WITH DISPLACEMENT VENTILATION
Natalia Lastovets 1,2, Risto Kosonen 1, Panu Mustakallio3
1Aalto University, School of Engineering, Department of Mechanical Engineering
2O.M. Beketov National University of Urban Economy in Kharkiv
3Halton Oy
ABSTRACT
To estimate the vertical temperature stratification in rooms with displacement ventilation, several simplified nodal models were developed and implemented in the various building simulation software. However, the temperature gradient in buildings is highly dependent on a variety of factors, such as different flow elements and the location of heat loads.
Inaccurate estimation can result in 2-3 °C temperature difference compared to the target design values, which could lead to poor thermal comfort in the occupied zone. In the present study, measurement data was compared with the commonly used models and novel four-nodal model. The differences between the measurements and simulations were indicated for the occupied zone temperatures. The four-nodal model provides an accurate prediction for all types and combinations of heat loads.
INTRODUCTION
Displacement ventilation (DV) is a well-known solution in industrial and non-industrial premises. First applied to industrial facilities with high thermal loads and contaminant distribution, nowadays this air distribution strategy is successfully implemented for the ventilation of offices and other commercial spaces.
In displacement ventilation systems cool air is supplied into the occupied zone of the room near the floor at low velocity and then entrained by buoyant plumes over any warm objects. As a result, a two layer room air temperature profile, stratified and mixed, is developed. Ideally, the air movements induced by thermal plumes transport heat and pollutants to the layer above the occupied zone, promoting a vertical temperature and contaminants stratification. The transition level between a mixed upper layer and stratified layer is called mixing height, which is related to the height where the inflow rate matches the airflow induced by the thermal plumes in the occupied zone. Controlling the mixing height position is one of the most challenging tasks in DV system design, since it directly relates to the calculation of supply air flow rate.
Nodal models treat the thermal stratification of the indoor air as an idealised network of nodes connected with flow paths. Such models vary according to the application, number of nodes, flow and heat load configuration and mixing height consideration /1/. The most common linear temperature modelling with two room air nodes has been proposed by Mundt /4/. The multi nodal models introduce the temperature profile composed by variable slopes between three nodes /2,3,5,6/. Several nodal models are currently available in thermal energy simulation tools. The Rees and Haves /6/ model can be
applied to ESP-r, Mundt /4/and Mateus and da Graça /3/ models are implemented in EnergyPlus and Mundt /4/ model is also available in IDA ICE.
Several analytical nodal models with semi-empirical correlations have been developed to estimate the temperature gradient in rooms with displacement ventilation. However, in order to evaluate the ability to calculate the occupied temperature the models, they need to be validated with the experimental results.
METHODS
Simplified nodal models
The purpose of this section is to introduce the simplified nodal models and compare them according to the ability to predict the temperature in the occupied zone. Three nodal models with different approaches were chosen in the present study: Mundt /4/, Nielsen /5/
and Rees /6/ models.
Mundt /4/ proposed the 2-nodal model where temperature gradient is calculated to be linear over the room height. The temperature at the height 0.1 m is determined by the dimensionless temperature that is obtained from the balance between radiative energy flux from the floor and convective heat transfer from the floor surface to the air. The temperature of the second exhaust node is calculated from the heat balance.
The dimensionless temperature calculation is also included to Nielsen model /5/.
However, in this model the temperature is estimated empirically from Archimedes number and the type of heat gain. The model also predicts mixing layer height as a height of neutral buoyancy. The temperature in this height is assumed to be the same as the exhaust temperature.
The alternative approach to consider the flow patterns between nodes was developed by Rees and Haves /6/. The model includes 11 interrelated nodes: 4 room air nodes out of the thermal plume, 4 nodes of the air flow within the plume and 3 surface nodes representing floor, ceiling and wall temperatures. In addition, this model uses 14 flow paths between the nodes with flow rate parameters that are pre-determined by experimental and numerical studies.
The four-nodal model /2/ predicts room air temperature at four heights: at the height of 0.1 m, at the height of the occupied zone, at the height of the mixed layer and the height of the exhaust air temperature that is equal to the room height. The room heat loads are divided between the nodes according to the heights of the heat sources. The air above the occupied zone is considered to be fully-mixed.
Thus, four analytical methods that use different semi-empirical correlation to estimate the temperature gradient for the displacement ventilation design are chosen to be validated according the ability to calculate the occupied zone temperature.
Experimental measurements
The test setup consists of displacement diffusers with perforated front face and ceiling exhaust in well-insulated room with 20.8 m2 floor area and room height of 5.12 m. The internal heat loads (Table 1) consist of heated cylinders representing persons, heated cube-shaped boxes representing computers, heated foils in one wall and ceiling representing solar load on window at different levels and fluorescent lighting units.
Table 1. Simulated head loads for the presented cases
Case Heat loads from the simulators, W Total heat
In the present cases vertical temperature profiles are measured from four locations at ten heights with calibrated PT100 sensors (accuracy ± 0.2 °C). Surface temperatures were measured with Testo 830-TI-infrared thermometer (accuracy ± 0.1 °C). Supply and exhaust air flows were measured with air flow rate measurement device MSD 100, that was calibrated with an orifice plate to reach the accuracy ±3%.
RESULTS
The measured data of the temperature gradient for the typical indoor heat loads (Table 1) were compared with the calculation results of the selected simplified nodal models:
Mundt /4/, Nielsen /5/, Rees and Haves /6/ and 4-nodal model /2/. The results of the corresponding measurements and calculations are presented at the Figure 1.
a) b)
c) d)
κ – dimensionless temperature H – room height
Figure 1. Measured and calculated room air temperature profiles of the cases: a) 6 people; b) 6 people and 6 computers; c) 10 people, window loads, lighting; d) 10 people, ceiling loads.
Accuracy of the models
To assess the accuracy of the models the following average error indicators is used:
Average norm of the error:
Ǥ Ǥ ൌσసభሺȁୗ୧୫୬ିୣୟୱȁሻ (1)
݊ – number of experiments.
The validation of the selected DV models was conducted based on simulation and measurement results for all four cases in three important temperatures at the heights of 0.1, 1.1 and 1.8 m. The average results of the all measured cases are presented in Table 2.
Table 2. Error indicators of the validated models
The occupied zone temperature at the height 1.1 m calculates by Mundt /4/ model was 2.8°C lower than the measured one. Rees and Haves /6/ model gave better results, however the different at the difference at the occupied zone lever was still 1.7°C. The prediction of the Nielsen /5/ model underestimates the temperature with the average difference of 1°C.
The negative values of average bias (Table 2) indicate that Mundt, Neilsen and Rees and Haves models predict lower temperature gradient that measured.
4-nodal model /2/ gave the best results of all compared models. The average difference between the estimated and measured values was 0.27 °C at the height 1.1 m.
DISCUSSION
The results represent typical temperature stratification in rooms with displacement ventilation, when the main gradient happens in low zone. Upper that level the
temperature stratifies in a case when there is no high heat loads, such as ceiling or high window heat gains. The ability of the models to calculate the most important occupied zone temperature is strongly dependent on the consideration of mixing height. It would result to overestimation of the supply air flow rate and therefore – poor comfort conditions and wrong sizing of the ventilation system.
Therefore, two-nodal Mundt /4/ model that does not count the level of stratification is not able to predict the temperature gradient. Rees and Haves /6/ model allows accounting the heat loans at different levels; however, it significantly underestimates the temperature in the occupied zone. The empirical correlations in Nielsen /5/ model lead to the good prediction of the air temperature near the floor. But the overestimation of the mixing height results to the inaccurate calculation of the occupied zone temperature. 4-nodal model /2/ that applies plume theory to calculate the mixing height and counts the load distribution between the nodes is able to estimate the occupied zone temperature with the lowest error.
In addition, all the presented models are steady-state, whereas the temperature gradient in buildings is highly dependent on environment dynamic weather conditions, thermal mass and changing occupancy. Therefore, there is also a need of dynamic validation of the simplified nodal model.
CONCLUSIONS
The present study presents the comparison and validation of four commonly used simplified nodal models in terms of their ability to calculate the temperature in the occupied zone of the room. The comparison with the experimental results indicates that the most commonly used nodal models estimate the temperature with significant error up to 3°C. The four-nodal model demonstrates the most accurate prediction for the typical indoor heat loads.
REFERENCES
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