Simulation Of Turbulent Pipe Flow Research Articles

Predictability of decay events in transitional wall-bounded flows

Extreme events in turbulent flows are in general linked with sudden changes in the dynamics of the system. Despite the increasing interest in modelling these events, their predictability remains largely unexplored. Here we focus on the case of sudden turbulence/chaos decay in pipe flow and in a reduced-order model of shear flows (Moehlis, Faisst and Eckhardt, 2004). We study the predictability of decay events with massive ensembles of simulations. For this purpose we introduce a new pseudo-spectral GPU code to perform fast simulations of turbulent pipe flow and describe a methodology to characterize predictability of decay events using the results of the ensembles of simulations. We report the decrease of predictability as one goes back in time with respect to a decay event, and show that this decrease does not need to be monotonic.

Direct numerical simulations of turbulent pipe flow up to

Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius $R$ and axial length $10{\rm \pi} R$ at friction Reynolds numbers up to $Re_\tau =5200$ using the pseudo-spectral code OPENPIPEFLOW. Various turbulence statistics are documented and compared with other DNS and experimental data in pipes as well as channels. Small but distinct differences between various datasets are identified. The friction factor $\lambda$ overshoots by $2\,\%$ and undershoots by $0.6\,\%$ the Prandtl friction law at low and high $Re$ ranges, respectively. In addition, $\lambda$ in our results is slightly higher than in Pirozzoli et al. (J. Fluid Mech., vol. 926, 2021, A28), but matches well the experiments in Furuichi et al. (Phys. Fluids, vol. 27, issue 9, 2015, 095108). The log-law indicator function, which is nearly indistinguishable between pipe and channel up to $y^+=250$ , has not yet developed a plateau farther away from the wall in the pipes even for the $Re_\tau =5200$ cases. The wall shear stress fluctuations and the inner peak of the axial turbulence intensity – which grow monotonically with $Re_\tau$ – are lower in the pipe than in the channel, but the difference decreases with increasing $Re_\tau$ . While the wall value is slightly lower in the channel than in the pipe at the same $Re_\tau$ , the inner peak of the pressure fluctuation shows negligible differences between them. The Reynolds number scaling of all these quantities agrees with both the logarithmic and defect-power laws if the coefficients are properly chosen. The one-dimensional spectrum of the axial velocity fluctuation exhibits a $k^{-1}$ dependence at an intermediate distance from the wall – also seen in the channel. In summary, these high-fidelity data enable us to provide better insights into the flow physics in the pipes as well as the similarity/difference among different types of wall turbulence.

Direct numerical simulation of turbulent pipe flow by large-scale control using buoyancy force

Skin-friction drag reduction control for a fully developed turbulent pipe flow is performed using direct numerical simulations. Heating and cooling of pipe wall is homogeneous in the streamwise direction and varies in the azimuthal direction and buoyancy force induces the flow to decrease the skin-friction drag. The control parameters are the amplitude of buoyancy force and wavenumber of heating and cooling in the azimuthal direction. There are two different mechanisms of skin-friction drag reduction: stable stratification and large-scale vortical structure. In the former, the buoyancy force attenuates the turbulence directly. In the latter, the buoyancy force creates wall jets along the pipe wall, and a large-scale streamwise vortex is formed. The vortex increases the coherent contribution to the skin-friction coefficient, but it reduces the random contribution indirectly.

Turbulence suppression by streamwise-varying wall rotation in pipe flow

Direct numerical simulations of turbulent pipe flow subjected to streamwise-varying wall rotation are performed. This control method is able to achieve drag reduction and even relaminarize the flow under certain control parameters at friction Reynolds number $Re_\tau =180$ . Two control parameters, which are velocity amplitude and wavelength, are considered. It is found that increasing the wavelength rather than increasing the amplitude seems to be a better choice to improve the control efficiency. An annular boundary layer, called the spatial Stokes layer (SSL), is formed by the wall rotation. Based on the thickness of the SSL, two types of drag-reduction scenarios can be identified roughly. When the thickness is low, the SSL acts as a spacer layer, inhibiting the formation of streamwise vortices and thereby reducing the shear stress. The flow structures outside the SSL are stretched in the streamwise direction due to the increased velocity gradient. Within the SSL, the turbulence intensity diminishes dramatically. When the thickness is large, a streamwise wavy pattern of near-wall streaks is formed. The streak orientation is dominated by the mean shear-strain vector outside the viscous sublayer, and there is a phase difference between the streak orientation and local mean velocity vector. The streamwise scales of near-wall flow structures are reduced significantly, resulting in the disruption of downstream development of flow structures and hence leading to the drag reduction. Furthermore, it is found that it requires both large enough thickness of the SSL and velocity amplitude to relaminarize the turbulence. The relaminarization mechanism is that the annular SSL can absorb energy continuously from wall-normal stress due to the rotational effect, thereby the turbulence self-sustaining process cannot be maintained. For the relaminarization cases, the laminar state is stable to even extremely large perturbations, which possibly makes the laminar state the only fixed point for the whole system.

Direct numerical simulations of turbulent pipe flow at high Reynolds number

This paper is associated with a video winner of a 2021 American Physical Society's Division of Fluid Dynamics (DFD) Gallery of Fluid Motion Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2021.GFM.V0053.

Precursors of backflow events and their relationship with the near-wall self-sustaining process

This study examines the precursors and consequences of rare backflow events at the wall using direct numerical simulation of turbulent pipe flow with a high spatiotemporal resolution. The results obtained from conditionally averaged fields reveal that the precursor of a backflow event is the asymmetric collision between a high- and a low-speed streak (LSS) associated with the sinuous mode of the streaks. As the collision occurs, a lifted shear layer with high local azimuthal enstrophy is formed at the trailing end of the LSS. Subsequently, a spanwise or an oblique vortex spontaneously arises. The dominant nonlinear mechanism by which this vortex is engendered is enstrophy intensification due to direct stretching of the lifted vorticity lines in the azimuthal direction. As time progresses, this vortex tilts and orientates towards the streamwise direction and, as its enstrophy increases, it induces the breakdown of the LSS located below it. Subsequently, this vortical structure advects as a quasi-streamwise vortex, as it tilts and stretches with time. As a result, it is shown that reverse flow events at the wall are the signature of the nonlinear mechanism of the self-sustaining process occurring at the near-wall region. Additionally, each backflow event has been tracked in space and time, showing that approximately 50 % of these events are followed by at least one additional vortex generation that gives rise to new backflow events. It is also found that up to a maximum of seven regenerations occur after a backflow event has appeared for the first time.

Wall-attached clusters for the logarithmic velocity law in turbulent pipe flow

The logarithmic law of the mean velocity is considered a fundamental feature of wall-bounded turbulent flows. The logarithmic velocity law is used widely to model the near-wall turbulence and to predict skin friction. Although classical scaling theory has been used to verify that the velocity profile in the overlap region follows the logarithmic behavior asymptotically, and thus recent experiments have attempted to assess the logarithmic law in large-scale facilities, there is a lack of understanding of the structural basis for the logarithmic law. Here, we show the logarithmic law by extracting the wall-attached structures of the streamwise velocity fluctuations through direct numerical simulation of turbulent pipe flow. The wall-attached structures exhibit self-similar behavior according to their height and have an inverse-scale population density, reminiscent of Townsend’s attached-eddy hypothesis. The wall-normal distributions of the streamwise velocity within the identified structures are conditionally averaged with respect to their height. The velocity profile is reconstructed by superimposing the velocity distributions of the objects that follow the inverse-scale population density. The indicator function of the resulting velocity profile shows a complete plateau for the high-speed structures due to their higher local Reynolds number. These findings provide strong evidence that the identified coherent structures are directly related to the logarithmic velocity law and serve as the structural basis for the inertial layer.

Reynolds number effects in pipe flow turbulence of generalized Newtonian fluids

Direct numerical simulations of turbulent pipe flow of power-law fluids show that the effect of shear thinning on turbulence statistics in the inner-wall region does not disappear as Re is increased. A log-law mean viscosity profile is also predicted that is self-similar in the inner region.

Overdamped large-eddy simulations of turbulent pipe flow up to Reτ = 1500

We present results from large-eddy simulations (LES) of turbulent pipe flow in a computational domain of 42 radii in length. Wide ranges of shear the Reynolds number and Smagorinsky model parameter are covered, 180 ≤ Reτ ≤ 1500 and 0.05 ≤ Cs ≤ 1.2, respectively. The aim is to asses the effect of Cs on the resolved flow field and turbulence statistics as well as to test whether very large scale motions (VLSM) in pipe flow can be isolated from the near-wall cycle by enhancing the dissipative character of the static Smagorinsky model with elevated Cs values. We found that the optimal Cs to achieve best agreement with reference data varies with Reτ and further depends on the wall normal location and the quantity of interest. Furthermore, for increasing Reτ, the optimal Cs for pipe flow LES seems to approach the theoretically optimal value for LES of isotropic turbulence. In agreement with previous studies, we found that for increasing Cs small-scale streaks in simple flow field visualisations are gradually quenched and replaced by much larger smooth streaks. Our analysis of low-order turbulence statistics suggests, that these structures originate from an effective reduction of the Reynolds number and thus represent modified low-Reynolds number near-wall streaks rather than VLSM. We argue that overdamped LES with the static Smagorinsky model cannot be used to unambiguously determine the origin and the dynamics of VLSM in pipe flow. The approach might be salvaged by e.g. using more sophisticated LES models accounting for energy flux towards large scales or explicit anisotropic filter kernels.

On the convergence and scaling of high-order statistical moments in turbulent pipe flow using direct numerical simulations

Direct numerical simulations of turbulent pipe flow in a flow domain of length L = 42R, friction Reynolds number in the range of 180 ≤ Reτ ≤ 1500, and two different wall-normal grid refinements were carried out and investigated in terms of high-order turbulence statistics. The phenomenology of large local wall-normal velocity fluctuations (velocity spikes) was discussed by means of time series and instantaneous flow-field realisations. Due to their rare appearance both in space and time, statistical high-order moments take a long time to converge. A convergence study was performed and for fully converged statistics the sensitivity of the grid resolution on the wall-normal kurtosis component value at the wall as well as the scaling behaviour of high-order statistics was investigated. The streamwise Reynolds stress as well as the streamwise skewness and the wall-normal flatness exhibited logarithmic Reynolds number dependencies in the vicinity of the wall and scaling laws were derived accordingly. In the bulk flow region, a sudden increase in magnitude in both the streamwise Reynolds stress and skewness was determined for the largest Reynolds number Reτ = 1500, while the profiles collapsed well in wall units for Reτ ≤ 720. Both Reynolds number dependencies in the near-wall and the bulk region could be related to large-scale outer-flow motions penetrating the buffer layer. While wavelengths related to larger-scale motions (λz ≈ 3R) were computed for Reynolds numbers up to Reτ = 720 by means of two-dimensional two-point velocity correlations, even larger wavelengths related to very-large-scale motions appeared for Reτ = 1500. They are probably the reason for the sudden increase in magnitude of streamwise Reynolds stress and skewness, respectively. With the aid of instantaneous flow-field realisations and conditional averaged statistics, the Reynolds dependency of the wall-normal flatness value at the wall was related to the scaling failure of the streamwise Reynolds stress peak. For the lowest Reynolds number (Reτ = 180), discrepancies between plane channel and pipe flow were found and discussed.

The influence of shear-dependent rheology on turbulent pipe flow

Direct numerical simulations of turbulent pipe flow of power-law fluids at $Re_{\unicode[STIX]{x1D70F}}=323$ are analysed in order to understand the way in which shear thinning or thickening affects first- and second-order flow statistics including turbulent kinetic energy production, transport and dissipation in such flows. The results show that with shear thinning, near-wall streaks become weaker and the axial and azimuthal correlation lengths of axial velocity fluctuations increase. Viscosity fluctuations give rise to an additional shear stress term in the mean momentum equation which is negative for shear-thinning fluids and which increases in magnitude as the fluid becomes more shear thinning: for an equal mean wall shear stress, this term increases the mean velocity gradient in shear-thinning fluids when compared to a Newtonian fluid. Consequently, the mean velocity profile in power-law fluids deviates from the law of the wall $U_{z}^{+}=y^{+}$ in the viscous sublayer when traditional near-wall scaling is used. Consideration is briefly given to an alternative scaling that allows the law of wall to be recovered but which results in loss of a common mean stress profile. With shear thinning, the mean viscosity increases slightly at the wall and its profile appears to be approximately logarithmic in the velocity log layer. Through analysis of the turbulent kinetic energy budget, undertaken here for the first time for generalised Newtonian fluids, it is shown that shear thinning decreases the overall turbulent kinetic energy production but widens the wall-normal region where it is generated. Additional dissipation terms in the mean flow and turbulent kinetic energy budget equations arise from viscosity fluctuations; with shear thinning, these result in a net decrease in the total viscous dissipation. The overall effect of shear thinning on the turbulent kinetic energy budget is found to be largely confined to the inner layers, $y^{+}\lesssim 60$.

Numerical Simulation of Turbulent Pipe Flow for Water Hammer

A numerical model of turbulent transient flow is used to study the dynamics of turbulence during different periods of water hammer in a polymeric pipe. The governing equations of the transient flow are solved by using the finite difference (FD) method, and the effects of viscoelasticity are modeled by means of a two-dimensional (2D) Kelvin–Voigt model. The experimental data with the Ghidaoui parameter P in the order of one are chosen in which the generated shear wave propagates toward the center of the pipe, while the pressure wave passes the length of the pipe. By studying the turbulence shear force during different times, it is shown that the turbulence structure changes considerably in the first cycle of water hammer. In the accelerated phases, the dominant feature is the creation of a shear wave near the wall, and in the decelerated phases the dominant feature is the propagation of the shear wave created in the accelerated phase.

Numerical prediction of the influence of uncertain inflow conditions in pipes by polynomial chaos

Nearly all types of flow measurement devices installed in pipes are affected by the flow conditions at their inlet section, which can lead to measurement errors of several per cent. To evaluate the influence of uncertain inflow profiles on the flow field at different positions of the flow meter, a non-intrusive polynomial chaos approach is applied to simulations of turbulent pipe flow. This allows us to estimate the expected variations of the flow profiles as a function of the distance to the inlet of the pipe in an efficient way. The polynomial chaos approach shows reasonable convergence already for a small number of function evaluations. The results are validated by comparison with a quasi-Monte Carlo method and an exact solution, where available. The approximation error of the polynomial chaos method with 10 function evaluations is smaller than the one for the quasi-Monte Carlo method with 100 runs.

On the origin of frequency sparsity in direct numerical simulations of turbulent pipe flow

The possibility of creating reduced-order models for canonical wall-bounded turbulent flows based on exploiting energy sparsity in frequency domain, as proposed by Bourguignon et al. [Phys. Fluids 26, 015109 (2014)], is examined. The present letter explains the origins of energetically sparse dominant frequencies and provides fundamental information for the design of such reduced-order models. The resolvent decomposition of a pipe flow is employed to consider the influence of finite domain length on the flow dynamics, which acts as a restriction on the possible wavespeeds in the flow. A forcing-to-fluctuation gain analysis in the frequency domain reveals that large sparse peaks in amplification occur when one of the possible wavespeeds matches the local wavespeed via the critical layer mechanism. A link between amplification and energy is provided through the similar characteristics exhibited by the most energetically relevant flow structures, arising from a dynamic mode decomposition of direct numerical simulation data, and the resolvent modes associated with the most amplified sparse frequencies. These results support the feasibility of reduced-order models based on the selection of the most amplified modes emerging from the resolvent model, leading to a novel computationally efficient method of representing turbulent flows.

Reynolds number effects in DNS of pipe flow and comparison with channels and boundary layers

Direct numerical simulations of turbulent pipe flow were performed at four Reynolds numbers: Reτ=180,500,1002and2003. Beyond Reτ=1000 viscous scaling holds near the wall for the mean velocity, Reynolds shear stress and wall-normal velocity variance. Streamwise and spanwise velocity variances do not exhibit inner (viscous) scaling due to increasing large-scale energy contributions. A comparison with channel and boundary layer DNS data shows negligible statistical differences between pipes and channels, whereas the transverse velocities for pipes/channels are significantly different when compared with boundary layers. A further comparison displays that the boundary layer pressure fluctuations is greater than pipes/channels. In addition, is it shown that the higher pressure fluctuations in the boundary layer is not the sole mechanism responsible for a stronger wake region in the flow.

Prediction of pressure drop and heat transfer coefficient in helically grooved heat exchanger tubes using large eddy simulation

Geometry of internally grooved tubes plays a significant role in the performance of heat exchangers. Although there are extensive databases of measurement data for some grooved tubes, it is generally challenging to predict the performance of nonexisting groove shapes. A computational fluid dynamics model based on wall-resolved large eddy simulation of turbulent pipe flow with heat transfer is proposed by using OpenFOAM simulation environment. Fully developed turbulence was simulated by solving the 3D unsteady Navier–Stokes equation in streamwise periodic variables. Simulations for a smooth pipe and a helically grooved tube were carried out at Re = 10,000 to 20,000. Mesh dependency study was performed. Simulation methodology was validated by collating simulated results with literature data and own measurements. The proposed model proved to be accurately predictive: 3.2% to 4.2% difference was found between simulations and measurements. The major novelties of this paper are the introduction of large eddy simulation technique in a new application area, validation for single-phase flow in the given Reynolds number regime, and guidelines for future modellers. This methodology can be used for optimizing parameters of future heat exchanger systems leading to more compact size and better performance.

Direct Numerical Simulation of Turbulent Pipe Flow at Moderately High Reynolds Numbers

Fully resolved direct numerical simulations (DNSs) have been performed with a high-order spectral element method to study the flow of an incompressible viscous fluid in a smooth circular pipe of radius R and axial length 25R in the turbulent flow regime at four different friction Reynolds numbers Reτ = 180, 360, 550 and \(1\text{,}000\). The new set of data is put into perspective with other simulation data sets, obtained in pipe, channel and boundary layer geometry. In particular, differences between different pipe DNS are highlighted. It turns out that the pressure is the variable which differs the most between pipes, channels and boundary layers, leading to significantly different mean and pressure fluctuations, potentially linked to a stronger wake region. In the buffer layer, the variation with Reynolds number of the inner peak of axial velocity fluctuation intensity is similar between channel and boundary layer flows, but lower for the pipe, while the inner peak of the pressure fluctuations show negligible differences between pipe and channel flows but is clearly lower than that for the boundary layer, which is the same behaviour as for the fluctuating wall shear stress. Finally, turbulent kinetic energy budgets are almost indistinguishable between the canonical flows close to the wall (up to y + ≈ 100), while substantial differences are observed in production and dissipation in the outer layer. A clear Reynolds number dependency is documented for the three flow configurations.

Direct numerical simulation of turbulent pipe flow up to a Reynolds number of 61,000

In this paper we will present results of several direct numerical simulations of turbulent pipe flow. The highest Reynolds number simulated in this study was 61, 000. Our numerical model uses Fourier expansions in axial and circumferential directions and 6th order staggered compact finite difference in the wall normal direction. Apart form standard turbulent statistics we also will present 1D energy spectra and autocorrelation functions.

Suboptimal control for drag reduction via suppression of near-wall Reynolds shear stress

We propose a new suboptimal control law for drag reduction in wall-turbulence, which requires the streamwise wall-shear signal only. The cost function is designed to reduce the near-wall Reynolds shear stress that is directly related to the turbulent skin friction drag. The suboptimal solution to minimize the cost function is analytically derived by using the procedure proposed by Lee et al. [J. Fluid Mech. 358 (1998) 245]. Direct numerical simulation of turbulent pipe flow shows that the friction drag can be successfully reduced by the derived control law. Moreover, the sign of Reynolds shear stress in the near-wall layer is found to be reversed with the present control.

Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations

A new finite difference scheme on a non-uniform staggered grid in cylindrical coordinates is proposed for incompressible flow. The scheme conserves both momentum and kinetic energy for inviscid flow with the exception of the time marching error, provided that the discrete continuity equation is satisfied. A novel pole treatment is also introduced, where a discrete radial momentum equation with the fully conservative convection scheme is introduced at the pole. The pole singularity is removed properly using analytical and numerical techniques. The kinetic energy conservation property is tested for the inviscid concentric annular flow for the proposed and existing staggered finite difference schemes in cylindrical coordinates. The pole treatment is verified for inviscid pipe flow. Mixed second and high order finite difference scheme is also proposed and the effect of the order of accuracy is demonstrated for the large eddy simulation of turbulent pipe flow.