# Best Practice Advice AC2-07

**Confined double annular jet**

**Application Challenge 2-07** © copyright ERCOFTAC 2004

**Best Practice Advice for the AC**

**Key Fluid Physics**

The AC entitled “Confined double annular jet“focuses on an axisymmetric double annular flow generated by a burner, and discharging into a confined combustion chamber.

The flow in the combustion chamber corresponds to an axisymmetric complex flow possessing several representative features of the flow in burners: several toroidal vortices, a stagnation point and stagnation lines, recirculation and high turbulence intensity in the mixing regions. Figure 1 shows the streamlines of the measured flow in the combustion chamber and designations of the specific position points for the assessment parameters.

Figure 1: Streamlines of the measured flow, and designation of the assessment parameter.

First the primary and secondary streams merge, creating a vortex bubble between them. This bubble corresponds to a pair of contra-rotating toroidal vortices. Then the simple annular stream becomes a central jet, creating a large central vortex bubble. This central vortex is less stable than the toroidal one.

This document corresponds only to a turbulent, incompressible, isothermal flow with circulation. For the flow in the combustion, the following assessment parameters were used:

- The central stagnation point (a);

- Center of the central toroidal vortex (b);

- Stagnation line associated to the toroidal vortex (c);

- Center of the first small toroidal vortex (d);

- Center of the second small toroidal vortex (e).

**Application Uncertainties**

The jet in the combustion chamber presents a complex flow. It possesses recirculation regions, several toroidal vortices, a stagnation point and stagnation lines. It improves available turbulence models for complex flows possessing swirls, anisotropies and recirculation. Different turbulence models were used: an algebraic (Baldwin Lomax), a one-equation (Spalart-Allmaras), several two-equation (Chien, Launder Sharma and Yang Shih) k-ε turbulence models and a non-linear turbulence model.

The uncertainties can be due by different assumptions:

- Only the axial and radial velocity profile at the inlets of the combustion chamber is measured on a very fine grid. This means that only a 2D velocity field can be imposed at the two inlets of the combustion chamber. The tangential velocity component is neglected.

- The turbulence kinetic energy and the turbulent dissipation of the k-ε turbulence models at the inlets of the combustion chamber are estimated. The construction of the inlet profile of k has been done with the assumption that the sum of the radial and the tangential turbulence intensity is equal to the axial turbulence intensity, which is more or less true in a fully developed pipe flow. The dissipation rate is specified by the ratio of the turbulent viscosity to the laminar viscosity and is on the basis of the k profile.

**Computational Domain and Boundary Conditions**

The geometry of the confined double annular jet and the mean flow is axisymmetric so the grid is axisymmetric. The whole combustion chamber is modeled because the boundary of the measured grid is not known.

The measured velocity at the outlet of the primary and the secondary ducts of the burner are imposed as the inflow condition. The turbulent kinetic energy is imposed with the assumption that the sum of the radial and the tangential turbulence intensity is equal to the axial turbulence intensity, which is more or less true in a fully developed pipe flow. The dissipation rate is specified by the ratio of the turbulent viscosity to the laminar viscosity and is on the basis of the k profile.

It is necessary to model the whole combustor, because the boundary condition of the measured grid is not known. The real outlets of the combustion chamber are 4 gaps, positioned on the outer side of the combustion chamber. To have an axisymmetric grid, an axisymmetric equivalent of the experimental outlet is modeled. The total surface of the equivalent outlet of the numerical model is similar to the one of the empirical model.

The numerical model is very sensitive for negative mass flow at the outlet. The geometry to the outlet has to be carefully dimensioned in order to avoid backflows at the downstream boundary. Increasing the surface of the outlet solves this problem

The solid boundaries are modeled as adiabatic walls with no-slip condition for the velocity field, except the symmetric axis, which is treated as an Euler wall.

Static pressure is prescribed to be atmospheric at the outlet.

The initial solution is generated from a uniform initial field. Constant pressure fields higher than the imposed pressure at the outlet is chosen and a constant non-zero axial velocity is chosen to prevent a negative mass flow at the outlet of the combustion chamber.

**Discretisation and Grid Resolution**

The empirical study of the structure of the measured flow identifies several zones, depending on the axial distance from the nozzle. Divide a structured mesh of one block in 2 zones: An area with a high spatial clustering of grid points in the recirculation and the vortices regions, and a mild clustering at the end of the combustion chamber. Stretching is applied towards the boundary of the outlet.

**Physical Modelling**

The fluid model is not a critical element. Use an incompressible perfect gas.

The confined double annular burner is accurately modeled by a time-marching finite volume Navier-Stokes solver. The three dimensional compressible Reynolds averaged continuity, turbulent Navier-Stokes with the k-ε turbulence model of Yang Shih, or Sharma Launder, and energy equations are solved using the structured meshes.

The system of equations is integrated in time using an explicit four-stage Runga-Kutta scheme and convergence towards steady state is accelerated using multigrid, combined with residual smoothing and local time stepping.

The convective fluxes are treated through a second-order central Jameson scheme with second- and fourth-order scalar dissipation, and a pseudo-compressibility method and a second-order dual-time stepping procedure are used.

The Full multigrid strategy is based on the V cycle. The system of equations is integrated in time using an explicit four–stage Runga-Kutta scheme and convergence towards steady-state is accelerated using multigrid combined with residual smoothing and local time stepping with a Courant-Friedrichs-Lewy number of three.

The preconditioning parameters β and the characteristic velocity are suggested as three and the maximum velocity in the flow yield (It is the maximum flow velocity at the inlet of the primary duct).

The experimental velocity profiles and the turbulence viscosity are imposed at the inlet. k-ε turbulence models gave the best result in the agreement in the nozzle region.

**Recommendations for Future Work**

It seems unlikely that any algebraic, one or two-equations RANS turbulence model can predict all flow quantities correctly in the complete domain: The flow is too complex. This is clearly a case for LES simulations.

Other k-ε and non-linear turbulence models have to be checked with these complex turbulent flows in the combustion chamber.

The influence of the inlet profile of the tangential, turbulent kinetic energy and the turbulence dissipation has to be assessed too.

© copyright ERCOFTAC 2004

Contributors: Charles Hirsch; Francois G. Schmitt - Vrije Universiteit Brussel

Site Design and Implementation: Atkins and UniS

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