Development of a Non-Reacting LES Solver for Unstructured Grid

Along with solving the Navier–Stokes equation, a convection diffusion equation for mass fraction is also solved, which would correct the equivalent density. The length and time scales of the mesh and the simulations are calculated based on Kolmogorov's hypothesis and the CFL number is calculated accordingly. An explicit solver is used due to the fact that the calculated CFL number is extremely lower than 1. The evolution of the plumes is captured. The evolution of the tabular structures in both cases is discussed.

Introduction

Turbulent Jets

In turbulent jets, the only source of momentum and kinetic energy for fluid motion is the pressure drop across the orifice. Vortex structures are also formed, which contribute to the growth of the pulse of turbulent jets.

Figure 2.1: Jet with Reynolds number 10 5 (Picture courtesy : Steven Crow and Cambridge University Press [1])

Laminar and Turbulent Flows

Numerical Methods

• Direct Numerical Simulation
• RANS

To obtain the feature of the largest vortex, the computational domain must be several times larger than their vortex sizes. The computational cost of DNS modeling a cubic domain depends on the length of the domain L, the grid spacing ∆x, and the time step ∆t. The grid spaces depend on the size of the dissipative scales to be solved. The number of total cells and the time step actually depend on the Reynolds number. The dependence of the number of grid nodes on the Reynolds number is given by. The number of grid points and the number of time steps therefore increase drastically as the flow becomes turbulent, i.e. the Reynolds number becomes high.

The simulation of large eddies is based on the philosophy that larger length scales are dependent on initial and boundary conditions, while smaller length scales are inherently isotropic. Large-scale eddies are resolved and models are used for smaller scales. Consequently, LES requires a coarser mesh compared to DNS. The computational cost is significantly lower when using LES compared to DNS. Here, µsgs is the subgrid-scale turbulent viscosity. The isotropic part of the subgrid-scale stress τkk is not modeled but is added to the filtered static pressure expression.

Reynolds Averaged Approach vs. LES

Wall functions in combination with a coarse wall mesh can be used, often with some success, to reduce the cost of LES for wall-bounded flows. However, one must carefully consider the ramifications of using wall functions for that flow. For the same reason (to accurately resolve the eddies), LES also requires very accurate spatial and temporal discretizations.

Effect of Grid Sensitivity on SGS LES models

Literature Review

Moments of velocity fluctuations up to fourth order were measured to characterize turbulent transport in the jet and to evaluate current models for triple moments appearing in the Reynolds stress equations. The following conclusions were made from the above experiment. Here they considered the helium jet[19], which is ten times lighter than that of air. With the same setup instead of air, the helium jet is allowed to flow to the floating air. The streaming facility is the same as explained in the above Setup. Here the Schmidt number is taken to be 0.7. The jet discharge Froude number was 1.4∗104 and the measurement region was in the intermediate region between the non-flowing jet region and the plume region.

The concentration fields and dispersion rates of the mean velocity show a turbulent Schmidt number of 0.7, which is consistent with other measurements of scalars in round jets. In this experiment, a significant increase in turbulent intensity is obtained compared to the non-buoyant jet. The origin of these higher values ​​is believed to be near the nozzle inlet, but this was not investigated in the study. Here in the present work, a LES-based turbulent model has been chosen for both the air and helium cases. The dynamic K-equation subgrid scale model is used in the simulation of both cases.

Figure 2.4: Experimental setup [2]

Governing Equation and Discretization

• Finite Volume Method
• Governing Equations
• Finite Volume Discretization
• Explicit Algorithm
• Boundary Conditions

The studies mentioned in the previous discussion are used in the design of the code in openFoam. The entire set of Navier-Stokes equations and the energy equation in three dimensions form a system of second-order nonlinear PDEs. In the cases discussed, we used the considered turbulence. The LES model was used.

Prediction step: The pressure terms are neglected in the above equations as follows, VpUp∗−Upn. Now that the velocities are known, these values ​​are used in the mass fraction convective diffusion equation. The discretized form is given by, .

Figure 3.1: A finite control volume (non-moving) [3]

Problem Definition

The zero gradient boundary condition is applied for velocity and atmospheric pressure is given for pressure.

Parallel Computing

• SMAC Algorithm

Furthermore, for cases involving complex geometries and larger computational domains, validation and verification of the solver becomes time-consuming as grids with millions of cells must be used. Both Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) turbulence modeling techniques are highly demanding. This architecture only scales well to a fixed number of processors due to the additional costs associated with creating high-bandwidth interconnection networks. Message passing between independent processes running on different nodes is the main bottleneck in such systems, in achieving linear speed where computation time scales as the inverse of the number of CPUs.

The level of parallelism is limited since processes can run different independent parts of the same code at any given point. At first it may appear that well-balanced data-parallel programs can provide a speedup equal to the number of independent processes used to run a program.

Computational Grid

This chapter is divided into two parts, first dealing with the case of air in air, followed by a discussion of helium in air. Simulations were performed using the dynamic k-equation LES model and the results were compared with the experimental results. This simulation is used as a benchmark to ensure results[2].

Figure 4.1: Computational Grid for air case

Air in quiscent atmosphere

The time-averaged velocity profile is shown in Figure 4.4 below. This is shown after a time 100 times greater than the residence time. The variation of the average axial velocity in the radial direction is shown in figure 4.5. The turbulent intensity in the axial, radial and azimuthal directions are shown in the figures below.

The turbulent intensity variations in the radial and azimuthal directions show similar variation, as the beam is symmetrical as shown in Figure 4.8. They actually represent the degree of momentum exchange at a given point in the flow.

Figure 4.4: Mean Velocity profile

Running Parallel Applications

As can be seen from the graphs, the energy spectrum of the two sites has a slope of -5/3 and the grid used in this simulation captures the flow dynamics down to the inertial scale and is therefore suitable for LES simulation. Scotch decomposition does not require any geometric input from the user and attempts to minimize the number of processor boundaries. The user can specify a weight for the inter-processor decomposition, via an optional processor-Weights keyword, which can be useful on machines with different performance between processors.

A comparison of the time required to run the simulation was performed using the above techniques using 2,4,8 and 16 processors in the same node for 100 iterations as shown in Figure 4.11. From the plot, the conclusion is drawn, which is that both the simple and Scottish techniques were comparable to each other.

Figure 4.11: (a)Time vs No. of processors plot(b)Actual vs Theoretical Speed up plot

Helium into quiscent atmosphere

The average velocity profile is shown in figure 4.13. Here the average speed change is done and the result is as expected. The profile figure is captured by taking a mid-plane of the mesh and cutting it. The average velocity profile in the radial direction is shown in figure 4.15. The obtained profile is very similar to the experimental result of Panchapakeshan and Lumley [19]. The change of the axial turbulent intensity in the radial direction is shown in figure 4.16. The simulated result is overpredicted but the trend in the graph is similar to the experimental result.

The intensity of the axial velocity fluctuations is almost twice as large as the radial and azimuthal components. Compared to the values ​​measured in the air stream, the axial velocity fluctuations are about 80% to 90% larger, while the radial intensities are approximately the same. the order. This xld range for their flow configuration is very close to the plume region. The profiles for the intensities of the azimuthal and radial velocity fluctuations in the helium jet are practically identical to those for the air jet. The intensity of the axial velocity fluctuations, as mentioned earlier, is higher than the values ​​of the air jet in the fully turbulent region near the jet axis. One such parameter is the Energy Spectrum chart. The velocity spectra are plotted at two different locations for the current simulation.

Figure 4.12: Mass fraction development of helium jet at various time

CoVo Test

Thus, the values ​​of the turbulent intensity and the Reynolds stresses are overestimated and the plume rises with much lateral dissipation. The underresolved buoyancy-induced turbulence is a likely cause for the overprediction of the central axis concentration values ​​since the mixing rates of ambient fluid in the plume would be suppressed. Time-averaged values ​​for the two velocity components and plume concentration showed little sensitivity to mesh spacing. The diagram of the case is given by Figure 4.20. In this case, an 80*80 grid is used for the simulation. This is done by using a MATLAB code that takes the areas of the non-uniform field and specifies the initial non-uniform conditions for pressures and velocities.

The decomposition of the mean velocity along the axis matches the scaling shown by the effective diameter for both cases, e.g. air in air and helium in flying air. The mean radial velocity profile of the helium jet is broader than that of the air jet. As a consequence of the average moment increased by the buoyancy. Significantly higher levels of axial velocity turbulent intensities are observed. It is believed that the origin of these higher levels must lie in the development of the near-field jet, an understudied region in Openfoam's Truth was also realized compared to other CFD software. Investigating the sensitivity of turbulent closures and coupling of hybrid RANS-LES models for predicting flow fields with separation and reconnection.

Figure 4.20: Geometry for CoVo test