Fully-developed Turbulent Flow Research Articles

Particle deposition model for a fully developed turbulent channel flow

This study aims to develop a mathematical model for solid particle deposition under a fully-developed turbulent flow in a rectangular channel, considering the effect of the change in geometry over time. The present study introduces a mathematical approach to predict the equilibrium thickness/mass of the deposition, saturation and equilibrium times, and their corresponding non-dimensionalized parameters. Scaling analysis, and parametric study are reported. For a fixed Reynolds number Re, the particle deposition increases with non-dimensional relaxation time. In general, as more particles are deposited, the surface takes less time to become saturated and approach equilibrium faster. The saturation and equilibrium times decrease with an increase in non-dimensional particle relaxation time. For a fixed particle concentration, as the inlet velocity increases, the saturation and equilibrium time decreases, and the asymptotic deposited mass decreases.

Collocated Finite Difference Method in General Coordinates for Simulation of Flow Over Arbitrary Geometry

A finite difference method to be used in simulations of turbulent flows such as Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) has been developed and verified for basic benchmark flows. The method is constructed using the general curvilinear coordinate system with the collocated grid arrangement of the variables so that it can be easily applied to various engineering flows including hydraulic applications involving complex geometry and moving boundary. The computer code is verified by test calculation of steady laminar internal flow in a curved cavity and an external flow above a curved hill. Furthermore the same code is used to conduct a DNS of fully-developed turbulent flow in a two-dimensional open channel and a LES of flow over curved hill. All results indicate that the method is sound with sufficient accuracy for the intended applications.

Hydrodynamics of finite-length pipes at intermediate Reynolds numbers

Extensive studies of the hydraulics of pipes have focused on limiting cases, such as fully-developed laminar or turbulent flow through long conduits and the accelerating flow through an orifice, for which there exist laws relating pressure drop and flow rate. We carry out experiments on smooth, circular pipes for dimensions and flow rates that interrogate intermediate conditions between the well-studied limits. Organizing this information in terms of dimensionless friction factor, Reynolds number and pipe aspect ratio yields a surface$f_D(Re,\alpha )$that is shown to match the three laws associated with developed laminar, developed turbulent, and orifice flows. While each law fails outside its applicable range of$(Re,\alpha )$, we present a hybrid theoretical–empirical model that includes inlet, development and transition effects, and that proves accurate to approximately 10 % over wide ranges of$Re$and$\alpha$. We also present simple formulas for the boundaries between the three hydraulic regimes, which intersect at a triple point. Measurements show that sipping through a straw is an everyday example of such intermediate conditions not accounted for by existing laws but described accurately by our model. More generally, our findings provide formulas for predicting frictional resistance for intermediate-$Re$flows through finite-length pipes.

A comparison of hydrodynamic and thermal properties of artificially generated against realistic rough surfaces

The mathematical roughness generation approaches enjoy outstanding flexibility in delivering desired roughness geometries to perform systematic research. However, whether an mathematically (artificially) generated roughness can be considered an adequate surrogate of a realistic surface in terms of its influence on the flow remains nonetheless an open question. Motivated by this, the present study discusses the possibility of reproducing flow properties over realistic roughness with artificial roughness. To this end, six types of artificial rough surfaces are generated through imitation of the realistic height probability density function (PDF) and the roughness power spectrum (PS) preserving the stochastic nature of the roughness structure. The flow properties of the artificial surfaces are assessed using direct numerical simulations (DNS) in a fully-developed turbulent channel flow at Reτ=500−2000. An excellent match in terms of global flow properties, mean velocity and temperature profiles, Reynolds stresses as well as equivalent sand grain sizes is found compared to their original counterpart with exception of a strongly anisotropic sample (surface anisotropy ratio SAR≈1.7). Additionally, some artificial surfaces are generated by matching only the PS, and it was shown that only at adequately low effective slopes this can lead to similar flow properties. Overall, the results suggest that artificial roughness generated using the employed method by mimicking realistic PDF and PS can be applied as a full-fledged surrogate for realistic roughness under the premise of surface isotropy.

Multi-fidelity uncertainty quantification of particle deposition in turbulent pipe flow

Particle deposition in fully-developed turbulent pipe flow is quantified taking into account uncertainty in electric charge, van der Waals strength, and temperature effects. A framework is presented for obtaining variance-based sensitivity in multiphase flow systems via a multi-fidelity Monte Carlo approach that optimally manages model evaluations for a given computational budget. The approach combines a high-fidelity model based on direct numerical simulation and a lower-order model based on a one-dimensional Eulerian description of the two-phase flow. Significant speedup is obtained compared to classical Monte Carlo estimation. Deposition is found to be most sensitive to electrostatic interactions and exhibits largest uncertainty for mid-sized (i.e., moderate Stokes number) particles.

Secondary Currents at Very Low and High Aspect Ratios of Open Channels

The present numerical study is an attempt to better understand the effect of the aspect ratio (AR) on the velocity field characteristics of the fully-developed turbulent flow in a straight open channel by contrasting a very low and very high aspect ratio cases (AR = 1 and 12). The AR is defined as the ratio of the width of the channel in a plane normal to the flow direction, to the flow depth. The bulk velocity and water depth considered in this study are 0.75 m/s and 30 mm, respectively, which yield a Reynolds number of ReH = 22,500. The transient three-dimensional Navier-Stokes equations were numerically solved using a finite-volume approach with improved-delayed detached-eddy simulation (IDDES) turbulence model. The results revealed that the normalized components of the normal stresses by the turbulent kinetic energy k are constant over most of the velocity field, although k varies in magnitude throughout the velocity field in both AR cases. In addition, the results also revealed a strong anisotropic flow which justifies the formation of secondary currents as a means for transporting the kinetic energy. The results also reveal that both vertical and transverse components of the normal stresses are correlated to the side-recirculation zone (SRZ) and bottom-recirculation zone (BRZ), respectively, which highlights the role of the mean recirculation zones (BRZ & SRZ) in the re-distribution of the turbulent kinetic energy k in the velocity field.

Parametric solutions of turbulent incompressible flows in OpenFOAM via the proper generalised decomposition

An a priori reduced order method based on the proper generalised decomposition (PGD) is proposed to compute parametric solutions involving turbulent incompressible flows of interest in an industrial context, using OpenFOAM. The PGD framework is applied for the first time to the incompressible Navier-Stokes equations in the turbulent regime, to compute a generalised solution for velocity, pressure and turbulent viscosity, explicitly depending on the design parameters of the problem. In order to simulate flows of industrial interest, a minimally intrusive implementation based on OpenFOAM SIMPLE algorithm applied to the Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model is devised. The resulting PGD strategy is applied to parametric flow control problems and achieves both qualitative and quantitative agreement with the full order OpenFOAM solution for convection-dominated fully-developed turbulent incompressible flows, with Reynolds number up to one million.

Effects of flow regime and conjugate heat transfer on particle deposition in heat exchange duct

Deposition of micron particles in heat exchange duct is commonly encountered in many thermal and HVAC engineering applications. Previous studies on this important issue always considered turbulent air flow regime without conjugate heat transfer (CHT). However, the flow regimes and the CHT may have significant influences on particle deposition behaviors. Therefore, this paper aims to study particle deposition characteristics in laminar flow (LF), developing turbulent flow (DTF) and fully developed turbulent flow (FDTF) regimes with and without CHT. The v′2‾−fturbulence model and discrete particle model (DPM) were used to predict gas phase and solid phase, respectively. Moreover, a modified discrete random walk method was adopted to model turbulent particle dispersion. The results showed that particle deposition velocities greatly increase for small particles (dp<20μm) but keep invariable for large particles (dp>20μm) due to thermophoretic deposition. WhenΔT=100Kanddp=1μm, the peak deposition velocity enhancement ratio reaches 3.8, 9.7 and 7.5 for LF, DTF and FDTF regimes respectively. Different flow regimes have obvious effects on the deposition characteristics. Particle deposition velocity for DTF regime is the highest, followed by FDTF case and LF case. Thermophoresis effect is reduced by the CHT, as the temperature difference decreases due to thermal conduction in solid domain. The CHT in DTF or FDTF regime has obviously larger effect on deposition characteristics, compared with the LF regime.

Predictive accuracy of wall-modelled large-eddy simulation on unstructured grids

The predictive accuracy of wall-modelled LES is influenced by a combination of the subgrid model, the wall model, the numerical dissipation induced primarily by the convective numerical scheme, and also by the density and topology of the computational grid. The latter factor is of particular importance for industrial flow problems, where unstructured grids are typically employed due to the necessity to handle complex geometries. Here, a systematic simulation-based study is presented, investigating the effect of grid-cell type on the predictive accuracy of wall-modelled LES in the framework of a general-purpose finite-volume solver. Following standard practice for meshing near-wall regions, it is proposed to use prismatic cells. Three candidate shapes for the base of the prisms are considered: a triangle, a quadrilateral, and an arbitrary polygon. The cell-centre distance is proposed as a metric to determine the spatial resolution of grids with different cell types. The simulation campaign covers two test cases with attached boundary layers: fully-developed turbulent channel flow, and a zero-pressure-gradient flat-plate turbulent boundary layer. A grid construction strategy is employed, which adapts the grid metric to the outer length scale of the boundary layer. The results are compared with DNS data concerning mean wall shear stress and profiles of flow statistics. The principle outcome is that unstructured simulations may provide the same accuracy as simulations on structured orthogonal hexahedral grids. The choice of base shape of the near-wall cells has a significant impact on the computational cost, but in terms of accuracy appears to be a factor of secondary importance.

Development of machine learning techniques to enhance turbulence models

The implementation of the machine learning methods of convolutional neural networks to enhance RANS closure models is presented. The RANS models are not universal and accurate, however they are computationally affordable. Finding a way to improve the model predictability will be an advantage. For this, machine learning algorithms based on available high-fidelity data sets for canonical flow cases obtained from DNS and measurements can be helpful. The application of these algorithms for a fully-developed turbulent channel flows with periodic hills, in a square duct and for other cases is considered.

Direct numerical simulation of turbulent flow separation induced by a forward-facing step

Direct numerical simulation is used to investigate turbulent flow separations generated by a forward-facing step exposed to an incoming fully-developed turbulent plane channel flow at Reτ=180. The step height is 25% of the inlet channel height. The results are analyzed in terms of the topology of the Reynolds stresses, transport of turbulence kinetic energy (TKE) and unsteadiness of separation bubbles using a broad range of post-processing techniques, including the Lumley triangle, quadrant analysis, auto-correlation, joint probability density function, proper orthogonal decomposition and linear stochastic estimation. The incoming turbulence intensity is elevated as the step is approached and peaks along the mean separating streamline over the step. The topology of the Reynolds stresses switches from two-component to axisymmetric along the mean separating streamline over the step. The production term of TKE peaks in the separated shear layer, while the turbulent diffusion term tends to transport TKE away from the shear layer. An expanded separation bubble upstream of the step is typically associated with a contracted separation bubble over the step. This pattern is captured by the first proper orthogonal decomposition (POD) mode. In the first POD mode, the streamwise and vertical fluctuating velocities switch signs abruptly near the mean separating streamline over the step. This is characterized by two pairs of counter-rotating vortices: one pair of counter-rotating vortices leaning over the step and another pair of opposite-signed counter-rotating vortices near the top surface of the step.

Effects of radius ratio on turbulent concentric annular pipe flow and structures

The effects of radius ratio on fully-developed turbulent concentric annular pipe flow and structures are investigated using direct numerical simulations (DNS). In order to study the radius ratio effects on the flow, four radius ratios of a concentric annular pipe (for Ri∕Ro=0.1–0.7) are compared at a fixed Reynolds number. Here, Ri and Ro are the radii of the inner and outer pipes, respectively. It is observed that the radius ratio influences the interaction of two boundary layers developed over the inner and outer cylinder surfaces, and has a significant impact on the turbulent flow structures and dynamics. The characteristics of the flow field are investigated in both physical and spectral spaces, which include the analyses of the first- and second-order statistical moments, budget balance of the transport equation of Reynolds shear stress, two-point correlation coefficients, and premultiplied spectra of velocity and vorticity fluctuations.

Direct numerical simulation of spray droplet evaporation in hot turbulent channel flow

We perform a direct numerical simulation (DNS) of 14081 “cold” spherical droplets evaporating in a “hot” fully-developed turbulent channel flow. This effort is the first extensive computation that employs four-way coupling of the droplet motion with the turbulent carrier phase and interface-resolved evaporation dynamics, for a flow configuration that approaches conditions encountered in spray combustion applications. The complex interaction of momentum, heat, species transfer and phase change thermodynamics is explored. Large-scale droplet motion, modulation of the carrier phase turbulence, and influence of the mean and turbulent mass transport on the evaporation dynamics are observed and quantified. Based on the data set, phenomenological explanations of the shear-induced migration of the dispersed phase and of the effect of turbulent mass transport on the evaporation are provided. The transient nature of the DNS is exploited to generate a novel database that samples a range of turbulence and evaporation timescales, from which a model for the enhancement of the evaporation rate by the ambient turbulence is extracted.

Geometric Effects of Shallow Dimples in Turbulent Channel Flows at $$Re_{\tau }\approx 180$$: A Vorticity Transport Perspective

Shallow dimples have shown a great potential to reduce turbulent drag in several experiments. However, the mechanism underlying their effects on turbulence dynamics remains a subject of deliberation. In this numerical study, a vorticity transport perspective is adopted to elucidate the geometric effects of shallow dimples on the turbulence dynamics in a fully-developed turbulent channel flow. The geometric modifications considered in the present direct numerical simulation at a bulk Reynolds number of 2800 include changing the planform design and modulating the streamwise wall slope. The planform design had a significant impact on the mean flow topology and the drag property. Out of the five planform designs, diamond (shape) dimples produced the highest amount of total drag reduction of $$\approx 7\%$$, whereas symmetric circular dimples caused the greatest increase in total drag by $$\approx 6\%$$. Results revealed that geometric modifications of shallow dimples mainly affect the vorticity redistribution process that predominates in the inner region of a turbulent boundary layer, and in turn the generation of Reynolds stress. The drag property of a dimpled surface was found to scale with the velocity–vorticity correlation term representing the physical process of vorticity stretching and reorientation. The occurrence of flow separation near the leading edge of the dimple altered the vorticity dispersion process in the outer region, thereby modifying the generation of Reynolds stress in the bulk flow. On the other hand, the vortex dispersion process in the inner layer can be altered by modulating the streamwise wall slope. Accordingly, the vorticity redistribution process was modified but the near-wall generation of Reynolds stress was unaffected. Thus, only the form drag varied with the streamwise wall slope, while the viscous drag remained largely the same.

Analysis of the numerical dissipation rate of different Runge–Kutta and velocity interpolation methods in an unstructured collocated finite volume method in OpenFOAM®

The approach used for computation of the convecting face fluxes and the cell face velocities results in different underlying numerical algorithms in finite volume collocated grid solvers for the incompressible Navier–Stokes equations. In this study, the effect of the following five numerical algorithms on the numerical dissipation rate and on the temporal consistency of a selection of Runge–Kutta schemes is analysed: (1) the original algorithm of Rhie and Chow (1983), (2) the standard OpenFOAM method, (3) the algorithm used by Vuorinen et al. (2014), (4) the Kazemi-Kamyab et al. (2015) method, and (5) the D’Alessandro et al. (2018) approach. The last three algorithms refer to recent implementations of low dissipative numerical methods in OpenFOAM®.No new computational methods are presented in this paper. Instead, the main scientific contributions of this paper are: (1) the systematic assessment of the effect of the considered five numerical approaches on the numerical dissipation rate and on the temporal consistency of the selected Runge–Kutta schemes within one unified framework which we have implemented in OpenFOAM, and (2) the application of the method of Komen et al. (2017) in order to quantify the numerical dissipation rate introduced by three of the five numerical methods in quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow. In addition, we explain the effects of the introduced numerical dissipation on the observed trends in the corresponding numerical results.As one of the major conclusions, we found that the pressure error, which is introduced due to the application of a compact stencil in the pressure Poisson equation, causes a reduction of the order of accuracy of the temporal schemes for the test cases in this study. Consequently, application of higher order temporal schemes is not useful from an accuracy point of view, and the application of a second order temporal scheme appears to be sufficient.

Local velocity scaling in upward flow to tooth impeller in a fully turbulent region

The hydrodynamics and flow field were measured in an agitated vessel using 2-D Time Resolved Particle Image Velocimetry (2-D TR PIV). The experiments were carried out in a fully baffled cylindrical flat bottom vessel 400 mm in inner diameter agitated by a tooth impeller 133 mm in diameter. Distilled water was used as the agitated liquid. The velocity fields were investigated in the upward flow to the impeller for three impeller rotation speeds – 300 rpm, 500 rpm and 700 rpm, corresponding to a Reynolds number in the range 94 000 &lt; Re &lt; 221 000. This means that fully-developed turbulent flow was reached. This Re range secures the fully-developed turbulent flow in an agitated liquid. In accordance with the theory of mixing, the dimensionless mean and fluctuation velocities in the measured directions were found to be constant and independent of the impeller Reynolds number. On the basis of the test results the spatial distributions of dimensionless velocities were calculated. The axial turbulence intensity was found to be in the majority in the range from 0.4 to 0.7, which corresponds to the middle level of turbulence intensity.

Direct Numerical Simulation of Turbulent Flow in a Circular Pipe Subjected to Radial System Rotation

Direct numerical simulations have been performed with a high-order spectral element method computer code to investigate the Coriolis force effect on a fully-developed turbulent flow confined within a circular pipe subjected to radial system rotations. In order to study the radially rotating effects on the flow, a wide range of rotation numbers (Roτ) have been tested. In response to the system rotation imposed, large-scale secondary flows appear as streamwise counter-rotating vortices, which highly interact with the boundary layer and have a significant impact on the turbulent flow structures and dynamics. A quasi Taylor-Proudman region occurs at low rotation numbers, where the mean axial velocity is invariant along the rotating axis. As the rotation number increases, laminarization occurs near the bottom wall of the pipe, and the flow becomes fully laminarized when the rotation number approaches Roτ = 1.0. The characteristics of the flow field are investigated in both physical and spectral spaces, which include the analyses of the first- and second-order statistical moments, pre-multiplied spectra of velocity fluctuations, budget balance of the transport equation of Reynolds stresses, and coherent flow structures.

Study of fully-developed turbulent flow and heat transfer in a rotating wavy-walled duct

Finite volume based computations of fully developed flow and heat transfer through rotating wavy-walled ducts using large eddy simulation (LES) has been carried out. The shear improved Smagorinsky model (SISM) is employed to model the unresolved turbulent fluctuations. The wavy-walls of the duct are described by the sine function y=2asin2(πx/L). The geometrical ratios Hmin/Hmax and L/a are kept fixed to 0.2 and 8 respectively. The effect of rotation on the fluid flow and heat transfer characteristics are presented. All the computations are at a Reynolds number of 5000 and the rotation number is varied in the range, 0–0.5. It has been observed that the pressure drop across the wavy-walled duct varies with increasing rotation number. It is also found out that with rotation, the heat transfer increases on the trailing wall while the leading wall shows the opposite trend. Both Nusselt number and pressure drop for the wavy-walled duct is observed to be less than the corresponding values in ribbed duct geometry.

Synthetic turbulent inflow generator using machine learning

We propose a methodology for generating time-dependent turbulent inflow data with the aid of machine learning (ML), which has a possibility to replace conventional driver simulations or synthetic turbulent inflow generators. As for the ML model, we use an auto-encoder type convolutional neural network (CNN) with a multi-layer perceptron (MLP). For the test case, we study a fully-developed turbulent channel flow at the friction Reynolds number of ${\rm Re}_{\tau} = 180$ for easiness of assessment. The ML models are trained using a time series of instantaneous velocity fields in a single cross-section obtained by direct numerical simulation (DNS) so as to output the cross-sectional velocity field at a specified future time instant. From the a priori test in which the output from the trained ML model are recycled to the input, the spatio-temporal evolution of cross-sectional structure is found to be reasonably well reproduced by the proposed method. The turbulence statistics obtained in the a priori test are also, in general, in reasonable agreement with the DNS data, although some deviation in the flow rate was found. It is also found that the present machine-learned inflow generator is free from the spurious periodicity, unlike the conventional driver DNS in a periodic domain. As an a posteriori test, we perform DNS of inflow-outflow turbulent channel flow with the trained ML model used as a machine-learned turbulent inflow generator (MLTG) at the inlet. It is shown that the present MLTG can maintain the turbulent channel flow for a long time period sufficient to accumulate turbulent statistics, with much lower computational cost than the corresponding driver simulation. It is also demonstrated that we can obtain accurate turbulent statistics by properly correcting the deviation in the flow rate.

DNS of turbulent low Mach channel flow under asymmetric high temperature gradient: Effect of thermal boundary condition on turbulence statistics

Direct Numerical Simulations have been performed for a fully-developed low Mach turbulent flow of an ideal gas with thermo-dependent viscosity and thermal conductivity in a flat channel at mean friction Reynolds number Reτ=180 submitted to asymmetric heating with a wall temperature ratio T2/T1=2. Mean and turbulent statistics of the flow have been studied and compared for two different thermal boundary conditions: fixed temperatures on the one hand and fixed heat flux densities on the other hand. The influence of the boundary condition type is studied. Temperature variance is particularly impacted by this choice and exhibits asymmetric profiles with different behavior depending on the boundary condition.