Confined double annular jet

Application Challenge 2-07 © copyright ERCOFTAC 2004

Introduction

The Application Challenge TA 2 - AC 7, "Confined Double Annular Jet" proposed by the VUB, Belgium, is an axisymmetric double annular flow field generated by a burner, and discharging into a confined combustion chamber (see Fig. 1 below). The flow is studied in cold conditions, and in a nozzle region going from the nozzle to 1.5 diameters downstream. The resulting mean flow is axisymmetric ; it can be qualified as a complex turbulent flow. The flow possesses a central vortex and two small toroidal contra rotating vortices. There are stagnation points and lines, mixing regions and recirculation regions (see Fig. 2 below). This is thus a good AC, since there is a relatively simple geometry (axisymmetric), and the ability of CFD codes to reproduce several properties of complex flows can be tested.

Figure 1: An overall display of the facility. Inlet arrangement, a cut on the burner, and the combustion chamber are shown. The nozzle region corresponding to the measurements is indicated.

The available experiments are the following:

Experimental data #1: Air flow with a 156 mm largest diameter jet, with a maximum velocity of 6.3 m/s, corresponding to a Reynolds number of 6 104. For this flow, 2D LDV data have been recorded, providing axial and radial mean velocities, axial and radial turbulence intensities and Reynolds stress. The data are provided on a dense experimental grid composed of 36 sections, each of which possessing 100 to 200 measurement points.

Experimental data #2: The flow field, generated in the combustion chamber model by water flow through the model, is measured with a 2D2C PIV system. A total of 271 instantaneous vector fields, each containing 5040 vectors in the near nozzle region, are presented. The flow rate through the burner was 4.09x10-5 m3/s giving a Reynolds number 180, based on nozzle opening dr (2 mm) and mean exit velocity Ue (0.09 m/s). This produces a central toroidal vortex in the transitional state.

Relevance to Industrial Sector

Industrial devices in fluid engineering quite often involve complex turbulent flows. This is the case for example in turbine engines, industrial furnaces, combustors and burners. Industrial burners are designed to generate stationary combustion in a confined chamber, with desired values of velocity, temperature and species concentrations at the exit of the combustion chamber. In general, they consist of several nozzles arranged around an axis in a confined space. The fuel and the oxidizer (usually air) issue out of the nozzles and these jets mix by turbulent diffusion. Burners are often installed to destroy pollutants gases resulting from industrial activities, before releasing them in the atmosphere.

Since international norms in matter of pollution are getting more and more binding, it is important to be able to modify the burner in order to minimize the emission of pollutant species. Since burners are usually designed and modified empirically by the manufacturer, the modifications cannot be optimal. It is therefore important to be able to better understand the flow field and the combustion process associated to burners. The turbulent diffusion of species is faster than the combustion process, so that the first step to understand a burner is to study the flow field in cold conditions. It is essential to understand the behavior of the various jets and their interaction with the neighboring jets and surrounding flows to successfully predict the performance of the device.

The test case provided here contains a complete database in axisymmetric conditions, providing the mean velocity field, turbulence intensity, Reynolds stress components, corresponding to 2 components of the mean velocity and 4 non-zero components of the Reynolds stress tensor. This test-case can thus be used to test the validity of CFD to reproduce the complex flow created by confined annular jets. For the nozzle region (up to 1.5 diameters) this AC is well understood, in terms of data available and overall quality (for experimental data #1, globally less than 2% axisymmetric errors).

Design or Assessment Parameters

The position of some particular points can be used as assessment parameters to judge the validity of CFD computations (more specific comparisons can be done later). Several locations have been selected below, as shown in Figure 2.

Figure 2: Streamlines of the flow, and designations of specific position points (DOAP).

Flow Geometry

Since the L/D of the channels of the burner are large, the fully-developed flows dominate over any influence from the inlet geometries. Therefore in this AC the geometry is determined only by dimensions of the exit of the burner and of the combustion chamber: see Table 1 and Figure 3 below.

Orientation of axis and sign conventions: since the geometry is axisymmetric, in the following a cylindrical coordinate system is considered (x,z,q), where x is the axial coordinate (the distance from the exit of the burner, along its axis), z is the radial coordinate (the distance from the axis) and q the tangential coordinate, not considered here due to axisymmetry.

**Table 1 Definition of Some Geometric Parameters**
Parameter	Description
$r_{1}$	radius of the primary jet
$r_{2}$	radius of the secondary jet
$dr$	width of annular jets
$r_{c}$	radius of the combustion chamber
$\beta ={\frac {r_{2}}{r_{1}}}$	secondary to primary radius ratio
${Y}={\frac {A_{e}}{A_{1}}}={\frac {r_{c}^{2}}{2r_{1}dr}}$	exit area to primary area ratio

Figure 3: The diameters of the boundaries of the streams produced by the burner.

Flow Physics and Fluid Dynamics Data

The mean flow is axisymmetric. Only the flow in the nozzle region has been recorded. For this region, the jet presents a complex flow: it possesses recirculation regions, several toroidal vortices, a stagnation point and stagnation lines. First the primary and secondary streams merge, creating a vortex bubble between them. This bubble corresponds to a pair of contrarotating toroidal vortices. Then the simple annular stream becomes a central jet, creating a big central vortex bubble. This central vortex is less stable than the toroidal one (see the streamlines in Figure 2).

The databases correspond to a turbulent, incompressible, isothermal flow with recirculation.

The following tables provide different informations characterizing the flow: The Problem Definition Parameters (PDP) are dimensional quantities characterizing the experiment, and Governing Non-Dimensional Parameters (GNDP) are non-dimensional numbers governing and characterizing the physics of the flow.

First, some useful fluid dynamics parameters are presented in Table 2. The PDP introduced here characterize the geometry of the burner, and determine the inflow (through the velocity ratio of primary to secondary bulk velocity). They are also presented in Table 2.

The GNDP are the Reynolds number and the Craya-Curtet numbers, presented in Table 2. The Reynolds number is defined using the bulk-averaged velocity of the secondary jet and its diameter. The Craya-Curtet number characterizes the recirculation of confined jet flows. It was shown experimentally for some simple annular jet flows that the flow and mixing properties of the classical axisymmetric confined jet depend only on the Craya-Curtet number. It is assumed here that this number is also governing the physics of the double annular jet flow. The Craya-Curtet number can be defined as a normalization of the stagnation pressure loss in the system:

Failed to parse (syntax error): {\displaystyle \[\frac{g\Delta{P}\star}{U_e^2p} = \frac{1}{C_t^2}\] } (1)

where the different parameters in this equation are defined in Table 2. A small value of the Craya-Curtet number corresponds to large static pressure loss, indicating recirculation.

Parameter	Symbol	Definition
	$U_{1}$	Bulk average velocity of the primal jet
	$U_{2}$	Bulk average velocity of the secondary jet
Fluid	$U_{e}$	Bulk average velocity of the average stream
Dynamic	Failed to parse (syntax error): {\displaystyle \[\Delta P\star = P\star_e - P\star_i\]}	Stagnation pressure loss in the system (difference between exit and entrance stagnation pressure)
Parameters	$\rho$	Density
Problem	Failed to parse (syntax error): {\displaystyle \[a = \frac{U_2}{U_1}\]}	Secondary to primary bulk-averae velocity ratio
Definition	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbases.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \[\beta = \frac{r_2}{r_1}\]}	Secondary to primary radius ratio
Parameters (PDP)	Failed to parse (syntax error): {\displaystyle \[Y = \frac{A_e}{A_1} = \frac{r^2_c}{2r_1dr}\]}	Exit area to primary area ratio
Governing	Failed to parse (syntax error): {\displaystyle \[Re = \frac{2U_2^r_2}{V}\]}	Reynolds Number
Non-Diamensional Parameters (GNDP)	Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbases.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \[C_t = \frac{1 + \beta}{\sqrt{Y(1 + a^2\beta)}}\]}	Craya-Curtet number