1. Types of turbulence parameters

In the turbulent flow setting of the FLUENT flow field simulation, it is necessary to set the turbulent flow parameters of the boundary conditions. Although the turbulent flow settings at the inlet and outlet of the flow often have no great influence on the calculation results. However, in some cases (the turbulence level at the flow inlet and outlet is close to the turbulence level in the boundary layer, or even higher than the turbulence level in the boundary layer, such as jets), the turbulence parameters will affect the convergence speed and simulation results, so a rough estimate is needed The value of each parameter.

As shown in the figure above, there are six commonly used boundary turbulence parameters in Fluent, namely: turbulent kinetic energy (k), turbulent dissipation rate (ε, using the k-epsilon turbulence model) or specific dissipation rate (ω, using the k-omega turbulence model ), turbulence intensity (Intensity), turbulence length scale (Length Scale), turbulence viscosity ratio (Viscosity Ratio), hydraulic diameter (Hydraulic Diameter). During the turbulence parameter setting process for Fluent inlet and outlet, it is often necessary to select two of the turbulence parameter settings.

Note: The turbulence parameter setting of the Outlet boundary condition will add Backflow before the parameter, which indicates the turbulence parameter of the backflow when backflow occurs at the outlet. If there is no reflow phenomenon, the parameters are invalid.

2. Calculation of turbulence parameters

1. Turbulence Intensity (I)

Turbulence intensity is the ratio of the root mean square u' of the velocity fluctuations to the average flow velocity $in_{aug}$ . Less than or equal to 1% indicates low turbulence intensity, and greater than 10% indicates high turbulence intensity. For internal flow, the formula when the airflow is fully developed is:

$I=\frac{u'}{u_{avg}}=0.16\cdot Re^{-\frac{1}{8}}$

$Re=\frac{\rho \cdot u\cdot D_{H}}{\mu }$

Among them, I is the turbulence intensity, Re is the Reynolds number, u is the fluid flow velocity, DH is the hydraulic diameter, and μ is the viscosity coefficient.

For internal flows, low turbulence intensity can be used if the upstream flow is not sufficiently developed and undisturbed. Fluent's default turbulence intensity is 5%. When setting this parameter, the Reynolds number of the working condition can be roughly estimated first, and then the turbulence intensity can be estimated. Or you can determine the level of turbulence in the working condition by yourself, and then roughly give the turbulence intensity.

2. Turbulence Length Scale (l)

The turbulence length scale l is related to the size of the eddy. In a fully developed flow in a pipe, there is an approximate relationship between the turbulence length scale l and the physical size of the pipe. The formula is:

$l=\frac{0.07L}{C_{\mu }^{0.75}}$

Among them, l is the turbulence scale, L is the characteristic scale, which can be regarded as the hydraulic diameter (however, if the turbulent disturbance is due to obstacles in the flow, such as rotary blades and perforated plates, then L should be the characteristic length of the obstacle, not the hydraulic diameter. diameter.). The factor 0.07 is based on the maximum mixing length in fully developed turbulent pipe flow. Cμ is a constant term coefficient of the ke turbulence model, and the general default value is 0.09. This coefficient can be queried in "Cmu" of "Model Constants" of the Fluent ke turbulence model.

For wall boundary flows with a turbulent boundary layer at the inlet, there is no need to calculate by the above formula. The turbulent length scale can be directly determined as 0.4 times the thickness of the boundary layer. The formula is:

$l=0.4\cdot \delta _{99}$

3. Turbulent Viscosity Ratio (μt)

This parameter is the ratio of turbulent viscosity to hydrodynamic viscosity. For the standard k-epsilon model, the most important assumption is to use the turbulent kinetic energy k and the turbulent dissipation rate ε to represent the turbulent viscosity $\mu _{t}$ :

$\mu_{t}=\rho \cdot C_{\mu }\cdot \frac{k^{2}}{\varepsilon}$

Among them, $C_{\mu }$ the meaning is the same as before. $\mu _{t}$ Generally, it is not necessary to calculate accurately, only a rough estimate is needed. Generally, the turbulent viscosity ratio is between 1-10, and the default value is 10. For low turbulence levels such as external free flow, the turbulent viscosity ratio can be set to 1. For moderate turbulence levels, the turbulent viscosity ratio can be set to 10. For high turbulence levels, this value can be set up to 100.

During the simulation process, the problem "Turbulent viscosity limited to viscosity ratio of 1.00e+05 in *** cells" often occurs. This is actually because the turbulence level during the calculation process is extremely high, which has reached the actual level. Impossible working conditions. If there is no such large turbulence in actual working conditions, this parameter needs to be appropriately reduced to eliminate this warning.

4. Kinetic Energy (k)

Turbulent kinetic energy is a physical quantity used to measure turbulent kinetic energy. The instantaneous value is replaced by the average value and the pulsation value and then averaged. Then the three-directional equations are added to obtain the turbulent kinetic energy equation.

$k=\frac{3}{2}\cdot (u_{avg}\cdot I)^{2}$

Among them, k is the turbulent kinetic energy, $in_{aug}$ is the average flow velocity of the fluid, and I is the turbulence intensity.

5. Turbulent Disspipation Rate (ε)

The turbulence dissipation rate is represented by different symbols in different turbulence models. In the k-epsilon model, it is represented by ε, while in the k-omega model, it is represented by ω.

$\varepsilon =\frac{k^{1.5}}{l}$

where k is the turbulent kinetic energy and l is the turbulence length scale. Another calculation using the turbulent viscosity ratio is:

$\varepsilon =\rho \cdot C_{\mu }\cdot \frac{k^{2}}{\mu}\cdot(\frac{\mu _{t}}{\mu })^{-1}$

Among them, k is the turbulent kinetic energy, μ is the fluid viscosity, and ρ is the fluid density.

6. Specific dissipation rate (ω)

$\omega =\frac{k^{0.5}}{C_{\mu }\cdot l}$

Among them, k is the turbulent kinetic energy, and l is the turbulence scale. Another calculation using the turbulent viscosity ratio is:

$\omega =\rho \cdot \frac{k}{\mu}\cdot (\frac{\mu _{t}}{\mu })^{-1}$

7. Hydraulic Diameter (DH)

The hydraulic diameter is four times the ratio of the flow cross-sectional area to the perimeter:

$D_{H}=\frac{4A}{P}$

Among them, A represents the cross-sectional area of the fluid, and P represents the wetted area of the fluid. For flow in a circular tube, its true diameter is the hydraulic diameter. For non-circular pipe flow or the fluid does not fill the pipe, the above formula needs to be used for calculation. For flow between parallel plates with quasi-infinite width (W >> H), the hydraulic diameter should be approximately 2 times the plate spacing (2H) rather than the plate spacing itself.

8. Estimate the modified turbulent viscosity (Modified Turbulent Viscosity, v)

When the turbulence model is the Spalart-Allmaras model (one-equation model), the boundary turbulence parameters will have settings to correct the turbulent viscosity. The calculation formula for this parameter is:

$\widetilde{\nu }=C_{\mu }\cdot \sqrt{\frac{3}{2}}\cdot u_{avg}\cdot I\cdot l$

9. Estimate Reynolds Stress Components

When the turbulence model is the Reynolds Stress Model (RSM), the boundary turbulence parameter will have the setting of the Reynolds stress component. The Reynolds stress formulas of uu, vv and ww are:

$\overline{u_{\alpha }^{'}u_{\alpha }^{'}}=\frac{2}{3}k$

The Reynolds stress formulas of uv, vw, and uw are:

$\overline{u_{i}^{'}u_{j}^{'}}=0$

3. Selection of turbulence parameters

(1) Fully developed internal flow, select turbulence intensity and hydraulic diameter (Intensity and Hydraulic Diameter);

(2) For the flow of guide vanes and perforated plates, select the intensity and length scale (Intensity and Length Scale);

(3) For the flow of the turbulent boundary layer caused by the wall, select the intensity and length scale (Intensity and Length Scale).

Fluent solver - setting of turbulence parameters