Turbulent Pipe Flow (LES)

This case verifies the Large Eddy Simulation (LES) capability in NekRS using fully developed turbulent pipe flow.

Flow parameters

The pipe has a nondimensional diameter $var element = document.getElementById("moose-equation-1519e837-6fe5-440f-8e36-e3a0cff7e09c");katex.render("D=1", element, {displayMode:false,throwOnError:false});$ and a bulk Reynolds number $var element = document.getElementById("moose-equation-8f71c7a9-a33c-423c-be66-733b2130f4e3");katex.render("Re_b=19000", element, {displayMode:false,throwOnError:false});$ , defined as

(1)var element = document.getElementById("moose-equation-84d95e50-ac0b-48ea-9765-8a976a22f305");katex.render("Re_b = \\frac{U_b D}{\\nu},", element, {displayMode:true,throwOnError:false});

where $var element = document.getElementById("moose-equation-ede202b1-8a10-4d79-a785-0ff15fd4ee33");katex.render("U_b", element, {displayMode:false,throwOnError:false});$ is the bulk velocity and $var element = document.getElementById("moose-equation-24fcdc38-3270-46e2-9c8b-c814daee71a1");katex.render("\\nu", element, {displayMode:false,throwOnError:false});$ is the kinematic viscosity. The corresponding friction Reynolds number is approximately $var element = document.getElementById("moose-equation-0f49fa78-8594-4e1c-a7f7-a94986bacc93");katex.render("Re_\\tau=550", element, {displayMode:false,throwOnError:false});$ .

Subgrid-scale model

Subgrid-scale modeling is performed using the high-pass filtering approach of Stolz et al. (Stolz et al., 2005). A cutoff wavenumber of $var element = document.getElementById("moose-equation-1411a822-5569-488d-91bb-352b97d55639");katex.render("N-1", element, {displayMode:false,throwOnError:false});$ is used to construct the low-pass filter, and the filter strength is set to 10.

Verification criterion

The simulation is qualified by computing the time-averaged velocity field and evaluating the friction velocity,

(2)var element = document.getElementById("moose-equation-f66ee3fa-db15-4ce5-8c3b-347bb0269adf");katex.render("u_\\tau = \\sqrt{\\frac{\\tau_w}{\\rho}},", element, {displayMode:true,throwOnError:false});

where the wall shear stress is

(3)var element = document.getElementById("moose-equation-bc4a9113-647f-4b5d-ab04-69215765367a");katex.render("\\tau_w = 2\\mu\\left|\\underline{S}\\cdot\\vec{n}\\right|_w,", element, {displayMode:true,throwOnError:false});

and the mean strain-rate tensor is

(4)var element = document.getElementById("moose-equation-c15fe064-9b7e-491a-80b1-2071b89a4cf2");katex.render("\\underline{S} = \\frac{1}{2}\\left(\\nabla\\vec{v}+\\nabla\\vec{v}^{\\,T}\\right).", element, {displayMode:true,throwOnError:false});

Here, $var element = document.getElementById("moose-equation-c7ea9b07-dccc-42bf-9a41-401c0328b32c");katex.render("\\vec{v}", element, {displayMode:false,throwOnError:false});$ is the time-averaged velocity, $var element = document.getElementById("moose-equation-a50178b7-75f5-44cc-9977-55cec08032f9");katex.render("\\tau_w", element, {displayMode:false,throwOnError:false});$ is the computed wall shear stress, $var element = document.getElementById("moose-equation-731c545f-9a16-496b-a832-3df2941047d3");katex.render("\\rho", element, {displayMode:false,throwOnError:false});$ is the fluid density, $var element = document.getElementById("moose-equation-1fcf1f10-fdf0-485b-b567-e19fdf3e9a3a");katex.render("\\mu", element, {displayMode:false,throwOnError:false});$ is the dynamic viscosity, $var element = document.getElementById("moose-equation-d93fa602-09c8-4cb8-96c5-f36faee0507a");katex.render("\\underline{S}", element, {displayMode:false,throwOnError:false});$ is the strain-rate tensor, and $var element = document.getElementById("moose-equation-6a7eacb5-5fbb-4705-95ef-73dc369bb119");katex.render("\\vec{n}", element, {displayMode:false,throwOnError:false});$ is the outward unit normal vector at the wall. The computed friction velocity is compared with the direct numerical simulation (DNS) reference of El Khoury et al. (El Khoury et al., 2013) using

(5)var element = document.getElementById("moose-equation-96447c2b-76a0-483a-b099-9e459d0aee0c");katex.render("\\mathrm{err} = \\left|u_\\tau-u_{\\tau,\\mathrm{DNS}}\\right|,", element, {displayMode:true,throwOnError:false});

where

(6)var element = document.getElementById("moose-equation-ae84b4fb-2f8a-4d1b-92fe-fdc9449559d1");katex.render("u_{\\tau,\\mathrm{DNS}} = 5.79\\times10^{-2}.", element, {displayMode:true,throwOnError:false});

References

George K El Khoury, Philipp Schlatter, Azad Noorani, Paul F Fischer, Geert Brethouwer, and Arne V Johansson. Direct numerical simulation of turbulent pipe flow at moderately high reynolds numbers. Flow, turbulence and combustion, 91(3):475–495, 2013.

BibTeX

@article{el2013direct,
    author = "El Khoury, George K and Schlatter, Philipp and Noorani, Azad and Fischer, Paul F and Brethouwer, Geert and Johansson, Arne V",
    title = "Direct numerical simulation of turbulent pipe flow at moderately high Reynolds numbers",
    journal = "Flow, turbulence and combustion",
    volume = "91",
    number = "3",
    pages = "475--495",
    year = "2013",
    publisher = "Springer"
}

RIS

TY  - JOUR
AU  - El Khoury, George K
AU  - Schlatter, Philipp
AU  - Noorani, Azad
AU  - Fischer, Paul F
AU  - Brethouwer, Geert
AU  - Johansson, Arne V
TI  - Direct numerical simulation of turbulent pipe flow at moderately high Reynolds numbers
JO  - Flow, turbulence and combustion
PY  - 2013
VL  - 91
IS  - 3
PB  - Springer
SP  - 475
EP  - 495
ER  -

Plain Text

George K El Khoury, Philipp Schlatter, Azad Noorani, Paul F Fischer, Geert Brethouwer, and Arne V Johansson. Direct numerical simulation of turbulent pipe flow at moderately high reynolds numbers. Flow, turbulence and combustion, 91(3):475–495, 2013.

S Stolz, Philipp Schlatter, and L Kleiser. High-pass filtered eddy-viscosity models for large-eddy simulations of transitional and turbulent flow. Physics of fluids, 2005.

BibTeX

@article{stolz2005high,
    author = "Stolz, S and Schlatter, Philipp and Kleiser, L",
    title = "High-pass filtered eddy-viscosity models for large-eddy simulations of transitional and turbulent flow",
    journal = "Physics of fluids",
    volume = "17",
    number = "6",
    year = "2005",
    publisher = "AIP Publishing"
}

RIS

TY  - JOUR
AU  - Stolz, S
AU  - Schlatter, Philipp
AU  - Kleiser, L
TI  - High-pass filtered eddy-viscosity models for large-eddy simulations of transitional and turbulent flow
JO  - Physics of fluids
PY  - 2005
VL  - 17
IS  - 6
PB  - AIP Publishing
ER  -

Plain Text

S Stolz, Philipp Schlatter, and L Kleiser. High-pass filtered eddy-viscosity models for large-eddy simulations of transitional and turbulent flow. Physics of fluids, 2005.

Flow parameters
Subgrid - scale model
Verification criterion
References