Design of Upper-Room UVGI Systems Computer …1 Design of Upper-Room UVGI Systems Computer Aided...

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Design of Upper-Room UVGI SystemsComputer Aided Calculations

Promises and Pitfalls

New York State Energy Research and Development Authority (NYSERDA)

CAD Design for Upper-room UVGI Installations: Development and Validation

CAD-UVGI Design Tool

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NYSERDA Objectives

• Develop a standardized protocol allowing UVGI equipment manufacturers to define and publish the emission characteristics of their fixtures

• Adapt existing lighting programs for use with germicidal radiation radiometric data by modifying existing electronic data files

• Determine average upper room UVGI intensity and distribution from multiple overlapping fixtures in a wide variety of existing rooms

• Validate the computer design tool using standard radiometers equipped with 360 degree UV

Visual Lighting Design Software

Visual is a collection of lighting calculation tools engineered to simplify the design process and provide comprehensive lighting analysis.

Basic Edition Professional Edition Roadway Tool

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Visual Professional Edition

Visual Professional Edition (Released 1999)

• The Professional Edition is comprehensive lighting design software with a 3-D modeling interface for the construction and analysis of interior and exterior lighting designs. It Imports DWG/DXF files.

• The Professional Edition generates high-quality construction documents of the lighting design. The final design can be exported to an AutoCAD DWG/DXF file to be transferred to the end customer.

20,000 Active Users

Decisions…

• There are two approaches to solving the so-called “Global Illumination”(in our case, “Global Irradiance”) problem– Raytracing– Radiosity

• Visual is a radiosity engine which implies certain assumptions and limitations.– All surfaces can be approximated by planar facets– All reflecting surfaces are perfectly diffuse– No attenuation or refraction of flux due to medium (smoke, glass, etc…)

• The tradeoff is that Visual is very fast compared to a raytracer.

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Garbage In / Garbage Out

• Both approaches suffer from limited available input data– Far-field radiometric data

• All sources are radiometered as point sources• Inherent measurement inaccuracies• Field differences from laboratory conditions

– Limited material reflectance (and transmittance) data• We need BRDF’s• We don’t have BRDF’s for most materials

Basic Radiometry

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Radiometrics' derived units are densities

• Surface density (watts/area)– Irradiance, E– Exitance, M

• Spatial density (watts/steradian)– Defining spatial extent: solid angle, ω– Radiant intensity, I

• Density of a density (intensity/area)– Radiance, L

The useful idea of a ray of flux

• Flux can be thought of as rays of power– Energy from a point through a vanishingly small aperture = cone of

flux– A ray of flux is this very small cone, represented by a single arrow

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• Irradiance is the density of flux falling onto a surface:

• If the area is very small, a single value describes what is happening

• The small area can be located by a single point• Non-directional

Irradiance, E

Area, AFlux, ΦA

E ontoΦ=

The non-directionality of irradiance

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• For average irradiance, the area is large, but the idea of an area density is still used

• Average irradiance has to be interpreted with care, since values of irradiance at a point can vary a lot over the large area

Average Irradiance, Ē

AE Φ

=

Material properties - Reflectance

• Reflectance is the ratio of flux off to flux on:

• A reflectance is diffuse if flux leaves the surface in this way:– It varies with the cosine of the emitting angle (most dense in the

perpendicular direction)– Varies this way regardless of the incident direction

on

offΦΦ

=ρArea, A

Flux, Φon

Flux, Φoff

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Material properties - Reflectance

• Directional reflectance is the ratio of light off to light on accounting for specific directions of incidence and reflectance:

• General reflectance properties can be described with BRDFs.

Diffuse versus specular reflectance

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Radiometrics' ancillary unit: Solid angle

• Spatial extent is measured in solid angle– Solid angle requires a cone (with a point)– Just like plane angle requires a point

Solid angle, ω Plane angle, θ

Solid angle

• A cone of solid angle is related to a sphere the same way a plane angle is related to a circle

– A plane angle has a maximum value of 360º or 2π radians (a full circle)

– A solid angle has a maximum value of 4π steradians (a full sphere)

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Solid angle

• Solid angle can be calculated (very nearly) as

Solid angle, ω

D

θ

Point of regard

A 2D)cos(A θ

=ω

Radiant Intensity

• Radiant intensity is the density of flux in space in a particular direction:

ω

Φ= angle solid theinI

Flux, Φ

Solid angle, ω

High density, high intensity

Low density, low intensity

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Radiant Intensity

• Intensity is invariant with distance• Spatial flux density is the same along a direction

Flux, Φ

Solid angle, ω

Intensity as a spatial density

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Intensity as a spatial density

Typical representation of Intensity

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The Indicatrix (Radiometric Web)

• Take slices of the intensity distribution using many successively oriented planes.

The germicidal zone

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The kill zone

Practical Radiometry

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Determining radiant intensity

• A spherical coordinate system is used to specify a direction from a source

nadir (0,0)

I(θ,ψ)

ψ

θ


• Intensity is used to calculate E• The definition of intensity seems to require a measurement

of flux

• It is very difficult to measure flux in just a cone

ωΦ

=I

Flux, Φ

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• Turn the inverse-square cosine law around• This is an operational definition of radiant intensity

)cos(DEI

2

θ⋅

=


• A schematic representation of the measurement of intensity:

Dtest

ψ

θ

irradiancemeter

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• Radiometrists measure irradiance at a fixed test distance Dtest

• Moving the position of the irradiance meter to different angles, (θ,ψ), gives irradiance in different directions

• The irradiance meter is aimed so that its perpendicular points back toward the source, so:

2testDEI ⋅=


• But E⋅D2 changes with distance– At close range, E diminishes; the “near-field effect”

Test Distance

E⋅D2

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• E D2 changes with distance• Not much for a small light source• A lot for a big light source

Test Distance

E⋅D2


• Increase test distance until E⋅D2 is within 2% of the asymptotic value

• This is (almost always) 5 times the largest dimensionof the luminaire

• This gives the so-called“5-times rule”

Test Distance

E⋅D2

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• Testing a luminaire as if it were a point• Dtest > 5 ⋅ maximum luminaire dimension

Dtest

ψ

θ

irradiancemeter

A moving-mirror goniophotometer

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Radiometric data file format

• IES LM-63– ANSI/IESNA Standard File Format for the Electronic Transfer of

Photometric Data and Related Information– Introduced in 1986 as IES Publication LM-63-1986– Revised in 1991,1995 and 2000. The current version was accepted

as an approved ANSI standard in August 2002.


• Two coordinate systems are commonly used for luminairephotometry:

TYPE B TYPE C

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Photometric data file format

IESNA:LM-63-2002[TEST] LTL7421[MANUFAC] LITHONIA LIGHTING[LUMCAT] 2GT8 3 32 A12 1/3 ADDE[LUMINAIRE] GT8 GENERAL PURPOSE T8 TROFFER 2'X4' 3 LP T8 #A12 LENS 1/3 ELEC[LAMPCAT] F32T8[LAMP] THREE 32-WATT T8 LINEAR FLUORESCENT.[BALLAST] REL-3P32-SC BF=.867[_PRODUCTGROUP] FLUORESCENTTILT=NONE3 2850 1 37 5 1 1 1.77 3.76 01 1 880 2.5 5 7.5 10 12.5 15 17.5 20 22.525 27.5 30 32.5 35 37.5 40 42.5 45 47.550 52.5 55 57.5 60 62.5 65 67.5 70 72.575 77.5 80 82.5 85 87.5 90 0 22.5 45 67.5 90 2583 2534 2527 2516 2499 2478 2449 2422 2385 23382287 2225 2158 2081 1999 1902 1803 1685 1562 14251268 1128 993 877 761 668 577 501 435 367316 277 239 182 123 61 0 2583 2559 2554 2543 2527 2508 2484 2456 2419 23792332 2275 2213 2136 2058 1961 1862 1751 1625 14871335 1192 1039 898 759 643 540 461 401 350311 267 226 175 123 67 0 ….

FILE FORMAT

KEYWORDS

TILT =

VERTICAL ANGLES

HORIZONTAL ANGLES

LUMINOUS INTENSITY

A typical photometric report

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Some photometric webs

Far-field versus near-field photometry

ILLUMINANCE COMPARISON

0.0

50.0

100.0

150.0

200.0

250.0

300.0

HORIZONT AL DIST ANCE (in)

MEASURED

FAR-FIELDPHOTOMETRY

NEAR-FIELDPHOTOMETRY

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Near-field photometry – Application Distance

LUMINAIRE

CEILING PLANES

Near-field photometry – Luminance Field

LUMINAIRE

COMPOUNDLUMINANCEMETER

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Basic Calculations

Predicting irradiance

• Predicting flux density at a point from a point source• Almost always based on radiant intensity, distance, and

orientation

• Radiant intensity is invariant with distance, so how does irradiance change?– Attenuation of density by inverse-square of distance– Attenuation of density by cosine of incidence angle

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• Attenuation of density by distance– Rays get further apart on the surface as it recedes Same flux, more

area, less irradiance.

2

on2 A

E Φ=

21 EE > so AA 21 <

1

on1 A

E Φ=

A1

A2


• Attenuation of density by inclination– Rays get further apart on the surface as it is inclined Same flux,

more area, less irradiance.

2

on2 A

E Φ=

21 EE > so AA 21 <

1

on1 A

E Φ=

A1

A2

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The Inverse-square cosine law

• E and Intensity can be related:

• The so-called "Inverse-square cosine law"

AE Φ

=

Intensity, I

Dξ Εp

ω=Φ I

2

I cos( )ED

ξ=

2

A cos( )D

ξω =

Fluence rate or “Spherical Irradiance”

• Instead of a surface in space, we think of an (infinitely small)sphere

• A sphere always presents the same cross-sectional area, regardless of orientation. That is, it always subtends the same solid angle to a point of regard.

• So, we drop the cosine term –which removes the attenuation due to orientation.

Intensity, I

D Εs

2D

IEspherical =

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• For predicting E at large distances, the five-times rule is usually satisfied

• Then:– Determine (θ,ψ) the direction from the source– Find intensity– Find distance– Find incidence angle

• The inverse-square cosine relationship is local– Source is very small compared to distance

• Extension of the inverse-square cosine relationship is by the calculus

Area sources

• Discretizing a luminaire:• Each piece produces it own I (θ,ψ) and has its own distance

and incidence angle

I1I2I3

I4

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Area Sources

• The total irradiance produced is the sum of that from each discrete piece:

• If the pieces are made vanishingly small, the calculus is used:

k k k2 2

k kk k

I cos( ) I cos( ) AED D A

ξ ξ Δ= =∑ ∑

2A

1 I cos( )E dAA D

ξ= ∫

A different approach

• Consider source as made of thin wedges• Apex of wedges are centered over the irradiated point

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Area source integration

• Each wedge can be specified by the two spherical coordinate angles, measured from the irradiated point.

• It is a relatively easy matter to calculate the irradiance produced by an arbitrary wedge

• Traveling around the boundary of the luminaire and summing the wedge irradiances (contour integration) gives a series of signed irradiances.

• Summing these irradiances gives us the total irradiance produced by the source.

• This is the technique that Visual uses for calculating direct irradiance at a point from an area source.

Area source integration

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Why this matters

Diffuse emitters

• A diffuse emitter has an intensity that varies only as the cosine of the emanation angle

θ

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Properties of diffuse emitters

• Idiffuse = I(θ,ψ) = I(θ)

• I(θ)=In cos(θ)

• In for a diffuse source is the largest Intensity– Perpendicular from surface– Related to how much flux leaves the surface

• In for a diffuse source is related to the total flux it emits:In = Φoff / π

Thinking of a surface as a source

• If the surface is diffusely reflecting then:

Φoff = E ⋅ ρ ⋅ A

In = Φoff / π

I(θ,ψ) = I(θ) = In cos(θ) = E ⋅ ρ ⋅ A ⋅ cos(θ) / π

θ

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Interreflection – The Form Factor

• Form Factor Fn→m is the fraction of fluxleaving An that gets to Am.

• Fn→m = Φnm / Φn

• Thus, it is always <= 1.0• Form factors are entirely

geometric – they do notdepend on reflectance oramount of flux.

Two surface interreflection

• Calculate the initial flux onto the 1st surface: Φ01

• Reflect this flux off the 1st surface: ρ1

• Determine how much of this gets to the 2nd surface (F1→2)• Reflect this flux, in turn, off the 2nd surface: ρ2

• Determine how much of this gets to the 1st surface (F2→1)• Add this to the initial flux• Repeat ad infinitum

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• Total flux on surface 1 after all interreflections:

( )( )( )( )

( )

Φ = Φ ρ ρ +

Φ ρ ρ +

Φ ρ ρ +

Φ ρ ρ +

Φ ρ ρ

M

01 01 1 2 12 21

101 1 2 12 21

201 1 2 12 21

301 1 2 12 21

n01 1 12 2 21

F F

F F

F F

F F

F F


Collect terms:

There are an infinite number of bounces, so:

The mathematicians tell us that this can be written as:

( )=

Φ = Φ ρ ρ∑n

k1 01 1 2 12 21

k 0F F

( )∞

=

Φ = Φ ρ ρ∑ k1 01 1 2 12 21

k 0F F

( )1 011 2 12 21

11 F F

Φ = Φ− ρ ρ

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If two surfaces receive initial flux:

Which simplifies to:

( ) ( )

( ) ( )

1 01 02 2 211 2 12 21 1 2 12 21

2 01 1 12 021 2 12 21 1 2 12 21

1 1 F1 F F 1 F F

1 1F1 F F 1 F F

Φ = Φ + Φ ρ− ρ ρ − ρ ρ

Φ = Φ ρ + Φ− ρ ρ − ρ ρ

( )

( )

01 02 2 211

1 2 12 21

01 1 12 022

1 2 12 21

F1 F F

F1 F F

Φ + Φ ρΦ =

− ρ ρ

Φ ρ + ΦΦ =

− ρ ρ


Divide by areas to convert to illuminances:

Which simplifies to:

( )

( )

01 1 02 2 2 1 2 211

1 1 2 12 21

2 01 1 1 2 1 12 02 2

2 1 2 12 21

A A A A FA 1 F F

A A A F AA 1 F F

Φ + Φ ρΦ=

− ρ ρ

Φ Φ ρ + Φ=

− ρ ρ

( )

( )

01 02 2 121

1 2 12 21

01 1 21 022

1 2 12 21

E E FE

1 F F

E F EE

1 F F

+ ρ=

− ρ ρ

ρ +=

− ρ ρ

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Interreflection between multiple surfaces

}E

E1 1 1 1 m 2 2 2 2 m 3 3 3 3 m N N N N m

m omm m m m

E A F E A F E A F E A FE E

A A A A→ → → →ρ ρ ρ ρ

= + + + + +

644444444444444474444444444444448

L

interreflecteddirect

Flux off A2 Fraction that gets to Am

Diving by the area of Am gives the E produced at Am by A2

The linear system

1 1 1 1 2 2 2 1 3 3 3 1 N N N 1

1 1 1 1

1 1 1 m 2 2 2 m 3 3 3 m N N N m

m m m m

1 1 1 N 2 2 2 N 3 3 3 N

N N N

A F A F A F A F

A A A A

A F A F A F A F

A A A A

A F A F A F

A A A

1 o1

m om

N oN

E E

E E

E E

→ → → →

→ → → →

→ → →

ρ ρ ρ ρ

ρ ρ ρ ρ

ρ ρ ρ

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥= +⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

L

M M M M M

L

M M M M M

L

M M

M M

M M

M M N N N N

N

A F

A

1

m

N

o

E

E

E

E E T E; T

→ρ

⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦

= +

M

M

M

M

r r t r twhere is the TRANSFER MATRIX of this system of surfaces

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Solving the matrix equation

( )( ) ( ) ( )

( )( )

o

o

o

1 1o

1o

1o

IE E T E

IE T E E

I T E E

I T I T E I T E

IE I T E

E I T E

− −

−

−

= +

− =

− =

− − = −

= −

= −

t r r t r

t r t r r

t t r r

t t t t r t t r

tr t t r

r t t r

The “Script-T” matrix

( )

( )( )

1o

o

1

E I T E

E E

I T

I T

−

−

= −

=

= −

−

r t t r

r t r

t t t

t t t

That is,

is the matrix inverse of the matrix

T

T

T

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The final solution

o

1 1 1 2 1 3 1 N 1 o1

m 1 m 2 m 3 m N m om

N 1 N 2 N 3 N N N oN

E E

E E

E E

E E

→ → → →

→ → → →

→ → → →

=

⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦

r t r

L

M M M M M M M

L

M M M M M M M

L

TT T T T

T T T T

T T T T

What can be expected, what can be counted on?

• Accuracy• Uncertainty

– Radiometric characteristics of surfaces– Radiometry of luminaires

• Representativeness• Applicability of far-field radiometry

• Verifying measurements– Uncertainty and calibration of equipment– Proper use– Real-life parameters

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An assessment of computer predictions

• CIBSE TM28/00• 6.72 x 6.78 m test room• 3 sets of 4 luminaires

– Bare CFLs, opal diffusers, semi-specular cones– Each luminaire was individually photometered– High-frequency power supply was closely monitored

• 2 sets of surface reflectances– 70/52/6 and 2.5/3.5/6

• 7 x 7 measurement grid– 7 illuminance meters mounted and levelled on trolley along X-axis– Trolley moved along Y-axis and bolted in position

• Horizontal illuminance only


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UVGI Validation

• Validate Visual’s irradiance predictions with measurements taken in Harvard’s test chamber as well as at the University of Colorado.

• Compare to field measurements at various locales as well.

• Waiting on radiometry of fixtures to be completed –sometime this fall?

But enough hand-waving, let’s do some layouts…

Design of Upper-Room UVGI Systems Computer …1 Design of Upper-Room UVGI Systems Computer Aided...

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Transcript of Design of Upper-Room UVGI Systems Computer …1 Design of Upper-Room UVGI Systems Computer Aided...