric) instability increase, whereas those for the second mode decrease. The overall effect of increasing curvature is to lower the transition Reynolds number at the Mach numbers studied

A spectral collocation method for compressible, non‐similar boundary layers

AbstractAn efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two‐dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth‐order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation method based on Chebyshev polynomial expansions in the wall‐normal (spacelike) dimension. The discrete governing equations are cast in residual form and the residuals are minimized at each marching step by a preconditioned Richardson iteration scheme which fully couples energy, momentum and continuity equations. Preconditioning on the basis of the finite difference analogues of the governing equations results in a computationally efficient iteration with acceptable convergence properties. A practical application of the algorithm arises in the area of compressible linear stability theory, in the investigation of the effects of transverse curvature on the stability of flows over axisymmetric bodies. The spectral collocation algorithm is used to derive the non‐similar mean velocity and temperature profiles in the boundary layer of a ‘fuselage’ (cylinder) in a high‐speed (Mach 5) flow parallel to its axis. The stability of the flow is shown to be sensitive to the gradual streamwise evolution of the mean flow and it is concluded that the effects of transverse curvature on stability should not be ignored routinely.