## Project Details

### Description

Objectives of the project. Our objective is to significantly improve the available turbulence models for complex flows possessing swirls, anisotropies, and recirculations. This will be done using as a test case the complex flow produced by a swirling double annular burner. Experimental data will be taken on a densified grid, and a powerful data analysis technique will be used to provide experimental estimates of several turbulent quantities such as the kinetic energy, eddy viscosity, and dissipation. Comparisons of these measurements with numerical models will then be used to provide tests, validations, and improvements of available turbulence models.

State-of-the-art. Industrial devices in fluid engineering quite often involve complex turbulent flows possessing recirculations, anisotropies, and swirls. This is the case for example in turbine engines, industrial furnaces, combustors and burners. A better understanding of these industrial devices is challenging in the context of energy savings and for environment concerns linked to pollution and global warming. Unfortunately, these flows are still badly modeled and need further research to be fully understood. This concerns turbulence modeling and its coupling with chemistry, involving scalar mixing. Indeed, the mixing in wakes or in complex flows is systematically under-estimated by available turbulence models. We will study this using as validation test a burner to generate a swirling flow representative from these industrial situations.

To solve Navier-Stokes equations for engineering applications Reynolds averaging is usually performed : with an adequate closure for the Reynolds stress, this provides an evaluation of first and second moments of turbulent quantities, that is mean velocity, mean pressure and turbulence intensity. Among this approach, the classical k-epsilon turbulence model is widely used for the solution of engineering and industrial problems (Rodi, 1980). This model introduces a linear eddy-viscosity representation for the Reynolds stress and two separated transport equations for the turbulent kinet energy k, and for epsilon, the scalar rate of dissipation of energy. In this representation, the Reynolds stress tensor is parallel to the mean rate of strain tensor. This model describes rather well the mean behavior of simple turbulent flows. Nevertheless, such equations have important deficiencies when considering more complex flows (Speziale, 1991; Wilcox, 1993). They cannot describe rotational strain or shear; they cannot modelize anisotropies (Oberlack, 1997; Speziale and Gatski, 1997), and they cannot predict amplification or relaxation of the components of the Reynolds stress tensor. To go further in the representation, it is necessary to generalize in some way the linear standard k-epsilon model.

Several generalizations have been proposed in the literature: nonlinear k-epsilon models (Speziale, 1988; Khodak and Hirsch, 1996; Pattijn, Steelant and Dick, 1999), explicit algebraic stress models (Speziale, 1997), Renormalization-Group based models (Yakhot et al., 1992), full Reynolds-stress closures (Launder, 1992). The different models which are proposed must satisfy several conditions. One is a practical condition : they must not be too complex, which would need too much computation time compared to a limited gain in precision. The other are theoretical conditions : the properties which the Reynolds stresses hold by definition must be preserved in the modelling. This includes invariance (frame indifference, see Lumley, 1970; Speziale, 1989) and the realizability (positive semi-definiteness, see Lumley, 1983; Wang, 1997). These conditions eliminate several commonly used models, and helped the development of improved models.

Another generalization corresponds to studying the transport equation for the dissipation, which is usually considered as one of the weak points of classical models. It is often argued that Kolmogorov's assumption of local isotropy does not hold in general, and that the turbulent dissipation rate can show significant anisotropies for complex flows (Durbin and Speziale, 1991; Sreenivasan, 1991). New models have been proposed that take into account an anisotropic dissipation (Yu and Speziale, 1996; Oberlack, 1997; Speziale and Gatski, 1997).

Since all these generalized models are built on unproved hypothesis, they need to be compared to data, either DNS data (e.g. Shih and Wu, 1993; Apsley and Leschziner, 1998) or experimental data (e.g. Zhu and Shih, 1994; Menter, 1996; Sheen, Chen and Wu, 1997). Unfortunately, these data validations usually possess clear limitations : DNS data do not reach high Reynolds numbers whereas experimental data have provided up to now only limited informations on the flow, such as mean velocity and stress tensor components.

This project proposes to give a balance between experiments and modelization.

State-of-the-art. Industrial devices in fluid engineering quite often involve complex turbulent flows possessing recirculations, anisotropies, and swirls. This is the case for example in turbine engines, industrial furnaces, combustors and burners. A better understanding of these industrial devices is challenging in the context of energy savings and for environment concerns linked to pollution and global warming. Unfortunately, these flows are still badly modeled and need further research to be fully understood. This concerns turbulence modeling and its coupling with chemistry, involving scalar mixing. Indeed, the mixing in wakes or in complex flows is systematically under-estimated by available turbulence models. We will study this using as validation test a burner to generate a swirling flow representative from these industrial situations.

To solve Navier-Stokes equations for engineering applications Reynolds averaging is usually performed : with an adequate closure for the Reynolds stress, this provides an evaluation of first and second moments of turbulent quantities, that is mean velocity, mean pressure and turbulence intensity. Among this approach, the classical k-epsilon turbulence model is widely used for the solution of engineering and industrial problems (Rodi, 1980). This model introduces a linear eddy-viscosity representation for the Reynolds stress and two separated transport equations for the turbulent kinet energy k, and for epsilon, the scalar rate of dissipation of energy. In this representation, the Reynolds stress tensor is parallel to the mean rate of strain tensor. This model describes rather well the mean behavior of simple turbulent flows. Nevertheless, such equations have important deficiencies when considering more complex flows (Speziale, 1991; Wilcox, 1993). They cannot describe rotational strain or shear; they cannot modelize anisotropies (Oberlack, 1997; Speziale and Gatski, 1997), and they cannot predict amplification or relaxation of the components of the Reynolds stress tensor. To go further in the representation, it is necessary to generalize in some way the linear standard k-epsilon model.

Several generalizations have been proposed in the literature: nonlinear k-epsilon models (Speziale, 1988; Khodak and Hirsch, 1996; Pattijn, Steelant and Dick, 1999), explicit algebraic stress models (Speziale, 1997), Renormalization-Group based models (Yakhot et al., 1992), full Reynolds-stress closures (Launder, 1992). The different models which are proposed must satisfy several conditions. One is a practical condition : they must not be too complex, which would need too much computation time compared to a limited gain in precision. The other are theoretical conditions : the properties which the Reynolds stresses hold by definition must be preserved in the modelling. This includes invariance (frame indifference, see Lumley, 1970; Speziale, 1989) and the realizability (positive semi-definiteness, see Lumley, 1983; Wang, 1997). These conditions eliminate several commonly used models, and helped the development of improved models.

Another generalization corresponds to studying the transport equation for the dissipation, which is usually considered as one of the weak points of classical models. It is often argued that Kolmogorov's assumption of local isotropy does not hold in general, and that the turbulent dissipation rate can show significant anisotropies for complex flows (Durbin and Speziale, 1991; Sreenivasan, 1991). New models have been proposed that take into account an anisotropic dissipation (Yu and Speziale, 1996; Oberlack, 1997; Speziale and Gatski, 1997).

Since all these generalized models are built on unproved hypothesis, they need to be compared to data, either DNS data (e.g. Shih and Wu, 1993; Apsley and Leschziner, 1998) or experimental data (e.g. Zhu and Shih, 1994; Menter, 1996; Sheen, Chen and Wu, 1997). Unfortunately, these data validations usually possess clear limitations : DNS data do not reach high Reynolds numbers whereas experimental data have provided up to now only limited informations on the flow, such as mean velocity and stress tensor components.

This project proposes to give a balance between experiments and modelization.

Acronym | FWOAL159 |
---|---|

Status | Finished |

Effective start/end date | 1/01/01 → 31/12/04 |

### Keywords

- Experiments
- turbulence models
- Modelisation

### Flemish discipline codes

- Mechanical and manufacturing engineering
- Electrical and electronic engineering
- Computer engineering, information technology and mathematical engineering