A new scaling is derived that yields a Reynolds-number-independent profile for all components of the Reynolds stress in the near-wall region of wall-bounded flows, including channel, pipe and ...boundary layer flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behaviour.
Well-resolved direct numerical simulations (DNS) have been performed of the flow in a smooth circular pipe of radius R and axial length 10 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,. 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 simulations, performed with a high-order spectral-element method, are used to study coherent structures in turbulent pipe flow at friction Reynolds numbers $Re_{\tau } = 180$ and ...$550$. The database was analysed using spectral proper orthogonal decomposition (SPOD) to identify energetically dominant coherent structures, most of which turn out to be streaks and quasi-streamwise vortices. To understand how such structures can be modelled, the linear flow responses to harmonic forcing were computed using the singular value decomposition of the resolvent operator, using the mean field as a base flow. The SPOD and resolvent analysis were calculated for several combinations of frequencies and wavenumbers, allowing the mapping out of similarities between SPOD modes and optimal responses for a wide range of relevant scales in turbulent pipe flows. In order to explore physical reasons behind the agreement between both methods, an indicator of lift-up mechanism in the resolvent analysis was introduced, activated when optimal forcing is dominated by the wall-normal and azimuthal components, and associated response corresponds to streaks of streamwise velocity. Good agreement between leading SPOD and resolvent modes is observed in a large region of parameter space. In this region, a significant gain separation is found in resolvent analysis, which may be attributed to the strong amplification associated with the lift-up mechanism, here understood as nonlinear forcing terms leading to the appearance of streamwise vortices, which in turn form high-amplitude streaks. For both Reynolds numbers, the observed concordances were generally for structures with large energy in the buffer layer. The results highlight resolvent analysis as a pertinent reduced-order model for coherent structures in wall-bounded turbulence, particularly for streamwise elongated structures corresponding to near-wall streamwise vortices and streaks.
The occurrence of secondary flows is investigated for three-dimensional sinusoidal roughness where the wavelength and height of the roughness elements are systematically altered. The flow spanned ...from the transitionally rough regime up to the fully rough regime and the solidity of the roughness ranged from a wavy, sparse roughness to a dense roughness. Analysing the time-averaged velocity, secondary flows are observed in all of the cases, reflected in the coherent stress profile which is dominant in the vicinity of the roughness elements. The roughness sublayer, defined as the region where the coherent stress is non-zero, scales with the roughness wavelength when the roughness is geometrically scaled (proportional increase in both roughness height and wavelength) and when the wavelength increases at fixed roughness height. Premultiplied energy spectra of the streamwise velocity turbulent fluctuations show that energy is reorganised from the largest streamwise wavelengths to the shorter streamwise wavelengths. The peaks in the premultiplied spectra at the streamwise and spanwise wavelengths are correlated with the roughness wavelength in the fully rough regime. Current simulations show that the spanwise scale of roughness determines the occurrence of large-scale secondary flows.
Suspensions of finite-size solid particles in a turbulent pipe flow are found in many industrial and technical flows. Due to the ample parameter space consisting of particle size, concentration, ...density and Reynolds number, a complete picture of the particle–fluid interaction is still lacking. Pressure drop predictions are often made using viscosity models only considering the bulk solid volume fraction. For the case of turbulent pipe flow laden with neutrally buoyant spherical particles, we investigate the pressure drop and overall drag (friction factor), fluid velocity and particle distribution in the pipe. We use a combination of experimental (MRV) and numerical (DNS) techniques and a continuum flow model. We find that the particle size and the bulk flow rate influence the mean fluid velocity, velocity fluctuations and the particle distribution in the pipe for low flow rates. However, the effects of the added solid particles diminish as the flow rate increases. We created a master curve for drag change compared to single-phase flow for the particle-laden cases. This curve can be used to achieve more accurate friction factor predictions than the traditional modified viscosity approach that does not account for particle size.
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•Combined experimental/numerical study in turbulent pipe flow with spherical particles.•Variations of flow rate, particle size and concentration in multiple flow setups and with DNS.•Non-trivial effects on pressure loss, velocity statistics and particle distribution.•A general normalized drag increase curve is obtained, together with a scaling parameter.•Particle size in relation to the friction length and the pipe diameter and conc. determine drag.
This work studies the dynamics of linear non-modal waves in viscoelastic pipe flows of FENE-P fluids using transient growth and resolvent analyses. We particularly focus on the time evolution of the ...amplification of the disturbance energy (using the 4th-order Runge–Kutta method) and discuss the dynamical traits of the Orr and the critical-layer mechanisms in the conformation tensor field when the transient energy increases. The helical mode undergoes a larger energy growth than the axisymmetric mode. The effects of various flow parameters have been investigated on the growth rate and energy amplification of the non-modal waves and the optimal flow structures. It is found that when the elastic effect is stronger, the amplitude of the optimal conformation tensor in the pipe centre region becomes greater from a non-modal perspective.
•Orr mechanism in the conformation tensor is at play when transient energy increases.•Conformation tensor in the pipe centre becomes greater when elasticity is stronger.•Helical modes, though stable, undergo larger energy growth than the axisymmetric mode.
A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale ...motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating helical velocity response modes that are harmonic in the wall-parallel directions and in time, permitting comparison of our results to experimental data. The steady component of the velocity field that varies only in the wall-normal direction is identified as the turbulent mean profile. A singular value decomposition of the resolvent identifies the forcing shape that will lead to the largest velocity response at a given wavenumber–frequency combination. The hypothesis that these forcing shapes lead to response modes that will be dominant in turbulent pipe flow is tested by using physical arguments to constrain the range of wavenumbers and frequencies to those actually observed in experiments. An investigation of the most amplified velocity response at a given wavenumber–frequency combination reveals critical-layer-like behaviour reminiscent of the neutrally stable solutions of the Orr–Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely wall layers that scale with R+1/2 and critical layers where the propagation velocity is equal to the local mean velocity, one of which scales with R+2/3 in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall. The model reproduces inner scaling of the small scales near the wall and an approach to outer scaling in the flow interior. We use our analysis to make a first prediction that the appropriate scaling velocity for the very large scale motions is the centreline velocity, and show that this is in agreement with experimental results. Lastly, we interpret the wall modes as the motion required to meet the wall boundary condition, identifying the interaction between the critical and wall modes as a potential origin for an interaction between the large and small scales that has been observed in recent literature as an amplitude modulation of the near-wall turbulence by the very large scales.
This work presents a detailed analysis of the flow structures relevant to extreme wall shear stress events for turbulent pipe flow direct numerical simulation data at a friction Reynolds number ...$\textit {Re}_{\tau} \approx 1000$. The results reveal that extreme positive wall-friction events are located below an intense sweep (Q4) event originated from a strong quasi-streamwise vortex at the buffer region. This vortex transports high streamwise momentum from the overlap and the outer layers towards the wall, giving rise to a high-speed streak within the inner region. This vortical structure also relates to regions with extreme wall-normal velocity. Consequently, the conditional fields of turbulence production and viscous dissipation exhibit peaks whose magnitudes are approximately 25 times higher than the ensemble mean quantities in the vicinity of the extreme positive events. An analysis of the turbulent inertia force reveals that the energetic quasi-streamwise vortex acts as an essential source of momentum at the near-wall region. Similarly, extremely rare backflow events are studied. An examination of the wall-normal vorticity and velocity vector fields shows an identifiable oblique vortical structure along with two other large-scale roll modes. These counter-rotating motions contribute to the formation of backflow events by transporting streamwise momentum from the inner to the outer region, creating a large-scale meandering low-speed streak. It is found that extreme events are clustered below large-scale structures of positive streamwise momentum that interact with near-wall low-speed streaks, related to regions densely populated with vortical structures. Finally, a three-dimensional model is proposed to conceptualise the flow dynamics associated with extreme events.
In this paper, we present a first direct numerical simulation (DNS) of a turbulent pipe flow using the mesoscopic lattice Boltzmann method (LBM) on both a D3Q19 lattice grid and a D3Q27 lattice grid. ...DNS of turbulent pipe flows using LBM has never been reported previously, perhaps due to inaccuracy and numerical stability associated with the previous implementations of LBM in the presence of a curved solid surface. In fact, it was even speculated that the D3Q19 lattice might be inappropriate as a DNS tool for turbulent pipe flows. In this paper, we show, through careful implementation, accurate turbulent statistics can be obtained using both D3Q19 and D3Q27 lattice grids. In the simulation with D3Q19 lattice, a few problems related to the numerical stability of the simulation are exposed. Discussions and solutions for those problems are provided. The simulation with D3Q27 lattice, on the other hand, is found to be more stable than its D3Q19 counterpart. The resulting turbulent flow statistics at a friction Reynolds number of Reτ=180 are compared systematically with both published experimental and other DNS results based on solving the Navier–Stokes equations. The comparisons cover the mean-flow profile, the r.m.s. velocity and vorticity profiles, the mean and r.m.s. pressure profiles, the velocity skewness and flatness, and spatial correlations and energy spectra of velocity and vorticity. Overall, we conclude that both D3Q19 and D3Q27 simulations yield accurate turbulent flow statistics. The use of the D3Q27 lattice is shown to suppress the weak secondary flow pattern in the mean flow due to numerical artifacts.
Large-eddy simulations of turbulent flow in partially filled pipes are conducted to investigate the effect of secondary currents on the friction factor, first- and second-order statistics and ...large-scale turbulent motion. The method is validated first and simulated profiles of the mean streamwise velocity, normal stresses and turbulent kinetic energy (TKE) are shown to be in good agreement with experimental data. The secondary flow is stronger in half- and three-quarters full pipes compared with quarter full or fully filled pipe flows, respectively. The origin of the secondary flow is examined by both the TKE budget and the steamwise vorticity equation, providing evidence that secondary currents originate from the corner between the free surface and the pipe walls, which is where turbulence production is larger than the sum of the remaining terms of the TKE budget. An extra source of streamwise vorticity production is found at the free surface near the centreline bisector, due to the two-component asymmetric turbulence there. The occurrence of dispersive stresses (due to secondary currents) reduces the contribution of the turbulent shear stress to the friction factor, which results in a reduction of the total friction factor of flows in half and three-quarters full pipes in comparison to a fully filled pipe flow. Furthermore, the presence of significant secondary currents inhibits very-large-scale motion (VLSM), which in turn reduces the strength and scales of near-wall streaks. Subsequently, near-wall coherent structures generated by streak instability and transient growth are significantly suppressed. The absence of VLSM and less coherent near-wall turbulence structures is supposedly responsible for the drag reduction in partially filled pipe flows relative to a fully filled pipe flow at an equivalent Reynolds number.
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