Effect of airflow direction on human perception of draught
Forty subjects, 20 women and 20 men, were exposed to airflows from five different directions: horizontally towards the front, the back, and the left side and vertically upwards and downwards. The subjects were exposed to stepwise increased air velocities ranging from less than 0.10 m/s to 0.40 m/s at three temperature levels 20, 23 and 26 o C. The results showed that airflow direction has an impact on perceived discomfort due to draught. At 20 o C and 23 o C, airflow from below was perceived as most uncomfortable followed by airflows towards the back and front. At 26 o C airflow from above and towards the back caused most dissatisfaction due to draught, but generally only a few of the subjects perceived discomfort at this temperature. Discomfort due to draught was most often felt at the body regions directly exposed to the airflow. These were the legs, the feet, and the lower back at airflow from below; the neck, the shoulders and the hands at airflow from above; the neck, the back, the shoulders and the legs at airflow from behind; the knee and the arm facing the windbox when exposed to air movements directed towards the side; and the hands and the knees when exposed to air movements towards the front.
Design Methods for Air Distribution Systems and Comparison Between Mixing Ventilation and Displacement Ventilation
The paper will discuss design models for the air distribution system in an office with two persons. The comparisons are made between mixing ventilation and displacement ventilation and they are based on a maximum velocity assumption and a restricted vertical temperature gradient in the room. The comparison is extended by considering both the local discomfort caused by draught rating (DR) and the percentage of dissatisfied due to the temperature gradient (PD). The two different systems are finally evaluated by measuring the variation of the equivalent homogeneous temperature (EHT) at the manikin when it is exposed to the environment generated by the two systems. INDEX TERMS Air distribution; Design; Mixing ventilation; Displacement ventilation; Comfort INTRODUCTION The aim of an air conditioning system is to remove excess heat in a room and replace room air with fresh air to obtain a high air quality. It is not just sufficient to remove heat and contaminated air, it is also necessary to distribute and control the air movement in the room in such a way that thermal comfort is obtained in the occupied zone. This paper addresses two air distribution systems, namely mixing ventilation and displacement ventilation, and discusses the design strategies for the two systems. The supply flow rate q0 and the temperature difference ∆T0 between return and supply are chosen as design parameters. The local discomfort caused by draught rating, DR, and the dissatisfied due to the temperature gradient, PD, as well as an evaluation of the air distribution systems based on measurements from a thermal manikin are also addressed. MIXING VENTILATION AND DISPLACEMENT VENTILATION Two important parameters are considered in the design of room air distribution. The parameters are the air velocity and the vertical temperature gradient, and they both have to be restricted to certain levels to ensure thermal comfort in the room. The air velocity can either be the maximum velocity urm inside the occupied zone in case of isothermal flow or it can be the velocity uocz of the jet when it penetrates the upper boundaries of the occuped zone in the case of non-isothermal flow, see Figure 1A. A third expression for high velocities is connected to the length xs of the wall jet below the ceiling (penetration length), see Figure 1A. A penetration length larger than half the room length, xs/L > 0.5, will normally ensure restricted velocities in the occupied zone. The vertical temperature gradient is not considered to be important for mixing ventilation. Nielsen (1991), Nielsen et al. (2001) and Jacobsen et al. (2002a,b) show details of design models based on the above-mentioned restrictions on the velocity level in the occupied zone. ∗ Corresponding author. E-mail: pvn@civil.auc.dk Figure 1 Room with mixing ventilation (A) and a room with displacement ventilation (B). Displacement ventilation has a high air velocity in the stratified flow at the floor. Restricted velocity in the occupied zone is therefore obtained by restricting the velocity in the stratified flow where it enters the vertical boundary of the occupied zone in front of the diffuser. This is expressed by the length of the adjacent zone Ρn, which is the distance from the diffuser to a given velocity level in the stratified flow, see Figure 1B and Nielsen (2000) and Skistad et al. (2002). The vertical temperature gradient is also important in displacement ventilation and it should be restricted to a certain level. A minimum stratification height is especially important when the air is contaminated. The idea behind a minimum stratification height is to keep the occupants’ breathing zone in the low zone, or close to the low zone, enabling them to inhale clean room air, see Brohus and Nielsen (1996) and Skistad et al. (2002). This has not been considered in the paper. COMPARISON BETWEEN MIXING VENTILATION AND DISPLACEMENT VENTILATION The comparisons are made in a room of typical size for a small office. The room was a standard room for the International Energy Agency Annex 20 work, see Nielsen et al. (2001). The room has the dimensions; length, width, height equal to 4.2 m, 3.6 m and 2.5 m, respectively. Figure 2 Office room with two manikins (A). ‘Annex 20’ diffuser (B), and diffuser for displacement ventilation (C). Two types of diffusers were used for displacement ventilation. Figure 2A shows the heat load locations in the room. The heat load consists of two PCs, two lamps and two manikins giving a total load of 460 W. The manikin on the right side of the picture is the measuring manikin, and the manikin on the left side of the picture is a manikin that imposes an additional heat load on the room. The two manikins change place during the measurements. The arrangement in Figure 2A is called an A-case and the reverse location of the measuring manikin is called a B-case. Figure 2B shows the ‘Annex 20’ diffuser for mixing ventilation mounted on the end wall below the ceiling, and Figure 2C shows the diffuser for displacement ventilation mounted in the same wall. Two different types of diffusers are used for the experiments on displacement ventilation described in this paper. Figure 3 Design graph for the two ventilation systems based on the temperature difference ∆T0 between return and supply and on the flow rate q0 to the room. The curves show different limitations for the velocity levels and the temperature gradient, which ensure thermal comfort in the room. Figure 3 can be considered as a design graph. The graph is based on temperature differences ∆T0 between return and supply and on flow rate q0 to the room. The curves, which are found by measurements in the two rooms, show the combination of ∆T0 and q0 which encloses an area that fulfils thermal comfort. A maximum velocity urm of 0.2 m/s restricts the flow rate to the room to 0.036 m/s, and the requirement of a penetration length of xx /L = 0.5 is expressed by the dotted curve in Figure 3. The area between the two curves will thus express an area allowed for variation of ∆T0 and q0 in the room with mixing ventilation. The combination of ∆T0 and q0 which gives the penetrating velocity uocz = 0.4 m/s is shown by another curve in Figure 3. The rather high velocity seems to give the same level of comfort as obtained by the consideration of the jet penetration length. An acceptance of a higher velocity in vertical downward direction is confirmed by Toftum et al. (1997). The length of the adjacent zone Ρn is given to 1 m with a reference velocity of 0.2 m/s in the case of displacement ventilation, and the temperature difference ∆T0 is in principle restricted to 12.5°C corresponding to a vertical gradient of 2.5°C/m in the room. Two curves show the corresponding area for fulfilment of thermal comfort in the ∆T0, q0 diagram. The figure indicates that the room to some extent will have the same level of comfort (with respect to maximum velocity and maximum temperature gradient) independent of the air distribution system. It became clear by this work that the results for displacement ventilation were very dependent on an efficient low-velocity diffuser. Generally, Figure 3 indicates that constant air volume systems (CAV) work well for mixing ventilation, while variable air volume systems (VAV) are easy to control in the case of displacement ventilation. LOCAL DISCOMFORT OBTAINED BY THE DIFFERENT AIR DISTRIBUTION SYSTEMS The design models discussed in the last two sections can only give the limits for the operation of the air distribution system. It is necessary to consider thermal comfort for all flow rates if the system has to be optimized. The thermal environment often exhibits temperature gradients, velocity gradients, different turbulence levels and an asymmetric radiant temperature distribution. The local discomfort, which is the result of this environment, is judged from measurements of the local values of air temperature, air velocity, turbulence level and from measurements of surface temperatures or asymmetric radiant temperatures (see Fanger and Langkilde, 1975; Olsen et al., 1979; Fanger et al., 1989; Toftum et al., 1997). Figure 4 Draught rating DR versus flow rate, and percentage of dissatisfied PDgrad due to vertical temperature gradient versus flow rate. The cooling load in both rooms is constant and equal to 460 W. Figure 4 shows the number of dissatisfied because of draught, DR. It is expected that the maximum velocity has a downward direction in the case of mixing ventilation, but the measurements show that this is only the case for the lowest air flow rate (n = 2.05 h). Air velocity in horizontal direction measured 10 cm above the floor gave the highest velocity at all other airflow rates (up to n = 3.66 h). The draught rating, DR, for displacement ventilation is in all cases a result of a horizontal flow from the wall-mounted diffuser. It is shown in Figure 4 that the draught rating, DR, for mixing ventilation has the highest level far away from the diffuser, while it is the opposite for displacement ventilation where a position close to the diffuser gives the highest risk of draught. The draught rating increases with increasing air change rate, independent of the type of air distribution system. Figure 4 also shows the percentage of dissatisfied due to the vertical temperature gradient in the occupied zone. There is a total lack of dissatisfied when the air distribution system is of the mixing type. Displacement ventilation shows a high percentage of dissatisfied at low flow rates, and the PDgrad decreases with increasing flow rate. Comparison between the two graphs in Figure 4 indicates that mixing ventilation has the lowest level of local discomfort at low flow rates, while an optimal flow rate exists for displacement ventilation because the DR is increasing with the flow rate and the PDgrad is decreasing. EVALUATION OF LOCAL THERMAL COMFORT BY A THERMAL MANIKIN The thermal manikin used in the experiments is described in detail 
How to do a p-descent on an elliptic curve
In this paper, we describe an algorithm that reduces the computation of the (full) p-Selmer group of an elliptic curve E over a number field to standard number field computations such as determining the (p-torsion of) the S-class group and a basis of the S-units modulo pth powers for a suitable set S of primes. In particular, we give a result reducing this set S of 'bad primes' to a very small set, which in many cases only contains the primes above p. As of today, this provides a feasible algorithm for performing a full 3-descent on an elliptic curve over Q, but the range of our algorithm will certainly be enlarged by future improvements in computational algebraic number theory. When the Galois module structure of E[p] is favorable, simplifications are possible and p-descents for larger p are accessible even today. To demonstrate how the method works, several worked examples are included.