Incompressible Turbulent Flow Research Articles

Large-eddy simulation of wall-bounded incompressible turbulent flows based on multi-moment finite volume formulation

The multi-moment based numerical model is proposed for performing large-eddy simulation (LES) of wall-bounded incompressible turbulent flows on the unstructured grids. In this model, velocity is defined as volume integral average (VIA) and point values (PVs) which are updated as prognostic variables simultaneously in time. Using VIA and PV in each cell, this method constructs higher-order polynomial on a compact stencil and more importantly, provides a new approach to design subgrid-scale (SGS) models for LES. Various SGS models are developed in this framework where the eddy-viscosity is computed separately at both VIA and PVs using the least-square method on different interpolation stencils. Compared with conventional finite volume schemes, the proposed method effectively reduces numerical dissipation and largely suppresses the sensitivity of numerical solution on SGS models and resolves more elaborated flow structures on the same mesh resolution. It also reduces solution dependence on the shape and quality of grid elements, as demonstrated by comparing numerical results on the different types of grids. The proposed method can attain high-fidelity simulation without loss of numerical efficiency and robustness, which is highly appealing for complex turbulent problems with high Reynolds numbers and complicated geometries.

Data-driven model for Lagrangian evolution of velocity gradients in incompressible turbulent flows

Velocity gradient tensor, $A_{ij}\equiv \partial u_i/\partial x_j$ , in a turbulence flow field is modelled by separating the treatment of intermittent magnitude ( $A = \sqrt {A_{ij}A_{ij}}$ ) from that of the more universal normalised velocity gradient tensor, $b_{ij} \equiv A_{ij}/A$ . The boundedness and compactness of the $b_{ij}$ -space along with its universal dynamics allow for the development of models that are reasonably insensitive to Reynolds number. The near-lognormality of the magnitude $A$ is then exploited to derive a model based on a modified Ornstein–Uhlenbeck process. These models are developed using data-driven strategies employing high-fidelity forced isotropic turbulence data sets. A posteriori model results agree well with direct numerical simulation data over a wide range of velocity-gradient features and Reynolds numbers.

Karhunen–Loéve decomposition of high Reynolds number turbulent pipe flows: a Voronoi analysis

We perform the Karhunen–Loéve decomposition of the data from direct numerical simulations pertaining to incompressible turbulent pipe flow at various Reynolds numbers, in order to identify large-scale coherent structures. A novel approach based on the Voronoi diagram is introduced to estimate the energy distribution along the radial direction as a function of the geometrical properties of the modes. In contrast to previous classifications, no user-defined criterion, threshold or ad-hoc separation of the eddies is required since the two most energetic branches are inherently present as the Reynolds number increases. Details about the Voronoi analysis are provided, together with a comprehensive validation and comparison with previous classifications at low Reynolds numbers. We discuss the results and potential of the presented approach at Reτ = 180 and 5200, commenting on the two classes of coherent structures with a varying and constant size in the radial direction appearing at Reτ = 5200.

Lighter and faster simulations on domains with symmetries

A strategy to improve the performance and reduce the memory footprint of simulations on meshes with spatial reflection symmetries is presented in this work. By using an appropriate mirrored ordering of the unknowns, discrete partial differential operators are represented by matrices with a regular block structure that allows replacing the standard sparse matrix–vector product with a specialised version of the sparse matrix-matrix product, which has a significantly higher arithmetic intensity. Consequently, matrix multiplications are accelerated, whereas their memory footprint is reduced, making massive simulations more affordable. As an example of practical application, we consider the numerical simulation of turbulent incompressible flows using a low-dissipation discretisation on unstructured collocated grids. All the required matrices are classified into three sparsity patterns that correspond to the discrete Laplacian, gradient, and divergence operators. Therefore, the above-mentioned benefits of exploiting spatial reflection symmetries are tested for these three matrices on both CPU and GPU, showing up to 5.0x speed-ups and 8.0x memory savings. Finally, a roofline performance analysis of the symmetry-aware sparse matrix–vector product is presented.

Validation of symmetry-induced high moment velocity and temperature scaling laws in a turbulent channel flow.

The symmetry-based turbulence theory has been used to derive new scaling laws for the streamwise velocity and temperature moments of arbitrary order. For this, it has been applied to an incompressible turbulent channel flow driven by a pressure gradient with a passive scalar equationcoupled in. To derive the scaling laws, symmetries of the classical Navier-Stokes and the thermal energy equationshave been used together with statistical symmetries, i.e., the statistical scaling and translation symmetries of the multipoint moment equations. Specifically, the multipoint moments are built on the instantaneous velocity and temperature fields other than in the classical approach, where moments are based on the fluctuations of these fields. With this instantaneous approach, a linear system of multipoint correlation equationshas been obtained, which greatly simplifies the symmetry analysis. The scaling laws have been derived in the limit of zero viscosity and heat conduction, i.e., Re_{τ}→∞ and Pr>1, and they apply in the center of the channel, i.e., they represent a generalization of the deficit law, thus extending the work of Oberlack etal. [Phys. Rev. Lett. 128, 024502 (2022)0031-900710.1103/PhysRevLett.128.024502]. The scaling laws are all power laws, with the exponent of the high moments all depending exclusively on those of the first and second moments. To validate the new scaling laws, the data from a large number of direct numerical simulations (DNS) for different Reynolds and Prandtl numbers have been used. The results show a very high accuracy of the scaling laws to represent the DNS data. The statistical scaling symmetry of the multipoint moment equations, which characterizes intermittency, has been the key to the new results since it generates a constant in the exponent of the final scaling law. Most important, since this constant is independent of the order of the moments, it clearly indicates anomalous scaling.

Characterization and evolution of local streamline geometry in an incompressible turbulent channel flow

We investigated the statistical characterization and time evolution of local streamline geometry in typical regions of an incompressible turbulent channel flow at the friction Reynolds number Reτ∼1000. Local streamline structure is completely and uniquely determined by one magnitude factor—the magnitude of velocity gradient tensor (VGT) A—and four shape parameters—the second and third invariants of normalized VGT q and r, the intermediate eigenvalue of normalized strain-rate tensor a2, and the cosine of the angle between vorticity and the intermediate eigendirection of normalized strain-rate tensor | cos β|. As the distance to the wall decreases, the joint probability distribution function of q and r becomes more symmetrical and concentrated, while outside the viscous sublayer, the distribution of A in q–r plane gets dispersed. Interestingly, the inertial conditional mean trajectories (CMTs) exhibit a symmetrical picture only in the buffer layer, and outside the viscous sublayer, the pressure CMTs contributing to slow evolution from unstable focus compression geometry to stable focus stretching geometry tend to dominate the q–r plane as getting closer to the wall. Due to combined effects of inertia and pressure, the origin of the q–r plane (pure-shear geometry) acts as an attractor in the central region, the logarithmic region, and the upper part of the buffer layer while acts as a repeller in the lower part of the buffer layer and the viscous sublayer.

Wall-modeled large eddy simulation of 90° bent pipe flows with/without particles: A comparative study

Wall-modeled large eddy simulation (WMLES) has been proven to be a cost-effective approach capable of resolving turbulence up to certain resolutions. Among the simplest wall models used are the equilibrium wall models, assuming the pressure gradient and convective terms balance out in the momentum equations. There is a lack of studies to assess the performance of these standard wall models in internal turbulent flows including separation regions with/without particles. Regarding this research gap, we have conducted WMLES of incompressible turbulent flows, to the authors’ knowledge, for the first time, in 90° bent pipes with and without particles using an algebraic equilibrium wall model (Spalding’s function). A pipe flow simulation was conducted to confirm the simulation setup and assess the sensitivity with respect to the modeling parameters. In each case, comparisons are made with experiment or direct numerical simulation (DNS), and depending on the case, with other existing simulation methods in the literature: WMLES, standard (wall-resolving) LES, and Reynolds stress model (RSM) for Reynolds-averaged Navier-Stokes (RANS) simulations. Despite the controversy on the performance of equilibrium wall models in nonequilibrium flows, our results show acceptable accuracy of this type of wall models. Specifically in the bent pipe flow with particles, WMLES succeeded in predicting particle deposition efficiency at Stokes numbers greater than 0.5, but obtained less accurate results for smaller Stokes numbers. The WMLES errors were, however, on par with those of the standard LES employed with a tenfold higher grid cell count. Improved results would be expected if combined with auxiliary mechanisms such as stochastic models.

A cell-based smoothed finite element model for the analysis of turbulent flow using realizable k-ε model and mixed meshes

Smoothed finite element method (S-FEM) has been widely employed in computational mechanics, particularly in computational solid mechanics (CSM) and, to a lesser extent, in computational fluid dynamics (CFD). The present work focuses on the development of S-FEM for solving three-dimensional incompressible turbulent flow problems using the realizable k-ε model. The Streamline Upwind Petrov-Galerkin approach combined with Stabilized Pressure Gradient Projection (SUPG/SPGP) was used to restrain/control the spatial oscillation and instability in conjunction with mixed meshes employed to discretize complex geometries. The presented turbulent cell-based S-FEM (CS-FEM) was validated under several common flow types, including mesh turbulence, turbulent channel flow, turbulent flow past a circular cylinder, flow separation around an obstacle, flow in the dimpled channel, and flow in the upper human airway. In particular, the presented work exhibited the latent capability of the CS-FEM in solving turbulent flows near boundary regions and strong convection regions. Meanwhile, the results of the CS-FEM were compared to those of the lowest equal-order finite element method (i.e. P1–P1 or Q1–Q1 elements) in simulating turbulent flows, and it was found that the CS-FEM had better agreement with other published works.

Reynolds number effects on a velocity–vorticity correlation-based skin-friction drag decomposition in incompressible turbulent channel flows

A form of skin-friction drag decomposition is given based on the velocity–vorticity correlations, $\langle v\omega _z\rangle$ and $\langle -w\omega _y\rangle$ , which represent the advective vorticity transport and vortex stretching, respectively. This identity provides a perspective to understand the mechanism of skin-friction drag generation from vortical motions and it has better physical interpretability compared with some previous studies. The skin-friction coefficients in incompressible turbulent channel flows at friction Reynolds numbers from 186 to 2003 are divided with this velocity–vorticity correlation-based identity. We mainly focus on the Reynolds number effects on the contributing terms, their scale-dependence and quadrant characteristics. Results show that the contributing terms and their proportions exhibit similarities and the same peak locations across the wall layer. For the first time, we find that the positive and negative regions in the spanwise pre-multiplied spectra of the turbulent inertia ( $\langle v'\omega _z'\rangle +\langle -w'\omega _y'\rangle$ ) can be separated with a universal linear relationship of $\lambda _z^+=3.75y^+$ . The linear relationship is adopted as the criterion to investigate the scale dependence of the velocity–vorticity coupling structures. It reveals that the negative and positive structures dominate the generation of friction drag associated with the advective vorticity transport and vortex stretching, respectively. Moreover, quadrant analyses of the velocity–vorticity correlations are performed to further examine the friction drag generation related to different quadrant motions.

Enhancing the performance of vertical axis hydrokinetic Savonius turbines using a novel cambered hydrofoil profile for rotor blades

A novel rotor blade configuration using a cambered hydrofoil profile is developed to enhance the output power. Several design variables are considered including camber angle, overlap ratio, and camber position, in addition to integrating endplates. To assess the performance parameters at different design conditions, a comprehensive three-dimensional unsteady incompressible turbulent flow model based on Reynolds-Averaged Navier-Stokes equations combined with k-ω model is developed. The predicted numerical results is validated using the available numerical and experimental data. The findings indicate that using Savonius rotor with hydrofoil profile results in a substantial increase in the maximum output power for all investigated camber angles compared to the conventional semi-circular rotor. At a flow velocity of 0.4 m/s and an overlap ratio of 0.15, the Savonius rotor with hydrofoil profile attains a maximum power coefficient of 0.21 at a camber angle of 105°. By increasing the camber angle to 140°, the maximum power coefficient reaches 0.26 whereas it is 0.13 for the conventional design. The camber position at 50 % of the chord length achieves the highest power coefficient for all studied cases. In addition, adding the endplates significantly enhances the power coefficient. The current findings provide a promising approach in developing Savonius rotor blades configuration by utilizing hydrofoil profile.

A resolvent-based prediction framework for incompressible turbulent channel flow with limited measurements

A new resolvent-based method is developed to predict the space–time properties of the flow field. To overcome the deterioration of the prediction accuracy with increasing distance between the measurements and predictions in the resolvent-based estimation (RBE), the newly proposed method utilizes the RBE to estimate the relative energy distribution near the wall rather than the absolute energy directly estimated from the measurements. Using this extra information from RBE, the new method modifies the energy distribution of the spatially uniform and uncorrelated forcing that drives the flow system by minimizing the norm of the cross-spectral density tensor of the error matrix in the near-wall region in comparison with the RBE-estimated one, and therefore it is named as the resolvent-informed white-noise-based estimation (RWE) method. For validation, three time-resolved direct numerical simulation (DNS) datasets with the friction Reynolds numbers $Re_\tau = 180$ , 550 and 950 are generated, with various locations of measurements ranging from the near-wall region ( $y^+ = 40$ ) to the upper bound of the logarithmic region ( $y/h \approx 0.2$ , where h is the half-channel height) for the predictions. Besides the RWE, three existing methods, i.e. the RBE, the $\lambda$ -model and the white-noise-based estimation (WBE), are also included for the validation. The performance of the RBE and scale-dependent model ( $\lambda$ -model) in predicting the energy spectra shows a strong dependence on the measurement locations. The newly proposed RWE shows a low sensitivity on $Re_{\tau }$ and the measurement locations, which may range from the near-wall region to the upper bound of the logarithmic region, and has a high accuracy in predicting the energy spectra. The RWE also performs well in predicting the space–time properties in terms of the correlation magnitude and the convection velocity. We further utilize the new method to reconstruct the instantaneous large-scale structures with measurements from the logarithmic region. Both the RWE and RBE perform well in estimating the instantaneous large-scale structure, and the RWE has smaller errors in the estimations near the wall. The structural inclination angles around $15^\circ$ are predicted by the RWE and WBE, which generally recover the DNS results.

Employment of roughened absorber palate and jet nozzles with different hole shapes for performance boost of solar-air-heaters

In this study, roughened absorber plate and jet nozzle are simultaneously employed to enhance the efficiency of a solar based air heater. The impact of jet nozzle hole shape is comprehensively investigated for the mentioned system which have not been investigated before. Three-dimensional steady-state simulations of incompressible turbulent fluid flow and heat transfer are performed using the Reynolds-Averaged Navier-Stokes (RANS) equations to model the jet solar air heater (JSAH). Five different jet hole shapes (circular, triangular, square, hexagonal, and rectangular) are examined and results are compared with conventional structure. The thermal and hydraulic performance of the JSAH is assessed using a variety of geometric and operating parameters, including jet diameter ratio (dj/Dh), jet hole streamwise pitch (Lj/Dh), and Re number (Re). The results show that the ratio of (Nu/Nus) initially increases and then decreases as the hydraulic diameter of the jet holes increases. Circular jet holes consistently outperform other shapes, while rectangular and triangular jet holes perform poorly. The pressure penalty (f/fs) decreases with increasing (dj/Dh), with circular jet holes exhibiting the lowest value. Increasing the Reynolds number enhances heat transfer and pumping power but leads to a decrease in (Nu/Nus) and negatively affects the THPP of the JSAH compared to a conventional smooth solar air heater. The study also reveals that the THPP initially increases with streamwise pitch (Lj/Dh) but then declines, following the trend of (Nu/Nus). The results demonstrate up to 4.5 times higher Nusselt numbers with a jet solar air heater versus a smooth solar heater. A maximum thermal-hydraulic performance parameter of 1.64 indicates the proposed design's efficacy. This research furnishes critical insights into optimizing solar air heater performance by examining jet nozzle hole shape, streamwise pitch, and Reynolds number. It enables enhancing thermal efficiency and thermo-hydraulic performance.

Numerical Investigation on Separation Efficiency of a Novel Hybrid Engine Air-Particle Separator

This paper proposes a novel design for a hybrid engine air-particle separator filter (HEAPS) that combines the vortex tube separator (VTS) with the inertial particle separator (IPS) to enhance separation efficiency. Helicopters often operate in harsh environments, such as deserts, and landing on unprepared runways poses a severe risk to turboshaft engines due to the ingestion of dust and sand. This can result in significant damage to the engine's rotating components, impacting its life, reliability, and performance. To protect the engine from erosion and damage, an engine air particle separator system (EAPS) is installed in the engine inlet. In this study, a comparative numerical simulation was conducted between the hybrid filter and the VTS using the commercial software ANSYS Fluent. The Reynolds-averaged Navier–Stokes equations (RANS) were used to simulate incompressible turbulent flow, and the trajectory of particles was tracked using the Discrete Phase Model (DPM). Particle trajectories and separation efficiency were analyzed for different particle sizes, inlet velocities, and bypass mass flow ratios between the scavenge channel and the core engine channel. The results show that the hybrid design provides excellent separation efficiency, with a recovery efficiency of over 97%.

On the convergence of statistics in simulations of stationary incompressible turbulent flows

When reporting statistics from simulations of statistically stationary chaotic phenomenon, it is important to verify that the simulations are time-converged. This condition is connected with the statistical error or number of digits with which statistics can be reliably reported. In this work we consider numerical experiments of low Reynolds number incompressible homogeneous and isotropic turbulence as a model problem to investigate statistical convergence over finite simulation times. Specifically, we investigate the time integration requirements that allow meaningful reporting of the statistical error associated with finiteness of the temporal domain. We address two key questions: (1) How long should a simulation be performed in terms of large eddy time, and (2) How should the simulation time be divided among temporal windows over which a quantity of interest is estimated so that its statistical error could be reliably reported? We find that reliable reporting of statistical errors requires simulations on the order of 104 large eddy times, which is orders of magnitude longer than typically performed. Additionally, data post-processing should employ windows of at least ten times the large eddy time scale, with the most robust computation of statistical error of the mean requiring window sizes of an additional factor of ten. For practical simulations, we demonstrate that it is possible to estimate the statistical error within a factor of two under a less stringent condition in which a minimum of four windows with size at least ten large eddy times are used. Our observations for homogeneous isotropic turbulence are also shown to hold in turbulent channel flow.

Numerical simulation of subsonic flow around oscillating airfoil based on the Navier–Stokes equations

ABSTRACT Unsteady Reynolds-averaged Navier–Stokes equations of an incompressible fluid are used to numerically simulate the flow around an oscillating airfoil. A comparison is made between two differential one-equation turbulence models SA and SALSA on the problems of subcritical and supercritical turbulent incompressible flow around an oscillating NACA 0015 airfoil. The numerical algorithm utilized for solving the governing equations is founded upon a three-layer implicit scheme, which exhibits second-order integration accuracy in time, third order of upwind approximation of convective terms, and second-order symmetric approximation of the diffusion terms. Pressure and velocity field coupling is achieved through the implementation of the artificial compressibility approach, which is employed for the computation of unsteady problems. The system of initial equations is numerically integrated using the control volume method. The resulting system of algebraic equations has been solved by the GMRES method with ILU(k) preconditioning. The obtained instantaneous streamlines, vorticity contours, and hysteresis curves of unsteady airfoil aerodynamic loads are analyzed for cases of weak ( α 0 = 4 ° ), developed ( α 0 = 11 ° ) and massive ( α 0 = 15 ° ) flow separation at Reynolds number Re = 1.95 × 10 6 . In the case of weak flow separation, the values of the lift coefficient obtained using the SA and SALSA models differ from the experimental data by 10% and 5%, respectively. With a developed separation, these values are already equal to 10–20% for the SA model and 6–8% for the SALSA model. The average values of the lift coefficient, which are obtained using the SA and SALSA models, in the case of massive flow separation, differ from the experimental data by 50–60% and 10–15%, respectively. Comparing the calculation results with both known experimental and calculated data demonstrates that in flows with developed and massive flow separation, which are characterized by unsteady effects in turbulence, the SALSA turbulence model performs better than other tested models. The aerodynamic coefficients obtained with the SALSA turbulence model are in 10–15% better agreement with experimental data than those obtained with other turbulence models.

Unsteady incompressible flow over a backward-facing step using FEniCS

This study demonstrates unsteady incompressible flow over a backward-facing step and a cylinder section using a finite element scheme for solving the unsteady Navier-Stokes equation called the incremental pressure correction scheme (IPCS). The speed and accuracy of the study were boosted by using an open-source framework. The formulation was done using the C++/Python-based computing platform called FEniCS. Gmsh is the mesh generator used to make the meshes. Krylov solvers, parallel processing, and higher-order function spaces of order above two are available in FEniCS and these enable faster and more accurate analyses. Most commercial software packages do not include these functionalities. The analysis of the backward-facing step was performed using legacy FEniCS. The DFG benchmark 2D-3 unsteady analysis in Featflow was conducted using FEniCSx. The pressure difference between the front and back of the cylinder and the drag and lift coefficients were calculated and compared to the benchmark. The graphs of these characteristics were plotted with respect to time along with their mean squared errors. The outcomes demonstrate how efficient the open-source FEM platform on display is at handling fluid flow simulations. Therefore, any turbulent incompressible flow may be simulated using the same open-source structure. [copyright information to be updated in the production process]

A three-dimensional high-order flux reconstruction lattice boltzmann flux solver for incompressible laminar and turbulent flows

A three-dimensional (3D) high-order flux reconstruction lattice Boltzmann flux solver (FR-LBFS) is developed in this paper for accurate and efficient simulations of incompressible laminar and turbulent flows. The original lattice Boltzmann flux solver (LBFS) is a second-order finite volume method (FVM) which combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice Boltzmann equation (LBE) solvers. But it is not convenient to construct high-order FVM, and the compactness is always a bottleneck. The present work separates LBFS from FVM and combines LBFS with high-order FR scheme. Thus, the FR-LBFS inherits the superiority of LBFS and FR and shares the following attractive features: (i) a fully-explicit arbitrary order compact method, (ii) weakly compressible (WC) model for unsteady incompressible flows and (iii) evaluating inviscid and viscous fluxes simultaneously and no particular technique requirement, such as local discontinuous Galerkin method (LDG), for viscous term discretization. To validate the current method, various 3D incompressible laminar isothermal and thermal numerical experiments are presented first. Good agreements are achieved between the current results and the previous experimental and numerical data whilst the present high-order solver adopt coarse meshes. Furthermore, the ability of the proposed method to perform accurate and stable computations of incompressible decaying homogeneous isotropic turbulent flows and turbulent channel flows with different mesh resolutions and accuracy orders are investigated. The results show that the present 3D FR-LBFS is a promising tool for under-resolved or implicit large eddy simulation (ILES) of incompressible turbulent flows.

Active control of pressure fluctuations in an incompressible turbulent cavity flow

Large-eddy simulations of incompressible turbulent boundary layer flows over an open cavity are conducted to investigate the effects of wall-normal steady blowing on the suppression of pressure fluctuations on the cavity walls. The length (L) to depth (D) ratio (L/D) of the cavity is 2 and the Reynolds number based on the cavity depth (ReD) is 12,000. Wall-normal steady blowing is imposed through a limited transverse slot in an upstream region of the cavity leading edge while varying the momentum coefficient (Cμ). As the value of Cμ increases, the pressure fluctuations on the cavity walls decrease mostly due to weakened impingement of turbulent vortical structures residing in the shear layer on the aft wall by lifting effects, reaching a maximum reduction of −7.61% compared to a baseline when Cμ=0.015. However, as the value of Cμ increases further, the pressure fluctuations increase gradually, exceeding that of a baseline when Cμ>0.05. Because intensified turbulent vortical structures in the shear layer with an increase of Cμ lead to strong interactions of small-scale vortices with the cavity walls with an accompanying large motion of the primary recirculation zone within the cavity, additional pressure fluctuations generated on the cavity walls deteriorate the control performance due to the blowing.

Neural networks for large eddy simulations of wall-bounded turbulence: numerical experiments and challenges.

We examine the application of neural network-based methods to improve the accuracy of large eddy simulations of incompressible turbulent flows. The networks are trained to learn a mapping between flow features and the subgrid scales, and applied locally and instantaneously-in the same way as traditional physics-based subgrid closures. Models that use only the local resolved strain rate are poorly correlated with the actual subgrid forces obtained from filtering direct numerical simulation data. We see that highly accurate models in a priori testing are inaccurate in forward calculations, owing to the preponderance of numerical errors in implicitly filtered large eddy simulations. A network that accounts for the discretization errors is trained and found to be unstable in a posteriori testing. We identify a number of challenges that the approach faces, including a distribution shift that affects networks that fail to account for numerical errors.

Analytical and numerical investigations of fluid flow and heat transfer in turbulent slip incompressible flow in a cylindrical channel

Based on two analytical approaches (Prandtl model and von Kármán model), turbulent flow in a cylindrical channel with flow slippage on the wall was considered. The results of the analytical solution are supplemented with numerical simulations based on the lattice Boltzmann model (LBM). Validations of the analytical model against numerical computations showed their good agreement. The analytical model enabled obtaining relations for the velocity profile, hydraulic resistance coefficient and Stanton number, which make it possible to evaluate the influence of the slip effect (Kn) and the flow rate (Re) on their variation.