THES‘S ABSTRACT A THEORETICAL ANALYSIS OF AIR VELOCITY DISTRIBUTION INSIDE A VENTILATED ROOM WITH A LONG SLOT INLET by Felleke Zawdu The purpose of the research study is to derive a theoretical equation that will describe the air velocity distribution inside a mechanically ventilated room--given the quantity of air discharging into the room through a long narrow slot. A theoretical analysis of a free Jet discharged into Open space and exhausted out through a circular sink was undertaken and an equation describing the mean air velocity magnitudes at given points inside the room was derived with the following general assumptions: 1. Flow is 3-dimensional 2. Flow is steady 3. Flow is incompressible Then, an experimental study was conducted where read- ings of actual velocity magnitudes were taken inside a 9' x 8' x 2' framed box using a hot wire anemometer. The results of the theoretical and the experimental studies showing mean velocities versus distance were plotted. All the theoretical and experimental plots clearly exhibit Fellexe Zawdu symmetries of velocity distributions about the center of the box. The theoretical as well as the experimental curves show higher velocity distributions at distances near the outlets and lower velocity magnitudes for points near the center of the box in both the x-y and x—z planes. Both the theoretical and the experimental curves also indicate higher velocity magnitudes at y = O and a gradual decline in ve- locity for points along lyl > O in the y-z plane. A general conclusion was reached where the shapes of the theoretical curves do follow the patterns of the experimental plots ex— cept where the physical boundaries of the box exaggerated the experimental velocity magnitudes of the air streams moving adjacent to these boundary layers. Comparison of absolute velocity magnitudes was not made because the low air flow rate employed in the study induced correspondingly low air velocity distribution in the box. In addition, experimental errors as well as the inherent limitations of the theoretical derivations become significant in the velocity range less than 15 fpm-—which is considered as stagnant air. Therefore, an unrealistic percent deviation between the theoretical and experimental valves results. A future research study employing air velocity of not less than 35 fpm--which is considered as satisfactory condition within the occupied zone—-is sug- gested. ’ ;Zi g?) " Approved: WM W Major Professor Approved: ”Maj M Department Chairman A THEORETICAL ANALYSIS OF AIR VELOCITY DISTRIBUTION INSIDE A VENTILATED ROOM WITH A LONG SLOT INLET By Felleke Zawdu A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1966 ACKNOWLEDGMENTS The author wishes to express his sincere appreciation to Professor M. L. Esmay of the Department of Agricultural Engineering, under whose general guidance this study was conducted. The author also wishes to thank Dr. D. R. Heldman for the help rendered in instrumentation. Appreciation is also extended to S. A. Weller for giving his assistance in writing programs for the computer. TABLE OF CONTENTS ACKNOWLEDGMENTS LIST OF FIGURES INTRODUCTION OBJECTIVE LITERATURE REVIEW A. Standard Requirements for Optimum Ventilation Conditions . B. Theory of Room Air Distribution. THEORETICAL ANALYSIS . . . . . . . . A. Kinematics of Fluids B Potential Flow and Velocity Potential Function . C. Sources and Sinks . D. A Source--Sink Pair. EXPERIMENTAL STUDY A Apparatus Used B Calibration C. Procedure . D. Calculations T A B RESUL Cf) Theoretical Experimental DISCUSSION OF RESULTS CONCLUSIONS SUGGESTED FUTURE RESEARCH. REFERENCES. APPENDIX . . . . . . . . iii Page ii iv l3 13 15 l7 19 21 21 21 21 22 28 28 28 35 38 140 141 AA Figure 1:: (DNO‘sU'I 10. ll. 12. 13. 14. 15. 16. LIST OF FIGURES Page An Elementary Parallelepiped Fluid . . . . 13 A Velocity Vector in Plane Polar Co-ordinate Axis . . . . . . . . . . . . . 16 A 3-Dimension Source of Radii of Spheres . . 17 A Source-Sink Pair . . . . . . . . . 19 Box Elevation . . . . . . . . . . . 25 Box Side Views. . . . . . . . . . . 25 Venturi Tube . . . . . . . . . . . 25 Hot Wire Anemometer Filament Calibration Chart . . . . . . . . . . . . . 26 Pictorial View of Apparatus Set- Up and Instrumentation. . . . . . . . 27 Hot-wire Anemometer Probe, Stand, and Probe Moving Mechanism . . . . . . . . . 27 Theoretical Velocity Magnitude versus Distance, x-y plane . . . . . . . . 29 Theoretical Velocity Magnitude versus Distance, x—y plane . . . . . . . . 30 Theoretical Velocity Magnitude versus Distance, y-z plane . . . . . . . . 31 Experimental Velocity Magnitude versus Distance, x-y plane . . . . . . . . 32 Experimental Velocity Magnitude versus Distance, x-z plane . . . . . . . . 33 Experimental Velocity Magnitude versus Distance, y-z plane . . . . . . . . 3A iV INTRODUCTION To obtain satisfactory results in ventilating, air- conditioning and warm air heating systems correct air distribution is highly essential. Even though a system delivers to a room the required quantity of conditioned air, unsatisfactory conditions will prevail if the air is poorly distributed. The purpose of air distribution in ventilating, air- conditioning and warm air heating is to create in the occu— pied zone of the conditioned room the desired combination of temperature, humidity, and air motion. To maintain com- fort conditions within this zone, standard limits have been established as acceptable effective temperatures comprising of air temperature, motion, humidity and the physiological effect on the surface of the human body. Any variation from accepted standards of one of these elements or lack of uniformity of conditions within the occupied space or ex— cessive fluctuation of conditions in the same part of the space may result in discomfort to the occupants. Such dis- comfort may be due to excessive room air temperature vari- ations (horizontally, vertically, or both), excessive air motion (draft), failure to deliver or distribute the air [\‘t according to the load requirements at the different loca- tions, or too rapid fluctuation of room temperature or air motion. To create optimum environmental conditions ventilation air exchanges are highly critical in confined housing of livestock and poultry. Air temperature and relative humidity affect the amount of heat and water dissipation and hence the productivity of livestock and poultry. In any confined ani- mal housing operation either natural or mechanical venti- lation, although the latter system is preferred, is designed to remove the moisture given off by the animals as rapidly as it is produced. The ideal ventilation rate would be generally geared to maintain the desired moisture balance at lower outside temperatures and the optimum heat balance at higher outside temperatures. Variations in building construction, system designs, and operating requirements make practical room air distri- bution problems quite complex. To analyze the performance of a jet discharged from any air supply outlet, the engineer needs answers to these questions: 1. What is the throw of the air jet? 2. What is its angle of divergence or spread and its velocity profile? 3. How can velocity at any given point within the jet be determined? (.2.‘ This thesis is directed towards question no. 3 and hence determining the velocity distribution of an air jet discharged into a room. OBJECTIVE Many confined livestock and poultry housing operations use mechanical ventilation systems where exhaust fans per- form the necessary air exchange discharging into the houses through long narrow crack inlets or slots. The objective of this research study is to formulate a theoretical equation that describes the velocity distribution of an air jet dis- charged into a room through a long slot and exhausted through a circular hole; and to compare the theoretical results with values obtained by taking measurements of actual velocity magnitudes at the specified points inside the room. LITERATURE REVIEW Literature is reviewed in regard to the following two general aspects of ventilation: A. Standard requirements for optimum ventilation conditions. B. Theory of room air distribution. A. Standard Requirements for Optimum Ventilation Conditions Barre and Sammet (2) state that air circulation may be required to remove moisture from a livestock shelter, to cool a room or the products stored in it, to dry or humidify the atmosphere or a product, or to maintain a standard of air purity. Barre and Sammet (2) present the Moisture- Balance equation as: W e M w (1) 81 where, M = air flow per hour, lb. We = moisture to be exchanged per hour, lb. degree of saturation in outgoing and in- coming air, respectively (for practical purposes u usually may be assumed equal to the relative humidity) u2 and “I water in saturated air-vapor mixtures at 1 temperature of outgoing and incoming air, respectively, lb./lb. dry air. W and W 82 s 5 and the Heat-Balance equation as: QL + QS + Ma (0.2u)(tO - ti) + A U — t AV(to where, QL latent heat exchanged, Btu/hr. Q = sensible—heat input, Btu/hr. M = air flow per hour, lb. A = total surface area eXposed to temperature difference, ft2 t0 and ti = outside and inside air temperatures, respectively UAV = average overall heat-transmission coeffi- cient (a weighted average in which the U value of each type of wall is included in proportion to its area). ASHAE Guide (1) points out that velocities less than 15 fpm generally cause a feeling of air stagnation, whereas velocities higher than 65 fpm may result in a sensation of draft. The Guide further reports that air velocities of 25 to 35 fpm in the occupied zone are considered satisfactory, but air motion of 20 to 50 fpm will usually be acceptable. In housing swine, Hazen and Mangold (10) mention that moisture and odor produced by the swine are to be removed by ventilation; and in particular where there is large differ— ential between the inside and outside temperatures, neces— sary amounts of air can create draftiness even though the velocity is low. Hazen and Mangold (10) further state that since a heat-balance of a swine-production unit reveals there is inadequate sensible heat production by the animal to maintain wide temperature differentials between outside and inside, the required supplemental heat could be used effectively to prevent drafts by preheating the ventilating air prior to the time it comes into contact with the animal. Cargill, Stewart, and Johnson (A) report that the ideal design environment-controlled summer shelter for dairy cows could be based on a limiting discomfort index of 75. The discomfort index is defined by the relationship: D1 = 0.55 Tdb + 0.2 po + 17.5 (3) where, D1 discomfort index Tdb dry-bulb temperature po Esmay (6) states that an actual ventilation air ex— dew-point temperature. change of 3 cfm per square foot of floor area should be pro— vided for poultry laying houses in the northern zones of the United States during the warmer seasons of the year. Esmay (6) further reports that a practical, economical and ef— fective ventilation system is the exhaust type where the exhaust fans are to be located and air is discharged into the house from the attic through a long narrow crack inlets of l- to lg-inches wide. B. Theory of Room Air Distribution The theory of room air distribution is not complete, but a considerable fund of knowledge supported by experi- mental guidance is available for the solution of many air distribution problems. Tuve (21) points out that both engineers and scientists have paid much attention to the free jet problem. A free jet is one discharged into a relatively large room or other free atmospheric Space. Limitations are imposed that no surfaces or objects are near enough to the stream to interfere with the formation of the natural flow-pattern and that the primary stream is straight-flowing, free from pulsations and helical flow. Tuve (21) established four major zones along the direction of a free jet. These zones are roughly defined in terms of the maximum or center-core velocity that exists at the cross-section being considered. Zone 1: A short zone of 2 to 6 diameters from the outlet face. Core-velocity is very nearly equal to the original outlet velocity throughout the length. Zone 2: A transition zone that usually extends 8 to 10 diameters. The maximum velocity may vary inversely as the square root of the distance from the outlet. Zone 3: An extensive zone of 25 to 100 diameters long, depending on the shape and area of' the outlet and initial velocity. Maximum velocity varies inversely as the distance from the outlet. Zone A: A terminal zone in which the residual velocity decays into a large scale turbu- lence. The maximum velocity subsides to the range below 50 fpm usually regarded as still air. These four zones indicated above do not fully describe the performance of a free jet. Tuve (21) states that the laws of continuity, conservation of momentum, conservation of energy, and dimensional analysis have been applied to the analysis of free jets. Vorticity transfer theory has also been developed. Tuve (21) further states that all the mathematical formulations defining jet performance call for experimental constants and in many cases these are not as yet well established. Therefore, by treating the air as an incompressible fluid and assuming that viscous flow is not encountered, Tuve (21) shows that the maximum center-core velocity in Zone 3 can be determined with good engineering accuracy for round outlets from the equation: 1 Vx = E Q (A) where Q = volume of air discharged V AO from outlet per unit time. A0 = effective area of stream at discharge. X = distance from outlet face. . K' = proportionality constant. Tuve (21) further indicates that theoretically, for an infinite slot the center-core velocity varies as the square root of the distance. Vc(x>2 = C (5) In regard to boundary layer problems Tuve (21) mentions that Nottage demonstrated clearly that when the axis of a long jet is too close to the wall, floor or ceiling, and parallel with it, the spread of the jet in that direction is reduced and a greater throw of the air stream occurs with the wall in place than that of the jet discharging into free Open space from the same outlet. Koestel and Austin velocity in a jet stream using the principle of co equation to determine the a given distance from the ON p V where, a = < ll < n Koestel (ll) applyi of momentum states that t can be found by the equat 10 (12) in analyzing the maximum issuing from two parallel nozzles nservation of momentum derived an maximum center—line velocity at outlet face for a single jet as: _ a 2 2 "' 2 DOD V0 (6) a 2 2 —2ar2 = 5 D00 VO e (7) c —%, a shape factor x 2 k2 constant, length in diameters of the constant velocity core distance, ft outlet velocity, ft/sec. diameter of nozzel, ft. jet velocity along stream lines through the nozzel, ft./sec. air density, slug/cubic foot jet velocity at radius r, at distance x, ft./sec. radius, ft. the base for the Napierian system of logarithms e = 2.718 ng the principle of conservation he maximum center-line jet velocity ion: ll yf‘k(HO/RO) cos e[k(HO/Ro)cos e + 11 y/R(R — a9: R o (8) where, VC = maximum velocity in air jet, fpm VO = maximum outlet velocity, fpm R = distance from geometric center of outlet to where maximum jet velocity is V , ft. c R0 = radius of outlet, ft. Ho = width of slot opening in outlet, ft. k = length of the constant velocity core in terms of the width, HO 9 = horizontal deflection of axis stream, degrees Elrod (5) in presenting a theoretical analysis of the performance of a jet states that Reichardt hypothesized that "momentum diffuses with distance from a source in the same manner that heat-energy diffuses with the square root of time." Then Elrod (5) further states that by analogy with the well—known equation of heat conduction the following equation may be written: ' 2 2 2 Boga = c [A LW%_ + 3 0W2:] (9) 3(22) 8X2 3y2 Elrod (5) then presents a general equation for the compu- tation of experimental results as: 12 erf (X+a - erf (513 erf (1:2) - erf (X:E) { cz }{ cz cz 73-; 2 2 } (10) )1. W o where, W time-mean velocity in z—direction WO mean peak velocity of the source a half—width of infinite slot along x—axis b = half—width of infinite slot along - y-axis c = empirical constant in Reichardt's turbulence. Equation Approximate Value: 0.08 x = Cartesian coordinate in plane of jet source y = Cartesian coordinate in plane of jet source z = Cartesian coordinate in plane of jet source. Elrod (5) concludes that with varying degrees of success, but with an accuracy sufficient for almost all engineering purposes, the free turbulence equation of Reichardt corre— lates the performance of free jets; and that value of 0.0805 for the constant c in equation (9) provides satisfactory agreement with the experiment. THEORETICAL ANALYSIS A. Kinematics of Fluids The kinematics of fluids is the branch of science dealing with the laws of motion of a fluid. The fluid is considered to be a continuum and its motion is treated as the continuous and constructive deformation of a continuous material medium. To describe mathematically the velocity distribution of the fluid motion certain assumptions will have to be made. Assumptions: 1. Flow is steady 2. Flow is 3—dimensional Therefore, if u is the velocity vector and P is the hydro—dynamic pressure: u = u(x,y,z) P = P(x,y,z) A Z b I 1 0 dz luz A -—d— —— .— Uy u} / / dy dx 0 ~—> x y Figure l.—«An Elementary Parrallelopiped Fluid. 13 IA In the co-ordinate axes above, the parallelepiped of volume dxdydz containing a point A, moving at velocity UA’ simultaneously participates in three types of motion- translation, deformation and rotation (Cauchy-Helmholtz Theorem, Reference 16). Therefore, if UA is the velocity of point A in the moving fluid, then the velocity of any point c is the geometrical sum of three velocity vectors — the translation velocity UA’ the deformational velocity Udef , and the rotational, or vortex, velocity Urot about an instantaneous axis through A. U = U + U + U (11) Cauchy-Helmholtz Equation (Reference 16) This equation may be written (Reference 16): X U 3X 8U x(c) = UX + [———dx + eydz + ezdy] + (dez - dey) —- —1 EU Uy = Uy + Ljagdy + ezdx + exdz + (dex — Qxdz) (12) "3U ” = Z '- UZ(C) UZ + 7;;dz + exdy + eydx + (nxdy dex) ._ .J U U U are the translation velocity components, the y’ Z terms in brackets are the deformational velocity components, x, and the terms in parentheses are the rotational velocity components, where (Reference 16): l5 BUZ 3Uy BUZ 3U —— - 1/ _ ex 2( a + 32 ) S2X 2(ay az) 3U 8UZ 3U dUz 1/ —— = 1/ —_ .. '3 9y 2( 82 + BK) 9y 2( 32 3X) (1.)) EU BUX 3U BUX = t __l ___' = L __X _.___ 9z 2( 8x + a ) Qz 2( 6x a ) B. Potential Flow and Velocity Potential Function For an incompressible fluid undergoing potential flow the vorticity vector and its components are all zero (Refer- ence 16); that is: = 1/ Z _ -——X = Qx 2( By 32) O 3UX SUZ = 1/ ._ —_ _ my 2(82 ax) 0 (1A) 8U aUX = t __X _ = 9z 2( 3x 8y ) 0 Or 3U 8U By 82 BUX aUZ ____.. = __._____ [I 82 3x (1’) 3U 8U __l = X 8x 3y These equations indicate that the velocity components Ux’ Uy’ Uz at each point of an irrotational fluid flow may be written as partial derivatives of some function ¢(x,y,z), (Reference 16), that is: U = M09352) x 8x vy= War“ um U = 6¢(x,y,z) Z 32 In the xy plane the function ¢ depends on two variables only, so that equation (16) becomes, (Reference 16): U = a¢(x,y) x 8x (17) U = a¢(x,y) y 8y In plane polar co—ordinates these equations have the form (Reference 16): yzi P «5 j/ \ v/ (M r O O 11> X. Figure 2.--A Velocity Vector in Plane Polar Co—ordinate Axis. l7 U =§¢ r or (18) U =fl=lfl s as r 36 Where Ur and US are the radial and tangential components of the velocity vector U at point M (Figure 2). C. Sources and Sinks A source is a particular point in the space filled by the fluid, from which fluid enters the surrounding medium at some rate Q. 49X Figure 3 -—A 3nDimension Source of Radii of Spheres The streamlines of the fluid are directed along the radii of the spheres drawn with the source as the center (Figure 3). A sink is a particular point at which fluid disappears at a rate Q. Consider a sphere of radius r measured from a source or sink, where source streamlines 18 have arbitrarily, a positive direction and sink streamlines have a negative direction. The flow velocity from a source or to a sink is then (Reference 16): _ _ Q _ . Q U - Ur - i; - :u 2 (19) TTI‘ In this case equations (18) reduce to (Reference 16): Q. .9. US = O; Ur = + a; (20) Equations (19) and (20) give (Reference 16): d¢=+ng (21) - A nr - _ - Q .'¢-+m 7 y (22) where r = /x2+y2+z2 ) ./ The velocity components are (Reference 16): _ 32 = j; - Q UX - 8X BX<+ Enr) =_a__¢i=._a__Q ’ “ Uy 3y 3y(+ 3??) (23) _ ii = er- _9_ Uz _ az 82)+ Anr' 19 D. A Source-~Sink Pair Z? m(x,y,z) //VR r1/ 52 ,/ ('a:y:O)/l __ (3,0,0) |>X +Q ~Q V Figure 4 Consider a long slot source located at (-a,y,0) and a circular sink located at point (a,0,0) on an imaginary co- ordinated axes x,y,z as shown in Figure A. The distance from an arbitrary point m(x,y,z) to the source rl and the sink r2 are: /(X+a)2 + Z2 *3 ll (24) VYx-a)2 + y2 + z2 I’2 The velocity potential function, equation (22) is in this case : — Q .3; EL - x _ HF (_ rl + r2) (35/ , . , _t , -9- . . a (x,y,Z) = §%l[(X-a)2 + y2 + Z2] 2 - [(X+a)a + 22] 2; (26) 20 Therefore the velocity components are: 3¢ (D: (x+a) 1 _ (X—a) A = 3; = H;1[(x+a)2+z212/2 [(x—a)2+y2+z2]3/2} = 2.? = _ Qy2 (27) By un£2 +y 2+z2J3/2 = 31?: Q2 1 - 1 } 32 2— [(x+a) 2+z2J3/2 [(x a)2 +y 2+z2J3/2 V = y/IJ2 + U2 + U2 (28) mean x y z EXPERIMENTAL STUDY A. Apparatus Used 1. An exhaust fan 2. A venturi tube A micro-manometer A. A hot-wire anemometer set-up 5. A pitot tube 6. A 9' x 8' x 2' box built from plywood; one side covered with glass. B. Calibration The hot-wire anemometer was calibrated in a wind tunnel using a pitot tube and a micro-manometer. Readings for zero velocity or still air and for maximum velocity were taken and the necessary calibration curve of I2vs. V12 was drawn as shown in Figure 8. C. Procedure The venturi tube was connected to the fan by a A-inch diameter U-pipe and the set up was mounted to the 4-inch diameter outlet as shown in Figure 9. The micro-manometer was carefully installed to the venturi connections. After checking that all connections were air—tight, the fan was started and readings were taken from the micro-manometer 21 22 scale. These readings were averaged and the computed average was used to calculate the rate of air flow, Q, discharging into the box. An imaginary x,y,z co-ordinate axes as shown in Figure 5 was drawn through the center of the box with the x—axis passing through the center of the exhaust outlet and the mid-point of the center line of the slot inlet. The probe of the hot-wire anemometer was placed inside the box and careful measurements of mean velocities were taken at the specified points with reference to the imaginary co- ordinate axes. At a given point three different measure- ments were taken by rotating the probe and hence the axis of the probe filament: l. The axis of the probe filament parallel to y-z plane. 2. The axis of the probe filament parallel to x-y plane and facing towards the y-axis. 3. The axis of the probe filament parallel to x—y plane and facing towards the x—axis. D. Calculations 1. Flow rate, Q: Assuming an expansion factor of l, i.e., assuming that the air is incompressible (Reference 2): 23 Q = C M A2 V2g/Y 'Pl—P2 (29) = c M A2 /2gh (30) Where, M = 1 -———l——— = 1.033 2" r— C I 0.965 (Discharge Coefficient, from Beckwith and Buck) h = 0.1 ft. of water (from micro—manometer) 0.1 x 62.A x 13.5 = 8A.25 ft. of air _ l 2 _ 2 A2 - “(i—2‘) - 0.0218 ft. 32.2 ft./sec.2 8 Q = 0.965 x 1.033 x .0218 /2x32.2x8u.2u x60 = 95.82 CFM 2. Mean velocity At a specified point inside the box three different measurements were taken as indicated above in Procedure. Let A, B, and C be the velocity measurements obtained re- spectively at a given point inside the box with the axis of the filament aligned in the aforementioned directions using the established co-ordinated axes as a frame of reference. Since the hot-wire anemometer filament detects velocity magnitudes along two perpendicular planes, then: 2 2 _ Vx + Vy - A v2 + V: = B (31) v2 + v2 = c X Z 2A The measured values A, B, and C were programmed and fed into the computer and the magnitudes for the velocity components Vx’ Vy’ and VZ; and for V mean were obtained: where, V mean = /V: + V3 + v: (32) z 25 A 1/2" inlet slot f/ __ // u" dia. I // 2' exhaust // outle /Jr .4 D 5L y / / fl . / x 0’ 8! G D Figure 5.--Box Elevation 2" 3 3/u" $ 6 6 142" -— Er :' i O E l'- t? A 14: v t k‘r :>|<: 2 {>1 I" 8 :> Box Side View Box Side View Figure 6.--Box Side Views Venturi Connections Figure 7.—-Venturi Tube phmzo coapmanfiamo pcmEmHHm memEoEmc< mhfiz pomlu.w mhswflm mm om fir ACHE\pM u >V m> mm om ma L a _ _ _ — _ meow H m.H magpmmmasme .m .m ooow ooom (VM 27 I S - s - 12¢“ ., 3|)“, . ‘ ‘ . .kih“ ‘ -r’2a Figure 9.—-Pictorial View of Apparatus Set—up and Instrumentation. Figure lO.--Hot Wire Anemometer Probe, Stand, and Probe Moving Mechanism. RESULTS A. Theoretical Q = 95.82 CFM (see page 23) was substituted into the theoretical velocity component equations and their magni— tudes were calculated for given values of x,y,z, in refer- ence to the established co-ordinate axes x,y,z within the 2 y desired points. The results are shown graphically, Figures box. Then, V mean = y/U: + U + U: was computed for these ll, 12, and 13, by plotting the mean velocities against distance. B. Experimental Measurements of velocity magnitudes at points corres- ponding to the theoretical case were taken and V mean = y/V: + Vi + Vi (see page 23) was computed for each point. The results are plotted on graph papers, Figures 14, 15, and 16, showing mean velocities versus distance. 28 mamam mix .mosmpmfia mamhm> coupficmmz zpfiooam> HmOHpmaomnBI|.HH madman .pm .moemsmao : m m H o H: m: m: N“ L. w T d»: % .r 0 iii IIII..II..I.1II|. II I. 'U7 a\ l/ \ / x / \ / \ .\ w \ Olllilb (\J + II >1. 0: was KQTOOIGA 30 QOHm Nix .mo:@pmfio mamnm> manpficmmz mpfiooao> Hmoapmpomzbll.ma mszwfim .pm .mocmpmfio H o a- AH.H- n N .o u w v, 0 SduuN.ous .!l|l|. aa.on u N .o u s «w. «a was KQIOOISA mcmHm Nix .mocmpmHQ msmho> mUSNHcmmz ANHOOHm> HmOHpmpomQBII.mH mpsmHm .pm .mocmpmHo s m m H o NH.H- u N .o u N . . NR?uN6uN7!!!1 NH.ou u N .o u N a a waa KQIOOISA C) II N (\J + II >4 q msmHm mix “megapmwm mampm> waspHcmmz thQOHm> HmpcmEHsmdxmnu.zH mustm .pm .mocmpmHm a m N H o H- m- m- L L L _ L N s. i G, \\9II..|II .I.|||I|ollll.l.llls|||.|l.| \ \ \ ouNSqullllo waa KQIOOIGA .53 mcmHQ Nix .moQMNmHQ mampm> mUSpchmz mpHOOHm> HmpsmEHpmdxmll.mH mssmHm 400 .ps .moeapmHo «4r-O $6: NHHI NH.QI My olllllo w allllllld i ON ‘KJIOOIGA Ndfl mqum NI» .mocmumHo m5m9m> mUSpHcmmz mpHOOHm> HapGoEHNoQNMII.mH mmswfim .pm .oocapmHa : m m H o H- m: m: :1 N H + N i 1 i N 1 ‘\\II, \\|IIA/P II'O‘II‘u. / 4 4 d / / MW / -,oH q . \ Ml.llnl.|\ 2/ /l\.\ 1-0m SauuNauN.!llJ NH.on u N .o u N v\. I. NH.H- u N .o u N allllllla .uom waa KQIOOIGA DISCUSSION OF RESULTS Figures 11 and 14 show the velocity distribution for the theoretical and experimental investigations respectively in the x—y plane along the x-axis. The general shape of the plots of the theoretical case do correspond to that of the experimental curves. Figures 12 and 15 indicate the velocity distribution in the x-z plane along the x—axis. The theoretical curves, Figure 12, predict smooth mean velocity distribution with low velocity magnitudes occurring around the center Of the box at x = 0. Figure 12 also shows the Y = 0, Z = -0.67 curve falling above the Y = 0, Z = -l.l7 curve while the experimental curves, Figure 15, show the Opposite. This is due to the bottom floor of the box which is a physical boundary and creates or promotes reflections and a greater throw to the bottom layer of the moving air, and hence causes an increase in the mean velocity magnitude of the bottom part of the moving air layer. In regard to boundary layers, Tuve (21), as mentioned in the literature review, points out that when the axis of a long jet is close to the wall or floor a greater throw of air stream results than a jet discharging into free open space which the theoretical curves, Figure 12, represent. 35 36 Figures 13 and 16 indicate the velocity distributions in the y—z plane along the y-axis. The shape of the plots of the theoretical case, Figure 13, correspond to that of the experimental curves, Figure 16, between the interval -2 i y i 2. However, between the intervals I2] > y the theoretical curves show a decline and the experimental curves show a rise in mean velocity magnitudes. This is again explained, as mentioned above, in terms of the sides of the box acting as physical boundaries and hence contri- buting to greater mean velocity magnitudes along the ex— treme right and left side layers of the moving air inside the box. Discussions regarding the merits and acceptance of each plot and any comparison between corresponding theoretical and experimental curves has been geared to aspects concerning the shape of the curves rather than the absolute magnitudes each curve represents. Such an analysis or approach is taken be— cause of the low flow rate, Q, employed in the study induced correspondingly low air velocity distribution in the box. In addition, the sources of error introduced in conducting the experimental study and the inherent limitations of the theoretical equations become significant at the low velocity range of less than 15 fpm. Hence, an unrealistic absolute average percent deviation between the experimental and theoretical investigations results. Here, average percent deviation is defined as: Average % of Deviation = where, Ve Ve — Vt {IT—IX 100 e N experimental velocity readings Vt N = total number of readings theoretical velocity prediction Some of the sources of error and limitations of the equations are: 1. Sources of error 8.. Minor periodical fluctuations of the fan capacity resulting into unsteady flow rate conditions. Imperfect alignment of the hot-wire anemometer probe filament to face perpendicular to the direction of air flow. Human error in reading the true velocity measurements, caused mainly by turbulence. Characteristics and limitations of the theoretical equations a. b. Flow is steady. Flow is incompressible. No physical boundary conditions, i.e., the air jet is discharged into free open space. CONCLUSIONS The following results based on the theoretical and experimental studies were obtained. 1. Symmetries of velocity distribution about the center of the box do occur for all the theoretical and experimental plots. The theoretical as well as the experimental curves show higher velocity distribution at distances near the outlets and lower velocity magnitudes near the center of the box in both x—y and x—z planes. Both the theoretical and experimental plots indi- cate higher velocity magnitudes at y = 0 and a gradual decline in velocity for points along Iyl > 0 in the y-z plane. In the x-z plane the experimental curves show the y = 0, z = -0.67 curve falling below the y = 0, z = -l.l7 curve, while the theoretical curves show the opposite. In the y-z plane the shapes of the theoretical curves correspond to that of the experimental plots between the interval -2 i y i 2. However, between the intervals |2| > y the theoretical curves show a decline and the experimental curves show a rise in velocity magnitudes. 38 39 In general, the shapes of the theoretical curves do follow that of the patterns of the experimental plots with the aforementioned exceptions where certain boundary condi- tions of the box modify the predictions of the theoretical equation. Since the sources of error involved in conducting the experimental study and the inherent limitations of the theoretical equations become significant at the low air velocity magnitudes of less than 15 fpm——which is considered as stagnant air—-the average percent deviation will not be a realistic value. SUGGESTED FUTURE RESEARCH l. A higher flow rate, Q, that will not yield a mean velocity magnitude of less than 35 fpm--which is con- sidered as satisfactory air flow within the occupied zone-- should be employed and the degree of acceptance of the average percent deviation could then be realistically analyzed. 2. A study of the effects of boundary layers on velocity distribution of adjacent air streams. NO REFERENCES 141 10. REFERENCES ASHAE: Heating Ventilating Air-conditioning Guide-—Air distribution. ASHAE Guide, 1959, p. 267. Barre, H. J., and L. L. Sammet. Farm Structures. New York: John Wiley and Sons, Inc., 1963. Beckwith, T. G., and N. L. Buck. Mechanical Measure- ments. Massachusetts: Addison-Wesley Publishing CO., Inc., 1961. Cargill, B. F., R. E. Stewart, and H. D. Johnson. Environmental Physiology and Shelter Engineering --Effect of humidity on total room heat and vapor dissipation of Holstein cows. University of Missouri Research Bulletin 794, 1962. Elrod, H. 0., Jr. "Computation charts and theory of rectangular and circular jets," ASHVE Research Report No. 1515. ASHVE Transactions, 60, (195A), p. A31. Esmay, Merle L. "Design Analysis for Poultry-House Ventilation," Journal of Agricultural Engineering, Vol. A1, No. 9 (September, 1960), pp. 576—78. Ginzburg, I. P. Applied Fluid Dynamics. Jerusalem: Israel Program for Scientific Translations, 1963. Haerter, Alex A. "Flow distribution and pressure change along slotted or branched ducts," ASHRAE Research Report No. 1816. ASHRAE Transactions, 69, (1963), p. 12a. Hayes, F. C., and W. F. Stoeker. "Velocity patterns at return-air inlets and their effect on flow measurement," ASHRAE Research Report No. 1912. ASHRAE Transactions, 71 (1965), p. 37. Hazen, T. E., and E. W. Mangold. "Functional and Basic Requirements of Swine Housing," Journal of Agricultural Engineering, Al, 9 (September, 1960), pp. 585-90. U2 ll. 12. 13. 15. l6. l7. l8. 19. 20. 21. 22. 43 Koestel, Alfred. ”Jet velocities from radial flow outlets," ASHAE Research Report NO. 1618. ASHAE Transactions, 63 (1957), p. 505. Koestel, Alfred and J. B. Austin, Jr. "Air velocities in two parallel ventilating jets," ASHAE Research Report No. 1580. ASHAE Transactions, 62 (1956), p. A25. Koestel, Alfred and G. L. Tuve. "The discharge of air from a long slot," ASHVE Research Report No. 1328. ASHVE Transactions, 5A (19A8), p. 87. Kratz, A. P., A. E. Hershey and R. B. Engdahl. "Development of instruments for the study of air distribution in rooms," ASHVE Research Report No. 1165. ASHVE Transactions, A6 (19AO), p. 351. Madison, R. D., and W. R. Elliot. "Throw of air from slots and jets," ASHVE Journal, Section, Heating, Piping and Air ConditioningITNovember, 19A6), p. 108. Mkhitaryan, A. M. Hydraulics and Fundamentals of Gas Dynamics. Jerusalem: Israel Program for Scientific Translations, 196A. Nelson, D. W., and D. J. Stewart. "Air distribution from side wall outlets," ASHVE Research Report No. 1076. ASHVE Transactions, AA (1938), p. 77. Nottage, H. B., J. G. Slaby and W. P. Gojsaza. "A V-wire direction probe," ASHVE Research Report NO. lAAl. ASHVE Transactions, 58 (1952), p. 79. ~___"__ "Isothermal ventilation--jet fundamentals," ASHVE Research Report No. 1AA3. ASHVE Transactions, 58, (1952), p- 107. Richardson, E. G. Dynamics of Real Fluids. London: Edward Arnold Publishers, LTd., 1961. Tuve, G. L. ”Air velocities in ventilating jets," ASHVE Research Report No. 1A76. ASHVE Transactions, 59, (1953), p. 261. Tuve, G. L., D. K. Wright, Jr., and L. J. Seigel. "The use of air velocity meters," ASHVE Research Report No. llA0. ASHVE Transactions, A5 (1939), p. 6A5. APPENDIX Table Showing Velocity Magnitudes at Specified Points Inside the Box AA A5 Plane Point Theoretical Experimental (x,y,z), ft. Vmean, fpm Vmean, fpm x-y _u.25, 2 , 0 122.0 126.5 —A.0 , 2 , 0 30.5 39.8 -3 5 , 2 , O 7.7 10.3 -3 0 , 2 , 0 3.5 16.2 -2 5 , 2 , 0 2.0 19.6 —2 25, 2 , 0 1.6 9.1 0, 2 , 0 0.7 6.5 2 25, 2 , 0 1.0 3:3 3 O , 2 , 0 l 3 11.0 3 5 , 2 , O 1 6 11.6 ‘ u 0 , 2 , 0 1 8 13.1 —A.25, 0 , 0 122.0 1A8.7 —u.0 , 0 , 0 30.5 32.7 -3 5 , 0 , 0 7.7 11.1 —3 0 , 0 , 0 3.5 11.9 -2 5 , O , 0 2.0 22.8 -2 25, O , 0 1.7 10.5 0, 0 , 0 0.8 11.3 2 25, 0 , 0 1.7 11.5 3 0 , 0 , 0 3.5 13.0 3 5 , 0 , 0 7.7 15.6 A O , 0 , O 30.6 16.5 A6 Plane Point Theoretical Experimental (x,y,z), ft. Vmean, fpm Vmean, fpm x-y —u.25, -2.0, 0 122.0 1A8.7 _u.0 , -2.0, 0 30.6 u6.6 -3 5 , -2 0, 0 7 7 19.1 —3 0 , —2.0, 0 3 5 21.6 -2 5 , -2.0, 0 2 0 31.0 -2 25, -2.0, o 1 7 9.5 O, -2 0, 0 O 7 9.0 2 25, —2.0, 0 1 0 5.A 3 0 , -2.0, 0 l 3 18.3 3 5 , -2.0, 0 1 6 11.0 A 0 , -2.0, 0 1 9 13.8 x—z -A.0 , 0, -0.17 27.A 11.9 —3.5 , 0, —0.17 7.5 1A.9 —3.0 , 0, —0.17 3.u 13.2 -2.25, 0, -0 17 1.7 2.6 0, 0, —0.17 0.8 7.3 2.25, 0, —0 17 1.7 1.9 3.0 , 0, -0.17 ' 3.5 11.0 3.5 , O, -0.17 7.5 l3.A u.0 , 0, -0.17 27.u 18.7 —u.0 , 0, -0.67 11.0 11.u -3.5 , 0, —0.67 5.A 12.6 A7 Plane Point Theoretical Experimental (x,y,z), ft. Vmean, fpm Vmean, fpm x-z -3.0 , 0, -0.67 3.0 11.0 —2.25, 0, —0.67 1.5 1.7 0, 0, —0.67 0.7 2.A 2.25, 0, —0.67 1.5 1.9 3.0 , 0, -0.67 2.9 9.7 3.5 , O, -0.67 5.A 10.5 u.0 , 0, -0.67 11.0 11.2 —u.0 , 0, —1.17 u.7 11.7 -3.5 , 0, -1.17 3.2 12.9 -3.0 , 0, -1.17 2.2 11.2 -2.25, 0, —1.17 1.3 2.0 0, 0, —1.17 0.7 u.7 2.25, 0, -1.17 1.3 2 u 3.0 , 0, —1.17 3.5 11.0 3.5 , O, -1.17 7.5 l3.A 4.0 , 0, -1.17 27.u 18.7 y—z 0, —3 9, -0.17 0 55 18 u 0, —3.5, —0.17 0.58 10.6 0, —2.75,-0.17 0.63 1A.9 0, -2.0, —0.17 0.67 5.1 0, 0, -0.17 0.75 6.2 A8 (.5217... 32:22:55.? 5:22:52? y-z 0, 2.75, -0.17 0.63 13.0 0, 3.5 , -0.17 0.58 10.5 0, 3.9 , -0.17 0.56 13.6 0,—3.9 , -0.67 0.5a 13.5 0,—3.5 , —0.67 0.56 16.2 0,-2.75, -o.67 0.61 13.6 0,—2.0 , -0.67 0.66 1.9 0, 0, -0.67 0.73 2.u 0, 2.0 , -0.67 0.66 2.1u 0, 2.75, -0.67 0.61 17.3 0, 3.5 , —0.67 0.56 17.7 0, 3.9 , -0.67 0.5A 1u.u 0,—3.9 , —1.17 0.51 30.9 0,—3.5 , —1.17 0.53 1A.9 0,—2.75, -1.17 0.58 19.1 0,—2.0 , —1.17 0.62 1.9 0, 0, —1.17 0.68 5.1 0, 2.0 , -1.17 0.62 2.1A 0, 2.75, -1.17 0.58 13.2 0, 3.5 , —1.17 0.53 16.1 0, 3.9 , —1.17 0.51 11.u MICHIGAN STATE UNIVERSITY LIBRARIES II III IIIIIIIIIIII 3 1293 3169 6887 i I I