A model of the dynamic thermal environment in livestock buildings

J. ugric. Engng Res. (1992) 53, 103-122

A Model of the Dynamic Thermal Environment Buildings Y.

ZHANG;*

E. M.

BARBER;t

S.

in Livestock

SOKHANSANJt

* Prairie Swine Centre Inc., Saskatoon, Saskatchewan, Canada S7H

5N9

t Department of Agricultural Engineering, University of Saskatchewan, Saskatoon, Saskatchewan, Canada S7N OWO (Received

2 April

1991; accepted

in revised

form

21 March

1992)

An understanding of the dynamics of the thermal environment in heated and ventilated spaces is needed for the selection of optimized equipment systems and control strategies. A simulation model is presented which describes the transient thermal responses within a ventilated livestock building. First, a mathematical model of heat and mass transfer within the airspace was tested for a single heating and cooling event using data from a laboratory chamber and from a pig farrowing room. This model was limited by a need for a better estimate of the convective heat transfer coefficients at the inside surfaces of the building shell. A further limitation was the complexity needed to simulate the rapid changes in pressure that occur in response to sudden temperture changes and, therefore, an inability to simulate accurately the exhaust air flow delivered by propellor fans. The airspace heat and mass transfer model was coupled with a model of an electromechanical temperature controller and the overall model was used to simulate a series of heating and cooling events within a pig farrowing room. The GASP IV simulation software was used because of the facility with which both discrete and continuous events can be modelled. Although the simulated temperature did not agree exactly over a 24 h period with real temperature data, the fit was sufficiently good to conclude that the simulation model is useful for analysing alternative control strategies for livestock building heating and ventilating systems. 1. Introduction

The transient responses of the thermal environment in ventilated livestock buildings are critical to the final selection of equipment and control strategies. The thermal environment is defined in terms of dry bulb temperature, relative humidity, air movement and radiant thermal exchange.’ Of these four parameters, dry bulb temperature and relative humidity have been most extensively studied. Barber and Ogilvie* reported the development of a GASP IV computer simulation program as an aid to the study of the dynamic thermal environment in livestock buildings. The GASP IV model was able to simulate both discrete events (e.g., fan and heater on and off) and continuous events (animal heat and moisture production, airspace temperature and humidity fluctuations). Comparison of simulated and real data was not provided. In this paper, further development of the GASP IV model is reported, particularly with respect to modelling the transient heat transfer at the boundaries of the airspace. The modified model was tested in a laboratory chamber study, and was calibrated for a farrowing room. Simulated data were compared with measured temperature and humidity data from a pig farrowing room. 103

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Notation A surface area, m2 c,, specific heat of heater body, kJ kg-’ “C-i cp specific heat of air or of building materials, kJ kg-’ “C-l cr specific heat of tern Perature sensor, kJ kg-’ “CDp perimeter of outside wall, m Ef factor for ventilation rate change due to pressure E,, factor of equivalent heat capacity F perimeter heat loss factor, kW m-’ “C-i h convective heat transfer coefficient, kW rn-“C-i H enthalpy, kJ/kg k thermal conductivity, kW m-’ ‘C-’ L thickness of ceiling, wall or floor, m @ mass, kg A4 mass flow rate of air, kg/h Nu Nusselt number P pressure, Pa Pr Prandtl Number 0 heat transfer rate, kJ/h R gas constant, kJ kg-’ ‘C-l Re Reynolds number resistance to heat transfer, &I mZoC W-’ S, heat source or sink T temperature, “C t time, h V volume of airspace. m3

2. Mathematical

Model

2.1. Overview

V

volumetric ventilation rate, m3/h Y specific volume of air, m3/kg W moisture content, kg H,O/kg air l@ rate of moisture transfer, kg/h x distance in the medium of heat conduction, m AX length of control element in heat conduction, m p density, kg/m’ t time constant, h 52 time limit of integral, h

Subscripts

a b e f h i j m n o p r s t v m

air building exhaust air floor heater inside the building airspace jth layer of the wall, ceiling or floor management animal outside the building perimeter temperator sensor supply air, or referring to supplemental heat or moisture total ventilation air at depth within floor where temperature is constant

of Heat and Mass Transfer of the model

The differential equations describing the transient heat and moisture transfer in a ventilated airspace have been presented previouslyJS4 but were used in a slightly modified form for this analysis. In the simplest case, a livestock building airspace can be treated as a single control volume (Fig. 1). Applying the principles of mass and energy conservation to the control volume results in a set of three differential equations:

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M. H. W

Fig. 1. Heat and moisture

balance for a ventilated

airspace

d(HW + (j, = dt

(2)

LvJf, - WC&f, + w, = ~d(WW

(3)

H&f,

- H&f,

dr

Since complete mixing was assumed, the thermodynamic properties of the exhaust air are equal to the average thermodynamic properties of the airspace. Furthermore, using volumetric flow rates instead of mass flow rates, Eqns (1) to (3) become:

v. v 2-.=“d v, v

1

dt 0 v

(4)

(5) (6)

Psychrometric properties of moist air within a control volume can be calculated from just two of the properties. Therefore, only two differential equations are needed to define uniquely the thermodynamic properties of an airspace. If Eqns (4) to (6) are simplified, two equations are obtained which completely describe the energy and water vapour balance within a livestock building airspace as follows: (7)

Components of e, and w, within the airspace include the housed animals, building shelter, auxilliary heat and moisture, and the management activities within the airspace: et=e”+o,+es+all w, = w, + Wh + es + w,

(9)

(10) All heat and water vapour source terms in Eqns (9) and (10) are time dependent. Some are continuous variables, such as the heat and moisture production rates of animals and

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the heat losses through the building shell, while others such as supplemental heat may be discontinuous. Heat and moisture production due to management activities (e.g., lights turned on and off, power washing of floors), Q, and W,, were modelled as discontinuous variables, or time events. Constant sources of heat and moisture not included in any other terms in Eqns (4) or (5) are included in Q, and W,,,. Animal heat (Q,) and moisture (W,,) production rates are expected to be functions of the time of day, hence:

a.=&( l+C,,sin[E(t-&,)I)

(11)

.=i,(l+&,sin[i(l-&,)I)

(12)

The terms, & and @,,, are 24 h average values for heat and moisture production rates, respectively. These values may be found in handbooks,‘*’ in reports of whole house calorimetry experiments,6 or in reports of mathematical models of animals7 and in all cases the values will be functions of temperature and room design and management. The factors, C,, and C,,, are factors determining the amplitude of fluctuation of heat and moisture production rates, respectively. Time, t,, the time of the day when Q, and W, are at their mean values, does not need to be the same for both heat and moisture production. heat. In the current The term, Q,, is used to represent auxiliary or supplemental model, only simple on-off feedback control is considered; hence, supplemental heat is treated as a discrete variable controlled by a thermostat. For cold climate buildings, supplemental water input, W,, will be zero. Transmission of moisture through the building shell, l&,, normally is set to zero in the model. Heat transfer through the building shell, Qh, is a transient process and represents the most detailed part of the mathematical model and will be discussed in the following section. 2.2. Heat transfer through the building

shell

For purposes of heat transfer calculations, the boundary of the control volume is considered to consist of walls, the ceiling, and the floor. When the objective of an energy simulation is to predict energy requirements over a day or longer, an hourly step-wise steady-state calculation of heat transfer is acceptable.**9 However, since the objective of the current model is to simulate responses to control actions that occur on a much smaller time scale, the short-term changes in heat flow at the boundaries of the airspace cannot be ignored. Several methods have been developed for the calculation of transient heat transfer rate to estimate the energy consumption of livestock buildings. For example, Albright’ and Timmons and Albright” developed transient heat transfer models based on steady periodic temperature cycles on a diurnal basis. The DOE computer program developed by the University of Berkeley” can be used for the hourly evaluation of heat transfer rates in livestock buildings,‘* but cannot be used to predict the instantaneous temperature change for analysis of controls. Alternative models and evaluation methods have been reported for applications other than livestock buildings4*‘s’5 but a model for prediction of the instantaneous temperature response of the livestock building airspace to heat and moisture inputs apparently has not been published.

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2.2.1. Heat transfer

through walls and ceiling

For walls, ceilings and floors which can be assumed as semi-infinite planes, onedimensional analysis will give accurate results.‘6 The building shell can be considered as being composed of n layers of homogeneous, uniform-thickness slabs. The transient conduction heat transfer equation for a single layer is written: kg+

PC,$,

t=O

T =f (x),

(13)

The boundary conditions are different for walls, ceiling and floor. Assuming the air within the airspace is well mixed so that the airspace temperature is uniform, then the heat flux at the inner surfaces is expressed as: k~=hi(T,-

~)

x =o,

t>O

The boundary condition at the outside surface is similar heat flux direction is reversed: kg=

Within

the multi-layer

-h,(T,

- TO)

x = L,

(14)

to the inner surface but the

t>O

(15)

slab the heat flux between two adjacent layers can be written as:

where j and j - 1 are two adjacent layers. 2.2.2.

Convective

heat transfer

coefficients

In a heated livestock barn, the convective heat transfer coefficient, hi, varies with room temperature as well as with air velocity.‘4*‘5 The correct calculation of the Nusselt number for the inside boundary layer is important in evaluating the total heat transfer rate. Even though some advanced methods have been used to study the airflow in a ventilated room,15 Reynolds and Nusselt Numbers remain difficult to calculate for any specific airspace. In this project, the air movement along the building inside surface was treated as laminar flow on a flat surface and the equation of Chapman” was used: Nu = 0.664 Re4’” Pr2’3

lo5 < Re < 10’

(17)

The characteristic dimension in evaluating the Reynolds Number and the Nusselt Number is the height of the wall or width of the ceiling. When the airspeed within the airspace is higher than O-05 m/s and lower than l-5 m/s, the Reynolds Number will be in the range of applicability of Eqn (17). Uncertainty in the value of hi is expected to arise from simplifying assumptions used in developing Eqn (17), particularly for the average airspeed and for the characteristic length of the bounding interior surface. Holma# indicates that a 25% error in hi may be expected from using an average Nusselt Number rather than a local Nusselt Number. For the present model, the effect of wind velocity on the outside of the building shell was neglected. Therefore, a constant convective heat transfer coefficient for the outside wall, h,, was assumed. The outside convective heat transfer coefficient has little effect on the dynamics of heat transfer inside the building.

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2.2.3. Heat transfer through the floor

Assuming the floor is a multi-layer slab with a total thickness of Lf, the heat transfer process can also be described by Eqns (13), (14) and (16) with the following additional boundary condition: T=

T,

x = LI,

t>O

(18)

Additionally, heat loss at the perimeter of the floor was treated as a steady-state variable and was calculated at each time step from the following equations:“.” 8, = D,F( T - TO) 2.2.4. Numerical

(19)

solution of 1-D heat transfer

Equations (13) to (19) represent the simulation model of the heat transfer processes of the building shell. To solve the model, the differential equations were transformed into linear algebraic equations using a fully implicit discretization scheme.” A typical control volume is shown in Fig. 2. Integrating Eqn (13) over the control volume of AX long and unit wide and over the time interval from t to t + At, r+Ar

PC,

dT

,dtdx=6”“‘~-$(k~dxdt

results in: ajq+bjTj+l+cjTj-l=dj

(21)

where “j” is a position index. The coefficients a), bj and ci can be calculated from the thermal properties, k,, kZ, and from the dimensions of the elements, (6X), and (6X),. The constants, dj, are related to the known boundary conditions. Each layer of the wall and ceiling was divided into 10 sublayers. The floor, which consisted of a concrete slab and an underlying soil layer 1 m deep was divided into 30 sublayers. Writing Eqn (21) for all grid points at each time step, At, yields a matrix equation:

[AI[Tl = [Dl

(22)

The solution to Eqn (22) can be obtained directly by the standard Gaussian-elimination method using the Tridiagonal-matrix Algorithm (TDMA) method.*’

AX

I

Fig. 2. A control volume element for heat conduction calculations

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Mhc,,

3

clt

Fig. 3. Energy balance for a heater

2.3. Time response of heat equipment

The energy balance of a heater is illustrated in Fig. 3. Assuming that the heat has an average convective heat transfer coefficient, h, and h,, for the heating and cooling period, respectively, the energy balance of a heater for the heating and cooling period can be expressed by & = &,,,( 1 - e-‘lrz) is the maximum

(23)

cooling period, E,, s 1

8, = Eh&,axe-“T1

where $,,, where:

heating period

rate of heat output,

E, is a proportionality

(24) constant, and

(26)

For some heating equipment,

t2 may be equal to tj. In the most general

Heater

loo0

off

2000 Time.

3ooo s

Fig. 4. Time response of a heater

4ooo

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cases, the two time constants may differ because of a difference in the heat transfer coefficient between when the heater is actuated and when the heater is off. For example, measurement with a 5 kW fan-forced electric unit heater (TEMPRO-GX) gave r2 = 175 s when the heater was on and r3 = 590 s when the heater and heater fan were off. The thermal response of this heater is illustrated in Fig. 4. The shaded area, A,, represents the energy stored within the heater body during the heating period. When the heater is turned off, there is a sudden drop in heat output to a level, EhQmax, which can be regarded as an equivalent heater capacity. The shaded area, AZ, represents the energy released from the heater after it is turned off. Theoretically, A, must be equal to AZ and thus E,, can be calculated by evaluating Eqns (23) and (24). While the full power output of a heater is achieved after an infinite time, in practice an operating time equivalent to some multiple of the time constant is used to calculate the output power of a heater. For instance, 99% of full power will be reached2’ after an operating time of 5t. To make the integration mathematically possible, assume that the upper time limit for A, is a large number, 52, and for A2 is infinity. Then Eh can be calculated as follows: “* &,,,( 1 - e-““) df, A, = dnax x A2 = Ehomax e-“” dt, AZ = &&nax I0 Eqns (27) and (28), yields: A,=&#-

Equating

I

(27) (28)

(29) If the time constants and E, are known, Eqns (23) and (24) can be used to simulate the dynamic power output of a heater. The effect of the heater time constant on the temperature-time response in a farrowing room is shown in Fig. 5. The time constant of the controller (t,) for the room was 75 s. When the time constants of the heater were assumed zero, both the simulated airspace temperature, Ta, and sensor temperature, T,, indicated larger overshoots and shorter heating periods. When the heater was modelled with the time constants, the heating period was longer, the temperature overshoot was eliminated, and the simulated sensor temperature agreed well with the measured data. 2.4. Dynamics 2.4.1.

of ventilation

Theory

The perfect gas law can be applied to moist air.” The pressure of the moist air within a fixed-volume airspace can be expressed in terms of its density, p, temperature, T, and the gas constant, R: P=RpT

All variables in Eqn (30) are time dependent. time yields Eqn (31):

Differentiating

(30) Eqn (30) with respect to

(31) The volumetric airflow rate of a propeller fan is dependent upon the pressure difference across the fan.‘* If the atmosphere pressure can be assumed constant, then any change in pressure within the airspace will directly introduce an airflow rate change.

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0

600

1200 Time,

1800 t 5

2400

3000

Fig. 5. Effect of controller and heater time constantson temperatureof an airspaceduring a heating and cooling cycle (- - - -, T, simulated, T, = tz = t3 = 0; -, T, simulated, t, = 75s, tz = z, = 0; .-. -, T, simulated, t, = 0, tz = 175s, t.?= 590 s; -, T, simulated, t, = 75 s, tz = 175 s, T.?= 590 s; . . . . ‘, T, measured). 2.4.2. Effect of temperature on pressure

From Eqn (31), the change of pressure is a function of both the temperature, T, and the air density, p. When T increases, p tends to decrease, and vice versa. T has a positive effect on P while p has a negative effect. To simplify analysis of the effects T and p on P, two extreme cases can be considered: Case A: The airspace is completely sealed. In this case, the mass of air and hence the air density cannot change when the temperature changes. Then the pressure change is proportional to the change of temperature with a coefficient Rp. During the heating period, dT/dt and dPldt are positive. During the cooling period, dTldt and dPldt are negative. Case B: The airspace is open to the atmosphere. In this case, the mass of air and the air density can change freely and the pressure does not change, thus dP/dt = 0. Temperature and density effects on pressure are cancelled as pdT/dt = -Tdp/dt. An enclosed airspace behaves as a control volume somewhere between a sealed and an open airspace. Therefore, during heating, dP/dt is positive and proportional to dT/dt with a factor greater than zero but less than Rp. During cooling, dP/dt is negative. Accordingly, the airflow rate of the exhausting fan is higher during the heating period than during the cooling period. The responses of T, dPldt, and ventilation rate, V, with respect to time during a heating and cooling cycle are illustrated in Fig. 6. Theoretically, Eqn (31) could be solved to predict the dynamic pressure change. However, the simulation result showed a severely unstable thermal response problem

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= .2 5 r= E 9

Fig. 6. Theoretical

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_-----_--_-_--____________ hl

r

I

1

Time

response of pressure and ventilation rate to a temperature enclosure (- - - -, mean ventilation rate)

change in a ventilated

when this equation was added to the heat transfer model. The pressure fluctuated with an impractical amplitude when the temperature changed. The reason for the instability was that the pressure is very sensitive to temperature change and the response to a small AT was almost instantaneous. Considering the tiny time interval for the response of pressure compared with the large time constant value of heating and ventilating equipment, simulation of the pressure change using Eqn (31) was unrealistic in the current model. 2.4.3. Experimental evidence of pressure changes Fig. 7 shows the pressure responses of an airspace during

heating and cooling cycles. The tests were performed in a laboratory chamber. A large mixing fan was used in test 1 and the pressure response gave a distinguishable step change as shown in Fig. 7a. In test 2, there was no mixing fan used. However, there was still a notable change in pressure between the heating and cooling period (Fig. 7b). These tests verified that the theory discussed above is meaningful. The graphs in Fig. 7indicate that, although there was a pressure difference between the heating and cooling periods, the pressure stayed relatively constant during each period. Thus, a step function was introduced in the current model to describe the ventilation changes that occur during short heating cycles: ri = Elljmin,

V = Vmin,

heating period cooling period

(32)

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45

yi@

30

0

300

I 600 Time.

I YW

I 1200

33

0

I 200

I 400

s (a)

I 600 Time. s

I 800

I low

I200

(h)

Fig. 7. Effect of changes in laboratory chamber (a) with forced air mixing

temperature on pressure drop acres the exhaust fan (b) without forced air mixing

where Vmi” is the ventilation rate during the cooling period and Ef is a multiplying factor which indicates the change of ventilation rate between the cooling and heating periods. From the curve fitting of experimental data collected from the laboratory chamber and from farrowing rooms, the factor Ef was taken as 1.1 for a very small airspace such as the laboratory chamber, 1.05 for small airspaces such as farrowing rooms and 1-O for large airspaces such as a dairy barn.= 3. Calibration and testing of the heat transfer model 3.1.

Description

of laboratory

chamber

A laboratory chamber experiment was conducted to test the mathematical models just described a A small chamber, as illustrated in Fig. 8, was built with inside dimensions of 4.72 x 2.23 x 2.4 m, giving a total surface area of 54.4 m2 and a volume of 25.26 m3. The walls and ceilings were constructed of the same materials as used in most barns in the Canadian prairie area. The interior and exterior surfaces were 10 mm plywood, and 90 mm fibreglass batts were used for insulation. The floor was different from most livestock buildings because of the limitation of location. The floor was built in the same way as the walls except the interior surface was covered with particle board. The chamber airspace was very well sealed. Tests indicated that leakage into the chamber through non-planned air inlets was less than 4 m3/h at 25 Pa. The temperature within the outer laboratory remained relatively constant near 21°C. Air entered the chamber from the larger airspace, supplied by a centrifugal fan at the end of the chamber to enable the high pressure for flow rate measurement, first through a flow measurement section and then through a single circular orifice in one endwall. Air was

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I

Al measurement

SUPPlY fan --J

-0

-4

L Inlet

Exhaust fan

Heating

\I/ Fig, 8. Schematic of laboratory

chamber

bulbs

\I/

and airflow

measurement

system

exhausted from another endwall of the chamber by a 450mm diameter propeller fan. During the experiment, the fan was operated at low speed to maintain a low ventilation rate. A propeller fan was mounted within the chamber and operated continuously in an attempt to create complete mixing, but no measurements were made to verify that complete mixing did occur. During the experiment, a constant heat input of 0.54 kW was supplied within the chamber by a group of light bulbs to simulate the heat production rate of the animals, and a 3.8 kW electric heater was used to provide the supplemental heat source. It should be noted that because the chamber was small, the fans and heaters were all oversized compared with most practical barns. Air temperatures were measured in the supply air duct (z) and immediately upstream of the exhaust fan (r,). Measurements were taken every 10 s with Type T thermocouples. The uncertainty in temperature measurements was expected to be less than fOe2”C. The time constant of the thermocouples was estimated to be less than 3 s because they were located in moving airstreams; hence, the thermocouple measurements were expected to be equal to the actual temperature. The relative humidity of the supply air was measured by an aspirated psychrometer (Cole-Parmer Instrument Co. Model 3312-40. Chicago, IL, USA). The airhow rate was measured by an AMCA-Standard flow measurement section. The pressure drop across the nozzle was measured with a micro-manometer (MERIAM Model 34FB2, MERIAM Instrument Co. Ohio, USA), which could be read to a resolution of 0.025 mm (0.3 Pa). The airhow, measured at the temperature of the supply air, was maintained nearly constant at 125 m3/h. The static pressure differential across the ventilation fan was maintained at approximately 25 Pa, and was measured continuously during the experiment with a variable reluctance pressure transducer (Vallidyne Model DP103-14, Vahdyne Engineering Corporation, Northridge, CA, USA). One port was open to the large laboratory outside the chamber. The other port was connected to a piezometer ring joining three pressure taps that were flush-mounted with the inside surfaces of the experimental chamber. The resolution of the instrument was about 1 Pa.

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During the test, a data logger was used to collect the incoming and outgoing air temperature, pressure across the exhaust fan, and the events of supplemental heat. A data collection program was run on a microcomputer to record the measured data for later data analysis.

3.2. Description

of the farrowing

rooms

Data were used from two of eight similar nine-crate farrowing rooms located at the Prairie Swine Centre, University of Saskatchewan. Room 3.08 is located on the north-east corner, and room 3.10 is located on the south-east corner, of the shorter wing in a T-shaped barn. Room 3.08 has more exposed exterior wall than room 3.10. Both rooms are wood-frame buildings and are insulated with fibreglass batt insulation. The inside dimensions of the rooms are 13.7 X 4.7 x 2.4 m. Details of the rooms are given in Table 1. The nine farrowing crates in each room were arranged in one row. The crates were raised above a 1.3 m deep, 0.9 m wide concrete manure gutter. The remainder of the floor of the rooms is concrete. Supply air to the rooms enters from an attic duct through a discontinuous slot inlet along the top of one long wall. A propeller fan recirculates barn air through a circular duct located directly beneath the slot inlet. For purposes of this paper, the airspeed along all interior surfaces of the rooms was assumed to be 0.3 m/s. Air is exhausted from the rooms by propeller fans located in the long wall opposite the air inlet. In both rooms the minimum winter ventilation rate is supplied by a 200 mm single-speed fan which, in tests in an AMCA-Standard fan-test facility, delivered approximately 342 I/s at a static pressure of 25 Pa. Supplementary heat was supplied to the rooms by 250 W heat lamps over the farrowing crates and by two electric space heaters. The data reported in this paper were collected on days when only one heater was operating in Room 3.10 and both heaters were operating in Room 3.08. State-two ventilation in both rooms was provided by 250 mm diameter fans. The operation of the stage-two fan and the heaters was controlled by a double-pole double-throw electromechanical thermostat. With this control system, the stage-two fan and the heaters cannot both operate at the same time, but there is an interstage temperature range within which neither the fan nor the heaters are operated. The data presented in this paper were collected under conditions in which the heaters cycled on and off and the stage-two fan never was activated.

Parameters

Parameter Airspace Area of Area of Area of R value Rs’ value Hzater Heating Number

volume, m’ ceiling, m2 outside wall, mr floor, m2 of ceiling, ,y’ “$of wall, m Cm i’-’ capacity, kW bulbs, kW of animals

Table 1 used in GASP

model

Laboratory chamber

Farrowing room 3.08

25.3 IO.5 33.3 10.5 1.7 1.7 3.8 0.54 0

170 70.4 43.5 70.4 3.7 3.6 8.4 1.7 8 sows

Farrowing room 3.10

with

170 70.4 35.2 70.4 3.7 3.6 4.2 0.33 litters

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3.3. Response

the

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model

The response to a single heating and cooling event is shown in Fig. 9 for the laboratory chamber and for a farrowing room (Room 3.08). The values of selected parameters used in the mathematical model of heat transfer are summarized in Table 1. In the case of the farrowing rooms, the ventilation rate was not well known so it was treated as the parameter that would be varied to calibrate the simulation model. The fit shown in Fig. 96 was obtained for an estimated ventilation rate of 340 m3/h, a value which is thought to be reasonable for the fan used. The small perturbations evident in the temperature signal from the laboratory chamber were not apparent in the signal from the farrowing rooms. The surface area to volume ratio was smaller for the farrowing rooms so

36.0

I 0

I

I

15n

300

I 450 Time.

I hOO

\

(a) 23.0

,

IS.0

1 0

1

i

SO0

1000

I 1500 Time.

I

I

2oou

*so0

s

(b)

Fig. 9. Comparison between simulated and measured temperature for one heating and cooling event (a) laboratory chamber (b) farrowing room (-, simulated; - - - -, measured)

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there would be less influence of conditions at the boundaries. Furthermore, the integrated circuit temperature sensors used in the farrowing rooms have a larger time constant than the thermocouples used in the laboratory chamber and their slower response would tend to mask some of the shorter duration temperature fluctuations within the airspace. Lastly, the rotational speed of variable speed fans tends to pulse when the speed is low and the pressure is high as in the laboratory chamber test. These results indicated that the heat transfer model could be used to simulate the response of an airspace to a single heating and cooling event. The temperature was very sensitive to the values chosen for the time constants of the heating equipment and for the convective heat transfer coefficient, hi. 4. Simulating

multiple

heating and cooling

4.1. The simulation

events

model

The mathematical model of heat and mass transfer which has been described and tested for a single heating and cooling event was combined with a model of an electromechanical temperature controller in order to simulate a series of heating and cooling events. Assuming that the controller is made of materials with high thermal conductivity, the temperature gradient within the controller will be negligible and the lumped capacitance method for heat conduction applies:23

dT,-

T,-T

dt ---

Tl

(33)

where

M t’ =h,A,

(34)

The time constants of temperature controllers used in Canadian livestock buildings were reported** to range from 50 to 450 s. In a real livestock building airspace, the air temperature fluctuates frequently during the heating season and the outside temperature is time dependent even within a short time interval. Therefore, Eqn (33) cannot be solved analytically and a numerical solution is required. The task of the simulation program is to combine the solution of Eqns (7) and (8) with that of Eqn (33) to simulate the dynamic response of the airspace. The simulation model for livestock building ventilation systems has been described previously and was based on the GASP IV simulation language.2s The model incorporates a variable time step advance procedure. When state variables are changing slowly and no events are occurring, the time step may be as large as 3 min. When state variables are changing rapidly or when an event is scheduled, the time step may be just a few seconds. In this way, computer time is economized, yet events, such as temperature crossing a thermostat setpoint, are approached with considerable precision for accurate simulation of control devices. 4.2. Simulation

results

Fig. 10 shows the temperature-time response of a pig farrowing room (Room 3.10) for a 20 h period during each of two successive days. The simulation used data for animal heat and moisture production from Clark and McQuitty.” The simulated and measured temperatures exhibited similar patterns. Predictably, when the outside temperature was high, the frequency of temperature fluctuations within the airspace was lower and less

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-30

I 4

0

1 8

THERMAL

I 12 Time.

I 16

ENVIRONMENT

IN

-30 20

I 4

0

h

LIVESTOCK

I 8

I 12 Time.

(a)

Fig. 10. Comparison (a) on 19 December

Comparison

Q., kJ/h

* Heat

20

h

simulated

and

Table 2 experimental results consecutive days

for

farrowing

room

3.10

on

two

Meusured

mean

max.

min.

mean

max.

min.

18.0 54.8 7014 14 800 17 630 4142 300

22.3 65.0 18400

15.4 42.0 3600

17.9 47.0 7229 14 800’

22.1 58.0 18.720

15.5 34.0 3txM

21430

8893

22.1 69.0 16 240

15.2 41.0 1200

18.0 47.0 7663 14,800:

22.1 65.0 16 320

15.7 28.0 1200

22,500

8893

I

Day 2 q, “C IfHa, %

,..I I6

(h)

Simulated

Day

-.--.

between simulated and measured thermal temperature in a pig farrowing room 1984 (b) on 20 December 1984 (top> simulated sensor temperature; middle, measured sensor temperation; bottom, outdoor temperature)

of

Parameter

BUILDINGS

18.2 55.0 6223 14800 17030 3949 300

and moisture

production

data

from

Clark

and McQuitty6.

Y.

ZHANG

ET

119

AL.

supplementary heat was consumed (Table 2). As the outside temperature decreased, the duration of each heater-off period was decreased and more supplementary heat was required. The predicted mean supplementary heat input over each 20-h interval agreed reasonably well with experimental data. Although the general pattern of temperature fluctuations was predicted by the model, the frequency of the simulated temperature signal was greater than that of the measured temperature signal. Most notably, the length of each cooling period within a temperature cycle generally was longer than that which was predicted. Four possible reasons for lack of fits between measured and simulated data have been identified and are described in the following sections. 4.2.1. Animal

heat loss

At 20°C an adult pig on a raised, perforated floor in an insulated building will lose approximately one-third of its total heat loss by convection.26 Convective heat loss is proportional to the difference between the surface temperature of the animal and the temperature of the airspace. A change in air temperature of 5°C as measured in the experimental room is expected to have a significant and immediate effect on the rate of convective heat loss. During the heating portion of a temperature cycle, convective heat losses will be decreasing, and during the cooling portion of the cycle, the convective heat losses will be increasing. The magnitude of changes in animal heat production are difficult to predict because the animal can physiologically adapt to changing temperatures through mechanisms such as vasomotor activity. It does seem possible that the cooling portion of the temperature cycle may have been extended because of an increase in convective heat loss by the animals in response to the sustained cooler temperature. 4.2.2. Convective

heat transfer

coefficient

A constant airspeed at the boundaries of the airspace was assumed. In fact, the airspeed at any one location was not likely to have been constant, and the airspeed certainly was not the same for all surfaces. The magnitude of the convective heat transfer coefficient, which is a strong function of airspeed, has a large influence on the pattern of are temperature fluctuations, especially in smaller airspaces, when large perturbations made to heating loads. 4.2.3. Incomplete

mixing

The model assumes that the airspace is completely mixed such that the temperature of the exhaust air is always equal to the mean airspace temperature. The good fit between actual and predicted supplemental heat requirement suggests that this assumption is valid. The model also assumes that the airspace is uniformly mixed such that the temperature is the same everywhere within the airspace. This assumption can never be correct for a real building, especially when point-source heaters are used and when the supply air enters the room at very cold temperatures. Given that there are likely to be temperature differences of at least 2°C between selected locations within a well-ventilated airspace, it is unlikely that the temperature measured at one location within the airspace will agree exactly with the simulated temperature. 4.2.4. Controller

model

For the period of time represented by the data presented in this paper, the inlet in the farrowing room was fixed and the exhaust fans operated at a fixed speed. Except for possible changes in ventilation rate due to wind effects and short-duration door openings, the ventilation rate can be considered to be constant. The amplitude of the airspace temperature-time response is totally a function of the heater control system.

120

DYNAMIC

THERMAL

ENVIRONMENT

IN

LIVESTOCK

BUILDINGS

In the farrowing room, the heater was controlled by an electromechanical thermostat. This controller has a switching differential (temperature hysteresis) of approximately 2°C. This switching differential is modelled in the GASP model as a fixed differential. However, the data show clearly that the amplitude of the temperature fluctuations measured in the farrowing room varied throughout the day. The thermal response of the temperature sensing elements of the controllers is expected to be a function of airspeed, an effect that was not modelled. Experience with electromechanical thermostats in livestock buildings has indicated that the microswitches do not always switch cleanly, possibly due to corrosion and dust contamination of the switch and switch contacts. The mathematical model of the controller will not be able to simulate corrosion effects, but it could be modified to simulate more accurately the time constant of the controllers’ temperature sensing elements. 4.3. Simulation

of relative humid@

levels

Relative humidity measurements are compared to results of the simulations in Fig. 11. Hourly data from a nearby weather station were used for outside relative humidity. The agreement between measured and simulated mean relative humidity data is surprisingly good. Not suprisingly, the pattern of fluctuations in relative humidity is not so well predicted by the model. First, relative humidity is strongly coupled to temperature such that any errors made in simulating the energy balance will compound in simulating the relative humidity. Second, the model assumes a constant release of water vapour into the air, an assumption that is flawed; however, a better assumption is not apparent. 1.0,

1

; II;--0

I.01

I

“,x;r I

I

4

8 Time. (a)

h

I

I

12

16

20

0

4

8

12 Time,

16

20

h

(h)

Fig. 11. Comparison between simulated and measured relative humidity in a pig farrowing room (a) on 19 December 1984 (b) on 20 December 1984 (top, simulated sensor temperature; middle, measured sensor temperation; bottom, outdoor temperature)

Y.

ZHANG

ET

121

AL.

5. Conclusions

1. The method and equations used to simulate heat exchange at the boundaries of the airspace appear to be satisfactory; however, better predictions for the convective heat transfer coefficient are necessary for accurate simulations of short-term temperature fluctuations, especially within smaller airspaces. 2. Values from the literature for animal heat and moisture production appear to have been accurate for the farrowing rooms studied in this project. Supplementary heat predictions by the simulation model agreed well with measured data. 3. The current simulation model assumes that animal heat and moisture production are constant. There is a need to model instantaneous heat loss from animals in order to give better prediction of the short-term temperature fluctuations within the ventilated airspace of a livestock building. 4. Ventilation rates can be affected by fluctuations in static pressure when propeller fans are used for a small airspace. The static pressure within the airspace needs to be modelled so that short-term fluctuations in air delivery of the propeller fan can be more accurately estimated. 5. The GASP IV simulation program is a good tool for the analysis of the dynamic thermal response of an enclosed airspace. Although the predicted and measured data for temperature and relative humidity did not agree precisely, the patterns of fluctuations in these two parameters were accurately simulated. The calibrated GASP IV program is useful for analysing alternative control strategies for livestock barn heating and ventilating systems. Acknowledgements This work is dedicated to Professor J. R. Ogilivie without whose inspiration and encouragement the study would not have begun. Financial support for this research has been provided by Saskatchewan Agriculture through a SARF Grant to E. M. Barber on “Improved swine barn ventilation systems”, and by the University of Saskatchewan through a postgraduate scholarship to Y. Zhang.

References ’ Hellickson, M. A.; Walker, .I. N. (eds). Ventilation of agricultural structures. ASAE, St Joseph, MI. 49085, 1983 * Barber, E. M.; Ogilvie, J. R. Simulation of dynamic livestock environment: GASP IV model. Paper No. 80-212, Canadian Society of Agricultural Engineering, 151 Slater Street, Ottawa, Ontario, Canada, 1980 ’ Cole, G. W. The derivation and analysis of the differential equations for the air temperature of the confined animal housing system. Transactions of the ASAE 1980, 20: 712-720 ’ Nakanishi, E.; Pereira, N. C.; Fan, L. T.; Hwang, C. L. Simultaneous control of temperature and humidity in a confined space. Part l-Mathematical modeling of the dynamic behavior of temperature and humidity in a confined space. Building Science 1973, 8, 39-49 ’ C.I.G.R. Climitisation of animal houses. Congress Internationale du Genie Rural, Agricultural University of Gent, Gent, Belgium ’ Clark, P. C.; McQuittty, 1. B. Heat and moisture loads in farrowing barns. Canadian Agricultural Engineering 1989, 31: 55-60 ’ Bruce, J. M.; Clark, J. J. Models of heat production and critical temperature for growing pigs. Animal Production 1979, 28: 353-369 * Albrigbt, L. D. Steady-periodic thermal analysis of livestock housing. Paper No. 81-4023, ASAE, St Joseph, MI 49085, 1981 ’ Cole, G. W. Predicting building air temperature using the steady state energy equation. Transactions of the ASAE 1981, 24: 1035-1040

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” Tiimons,

THERMAL

ENVIRONMENT

IN

LIVESTOCK

BUILDINGS

M. B.; Albright, L. D. Finite element analysis of floor heat loss. Paper No. 77-4521, St Joseph, MI 49085, 1977 ” Anonymous DOE-2 engineers manual, Version 2.1A, Part III: Loads Simulator. Lawrence Berkeley Laboratory, Los Alamos, New Mexico, 1982 ” Bantle, M. R. L.; Barber, E. M. Energy simulation of a poultry house using DOE 2.1C. Paper No. 89-4085, ASAE, St Joseph, MI 49085, 1989 ” Chen, Q.; Kooi, J. V. D. Accuracy-a program for combined problems of energy analysis, indoor airflow and air quality. Transactions of the American Society of Heating, Refrigerating and Air-conditioning Engineers 1988, 94(2): 196-214. ” Harris, S. M.; McQuiston, F. C. A study to categorise walls and roofs on the basis of thermal response. Transactions of the American Society of Heating, Refrigerating and Airconditioning Engineers 1988, 94(2): 688-715. l5 Murakami, S.; Kato, D. E. S.; Suyama, Y. Three-dimensional numerical simulation of turbulent airflow in ventilated room by means of a two-equation model. Transactions of the American Society of Heating, Refrigerating and Air-conditioning Engineers 1987. 93(2): 621-641. ” Holman, J. P. Heat transfer (6th ed.) McGraw Hill, New York, 1986 ” Chapman,A. J. Heat transfer. New York; Macmillan, 1984, pp. 267-279 ” ASHRAE Fundamentals.ASHRAE Inc., 1791 Tullie Circle NE, Atlanta, GA 30329, 1989 ” Turnbull, J. E.; Montgomery, G. F. Insulation in farm buildings. Publication 1601/E, Agriculture Canada, Ottawa, Ontario, 1983 ” Patanker, S. V. Numerical heat transfer and fluid flow, Washington, D.C.: McGraw Hill, 1980 ” Ogata, K. Modem control engineering. Eaglewood Cliffs, NJ: Prentice-Hall, 1970 n Zhang, Y. 1989. Analysis of Heating and Ventilating Control Strategies for Cold-climate Livestock Housing. Unpublished Ph.D. thesis, University of Saskatchewan, Saskatoon, SK, Canada 23 Incropera, F. P.; Dewitt, D. P. Fundamentals of heat transfer. New York: John Wiley, 1981 24 Bayue, G. R.; Barber, E. M.; Jorgenson, M. Selection criteria for livestock ventilation control systems. Paper No. 89-6075, ASAE, St Joseph, MI 49085, 1989 zs Pritsker, A. A. B. The GASP IV simulation language. New York: John Wiley & Sons, 1974 26 Curtis, S. E. Environmental management in animal agriculture. Ames, IA: Iowa State University Press, 1983 ASAE,