Turbulence modeling

Sloshing refers to the oscillating movement of free surface of the liquid. This paper presents various methods proposed for simulation of sloshing phenomenon in partially filled liquid containers. Understanding slosh dynamics has several applications in different fields of engineering. The impact pressure on the container due to liquid sloshing governs numerous designs of machinery ranging from simple liquid carrying truck to propellant tanks in spacecrafts and tanks in ships and the design of liquid retaining structures prone to seismic excitation. Experimental method, analytical approach and numerical methods are used to predict sloshing responses. This paper focuses on various numerical methods proposed, validated, and are widely used in liquid sloshing. The methods differ from each other in ways of treating the free surface of the liquid, discretization methods used, assumptions made and consequently the governing equations of flow chosen.

This book contains a collection of the main contributions from the first five workshops held by Ercoftac Special Interest Group on Synthetic Turbulence Models (SIG42. It is intended as an illustration of the sig’s activities and of the latest developments in the field.

This volume investigates the use of Kinematic Simulation (KS) and other synthetic turbulence models for the particular application to environmental flows.
This volume offers the best syntheses on the research status in KS, which is widely used in various domains, including Lagrangian aspects in turbulence mixing/stirring, particle dispersion/clustering, and last but not least, aeroacoustics. Flow realizations with complete spatial, and sometime spatio-temporal, dependency, are generated via superposition of random modes (mostly spatial, and sometime spatial and temporal, Fourier modes), with prescribed constraints such as: strict incompressibility (divergence-free velocity field at each point), high Reynolds energy spectrum. Recent improvements consisted in incorporating linear dynamics, for instance in rotating and/or stably-stratified flows, with possible easy generalization to MHD flows, and perhaps to plasmas. KS for channel flows have also been validated. However, the absence of "sweeping effects" in present conventional KS versions is identified as a major drawback in very different applications: inertial particle clustering as well as in aeroacoustics. Nevertheless, this issue was addressed in some reference papers, and merits to be revisited in the light of new studies in progress.

Content Level » Research

Keywords » atmospheric flows - fractal fluids - isotropic turbulence - lagrangian dispersion - multiphase flows - super fluids - synthetic turbulence models

We present some remarks about the CFL condition for explicit time discretization methods of Adams–Bashforth and Runge–Kutta type and show that for convection-dominated problems stability conditions of the type Δt≤CΔx^α are found for high order space discretizations, where the exponent α depends on the order of the time scheme. For example, for second order Adams–Bashforth and Runge–Kutta schemes we find α=4/3.

The Navier-Stokes differential equations describe the motion of fluids which are incompressible. The three-dimensional Navier-Stokes equations misbehave very badly although they are relatively simple-looking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would dramatically alter the
field of fluid mechanics. This paper describes why the three-dimensional Navier-Stokes equations are not solvable, i.e., the equations cannot be used to model turbulence, which is
a three-dimensional phenomenon.

This guide recommends methods for the estimation of pressure drop for the steady state flow of single phase Newtonian liquids and compressible fluids (gases and vapors) in pipe systems. It covers most of the geometries likely to be encountered in normal design cases.

"Quantitative methods are increasingly important in the earth sciences but there are few good books specifically written to help earth scientists develop the mathematical tools that they need. This book helps to fill the gap by providing a concise introduction to mathematical modelling with an emphasis on examples taken from the earth sciences. One of the major strengths of the book is that it is possible to get a good overview of a whole topic during an initial read of the relevant chapter without getting too bogged down in detail. Where additional detail is provided it is invariably worth further study. Another strength of the book is the large number of worked examples embedded in the text almost every other double-page spread seems to have one. With very few exceptions, these examples are of great help in providing both focus and clarity to what may sometimes seem a little obscure. The style of the book is informal - I wish that it had been available when I was an undergraduate to help counterbalance the theorem-and-proof approach that I was subjected to... In short, the book provides excellent value for money and is a well-crafted introduction to mathematical modelling for earth scientists. Armed with insights obtained from this book, the reader will be well placed for further study of selected topics at the next level of detail. "
--Geoscientist, January 2009


Mathematical modelling and computer simulations are an essential part of the analytical toolset used by earth scientists. Computer simulations based on mathematical models are routinely used to study geophysical, environmental and geological processes in many areas of work and research from geophysics to petroleum engineering and from hydrology to environmental fluid dynamics. Dr Yang has carefully selected topics which will be of most value to students and has recognised the need to be careful in his examples whilst being comprehensive enough to include important topics and popular algorithms. The book is designed to be theorem-free and yet to balance formality and practicality. Using worked examples and tackling each problem in a step-by-step manner the text is especially suitable for non-mathematicians approaching this aspect of earth sciences for the first time, The coverage and level, for instance in the calculus of variation and pattern formation, that even mathematicians will find the examples interesting. Topics covered include: vector and matrix analysis ordinary differential equations partial differential equations calculus of variations integral equations probability geostatistics numerical integration optimisation finite difference methods finite volume methods finite element methods reaction-diffusion system elasticity fracture mechanics poroelasticity, and flows in porous media. Mathematical Modelling for Earth Sciences introduces a wide range of mathematical modelling and numerical techniques, and is written for undergraduates and graduate students.

This document is one of a series on fluid flow produced by GBH Enterprises.

If a rapid change is made to the flowrate of a liquid in a piping system, for example by the operation of a valve, a transient pressure change will be propagated through the system. This transient pressure may be significantly greater than either the initial pressure or the final steady state pressure which the system reaches. This may cause damage to the piping system; either by exceeding the design pressure of the piping system with consequent risk of rupture, or by producing out of balance forces which are greater than can be sustained by the pipe supports. The phenomenon known as 'water hammer' is a special case of 'pressure surge'.

This work aims for the numerical study of gas turbine combustors using the
computational tool ANSYS® WorkbenchTM, having as a proposal an approach of using the k-ω SST model combined with the steady flamelet PDF model with treatment of radiation by the DO model. Based on this objective, the proposal was the study of two combustors, one of low-emission based on references and the other designed using a simple thermal cycle of gas turbines.
On what refers the reference combustor, this was treated to concretize the
methodology to be applied on the study of the designed tubular diffusion combustor. It was identified that the approach used gives the best results when using a SOU scheme for the treatment of the advective terms. From what resulted the precision limits of the applied methodogoly considering the experimental and numerical results obtained for the low-emission combustor.
For the design of the diffusion combustor, it was used zero and one-dimensional
analysis, from what the combustor was numerically implemented. Between the objectives of this numerical study, the main one was to evaluate the effect of centrifugal forces on combustion focusing on the investigation of the influences of these on a reactive flow of a generic tubular combustor, using a moving wall boundary condition applied on the combustor casing.

Single-phase Euler-Euler based wall-resolving LES with the dynamic Smagorinsky
model is used to investigate suspended sediment transport in a turbulent
open channel
ow. Aspect ratio of the open channel is high. Bottom bed is
smooth. For the clear water
ow, streamwise and vertical turbulence intensities
in experiments of Muste et al. [2005] are much bigger than those in the
wall-resolving LES and DNS by Hoyas and Jimenez [2008]. Bulk velocity in the
sediment-laden
ow is lesser than that in the clear water
ow. Friction velocity
is same for both
ows. While Muste et al. [2005] recorded that in the inner
region, the streamwise velocity of the sediment-laden
ow was higher than that
of the clear water
ow, wall-resolving LES shows no alteration. In the outer region,
the depth-resolved streamwise velocity of the sediment-laden
ow is lower
than that of the clear water
ow. Introduction of suspended sand particles into
the turbulent open channel
ow of the clear water results in the decrease of the
drag force while shear stress on the channel bed is constant. To get reduction
of the bulk velocity, the fast Eulerian method in the two-way coupling should
be employed.
Single-phase Euler-Euler based unresolved wall-function LES with the Smagorinsky
model under the equilibrium stress assumption is implemented to understand
interactions between turbulence and suspended sand particles in a turbulent
open channel
ow. Channel bed is rough. Aspect ratio of the open channel
is low. To treat erosion from the bed, the reference concentration method
together with the Shields diagram is used. Results are compared against experiments
of Cellino [1998]. Suspended particles engender reduction of the friction
velocity, bulk velocity and roughness in contrast to the clear water
ow.
Streamwise velocity is decreased in the outer region while it is expedited in the
super-saturated region near the channel bed. It is due to high inter-particle
collisions between sediment particles which are not bounded by viscosity. In
upper levels, remarkable weakening of the vertical turbulence intensity is seen.
When the buoyancy term is deactivated, the sediment concentration gets high
and unsatisfactory turbulence statistics are obtained. Wall shear stress on the
sidewalls of narrow open channels must be considered.
Eects of lateral and bottom macro-rough boundaries on the propagation of
a suspended sediment wave in a turbulent open channel
ow are shown experimentally.
Least decay of the normalized concentration is for the reference case in absence of trapping zone. Least sedimentation among lateral congurations
is for case L4 with the highest roughness aspect ratio, cavity density and
medium
ow discharge. Length of the inlet reach is lowest and it boosts mixing.
Highest deposition of the Polyurethane particles is for case L5 with the lowest
roughness aspect ratio and cavity density. Discharge is also low. Turbulence is
most attenuated for case L2 with the medium
ow discharge due to adequate
lengths of the inlet and outlet reach. Deposition of the Polyurethane particles
and turbulence in the lateral macro-rough
ows depend on the cavity aspect
ratio,
ow discharge, roughness aspect ratio, cavity density and location of the
lateral cavities. In the bottom macro-rough
ows, eects of spacing between
bottom macro-rough elements on the deposition and turbulence characteristics
are seen. Turbulence characteristics of upstream C1 and downstream C2 signals
are identical for reference, B1 and B1:5 cases. When spacing is 2, highest trapping
and deposition take place. Most weakening of the turbulence is seen for
spacing 2. When spacing is augmented from 2 to 5, the turbulence is enhanced
and trapping becomes lesser. Bottom macro-rough elements change signicantly

ow pattern and turbulence characteristics in a specic spacing. As spacing gets
larger, eects of bottom macro-roughness elements on each other reduces more.

This work deals with the development of the standard Spalart-Allmaras (SA) one equation eddy viscosity turbulence model. The SA model saves considerable amount of computational effort compared to two-equation models like k-epsilon or k-ω while giving fairly good and more accurate results than the algebraic models. The rationale behind the formulation of its individual terms is discussed on the basis of physics of turbulence and the requirements of dimensional homogeneity, Galilean invariance and scalar form. The model gives fairly accurate results for incompressible and weakly compressible flows. However, depending on the conditions of the flow, it can be calibrated by adding new terms or modifying the already existing terms. To extend
its predictive capability for compressible flows for e.g. in cases of supersonic and hypersonic flows, compressibilty corrections suggested by Catris et al. and Allmaras et al. have been discussed. Modifications for non-equilibrium flow conditions and for compressible mixing layers are also described briefly.

In spite of the attractiveness of CFD methods and advanced measurement methods, there is still no full analysis of aerodynamic blade loads for vertical axis Darrieus-type wind turbines. Due to an inherently unsteady flow around the rotor blades, blade-wake-blade interaction and the occurrence of dynamic stall, the aerodynamics of this type of wind turbine is very complex. A two-bladed rotor have been investigated numerically for the tip speed ratio of 5.0. This paper compares results for aerodynamic blade loads obtained applying such turbulence models as: the standard k-ε; the RNG k-ε; the Realizable k-ε and the SST k-ω. As a result, quantitative instantaneous blade forces as well as instantaneous wake profiles behind the rotor have been obtained. Aerodynamic wake behind the rotor is also visualized by using streak lines. All CFD results are compared with experimental data taken from literature. Good agreement between the numerical results and the experiment is shown for the aerodynamic blade loads as well as for aerodynamic wake behind the rotor.

The study provides two-dimensional numerical results of flashing liquid oxygen flow in a converging diverging flow meter with different operating conditions. The main difference being the 1136 𝑘𝑃𝑎 and 1830 𝑘𝑃𝑎 inlet pressures. Numerical results utilized two different turbulence models being SST k-omega and realizable k-epsilon models, and a mass transfer model using the Hertz-Knudsen equation with the accommodating coefficient (𝜆) set to 0.1 and 0.07. The numerical results were presented in a comparative manner. Flow behavior such as choked flow due to sonic velocity and phase-change at the throat and shock wave formation downstream of the throat were captured and compared between the different models utilized. SST k-omega proved to be the more suitable turbulence model due to its ability to capture the shock wave at the correct location and the subsequent re circulation occurring at the nozzle wall. The k-epsilon model failed to capture this effectively due to its known insensitivity of adverse pressure gradients. The lower accommodating coefficient (𝜆) produces results with greater vapor generation around the throat region however both accommodating coefficients overestimated this vapor generation near the throat region and did not produce a close agreement with the experimental results.

A parametric study on a 2D rectangular nozzle is numerically simulated using ANSYS Fluent. Turbulent model of RNG K-ε is used with a UDF turbulent viscosity treatment. The Schnerr and Sauer Model is used to model the evaporation and condensation of the cavitation behaviour. Round, sharp, and chamfered upstream corner is analysed to see
their affect on the cavitation with r/D value of 1/10 for round and chamfered. The round and chamfered is found to reduce the cavitation length from the outlet to about 1.5mm down the upstream corner. Two tapered nozzles of K factor 1.5 and 20 are analysed and found the K factor of 1.5 severely reduced the cavity formed and when K = 20, the cavitation is completely reduced. Bubble number density is varied by a magnitude of 3 higher and lower. The lower change did not produce any significant changes whereas the higher one produced a smaller cavitation bubble that is seen to be more unstructured. Increasing the bubble number density did not see the increase of the mass transfer rate as expected.

This paper presents aerodynamic investigations of the DU-91-W2-250 airfoil at Reynolds number of 3·10 6 employing 2D Reynolds-averaged Navier–Stokes (RANS) solver and 3D detached eddy simulation (DES) technique. RANS simulations are performed in the angle of attack range between-20° and +20° whereas DES results are given only for the angle of attack of 7.08°. Measurements have been done at the LM Wind Power Low Speed Wind Tunnel. The lift and drag are obtained from airfoil pressure and wake rake respectively. The obtained numerical results, lift and drag coefficients as well as static pressure distributions are in a good agreement with the experimental results in the linear part of the lift coefficient curve. The Transition SST turbulence model gives much more appropriate results in comparison with the k-ω SST model, especially for the drag at low angles of attack. The DES approach allows to obtain 3D flow characteristics near the S-shaped airfoil tall. 1. Introduction In multi-megawatt horizontal-axis wind turbines thick profiles (≥25%) are used at inboard and mid-span regions. Thick airfoils provide higher stiffness of blades and lower weight reducing costs and fatigue loads. The following aerodynamic requirements are desirable at midspan: low roughness sensitivity, moderate to high lift and high lift-to-drag ratio. A DU 91-W2-250 airfoil with a maximum thickness of 25% thickness is developed at the Delft University of Technology. Small upper surface thickness of the DU 91-W2-250 reduces roughness sensitivity. In order to achieve sufficient lift an S-shaped aft-loading tail is used. Timmer and van Rooij [1] investigated aerodynamic performance of a series of DU airfoils in a wind tunnel and using a modified version of XFOIL. Aerodynamic performance of the DU91-W2-250 profile can be significantly increased by using vortex generators [2]. Rooij and Timmer [3] examined the effect of roughness on the performance of a few airfoils dedicated for large wind turbines. These authors concluded that the DU 91-W2-250 profile is one of the special purpose airfoils that has the lowest roughness sensitivity and the best overall performance. Lift and drag coefficients and pressure coefficients for the DU 91-W2-250 airfoil were computed using XFOIL and RFOIL programs at a Reynolds number of 1·10 6 [4]. Nowadays computational methods in fluid dynamics have become a popular tool in the design of aircraft and wind turbines airfoils. Raciti Castelli et al. [5] investigated capabilities of two turbulence

Although the problem of 2D ribbed channels has been studied heavily in the literature as a benchmark or basic case for cooling of electronic packing, there is still a contradiction in the literature about the suitable turbulence model that should be used in such a problem. The accuracy of the computational predictions of heat transfer rates depends mostly on the choice of the proper turbulence model that is capable of capturing the physics of the problem, and on the corresponding wall treatment. The main objective of this work is to identify the proper turbulence model to be used in thermal analysis of electronic systems. A number of available turbulence models, namely, the standard k-ε, the renormalization group k-ε, the shear stress transport (SST), the k-ω, and the Reynolds stress models, have been investigated. The selection of the most appropriate turbulence model has been based upon comparisons with both direct numerical simulations (DNSs) and experimental results of other wor...

A set of three tubes, namely, Simple Metallic Tube (SMT), the Straight Groove Tube and the Groove Tube with 12 inch pitch were numerically studied. The tube data and experimental findings on it were extracted from published article by Arunrat. Performance criteria was based on the heat transfer via Nusselt number as well as the friction factor. For numerical performance, the performance was evaluated on the basis of turbulence models, while for the heat transfer performance, it was evaluated with the thermal performance factor. Between the two turbulence models tested and the given range of Reynolds number, it was found that k-ω SST is the most suitable candidate for this range of Reynolds number due to its closeness to the experimental data. Among the three tubes tested and making the SMT the baseline, the GT12 performed better and has η better at most of the Reynolds numbers.

We present and evaluate a two-phase model for Eulerian large-eddy simulations (LES) of liquid-fuel injection and mixing at high pressure. The model is based on cubic equations of state and vapor-liquid equilibrium calculations and can represent the coexistence of supercritical states and multi-component sub-critical two-phase states via a homogeneous mixture approach. Well-resolved LES results for the Spray A benchmark case of the Engine Combustion Network (ECN) and three additional operating conditions are found to agree very well with available experimental data. We also address well-known numerical challenges of trans-and supercritical fluid mixing and compare a fully conservative formulation to a quasi-conservative formulation of the governing equations. Our results prove physical and numerical consistency of both methods on fine grids and demonstrate the effects of energy conservation errors associated with the quasi-conservative formulation on typical LES grids.

A recent Letter by Oberlack et al. [Phys. Rev. Lett. 128, 024502 (2022)] claims to have derived new symmetry-induced solutions of the non modelled statistical Navier-Stokes equations of turbulent channel flow. A high accuracy match to DNS data for all streamwise moments up to order 6 is presented, both in the region of the channel-center and in the inertial sublayer close to the wall. Here we will show that the findings and conclusions in that study are highly misleading, as they give the impression that a significant breakthrough in turbulence research has been achieved. But, unfortunately, this is not the case. Besides trivial and misleading aspects, we will demonstrate that even basic turbulence relevant correlations as the Reynolds-stress cannot be fitted to data using the proposed symmetry-induced scaling laws. The Lie-group symmetry method as used by Oberlack et al. cannot bypass the closure problem of turbulence. It is just another assumption-based method that requires modelling and is not, as claimed, a first-principle method that leads directly to solutions. Next to PRL, two more papers by Oberlack et al. are called out for correction or a retraction.

"This paper describes a Chebyshev collocation method for solving the eigenvalue problem that governs the linear stability of fluid film flow down an inclined plane in presence or absence of surfactant at arbitrary Reynolds numbers. The method is based on the expansion of the eigenfunctions in terms of Chebyshev polynomials, point collocation, and the subsequent solution of the resulting generalized eigenvalue problem with the QZ-algorithm. This method is developed to solve Orr-Sommerfeld equation. The results in the absence of surfactant are compared with those presented by Yih. Finally the effect of inertia and Marangoni mode which appears when insoluble surfactant is present is investigated. The effect of instability modes, the Yih mode which is associated with perturbation on fluid film surface and Marangoni mode which is associated with variation of surfactant surface concentration, are studied for flow instability at arbitrary Reynolds numbers. The agreement between the obtained results at limited conditions and also results from other researchers shows the effectiveness of Collocation Method and suggested profiles.
Key words: Collocation, linear stability; Orr-Sommerfeld; Marangoni; Surfactant; Perturbation analysis"

55 pages

including patents
Wo 2013,017,232 (AVL)
US 3,39,724 by Daimler-Benz
JP 60,001,327 (Mazda)
+ the papers:
  » Effect of spark plug arrangement on flame propagation of rotary engine
  » Amelioration of combustion of hydrogen rotary engine (influence of turbulence)

german keywords: Wankelmotor / Kreiskolbenmotor
English Keywords: Wankel Engine / Wankel Rotary Engine / Rotary Piston Engine / Rotary Combustion Engine

With the observation that the TENO weighting strategy can explicitly distinguish smooth scales from nonsmooth scales in spectral space, in this paper, a new discontinuity indicator is proposed based on the high-order TENO paradigm [Fu et al., JCP 305(2016): 333-359]. The local flow structures are classified as smooth or non-smooth scales, and the hybrid numerical discretization scheme is applied correspondingly , i.e. the high-order upwind linear scheme without characteristic decomposition is employed for resolving smooth scales while the nonlinear low-dissipation TENO scheme is adopted to capture discontinuities. Since the time-consuming characteristic decomposition and smoothness-indicator computation of TENO are avoided in smooth regions, the overall computational efficiency can be improved significantly. Moreover, the cutoff wavenumber separating smooth and nonsmooth scales is determined by the parameter C T. In contrast to the thresholds of other discontinuity indicators , which are typically defined in physical space, C T takes effects in wavespace rendering its high generality. A set of benchmark cases with widespread length-scales is simulated to assess the performance of the proposed discontinuity indicator and the resulting hybrid shock-capturing scheme. Compared to the monotonicity-preserving discontinuity indicator and the TVB discontinuity indicator, the proposed algorithm delivers better performance with a fixed set of parameters for all considered benchmarks .

This paper presents numerical results of the DU-91-W2-250 airfoil. Reynolds-averaged Navier–Stokes (RANS) simulations of the 2D profile are performed employing the Transient SST turbulence model. The airfoil was investigated for the Reynolds number of 6·10 6. Lift and drag coefficients are compared with the experimental data from LM Low Speed Wind Tunnel (LSWT). The results of lift and drag coefficients obtained using the SST Transient model are in a good agreement in comparison with the experiment in the angle of attack range from-10° to 10°. The static pressure distributions calculated by the SST Transition model are also in good agreement with the experiment.

This research was funded by, and implemented within, a UK national research organisation, while the author was the KE and Impact Evaluation Manager responsible for assessing impact on a £15m UK government-funded research programme.

This work was also submitted as the authors MBA dissertation which was accepted and awarded in 2009.

ABSTRACT: A methodology and methods ‘toolbox’ is proposed for conducting impact research and assessment from within research programmes. The emphasis is upon how to clarify and assess the wider impacts from the early stages onwards.

The approach explicitly acknowledges, and attempts to address, the known issues and challenges of impact assessment while drawing upon the resources and opportunities available to research managers and researchers within such programmes.

The study has two triangulating foundations. Firstly, it examines the academic literature to help identify and design the pilot methodology and methods. Secondly it trials these in a real programme to both test and improve them.

The study was conducted over one year within one leading UK research organisation, where two research programmes (and around 60 research projects of £15m total value) were being assessed for their impacts. The study draws upon actual impact management experience and reflection, prospective (ex ante) and retrospective (ex post) assessments, participatory contributions from leading researchers undergoing assessment, and consultation with external users. The findings of this study outline the pilot and its first iteration. Recommendations are made for improvement to the methodology and methods.

A subsequent follow-on bid to UK government incorporating the impacts identified from implementing this methodology, successfully led to a further £15m of government funding.

It is expected the pilot methodology and methods will be applicable to other organisations, conducting and funding such research programmes, required to research and assess the wider research impacts.

Although primary focus of implemetation trials was upon research in physical sciences, technology, high-tech engineering, computing/IT, and environment, the wider literature study, the methodology design and justification, the methods proposed and used, and the resulting general recommendations and lessons are expected to apply more broadly to many other research areas, where the impact is to be found more widely in the society, economy, government or public sector or within organizations, policies, professions or the public.

Interest in this work is expected from research programme managers, impact managers and assessors, management consultants advising in this area, and government funding managers, all seeking to embed a developing approach to understand, capture, and enhance wider impact.

We present explicit and implicit large eddy simulations for fully developed turbulent pipe flows using a continuous-Galerkin spectral element solver. On the one hand, the explicit stretched-vortex model (by Misra & Pullin [45] and Chung & Pullin [14]), accounts for an explicit treatment of unresolved stresses and is adapted to the high-order solver. On the other hand, an implicit approach based on a spectral vanishing viscosity technique is implemented. The latter implicit technique is modified to incorporate Chung & Pullin virtual-wall model instead of relying on implicit dissipative mechanisms near walls. This near-wall model is derived by averaging in the wall-normal direction and relying in local inner scaling to treat the time-dependence of the filtered wall-parallel velocity. The model requires space-time varying Dirichlet and Neumann boundary conditions for velocity and pressure respectively. We provide results and comparisons for the explicit and implicit subgrid treatments and show that both provide favourable results for pipe flows at Re τ = 2 × 10 3 and Re τ = 1.8 × 10 5 in terms of turbulence statistics. Additionally, we conclude that implicit simulations are enhanced when including the wall model and provide the correct statistics near walls.