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A new correction method for laser Doppler velocimetry (LDV) measurement volume effects on the time-averaged velocity statistics is proposed by considering the probability density function of streamwise fluctuating velocity and the streamwise cross-sectional area of the measurement volume. The proposed correction method is fundamentally different from previous correction methods using a laser intensity profile of LDV. We propose a simple equation to correct the measurement volume effects. By using the equation and calculating both measurement locations and volumes precisely, the correction for the measurement volume effects on time-averaged velocity statistics can be performed on the basis of LDV measurement data. By comparing with the correction method proposed by Durst et al. (1995), the two correction methods provide almost the same results. In addition, the validity and applicability to high Reynolds numbers or low spatial resolution conditions of the two correction methods are confirmed.

Three-dimensional (3D) direct numerical simulations (DNS) of the viscous incompressible fluid flow through a helical pipe with circular cross section were performed. The flow is governed by three parameters: the Dean number (or the Reynolds number), curvature, and torsion. First, we obtained steady solutions by steady 3D calculations, where dual solutions were found, one was uniform in the pipe axial direction and the other varied very slowly, if torsion exceeded a critical value. Then, the instability of the steady solutions obtained was studied by unsteady 3D calculations. We obtained critical Reynolds numbers of steady to unsteady transition by observing the behaviors of the unsteady solutions. The present results of the critical Reynolds number nearly agreed with those by the 2D linear stability analysis (Yamamoto et al. [9] ) except for the lowest critical Reynolds number region, where the present study gave the critical Reynolds number much less than that obtained by the 2D linear stability analysis. We found the vortical structures in the form of a standing wave slightly above the marginal instability state, which is a trigger of explosive 3D instability.

A numerical framework for accurately computing electrically charged particles in wall-bounded flows is presented. This work builds upon the particle-particle particle-mesh (P3M) approach, which is traditionally restricted to cubic periodic domains. Here we propose an extended approach that retains the same accuracy and cost savings for non-periodic wall-bounded flows. The solution to the electric Poisson equation is performed agnostic to the presence of any walls, allowing for the use of fast Fourier transforms. The contribution from periodic images are removed by exploiting the linearity of the Poisson equation and strategically mapping the particle charge to the grid. A signed-distance levelset function is used to enforce appropriate boundary conditions. The accuracy of the proposed approach is quantified and compared to existing schemes. The framework is then demonstrated on a polydisperse distribution of charged particles in a turbulent pipe flow. The effect of charge on velocity statistics and deposition rate is reported.

This paper studies the transition to turbulence of pipe flow for a system rotating about the streamwise direction. The linearized Navier–Stokes equations are numerically solved using the Petrov–Galerkin discretization. Both destabilizing and stabilizing effects of the rotation are highlighted. We show that in comparison to the linear stability situation at the Reynolds number going up to $$10^7$$ , for the non-rotating case, pipe flow is linearly unstable to infinitesimal perturbations at low rotation numbers. By fixing the Reynolds numbers, small rotation numbers increase the amplitude of perturbations, which attain the maximum values in the region of the unstable modes. As they exceed their maximum values, these perturbations are attenuated. When the rotation number is increased further, perturbations are progressively damped until a critical value above which the flow becomes linearly stable. We determine the region in perturbation amplitude which separates perturbations that trigger instabilities and perturbations that decay toward the laminar profile. This study also reveals that the large values of rotation numbers cause a symmetric structure onto the flow, in a domain that is periodically continued in the axial direction.

Turbulent kinetic energy (TKE) equation based on the Reynolds averaging hypothesis was approximated in the near wall region of turbulent channel flows and an analytical solution for TKE was proposed by Absi for $$y^{ + } < 20$$ (R. Absi, Analytical solutions for the modeled k equation, Trans. ASME: J. Appl. Mech. 75 (2008) 044,501). While, comparisons with DNS data show very good agreement, some of the model approximations employed previously require revision which is the main motivation of this work. We here present an alternate formulation for the smooth near wall TKE budget and propose an improved method of solution. Results are compared against wide range of friction Reynolds numbers, Reτ DNS datasets and found to be in good agreement. Interestingly the proposed improved method reveals that beyond Reτ, = 5200 TKE profiles collapse meaning that the TKE remains independent of Reτ that is consistent with high Reynolds number turbulent characteristics reported in the DNS (Hultmark et. al., Turbulent pipe flow at extreme Reynolds numbers, Phys. Rev. Lett., 108 (2012) 094,501). Although there exist two parameters in the paresent work to be determined empirically from DNS data it is reported that these parameters become empirically free at high turbulent Reynolds numbers, Reτ → ∞.The other interesting aspect of this work is that one of these parameters may be sensitized to other additional effects viz., wall roughness, pressure gradient, magnetic field, etc. One of the potential advantages of these near wall smooth turbulent channel flow analytical solutions is to obviate the need for solving the TKE equation near the smooth wall in the RANS, hybrid RANS/LES closures thus resulting in quicker and accurate engineering computations.

The principle of centrifugal force produced by flowing fluid through the semicircular section of a pipe line is not sufficient to explain the characteristic of the centrifugal force type flow transducer developed from this principle. In this study, a modified form of this flow transducer is developed using a modified force sensing technique. This modified force principle explains the characteristic of the flow transducer to a very good extent. The modified force produced in the modified transducer system is composed of four components namely, centrifugal force, momentum force, damping force and restoring force. These forces produce the identical downward and upward movements of the lever ends of a common balance which is initially made horizontal at zero flow by using similar sensing U-tube and dummy U-tube. These movements are sensed by two identical inductive sensors. The static characteristic equation of the prototype unit of the transducer using the modified force sensing technique is derived mathematically in the study. The equation coefficients are calculated from the design parameters and are found to be matched with the same obtained from the average characteristic of repeated experiments performed under the same laboratory environment. Thus the proposed modified model appears to be established.

The influence of particle concentration on the drag force of a particle deserves attention when using the Lagrangian Particle Tracking methods for the prediction of industrial type gas-solid flows. The Lagrangian approach is best suited to applications where the solids volume fraction is low, and the effect of particle concentration can be ignored. In the present work, a 3D time dependent numerical analysis is performed to study the effect of Lagrangian model improvements to replicate experimental studies of straight horizontal pipe flow and flow through a 90° horizontal-to-vertical bend. The present predictions are compared with published experimental data of Tsuji and Morikawa (1982) , and Yilmaz (1997) . Special attention is paid to influence of particle mass-flow rates and conveying velocity on the particle motion within the system. This study used a CFX-4 package, where the ability to modify the code was necessary to include particle model improvements. These improvements included implementing a newly drag force model developed as a part of this research work. Particle-wall collision and particle-particle collision models developed by Sommerfeld (1992) , and Sommerfeld (2001) are also implemented in the CFD model. The standard k–e dispersed turbulence model was utilized as the predictions for the gas phase only gave similar predicted axial velocity compared to the more computationally demanding Reynolds stress model. The results showed that the inclusion of the various improvements lead to reasonable predicted particle velocities in both the upper and lower regions of the straight horizontal pipe which denote the dilute and dense regions respectively. It was also found that the inclusion of the rough-wall particle wall collision model decreases the axial particle velocity in the lower region where the bulk of the particle wall collisions occur. While the inclusion of the particle collision models tends to disperse the particles away from the lower region resulting in a less dense lower section and a distinctly more homogenous particle distribution compared with the standard model predictions. Further, the increase in particle concentration leads to a reduction in axial velocity due to a loss of momentum through particle-wall and particle-particle collisions. Finally, the improved CFD model best predicted both the reduction and increase in the particle velocities in the different regions.

Recent work on the dissipation theorem of turbulent flow is reviewed, with examples in rotating cylinders, pipe flow, and flow past a flat plate at zero incidence. The dependence of the eddy viscosity and eddy diffusivity on distance from a solid wall is reviewed and is supported by treatment of fluctuations. The role of the viscous sublayer in fluid friction is discussed.

In this work, an efficient model for simulating bubble dispersion and coalescence due to turbulence is developed in the Euler-Lagrange framework. The primary liquid phase is solved on the Euler grid with the RANS turbulence model. Bubble motion is computed with the force balance equations. One-way coupling between two phases is assumed and the framework is designed for the computation of disperse bubbly flows at low Eötvös number. The turbulent dispersion of the dispersed phase is reconstructed with the continuous random walk (CRW) model. Bubble-bubble collisions and coalescence are accounted for deterministically. To accelerate the time-consuming search for potential collision partners in dense bubbly flows, the sweep and prune algorithm is employed, which can be utilized in arbitrary mesh types and sizes. Validation against experiments of turbulent pipe flows demonstrates that the one-way coupled EL-CRW dispersion model can well reproduce the bubble distribution in a typical dense bubbly pipe flow. Good agreement of the bubble size distribution at the pipe outlet between the simulation and the experiment is obtained.

Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite amplitude are found to excite a state consisting of helical vortices during flow deceleration. The resulting flow pattern grows rapidly in magnitude, breaks down into turbulence, and eventually returns to laminar when the flow accelerates. This scenario causes shear stress fluctuations and flow reversal during each pulsation cycle. Such unsteady conditions can adversely affect blood vessels and have been shown to promote inflammation and dysfunction of the shear stress sensitive endothelial cell layer., Comment: for supporting information, see doi:10.1073/pnas.1913716117/-/DCSupplemental

Turbulent co-current Taylor bubble flow was modeled with LES alongside the VOF interface tracking solver. The method is first validated in the context of single phase turbulent pipe flow and three distinct laminar Taylor bubble flow cases. The turbulent co-current Taylor bubble flow is simulated using a moving frame of reference which is attached to the bubble, allowing for a straight-forward time averaging and Dirichlet-type flow recycling inlet boundary condition. In contrast to periodic inlet and outlet boundary conditions, the Dirichlet one assures that small bubbles which are lost by the Taylor bubble are removed from the computation once they leave the domain, therewith not interfering with the nose of the Taylor bubble. The transient loss of small bubbles which is observed in our simulations implies that the problem is inherently unsteady. We therefore present an averaging strategy which consists of combined time, space and ensemble averaging. This strategy allows systematic comparison of results across different computational meshes. The results show that the approach captures distinct features of turbulent co-current Taylor bubble flow well, in the sense that good agreement is observed with experimental data from literature in terms of the toroidal vortex flow field in the wake of the Taylor bubble. Agreement with measured velocity fluctuation profiles in the wake of the Taylor bubble is less pronounced, and is discussed in the paper. Nevertheless, the simulation approach of co-current Taylor bubble flow proposed in this paper may serve as a tool that will provide deeper insights in two-phase turbulent flow for future research.

This study aims to express an optimize temperature profile with the most heat transfer and least work loss by minimizing the total entropy generation of a pipeline under external magnetic field. This study has investigated in low Stokes number and low Reynolds number conditions. It shows that, the fluid’s shear stress increases around the wall (r* > 0.8), due to presence of magnetic field. As a consequence, the magnetic field boosts the dissipation term. However, the velocity gradient over a wide range of radius 0

An analysis is presented for the liquid flow-induced motion of a solid in partially filled pipes. A general equation of the flow-induced motion of a solid is developed. Two alternate force models, one (F(v)) based on free stream velocity and another (F(m)) based on free stream momentum flux, are formulated to simplify the general equation. The equation of motion is solved for the motion of a cylindrical solid with steady-uniform liquid flows and the effects of relevant variables on the motion of a solid are predicted. The variables considered include: volume rate of liquid flow, Q; pipe diameter, D; Manning coefficient, n; and slope, S; solid diameter, d; length, L; specific gravity, σ; coefficient of friction between a solid and the pipe wall, η; and the two force functions, F(v) and F(m). The flow rate, Q(v) required to initiate the motion of a solid increases with an increase in D, n, d, L, σ, and η(s), and decreases with an increase in S. The force function F(m) predicts a lower value of Q(t) than does the force function F(v) The velocities of a solid increase with an increase in Q and S and decrease with an increase in D, n, d, L, σ, and η. The force function F(m) predicts higher values of the velocity of a solid than does the force function F(v). The effects of the variables Q(o), D, S, d, L, and η(s), on the velocities of a solid are qualitatively consistent with the available experimental data. The qualitative agreement between the predicted results and experimental data demonstrate the validity of the analysis presented.

We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number $({\textit {Re}}_{\tau }) \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately $2\,\%$ , which would extrapolate to approximately $4\,\%$ at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant $k \approx 0.387$ , which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at ${\textit {Re}}_{\tau } \gtrsim 10^4$ , as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

Low frequency dynamics of shock–turbulence interactions in constant area pipe flow with centre-line Mach number of 1.7 and friction Reynolds number of 245 is analysed using dynamic mode dec...

In this work, an improved implicit discrete velocity method (DVM) on unstructured meshes is developed for simulation of three-dimensional (3D) flows in all flow regimes. Different from the conventional DVM, in which only the kinetic governing equation (i.e., Boltzmann equation) is resolved in each time step, both the kinetic and macroscopic governing equations are solved simultaneously in the present method. On one hand, the solution of macroscopic governing equation yields the predicted equilibrium distribution function at cell center, which enables the fully implicit discretization of the collision term in solving the Shakhov-model kinetic equation. On the other hand, the collisional effect at the cell interface can be incorporated into the evaluation of numerical flux through the solution process of macroscopic governing equation. Thanks to these two improvements, the developed scheme can effectively overcome the defects of low efficiency and poor accuracy of the conventional semi-implicit DVM in the continuum flow regime. In addition, for practical applications of flow problems with complicated geometry, in the present work, the unstructured mesh-based solver is developed. The accuracy, efficiency, stability and flexibility of the developed solver are demonstrated by its application to simulate pipe flow, lid-driven cavity flow and supersonic flow around a blunt body.

This research presents a new theory that explains analytically the behaviour of any fully developed incompressible turbulent pipe flow, steady or unsteady. We propose the name of theory of underlying laminar flow (TULF), because its main consequence is the description of any turbulent pipe flow as the sum of two components: the underlying laminar flow (ULF) and the purely turbulent component (PTC). We use the framework of the TULF to explain analytically most of the important and interesting phenomena reported in He & Jackson (J. Fluid Mech., vol. 408, 2000, pp. 1–38). To do so, we develop a simple model for the pressure gradient and Reynolds shear stress that could be applied to the linearly accelerated pipe flow described by He & Jackson (2000). The following features of the unsteady flow are explained: the deformation undergone by the mean velocity profiles during the transient, the velocity overshoot observed in the more rapid excursions, the dual deformation of mean velocity profiles when overshoots are present, the laminarisation effects described during acceleration, the rapid decrease of the Reynolds shear stress upon approaching the wall that brings forth the laminar sublayer, and some other minor effects. A new field is defined to characterise the degree of turbulence within the flow, directly calculable from the theory itself. Arguably, this new field would describe the degree of turbulence in a pipe flow more accurately than the familiar turbulence intensity parameter. Finally, a paradox is found in the deformation of the unsteady mean velocity profiles with respect to equal-Reynolds-number steady profiles, which is duly explained. The research also predicts the occurrence of mean velocity undershoots if the flow is decreased rapidly enough.

In two previous papers, Ozcakir, Tanveer, Hall, & Overman (2016, Travelling waves in pipe flow, J. Fluid Mech., 791, 284–328) and Ozcakir, Hall & Tanveer (2019, Nonlinear exact coherent structures in pipe flow and their instabilities, J. Fluid Mech., 868, 341–368) investigated numerically and asymptotically high Reynolds number exact coherent structures in pipe flow. It was found that, in addition to the structures described by the vortex–wave interaction theory by Hall & Smith (1991, On strongly nonlinear vortex/wave interactions in boundary layer transition. J. Fluid Mech., 227, 641–666), there exists vortical structures localized near the centre of the pipe with a core of size $O(Re^{-1/4})$ convected downstream at a speed that deviates from the pipe centreline speed by $O(Re^{-1/2})$, where $Re$ is the Reynolds number. In the finite Reynolds number calculations by Ozcakir, Tanveer, Hall & Overman (2016, Travelling waves in pipe flow, J. Fluid Mech., 791, 284–328), asymptotic state was referred to as a nonlinear viscous core state (NVC). However the reduced asymptotic equations were not solved and only limited confirmation of the theory was found numerically. Here, in order to conclusively confirm the existence of the NVC state we first describe direct numerical calculations on the asymptotically reduced $Re>>1$ equations for such state states. The results are then compared in detail to the finite $Re$ calculations up-to $Re=10^6$; the latter regime is at much higher values of the Reynolds number than those reported in Ozcakir, Tanveer, Hall & Overman (2016, Travelling waves in pipe flow, J. Fluid Mech., 791, 284–328). The results are found to be in excellent agreement with the finite $Re$ calculations in a region between $Re=10^5$ and $10^6$, thereby confirming that the structure observed by Ozcakir, Tanveer, Hall & Overman (2016, Travelling waves in pipe flow, J. Fluid Mech., 791, 284–328) is indeed a finite Reynolds number realization of an asymptotic NVC state.

The most important unanswered questions in turbulence regard the nature of turbulent flow in the limit of infinite Reynolds number. The Princeton superpipe (PSP) data comprise 26 velocity profiles that cover three orders of magnitude in the Reynolds number from $Re=19\,639$, to $Re=20\,088\,000$ based on pipe radius and pipe centreline velocity. In this paper classical mixing length theory is combined with a new mixing length model of the turbulent shear stress to solve the streamwise momentum equation and the solution is used to approximate the PSP velocity profiles. The model velocity profile is uniformly valid from the wall to the pipe centreline and comprises five free parameters that are selected through a minimization process to provide an accurate approximation to each of the 26 profiles. The model profile is grounded in the momentum equation and allows the velocity derivative, Reynolds shear stress and turbulent kinetic energy production to be studied. The results support the conclusion that logarithmic velocity behaviour near the wall is not present in the data below a pipe Reynolds number somewhere between $Re=59\,872$, and $Re=87\,150$. Above $Re=87\,150$, the data show a very clear, nearly logarithmic, region. But even at the highest Reynolds numbers there is still a weak algebraic dependence of the intermediate portion of the velocity profile on both the near-wall and outer flow length scales. One of the five parameters in the model profile is equivalent to the well-known Kármán constant, $k$. The parameter $k$ increases almost monotonically from $k=0.4034$ at $Re=87\,150$ to $k=0.4190$ at $Re=20\,088\,000$, with an average value, $k=0.4092$. The variation of the remaining four model parameters is relatively small and, with all five parameters fixed at average values, the model profile reproduces the entire velocity data set and the wall friction reasonably well. With optimal values of the parameters used for each model profile, the fit to the PSP survey data is very good. Transforming the model velocity profile using the group, $u/u_{0}\rightarrow ku/u_{0}$, $y^{+}\rightarrow ky^{+}$ and $R_{\unicode[STIX]{x1D70F}}\rightarrow kR_{\unicode[STIX]{x1D70F}}$ where $R_{\unicode[STIX]{x1D70F}}$ is the friction Reynolds number, leads to a reduced expression for the velocity profile. When the reduced profile is cast in outer variables, the physical velocity profile is expressed in terms of $\ln (y/\unicode[STIX]{x1D6FF})$ and a new shape function $\unicode[STIX]{x1D719}(y/\unicode[STIX]{x1D6FF})$. In the limit of infinite Reynolds number, the velocity profile asymptotes to plug flow with a vanishingly thin viscous wall layer and a continuous derivative everywhere. The shape function evaluated at the pipe centreline is used to produce a new friction law with an additive constant that depends on the Kármán constant and a wall damping length scale.

A brief introduction of the time-filtered Navier–Stokes (TFNS) equations for very large eddy simulation (VLES) and its distinct features is presented. A set of nonlinear subscale models and their advantages over the linear subscale eddy viscosity models are described. A guideline for conducting a TFNS/VLES simulation is also provided. In this paper, we present simulations for three turbulent flows. The first one is the turbulent pipe flow at both low and high Reynolds numbers to illustrate the basic features of TFNS/VLES; the second one is the swirling turbulent flow in an LM6000 single injector to further demonstrate the differences between the results from nonlinear models versus linear viscosity models; the third one is a more complex turbulent flow generated in a single-element lean direct injection combustor, which demonstrates that the current TFNS/VLES approach is capable of predicting dynamically important, unsteady turbulent structures even with a relatively coarse mesh grid.

Transient, steady and oscillatory flows in a $180^{\circ }$ curved pipe are investigated both numerically and experimentally to understand secondary flow vortex formation and interactions. The results of numerical simulations and particle image velocimetry experiments are highly correlated, with a low error. To enable simulations in a smaller domain with shorter inlet section, an analytical solution for the unsteady Navier–Stokes equation is obtained with non-zero initial conditions to provide physical velocity profiles for the simulations. The vorticity transport equation is studied and its terms are balanced to find the mechanism of vorticity transfer to structures in the curved pipe. Several vortices are identified via various vortex identification (ID) methods and their results are compared. Isosurfaces of the $\unicode[STIX]{x1D706}_{2}$ vortex ID are used to explain the temporal and spatial evolution of vortices in the curved pipe. Eigenvalues and eigenvectors of the velocity gradient tensor are calculated for the swirling strength vortex ID method, which also determines vortex axis orientation. The classical Lyne vortex in oscillatory flow with an inviscid core is also revisited and its results are compared with the transient and steady flows. These in-depth analyses provide a better understanding and characterization of vortical structures in the curved pipe flow. Our findings show that, although there are some visual similarities between cross-sectional views of steady/transient flows and oscillatory flows, the structure herein designated as Lyne-type vortex detected in the cross-sections (under steady, transient and pulsatile flows) is not the same as the classical Lyne vortex pair (in oscillatory flows).

Polymer additives can substantially reduce the drag of turbulent flows and the upper limit, the so-called state of ‘maximum drag reduction’ (MDR), is to a good approximation independent of the type of polymer and solvent used. Until recently, the consensus was that, in this limit, flows are in a marginal state where only a minimal level of turbulence activity persists. Observations in direct numerical simulations at low Reynolds numbers ($Re$) using minimal sized channels appeared to support this view and reported long ‘hibernation’ periods where turbulence is marginalized. In simulations of pipe flow at $Re$ near transition we find that, indeed, with increasing Weissenberg number ($Wi$), turbulence expresses long periods of hibernation if the domain size is small. However, with increasing pipe length, the temporal hibernation continuously alters to spatio-temporal intermittency and here the flow consists of turbulent puffs surrounded by laminar flow. Moreover, upon an increase in $Wi$, the flow fully relaminarizes, in agreement with recent experiments. At even larger $Wi$, a different instability is encountered causing a drag increase towards MDR. Our findings hence link earlier minimal flow unit simulations with recent experiments and confirm that the addition of polymers initially suppresses Newtonian turbulence and leads to a reverse transition. The MDR state on the other hand results at these low$Re$ from a separate instability and the underlying dynamics corresponds to the recently proposed state of elasto-inertial turbulence.

Prandtl’s two-layer model of the turbulent boundary layer is considered and the expression obtained through the use of the model is applied to calculate the heat transfer coefficient, calculations for which agree well with experimental data on mean values of the coefficients for various bodies. Determination of parameters of this expression is shown for the case of calculating local heat transfer coefficients in the entrance regions of the channels. The main parameters are dynamic velocity, dimensionless thickness of the boundary layer and dimensionless thickness of the viscous sublayer. Based on the power-law and logarithmic velocity profiles, expressions are obtained for calculating the dimensionless parameters of the turbulent boundary layer. A satisfactory agreement of the results of calculations of loc al heat transfer coefficients for the flow over a flat plate and the pipe flow is shown. The presented approach represents a theoretical basis for modeling the local heat transfer for bodies of more complex shapes, if the friction coefficients are known.

The phenomena of initially subcooled liquid flashing into vapour due to depressurization frequently occur in the nature and technology. They are very complex systems, and the fluid dynamics is affected by the interplay of many different sub phenomena, including bubble nucleation, evaporation, condensation, coalescence, and breakup. Research on the flashing flows has received much attention, but CFD modelling and simulation of such scenarios is still challenging, because knowledge is often insufficient for a precise mathematical description of the physical problems. Attempts of numerical analysis having been made before are all based on the assumption of mono-disperse bubbles by prescribing either the size or number density or using a mixture model, which deviates largely from the physical picture. In the present work, a CFD-PBM coupled approach is extended for the investigation of bubble dynamics in a flashing pipe flow. The comparison with experimental data demonstrates that the model is effective in capturing the physics of vapour bubbles’ generation and growth as well as their spatial motion and distribution during the decompression. Although further polishing of the bubble coalescence and breakup as well as interphase momentum and turbulence transfer models is necessary, the agreement between measured and simulated cross-section averaged flow parameters such as void fraction, liquid temperature and bubble size distribution is satisfying. The wide range of bubble size changing confirms the necessity of using a poly-disperse approach instead of mono-disperse assumptions.

Flow transition from laminar to turbulent mode (and vice versa)—that is, the initiation of turbulence—is one of the most important research subjects in the history of engineering. Even for pipe flow, predicting the onset of turbulence requires sophisticated instrumentation and/or direct numerical simulation, based on observing the instantaneous flow structure formation and evolution. In this work, a local Reynolds number equivalence γ (ratio of local inertia effect to viscous effect) is seen to conform to the Universal Law of the Wall, where γ = 1 represents a quantitative balance between the abovementioned two effects. This coincides with the wall layer thickness (y+ = 1, where y+ is the dimensionless distance from the wall surface defined in the Universal Law of the Wall). It is found that the characteristic of how the local derivative of γ against the local velocity changes with increasing velocity determines the onset of turbulence. For pipe flow, γ ≈ 25, and for plate flow, γ ≈ 151.5. These findings suggest that a certain combination of γ and velocity (nonlinearity) can qualify the source of turbulence (i.e., generate turbulent energy). Similarly, a re-evaluation of the previous findings reveals that only the geometrically narrow domain can act locally as the source of turbulence, with the rest of the flow field largely being left for transporting and dissipating. This understanding will have an impact on the future large-scale modeling of turbulence. Keywords: Local Reynolds number equivalence, Flow transition from laminar to turbulent mode, Universal Law of the Wall, Pipe flow, Plate flow, Modeling

We present a linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles, two-way coupled to the fluid velocity field via Stokes drag (Saffman, J. Fluid Mech., vol. 13 (01), 1962, pp. 120–128). We extend previous analysis in a channel (Klinkenberg et al., Phys. Fluids, vol. 23 (6), 2011, 064110) to allow for the initial distribution of particles to be inhomogeneous in a similar manner to Boronin (Fluid Dyn., vol. 47 (3), 2012, pp. 351–363) and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability offering an alternative route to turbulence within this problem.

A series of analytic models are presented of a partially-submerged, straight circular cross-section pipe subjected to reciprocating flow, incorporating viscous and turbulent boundary-layer dissipation. This pipe is the most elementary paradigm for a fixed-type Oscillating Water Column (OWC), and its analysis more generally addresses one aspect of reciprocating pipe flow. The derivation of the dissipation terms in the momentum conservation equations from their origin in the Navier–Stokes equation are explicitly identified. The contribution of different damping sources to the overall energy loss is compared. The flow inside the pipe is assumed fully developed along the entire length, neglecting the effect of the flow development region. For relevance to engineering applications, a power take-off system is modelled assuming that the air compresses and expands isentropically in an air chamber at the top of the pipe. Existing theory is adapted into the current models for computing the hydrodynamic coefficients related to the scattered wave and radiation wave. A novel contribution of this paper is the inclusion of damping due to the wall shear stress, modelled for the reciprocating flow system inside the pipe. Comparison between the damping factors in relatively short OWCs confirms the findings in the literature that the major part of the damping is due to the radiation wave. However, it is found that with the increase of the draft length, the wall shear stress damping may also become an important factor in the resulting dynamics.

Experimental studies in isothermal steady state conditions with laminar flow of Newtonian fluids is carried out for fluid flow and heat transfer through spiral coils. Based on the viscous and form drag existing in pipe flow innovative analogy equations have been developed for laminar and turbulent flow through spiral coils considering the curvature ratio ( D i D ) and pitch to diameter ratio ( P D i ) of the curved coils. Dependency of analogy equations on the geometrical parameters of the spiral coils is investigated successfully. Also, an innovative general analogy equation is suggested for curved coils. Innovative correlations for fluid flow and heat transfer through spiral coils of different geometries is developed and validated based on Dean number and Reynold's number. Nine spiral coils with ( D i D ) ratio ranging from 0.019 to 0.0301 and ( P D i ) ratio ranging from 1.88 to 6.31 are used in the present study.

This study presents findings from a first-of-its-kind measurement campaign that includes simultaneous measurements of the full velocity and vorticity vectors in both pipe and boundary layer flows under matched spatial resolution and Reynolds number conditions. Comparison of canonical turbulent flows offers insight into the role(s) played by features that are unique to one or the other. Pipe and zero pressure gradient boundary layer flows are often compared with the goal of elucidating the roles of geometry and a free boundary condition on turbulent wall flows. Prior experimental efforts towards this end have focused primarily on the streamwise component of velocity, while direct numerical simulations are at relatively low Reynolds numbers. In contrast, this study presents experimental measurements of all three components of both velocity and vorticity for friction Reynolds numbers$Re_{\unicode[STIX]{x1D70F}}$ranging from 5000 to 10 000. Differences in the two transverse Reynolds normal stresses are shown to exist throughout the log layer and wake layer at Reynolds numbers that exceed those of existing numerical data sets. The turbulence enstrophy profiles are also shown to exhibit differences spanning from the outer edge of the log layer to the outer flow boundary. Skewness and kurtosis profiles of the velocity and vorticity components imply the existence of a ‘quiescent core’ in pipe flow, as described by Kwonet al. (J. Fluid Mech., vol. 751, 2014, pp. 228–254) for channel flow at lower$Re_{\unicode[STIX]{x1D70F}}$, and characterize the extent of its influence in the pipe. Observed differences between statistical profiles of velocity and vorticity are then discussed in the context of a structural difference between free-stream intermittency in the boundary layer and ‘quiescent core’ intermittency in the pipe that is detectable to wall distances as small as 5 % of the layer thickness.

In this paper, we present computational results of some two-fold azimuthally symmetric travelling waves and their stability. Calculations over a range of Reynolds numbers ($Re$) reveal connections between a class of solutions computed by Wedin & Kerswell (J. Fluid Mech., vol. 508, 2004, pp. 333–371) (henceforth called the WK solution) and the $Re\rightarrow \infty$ vortex–wave interaction theory of Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666) and Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). In particular, the continuation of the WK solutions to larger values of $Re$ shows that the WK solution bifurcates from a shift-and-rotate symmetric solution, which we call the WK2 state. The WK2 solution computed for $Re\leqslant 1.19\times 10^{6}$ shows excellent agreement with the theoretical $Re^{-5/6}$, $Re^{-1}$ and $O(1)$ scalings of the waves, rolls and streaks respectively. Furthermore, these states are found to have only two unstable modes in the large $Re$ regime, with growth rates estimated to be $O(Re^{-0.42})$ and $O(Re^{-0.92})$, close to the theoretical $O(Re^{-1/2})$ and $O(Re^{-1})$ asymptotic results for edge and sinuous instability modes of vortex–wave interaction states (Deguchi & Hall, J. Fluid Mech., vol. 802, 2016, pp. 634–666) in plane Couette flow. For the nonlinear viscous core states (Ozcakir et al., J. Fluid Mech., vol. 791, 2016, pp. 284–328), characterized by spatial a shrinking of the wave and roll structure towards the pipe centre with increasing $Re$, we continued the solution to $Re\leqslant 8\times 10^{6}$ and we find only one unstable mode in the large Reynolds number regime, with growth rate scaling as $Re^{-0.46}$ within the class of symmetry-preserving disturbances.

A simple lecture demonstration has been developed which demonstrates how viscosity dramatically changes fluid flow in a pipe. Water in an open reservoir is first allowed to escape through circular apertures near the bottom of the reservoir, which shows volume flow rates proportional to the area of the aperture for a low viscosity fluid. Then, a viscous 60% glycerol–40% water solution escapes from the same open container but through long horizontal tubes, with the flow rate proportional to the square of the area. This is direct visual confirmation of the Hagen–Poiseuille prediction that volume flow rates scale as the fourth power of the tube radius for laminar flow. Overcoming experimental complications involving vena contracta and entry length issues is discussed, along with detailed measurements and fits to theory.

We study compressible turbulent flow in a circular pipe at computationally high Reynolds number. Classical related issues are addressed and discussed in light of the DNS data, including validity of compressibility transformations, velocity/temperature relations, passive scalar statistics, and size of turbulent eddies. Regarding velocity statistics, we find that Huang’s transformation yields excellent universality of the scaled Reynolds stresses distributions, whereas the transformation proposed by Trettel and Larsson (2016) yields better representation of the effects of strong variation of density and viscosity occurring in the buffer layer on the mean velocity distribution. A clear logarithmic layer is recovered in terms of transformed velocity and wall distance coordinates at the higher Reynolds number under scrutiny (Reτ ≈ 1000), whereas the core part of the flow is found to be characterized by a universal parabolic velocity profile. Based on formal similarity between the streamwise velocity and the passive scalar transport equations, we further propose an extension of the above compressibility transformations to also achieve universality of passive scalar statistics. Analysis of the velocity/temperature relationship provides evidence for quadratic dependence which is very well approximated by the thermal analogy proposed by Zhang et al. (2014). The azimuthal velocity and scalar spectra show an organization very similar to canonical incompressible flow, with a bump-shaped distribution across the flow scales, whose peak increases with the wall distance. We find that the size growth effect is well accounted for through an effective length scale accounting for the local friction velocity and for the local mean shear.

A numerical study was conducted by using the finite difference technique to investigate the mechanism of the fully developed turbulent flow and heat transfer in a circular tube in company of large Reynolds number with constant heat flux and at constant wall temperature condition. The methodology of solving the thermal problem is based on the equation of energy for a fluid of constant properties while taking into consideration the hypothesis of the axisymmetric and fully developed pipe flow in steady state. The global equation and the initial and boundary conditions acting on the problem have been configured here in dimensionless form in order to predict the turbulent behavior of the fluid inside the tube. Thus, using Thomas’ algorithm, a program in FORTRAN version 95 was developed in order to numerically solve the discretized form of the system of equations describing the problem. Finally, thanks to this elaborate program, we were able to play on some parameters involved such as the Reynolds number, the number of Peclet, and the longitudinal coordinate to obtain important results of the treated thermal model which are discussed and well detailed of this work. Comparison between the literature correlation data and the calculated simulation indicates that it is a good match of the results.

The literature already offers analytic solutions for steady-state laminar (Hagen–Poiseuille), transient laminar (Szymanski) and steady-state turbulent (Pai) incompressible pipe flows. However, no reference could be found for the most general case that encompasses all of them: the unsteady turbulent incompressible pipe flow. This study presents a General Analytic Solution (GAS) for the Reynolds–averaged Navier–Stokes equations corresponding to unsteady turbulent incompressible circular pipe flow, which is composed of the transient response of the initial mean velocity field to external interactions, the unsteady response to time-dependent pressure gradient, and the unsteady component due to the turbulence’s Reynolds stress. The particular cases of laminar, turbulent, steady-state and transient incompressible pipe flows emanate directly from such solution. A general method is proposed to obtain an analytical solution for any particular pipe flow problem for which some relevant function could be provided. That general method is exemplified in a test case, a much simplified version of the starting flow initiated in a circular pipe, after suddenly applying a constant pressure gradient. The time evolution for such starting flow, with a growing stage and a shrinking stage, is presented graphically and discussed.

This paper numerically simulates turbulent heat transfer in a round pipe in a wide range of Reynolds numbers using the CABARET nonparametric MILES method on grids with an incomplete resolution of the turbulence spectrum and the STAR-CCM+ CFD code in the LES approximation. The calculation results are compared with the DNS calculations of other authors found in the literature and with the RANS calculations implemented in the STAR-CCM+ CFD code. The simulation showed a satisfactory accuracy in determining the mean, root-mean-square, and integral characteristics of the flow; and it allowed us to identify the shortcomings of the existing model relations describing local turbulence characteristics. The authors propose a thermal wall function implemented in the RANS approximations.