Turbulence Models Validation in a Ventilated Room by a Wall Jet

Guangyu Caogcao@cc.hut.fi

02-04-2007Laboratory of Heating, Ventilating and Air-Conditioning, Faculty of Mechanical Engineering, Helsinki University of

Technology

Ene-39.4053 Postgraduate Seminar on Energy Technology

Content

1 Introduction2 Description of the experiment 3 Air jet distribution in the space4 Airflow modeling 4.1 Turbulence modelling 4.2 Near-wall treatment 4.3 Boundary conditions5 Results and discussions6 Conclusion

Why?

1 Predicting indoor comfortable level2 Evaluate the ventilation effectiveness3 Indoor gaseous pollutants and associated air

quality control

1 Introduction

The draught rate model(ISO 7730:2005 standard)

)14,337,0()05,0)(34( ,62,0

,, TuvvtDR lalala

where DR is the draught rate, ta,l is the local air temperature, va is the local mean air velocity, Tu is the local turbulence intensity

The ventilation effectiveness

• CR pollutant concentration in exhaust air;• CS pollutant concentration in supply air;• CP pollutant concentration in the inhalation zone.

SP

SRV CC

CC

2 Description of the experiment

Air jet outlet and inlet

Investigation of 4 plans

The median plan x = 1.55 m Three vertical plans located at y = 0.60m,

y =1.10 m and at y = 1.60m

The median plan is scanned with 1892 positions of the mobile arm; each vertical plan is scanned with 440 positions.

3 Air jet distribution in the space

Only the values superior to 0.05 m/s were retained

Figs. 4–6 present the velocity isovalue lines obtained with the experimental set-up. The hot case is reaching the ceiling faster than the isothermal case. The jet in the cold case does not attach but collapse from the ceiling.

4 Airflow modeling

What kind of problems will be confronted by CFD modelling ? Inside heat plumes will disturb the normal air jet performance.Low air inlet velocity will result in incompletely mixing of indoor air with large temperature gradient from ceiling to floor.The ineffective simulation of air outlet will underestimate the percentages of the uncomfortable people due to draught.

(1) What kind of model can be used to predict the turbulence of indoor air distribution?

(2) What kind of CFD models can predict indoor air distributions accurately?

4.1 Turbulence modelling

Reynolds-averaged Navier-Stokes (RANS)

• The equations represent transport equations for the mean flow quantities only, with all the scales of the turbulence being modeled.

• The approach of permitting a solution for the mean flow variables greatly reduces the computational effort. If the mean flow is steady, the governing equations will not contain time derivatives.

• A computational advantage is seen even in transient situations, since the time step will be determined by the global unsteadiness rather than by the turbulence.

The k–ε realizable model • This model uses the transport equations of k and

ε to compute the turbulent viscosity by Shih,• Compared with the other k–ε models, the

realizable one satisfies certain mathematical and consistent with the physics of turbulent flows (for example the normal Reynolds stress terms must always be positive).

• A new model for the dissipation rate

RNG k–ε Model

• The RNG k–ε Model is derived from the instantaneous Navier- Stokes equations, using a mathematical technique called renormalization group methods.

• The RNG theory provides an analytical formula for Prt.

• It provides an analytically derived differential formula for effective viscosity.

The standard k– ω model

• The two equation k– ω models are based on model transport equations for the turbulent kinetic energy and the specific dissipation rate which can also be thought of as the ratio of ω to k.

The Shear-stress transport (SST) k–ω model

• The standard k- ω model and the transformed k- ω model are both multiplied by a blending function and both models are added together. The blending function is designed to be one in the near-wall region, which activates the standard k- ω model, and zero away from the surface, which activates the transformed k- ε model.

4.2 Near-wall treatment

Correct calculation of a wall-bounded flow and its associated transport phenomena is not possible without the adequate description of the flow in the near wall region.

Near wall treatment for the k– ε models

In FLUENT, the near-wall treatment combines a two layer model with enhanced wall functions. In other words, the first cell values of temperature and velocity are given by enhanced wall functions applicable in the entire near-wall region, and the viscosity affected region is resolved by the two-layer model.

Near-wall treatment for the k– ω models

The near-wall treatment for the k– ω and k– ω SST models is computed following the same logic as for the k– ε realizable model. However, there is no need for a special treatment for the viscosity affected region because of the low-Reynolds correction in the k– ω and k– ω SST models.

4.3 Boundary conditions

In our case, there are three kinds of boundary conditions: air inlet conditions, air outlet conditions and wall boundary conditions.

5 Results and discussions

The axisymmetric wall jet

Fig. 10 presents the maximum velocity decay for the experimental data and the numerical models for the isothermal case.

Fig. 11 presents the maximum velocity decay for the experimental data and the numerical models for the hot case.

• Concerning the maximum temperature presented Fig. 12, the k– ω model is in good agreement with the experiment.

Fig. 13 is the maximum velocity curve for the cold case.

Fig. 14 shows that none of the models can give the good maximum position value.

Fig. 14. Velocity profile—hot case—median plan y= 1.60 m.

The velocity profile of Fig. 15 illustrate the incapacity of the numerical models to predict the jet behavior.

Fig. 15. Velocity profile—cold case—median plan y= 1.60 m.

Jet expansion

rates

The experimental data show that the axisymmetric wall jet is highly anisotropic.

6. Conclusion1 None of the four numerical models can predict

correctly the expansion rates for the cold case. 2 None of the turbulence models is reliable for predicting

either the global values for temperature and velocity or the maximum velocity decay.

3 The k–ω model seems to give better results for the expansion rates. The three other models give expansion rates lower than the experimental results.

4 For the hot case, the k–ω and k– ε realizable models are closer to the experiment.

Thank you!