DNS 1-2 Quantification of Resolution: Difference between revisions

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=DNS Channel Flow=


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|[[Image:Average_u_logscale.png|400px]]
|[[Image:Average_u_logscale.png|400px]]
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|'''Figure 2:''' Average streamwise velocity, <math>Re_\tau=180</math>,  vs data from Moser et al. (1999)                             
|''Figure 3:'' Average streamwise velocity, <math>Re_\tau=180</math>,  vs data from Moser et al. (1999)                             
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The turbulent stress profiles agree well with the data from Moser et al.
The turbulent stress profiles, shown by the solid lines, and the turbulent kinetic energy profile, represented by the dashed line, in figure 4 agree well with the data from Moser et al., which is indicated by the markers.
<div id="figure3"></div>
<div id="figure3"></div>
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{|align="center"
|[[Image:Channel_turbulent_stress.png|400px]]
|[[Image:Channel_turbulent_stress.png|400px]]
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|'''Figure 3:''' Average streamwise velocity, <math>Re_\tau=180</math>,  vs data from Moser et al. (1999)                           
|''Figure 4:'' Turbulent stress profiles                           
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The expected near wall behaviour of turbulent stresses are <math>\widetilde{u^{\prime\prime2}},\widetilde{w^{\prime\prime2}}\sim y^2,\ \widetilde{v^{\prime\prime2}}\sim y^4</math> and <math>\widetilde{u^\prime v^\prime}\sim y^3</math>. These stresses near the wall from the current set of simulations are shown below.
The expected near wall behaviour of turbulent stresses are <math>\widetilde{u^{\prime\prime2}},\widetilde{w^{\prime\prime2}}\sim y^2,\ \widetilde{v^{\prime\prime2}}\sim y^4</math> and <math>\widetilde{u^\prime\prime v^\prime\prime}\sim y^3</math>. These stresses near the wall from the current set of simulations are shown below.
<gallery widths=300px heights=240 mode="packed-hover">
<gallery widths=250px heights=200 caption="Figure 4: Near wall turbulent stress" mode="packed-hover">
Image:Near_wall_uu.png|<math>\widetilde{u^{\prime\prime} u^{\prime\prime}}</math>
Image:Near_wall_uu.png|<math>\widetilde{u^{\prime\prime} u^{\prime\prime}}</math>
Image:Near_wall_vv.png|<math>\widetilde{v^{\prime\prime} v^{\prime\prime}}</math>
Image:Near_wall_vv.png|<math>\widetilde{v^{\prime\prime} v^{\prime\prime}}</math>
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</gallery>
</gallery>


One way to verify that the DNS are properly resolved is to examine the residuals of the Reynolds-
The turbulent kinetic energy budget [[lib:DNS_1-2_quantification_#figure6|(Fig. 6)]], as well as budgets of the diagonal components of the turbulent stress tensor (fig. 7-9) across the channel, is compared with data from Moser et al. The budget of <math>R_{uv}</math>, the shear stress responsible of turbulent energy production is also shown (fig. 10). The budget quantities are non-dimensionalized using <math>u_\tau^3/\delta_\nu</math>. The lines represent data from the current set of simulations, compared against Moser's data represented by circles. The dashed black line denotes the residual of the budget. The legend shown in the turbulent kinetic energy budget applies to all the budget plots. The green line in the turbulent kinetic energy budget represents the trace of the pressure-strain tensor, known as pressure-dilatation. In other budget plots, the green line is for corresponding pressure-strain correlation.
stress budget equations. These residuals are among the statistical volume data to be provided as
<div id="figure6"></div>
described in Statistical Data section.
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|[[Image:tke_budget_new.png|400px]]
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|''Figure 6:'' Turbulent kinetic energy budget.                           
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|[[Image:Ruu_budget.png|400px]]
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|''Figure 7:'' Budget of the normal stress component, <math>\widetilde{u^{\prime\prime2}}</math>.                           
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|[[Image:Rvv_budget.png|400px]]
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|''Figure 8:'' Budget of the normal stress component, <math>\widetilde{v^{\prime\prime2}}</math>.                           
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<div id="figure9"></div>
{|align="center"
|[[Image:Rww_budget.png|400px]]
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|''Figure 9:'' Budget of the normal stress component, <math>\widetilde{w^{\prime\prime2}}</math>.                           
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<div id="figure10"></div>
{|align="center"
|[[Image:Ruv_budget.png|400px]]
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|''Figure 10:'' Budget of turbulent shear stress, <math>\widetilde{u^{\prime\prime} v^{\prime\prime}}</math>.                            
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<br/>
<br/>
----
----
{{ACContribs
{{ACContribs
| authors=Lionel Agostini
| authors=Arun Soman Pillai, Peter Vincent
| organisation=Imperial College London
| organisation=Imperial College London
}}
}}
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Latest revision as of 09:33, 5 January 2023

DNS Channel Flow

Front Page

Description

Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

Storage Format

Quantification of resolution

Mesh resolution

The grid resolution corresponds to uniform and ranges from near the wall (first solution point) to at the centre of the channel. The near-wall Kolmogorov length scale, , in wall units is .

Solution verification

The solution accurately captures the near wall and log-law behaviour of averaged streamwise velocity profile as shown in Fig. 2.

Average u logscale.png
Figure 3: Average streamwise velocity, , vs data from Moser et al. (1999)

The turbulent stress profiles, shown by the solid lines, and the turbulent kinetic energy profile, represented by the dashed line, in figure 4 agree well with the data from Moser et al., which is indicated by the markers.

Channel turbulent stress.png
Figure 4: Turbulent stress profiles

The expected near wall behaviour of turbulent stresses are and . These stresses near the wall from the current set of simulations are shown below.

The turbulent kinetic energy budget (Fig. 6), as well as budgets of the diagonal components of the turbulent stress tensor (fig. 7-9) across the channel, is compared with data from Moser et al. The budget of , the shear stress responsible of turbulent energy production is also shown (fig. 10). The budget quantities are non-dimensionalized using . The lines represent data from the current set of simulations, compared against Moser's data represented by circles. The dashed black line denotes the residual of the budget. The legend shown in the turbulent kinetic energy budget applies to all the budget plots. The green line in the turbulent kinetic energy budget represents the trace of the pressure-strain tensor, known as pressure-dilatation. In other budget plots, the green line is for corresponding pressure-strain correlation.

Tke budget new.png
Figure 6: Turbulent kinetic energy budget.
Ruu budget.png
Figure 7: Budget of the normal stress component, .
Rvv budget.png
Figure 8: Budget of the normal stress component, .
Rww budget.png
Figure 9: Budget of the normal stress component, .
Ruv budget.png
Figure 10: Budget of turbulent shear stress, .




Contributed by: Arun Soman Pillai, Peter Vincent — Imperial College London

Front Page

Description

Computational Details

Quantification of Resolution

Statistical Data

Instantaneous Data

Storage Format


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