TKE and EDR (TDR) for SBES in Fluent

sp_0y · January 28, 2025, 15:28

I am simulating a mixing tank with a 6-blade impeller using the sliding mesh approach in ANSYS Fluent 2023R2. I aim to compare the RANS (SST k−ω) method with the RANS-LES hybrid (SST k−ω with SBES + WALE) method. Specifically, I want to compare the energy dissipation rate (EDR) and turbulent kinetic energy (TKE) estimated using these approaches.
I am relatively new to LES and CFD, so any guidance would be greatly appreciated. I am happy to read more literature, but I should point out that I am on a tight timeline so may not be able to go very deep into it.So far, I’ve found the following resources very helpful:

Below are my questions divided into two main topics: Energy Dissipation Rate (EDR) and Turbulent Kinetic Energy (TKE).

Energy Dissipation Rate (EDR)
To calculate the energy dissipation rate, I used the following custom field function based on a response by CeesH (Link 1):
Total Energy dissipation rate = [eff-viscosity][strain-rate-mag][strain-rate-mag]

I have the following questions:

Resolved vs. Total EDR:
Does this formula give the total energy dissipation rate, or only the resolved part?
From LuckyTran’s response (Link 2), this formula seems to calculate only the resolved dissipation rate. To obtain the modeled dissipation rate, I understand $\epsilon_{\text{sgs}}$ can be calculated as:
$\epsilon_{{sgs}} = \frac{{k_{sgs}}^{3/2}}{L_s}$
Could someone confirm this or provide clarity?
Should this formula work for calculating EDR in RANS as well?
Fluent provides a default turbulence dissipation rate. However, when I compare this to the custom EDR formula above (averaged over a specific volume near the impeller), I observe discrepancies. I assumed Fluent uses the same equation for reporting dissipation rate under RANS, but I couldn’t find this confirmed in the Fluent manual.
Am I missing something fundamental here?
For SBES, is it better to compare instantaneous EDR (at specific blade positions) or mean EDR over several revolutions?
My initial plan was to compare instantaneous values, but with the fluctuations in the results, averaging over a few revolutions after the flow has stabilized might be more meaningful.
Any advice on best practices here?

Turbulent Kinetic Energy (TKE)
I intend to analyze the fraction of resolved TKE vs. total TKE using the following approach:

Resolved TKE ( $k_{res}$ ) is computed using: $k_{res} = 0.5\cdot \left( V_x'^2 + V_y'^2 + V_z'^2 \right)$
For Fluent, I defined a custom field function: $k_{res}$ = 0.5*((Vx - mean-x-velocity)^2 +(Vy - mean-y-velocity)^2 + (Vz - mean-z-velocity)^2)

Sub-grid TKE ( $k_{sgs}$ ), I found several formulations:
1. From LuckyTran (Link 2): $k_{sgs} = \left(\frac{\mu_t}{L_s} \right)^2 , \quad L_s = \min (\kappa d, C_w \cdot \delta)$
2. From Andrea1984 (Link 3): $k_{sgs} = \left(\frac{\nu_{sgs}} {\rho \cdot l_{sgs}} \right)^2$
  Most probably I am missing something very basic because it appears that one of them has a typo (assuming $\nu_{sgs} = \frac{\mu_t} {\rho}$ ). L_s and l_sgs in the above expressions both represent the length scale.
3. From Fluent manual (Link 4) and FoxInCFD (Link 3): $k_{sgs} = \frac{1}{0.3} \cdot \frac{\mu_t}{\rho} \cdot \left| S \right|$

My questions are:

Which of these $k_{sgs}$ formulations is most suitable for SBES? Are there assumptions that make one less applicable or more fundamental?
Are there any errors in my formulations for $k_{res}$ or $k_{sgs}$ ?

I deeply appreciate the feedback and apologize if I’ve missed any forum rules. Thanks in advance for your guidance!

sp_0y · February 6, 2025, 17:04

Hi,

I hope this is sufficient time gap to give this post a minor boost. I am running a simulation in the meantime with different formulations to compare the values.

Regarding the Sub-grid TKE formulations, I am testing the equations from (1) and (3), with minor changes in equation (1). I realized, after some dimensional analysis, that dividing LuckyTran's formulation by density gives the same units as Fluent's energy dissipation. Below is the formulation I am using.

$k_{sgs} = \left(\frac{\mu_t}{\rho \cdot L_s} \right)^2 , \quad L_s = \min (\kappa d, C_w \cdot \delta)$

I will update this post as soon I have some results from the simulation.

LuckyTran · February 8, 2025, 16:03

EDR
Note that you should be using the regular viscosity (the property) to get the resolved epsilon, not the effective viscosity. Notice also that strain-rate-mag has a mean and fluctuating part. That's the other hint that you should be using the same viscosity.

2. It's the same two formulas but you need to use the right one at the right time. If there is turbulent viscosity involved, then you have a modeled quantity. Dissipation is just the viscous conversion of flow-work into heat and can be calculated if you have the velocity field. With RANS you have the mean strain but not fluctuating strain. With LES you have mean strain and resolved part of the strain (so you can directly calculate the resolved part without any turbulent viscosity). You only need the turbulent viscosity to calculate the subgrid scale dissipation.

3. up to you

TKE
Not necessarily a typo. It depends whether k is from a compressible or incompressible solver. That is, in your solver, does k have units of kinetic energy or does it have units of m^2/s^2

Note that your own custom field function does not have a density in it and does not have units of kinetic energy.

The random 0.3 is the C_mu, a model constant and is used to calculate the turblent viscosity. Some people absorb the model constant into the turbulent viscosity, some people don't and put it in the length scale. It may be correct or incorrect, you have no way of knowing unless you write down the entire formula for how the turbulent viscosity is calculated and how the transport equation for k is formulated. You cannot quote formulas out of context.

sp_0y · February 10, 2025, 22:58

Hi LuckyTran,

Thank you so much for your reply, it helps a lot.
After pondering over it for the last two days and reading a bit further, below are the formulations that I have decided to use going forward.

For EDR (in m2/s3),

1. SBES
Total EDR = ([effective-viscosity][strain-rate-mag-instantaneous][strain-rate-mag-instantaneous])/[density]
EDR_Resolved = ([molecular-viscosity][strain-rate-mag-instantaneous][strain-rate-mag-instantaneous])/[density]
EDR_Sgs = $\frac{{k_{sgs}}^{3/2}}{L_s}$

2. RANS
Total EDR = ([effective-viscosity][strain-rate-mag-instantaneous][strain-rate-mag-instantaneous])/[density]
i. Should this be turbulent or effective, I think it should be effective viscosity here as well, as the total would be a combination of molecular and tuburlent viscosity. Please correct me if I am wrong here.
ii. I tested using both the turbulent and effective viscosity in the above formula and comparing with what Fluent gives under Turbulent dissipation rate. While Fluent gives 0.0679 m2/s3, using u_turb and u_eff give 0.0637 and 0.072 respectively. What do you think could be the cause behind this difference?

For TKE (in m2/s2),
k_resolved = 0.5*((Vx - mean-x-velocity)^2 +(Vy - mean-y-velocity)^2 + (Vz - mean-z-velocity)^2)
k_SGS = $\left(\frac{\mu_t}{\rho \cdot L_s} \right)^2 , \quad L_s = \min (\kappa d, C_w \cdot \delta)$

I just want to ensure that I have understood your explanations correctly.
Thank you again for your time.

Edits in purple

January 28, 2025, 15:28	TKE and EDR (TDR) for SBES in Fluent	#1
sp_0y New Member Sahil Join Date: Jan 2025 Posts: 3 Rep Power: 2	I am simulating a mixing tank with a 6-blade impeller using the sliding mesh approach in ANSYS Fluent 2023R2. I aim to compare the RANS (SST k−ω) method with the RANS-LES hybrid (SST k−ω with SBES + WALE) method. Specifically, I want to compare the energy dissipation rate (EDR) and turbulent kinetic energy (TKE) estimated using these approaches. I am relatively new to LES and CFD, so any guidance would be greatly appreciated. I am happy to read more literature, but I should point out that I am on a tight timeline so may not be able to go very deep into it.So far, I’ve found the following resources very helpful: Turbulent dissipation rate in LES TKE in LES with WALE SGS TKE formulas and comparison ANSYS Fluent Beta Features Manual (2023R2) Below are my questions divided into two main topics: Energy Dissipation Rate (EDR) and Turbulent Kinetic Energy (TKE). Energy Dissipation Rate (EDR) To calculate the energy dissipation rate, I used the following custom field function based on a response by CeesH (Link 1): Total Energy dissipation rate = [eff-viscosity][strain-rate-mag][strain-rate-mag] I have the following questions: Resolved vs. Total EDR: Does this formula give the total energy dissipation rate, or only the resolved part? From LuckyTran’s response (Link 2), this formula seems to calculate only the resolved dissipation rate. To obtain the modeled dissipation rate, I understand $\epsilon_{\text{sgs}}$ can be calculated as: $\epsilon_{{sgs}} = \frac{{k_{sgs}}^{3/2}}{L_s}$ Could someone confirm this or provide clarity? Should this formula work for calculating EDR in RANS as well? Fluent provides a default turbulence dissipation rate. However, when I compare this to the custom EDR formula above (averaged over a specific volume near the impeller), I observe discrepancies. I assumed Fluent uses the same equation for reporting dissipation rate under RANS, but I couldn’t find this confirmed in the Fluent manual. Am I missing something fundamental here? For SBES, is it better to compare instantaneous EDR (at specific blade positions) or mean EDR over several revolutions? My initial plan was to compare instantaneous values, but with the fluctuations in the results, averaging over a few revolutions after the flow has stabilized might be more meaningful. Any advice on best practices here? Turbulent Kinetic Energy (TKE) I intend to analyze the fraction of resolved TKE vs. total TKE using the following approach: Resolved TKE ( $k_{res}$ ) is computed using: $k_{res} = 0.5\cdot \left( V_x'^2 + V_y'^2 + V_z'^2 \right)$ For Fluent, I defined a custom field function: $k_{res}$ = 0.5*((Vx - mean-x-velocity)^2 +(Vy - mean-y-velocity)^2 + (Vz - mean-z-velocity)^2) Sub-grid TKE ( $k_{sgs}$ ), I found several formulations: From LuckyTran (Link 2): $k_{sgs} = \left(\frac{\mu_t}{L_s} \right)^2 , \quad L_s = \min (\kappa d, C_w \cdot \delta)$ From Andrea1984 (Link 3): $k_{sgs} = \left(\frac{\nu_{sgs}} {\rho \cdot l_{sgs}} \right)^2$ Most probably I am missing something very basic because it appears that one of them has a typo (assuming $\nu_{sgs} = \frac{\mu_t} {\rho}$ ). L_s and l_sgs in the above expressions both represent the length scale. From Fluent manual (Link 4) and FoxInCFD (Link 3): $k_{sgs} = \frac{1}{0.3} \cdot \frac{\mu_t}{\rho} \cdot \left\| S \right\|$ My questions are: Which of these $k_{sgs}$ formulations is most suitable for SBES? Are there assumptions that make one less applicable or more fundamental? Are there any errors in my formulations for $k_{res}$ or $k_{sgs}$ ? I deeply appreciate the feedback and apologize if I’ve missed any forum rules. Thanks in advance for your guidance!

February 8, 2025, 16:03		#3
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,810 Rep Power: 68	EDR Note that you should be using the regular viscosity (the property) to get the resolved epsilon, not the effective viscosity. Notice also that strain-rate-mag has a mean and fluctuating part. That's the other hint that you should be using the same viscosity. 2. It's the same two formulas but you need to use the right one at the right time. If there is turbulent viscosity involved, then you have a modeled quantity. Dissipation is just the viscous conversion of flow-work into heat and can be calculated if you have the velocity field. With RANS you have the mean strain but not fluctuating strain. With LES you have mean strain and resolved part of the strain (so you can directly calculate the resolved part without any turbulent viscosity). You only need the turbulent viscosity to calculate the subgrid scale dissipation. 3. up to you TKE Not necessarily a typo. It depends whether k is from a compressible or incompressible solver. That is, in your solver, does k have units of kinetic energy or does it have units of m^2/s^2 Note that your own custom field function does not have a density in it and does not have units of kinetic energy. The random 0.3 is the C_mu, a model constant and is used to calculate the turblent viscosity. Some people absorb the model constant into the turbulent viscosity, some people don't and put it in the length scale. It may be correct or incorrect, you have no way of knowing unless you write down the entire formula for how the turbulent viscosity is calculated and how the transport equation for k is formulated. You cannot quote formulas out of context. sp_0y likes this.

February 10, 2025, 22:58		#4
sp_0y New Member Sahil Join Date: Jan 2025 Posts: 3 Rep Power: 2	Hi LuckyTran, Thank you so much for your reply, it helps a lot. After pondering over it for the last two days and reading a bit further, below are the formulations that I have decided to use going forward. For EDR (in m2/s3), 1. SBES Total EDR = ([effective-viscosity][strain-rate-mag-instantaneous][strain-rate-mag-instantaneous])/[density] EDR_Resolved = ([molecular-viscosity][strain-rate-mag-instantaneous][strain-rate-mag-instantaneous])/[density] EDR_Sgs = $\frac{{k_{sgs}}^{3/2}}{L_s}$ 2. RANS Total EDR = ([effective-viscosity][strain-rate-mag-instantaneous][strain-rate-mag-instantaneous])/[density] i. Should this be turbulent or effective, I think it should be effective viscosity here as well, as the total would be a combination of molecular and tuburlent viscosity. Please correct me if I am wrong here. ii. I tested using both the turbulent and effective viscosity in the above formula and comparing with what Fluent gives under Turbulent dissipation rate. While Fluent gives 0.0679 m2/s3, using u_turb and u_eff give 0.0637 and 0.072 respectively. What do you think could be the cause behind this difference? For TKE (in m2/s2), k_resolved = 0.5((Vx - mean-x-velocity)^2 +(Vy - mean-y-velocity)^2 + (Vz - mean-z-velocity)^2) k_SGS = $\left(\frac{\mu_t}{\rho \cdot L_s} \right)^2 , \quad L_s = \min (\kappa d, C_w \cdot \delta)$ I just want to ensure that I have understood your explanations correctly. Thank you again for your time. Edits in purple Last edited by sp_0y; February 21, 2025 at 19:20.*

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February 6, 2025, 17:04		#2
sp_0y New Member Sahil Join Date: Jan 2025 Posts: 3 Rep Power: 2	Hi, I hope this is sufficient time gap to give this post a minor boost. I am running a simulation in the meantime with different formulations to compare the values. Regarding the Sub-grid TKE formulations, I am testing the equations from (1) and (3), with minor changes in equation (1). I realized, after some dimensional analysis, that dividing LuckyTran's formulation by density gives the same units as Fluent's energy dissipation. Below is the formulation I am using. $k_{sgs} = \left(\frac{\mu_t}{\rho \cdot L_s} \right)^2 , \quad L_s = \min (\kappa d, C_w \cdot \delta)$ I will update this post as soon I have some results from the simulation.