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=DNS Channel Flow= | |||
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= Introduction = | = Introduction = | ||
The turbulent Channel Flow is one of the canonical flows used to study turbulence in wall bounded turbulence. DNS of turbulent channel flow were undertaken at <math>Re_\tau=180</math>. | |||
DNS were undertaken using PyFR (http://www.pyfr.org/) version 1.12.0: | DNS were undertaken using PyFR (http://www.pyfr.org/) version 1.12.0: | ||
<ul> | <ul> | ||
<li> based on the high-order flux reconstruction method of Huynh </li> | <li> based on the high-order flux reconstruction method of Huynh<ref name="hyunh">''Huynh, H. T.'', A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods, AIAA, 2007-4079, 1-42, 2007.</ref> </li> | ||
<li> compressible solver </li> | <li> compressible solver </li> | ||
<li> a Rusanov Riemann solver was employed to calculate the inter-element fluxes </li> | <li> a Rusanov Riemann solver was employed to calculate the inter-element fluxes </li> | ||
<li> an explicit RK45[2R+] scheme was used to advance the solution in time </li> | <li> an explicit RK45[2R+] scheme<ref name="rk452r">''Kennedy, C. A., Carpenter, M. H. & Lewis, R. M'', Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations, Appl. Numer. Maths, 35(3), 177-219, 2000.</ref> was used to advance the solution in time </li> | ||
<li> Fifth order polynomials are used for the computations </li> | <li> Fifth order polynomials are used for the computations </li> | ||
</ul> | </ul> | ||
= Review of previous studies = | = Review of previous studies = | ||
Provide a brief review of related past studies, either experimental or computational. Identify | Turbulent channel has been one of the canonical test cases to study the characteristics of wall bounded turbulence. | ||
The simplified setup proposed by Kim et al. (1987)<ref>''Kim,J., Moin, P. & Moser, R.'', Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177, 133-166, 1987</ref> is now a standard test case for wall bounded turbulent flow simulations. | |||
The setup is computationally inexpensive as it a periodic channel flow with periodic boundary conditions in the spanwise and streamwise directions. | |||
With recent progress made in computing infrastructure, Reynolds numbers as large as <math>Re_\tau=4000</math> (Bernardini et al. 2014) and <math>Re_\tau=6000</math> (Pirrozoli et al. 2021) are now available. Nevertheless, the <math>Re_\tau=180</math> case by Kim et al. still remains | |||
as a benchmark case for wall bounded turbulent flow simulations. | |||
<!--Provide a brief review of related past studies, either experimental or computational. Identify | |||
the configuration chosen for the present study and position it with respect to previous studies. | the configuration chosen for the present study and position it with respect to previous studies. | ||
If the test case is geared on a certain experiment, explain what simplifications ( e.g. concern- | If the test case is geared on a certain experiment, explain what simplifications ( e.g. concern- | ||
ing geometry, boundary conditions) have been introduced with respect to the experiment in the | ing geometry, boundary conditions) have been introduced with respect to the experiment in the | ||
computational setup to make the computations feasible and avoid uncertainty or ambiguity. | computational setup to make the computations feasible and avoid uncertainty or ambiguity.--> | ||
= Description of the test case = | = Description of the test case = | ||
A | An idealised channel flow, without side walls, is considered. The details of the case are given in [https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/identifying-eigenmodes-of-averaged-smallamplitude-perturbations-to-turbulent-channel-flow/EF03E2FFFF1A481FC55448B3F11496F2 Iyer et al.(2019)]<ref name="iyer2019">''A. Iyer, F. D. Witherden, S. I. Chernyshenko & P. E. Vincent'', Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow, Journal of Fluid Mechanics, 875 (758-780), 2019</ref>. The current set of simulations has a higher grid resolution in the wall normal direction where there are 174 solution points compared to 95 points in the simulations of Iyer et al. | ||
==Geometry and flow parameters== | ==Geometry and flow parameters== | ||
Describe the general set up of the test case and provide a sketch of the geometry, clearly identifying location and type of boundaries. Specify the non-dimensional flow parameters which define the flow regime (e.g. Reynolds number, Rayleigh number, angle of incidence etc), including the scales on which they are based. Provide a detailed geometrical description, by preference in form of a CAD, or alternatively as lists of points and a description of the interpolation. | The geometry is a cuboid of dimensions <math>8\pi</math> units in the streamwise direction <math>(x)</math>, 2 units in the transverse direction <math>(y)</math> and <math>4\pi</math> units in the spanwise direction <math>(z)</math>, as shown in figure 1. The dimensions are normalised by the channel half-width, <math>h</math> and centreline velocity. | ||
<div id="figure2"></div> | |||
{|align="center" | |||
|[[Image:Channel iyer2019.gif|400px]] | |||
|- | |||
|''Figure 1:'' Computational domain from Iyer et al. (2019) | |||
|} | |||
<!-- Describe the general set up of the test case and provide a sketch of the geometry, clearly identifying location and type of boundaries. Specify the non-dimensional flow parameters which define the flow regime (e.g. Reynolds number, Rayleigh number, angle of incidence etc), including the scales on which they are based. Provide a detailed geometrical description, by preference in form of a CAD, or alternatively as lists of points and a description of the interpolation. --> | |||
==Boundary conditions== | ==Boundary conditions== | ||
Specify the prescribed boundary conditions, as well as the means to verify the initial flow development. In particular describe the procedure for determining the in flow conditions comprising the instantaneous (mean and fluctuating) velocity components and other quantities. Provide reference profiles for the mean flow and fluctuations at in flow - these quantities must be supplied separately as part of the statistical data as they are essential as input for turbulence-model calculations. For checking purposes, these profiles should ideally also be given downstream where transients have disappeared; the location and nature of these cuts should be specified, as well as the reference result. | Periodicity conditions are imposed in the streamwise and spanwise boundaries which gives a flow developing in time. The transverse boundaries are no-slip walls. The initial density and pressure fields are uniform. The initial velocity field is <math>(u,v,w)=\left(1-y^2/h^2,0,0\right)</math>. The solution is started at order 2 and progressively increased to order 5. | ||
<!-- Specify the prescribed boundary conditions, as well as the means to verify the initial flow development. In particular describe the procedure for determining the in flow conditions comprising the instantaneous (mean and fluctuating) velocity components and other quantities. Provide reference profiles for the mean flow and fluctuations at in flow - these quantities must be supplied separately as part of the statistical data as they are essential as input for turbulence-model calculations. For checking purposes, these profiles should ideally also be given downstream where transients have disappeared; the location and nature of these cuts should be specified, as well as the reference result. --> | |||
<br/> | <br/> | ||
---- | ---- | ||
'''References''' | |||
<references/> | |||
{{ACContribs | {{ACContribs | ||
| authors=Lionel Agostini | | authors=Arun Soman Pillai, Lionel Agostini, Peter Vincent | ||
| organisation=Imperial College London | | organisation=Imperial College London | ||
}} | }} | ||
{{ | {{DNSHeader | ||
|area=1 | |area=1 | ||
|number=2 | |number=2 | ||
Latest revision as of 09:29, 5 January 2023
DNS Channel Flow
Introduction
The turbulent Channel Flow is one of the canonical flows used to study turbulence in wall bounded turbulence. DNS of turbulent channel flow were undertaken at . DNS were undertaken using PyFR (http://www.pyfr.org/) version 1.12.0:
- based on the high-order flux reconstruction method of Huynh[1]
- compressible solver
- a Rusanov Riemann solver was employed to calculate the inter-element fluxes
- an explicit RK45[2R+] scheme[2] was used to advance the solution in time
- Fifth order polynomials are used for the computations
Review of previous studies
Turbulent channel has been one of the canonical test cases to study the characteristics of wall bounded turbulence. The simplified setup proposed by Kim et al. (1987)[3] is now a standard test case for wall bounded turbulent flow simulations. The setup is computationally inexpensive as it a periodic channel flow with periodic boundary conditions in the spanwise and streamwise directions. With recent progress made in computing infrastructure, Reynolds numbers as large as (Bernardini et al. 2014) and (Pirrozoli et al. 2021) are now available. Nevertheless, the case by Kim et al. still remains as a benchmark case for wall bounded turbulent flow simulations.
Description of the test case
An idealised channel flow, without side walls, is considered. The details of the case are given in Iyer et al.(2019)[4]. The current set of simulations has a higher grid resolution in the wall normal direction where there are 174 solution points compared to 95 points in the simulations of Iyer et al.
Geometry and flow parameters
The geometry is a cuboid of dimensions units in the streamwise direction , 2 units in the transverse direction and units in the spanwise direction , as shown in figure 1. The dimensions are normalised by the channel half-width, and centreline velocity.
|
| Figure 1: Computational domain from Iyer et al. (2019) |
Boundary conditions
Periodicity conditions are imposed in the streamwise and spanwise boundaries which gives a flow developing in time. The transverse boundaries are no-slip walls. The initial density and pressure fields are uniform. The initial velocity field is . The solution is started at order 2 and progressively increased to order 5.
References
- ↑ Huynh, H. T., A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods, AIAA, 2007-4079, 1-42, 2007.
- ↑ Kennedy, C. A., Carpenter, M. H. & Lewis, R. M, Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations, Appl. Numer. Maths, 35(3), 177-219, 2000.
- ↑ Kim,J., Moin, P. & Moser, R., Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech. 177, 133-166, 1987
- ↑ A. Iyer, F. D. Witherden, S. I. Chernyshenko & P. E. Vincent, Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow, Journal of Fluid Mechanics, 875 (758-780), 2019
Contributed by: Arun Soman Pillai, Lionel Agostini, Peter Vincent — Imperial College London
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