KUBOTA  Hideki

Muroran-IT Academic Resource Archive

Predicting and Evaluating Draft in SummerCooling著者 KUBOTA  Hidekijournal orpublication titleMemoirs of the Muroran Institute ofTechnology. Science and engineeringvolume 10number 3page range 493-503year 1981-11-30URL http://hdl.handle.net/10258/3734Predicting and Evaluating Draft in Summer Cooling Hideki Kubota ABSTRACT A scale for evaluating draft in summer cooling is derived in terms of the Predicted Percentage of Dissatisfied (PPD) by applying Fanger's Predicted Mean Vote (PMV) equation and by introducing a model of air distribution. An analytical procedure to predict values of the maximun air velocity and also the lowest air temperature in an occupied zone is presented. Based on these techniques， the optimum value of a product : (diameter of the outlet) x (air velocity at the outlet) is suggested for high sidewall air-supply systems. The values of PPD for drafts analytically obtained in this saper are correlated to the values of ADPI proposed by Mi1ler et al.， and it is observed that the minimum PPD corresponds to the maximum ADPI. INTRODUCTION This paper presents a guide for optimum design for room air distribution in summer cooling in which the main problem to be solved will be dealing with local areas of discomfort caused by excessive air motion combined with lowered air temperature. In 1938 Houghten et al.l) first presented the relationship between draft and the sensory responces from human subjects. However， this relationship is not always applicable for summer cooling， since the experiments in which this relationship was observed were conducted at a temperature level of 210C for subjects with one clo insulation of clothing， while summer cooling temperatures are around 260C and summer clothing is about O.5clo or les. Rydberg et a}2). derived an equation for draft temperature in 1949. As recommended by Miller3)， this scale now needs to be updated. Miller et a14J.proposed a single number index， Air Diffusion Performance Index (ADPI)， in 1964 which enables us to evaluate three dimensional room air distribution. Miller also expanded the defintion of the ADPI by applying the new Effective Temperature in 19763) and the Predicted Percentage of Dissatisfied (PPD) in 19755) so that the new ADPI (designated as ADPI-2) is more closely related to modern comfort criteria. This method of using a single number index has made a very significant contribution and has helped make a lot of data available for practical use. The present paper derives a scale for evaluating draft by applying fanger's Predicted Mean V ote (PMV) and the PPD techniques， and may provide another basis for the support of the ADPI-2 scale. To provide a clear basis for this scale， a model of room air distribution is established， after considering the most extreme conditions of the draft in the occupied zone which are expected to appear in the region where a discharged cooled air mass hits the subjects. The analytical procedure described in this paper to predict both maximum air velocity (105) 494 Hideki Kubota and air temperature difference in the occupied zone enables us to estimate both the optimum condition for the air being supplied and the size of the outlet. Our present discussion deals with a high sidewall air-supply system， however， the principles described can be applied to other air-supply systems. PREDICTED PERCENTAGE OF DISSATISFIED(PPD)IN AN AIR JET An actual system of air distribution is too complex for direct analysis but by simpli-fying assumptions an adequate model may be obtained. Consider a system in which the following assumptions apply: 1. The occupied zone is divided into two regions : one is a stil air region and the other a cool air jet region. 2. The stil air region is maintained at 26.50C dry-bulb， air velocity 0.15m/s and relative humidity 50% to satisfy the comfort requirments of normally clothed sedentary human subjects (0.5 clo， lMet). 3. Mean radiant temperature is the same al over the room and equal to the temperature in the stil air region. 4. In the jet region both air velocity and temperature are represented respectively by the highest and lowest values appearing in this region. When the occupants take position in the cool jet region， they may feel to be cool. The degree of coolness can be estimated by using the equation for the Predcted Mean V ote (PMV) proposed by Fanger. The value of PMV can be used to estimate the Predicted Percentage of Dissatisfied (PPD). Fig.l shows the combinations of air velocity and temperature difference between jet and stil air for which the PPD remains constant. The analytical procedure for deriving this relationship is presented in Appendix A. 1.0 0.8 山吉0.6} 〉ト同504 凶〉PPD -PREDICTED PERCENTAGE OF DI55ATI5FIED 01 L .. ち7 、司 I 10 -5 ・4 -3 ・2 -1 0 DRAFT TEMPERATURE D1FFERENCE (Oc) Fig.l Predicted Percentage of Dissatisfied for subjects in cool jet region (106) Peredicting and Evaluating Draft in Summer cooling 495 It appears that the line representing the cool-side limit for ADPI-2 coinsides with the curve for 10% of PPD. This result could support the basis for ADPI-2. An approximate function for lines of constant PPD value derived by trial and error is as follows: PPD=(6 jv戸瓦百+LlTj)2 (for PPD<30) ( 1 ) where V J = airvelocity in the jet region， m/ s 1 T J = airtemperature difference between jet and stil air regions， oK. The broken line in Fig.1 indicates Houghten's 80% comfort data. PREDICTION OF THE MAXIMUM VELOCITY AND AIR TEMPERATURE DIFFERENCE BETWEEN JET REGION AND STILL AIR REGION The maximum air velocity and the lowest air temperature in the jet region are given respectively as centerline velocity and air temperature of air jet at a point where the centerline meets the upper boundary of the occupied zone (see Fig.2) . By assuming that the drop of jet is not too great， the centerline air velocity at the upper boundary can be approximated by the following equation: VJ=KpDo Vo/XJ ( 2 ) where VJ =Centerline velocity of the jet at the point where the centerline meets the upper boundary of the occupied zone， m/s Kp = constant Do = diameter of the outlet， m Vo=air velocity at the outlet， m/s XJ =horizontal distance from the outlet to the point where the centerline meets the upper boundary of the occupied zone， m. The drop of the cool air jet was given by KoesteFl as the equation: gβLlToDo (X V -一 =0.42一一一一ー一一← I~ I Do V.~~ Kp Vo ¥ DoJ STILL AIR REGION AIR JET REGION Xr UPPER BOUNO.<-l.RY OF OCCUPIEO ZONE Fig.2 Schematic flow: pattern in summer cooIing (107) ( 3 ) 496 or Hideki Kubota where Y =vertical distance from the center of the outlet to a point on the centerline of jet， m X = horizontal distance from the outlet to a point on the centerline of jet， m s T 0 = air temperature difference between outlet and stil air， 'K g = gravitational acceleration， m2 /s β=volume coefficient of thermal expansion. This equation can be rearranged into the following form : DoVo ^^^'~( q Vl3 --'J~T' U = 0.02461TT 'u 1 ¥ KpY ) (Kn Y ¥113 X=40.7(~一一 1 DoV。¥ q / where q=sensible heat load of room supplied from an outlet， W ェcρJ7DBVOToc=heat capacity of air， J/K ρ二 densityof air， Kg/m3. Substitute Eq.4 into Eq.2， we have， /口¥113 ( 4 ) ( 5 ) ( 6 ) VJ二 0.024即 3(τ(7) where Y J = vertical distance from the center of the outlet to the upper boundary of the occupied zone， m. This result suggests that the maximum air velocity is independent of the conditions at the outlet : V 0， s T 0 and Do. In a similar way， the lowest air temperature is given in the form of air temperature difference as follows: s TJ =0.82KpDos T o/XJ ( 8 ) whereムTJ二 maximumair temperature difference between jet and stil air region， K. EliminatingムT0 from Eq.8 by applying Eq.5 and 6， we have， ムTJニ O0365K;v;/3q2 ( 9 ) or ムTJ=2Z×106kp/3dl3/[yf(DoVo)21. (10) The maximum difference s Tj appears to decrease with increasing Do VO. From the results described above， the larger value of Xj(or Do VO) will be recom-mended， since the value s T J decreases with increasing X J， while the value of V J does not vary with XJ. However， this recommendation is only applicable where the value of Xj issmaller than the distance to the wall perpendicular to the jet or mid-plane between opposite (108) Peredicting and Evaluating Draft in Summer cooling 497 outlets. When the value of XJ exceeds room length parallel to the jet， supposing the opposite wall is not located， the jet comes into the occupied region after being disturbed by the opposite wall. In this case， the maximum air velocity and air temperature difference may appear near the opposite wall， and these values are approximated as follows: VJ二 ω揃 K勺1Y13(毛 -V.VL.'iV I"-P ¥ -V;-) ¥ L (11) 6.TJニ0.0365KpYJ q2/3/ (LXJ) (12) where L= distance from outlet to the nearest wall perpendicular to jet or mid-plane between opposite outlet， m XJ = in this case， an imaginary horizontal distance supposing the opposite wall is not located， m (see Fig.2). As may be seen in the above equation， an increase in XJ (or Do Vo) raises VJ while reducing 6. TJ. From the standpoint of PPD， itcan be concluded that the value of PPD increases with XJ according to the results of the calculations being made for PPD appllying the values to practical situations. From the facts described above， we can conclude that the minimum value of PPD will be obtained when we make the value of XJ equal to the room length L. This optimum condition is expressed as fo1tws. /円、1/3(Do V o)oPt = 0.0246 ( TT Y一一)¥ Kp YJ J COMPARISON WITH TEST DATA (13) In Table 1， the analytical values estimated by Eq.5， 7 and 10 are compared with the test data obtained by N elson and Stewart8) on chilled air projected into a room from outlets of various dimensions with the same opening area. It gives good agreement between test and analytically estimated values. TABLE 1 Comparison between experimental data by Nelson & Stwart and analytical values derived in this paper 。rigir市l口ata 戸redictedVa!ues Outlet XI VJ 。TJ XJ VJ ゐTJDimension (川 xM) (M) (判/S) (degOC) (M) (M/S) ( degOc ) 0.28 x 0.36 6 1目5 -2.4 0.40 x 0.20 6 T目25 -1.9 0.48 x 0.18 6 1.25 -1.9 6.3 1.5 由2.70.71 x 0.13 6 1.5 -2.3 0.91 x 0.10 6 1.75 -2.7 00 = O.324(川)， Vo =5.0(同/S)，dTo"-11.1(degoC)， q "5.8x10'(W)， y，."O.8(M)， Kp"6 (109) 498 Hideki Kubota COMP ARISON WITH V ALUES OF ADPI OBTAINED BY MILLER ET AL. It is of considerable interest to correlate the analytical values of PPD with the ADPI experimental results obtained by Miller et a19). As indicated inAppendix B， based on flow patterns and data shown in his paper， the value of Kp isassumed to be about 3 and the drop of the cool air jet trajectory to be about 30% of the value calculated by Eq.3. This may be attributed to the effect of the ceiling surface: a kind of Coanda Effect. As we have litle knowledge of this effect， we will tentatively apply the following expression as an equation for the drop of the cool air jet : gβAToDo (X V 一一一二0.42"'::-:-:'-VI一一lDo -v..~ Kp V20 ¥ DoJ where A=coefficient representing ceiling effect (=0.3). This change of equation will lead to the following equations. 2/3 ( Aq¥川VJ二 0.0246KP ¥ y;) =0.0397ql/3 ムTJ=0.0365KpYJ q2/3/(A XJ) = 0.20q2/3 jXJ where Kp =3， A=0.3 and YJ =0.64m. (14) (15) (16) In Miller's paper， the values of ADPI were plotted as a function of the ratio T O•2S j L. The value of L (room length) was 6.1m (20ft). The synbol TO・2Sdescribes "the throw" of the jet which is definds as the distance from the outlet to a point in the air stream where the maximum velocity occuring in the stream cross-section has been reduced to a selected terminal velocity of 0.25mjs. Based on this definition， the following relationship is given from Eq.l. KpDo VO =0.25To.2S (17) Combining Eq.2， 15 and 17， we have， 。25Tn" 0沼Tfl?I';. … XJ=一一-~ ~ v."" 一一」今 =6.3q-1/3To.2SVJ り.0397q(18) Substituting Eq.18 into 16， the following is given for A TJ : ATJ =5.1 x 10-3 q4J3jTo.2S (19) The value of T O•2S jL at XJ=L， where it is suggested the smallest value of PPD occurs， is given from Eq.18 as follows: 千=0.16ql/3 (20) (110) Peredicting and Evaluating Draft in Summer cooling 499 TABLE 2 Correlation between ADPI by Miller and analytically estimated values of PPD 100 16 I '0.44 250 q SYMBOL wjSQ-阿0・63マ"126 口・ 189ム企 252OPEN Xy :0 L 5OLIO: )くr>しoL-------________ _i o 50 1口OPREDICTED PERCENTAGE OF DISSATISFIED (PPD) OrIginol 001ロR町し副(WjSQ_M) I To.';しV;J I d.γs ( %) I (%) I (MjS) I (d句。c)63 0.95 " フ" 0.56 " " 。出2.1'隆'" " 0.8B I _0.67 '" 65 0.63 69 2.4. " '" " フ70 0.70 -5.1 2.6* 3.5 Fig.3 Correlation between PPD and ADPI ???? ???????????????In the c出e:XJ>L The following equations give the expressins for VJ and ムTJ •V，= KpD内V0 = 0 . 2S T~.2 J 二 T 一一二 25~ (21) 「Kp YJ q213 ムTJ二 0.0365a: l/; V'1. = 8.4 X 1O-4qj (二主主)AII3LXJ (22) The values of VJ and D.TJ corresponding to To・25/Las tested by Miller have been calculated and are listed in Table 2. Fig.3 shows ADPI plotted as a function of the PPD value. As may be seen from Fig.3 and Table 2， the maximum values of ADPI closely correspond to the minimum PPD and they appear to be centered around XJ二 LCONCLUSION 1. A scale for evaluating draft in summer cooling was derived in terms of Predicted Percentage of Dissatisfied (PPD) by applying Fanger's Predicted Mean Vote (PMV) equation and by introducing a model of air distribution. 2. An analytical procedure to predict values of the maximum air velocity and the maximum air temperature difference between jet and stil air regions in the occupied zone was presented for high sidewall air-supply systems. 3. A comparison between data obtained by Nelson et al. and the caluculated values was made and showed good agreement. 4. The values of PPD， analytically obtained in this paper， were compared with the values (111) 500 Hideki Kubota of ADPI obtained by Miller et al. and it was observed that the minimum PPD cor-responded approximately to the maximum ADPI. 5. For minimizing the PPD caused by drafts， the horizontal distance XJ， from the outlet to a point where the air jet centerline meets the upper boundary of the occupied zone， was suggested to be equal to the distance from the outlet to the nearest wall perpendicular to the jet. REFERENCES 1. Houghten， F.C.， Gutberlet， C.and Wilkowski， E.，"Draft Temperatures and Velocities in Relation to Skin Temperatures and Feelingof Warmth"， ASHVE TRANSACTIONS， 44， 1938. 2. Rydb 巴ぽrg，]. and N orback， P.，"電"AirDistribution ana Dr悶af仕t3丸.Miller， P.L.，"Application Criteria for the Air Diffusion Performance lndex (ADPI)，" ASHRAE TRANS. ACTION， 8.乙2，1976. 4. Fanger， P.O.， The門加1Comfort， McGraw-Hill， 1972. 5. Koestel， A.，"Paths of Horizontally Projected Heated and Chilled Air Jet，" ASHVE TRANSACTION， 61. 1955. 6. Nelson， D.W. and Stewart， D.].， "Air Distribution from Side Wall Outlets，"ASHVE TRANSACTION， 44， 1938. 7. Miller， P.L. and Nash， R.T.， "A Further Analysis of Room Air Distribution Performance"， ASHRAE TRANSACTION， 77， 1971 APPENDIX (A) The following equation for Predicted Mean V ote proposed by Fanger was modified by introducing linear approximation for radiant heat exchange. P川M肝Vド刊山二斗哨叩(仰川0ω303e釘ザ円一Iで'l.Ouω5[57300071(H)-PJlM[且 (1-r;)-58.1]-.t1.DU .t1.Du 001733ι(587PJ)000lA(34ω r1..Du n.Du 3.95fcれCl-tmrt) -f clhc( tCl-tJ)] where tC1 is determined by the equation tCl= [ /[1 + 0.155Ic!Icl( 3.95 + hc)] and hc by hc二 12.1〆Vwhere M=metabolic rate， W 1m2 Aou二 DuBoisarea， m2 PJ=partial pressure of water vapour in jet region， kPa tJ = air temperature in jet region， oc(112) (A -1) (A -2) (A -3) Peredicting and Evaluating Draft in Summer cooling tC1 =mean temperature of outer surface of clothed boby， 'ctmrt =mean radiant temperature in jet region， 'cfC1ニratioof the surface area of the clothed body to the surface area of the nude boby， ND hc = convective heat transfer coefficient， W /(m2 • K) 501 ICl二 thermalresistance from the skin to outer surface of the clothed body， clo η=external mechanical efficiency of the boby， ND From the assumptions concerning air distribution， the conditions in the jet region are expressed as follows : mean radiant temperature air temperature vapor pressure tmrt二 taニ 26SCtJ =ta +.0. T/C PJ=Pa+ムPJkPa where suffix "a" implies the value for stil air region. (A -4) When the sensible heat ratio (SHR) of the room concerned was given， the value of t.PJ can be expressed in the function of .0 T J・SHR=ct. To/ (ct. To +λムWo)=l/[1+λWo/ (ct.To) ] where .0 T 0 = air temperature difference at the outlet， 'K .0 W 0 = humidity ratio difference at the outlet， g/Kg λ=heat of vaporization of water， J/Kg. (A -5) In the jet stream， where the process of vapor diffusion is similar to that of heat diffusion， we have the following relations. t.WJ t.Wo t.TJ t.T。Substituting Eq. A-6 into A-5， we have， t.WJ =三(--L一一1) 企TJ •λSHR-1 As the vaule of SHR for an office room is around 0.7， let SHR=0.7， .0 WJ =0.17.0 TJ • By conversion of units from g/Kg to kPa， the value ofムPJis obtained : ムPJ=0.16ムWJ二 0.027ムTJ.(A -6) (A -7) (A-8) (A -9) Substituting Eq. A -2， A -4 and A -9 into Eq. A -1， and solving the Eq. A -1 for .0 T J TABLE 3 PMV vs. PPD Neutral Slightly Cool -1 令2(113) 502 Hideki Kubota gives the following expressions : L1TJ = [PMV -Al(A2-A3十A4Pa+A5ta-fdA9+ AI0(3.95十hc)ta])]/All (A -10) where Al = 0.303e-o.036(M/ADU) + 0.028 A2二子ι(1-q)-0424(l q) 5811 1"iDu 1J..Du A3三 3附 73-0.00片(l一川町3×5873Loo似×34孔fnoo nw nυu A4三 3.05十001732ιA5=000143ι_L-inu F1.Du A6Z357-002751(1一平) A7エ 0.1551心nDu As =1+0.155Ic!Icl(3.95+hc) A9二 (3.95+hc)A6/ As AI0エ (3.95十hc)A，jAs-1 Alニ Al[0.027A4十A5-AlOfcι] Using Eq. A -10， itis possible to calculate combinations ofムTJand VJ that correspond to a certain value of PPD. The relationship between PPD and PMV is listed in Table 3. APPENDIX (B) The value of Kp isassumed by using the following equation for isothermal free jets. Vc=KpDoVo/X (B -1) Kp = VcX/ (Do Vo) (B -2) From the definition of the throw， when the value of X equals T O•25 the value of Vc is0.25m/s， then we have， Kp=0.25To・25/(Do Vo) (B-3) The diameter of the outlet and the air velocity at the outlet are as follow， P20二日0929m2 (24" x 6" ) Do二fS=0.344 m2 V。ニG/Swhere S二 areaof the outlet， m2 G二 airflow rate through the outlet， m3/s. Miller's paper shows the values of T O•25/L for values of G. (B -4) (B -5) (B -6) Applying these values for the equations described above， we can get the value of Kp to be around 3. (114) Peredicting and Evaluating Draft in Summer cooling 503 The value of coefficient "A" representing the ceiling effect， isdefined as follows : (B ~ 7) This equation can be rearranged in the following form in the same way as Eq.5. KpY I DハV"¥3 A二 (40.7)3~-;~，-=γ) (B ~ 8) Miller displays the flow patterns for a room load of 20 Btuhjsq-ft ( 63W jsq-m) with changing flow rates. We can obtain two values of X for the drop of Y (= 0.64m) ; about 1.7m for 0.6cfmjsq-ft and 2.8m for 1.0 cfmjsq-ft. Based on these values， we can assume the value of A to be around 0.3. (Received May 18， 1981) (115) 

Predicting and Evaluating Draft in Summer Cooling

Abstract

Similar works

Full text

Available Versions

Muroran-IT Academic Resource Archive