A Matched Asymptotic Expansion Analysis of Highly Unsteady Porous Media Flows

The method of matched asymptotic expansions is used to analyse a mixture of wave and diffusive behaviours governing flow in a saturated porous medium inside an elastic pipe that is suddenly subjected to a large hydraulic gradient at its entrance. At early times and near the entrance, the head is a diffusing wave that can be reduced to the linear and non-linear telegrapher equations for the laminar and partially developed turbulent flows, respectively. At later times, laminar flows are diffusive and partially developed turbulent flows follow a ‘fast diffusion’ behaviour. In the case of fully developed turbulence, flows at later times follow a fast diffusion form which is complicated by advection at extremely high gradients. A matched asymptotic expansion approach is used to match flows at early times and near the entrance, with complementary forms that are away from the entrance and which occur at later times.     

A new evaluation method for Nusselt numbers in naphthalene sublimation experiments in rotating-disk systems

A comparative analysis of theoretical and empirical relations, as well as experimental data for mass transfer of a rotating disk in laminar, transitional and turbulent flows for naphthalene sublimation in air was done. New correlations between local and average Sherwood numbers for the entire disk were offered. A new evaluation approach for Nusselt numbers based on the experimental data for naphthalene sublimation in laminar, transitional and turbulent flows was developed.     

Effect of the pattern of initial perturbations on the steady pipe flow regime

The influence of the inlet flow formation mode on the steady flow regime in a circular pipe has been investigated experimentally. For a given inlet flow formation mode the Reynolds number Re* at which the transition from laminar to turbulent steady flow occurred was determined. With decrease in the Reynolds number the difference between the resistance coefficients for laminar and turbulent flows decreases. At a Reynolds number approximately equal to 1000 the resistance coefficients calculated from the Hagen-Poiseuille formula for laminar steady flow and from the Prandtl formula for turbulent steady flow are equal. Therefore, we may assume that at Re > 1000 steady pipe flow can only be laminar and in this case it is meaningless to speak of a transition from one steady pipe flow regime to the other. The previously published results [1–9] show that the Reynolds number at which laminar goes over into turbulent steady flow decreases with increase in the intensity of the inlet pulsations. However, at the highest inlet pulsation intensities realized experimentally, turbulent flow was observed only at Reynolds numbers higher than a certain value, which in different experiments varied over the range 1900–2320 [10]. In spite of this scatter, it has been assumed that in the experiments a so-called lower critical Reynolds number was determined, such that at higher Reynolds numbers turbulent flow can be observed and at lower Reynolds numbers for any inlet perturbations only steady laminar flow can be realized. In contrast to the lower critical Reynolds number, the Re* values obtained in the present study, were determined for given (not arbitrary) inlet flow formation modes. In this study, it is experimentally shown that the Re* values depend not only on the pipe inlet pulsation intensity but also on the pulsation flow pattern. This result suggests that in the previous experiments the Re* values were determined and that their scatter is related with the different pulsation flow patterns at the pipe inlet. The experimental data so far obtained are insufficient either to determine the lower critical Reynolds number or even to assert that this number exists for a pipe at all.     

On the impedance of the pipe in laminar and turbulent pulsating flows

The response of a facility, consisting of a valveless reciprocating pump, a large settling chamber and a long straight smooth pipe, to a periodic change in the volume was analysed. The impedance of the pipe was estimated in both laminar and turbulent flow regimes under otherwise identical flow conditions. A good agreement with theory was obtained for the laminar flow. The estimate of the pipe impedance from the experimental data in turbulent flow was based on the momentum equation as well as on the measured resonant frequency of the system. These independent methods show that the inertance of the pipe has a qualitatively different behavior in laminar and turbulent flow regimes.     

A generalized Brinkman number for non-Newtonian duct flows

When viscous dissipation effects are important in duct flows the Brinkman number is widely used to quantify the relationship between the heat generated by dissipation and the heat exchanged at the wall. For Newtonian laminar fully developed pipe flow the use of the classical expression for this dimensionless group is appropriate, but under different conditions it can lead to misleading conclusions, such as when comparing flows through different cross-section ducts, flow regimes and mainly non-Newtonian flows. In this work a generalized Brinkman number is proposed, based on an energy balance for the power dissipated by friction, that allows proper quantification of viscous heating effects and reduces to the classical definition in laminar Newtonian pipe flow. The advantages of the new definition are shown and expressions are given for generalized Brinkman numbers in the most common cases.     

An improved EMMS model for turbulent flow in pipe and its solution

Based on the existing energy-minimization multi-scale (EMMS) model for turbulent flow in pipe, an improved version is proposed, in which not only a new radial velocity distribution is introduced but also the quantification of total dissipation over the cross-section of pipe is improved for the dominant mechanism of fully turbulent flow in pipe. Then four dynamic equality constraints and some other constraints are constructed but there are five parameters involved, leading to one free variable left. Through the compromise in competition between dominant mechanisms for laminar and fully turbulent flow in pipe respectively, the above four constructed dynamic equality constraints can be closed. Finally, the cases for turbulent flow in pipe with low, moderate and high Reynolds number are simulated by the improved EMMS model. The numerical results show that the model can obtain reasonable results which agree well with the data computed by the direct numerical simulation and those obtained by experiment. This illustrates that the improved EMMS model for turbulent flow in pipe is reasonable and the compromise in competition between dominant mechanisms is indeed a universal governing principle hidden in complex systems. Especially, one more EMMS model for a complex system is offered, promoting the further development of mesoscience.     

A Modelling Study of Evolving Particle-laden Turbulent Pipe-flow

An Eulerian turbulent two phase flow model using kinetic theory of granular flows for the particle phase was developed in order to study evolving upward turbulent gas particle flows in a pipe. The model takes the feedback of the particles into account and its results agree well with experiments. Simulations show that the pipe length required for particle laden turbulent flow to become fully developed is up to five times longer than an unladen flow. To increase the understanding of the dependence of the development length on particle diameter a simple model for the expected development length was derived. It shows that the development length becomes shorter for increasing particle diameters, which agrees with simulations up to a particle diameter of 100 ??m. Thereafter the development length becomes longer again for increasing particle diameters because larger particles need a longer time to adjust to the velocity of the carrier phase.     

Characteristics of strongly-forced turbulent jets and non-premixed jet flames

Previous researchers have demonstrated that strong pulsations of the fuel flow rate can significantly reduce the flame length and luminosity of laminar/transitional non-premixed jet flames. The physical mechanisms responsible for these changes are investigated experimentally in acoustically-forced jet flows where the peak velocity fluctuations are up to eight times the mean flow velocity. Both reacting and non-reacting flows were studied and Reynolds numbers, based on the mean flow properties, ranged from 800 to 10,000 (corresponding to peak Reynolds numbers of 1,450–23,000), and forcing frequencies ranged from 290 to 1,140 Hz. Both the first and second organ-pipe resonance modes of the fuel delivery tube were excited to obtain these frequencies. An analysis of the acoustic forcing characteristics within the resonance tube is provided in order to understand the source of the high amplitude forcing. Flow visualization of jets with first resonant forcing confirms the presence of large-scale coherent vortices and strong reverse flow near the exit of the fuel tube. With second-resonant forcing, however, vortices are not emitted from the tube as they are drawn back into the fuel tube before they can fully form. Increased fine-scale turbulence is associated with both resonant cases, but particularly at second resonance. The power spectra of the velocity fluctuations for a resonantly pulsed jet show the presence of an inertial subrange indicating that the flow becomes fully turbulent even for mean-Reynolds-number jets that are nominally laminar. It is shown that these pulsed jet flows exhibit strong similarities to synthetic jets and that the Strouhal number, based on the maximum velocity at the fuel tube exit, is the dominant parameter for scaling these flows. The Strouhal number determines the downstream location where the coherent vortices breakdown, and is found to provide better collapse of flame length data (both current and previous) than other parameters that have been used in the literature.     

Numerical simulation of turbulence suppression: Comparisons of the performance of four k-? turbulence models

The standard k-ε model and three low-Reynolds number k-ε models were used to simulate pipe flow with a ring device installed in the near-wall region. Both developing and fully developed turbulent pipe flows have been investigated. Turbulence suppression for fully developed pipe flows revealed by hot-wire measurements has been predicted with all three low-Reynolds number models, and turbulence enhancement has been predicted by the standard k-ε model. All three low-Reynolds number models have predicted similar distributions of velocities, turbulence kinetic energy, and dissipation rate. For developing pipe flows, the region of turbulence suppression predicted by the three low-Reynolds number models is much more extensive (up to 30 pipe diameters downstream of the device) than for full developed flow; whereas the standard k-ε model has only predicted turbulence enhancement.     

Reynolds number effects on the behavior of a non-buoyant round jet

The behavior of a non-buoyant circular water jet discharged from a contraction nozzle was experimentally investigated. In this experiment, the Reynolds number of the jet, based on the mean velocity results obtained by particle image velocimetry (PIV), ranged from 177 to 5,142. From the experimental results, we found that the cross-sectional profile of the axial velocity for a laminar flow near the nozzle did not show a top-hat distribution, whereas the profiles with Reynolds number higher than 437 were almost top-hat. The length of the zone of flow establishment (ZFE) was found to decrease with increasing Reynolds number. The measured centerline velocity decayed more rapidly and, consequently, approached the theoretical equation earlier near the nozzle as the Reynolds number increased. The decay constant for the centerline velocity of the turbulent cases was relatively lower than that discovered in theory. It is assumed that this probably resulted from the use of the contraction nozzle. Verifying the similarity of the lateral velocity profiles demonstrated that the Gaussian curve was properly approximated only for the turbulent jets and not for the laminar or transitional flows. The jet half width seldom grew for the laminar or transitional flows, whereas it grew with increasing axial distance for the turbulent flows. The spreading rates for the turbulent flows gradually decreased with increasing Reynolds number. The normalized turbulence intensity along the jet centerline increased more rapidly with the axial distance as the Reynolds number increased, and tended to the constant values proposed by previous investigators. The Reynolds shear stress levels were also found to increase as the Reynolds number increased for the turbulent jets.     

Evolution of turbulence characteristics from straight to curved pipes

Fully developed, statistically steady turbulent flow in straight and curved pipes at moderate Reynolds numbers is studied in detail using direct numerical simulations (DNS) based on a spectral element discretisation. After the validation of data and setup against existing DNS results, a comparative study of turbulent characteristics at different bulk Reynolds numbers Re_b = 5300 and 11,700, and various curvature parameters κ = 0, 0.01, 0.1 is presented. In particular, complete Reynolds-stress budgets are reported for the first time. Instantaneous visualisations reveal partial relaminarisation along the inner surface of the curved pipe at the highest curvature, whereas developed turbulence is always maintained at the outer side. The mean flow shows asymmetry in the axial velocity profile and distinct Dean vortices as secondary motions. For strong curvature a distinct bulge appears close to the pipe centre, which has previously been observed in laminar and transitional curved pipes at lower Re_b only. On the other hand, mild curvature allows the interesting observation of a friction factor which is lower than in a straight pipe for the same flow rate.All statistical data, including mean profile, fluctuations and the Reynolds-stress budgets, is available for development and validation of turbulence models in curved geometries.     

Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach

A Lagrangian continuous random walk (CRW) model is developed to predict turbulent particle dispersion in arbitrary wall-bounded flows with prevailing anisotropic, inhomogeneous turbulence. The particle tracking model uses 3D mean flow data obtained from the Fluent CFD code, as well as Eulerian statistics of instantaneous quantities computed from DNS databases. The turbulent fluid velocities at the current time step are related to those of the previous time step through a Markov chain based on the normalized Langevin equation which takes into account turbulence inhomogeneities. The model includes a drift velocity correction that considerably reduces unphysical features common in random walk models. It is shown that the model satisfies the well-mixed criterion such that tracer particles retain approximately uniform concentrations when introduced uniformly in the domain, while their deposition velocity is vanishingly small, as it should be. To handle arbitrary geometries, it is assumed that the velocity rms values in the boundary layer can locally be approximated by the DNS data of fully developed channel flows. Benchmarks of the model are performed against particle deposition data in turbulent pipe flows, 90° bends, as well as more complex 3D flows inside a mouth-throat geometry. Good agreement with the data is obtained across the range of particle inertia.     

Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries

The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800 ≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these “trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.     

An improved anisotropy-resolving subgrid-scale model for flows in laminar–turbulent transition region

Some types of mixed subgrid-scale (SGS) models combining an isotropic eddy-viscosity model and a scale-similarity model can be used to effectively improve the accuracy of large eddy simulation (LES) in predicting wall turbulence. Abe (2013) has recently proposed a stabilized mixed model that maintains its computational stability through a unique procedure that prevents the energy transfer between the grid-scale (GS) and SGS components induced by the scale-similarity term. At the same time, since this model can successfully predict the anisotropy of the SGS stress, the predictive performance, particularly at coarse grid resolutions, is remarkably improved in comparison with other mixed models. However, since the stabilized anisotropy-resolving SGS model includes a transport equation of the SGS turbulence energy, k_SGS, containing a production term proportional to the square root of k_SGS, its applicability to flows with both laminar and turbulent regions is not so high. This is because such a production term causes k_SGS to self-reproduce. Consequently, the laminar–turbulent transition region predicted by this model depends on the inflow or initial condition of k_SGS. To resolve these issues, in the present study, the mixed-timescale (MTS) SGS model proposed by Inagaki et al. (2005) is introduced into the stabilized mixed model as the isotropic eddy-viscosity part and the production term in the k_SGS transport equation. In the MTS model, the SGS turbulence energy, k_es, estimated by filtering the instantaneous flow field is used. Since the k_es approaches zero by itself in the laminar flow region, the self-reproduction property brought about by using the conventional k_SGS transport equation model is eliminated in this modified model. Therefore, this modification is expected to enhance the applicability of the model to flows with both laminar and turbulent regions. The model performance is tested in plane channel flows with different Reynolds numbers and in a backward-facing step flow. The results demonstrate that the proposed model successfully predicts a parabolic velocity profile under laminar flow conditions and reduces the dependence on the grid resolution to the same degree as the unmodified model by Abe (2013) for turbulent flow conditions. Moreover, it is shown that the present model is effective at transitional Reynolds numbers. Furthermore, the present model successfully provides accurate results for the backward-facing step flow with various grid resolutions. Thus, the proposed model is considered to be a refined anisotropy-resolving SGS model applicable to laminar, transitional, and turbulent flows.     

管内定型流传热过程的有效能损失

对管道内充分发展对流传热过程的有效能损失进行了分析．根据定型流状态下定热流与定壁温换热条件的特点,经代数推演,得到了这两种条件下的表征换热状态、流动功耗以及黏性变化的无量纲形式的有效能损失关系式,适用于不同截面形状的管道内的层流与湍流工况下的有效能分析．     

Experimental investigation of the coherent structures in a spirally corrugated pipe

Previous numerical and theoretical results (Chen et al., 2019; Liu et al., 2018; Zhao et al., 2019) based on the optimization theory of convective heat transfer reveal that the optimized flow structures in a straight circular pipe enhancing convective heat transfer are multiple longitudinal vortices. This conclusion encourages us to find out whether such flow structures really exist in some enhanced heat transfer pipes by means of advanced experimental techniques. Therefore, a typical enhanced heat transfer pipe was selected, namely a spirally corrugated pipe, and stereoscopic particle image velocimetry (SPIV) was employed to measure its internal instantaneous flow field. Moreover, the proper orthogonal decomposition (POD) method was used to extract the large-scale coherent structures from the measured instantaneous velocity fields. Besides the spirally corrugated pipe, the fully developed turbulent flow in a straight pipe was also analyzed as benchmark of the enhanced heat transfer pipes. The results reveal that longitudinal whirling flow with multi-vortices is formed in both the fully developed turbulent flow field of the straight pipe and the spirally corrugated one. It is thus easy to explain the heat transfer enhancement mechanism of the above flow structures from the perspective of momentum transfer. The flow structures of the fully developed turbulent flow in a straight pipe are quite similar to the optimal flow pattern from the optimization theory. More specifically, multiple longitudinal vortices are spontaneously generated due to turbulence without external heat transfer enhancement techniques. Furthermore, the flow structures similar to multiple longitudinal vortices also exist in the spirally corrugated pipe, although these flow structures deviate from symmetric multiple vortices. Moreover, the flow structures in the spirally corrugated pipe are much more energetic than those in the fully developed turbulent flow in a straight pipe. This is probably the reason why a spirally corrugated pipe can enhance heat transfer compared with a straight circular pipe.     

高亚临界雷诺数圆柱绕流的尺度自适应模拟

借助γ-Re_θ转捩模型,实现了高亚临界雷诺数（Re=1.4×105）下圆柱层流分离流动的尺度自适应模拟.统计平均结果表明数值计算和实验测量较为接近,尤其在圆柱后半段的分离区中,压力系数和实验符合得很好,误差主要源于分离点预测的不准确. 瞬态流动则显示,层流分离的剪切层中出现了展向不稳定,且在向下游的输运过程中不断增强,最后转捩为完全湍流. 在湍流分离模拟中,由于缺乏剪切层失稳的非定常性,SST-SAS 模型的尺度分辨能力变弱,因此在分离区以及下游尾迹中求解出的湍流尺度要明显较层流分离时大.      

SCALE ADAPTIVE SIMULATION OF FLOWS AROUND A CIRCULAR CYLINDER AT HIGH SUB-CRITICAL REYNOLDS NUMBER

借助γ-Re_θ转捩模型,实现了高亚临界雷诺数（Re=1.4×10⁵）下圆柱层流分离流动的尺度自适应模拟.统计平均结果表明数值计算和实验测量较为接近,尤其在圆柱后半段的分离区中,压力系数和实验符合得很好,误差主要源于分离点预测的不准确. 瞬态流动则显示,层流分离的剪切层中出现了展向不稳定,且在向下游的输运过程中不断增强,最后转捩为完全湍流. 在湍流分离模拟中,由于缺乏剪切层失稳的非定常性,SST-SAS 模型的尺度分辨能力变弱,因此在分离区以及下游尾迹中求解出的湍流尺度要明显较层流分离时大.     

A numerical study of fully developed laminar flows in pipes with two planar curvatures

The spectral element method is applied on unstructured tetrahedral elements to solve the Navier–Stokes equations for fully developed laminar flow in pipes with two planar curvatures. Specific implementations of the spectral element method to double curved pipes and parallelization are described. Previous studies on flows in pipes focused on constant curvature or torsion geometries, as well as pipes with varying curvature. This study focuses on the periodic variation of both the curvature as well as torsion by analysing a pipe having two planar curvatures. The effects of the three parameters defining the pipe are studied to isolate the curvature and torsion effect on the magnitude and angle of the secondary flow. Furthermore, the geometric effects on the wall shear stress are studied, as it is an important fluid flow property, especially in blood flows. Copyright © 2006 John Wiley & Sons, Ltd.     

High‐order stable interpolations for immersed boundary methods

The analysis and improvement of an immersed boundary method (IBM) for simulating turbulent flows over complex geometries are presented. Direct forcing is employed. It consists in interpolating boundary conditions from the solid body to the Cartesian mesh on which the computation is performed. Lagrange and least squares high‐order interpolations are considered. The direct forcing IBM is implemented in an incompressible finite volume Navier–Stokes solver for direct numerical simulations (DNS) and large eddy simulations (LES) on staggered grids. An algorithm to identify the body and construct the interpolation schemes for arbitrarily complex geometries consisting of triangular elements is presented. A matrix stability analysis of both interpolation schemes demonstrates the superiority of least squares interpolation over Lagrange interpolation in terms of stability. Preservation of time and space accuracy of the original solver is proven with the laminar two‐dimensional Taylor–Couette flow. Finally, practicability of the method for simulating complex flows is demonstrated with the computation of the fully turbulent three‐dimensional flow in an air‐conditioning exhaust pipe. Copyright © 2006 John Wiley & Sons, Ltd.