NUMERICAL AND EXPERIMENTAL INVESTIGATIONS OF AIR FLOW AND TEMPERATURE PATTERNS OF A LOW VELOCITY DIFFUSER

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1 NUMERICAL AND EXPERIMENTAL INVESTIGATIONS OF AIR FLOW AND TEMPERATURE PATTERNS OF A LOW VELOCITY DIFFUSER M Cehlin and B Moshfegh Division of Energy and Mechanical Engineering, Department of Technology, University of Gävle, Gävle, Sweden ABSTRACT In this article, four turbulence models are studied to capture the flow and temperature behavior of the air close to a low-velocity diffuser for displacement ventilation. Turbulence is modeled by means of one zero-equation model and three different two-equation models, i.e. the, the, the Standard ε, and the -Kim model. They are evaluated for their performance in predicting the air flow patterns and temperature profiles close to the diffuser. The models are validated with measurements performed both with traditional point measuring techniques and a whole-field measurement method. The prediction of the velocity and the temperature by the three two-equation models is generally satisfactory. The predictions from the and the -Kim model were almost the same and slightly different than the standard ε model. The model and the Standard ε model are computationally much more stable than the -Kim model. INDEX TERMS Numerical simulation, Displacement ventilation, Turbulence model, Whole field measurements INTRODUCTION Computational Fluid Dynamics, CFD, simulations are more and more common for prediction of airflows and air temperatures in ventilated rooms. Simulation of airflows near low-velocity diffusers for displacement ventilation is particularly troublesome, because of the low momentum and strong negative buoyancy. There is no dominating mechanism controlling the airflow. Also the modeling of the low-velocity diffuser is critical. The design and geometry of the supply obviously influence the pattern close to the diffuser. Defining the correct inlet boundary conditions is rather complicated, due to the non-uniformity of the inlet velocity. Due to limited computer capacity available at present, turbulence models has to be used in order to solve flow motion. It is essential to validate these models by al data. Many turbulence models have been developed during the past decades with different level of complexity. Presumably the most widely used turbulence model in indoor applications is the standard ε model (Launder and Spalding 74). However, it has occasionally shown to provide poor results for indoor airflows. Many modifications have been applied on the standard ε model to improve the computed results. However, most of these models are limited to particular cases. Recently, Yuan et al. (99) presented CFD validation by al data for displacement ventilation. They report that there is good agreement between CFD calculation with the ε model and the measurements. This is in line with (95) who studied the accuracy of five different ε turbulence models for various Contact author mcn@hig.se 765

2 indoor flows. He concluded that the ε model (Yakhot et al. 92) is most accurate among the eddy-viscosity models tested. This paper presents reports a validation of turbulence models by al data from both point measurements and whole-field measurements near a diffuser in a displacement ventilated office room. Turbulence is modeled by means of a zero-equation model and three two-equation eddy-viscosity models: the model (Spalding 94), the model, the Standard ε model, the -Kim model ( and Kim 87). The whole-field measurements were conducted with help of an infrared camera in conjunction with a measuring screen. In this technique, air temperature is measured with high resolution within a relatively large area (Cehlin et al ). This method can be a very powerful tool for comparison between CFD simulation and real-scale measurements. y z Original 5l/s Modeled 5l/s x outlet back wall right wall traverse left wall 36 openings 2 openings 2.7 m inlet screen front wall IR camera 4. m Figure. Sketch of the test room. 3.4 m Figure 2. Sketch of the original and the modeled diffuser. EXPERIMENTAL SET-UP The s were performed in a full-scale test room and detailed temperature and velocity measurements were performed in the near zone of the low-velocity diffuser. All s were performed at the Laboratory of Ventilation and Air Quality at the Centre of Built Environment, University of Gävle, Sweden. A test room of size m was used in order to compare the results of al tests with numerical calculation results. The test room is shown in Figure. The air was supplied through a flat low-velocity diffuser,.525m wide and.23m high, located.24m above the floor level at one of the walls. The air in the test room was held at an appropriate temperature with an electric mat (effect of 5W) covering the whole floor. In the investigation a measuring screen,..6m in size, made of paper with an emissivity of.9, was used. The air temperatures and the surrounding surface temperatures were measured by thermocouples with an accuracy of ±. C, while the temperature of the measuring screen was measured with an infrared camera (Agema 57) with an accuracy of ±.3 C for a well-defined location on the screen. Measurements of air velocities were carried out with a D hot-wire anemometer, and they were time-averaged over 6s. COMPUTATIONAL SET-UP AND NUMERICAL PROCEDURES A three-dimensional CFD model was built in a way geometrically similar to the test room. The steady-state, three-dimensional, non-isothermal flow field was simulated by means of a numerical solution of the governing equations for continuity, momentum and energy. Turbulence is modeled by means of the, the, the Standard ε and the -Kim model. The Standard ε model is well known and documented. The basic idea behind the 766

3 model is to systematically filter out the small scale turbulence to a degree that the remaining scales can be resolved. This effect can be captured by introducing an additional term in the ε-equation, which is the ratio between the time scales of the turbulence and the mean flow. The reason for using the -Kim ε model is that the model improves the dynamic response of the ε-equation compared to the standard ε model, which provides predictions that are less diffusive for flows with recirculation and separation. Effects of buoyancy were modeled based on the Boussinesq-approximation. Standard wall functions were applied on all surfaces. The discretization of the governing equations is based on the finite volume method, and the computations were carried out using Phoenics 5., see Spalding (94). The SIMPLE algorithm was used for coupling velocities and pressure. The flow was assumed to be steady and incompressible, and the boundary conditions of the simulations duplicated s performed in the test room. The grid dependence was tested with different grid densities and shaping. The final mesh consisted of grid points and was clustered towards the diffuser and the walls. The simulation was declared converged when the parameters and the residuals were no longer changing with successive iteration and the error for the overall heat balance was less than.3%. To achieve and ensure convergence approximately 6 iterations had to be completed. Performing more iterations did not affect the result. The simulations were performed on a 95MHz Enterprise Sun computer and the computational time was around 8 hours. Table. Boundary conditions for the walls and the inlet Front Back Left Right Ceiling Floor Inlet Temperature ( o C) Effect (W) 5 Flow rate (l/s) 5. Turb. Intensity (%) 5. The modeling of the air diffuser is critical. The design and geometry of the supply obviously influence the pattern close to the diffuser. The diffuser consisted of 36 rectangular openings with a total area (free area) of.63m 2. Therefore, detailed supply diffuser characteristics cannot be modeled, due to restrictions in computer capacity. Instead a simplified model must be used to describe the performance of the diffuser. Different methods to model complicated air terminal devices are described by Heikkinen (9), Moser (9), and and Moser (9). However, problems appear with each of the models (Koskela 2; Loomans 98; Emvin and Davidson 96). For the present study none of these methods were used in the end. Instead the diffuser was simulated by 2 rectangular openings (9mm 9mm) with the same total area as the original diffuser, see Figure 2. The flow rate of the inlet air was defined at the top of the diffuser. No significant change in the result was observed when the flow rate was defined in the ventilation duct at different upstream location from the diffuser. RESULTS AND DISCUSSION The cold air from the displacement diffuser drops immediately to the floor in front of the diffuser because of the low momentum, direction of the flow and strong negative buoyancy. The airflow acts as a jet and induces the surrounding air. This induction causes re-circulation beneath the diffuser and just above the cold airflow, which is clearly shown in Figure 3. The flow from the diffuser is unstable and velocities and temperatures fluctuate substantially. However, all two-equation models captures the recirculations of the air flow close to the supply diffuser and agree fairly with the instantaneous infrared thermography image. Still, for all models there is a slight displacement of the bubble and the airflow pattern is somewhat 767

4 different. For the model, the size of the bubbles is to some extent larger than the twoequation models. It is worth to mention that the measuring screen has higher temperatures due to surrounding radiation. Figure 4 presents the vertical air temperature and air velocity (speed) distribution in the centerline of the test room at four different distances from the inlet diffuser. According to Figure 4, all two-equation models are capable of predicting the velocities and the temperatures in accord with al findings. However, the model is not as good as the two-equation models, see Figure 4. For all models, the accuracy is not perfect very close to the diffuser, at x=. m, because the flow patterns are to great extent affected by the diffuser characteristics and modeling. However, the results indicate that the modeling of the inlet device seems to be quite acceptable. According to Figure 5, the maximum velocities predicted by two-equation models are higher than the al data. The difference lies between 2-4% compared with al data. The model underpredicts the maximum velocity especially close to the floor. The difference lies between 4-6% compared with al data. These underpredictions of the velocities for the model results in high temperatures near the floor. The temperature is overestimated by up to. C. Among the two-equation models, the and the -Kim model seem to predict the temperature profile slightly better than the Standard ε model. However, employed turbulence models overpredict the temperature gradient, especially at x=.5m from the diffuser, indicating poor heat transfer analysis near the floor. Nevertheless, in this study, the y + value at the first grid along the floor is around, as recommend by (95). Loomans (98) have also concluded that CFD-simulations in which the heat transfer is determined by use of wall functions do not always present a good agreement with the al results. The and the Standard ε models are very stable during computations, while the - Kim model is quite unstable and requires more iterations to converge. The model is less computational expensive (around 2%) than the two-equation models, but as with the -Kim model it requires many iterations to converge. Overall, all 2-equation models are in good agreement with al findings. The predictions from the and the -Kim model were almost the same and slightly different than the standard ε model. y x Figure 3. Thermal image compared to predicted temperatures with the model. 768

5 y z A=mm B=2mm C=3mm D=5mm,8 x ε A B ε C ε ε,8,8,8 D,6,6,6,6 U (m/s),4,4,4,4,2,2,2,2 Temperature ( o C) 2 ε A B C ε ε ε D Figure 4. The vertical temperature and velocity profile at four different distances (, 2, 3 and 5mm) from the diffuser..8 ε U max /U in x/y.5 Figure 5. The maximum velocities at different downstream distances from the diffuser. y.5 is the position where the velocity is half of the maximum velocity. CONCLUSION In the present study the air flow from a low-velocity diffuser has been simulated with a zeroequation model and three two-equation turbulence models. The diffuser was simulated by 2 rectangular openings, and the flow rate of the inlet air was defined at the top of the diffuser. 769

6 The modeling of the inlet device seemed to be quite acceptable and all two-equation models proved to be capable of predicting the velocity and the temperature in accord with al data. The result indicated that the model is not recommended for prediction of air flow from a low-velocity diffuser. The predictions from the and the -Kim models were almost the same and slightly different than the standard ε model. The model and the Standard ε model are computationally much more stable than the -Kim model. ACKNOWLEDGEMENTS The authors are thankful for the financial support from KK-Foundation (Stockholm, Sweden) and University of Gävle (Gävle, Sweden). The authors gratefully acknowledge the assistance received by Ulf Larsson at the Department of Technology, University of Gävle. REFERENCES Cehlin, M., Moshfegh, B. and Sandberg, M.. Measurements of Air Temperatures Close to a Low-Velocity Diffuser in Displacement Ventilation Using Infrared Camera: Parameter and Error Analysis, accepted for publication in Energy and Buildings., Q. and Moser, A. 9. Simulation of a multi-nozzle diffuser. Proceedings of the 2 th AIVC Conference, Ottawa, vol.2, pp.-3., Q. 95. Comparison of different e models for indoor air flow simulations. Numerical Heat Transfer, vol.28, part B, pp , Y. and Kim, S. 87. Computation of turbulent flows using an extended ε turbulence closure model, NASA CR-924. Emvin, P. and Davidson, L. 96. A numerical comparison of three inlet approximation of the diffuser in case E Annex 2. Proceedings Roomvent 96, vol., pp.9-6, Japan. Heikkinen. J, 9. Modelling of a supply air terminal for room air flow simulation. Proc. 2th AIVC Conf., Ottawa, Canada. Koskela, H. 2. CFD-modelling of active displacement air distribution. Proceedings ROOMVENT2, vol., pp , Reading, England. Launder, B. and Spalding, D. 74. The numerical computation of turbulent flows, Comp. Meth. in Appl. Mech. & Eng., vol.3, pp.269. Loomans, M. 98. The measurement and simulation of indoor air flow. Ph. D Thesis, ISBN X, Eindhoven University of Technology, Eindhoven, The Netherlands. Moser, A. 9. The message of Annex 2: Air flow patterns within buildings. Proceedngs of the 2 th AIVC Conference, Ottawa, vol., pp.-26. Spalding, D. 94. The PHOENICS Encyclopedia, CHAM Ltd., London, U.K. Yuan X, Q Glicksman, L 99. Measurements and computations of room airflow with displacement ventilation. ASHRAE Transactions, vol.5, pp Yakhot, V., Orszag, S., Thangam, S., Gatski, T. and Speziale, C. 92. Development of turbulence models for shear flows by a double expansion technique', Phys.Fluids A, Vol.4. 77