analysis of passively automatic air inlets for livestock

Analysis of passively automatic air inlets forlivestock buildings

M.R.L. BANTLE1, E.M. BARBER2 and G.R. BAYNE3

Bantle Engineering Research, P.O. Box 7805, Saskatoon, SK, Canada S7K 4R5; Department of Agricultural Engineering,University ofSaskatchewan, Saskatoon, SK, Canada S7N0W0; andAgricultural Engineering Branch, Saskatchewan Agriculture&Food,Regina, SK, Canada S4S OBI. Received28 August 1990; accepted 7 February 1991.

Bantle, M.R.L., Barber, E.M. and Bayne, G.R. 1991. Analysis ofpassively automatic air inlets for livestock buildings. Can. Agric.Eng.33:363-371.The aerodynamicmoment acting on a hinged baffleof a passivelyautomaticair inlet was measured for three different flowconfigurations at pressure drops of 5, 20, 35 and 50 Pa. In two of theconfigurations, air entered the inlet from a plenum above the inlet,therebysimulating air entry from an attic. In the third configuration,airentered the inlet from a plenum beside the inlet, thereby simulatinga sidewall inlet. When the inlet pressure drop was maintained constant,themoment actingon the inlet baffle due to airflowthroughthe inlet(aerodynamic moment) decreased as the airflowrate increased for allthreeinlet configurations. This result indicates that a restraint systemwhich exerts a constant counter moment may not be workable if aconstant pressure is required. However, the condition of a constantpressure with a constant counter moment may beapproached with thetwo attic inletconfigurations provided the maximum inletopening isrestricted. The open wall configuration inlet is not suitablefor use asa passively automatic inlet because the aerodynamic moment decreased very sharply for increasing airflow ratesevenwhen the inletwas only 20% open. A numerical model was developed which accurately predicted the aerodynamic moment on the baffles underconditions of low airflow rates. However, the model was not accuratefor higher flow rates. It is believed that separation within the flowchannel, which could not be accounted for in the model, was the majorreason for thepoorperformance of themodel athigherflow rates.

On a mesure le moment aerodynamique agissant sur la chicanearticulee d'une entree d'air a systeme automatique passif, et ce, pourtrois differentes configurations d'ecoulementa des variations de pres-sionde 5,20, 35 et 50 Pa. Dansdeux des cas, Fair entrait a partir d'unplenum sitae au-dessus de Fentree, simulant ainsi uneventilation parlescombles. Dans le troisiemecas, Fair penetrait a partir d'un plenumsituea cote, simulantune ventilationpar les murs lateraux.Lorsquelachute depression etaitmaintenue constante, le moment agissant sur lachicane, du a Fecoulement d'air a travers Fentree (momentaerodynamique), diminuait a mesureque le debit augmentait pour lestrois configurations. Ce resultat indique qu'un systeme de retenueexer9ant un moment contraire constant peut ne pas etre praticable siune pression constante est necessaire. Toutefois, il est possibled'approcher de Fetat de pression constante et de moment contraireconstant avecles deuxconfigurations de ventilationpar les combles,acondition querouvertured'entreemaximalesoitrestreinte. Laconfiguration de mur ouvert ne convient pas en tant qu'entree a systemeautomatique passif,parceque le momentaerodynamique diminuetresbnisquement avec des augmentations de debits d'air, meme lorsqueFentree n'est ouverte qu'a 20 %.On a elabore un modele numeriquequi prevoyait de maniere precise le moment aerodynamique sur leschicanes, avec de faibles ecoulements d'air. Cependant, le modelemanquait de precisionquand les debits etaient plus eleves. On penseque la separation a Finterieur du canal d'ecoulement - dont on nepouvaitpas tenir compte dans le modele - est la cause principale dufaible rendement de ce dernier a des debits eleves.

CANADIAN AGRICULTURAL ENGINEERING

INTRODUCTION

In a typical livestock building, the ventilation rate must bevaried by as much as a factor of twenty between winter andsummer. Much effort has been expended to develop automaticcontrol of fans to achieve automatically this modulation ofairflow rate. Much less effort has gone into automation of airinlets.

Experience has indicated that poor air distribution anddraftsresult fromimproperadjustmentof air inlets.Therefore,some form of automation is required. Complete automation ofinlets, fully synchronized with the operation of fans, can beachievedwithmodernmicroprocessor-based controllers; however, such control systems are expensive and have not beenwidely adopted to date in Canada. Gravity shutters, spring-loaded baffles, and counterweighted baffles, such as thoseillustrated in Fig. 1, are conceptuallyappealing as a low costway to automate air inlets. However, field experience hasindicated that these passively automatic inlets do not alwaysprovide proper airflow modulation from summer towinter andthat the pressure difference across the inlets may vary toomuch as the ventilation rate changes.

The objectives of thisproject were to measure theaerodynamic moment on the inlet baffle of three commonly used inletconfigurations, to develop a theoretical model which wouldpredict the performance of a passively automatic air inletbased on some basic test data, and to evaluate the performanceof the three inlet configurations.

PREVIOUS INVESTIGATIONS OF AIR INLETS

The literature on the design of passively controlled automaticair inlets is very limited.Carsonet al. (1988) studied the operation ofa passive air inletthatreliedontheweight ofthebaffleto close the baffle (similar to configuration d, Fig. 1). Theoreticalpredictions of the inletperformance weremade assumingincompressible inviscid flow. The unique geometry of thistypeof inletmadeit possibleto modeltheinletas a one-dimensional airflow problem. The model was reported to predictaccurately the pressuredifference and inlet jet velocitiesovera 10-foldrange of ventilation rates. The study was limited tojust the one particular inlet configuration.

Munroe et al. (1988) studied the performance of a passiveair inlet (CPS Plan M-9715) similar to configuration b, Fig. 1.The adjustmentof the inlet was controlled by counterweights.The authors presented only a limited theoretical analysis.Based on experimental observations, it was concluded that at

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least a 10-fold range of ventilation rates could be achievedwith relatively small changes in static pressure (10-15 Pa)andwithoutchanging the length of the momentarm on the counterweight. With an adjustment of the counterweight momentarm twice yearly, a 20-fold change of ventilation rate wasconsidered possible.

Albright (1978, 1976) considered the airflow through abaffled, centre-ceiling slot inlet and a hinged-baffle slot inlet.The hinged-baffle inlet was similar to configurationsb and c,Fig. 1, but without the counterweight. In both cases, dimensional analysis was used to obtain an equation which predictedthe airflow rate through the inlet as a function of inlet geometry and the static pressure drop across the inlet.The results ofthese investigations cannot be applied directly to predict thefunctioning of a passively controlled air inlet because no information was given on the pressure profile across the baffle.

(a) spring restrained attic inlet (b) counterweighted attic inlet

9///////////////////\

yyyyyyyyyy/yyyyyyyA

(c) counterweighted side wall inlet (d) gravity shutter

Fig. 1. Configurations of passively automatic air inlets.

DEVELOPMENT OF THE THEORETICAL MODEL

Airflow through slot air inlets in livestock buildings can bemodelled asa two-dimensional flow. Thisassumption maynotbevalid forvery shortair inletmodules where endeffects maybe significant.

Because most livestockbuildings are ventilated usingpropellerfans, the pressuredropacross air inlets usuallyis limitedto less than 50 Pa; therefore, the flow may be considered to beincompressible.

Inertial, pressure, and viscous forces are involved in the slotinlet flow problem. However, in this analysis the viscouseffects were assumed to be confined to a small region next tothe boundary such that the bulk of the flow could be treated asan inviscid flow. An inviscid flow implies that the fluid acceleration is due entirely to pressure differences and that theno-slip boundary condition at a solid wall must be relaxed.

If air enters the inlets from a large reservoir, as from an attic,directly through an outside wall, or from a large duct, and ifthe entrance to the inlet is smooth, the flow will enter with novorticity. Once the flow is in the inlet itself, the viscous effectsof the wall will cause vorticity to diffuse but if the boundarylayer is small then the bulk of the fluid can be consideredirrotational. The combination of an inviscid and iirotationalflow is an ideal or potential flow.

For a potential flow, the shape and location of the walls ofthe flow passage completely establish the flow velocities and

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streamlines. Sincethe geometrycontrols the flow patterns,thevelocity may be found without ever solving the momentumequation. The momentum equation is only used to determinethe pressure field.

Flow separation invalidates the use of potential flow theoryin solving a flow problem. Flow which separates and leavesthe wall carries with it vorticity and viscous effects from theboundary layer. A large region of back flow or recirculatingflow exists downstream of the separation and frequently leadsto an unsteady turbulent wake (Panton 1984). Thus, whenseparation occurs, the viscous effects and the vorticity diffusion can not be assumed to be confined to a thin layer near thewalls. Some specific numerical calculations of separated flowhave been made but this subject still remains an unresolvedarea of fluid mechanics. To study the flow through a passiveair inlet, the assumption of an ideal flow is thought to beacceptable if no vorticity is present in the flow upon entry tothe inlet and if flow separation within the inlet is minimized.

The one-dimensional modelling approach used by Carsonetal (1988) could not be applied to the two-dimensional flowchannel of a generalized hinged-baffle air inlet. An alternativeanalytic solution procedure was sought. The flow passagethrough an air inlet such as shown in Fig. 1 is a polygon andthus it was expected that, with some simplification of the flowpassage, it would be possible to apply the Schwarz Christoffeltransformation to obtain an analytical solution. The SchwarzChristoffel transformation (Churchill et al. 1976) maps a polygon which is a closed contour in one plane to the upper halfplanein anotherplane. This transformation permitsa complicated flow in the one plane to be transformed into a simpleflow in another plane for which an analytical solution exists.However, investigation of this concept indicated that evenwitha simplified flow passage geometry, the analytical solution became very complex. Therefore, a numerical solutionwas thought to be more appropriate.

The analysis of problems by numerical methods is based onapproximating conditions in a continuous field by a finitenumber of values at discrete points. For this two-dimensionalproblem, theflow wasdivided intoa two-dimensional gridofequally spaced latticepoints. Figure2 shows a typical grid.Inthis modeldevelopment, the grid was 10 mmby 10 mm.

3 0 1o o o

4

Fig. 2. Grid for numerical computation of stream function.

Stream function computation

Since the flow is an ideal flow, the stream function satisfiesLaplace's Equation. The stream function at any point in theflow is the average of the stream function at four adjacentpoints:

BANTLE, BARBER and BAYNE

V0= (Vl +\|/2 +\|/3 +\|/4)/4

where \\fj = stream function at position;.(1)

Thorn's Square Method (Robertson 1965) wasusedtosolvethe stream function inside theflow boundary. This method wasselected because it is much faster and is more amenable tosolution oflarge flow grids than a simple averaging ofthe fouradjacent points.

The boundaries of the air inlets being studied have flowgeometries which result in some of the lattice points in therectangular grid lyingoutside the boundary of the flow channel.For example,in Fig. 3, calculation of the stream functionatpoint"0" involves the twogridpoints,"1" and"2" whichlieoutside the boundary. The method reported by Robertson(1965) was used to calculate the stream function at a pointadjacent to a boundary:

Yo= (ryi + ^2 + V3 + Y4)/(2 + r + s) (2)

wherethe scalingfactors,r and s, are as shown in Fig. 3.

z/r""-

W. 1/> z/s

Fig. 3. Grid for computation of stream function at latticepoints near the boundaries of the flow channel.

Flow velocity

The stream function was calculated at all of the lattice pointsin the flow field, and then the velocity was computed at thesame lattice points using:

u= dy/dx : v = -3\|//3y (3)

where:

u = velocity in the x-direction (m/s), andv = velocity in the y-direction (m/s).

The velocities of most interest were those along the bafflesurface. Since the velocity can change dramatically at shortdistances from the boundary, it is important to compute thederivative at the boundary rather than at lattice points someshort distance away from the boundary. Equation 4a (Robertson 1965) was used to calculate the velocity, v, at the boundary(refer to Fig. 4):


dyI boundary v ' z \+r z K }

Calculation of thevelocity, u,requires interpolation tofindya' and \|fa" in Fig. 4, andthen Eq.4bcanbeapplied:

dx\ boundary~(1 +r) z "l +r z (4b)

This procedure was repeated at equally spaced intervalsalong the baffle.

4o

a" 6o o

Fig. 4. Grid for computation of stream function at theboundary of the flow channel.

Aerodynamic moment

The position of the baffle in a passively automatic air inletis determined by the balance between the aerodynamic moment exerted on the baffle by the airflow through the inlet andthe counter moment developed by the restraint system. Theaerodynamic moment is the result of the pressure differencebetween the two sides of the baffle.

For a steady, irrotational flow, the pressure and the fluidvelocity are related by Bernoulli's Equation:

P/p +0.5(w2 +v2) =Constant (5)where:

P = air pressure (Pa), andp = air density (kg/m ).

This equation was used to calculate the pressure at pointsalong the baffle. The constant in Eq. 5 was computed byassuming that flow separation would occur at the minimumflow area in the flow passage. It then was assumed that theaverage pressure at this section would be equal to the pressureon the leeward side of the baffle. Since only the net pressureon the baffle was required, the pressure on the leeward side ofthe baffle was set equal to zero and the constant in Eq. 5 wascomputed from:

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Constant = 0.5(I/max)2 (6)where

t/max = averageair velocityat the minimum flowarea (m/s).

The maximum velocity was calculated from:

UmuL = ql{Cdh) (7)

where:

q=airflow per unit length of inlet (m3»s"1»m' ),h = the inlet opening height (m), and

Cd= discharge coefficient.

Figure 5 shows a baffle in a flow field. The moment actingon the baffle, per unit length of the baffle, with respect to thehinge at point "O" was computed from:

/-l

M=X0^2(/,/ +/,/-l)(i-0.5) +^(/,/-i)[0.5/ +(/-l)6]i=l

(8)All dimensions are illustrated in Fig. 5.

In the idealization of the inlet flow, the streamlines werecontinued around the tip of the baffle. This simplificationresulted in very high velocities at the tip. To overcome thisproblem,thepressurecalculatedat point"I" wasneglected andthepressure ?m was assumed to act uniformly from thepoint"I-rtothetip.

Fig. 5.Grid forcomputationof pressuresand aerodynamicmoment on the hinged inlet baffle.

EXPERIMENTAL PROCEDURE

Three inlet configurations were tested in a chamber at theUniversity of Saskatchewan Agricultural Engineering HardyLaboratory. Figure 6 shows the chamber and the inlet attachment positions. The original chamber had inside dimensions of4.88 m x 2.30 m x 2.44 m, but for these tests one corner of thechamberwas reconstructed to accommodate testingof an atticentry inlet configuration. In the reconstructed chamber, thedistance between the roof of the test chamber and the entranceto the simulated ceiling inlet port was 0.75 m. The distancebetween the endwall of the test chamber and the trailingedgeof that inlet port was 0.70 m. The chamber was located withina larger airspace in which the temperature was maintainedrelatively constant near 23°C.

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-Port for OAC Iond RAC inlet I

L

Port for OWC

inlet

Settling screens

Air intake" from airflow

measurement

section

I I I

Fig. 6. Longitudinal section through the test chamber.

Air was forced through the chamber by two centrifugal fansoperated by a variable speed drive. Air delivered by the fansentered the chamber through an AMCA-Standard airflow measurement section (AFMS). The AFMS consisted of sixprecision flow nozzles. By manually changing the combination ofnozzles that were open, airflow rates of0.04 -1.6 m3/swere possible. The pressure drop across the nozzles was measured using a manometer (Model MICRO 34FB2, MeriamInstruments, Zurich, Switzerland) having a resolution of ± 1.3Pa. Airtemperature wasmeasured in the supply air duct usinga precision mercury thermometer. After the air entered thechamber from the AFMS, it passed through a set of threesettling screens placedthere to promote uniform velocity approaching the inlet section. Previous tests indicated thatleakage inthe shell of the chamber was less than 0.001 m3/s ata pressure difference of 25 Pa.

The static pressure difference across the test inlet was measured with the same manometer as that used at the AFMS. Oneport was open to the large laboratory outside the chamber. Theother port was connected to a piezometer ring joining threepressure taps that were flush-mounted with the inside surfacesof the experimental chamber. The three pressure taps werelocated in the ceiling and the two side walls of the chamber.

Two ports were constructed in the chamber to which the testinlet modules wereattached. The largerport was 255 x 1200mm andsimulated an air entry from an attic. Thesmaller portwas 105 x 1200 mm andsimulated an air entry through a sidewall.Eachport was fittedon the upstream side witha 285 mmdeep entry channel to simulate an attic insulation stop or achannel through a wall.

Threeof the four inlet configurations shown in Fig. 1 weretested. In the open attic configuration (OAC), the air enteredthe inlet from above (Fig. 7). The baffle was hinged at theceiling and the axis of rotation of the baffle was such that thebaffle was always angled away from the ceiling. At an angleof 0°, the inlet opening was 23 mm. In the restricted atticconfiguration (RAC), air also entered from above, but thebafflewashinged 105mm below the ceiling. In thisconfiguration, the baffle was always angled toward the ceiling. In theopen wall configuration (OWC), air entered the inlet horizontally. As with the RAC inlet, the baffle was hinged 105 mmbelow the ceiling and the baffle was always angled toward theceiling.

The inlet baffle was constructed of 2.66 mm thick aluminumplate.Oneedgeof the baffle wasattachedto a 12.7mmsquareshaft. The overall dimension of the baffle with the attached

BANTLE, BARBER andBAYNE

shaft was 305 x 1200 mm. The trailing edge ofthe baffle wasturned over at90° to form a 37 mm lip and thus to simulate thethickness ofpolystyrene baffles thatoftenare used in livestockbuildings.

The inlet baffle was held within a mounting frame. Theshaft supporting thebaffle was held at both ends by two smallbearings. This design was intended to minimize the countermoment due to friction at the hinge. The bearings weremounted in aluminumend plates which in turn were attachedto the chamber using a mounting flange. The three differentinlet configurations were achieved bychanging theorientationof theendplates and theposition of the hinge. Theendplateswere mounted to achieve a close fit between them and the endsof the baffleand thus to minimize air leakagearound the endsof the baffle. Also to minimize leakage, the end plates were

Hinge

(a) Open attic configuration (OAC)

Hinge

(b) Restricted attic configuration (RAC)

_LhPlostic strip

(c) Open wall configuration (OWC)

Fig. 7. Schematic of the three inlet configurations.


sealed to thechamber with duct tape. Thespace between theshaft and the chamber was bridged with astrip ofpolyethylenesheet which was taped along one edge to the chamber andalong the other edge to the baffle, thus creating an airtighthinge with negligible rotational resistance.

Theinletmodulewasdesignedso theaerodynamic momenton the baffle could be measuredaccurately (Fig. 8). A 312.9mm diameter wheel was attached to one end of the shaft whichformed the hinge of the baffle. A weight was attached to thecircumference of the wheel by a small diameter cable. Thelength of thecablewasadjusted using turnbuckles. Theweightwas supported on an electronic scale (Model PL1200, MettlerInstruments, Cleveland, OH) and remained stationary on thescale. As air was forced through the inlet, the aerodynamicmoment on the baffle tended to rotate it clockwise and thus tolift the weight off the scale. The moment due to the weightofthe baffle itself was constant. Therefore, the change in thescale reading, multiplied by the moment arm (wheel radius =0.1565 m) was a direct measure of the aerodynamic momenton the baffle.

For these tests, the baffle position and the inlet pressuredrop were fixed and the airflow rate through the inlet at theseconditions was measured. Data were collected at pressuredrops of 5,20, 35 and 50 Pa at each of 3 or 4 baffle positions.

A test proceeded by first adjusting the baffle and the cableand scale apparatus until the desired baffle angle was attainedwith nearly the full weight of the counterweight bearing on thescale. During this procedure, the airflow rate was zero. Theairflow rate then was increased until the desired pressure dropwas achieved, and this flow rate was measured. The baffleangle was retained at the desired value by adjustment of theturnbuckles.

Hinge

Baffle

Turn buckle

Fig. 8. Schematic of system for measuring aerodynamicmoment.

RESULTS AND DISCUSSION

The experimental conditions under which each inlet was testedare summarized in Table I. The measured aerodynamic moment and the airflow rate at each of the experimentalconditions are shown in Fig. 9-11 respectively for the OAC,

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RAC and OWC inlets.At any fixed inlet opening, both the moment and the pres

sure drop increased as the airflow rate increased. For a fixedpressure drop and baffle opening, the moment was larger forthe RAC inlet than for the other two inlets. The RAC configuration is less efficient in providing airflow with a minimalpressure loss than are the other two, relatively more streamlined, inlet configurations.

A passively-operated air inlet baffle for cold region livestock buildings should provide a 20-fold change in air deliveryrate while maintaining a nearly constant pressure drop acrossthe inlet. Fan energy could be reduced by decreasing inlet airspeeds during warm weather operation. Therefore, in someventilation systems, it may be best if the pressure drop decreases, and hence the jet velocity decreases, as the flow rateincreases. The opposite effect was shown for the three inletconfigurations that were tested. That is, for a constant countermoment, the pressure drop across the inlet will increase as theinlet opens in response to higher airflow rates.

Table I. Conditions under which the inlets were tested

Inlet Baffle Angle Inlet Slot DischargeConfiguration (deg) Height (mm) Coefficient

OAC 0 23 0.72

15 88 0.73

30 148 0.68

60 234 0.69

RAC 16 20 0.59

8 60 0.71

1 100 0.67

OWC 16 20 0.74

8 60 0.94

1 100 0.72

The results of these tests canbe used in two ways. First, thedata can be used to design a restraint system in which thecounter moment is decreased as the airflow rate increases,while maintaining a prescribed relationship between flow rateandpressure drop. Forexample, thecounter moment requiredfor die OAC inlet intended to maintain a constant pressuredrop of 20 Pa will decrease from 0.65 N»m/m at a flow of 0.1m «s" -m"1 to0.22 N«m/m at a flow rate of0.9 m^s'W1. Afixed counterweight system could notbe used, buta properlydesigned spring-restraint system could provide this modulation of the counter moment.

The seconduse of the data is to identifythe maximum inletopening beyond which the required counter moment for agiven pressure drop decreases rapidly, or beyond which thepressure drop increases rapidly if the counter moment is heldconstant. Therangeofairflowandpressuredropsforeachinletfora fixed moment are shown by the dotted lines in Fig. 9 to11. If the OAC inlet was fitted with a constant counter momentof0.65 N«in/m, the inlet would open to 23 mm (0^for aflowof 0.1 m -s" •m" and a pressuredropof 20 Pa. If the flowwasincreased 10 fold to 1 m3«s"1«m"1, the inlet would open to

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approximately 45° and the pressure drop would increase togreater than 40 Pa. The data indicate that the maximum openingshould be restricted to less than 15°if the pressure dropisto be kept nearly constant at 20 Pa for a fixed counter momentof 0.65 N«m/m. Similarly, for the RAC inlet, if the pressuredrop is to be kept nearly constant at 20 Pa, the maximum inletopening should be less than 60% of the fully open, horizontal

2.2-

-r-

0.4 0.6 0.8 1.0 1.2Air flow (m3/s.m)

1.4 1.6

Fig. 9. Measured aerodynamic moments for OAC inlet.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Air flow (m3/s.m)

Fig. 10. Measured aerodynamic moments for RAC inlet.2.2-

-i 1 1 r

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Air flow (m3/s.m)

Fig. 11. Measured aerodynamic moments for OWC inlet.


baffleposition. Given thisrestriction, thepressure drop willbenearly constant at 20 Pa for a fixed counter moment of 0.84N»m/m.Forthe OWC inlet at an opening of20 mm, or approximately 20% of the fully open, horizontal baffle position, theinlet is already beyond the opening at which a nearly constantpressure of 20 Pa is possible at a constant counter moment.

Further measurements are needed to test the performance ofthe three inlet configurations at inlet openings smaller than 20mm. The relationship between inlet opening height and airflow rate is approximately linear for small inlet openings.Then, for the RAC inlet with a maximum opening of 60 mm,a minimum opening of 3 mm would be required to makepossible a 20 fold modulation of ventilation rate. A similarminimum opening for the OAC inlet is also needed. Becausethe slope of the moment versus flow rate curve is quite flat atlow flow rates, it seems possible that these two inlet configurations might afford a 20 fold modulation of ventilation ratefor a constant counter moment and a constant pressure drop of20 Pa. This hypothesis needs further testing. The OWC inlet,on the other hand, does not offer much promise as a passivelyautomatic inlet because the aerodynamic moment at a constantpressure is strongly dependent upon the airflow rate, even atrelatively small inlet openings.

COMPARISON BETWEEN PREDICTIONS ANDMEASUREMENTS

The theoretical predictions were developed by specifying theflow geometry (ie., the inlet type and the baffle position) andthe flow rate and then computing the aerodynamic momentacting ontheinletbaffle. Two critical variables in thecomputation of theaerodynamic moment were theinletpressure lossand the maximum jet velocity.

Early in the analysis of the results, it became apparent thatthe pressure loss atthe entry into the inlet channel could not beneglected. Theentrance pressure loss was calculated using:

APe = 0.5pCeUe2

where:

APe =entrance pressure drop (Pa),Ce =entrance pressure loss coefficient, andUe= entrance mean velocity (m/s).

(9)

The velocity at theentrance to the inlet, Ue, was calculatedas:

Ue = qlb

where:O 1 1

q=airflow rate per meter length of inlet (m -s" -m" ),andb = width of the entrance channel (m).

The pressure losscoefficientswerenotmeasured andtherefore were estimated as 0.69 for the OAC and RAC inlets and0.50 for the OWC inlet (ASHRAE 1989).

The estimate of the maximum velocity, C/max, was calculated using Eq. 7. Ideally, a single discharge coefficient, Cd,wouldbe known apriori for each inlet. However, in this analysis,Cd hadto be estimatedfrom theknown values forthe inletpressure loss,P, the airflowrate,q, and the inlet slot height, h.


(10)

The discharge coefficient was determined for each openingwidth of each inlet configuration using the linear model:

(APt - APe)measured =0.5 Pp(qlhfwhere P is the least squares estimator of Cd-2.

(11)

Estimates for Cd are given in Table I. That the RAC inlethad the lowest apparent discharge coefficient is consistentwith the rather poorly streamlined shape of this flow channelcompared to the other two inlet configurations. The dischargecoefficient approaching 1 for the OWC inlet at an opening of60 mm is consistent with the very streamlined shape of theinlet at that inlet opening. Because the discharge coefficientappeared to be relatively sensitive to the inlet opening for theRAC and OWC inlets, the individual estimates were usedrather than an average value for each inlet type in subsequentcalculations of the aerodynamic moment.

The model predictionsand the measurements for inlet pressure drop andthe aerodynamic moment are compared in Fig.12 to 14. The near perfect agreementbetween measured andpredicted pressure drop was forced by the least-squares estimation procedure for estimating an apparent dischargecoefficientas oudined previously. The purpose of the modelwas notto predict the pressure drop, but rather to predict theaerodynamic momentgivena known pressure drop.

Agreement between predictions and measurements of theaerodynamic moment for the RACinlet was very good atallinlet openings. The fitwas good for theOWC inlet atthe twolowest opening widths. For the OAC inlet, themodel consistently overestimated the aerodynamic moment, the size of theerror increasing as the flow rate and the inlet opening heightincreased.

Two possible reasons were identified to explain the poorprediction of the aerodynamic moment by the model for theOAC inlet and for the OWC inlet at larger opening widths.First, whereas the model accounts for pressure losses at theentrance to the inlet, it does not account for friction losseswithin the inlet. Consequently, the predicted values for themaximum inletdischarge velocity maybe toohigh. Overesti-mation of this maximum velocity would result in anoverestimation of thepressures onthetopsideof thebaffleandhence of theaerodynamic moment. Neglecting friction losseswithinthe inlet, however, is not expected to havebeen amajorcontributor to the error.

The second andmore significantproblem is thatthe modelassumed noseparation anywhere within the flow field. For theOAC inlet, flow will separate at the exit from the entrancechannel, resulting in higher velocities along thebafflesurfacethan the model predicts. The model forces the flow to bendaround thecorner, spreading the flow overmore area than if itseparates. The higher velocities in practice will result in alower pressure profile and a smaller aerodynamic moment. Asimilar effect likely occurred for the OWC inlet at maximumopening. Flow separation may have occurred at the sharpentrance to the inlet channel. For small inlet slot openings, theconverging flow channel would have reduced the effects offlow separation at the entrance, but at full inlet opening theflow may not havereattached to both boundaries of the flowchannel before the inlet discharge at the baffle tip.

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60

= 15° 0 = 30° 0 = 60°

O—O Measured

Model

1 i i 1 1 i 1

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Air flow (m3/s.m)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6Air flow (m3/s.m)

Fig. 12. Comparison between measurements and modelpredictions for OAC inlet.

CONCLUSIONS

Three inlet configurations were tested to determine the aerodynamic moment on the baffle as the airflow rate wasmodulated. A mathematical model was developed to predictthe moment, given test data for the total pressure drop acrossthe inlet. The following conclusions can be drawn as a resultof this work:

(1)The testdataacquired for the three inlet configurationsmay be used to design a restraint system for passively automatic inlets. For all three configurations, the counter momentmust decrease as the flow rate increases if the inlet pressuredrop is to be kept constant.

(2) Where a constant counter moment is to be used with theOAC and the RAC inlets, the extent of the pressure dropdependence on airflow rate can be minimized by limiting themaximum inlet opening. For the particular inlets tested, theselimits were 15° for the OAC inlet and 60% of the fully openposition for the RAC inlet. At even 20% of the fully openposition, the OWC inlet exhibited a large decrease in theaerodynamic moment for small increases in airflow rate at afixed inlet pressure drop; therefore, this inlet configurationoffers little promiseas a passivelyautomaticinlet system.

(3) A numerical model was developed which accuratelypredicted the aerodynamic moment on the baffles for low

370

60

(0

£40

£ 30

D- 20

10-

h= 20mm h= 60mm h= 100mm

0--0 Measured>Model

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Air flow (m3/s.m)

h= 20mm

h= 60mm

A>O—O Measured

>Model

h= 100mm

—i 1 1 1 1 1 1 1——i 10.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Air flow (m3/s.m)

Fig. 13. Comparison between measurements and modelpredictions for RAC inlet.

airflow rates. However, the model was less accurate for higherflow rates. It is believed that flow separation within the flowchannel, which couldnot be accounted for in the model,is themajor reason for thepoor performance of themodel at higherflow rates.

ACKNOWLEDGEMENT

Funding for this project was providedby the Agriculture Development Subsidiary Agreement, Canada/SaskatchewanEconomicand Regional Development Agreement, Saskatchewan Agriculture.


60

50-

£40

Q-* 20

10-

h= 20mm h= 60mm

h=100mm

O-o Measuredt Model

i i i i i i i i i—

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Air flow (m3/s.m)

h= 20mm

h= 60mm

O—O Measured> Model

h= 100mm

O

—i 1 1 1 i i r—

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Air flow (m3/s.m)

Fig. 14.Comparison between measurements and modelpredictions for OWC inlet.


REFERENCES

ALBRIGHT, L.D. 1976. Air flow through hinged baffle slotted inlets. Trans. ASAE 19(4):728-732,735.

ALBRIGHT, L.D. 1978. Air flow through baffled, center-ceiling, slotted inlets. Trans ASAE 21(5):944-947,952.

ASHRAE. 1989. Handbook of Fundamentals. Am. Soc.Heating, Refrigerating and Air Conditioning Engineers, Atlanta, GA.

CARSON, J.M., P.N. WALKER and H.B. MANBECK. 1988.Gravity controlled ventilation inlet analysis. Paper No. 88-4508. Am. Soc. Agric. Engrs., St. Joseph, MI.

CHURCHILL, R.V., J.W. BROWN and R.F. VERHEY. 1976.Complex Variables and Applications. McGraw-Hill BookCompany, New York, NY.

MUNROE, J.A., J.E. TURNBULL and D.G. HODGKINSON.1988. Performance of automatic counterbalanced air inlets

with and without recirculation. In: Livestock Environment III,Proc. Third International Livestock Environment Symposium,ASAE Publ. 1-88, Am. Soc. Agric. Engrs., St. Joseph, MI.

PANTON, R.L. 1984. Incompressible Flow. John Wiley &Sons, New York, NY.

ROBERTSON, J.M.. 1965. Hydrodynamics in Theory andApplication. Prentice-Hall, Inc.,Englewood Cliffs,NJ.

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analysis of passively automatic air inlets for livestock

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