Research and Development of Criterial Correlations for the Optimal Grid Element Size Used for RANS Flow Simulation in Single and Compound Channels
- Irregularity, lack of strict order in time;
- Viscous and vortex nature of the flow;
- Coherence of large vortex structures.
- —characteristic size, m.
- —characteristic velocity, m/s;
- —viscosity, m2/s. There are currently several main approaches to modeling turbulence:
- Direct numerical simulation (DNS)  calculates the Navier–Stokes equations for eddies of all scales up to the Kolmogorov scale. With an increase in the size of the computational cell, the system of equations for DNS, as a rule, does not converge. At present, the DNS is used mainly for research purposes and in modeling low-Re currents.
- Large eddy modeling (LES)  uses the separation of eddies by scale: large eddies are directly resolved, small eddies are modeled using subgrid models. LES methods require a grid of the order of the scale of large eddies. Currently, LES is used in scientific research and technical applications as a highly accurate method.
- Modeling of Reynolds-averaged Navier-Stokes equations or unsteady Reynolds-averaged Navier-Stokes equations (RANS, URANS) . Modeling is done by closing the equations through Boussinesq hypothesis and semi-empirical turbulence models over the entire energy spectrum.
- y—wall distance, m.
- —shear velocity, m/s.
- —viscosity, m2/s.
- The size of the grid element in correlations should be associated with characteristic hydrodynamic quantities that have a length scale and characterize the flow regime.
- The nature of the quantities used should allow one to estimate the scale of the element a priori, before conducting numerical studies.
- Correlations should take into account the results of empirical and analytical studies of turbulent flows in channels.
2. Research Object
3. Research Method
- —channel characteristic size, m;
- —optimal linear size of the global element of the grid model, m;
- —dimensionless distance from the wall corresponding to the transition to the flow core, ;
- —the Reynolds number in the characteristic cross section of the channel, ; where is the characteristic flow velocity.
- Conducting research on grid convergence for single channels with various regime and geometric characteristics.
- Revealing transition points to grid convergence using approximation power expressions.
- Reducing the values of the size of the element corresponding to the transition to the grid convergence to the dimensionless form Ko by dividing by the thickness of the turbulent boundary layer.
- Formation of correlations Ko(Re’) for individual channels with a test of statistical significance.
- Formation of the overall correlation Ko(Re’) with a test of statistical significance.
- Verification of the obtained general correlation dependence on the compound channel.
4. Results and Discussion
- There are regularities that relate the size of the grid model element, which ensures convergence along the grid, with the regime and geometric parameters of the flow in the channel;
- As a dimensionless similarity criterion, one can introduce the coefficient Ko, the ratio of the size of the grid model element that ensures grid convergence to the thickness of the turbulent boundary layer;
- There are statistically significant correlations Ko(Re’) for channels with sudden expansion, sudden contraction and diffusers, and there is also an overall statistically significant correlation Ko(Re’);
- This correlation makes it possible to a priori estimate the required size of the grid model element, including for compound channels, the simulation results using the obtained grid settings are within acceptable limits compared to the literature data.
Data Availability Statement
Conflicts of Interest
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|Channel with a Sudden Expansion|
|20,000; 60,000; 100,000||20,000; 60,000; 100,000||20,000; 60,000; 100,000|
|Channel with a sudden contraction|
|20,000; 60,000; 100,000||20,000; 60,000; 100,000||20,000; 60,000; 100,000|
|General||Steady State RANS, 2D Axisymmetric||Turbulence Model||k-ω SST|
|Velocity inlet, m/s||3.478|
|Gauge pressure outlet, Pa||0|
|Fluid||First near-wall prismatic layer y+||1|
|, kg/m3||1.225||Number of prismatic layers||10|
|, M2/c||1.46 ·10−5||Growth coefficient||1.1|
|Meshing method||Unstructured, triangles||Global element size, mm||0.2–40|
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Bryzgunov, P.; Osipov, S.; Komarov, I.; Rogalev, A.; Rogalev, N. Research and Development of Criterial Correlations for the Optimal Grid Element Size Used for RANS Flow Simulation in Single and Compound Channels. Inventions 2023, 8, 4. https://doi.org/10.3390/inventions8010004
Bryzgunov P, Osipov S, Komarov I, Rogalev A, Rogalev N. Research and Development of Criterial Correlations for the Optimal Grid Element Size Used for RANS Flow Simulation in Single and Compound Channels. Inventions. 2023; 8(1):4. https://doi.org/10.3390/inventions8010004Chicago/Turabian Style
Bryzgunov, Pavel, Sergey Osipov, Ivan Komarov, Andrey Rogalev, and Nikolay Rogalev. 2023. "Research and Development of Criterial Correlations for the Optimal Grid Element Size Used for RANS Flow Simulation in Single and Compound Channels" Inventions 8, no. 1: 4. https://doi.org/10.3390/inventions8010004