RANS simulations for transition and turbulent flow regimes in wire-wrapped rod bundles

Internal flows through rod assemblies are commonly found in heat exchangers, steam generators, and nuclear reactors. One of the fuel assembly designs considered for liquid metal-cooled reactors utilizes wires helically wrapped around each fuel rod as spacers. The wires keep the fuel pins separated, enhancing the turbulent mixing, and heat transfer, but also affecting the pressure drop. It is of interest the understanding of the fluid flow phenomena in the sodium-cooled fast reactor as it is one of the Generation IV advanced reactor designs and it has been a motivating topic of research for the last decade. A wire-wrapped fuel assembly replica with 61-pins has been in operation at the Thermal-Hydraulic Research Laboratory of Texas A&M University. This facility produced high-fidelity velocity and pressure drop data for validation of computational fluid dynamics codes. This study investigates the effects of geometrical features and operating conditions on the flow behavior of the 61-pin wire wrapped bundle using Reynolds-Averaged Navier-Stokes (RANS) models to predict the axial and transverse pressure drops for a range of Reynolds numbers from 1,270 to 100,000. The friction factor predictions were in satisfactory agreement with the experimental data and the Upgraded Chen and Todreas correlation. The internal subchannel velocity results were compared with experimental data and Large Eddy Simulations (LES) and found in reasonable agreement. This study demonstrates that RANS is a suitable approach in predicting velocity and pressure fields in wire-wrapped rod bundles, with a relatively low computational effort.     

Velocity field analysis of the high density,high pressure diesel spray

In this study, particle image velocimetry (PIV) measurements have been performed extensively on a non-reactive dense diesel spray injected from a single orifice injector, under various injection pressure and steady ambient conditions, in a constant flow chamber. Details of PIV setup for diesel spray measurement without additional seeding are explained first. The measured velocity profiles are compared to those obtained from other similar measurements performed in a different institution, as well as those obtained from a 1D spray model simulation, presenting in both cases a good level of agreement. In addition, the velocity fields under various injection pressures and ambient densities show the dominant effects of these parameters on the behavior of diesel spray. The self-similarity of the transverse cut profiles of axial velocity is evaluated, showing that the measurements are in agreement with the hypothesis of self-similar velocity profiles. Finally, the effect of injection pressure and ambient density on the velocity fluctuations is presented and analyzed as well. While the experimental results presented here could help to understand the complex diesel fuel–air mixing process during injection, they also provide additional spray velocity data for future computational model validation, following the main idea of the Engine Combustion Network.     

Correlation coefficients of the fluctuating density in turbulent premixed flames

 Two-point density measurements by laser induced Rayleigh scattering are used in this study to fully characterise the scalar field in a Bunsen type turbulent premixed flame. The two points are separated within the flame brush in the axial or radial directions. Correlation coefficients are obtained by comparing the evolution of one-point density fluctuations in time or the two-point density fluctuations in both space and time. Time and length scales of the scalar field, and the mean convection velocity of the turbulent scalar structures are deduced from these correlation coefficients. Time scales are calculated from the auto-correlation coefficients, length scales are determined from the space correlation coefficients and the mean convection velocity of the scalar structures in the axial direction is deduced from the space–time correlation coefficients. The relevance of these results for analysing and modelling the structure of turbulent premixed flames is discussed. Received: 30 April 1996 / Accepted: 2 September 1997     

Direct numerical simulation of the turbulent energy balance and the shear stresses in power-law fluid flows in pipes

The results of direct numerical simulation of turbulent flows of non-Newtonian pseudoplastic fluids in a straight pipe are presented. The data on the distributions of the turbulent stress tensor components and the shear stress and turbulent kinetic energy balances are obtained for steady turbulent flows at the Reynolds numbers of 10⁴ and 2×10⁴. As distinct from Newtonian fluid flows, the viscous shear stresses turn out to be significant even far from the wall. In power-law fluid flows the mechanism of the energy transport from axial to transverse component fluctuations is suppressed. It is shown that with decrease in the fluid index the turbulent transfer of the momentum and the velocity fluctuations between the wall layer and the flow core reduces, while the turbulent energy flux toward the wall increases. The earlier-proposed models for the average viscosity and the non-Newtonian one-point correlations are in good agreement with the data of direct numerical simulation.     

Ion slip effect on a steady flow through a circular pipe of a dusty conducting Oldroyd 8-constant fluid

In this paper, a steady magnetohydrodynamic (MHD) flow of a dusty incompressible electrically conducting Oldroyd 8-constant fluid through a circular pipe is examined with considering the ion slip effect. A constant pressure gradient in the axial direction and an external uniform magnetic field in the perpendicular direction are applied. A numerical solution is obtained for the governing nonlinear momentum equations by using finite differences. The effect of the ion slip, the non-Newtonian fluid characteristics, and the particle-phase viscosity on the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is reported.     

Velocity field of convergent flow into a rectangular slit for a polymeric fluid

Three-dimensional velocity distributions in the entry region of a rectangular slit contraction were investigated using a dual-beam laser Doppler velocimeter. The flow of a silicone oil (a Newtonian fluid) and a solution of silicone rubber in the same silicone oil (a viscoelastic fluid) was studied at low Reynolds numbers (Re < 0.5). In contrast to the usual velocity distribution of a Newtonian fluid, the viscoelastic fluid showed the following characteristic features: (1) a pronounced axial velocity overshoot immediately after the slit entrance and a maximum before the slit exit; (2) appearance of an axial flow deceleration region just before the sharp acceleration near the slit entrance. Even more remarkably, a saddle form of velocity profile was found in the entrance region. This flow pattern is completely different from that found for Newtonian fluids and has not yet been explained using existing rheological analysis.Parts of this paper were presented at the IX. Intern. Congress on Rheology at Acapulco (Mexico), October 8–13, 1984     

Velocity measurements based on shadowgraph-like image correlations in a cavitating micro-channel flow

Cavitation is generally known for its drawbacks (noise, vibration, damage). However, it may play a beneficial role in the particular case of fuel injection, by enhancing atomization processes or reducing nozzle fouling. Studying cavitation in real injection configuration is therefore of great interest, yet tricky because of high pressure, high speed velocity, small dimensions and lack of optical access for instance. In this paper, the authors proposed a simplified and transparent 2D micro-channel (200–400 μm), supplied with test oil at lower pressure (6 MPa), allowing the use of non-intrusive and accurate optical measurement techniques. A shadowgraph-like imaging arrangement is presented. It makes it possible to visualize vapour formations as well as density gradients (refractive index gradients) in the liquid phase, including scrambled grey-level structures connected to turbulence. This optical technique has been already discussed in a previous paper (Mauger et al., 2012), together with a Schlieren and an interferometric imaging technique. In this paper, the grey-level structures connected with turbulence are considered more specifically to derive information on flow velocity. The grey-level structure displacement is visualized through couples of images recorded within a very short time delay (about 300 ns). At first, space and space–time correlation functions are calculated to characterize the evolution of grey-level structures. Space–time correlations provide structure velocity that slightly under-estimates the real flow velocity deduced from flowmeter measurements. Since the grey-level structures remain correlated in time, a second velocity measurement method is applied. An image correlation algorithm similar to those currently used in Particle Image Velocimetry (PIV) is used to extract velocity information, without seeding particles. In addition to the mean velocity of grey-level structures, this second method provides structure velocity fluctuations. In particular, an increase in structure velocity fluctuations is observed at the channel outlet for a critical normalized length of vapour cavities equals to 40–50%, as expected for the real flow velocity fluctuations. The present study is completed by a parametric study on channel height and oil temperature. It is concluded that none of them significantly impact the critical normalized length for which the fluctuation increase is observed, even though the magnitude of these fluctuations is larger for the higher channel.     

3D Velocimetry and droplet sizing in the Ranque–Hilsch vortex tube

The Ranque–Hilsch vortex tube (RHVT) is a device currently used to generate local cooling. In general, the fluid that is injected into the RHVT is a single-phase gas. In this study, however, we have added a dispersed phase (water droplets) to the gas (nitrogen). By means of phase Doppler particle analysis, three velocity components, their higher order moments, and sizes of droplets were measured, showing high intensity velocity fluctuations in the core region of the main vortex. The frequency spectrum of the velocity is presented and reveals that wobbling of the vortex axis is the cause of the high intensity fluctuations. The wobbling motion reduces the influence of the droplet size on the radial droplet velocity.     

Asymptotic solutions of the flow of a Johnson-Segalman fluid through a slowly varying pipe using double perturbation strategy

A double perturbation strategy is presented to solve the asymptotic solutions of a Johnson-Segalman (J-S) fluid through a slowly varying pipe. First, a small parameter of the slowly varying angle is taken as the small perturbation parameter, and then the second-order asymptotic solution of the flow of a Newtonian fluid through a slowly varying pipe is obtained in the first perturbation strategy. Second, the viscoelastic parameter is selected as the small perturbation parameter in the second perturbation strategy to solve the asymptotic solution of the flow of a J-S fluid through a slowly varying pipe. Finally, the parameter effects, including the axial distance, the slowly varying angle, and the Reynolds number, on the velocity distributions are analyzed. The results show that the increases in both the axial distance and the slowly varying angle make the axial velocity slow down. However, the radial velocity increases with the slowly varying angle, and decreases with the axial distance. There are two special positions in the distribution curves of the axial velocity and the radial velocity with different Reynolds numbers, and there are different trends on both sides of the special positions. The double perturbation strategy is applicable to such problems with the flow of a non-Newtonian fluid through a slowly varying pipe.     

Ignition of liquid and dust fuel layers by gaseous detonation

Abstract. Ignition of a liquid layer and dust fuel layer by a detonation wave propagating in hydrogen-oxygen and acetylene-oxygen mixtures is reported. Experiments were carried out using a shock tube equipped with optical-quality observation windows. A schlieren system and a high-speed camera were used for measurements of ignition delay. Pressure transducers provided data necessary for measurements of the detonation wave velocity and pressure variation within the front of the interacted detonation wave and fuel layer. Kerosene, nitroglycerin and PETN were used as fuels. Investigation shows that the layer of liquid fuel can be efficiently ignited by detonation wave. It was found that the ignition delay of the fuel layer depends mostly on the detonation wave velocity and sensitivity of igniting fuels, and slightly on the layer thickness. Received 12 August 2001 / Accepted 1 July 2002 Published online 4 February 2003 Correspondence to: P. Wolanski (e-mail: wolanski@itc.pw.edu.pl) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001     

Modal expansion of the perturbation velocity potential for a cantilevered fluid-conveying cylindrical shell

The subject of this paper is the application of the method of separation of variables and the Galerkin method for discretization of the equations of motion for a cantilevered cylindrical fluid-conveying shell. The perturbation velocity potential is expressed in terms of a series of orthonormal beam modal functions. The final Galerkin generalized fluid force coefficients are simple, compact, and easy to evaluate numerically. To validate the method, comparisons with results obtained from the Fourier transform method are made. Mismatch between the actual axial fluid modes and the assumed modes affects the Galerkin coefficients to some extent, but the unstable eigenvalue branch is only affected slightly over a wide range of system parameters, and critical flow speeds predicted by the two methods generally agree well.     

Flow of Particulate-Fluid Suspension in a Channel with Porous Walls

The problem of the dispersed particulate-fluid two-phase flow in a channel with permeable walls under the effect of the Beavers and Joseph slip boundary condition is concerned in this paper. The analytical solution has been derived for the longitude pressure difference, stream functions, and the velocity distribution with the perturbation method based on a small width to length ratio of the channel. The graphical results for pressure, velocity, and stream function are presented and the effects of geometrical coefficients, the slip parameter and the volume fraction density on the pressure variation, the streamline structure and the velocity distribution are evaluated numerically and discussed. It is shown that the sinusoidal channel, accompanied by a higher friction factor, has higher pressure drop than that of the parallel-plate channel under fully developed flow conditions due to the wall-induced curvature effect. The increment of the channel’s width to the length ratio will remarkably increase the flow rate because of the enlargement of the flow area in the channel. At low Reynolds number ranging from 0 to 65, the fluids move forward smoothly following the shape of the channel. Moreover, the slip boundary condition will notably increase the fluid velocity and the decrease of the slip parameter leads to the increment of the velocity magnitude across the channel. The fluid-phase axial velocity decreases with the increment of the volume fraction density.     

Numerical Evaluation of Combustion Regimes in a GDI Engine

There is significant interest in the gasoline direct-injection engine due to its potential for improvements in fuel consumption but it still remains an area of active research due to a number of challenges including the effect of cycle-by-cycle variations. The current paper presents the use of a 3D-CFD model using both the RANS and LES turbulence modelling approaches, and a Lagrangian DDM to model an early fuel injection event, to evaluate the regimes of combustion in a gasoline direct-injection engine. The velocity fluctuations were investigated as an average value across the cylinder and in the region between the spark plug electrodes. The velocity fluctuations near the spark plug electrodes were seen to be of lower magnitude than the globally averaged fluctuations but exhibited higher levels of cyclic variation due to the influence of the spark plug electrode and the pent-roof geometry on the in-cylinder flow field. Differences in the predicted flame structure due to differences in the predicted velocity fluctuations between RANS and LES modelling approaches were seen as a consequence of the inherently higher dissipation levels present in the RANS methodology. The increased cyclic variation in velocity fluctuations near the spark plug electrodes in the LES predictions suggested significant variation in the relative strength of the in-cylinder turbulence and that may subsequently result in a thickening of the propagating flame front from cycle-to-cycle in this region. Throughout this paper, the numerical results were validated against published experimental data of the same engine geometry under investigation.     

Modelling of pipeline integrity taking into account the fluid–structure interaction

Two mechanical models have been presented in this paper for structural failure prediction of piping systems conveying liquids subjected to pressure transients. One model takes into account the axial fluid–structure interaction (FSI) phenomenon between fluid and pipe motion, whereas the other refers to an extension of the well-known waterhammer formulation. Both models are described by a system of non-linear hyperbolic equations which are solved by using a numerical procedure based upon the operator splitting technique and Glimm's scheme. To implement Glimm's method, it is presented the solution of a 4×4 Riemann problem with discontinuous coefficients. Numerical predictions of both models are presented and compared, so that the influence of the FSI term on the failure analysis is focused on. © 1998 John Wiley & Sons, Ltd.     

Intermittency in a cantilever plate in a randomly fluctuating fluid flow

Fluid–elastic systems nearing dynamic instabilities are known to be sensitive to fluctuations in fluid flow. A cantilever plate in axial flow with random temporal fluctuations, is examined numerically for its dynamical behaviour. The numerical model comprises of a nonlinear structural model for the flexible plate, coupled with unsteady lumped vortex model for the fluid forces. As the mean flow velocity is increased, the system transitions to limit cycle oscillations from a state of rest, through a regime of intermittent oscillations. The conditions for onset and disappearance of intermittency are discussed and are interpreted using stochastic bifurcation theories. While the onset of intermittency is found to be unaffected by the time scales of the flow fluctuations, they are observed to affect the length of the intermittency regime. The effect of plate flexibility on intermittency is also discussed.     

Simulating the fluid forces and fluid-elastic instabilities of a clamped–clamped cylinder in turbulent axial flow

In this paper, the fluid forces and the dynamics of a flexible clamped–clamped cylinder in turbulent axial flow are computed numerically. In the presented numerical model, there is no need to tune parameters for each specific case or to obtain coefficients from experiments. The results are compared with the dynamics measured in experiments available in the literature. The specific case studied here consists of a silicone cylinder mounted in axial water flow. Computationally it is found that the cylinder loses stability first by buckling. The threshold for buckling is in quantitative agreement with experimental results and weakly nonlinear theory. At higher flow speed a fluttering motion is predicted, in agreement with experimental results. It is also shown that even a small misalignment between the flow and the structure can have a significant impact on the dynamical behavior. To provide insight in the results of these fluid–structure interaction simulations, forces are computed on rigid inclined and curved cylinders, showing the existence of two different flow regimes. Furthermore it is shown that the inlet turbulence state has a non-negligible effect on these forces and thus on the dynamics of the cylinder.     

Stability analysis of cylindrical shells containing a fluid with axial and circumferential velocity components

The stability of an elastic circular cylindrical shell of revolution interacting with a compressible liquid (gas) flow having both axial and tangential components is analyzed. The behavior of the fluid is studied within the framework of potential theory. The elastic shell is described in terms of the classical theory of shells. Numerical solution of the problem is performed using a semianalytical finite element method. Results of numerical experiments for shells with different boundary conditions and geometric dimensions are presented. The effects of fluid rotation on the critical flow velocity and the effect of axial fluid flow on the critical angular velocity of fluid rotation were estimated.     

The turbulent/non-turbulent interface at the outer boundary of a self-similar turbulent jet

The flow at the outer boundary of a submerged self-similar turbulent jet at Re=2᎒³ is investigated experimentally by means of combined particle image velocimetry (PIV) laser-induced fluorescence (LIF) measurements. The jet fluid contains a fluorescent dye so that the LIF data can be used to discriminate between the jet fluid and the ambient fluid. The axial velocity, Reynolds stress, and vorticity are determined relative to the jet boundary. The results are compared against the conventional profiles, and the results of a direct numerical simulation of the turbulent far-wake behind a flat plate. The results show a sharp transition between rotational and irrotational fluid at the fluid interface, and the existence of a layer of irrotational velocity fluctuations outside the turbulent region.     

Flow instabilities during annular displacement of one non-Newtonian fluid by another

This paper describes an experimental setup for axial laminar flow of liquids in the annulus between two eccentered cylinders. The design uses a conductivity method for measuring peak axial velocities around the annulus, and for the determination of displacement efficiency when displacing one fluid by another (displacement efficiency being defined as the ratio of volume of displaced fluid removed from the annulus, to the volume of the annulus, after a given number of annular volumes have been pumped). In an eccentric annulus, lower axial velocity in the narrow side produces “channeling” of the displacing fluid in the wide side and reduces the displacement efficiency. A positive density contrast between the two fluids can increase the efficiency by promoting azimuthal flow of the (denser) displacing fluid towards the narrow side. In this paper we report that gravity driven azimuthal flow is prone to severe instabilities which accelerate the displacement process but may leave behind an immobile strip of the displaced fluid in the narrow side.     

Simultaneous quantitative flow measurement using PIV on both sides of the air–water interface for breaking waves

An experimental method for simultaneously measuring the velocity fields on the air and water side of unsteady breaking waves is presented. The method includes a novel technique for seeding the air flow such that the air velocity can be resolved in the absence of wind. Low density particles that have large Stokes drag and ability to respond to high-frequency flow fluctuations are used to seed the air flow. Multi-camera, multi-laser particle image velocimetry setups are applied to small-scale unsteady breaking waves, yielding fully time-resolved velocity fields. The surface tension of the fluid is altered and controlled to form spilling breaking waves. Results for the velocity and vorticity fields of representative spilling breakers, which show shedding of an air-side vortex and well-documented generation of water-side vorticity, are presented and discussed.