DIMcomfort 4.0 - Theorymanual

8/11/2019 DIMcomfort 4.0 - Theorymanual

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DimComfort 4.0 Theory manual

Theory manual for calculations in DimComfort 4 0

When dimensioning diffusers in DimComfort 4.0 a basic knowledge of ventilationtechnique is necessary. Terms as throw length, velocity in the occupied zone, soundeffect and sound level pressure is used to describe the thermal and acoustic indoorclimate. In this manual the theory behind the calculations in DimComfort 4.0 is described.

Short description of me nus

Room Setup

In the Room Setup Menu the user defines the room, which is going to be ventilated, andwhat requirements of velocities and sound there are in the room. The calculation of thenecessary flow depends of ventilation principle (mixing ventilation or displacementventilation).

Select terminal device

In the menu Select terminal device the choice of diffusers takes place. All diffusers arepresented with picture, 3D-model and a description of the diffuser. It is possible to searchfor products by placement, function, shape, connection or by picture sorted by productgroup. Number or size can be determined from the sound requirement of the room. By for

example determination of the number of supply diffusers, the calculation takes intoaccount that there also has to be exhaust diffusers in the room with a margin of 3 dB,which corresponds to the assumption that the exhaust diffusers causes the same soundas the supply diffusers. The velocity in the occupied zone is not taken into account in thiscalculation, because the velocity in the occupied zone is dependent of the placement ofthe diffusers.

2D/3D work space

In the general work space the diffusers can be moved around when being in 2D-view.Here, there is also the possibility to change the placement of the false ceiling. In 3D-viewthe room can be studied from all angles. At the same time you can verify the

requirements and results in the lower left corner for the room and the selected diffuser

Print ResultRoom Setup Select device 2D/3D Work Space

Room requirements:Sound requirementsComfort zone

Velocity requirements

Room dimensions:GeometryFalse ceiling

Ventilation criteria:Temperature

Necessary flow

Selection/dimensioning ofdiffusers

Sound requirements aresupervised

Flow is supervised

General work space Results are printed as pdf

Placement of diffusers Opportunities:Standard pageProduct descriptionInfo and results:Room informationRoom / diffusersDiffuser placements

Air particle spread

VelocitiesSound

Visualisation:Air particles

Sound picture


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respectively. There is also placed a velocity diagram, where the velocity in the occupiedzone is shown as a function of the temperature difference (between room and supplytemperature).

Print

In the print menu you can select which information and showings of the room you want inthe result chart. A pdf file is created, which subsequently is opened in a pdf viewer.

Determining venti lation parameters

In DimComfort 4.0 there are different ways to determine the parameters for the ventilationin the room. The necessary ventilation rate can be determined on basis of cooling orheating needs or the need for outdoor air determined by the dilution equation fromoccupant generated CO

2.

Heat balance

( )espvv TTcq =

vis the effect for cooling or heating (cooling will be shown with negative sign) [W]

qvis the air flow [m

3/s]

is the air density [kg/m3]c

pis the specific heat capacity of air [J/(kgK)]

Tsis the supply temperature [C]

Teis the exhaust temperature [C]

At normal air conditions (20C og 101,3 kPa) the formula can be shortened to

( )esvv TT2,1q =

qvis the air flow [l/s]

Mixing ventilationFully mixing in the room is assumed, which implies that the room temperature is equal tothe exhaust temperature (T

r= T

e). The room temperature must always be specified. In

addition two of the three parameters (v, q

v, T

s) must be specified, the remaining will

subsequently be calculated. In stead of qvthe max allowed CO

2concentration can be

specified, qvwill then be calculated from the dilution equation.

Displacement ventilationBy displacement ventilation cold air is supplied at floor level, which will give occasion for

a vertical temperature gradient in the room. The vertical temperature distribution dependson many factors placement, extent and convection flow of heat sources, room geometryand air flow. The 50%-rule, which applies that 50% of the temperature increase fromsupply to exhaust takes place by the floor, is a simple model. But several laboratory testshas shown that the temperature gradient most often is larger in the lower part than in theupper part of the room. DimComfort uses the following model to give a better predictionof the temperature gradient in the occupied zone, which is defined as the temperature in1.1 m the temperature in 0.1 m (T

r-T

f).


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Temperature

H

eight

Detailed model

50%

Tsupply Tfloor(0.1)

Texhaust

Troom(1.1)

Tgr

The assumption is done that the air temperature close to the floor (0.1 m) T

fis the mean

value of room temperature Tr(in 1.1 m) and the supply temperature T

s. Hereby follows that

the temperature increase between 0.1 m and 1.1 m (which is the temperature gradient inthe occupied zone T

gr) can be determined as

( )2

TTT srgr

=

In addition comes the temperature efficiency T

( )( )

sr

seT

TT

TT

=

The temperature efficiency depends on the room height and the thermal load.

0 50 100 150[W/m

2]

100

150

200

250[%]

Roomheight [m]

T

= 100

2.5

3

4

5

6

7

8

T

u

- T

i

T

r

- T

i

Combining the formula for temperature gradient in the occupied zone with the diagram,the formula for the temperature efficiency and the general formula for the heat balance

gives us connection between the parameters (v, q

v, T

gr) and the room temperature T

r,

which always must be specified. Like mixing two of the three parameters must bespecified, the remaining will subsequently be calculated. In stead of q

vthe max allowed

CO2concentration can be specified, q

vwill then be calculated from the dilution equation.


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Dilution equation

( ) i6V

q

v

mi

6V

q

i0V

q

v

m c10e1q

qcc10ecce1

q

qc

vvv

+

=+

+

=

c is the concentration of CO2in the room at the time implying ideal mixing [ppm] (ppm = cm3/m3)

qmis added amount of CO

2(depending of activity level) [m

3/h]

qvis the air flow [m

3/h]

V is the volume of the room [m3]

is the time [h]c

0is the start concentration (set to the same as c

iwhich makes this part of the equation zero) [ppm]

ciis the concentration of CO

2in the supply air (outdoor concentration is normally 300-400) [ppm]

Sound calculations

In sound diagrams and diffuser data the A-weighted sound effect level LWA

is specified. Itis specified for a diffuser and the plenum box (if any) connected with a straight channel on

1 m and the same size as the diffuser. Sound pressure levelis a measure for the intensityof the sound, that is the pressure vibrations we perceive, while sound effect levelis aparameter, which characterizes the sound source. Both things is normally specified in theunit dB (decibel), which can cause confusion.

Sound pressure (Lp)

Is a measure for the intensity of the sound, characterized by the pressurevibrations perceived by the ear or measured with a microphone on a soundlevel meter. Sound pressure is measured in Pascal (Pa) and is most oftenspecified as sound pressure level in decibel (dB) or dB(A).

Sound power (LW)Is the power a sound source (fx a machine) sends out in the shape of sound.The sound power is measured in Watt (W) and is most often specified assound power level in decibel (dB) or dB(A).

In the Select terminal device menu is the sound properties of the diffusers specified assound power.

Sound power ]dB[N

Nlog10L

rew =

N is the actual sound power [W], which is send out to the air in the shape of pressure vibrationsN

re=10

-12W is the reference sound power

Sound pressure ]dB[pplog20Lre

p =

p is the actual sound pressure [N/m2]

pre=210-5N/m2is the reference sound pressure

The room attenuation D [dB] is the difference between sound effect level and soundpressure level

DLL Wp =

Sound calculations in Select Terminal Device Menu

In the Select Terminal Device menu is the sound pressure level in the room calculated by


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+

+=A

n4

r4

Qlog10LL

2Wp

Q is the direction factor, which is dependent of the placement of the diffuser. Inthe Select Terminal Device menu it is assumed to be 2 (placed by ceiling)

n is the number of diffusers

A is the room absorption

sT

V16,0A =

V is the volume of the room [m3]

Tsis the reverberation time of the room [s]

Sound calculations in 2D view

When the diffusers are placed in the room the sound pressure level is calculated innumerous points in the plane y = height of the occupied zone. In each point the

placement in the room of every diffuser is taken into account.The sound pressure level from diffusers in one point is calculated by

+

+=

A

4

r4

Qlog10LL

21d1p

1d,W1p,p

+

+

A

4

r4

Qlog10L

22d1p

2d,W

LW,d1

and LW,d2

is the sound effect from each diffuser respectivelyr

p1-d1and r

p1-d2is the distance from the point to the diffuser

is logarithmic addition determined by: L1L

2=

+ 10

L

10

L 21

1010log10


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Velocity ca lculations

Mixing

The velocity in the occupied zone will always be dependent of the placement/distribution

of the thermal loads in the room.

Calculation of velocities with thermal air flows taken into account demands very detailedinformation of all thermal conditions in the room and advanced tools to solvecomprehensive and complicated equation systems (e.g. CFD). In DimComfort 4.0 simplerformulas is used based on air jet theory and experience from laboratory tests. Thereforecalculations must be considered as a realistic estimate of the maximal velocity in theoccupied zone.The occupied zone is defined in the Room Setup menu with the following defaults formixing ventilation: height h

occ= 1,8 m, distance from wall x

occ= 0.6 m and velocity

requirement of 0,2 m/s.

Air jet velocityThe air jet velocity v

xof a diffuser decreases with the distance from the diffuser. The

general formula of the velocity decay for a free and wall jet is:

free jet 00a

x vxA

2Kv = wall jet 0

0ax v

xAKv =

Kais a diffuser constant, which is determined from diffuser specified data, fx throw length

A0is the freearea of the diffuser [m

2]

x is the distance from the diffuser [m]v

0is the supply velocity [m/s]

When the diffuser is placed 300 mm from the ceiling the formula for wall jet will be used.

Diffusers with horizontal air patternThe air jet velocity is calculated from the formulas of free and wall jet with the critical

length lcritis inserted instead of x. The critical length can be shown as a green/redindicator in the 2D-/3D-view.lcrit

will be determined as the least of following distances:

Horizontal distance to the nearest wall + vertical distance to the occupied zone Horizontal distance to the nearest air jet (weighted by local air flow) + vertical

distance to the occupied zone

(When cooling) Penetration depth + vertical distance to the occupied zone

Penetration depth xmis determined as 0

asam A

Ar

KKx

= [m]

Ksais determined from laboratory tests


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Ar is Archimedes number defined as20

se0

v

TTAgAr

=

and g is coefficient for thermal expansion [C-1] and gravity [m/s2] respectivelyT

e

and Ts

is exhaust and supply temperature respectively [C]

Wall diffusers:When two or more diffusers with paralleldirected supply is placed with a mutualdistance A, which is less than b

h, the throw is

lengthened by

l0.2

(corrected) = K l0.2

K is a correction factor, which can be read from the

diagram

or more

Termisk hastighed v term Varmekilde

Konvektions-

hastighed

T termermisk hastighed v Varmekilde

Konvektions-

hastighedConvection

velocity

Heat Sourcehermal velocity

Supply with cold air:When cooling a so called thermal velocity willbe calculated additionally. Heat sources in theroom generate convection air flows, whichintensifies the drop effect of the cold supply air.These thermal conditioned downwards air fcauses a draught risk independent of thevelocity of the supply air jet.

lows

This velocity is called thermal velocity to avoid confusion between the concept ofconvection velocity, which normally is perceived as the up going flow above heatsources. The thermal velocity is determined from an empirical model with the heat load[W/m

2], number of diffusers [W/diffuser], air pattern (1-, 2-, 3-, 4-way, rotation etc.), and

the height of the room.

Height = 2,5 Height 4 m:

0 50 100 150 200

[W/m2]

0

100

500

1000

1500

4 ways

0

100

500

1000

3 way

0

100

500

2 way

0

100

200

300

400

500

1 way Maksimum velocity v in the occupied zone [m/s]Grills Rotation

Heat load[W/diffuser]

term


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The resulting velocity in the occupied zone is the highest of the air jet velocity and thethermal velocity.

Diffusers with vertical air patternThe air jet velocity is calculated by a variant of the formula for a free air jet

Hot jet

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0a2v,type

0a0y

A

y

KK

Ar1

y

A

2

Kvv

= ,

Ar

KAKy a0v,typem=

Cold or isothermal jet

3/12

0a2v,type

0a0y

A

y

KK

Ar1

y

A

2

Kvv

+= , y

m= H


se0

u

TTAgAr =

Ktype

is a type constant, which is determined from turning point datay is the vertical distance from the diffuser to the occupied zone [m]y

mis the distance to where the air jet turns/stops [m]

H is the distance from diffuser to floor

The resulting velocity in the occupied zone is only determined from the air jet velocity.


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Displacement

The occupied zone is defined in Room Setup with the following default settings fordisplacement: distance from diffuser x

occ= 1.5 m and max velocity requirement of 0.2 m/s.

Air jet velocityThe direct velocity caused by the single diffuser is determined as

=

,occ

,Dr,xx

qKv

the index indicates the angle according to the centreline of the diffuser (symmetry axis)q is the flow of the diffuser [m

3/s]

,occx is the distance between diffuser and occupied zone in the angle , where the velocity is highest []

( )=cos

xx occ,occ

KDr,is a velocity decay coefficient depending of diffuser specific data (e.g. near zone) and Ar

D

ArDis Archimedes number defined as

20

sr

v

TThgAr

=

and g is coefficient for thermal expansion [C-1] and gravity [m/s2] respectivelyh is the height of the diffuser [m]T

rand T

sis room and supply temperature respectively [C]

Lindab displacement diffusers (COMDIF) can be adjusted to both small diffusion (radial)and large diffusion (semi radial, where the supplied flow is largest in directions parallel tothe wall and less in forward direction). At large diffusion will the velocity typically be

highest in an angle of = 45.

Floor velocityWhen more diffusers are placed at the same wall or around corner at two adjacent wallsthere is a risk of velocities at the floor in the occupied zone, which are higher than the airjet velocity from the single diffuser, where the air jet enters the occupied zone. Whencalculating this floor velocity the programme distinguishes between if the diffusers areplaced at the same wall or if they are placed around a corner.

Diffusers placed at the same wall:The air flow from closely placed (but evenly distributed) diffusers will at some distance runtogether to a plane flow regardless of the air pattern from the single diffusers is plane,radial or different shaped. The velocity in this linear front is only dependent of the air flowper m wall and the temperature difference between room and supply but not of thesupply velocity of the diffusers.

( )( )3sr2total

1floor kTTlnkL

qlogkv +

=

k1, k

2og k

3are constants

qtotal

is the total air flow for all diffusers [m3/h]

L is the length of the wall, which the diffusers are placed at [m]T

rand T



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100 200 300 400 500 600 700 1000

qtotalpr m wall [m3/(hm)]

0.0

0.1

0.2

0.3

0.4

0.5

vfloor[m/s] Tr

-T

s

-1 K

-2 K

-3 K

-4 K-5 K-6 K

Diffusers placed around a corner:The max floor velocity in the occupied zone is dependent of the number of diffusers andhow they are placed, as diffusers placed close to each other can give occasion for jetsbetween diffusers and thereby relative high velocities in the occupied zone. The velocityis calculated by

=w

qKv totalDwfloor

KDw

is a coefficient dependent of2total

sr

q

TT

qtotal

is the total air flow for all diffusers [m3/s]

w is a characteristic (geometrical) unit, which is calculated from the length of a wall and the distance fromthe corner to the most distant diffusersT

rand T


ir particle trajectory calculations

In 3D-view it is possible to see a visualisation of how the air will flow out from the supplydiffusers. The visualisation happens with streaming particles. The trajectory of theparticles depends of the supply velocity and temperature, but the calculation of thetrajectory does not take mutual placement or the heat/cooling effect, which is applied tothe room, into account. So it is theoretical trajectories shown in the visualisation.


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By mixing ventilation colliding particles from different diffusers will change colour and falldownwards to show that the air from the diffusers theoretically will collide at thesepoints. Furthermore particles, which are colliding with a wall, will follow the wall down tothe occupied zone. When the particles enter the occupied zone they will change colour

and disappear.By displacement ventilation both colliding particles and particles colliding with a wall willchange colour and disappear. In addition the particles will change colour to green whenthe air jet velocity from the single diffuser is lower than the velocity requirement (normally0.2 m/s). From that you get an indication of if the near zones will overlap.

Formulas for the trajectory of the air jet

Mixing

Horizontal air pattern: 0

3

0

m

a

catype A

A

xx

K

ArKKy

=

Ktype

, Kcais diffuser type constants, which are determined from lab tests

Kais a diffuser constant, which is determined from diffuser specified data, e.g. throw length

A0is the free area of the diffuser [m

2]

x is the distance from the diffuser [m]

xmis the penetration depth, which is determined from 0

asam A

Ar

KKx

=

Ksais determined from lab tests


se0

v

TTAgAr

=

and g is coefficient for thermal expansion [C-1] and gravity [m/s2] respectivelyTeand Tsis exhaust and supply temperature respectively [C]v

0is the supply velocity [m/s]

Vertical air pattern: xtan

1x

tany4

1y 2

2m

+

=

is the angle of the outer core jet according to vertical

ymis the turning point for a warm jet determined by

Ar

KAKy a0v,typem= , for a cold or isothermal air jet yy

equals to the distance from diffuser to floor.

Displacement3

Dr0

Dtype x

KA

ArKhy

=

h is the height form the ceiling to top of the diffuserK

Dris a diffuser constant, which is determined from diffuser specific data, e.g. the near zone at -3K and -6K

ArDis Archimedes number for displacement defined by

20

srD

v

TThgAr

=

and g is coefficient for thermal expansion [C-1] and gravity [m/s2] respectivelyT

rand T


v0is the supply velocity [m/s]

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DIMcomfort 4.0 - Theorymanual