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Notes: The equations for the higher-order moments of turbulent velocity fluctuations are considered. These are derived utilizing truncated, cumulant expansions as an approximation for the probability density distributions of the corresponding turbulence properties. By applying different degrees of truncations to these expansions, an alternative set of equations for the moments is formulated that contains only velocity correlations. From these equations, interrelations between the higher-order moments are deduced and are experimentally verified using data available in the literature and also data measured by the authors.

Notes: The bifurcation structure of two-dimensional, pressure-driven flows through a rectangular duct that is rotating about an axis perpendicular to its own is examined at a fixed Ekman number (Ek=ν/b2Ω) of 0.01. The solution structure for flow through a square duct (aspect ratio γ=1) is determined for Rossby numbers (Ro=U/bΩ) in the range of 0–5 using a computational scheme based on the arclength continuation method. The structure is much more complicated than reported earlier by Kheshgi and Scriven [Phys. Fluids 28, 2968 (1985)]. The primary branch with two limit points in Rossby number and a hysteresis behavior between the two- and four-cell flow structure that was computed by Kheshgi and Scriven is confirmed. An additional symmetric solution branch, which is disconnected from the primary branch (or rather connected via an asymmetric solution branch), is found. This has a two-cell flow structure at one end, a four-cell flow structure at the other and three limit points are located on the path. Two asymmetric solution branches emanating from symmetry breaking bifurcation points are also found for a square duct. Thus even within a Rossby number range of 0–5 a much richer solutions structure is found with up to five solutions at Ro=5. An eigenvalue calculation indicates that all two-dimensional solutions develop some form of unstable mode by the time Ro is increased to 5.0. In particular, the four-cell solution becomes unstable to asymmetric perturbations as found in a related problem of flow through a curved duct. The paths of the singular points are tracked with respect to variation in the aspect ratio using the fold following algorithm. A transcritical point is found at an aspect ratio of 0.815 and below which the four-cell solution is no longer on the primary branch. When the channel cross section is tilted even slightly (1°) with respect to the axis of rotation, the bifurcation points unfold and the two-cell solution evolves smoothly as Rossby number is increased. The four-cell solutions then become genuinely disconnected from the primary branch. The uniqueness range in Rossby number increases with increasing tilt.

Notes: Higher-order correlations were measured in a turbulent boundary layer using the LDA measuring technique. In the paper, comparisons are made between the measured and predicted correlations obtained by utilizing the properties of truncated Gram–Charlier series expansions. Several theoretically derived relationships between correlations of different orders were confirmed by the experimental data. The experimental and theoretical results support the applicability of truncated Gram–Charlier series expansions for a refined statistical analysis of the conservation equations for higher-order moments of turbulent property fluctuations.

Notes: A numerical study of the viscous supersonic flow past a flat plate is presented. The objective is to investigate the supersonic flow at high angles of incidence where large flow gradients occur. The effect of the angle of incidence and the Reynolds number (Re) in the flow structure especially in the formation of the separation region is investigated. The study is based on the solution of the full Navier–Stokes equations by high resolution schemes, and it focuses on the supersonic flow over the plate at Re≤105. Results on fine computational grids are presented for flow angles up to 20°. The calculations reveal that the flow remain attached for angles of incidence less than a=5°. For a=5° and Re=105, separation of the flow at the trailing edge appeared. Increasing the flow angle (a(approximately-greater-than)5°) moves the separation point upstream while a reverse flow region forms for the entire range of the Reynolds numbers used in this study. The results reveal that for large angles of incidence, the variation of the Reynolds number has significant effects on the variation of the flow variables. The flow behind the trailing edge is also affected from the flow angle as well as from the Reynolds number. Comparisons are also presented between viscous and inviscid solutions. The comparisons show that the viscous effects are dominant on the upper surface of the plate as well as behind the trailing edge. These effects become stronger when the flow angle is a=20°.

Notes: A two-dimensional numerical study on the laminar flow past a circular cylinder rotating with a constant angular velocity was carried out. The objectives were to obtain a consistent set of data for the drag and lift coefficients for a wide range of rotation rates not available in the literature and a deeper insight into the flow field and vortex development behind the cylinder. First, a wide range of Reynolds numbers (0.01≤Re≤45) and rotation rates (0≤α≤6) were considered for the steady flow regime, where α is the circumferential velocity at the cylinder surface normalized by the free-stream velocity. Furthermore, unsteady flow calculations were carried out for one characteristic Reynolds number (Re=100) in the typical two-dimensional (2D) vortex shedding regime with α varying in the range 0≤α≤2. Additionally, the investigations were extended to very high rotation rates (α≤12) for which no data exist in the literature. The numerical investigations were based on a finite-volume flow solver enhanced by multi-grid acceleration and the local grid refinement technique to achieve efficient computations and accurate numerical results. The predictions show that the rotation of the cylinder suppresses the vortex development in both the steady and the unsteady flow regimes and significantly changes the flow field close to the cylinder. For very low Reynolds numbers, the drag force is not affected by rotation and the lift force is a linear function of α. For higher Re in the steady flow regime, the drag force decreases with increasing rotational velocities even leading to negative values. The lift force is almost a linear function of the rotational velocity and nearly independent of Re for low rotational speeds of α〈2. However, for higher α values and larger Reynolds numbers (Re〉1), a progressive increase in the lift force is observed. A very interesting phenomenon was found in the unsteady flow regime at Re=100. For low rotation rates (α≤2) the flow exhibits the behavior known from the literature, e.g., a linear increase of the mean lift coefficient with increasing α and the suppression of vortex shedding beyond a critical α value of about αL(approximate)1.8. However, for α(approximate)5, an unsteady periodic flow motion was found in the wake which is characterized by a frequency much lower than that known for normal vortex shedding. The change in the flow structure also leads to a distinct change in the mean lift coefficients which exhibits a linear relation of very high rotations rates and asymptotically converges to the values known from the potential flow theory. © 2002 American Institute of Physics.

Notes: The continuity and momentum equations do not imply a Reynolds number dependence of turbulence data when wall variables are used for normalization. However, experimental and numerical results show a Reynolds number dependence of turbulence intensity very close to the wall. The cause of this is explained. It results from the behavior of a sink term in the dissipation rate equation which shows a Reynolds number dependence in the limit of two-component two-dimensional turbulence as it exists close to walls. Away from the near-wall region the Reynolds number dependence originates from the streamwise pressure gradient which enters into the equations for the turbulent kinetic energy and turbulent dissipation rate through the gradient production processes. The low-Reynolds number effects in turbulent channel flow were investigated experimentally using the laser Doppler anemometry (LDA) measuring technique. A new method was used to eliminate the influence of the limited spatial resolution of the LDA measuring control volume. Results are presented for the limiting behavior of the turbulent intensity near the wall and its variation with the Reynolds number. The present LDA measurements confirm the trend in the data of direct numerical simulations. © 2001 American Institute of Physics.

Notes: Notes that, in a full-scale application of the Monte Carlo method for combined heat transfer analysis, problems usually arise from the large computing requirements. Here the method to overcome this difficulty is the parallel execution of the Monte Carlo method in a distributed computing environment. Addresses the problem of determination of the temperature field formed under the assumption of radiative equilibrium in an enclosure idealizing an industrial furnace. The medium contained in this enclosure absorbs, emits and scatters anisotropically thermal radiation. Discusses two topics in detail: first, the efficiency of the parallelization of the developed code, and second, the influence of the scattering behavior of the medium. The adopted parallelization method for the first topic is the decomposition of the statistical sample and its subsequent distribution among the available processors. The measured high efficiencies showed that this method is particularly suited to the target architecture of this study, which is a dedicated network of workstations supporting the message passing paradigm. For the second topic, the results showed that taking into account the isotropic scattering, as opposed to neglecting the scattering, has a pronounced impact on the temperature distribution inside the enclosure. In contrast, the consideration of the sharply forward scattering, that is characteristic of all the real combustion particles, leaves the predicted temperature field almost undistinguishable from the absorbing/emitting case.

Notes: Thermal flow sensors with a wide dynamic range are at present not available in spite of the large demand which exists for such sensors in practical fluid flow measurements. In this paper, it is shown that the velocity range of a "time-of-flight" thermal flowmeter for slowly changing flows can be increased by using wires (or other heating/sensing elements) with large thermal inertia (time constant) and heating the sending wire with a continuous sinusoidal current, instead of discrete, very short, square-wave pulses as in the usual pulsed-wire anemometer. The device described here uses two parallel wires of 12.5µm diameter and its usable speed range is 0.05 to 25m/s. Although the present thermal flowmeter can be applied as a point measurement device, the main applications are in pipe flow, especially at very low flow rates. The high sensitivity at low flow rates makes the device especially suitable for this purpose.

Notes: Summary The paper aims at a detailed description of the physical background, for the so-called Coriolis mass flow meter. It presents essentially an analysis of the (free) vibration modes of a fluid conveying straight pipe segment. Due to the inertial effects of the flowing fluid, mainly the Coriolis force, these modes deviate in shape (and in frequency) from those appearing in the absence of fluid motion. The effect of fluid inertia may, therefore, be exploited for the purpose of flow measurement. The analysis is performed under a simplifying approximation: The pipe is considered as a beam, the fluid as a moving string. This approximation leaves the fluid with only one degree of freedom, connected with its mean velocity, and eliminates an infinity of degrees of freedom of the pipe. Yet it keeps, the essential features of the phenomenon. The equations describing the vibrations are derived variationally, with the constraint of a common vibration amplitude of both fluid and pipe. The Lagrange multiplier associated with the constraint gives the interaction force between pipe and fluid. The modes are determined by a perturbation procedure, wherein the small (perturbation) parameter is related to the fluid velocity. The analysis shows, as main result, how the time delay between the vibrations of two appropriately chosen points of the pipe may serve to determine the mass flow rate of the fluid. Other aspects of the problem, like the precise role of the Coriolis force, are considered. The possible improvement of the used approximation is discussed.

Notes: Summary Usually a Coriolis mass flowmeter consists of a fluid conveying vibrating pipe segment with a reflection symmetry, on which the time delay Δτ is measured between the vibrations of two symmetrically situated cross sections. For a homogeneous pipe segment, the proportionality factorK c between Δτ and the mass flowrate $$\dot Q_m$$ , i.e. the calibration factor of the instrument, is independent of the nature of the flowing fluid. Fixing a concentrated massm c at the middle of the pipe segment — as required e.g. for the purpose of a symmetric excitation of the vibration — brings about a dependence of the factorK c on the fluid density. In the present paper the influence of the massm c on the vibration spectrum and on flowmetering is investigated in detail for an instrument working with a straight pipe segment. It turns out that, whereas the frequency of the fundamental vibration mode is strongly influenced bym c , the calibration factorK c is practically independent of the massm c , up to fairly high values compared to the mass of the fluid filled pipe segment.