Document LKKvgMEJgyZ3gNVbd341mar3g

544 CHAPTER 29 1965 Guide'And Data Book jets are the effects &t various Reynolds numbers fully, known. /; 3. The quantitative treatment of the forces that govern room air distribution problems has been limited, and non-isothermal conditions involving buoyant forces have not yet been fully explored. 4. Most investigations have been concerned with free jets, whereas air streams in practical room air distribution are not free streams but are influenced by walls, ceilings, floors, and obstructions. Angle of Divergence The angle of divergence is very definite close to the outlet face, but the boundary contours are somewhat billowy and are easily affected by external influences. Here, as in air dis tribution generally, room air movement is replete with* local eddies, vortices, and surges, which are manifestations of un balance in the forces acting within the air stream. These in ternal forces govern the air motion, yet they are extremely delicate.* Measured angles of divergence (spread) for discharge into large open spaces have usually ranged from 20 to 24 deg with an average of 22 deg. Coalescing jets for closely spaced mul tiple outlets expand at somewhat smaller angles, averaging 18 deg, and jets discharging into relatively small spaces show even smaller angles of expansion.' Tests indicate that in cases where the outlet area itself is small compared to. the dimensions of the space-normal to the jet,' the*jet may be considered free as long as: - - ' ` : ' ` ! tohere X < l.5y/Ai . ` X = distance from face of outlet, feet. _ - , - . Ag -- cross-sectional area of the confined space, square feet. Four Zones in Jet Expansion Approximately the same values of K' apply as for Zone 3 expansion from axial outlets. In Zone 1, the ratio VJV* is constant and equal to the ratio of the enter velocity of the jet at start of expansion to the average velocity, ranging from approximately 1.0 for roundedentrance nozzles to about 1.2 for straight pipe discharge, but with much higher values for diverging-discbkrge outlets. . Since aspect ratio7 and turbulence' primarily-affect the center line velocities in Zones 1 and 2, the importance of is obvious. In commercial testing it has been shown, that aspect ratio has little effect on the terminal zone'of'the jet when He is greater than 4 in. This is particularly true in the case of non-isothermal jets. When Ht is very small,'it is possible for the induced air .to penetrate the core of the jet, and thus effectively to reduce center line velocities. The dif ference in performance between the radial type outlet with a small He and the axial type outlet with a large H shows the importance of the thickness of the jets. When air is discharged from perforated panels of relatively large sizes the constant velocity core formed by the coales cence of -the individual jets extends a considerable distance from the panel face. In this Zone 1 region, when the ratio Dis tance from panel/VPanel area is less than 5, the equation V, m Vfl.2y/Cd X ft/. , (3) Centerline Velocity in Zone 3 ' ' Research has shown that maximum or centerline' velocities in Zone 3 of straight flow' isothermal'jets con be determined with good engineering accuracy from * In analyzing the performance of jets, four major zones can be distinguished. They may be roughly defined in terms1 of the maximum or centerline velocity existing at the .cross- section being considered: Zone 1: A short sone, extending about 4 diameters or widths from the outlet face .(or vena contracts for orifice discharge), in which the maximum velocity of the air stream remains prac tically unchanged. Zone B: A transition zone, extending to about 8 diameters for round outlets, or for. rectangular outlets of small.aspect ratio, over most of which maximum velocities vary.inversely as the square root of the distance from the outlet. For rectangu lar outlets of large aspect ratio, this sone is elongated and ex tends from about 4 widths to a distance approximately equal to the width multiplied by. four-times the aspect ratio.-/-.-.--' Zone S: A long zone, .of major engineering importance,.in in which the maximum velocity varies inversely as the.distance from the outlet. This sone is often called' the cone of fully etabhaked turbulent flow and may be 25 to 100 diameters long (or equivalent diameters of equal areas), depending on the shape and area of the outlet, the initial velocity, and the dimensions of the space into which the outlet discharges. Zone 4: A terminal tone in which, in the case of confined spaces, the maximum velocity decreases at an increasing, rate', or, in the case of large spaces free from wall effects, the maxi mum velocity decreases.rapidly in a few diameters to the ve locity range below 50 fpm which is usually regarded as stiff air. Centerline Velocities-In Zones 1 and 2 Experimental evidence indicates that in Zone 2 V, TcWl V, x (2) where H% * width of jet at outlet or at vena contracta. where - XVA, X Ci-X Bf. V, centerline.velocity, feet per minute; ' v, - V. 1 average initial velocity &tdischarge Ct X R/, from open-end duct or across contracted stream - " at vena contracta of orifice or. multiple-opening , : . outlet, feet per minute. ; . - . ,. c , Vt = nominal velocity of discharge based on th? core area,' feet per minute. , Ctcoefficient of discharge (usually between 0.65 .' - "and 0.90). ' . ' . ' " .` '// ' . . fi/, - ratio of free area to gross (core) area:. ,, .< x. -- distance from face of outlet,.feet.'; K and K' - proportionality constants, 'with 'iT-1.13 K. j' Dt -- effective or equivalent diameter of stream-at discharge . from open-end duct - or. .at a con- . tracted section, feet. ...... d* -- A, X Ct X1 Rf. -- effective area of stream at discharge from an open-end duct or at a'con- ... tracted section, square feet. , A, -- measured gross (core) area .of outlet, .square - -- - - feet. Q " discharge from outlet, cubic feet per minute. Since A$ equals the effective area of the stream, the flow Space'Air Distribution Table 2 . .. Recommended Vahiesofthe Centerline Velocity Constant K orK' (See fqvofioA 4) . X Type of ObW V, - V, " V, V, 500 to 2000 to 500 to 2000 to 1000 10,000 1000 10,000 Free Opening'. . Round or Square Rectangular, large aspect ratio (<40) Annular slots axial or radial* Grilles and Grids Free area 40% or more Perforated Panels' Free area 3 to 5% Free area 10 to 20%. 5.0 4.3 _ 4.1 2.7 3.5 6.2 ' 5.3 _ 5.7, 4.9 3.9 7.0, 6.0 4.8 5.0 4.7 5.7 3.3 3.0 ' 3.7 .4.3 4.0 4.9 Far ndial dot* aae X/H instead ol H it tbeheicfct width of the lot. Sett: K aad K' aie indent ot loss in axial kinetic eacror. Interpolate as re quired. Departures from maximom value indicate kaaee in firstaad aeeoad tones. when compared with the jet bom e toonded-entfanee, circular raraU 545 area for commercial registers and diffusers according to the Equipment Test Code11 of the Air Diffusion Council, may be itapH in Equation 4 with the appropriate value of K and K1. Equation 4 is nondimensional and requires only that con sistent units be used, as in the above nomenclature. Values of K and K' are listed in Table 2.7>u In the cftww of multiple-opening outlets and annular-ring outlets, the streams coalesce into a solid jet before actual jet expansion takes place. This coalescence affects the experimentally determined proportionality constants K or K' and ac counts for some of the divergence in reported values for simi- lar outlets. .. For perforated panels of relatively large size, the values of K and X'.given in Table 2 apply only when the ratio Distance , from Panel/vTancl area is larger than'5. (See 'Centerline1'Velocities in Zones 1 and 2.) ; Low. velocity test results, in the range P,<150 fpm, indi cate that the normal values'of K and K* should be reduced about 20 percent for V, = 50 fpm, `as used, in later. Equation 9;for throw. Fig. 7 gives the .effective diameter D0 in inches for single openings and includes the coefficient of discharge.12 *. The following Example 1 which is solved on Fig. 8 will illustrate the use of the chart. Example t: A grille hsa a core area 12 in. x 18.75 to., R/m = 0.90, Ct " 0.80, and K' " 5.0. Find V, (velocity through core area) when V, is 50 fpm for throw of 50 feet (X " 50). Solution:; 12 X 18.75 At -. .144 1.56 sq ft X 50 ~ 1.25 TM ,40. , 1.56 X 0.80 X 030 1,123 50 ` ` Determining Centerline Velocities : To permit correlation of data from all four zones, centerline velocity .ratios are plotted against distance from outlet in Fig. 8 in accordance with the basic relation of Equation 2, and a nomogram for calculating the parameters X . V't X a F and -- from and ~ . A* through'!^ and Ct is given in the same illustration. The variation of-the centerline velocity ratio with distance from outlet.or, more properly, from start of jet expansion, is also shown on Fig.18 for Zones 1 and 2. V^/V* is plotted against X/tf# and, for a range of aspect ratios, against X/y/A for the single value of K'"7.0. Values of VJVt for other values of K' may be obtained by direct proportion ing of VK' to y/7XL V. K'y/At .s Sy/Tm vt X , "y -50" ' 0.106 -- m"i--"mi---1--^0.147 .Vi V,(C*R/J '0A0 X 0^0 For Vt -- 50, t> . v--p^ " S40,p,a' The quantity of aii discharged isitheD, .' . Q = VmA< - 340 X 156/ .530 cfm.. - Throw '' --i:i "!>'. -r ' f - 11 Equation 6 can Be used to deterinine the throw X'ol an