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Using Ratings Data to Predict Field Performance of Residential Water Heaters

Jay Burch National Renewable Energy Lab ARBI Water Heater Experts Meeting National Renewable Energy Laboratory September 28, 2012

2

Presentation Outline

• Field performance vs. rated energy factors – Reflects variances in use conditions vs. test conditions – Models needed to extrapolate from ratings data

• Simple performance models – Storage tank water heaters: paradigm – No model for tankless or HPWH taking existing data

• Future work – HPWH simple model – Validation of simple tankless and HPWH model

BA Hot Water Experts Meeting; 9/27/12; NREL

3

Water Heater Field Data

Daily Hot Water Energy Output [kBtu/day]

Daily

Eff

icie

ncy/

Ener

gy F

acto

r [-]

0 10 20 30 40 50 60 70 80 90 100

0

.1

.2

.3

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1

Test load

Field load


From: “Actual Savings and Performance of Natural Gas Tankless Water Heaters”, MN Center for Energy and Environment

Gas storage tank WH Non-condensing tankless WH Condensing tankless WH

All systems fall off at low loads

Test EFs

Storage tank WH varies the most

Tankless vary the least

Field EF mostly lower than rated EF

4

Is Discrepancy between EFfield vs. EFtest a Problem?

NO!! • Efficiency naturally varies with use conditions

– Rated EF holds only at rated conditions – Key factor: volume of draw – Other factors: Tmains, Tset, Tenv, usage profile – Does not generally indicate equipment degradation

• Need models to extrapolate from rating conditions • There can be real degradation in the field

– Storage: probably not significant (Navigant study; PGE result) – Tankless: Little data, but highly likely (scale on hx w/ hard H2O) – Heat pump: Likely, but little data (?)


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Water Heater Model Types: Three levels

2 or 3 Dimensional finite element – T,v fields as f(t) – Design of water heater – CFD: FLUENT,...

1 Dimensional finite difference – Includes stratification, run-out from heavy draw, use any heat sources – Accurate annual performance predictions – For storage tank water heaters and tankless: TRNSYS

Algebraic Models – One-node models, time-integrated energy balance – Quick and dirty annual performance prediction – Focus on only algebraic models for this presentation


Models predict performance for any set of use conditions

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Key Issue: Getting Model Input Parameters

Can one get key inputs from ratings test data? • Storage tank water heaters

– Key parameters inferable for simulation and algebraic models – Good simulation and algebraic models exist

• Tankless water heaters – One parameter inferable, others must be gotten elsewhere – No algebraic model exists

• Heat pump water heaters – No parameters inferable – No algebraic model exists

• Solar water heaters – No parameters inferable – Empirical algebraic model exists


7

Energy Factor Test Summary Useful ratings data (AHRI residential water heater directory)

• Storage tank water heaters (STWH)

– Energy Factor: EF » EF = Qout,test day/Qaux,test day

– Recovery Efficiency: RE » RE = Qout,1draw/Qaux,1draw-recovery » RE embodies conversion efficiency ηconv AND tank losses during draw » RE is NOT MEASURED for electric STWHs, REelec ≡ .98 by fiat

– Input power/capacity: Pin – MISSING outputs: measured UAtotal and measured volume (BooHoo)

• Tankless water heaters (TWH) – EF and Qdot,gas,max (RE, given but RE ≈ EF; mdot,max given but redundant)

• Heat pump water heaters (HPWH) – EF (RE given but meaningless)

• Test issues:

– 64.3 gal drawn @ Tset = 135 oF, Tmains,in = 57.5 F – 6 equal draws, one hour apart


Gas Storage Tank Water Heater Models


9 BA Hot Water Experts Meeting; 9/27/12; NREL

Schematic Gas Tank

Cold in Hot out P/T Valve

Gas Burner/pilot

Convection loop through flue to outside and back

Key inputs

UAflue Central flue

ηconv

Thermal shorts UAshorts

Insulated jacket UAskin

Other inputs

Capacitance Ctank Burner power Pburner

Sum = UAtotal

10 BA Hot Water Experts Meeting; 9/27/12; NREL

Gas Tank Model and Parameter Inference

1/UAtotal

Tenvirons

Tstore

1/mdotcp

Tmains

Ctank

Qdot,fuel

* ηconv

CdTtank/dt = ηconvPaux – UAt∆Tt-env – mdotcp∆Tout-in.

⇓

Key parameters Variables Dependent variables

UAt,gas = (RE/EF–1)/[∆Tt-env(∆tday/Qout,day–1/(PauxEF))] ηconv = RE + UAt,gas(∆Tt-env)/Paux

⇓ XXX = rating data

*

* see backup slides at end for derivation

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Algebraic storage tank models

1. Predict annual performance: QStWH,yr = [Qload + Qtank-losses]/ηconv = [Myrcp∆Tout-in + UAtotal(Tset – Tenv)]/ηconv

2. Calculate EFday:* EFday = Qload,day/Qfuel,day = ηconv [1/(1 + UAtotal∆Tset-env ∆tday/Mdaycp∆Tout-in )]

* see backup slides at end for derivation


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StWH Field Data vs. Model


Daily

Eff

icie

ncy/

Ener

gy F

acto

r [-]

0 10 20 30 40 50 60 70 80 90 100

0

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Test load

Field load


EFtest, storage tank TWH

Storage tank algebraic model

Storage tank WH data

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EFin-use vs. Qload,day, Model vs. Data

Data from “Actual Savings and Performance of Natural Gas Tankless Water Heaters”, MN Center for Energy and Environment

.6

Q draw [kBtu/day]

Ener

gy F

acto

r EF

day

Potential Tankless Water Heater Algebraic Models


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Gas Tankless Schematic (Rinnai)

Exhaust Fan Gas in

Combustion chamber

X

Control valve

X X

Heat Exchanger

3 burners

Exhaust

Hot out Cold in Adapted from the Rinnai users manual

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Gas Tankless One-node Thermal Model

TenvTin

TTWH

mcp.

CTWH

UA

η.Qgas,in

x

TenvTin

TTWH

mcp.mcp.

CTWHCTWH

UAUA

η.Qgas,in

x

Simplest possible model: one mass node (multi-node model gives better results)

= system variable

= parameter From: “Tankless Water Heater” Burch, J, and J. Thornton


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Input-Output Method: Possible Method

From: “Application of a Linear Input/ Output Model to Tankless Water Heaters” Butcher, Thomas A., Ben Schoenbauer

Major issue: Requires changing the current test method (simulated use test) to another method

Not clear how to handle wide variety of ∆tprevious


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Tankless Data and Models

Ratings data: EF, RE, Qdot,gas,max, mdot,draw,max Observe: EF ≈ RE ≈ ηconv Other parameters needed*: any two of τhx,decay, UA, C (τhx,decay = C/UA)

*use parameter tests on similar models; or calculate from unit’s description;...

Draw data needed: – ∆tbetween-draw , ∆tduration-draw, mdraw

Models: – 1-D Simulation models:

» TRNSYS one-node and multi-node

– Algebraic model: presently non-existent » Proposed: draw efficiency model » For in-use: analyze “average draws” in 3 bins (hot, warm, cold start)


.

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Analysis of a Draw (One-node model)

previous draw

draw to analyze

next draw

Time

TWH Temperature

decay

Tset

Tenv

TWH Gas Flow Rate

mgas,max .

decay

TTWH

mgas .

Waste: * Gas input during ramp-up * Qwaste = mgas,max*hng ∆tramp Useful hot water: * Only when T = Tset

ηdraw ≡ Qto-load@Tset/(Qto-load@Tset/ηconv + Qwaste) = ηconv/(1 + ηconv Qwaste/ Qto-load@Tset)

.

steady state

∆tprev ∆tramp ∆tdraw

Ramp-up


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Tankless WH Simple Algebraic Performance Model

• Input data Draw inputs: ∆tlast-draw, ∆tdraw, mdot-draw; Tmains, Tenv, Tset Tankless unit:

Ratings data: ηconv, mdot,fuel,max

Parameter test results, or hand estimates,...: UATWH, CTWH

• Derived data* τdecay, T@draw start, Qcharge, ∆tramp Draw efficiency: ηdraw = Quseful/Qinput,draw = ηconv{1/[1 + (ηconvQcharge)/Quseful]}


* see backup slides for derivations

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Data & Model Efficiency vs. Draw Volume, @ 5/45m Delays

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5 min

50 min

data);

data);

Simple model

Simple model

Data from DEG TWH lab report


45 min

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In-use Prediction: 3 Bins of ∆tlast-draw

• Each draw is 2 gallons • Three delays since last

draw: 5, 25, 480 min ⇒ ηdraw = 0.52, 0.61, 0.74

• Specified # of each delay vs. Qload,day

• EFday weighted by volume at each delay time


0

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30

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1 2 3 4 5 6 7 8 9 10 11 12

Num

ber o

f dra

ws

Qto-load, day [Btu]

Draw Start Temperatures vs. Qday

Hot

Warm

Cold

0.0

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Cold Warm Hot

Draw

Effic

ienc

y

Draw Efficency vs Start Temp

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Tankless Field Data vs. Model Da

ily E

ffic

ienc

y/En

ergy

Fac

tor [

-]

0 10 20 30 40 50 60 70 80 90 100

0

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Test load

Field load


EFtest, non-condensing TWH

Non-cond. TWH

0

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0 10000 20000 30000 40000 50000 60000

Simple ηdraw model


Future work

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Future Work

• Refine/validate tankless algebraic model – Assuming simulated use test input data (yields ηconv only)

• Develop algebraic model for heat pump WHs – Performance from heat pump performance maps, tank

volume, electric element locations, and element/heat pump control logic

• Develop user tool embodying: 1. Parameter extraction from ratings data 2. Algebraic models


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Thank you for your attention.

Questions?


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Backup Slides


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Basic Definitions

Energy factor (EF): EF = [Qout-to-load/Qfuel,in]∆t

where ∆t is integration period

– EFtest: sum Qs over 24 hour period of standard test

– EFfield: sum Qs over each day or over year


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Water Heater Field Data


Daily

Eff

icie

ncy/

Ener

gy F

acto

r [-]

0 10 20 30 40 50 60 70 80 90 100

0

.1

.2

.3

.4

.5

.6

.7

.8

.9

1

Test load

Field load


From: “Actual Savings and Performance of Natural Gas Tankless Water Heaters”, MN Center for Energy and Environment

Gas storage tank WH Non-condensing tankless WH Condensing tankless WH

Rated EFtest EFtest applies only at test loads!!! Don’t draw EFtest lines at varying loads X

X

X

29

Gas Tank Complications

Gas Burner: – Key, complex combustion process ⇒ ηconv must be measured

Pilot: – Assume ηpilot = ηconv (proven in one case) – Should include in simulation models

» increases overheating significantly for solar in hot climates

Central Flue: – Natural convection loop

» flue to outside, down/back into house, to flue – Complex: UAflue subsumed in UAtank with 1-D models

» Flue losses ~ 1/3 Total losses – Subsumed in UAtotal


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Deriving UAtank and ηconv as f(ratings data) for Gas Storage Tank Water Heater

Assume isothermal tank (one node) ⇒ • Write dynamic energy balance:

CdTtank/dt = ηconvPaux – UAt∆Tt-env – mdotcp∆Tout-in.

• Integrate over time ∆t (with Tt,end = Tt,start) ⇒ ηconvQaux,∆t = (M∆t cp∆Tout-in + UAt∆Tt-env∆t)

• Use balances in definitions of EF and RE: EF ≡ Qto-load/Qaux,∆t = M∆Tcp∆Tout-in/[(M∆t cp∆Tout-in + UAt∆Tt-env∆ttest)/ηconv

RE ≡ Qdraw/Qaux,recover = Qdraw/[Qdraw + (UAt∆Tt-env)Qdraw/Pfuel,in]/ηconv

• Solve for key parameters: UAtotal and ηconv UAt,gas = (RE/EF–1)/[∆Tt-env(∆tday/Qout,day–1/(PauxEF))] ηconv = RE + UAt,gas(∆Tt-env)/Paux


Reference: J. Burch, Using Ratings Data to Derive Simulation Model Inputs for Storage-tank Water Heaters, ASES Conf. 2004.

Danger: Math slide!

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EFday Derivation for gas storage tank WH

EFday = Qload,day/Qfuel,day = Qload,day/[(Qload,day + Qlosses,day )/ηconv]] = ηconv (1/(1 + Qlosses,day / Qload,day ) = ηconv [1/(1 + UAtotal∆Tset-env ∆tday/Mdaycp∆Tout-in )]

Danger: Math slide!

32

EFday Derivation for gas storage tank WH

EFday = Qload,day/Qfuel,day = Qload,day/[(Qload,day + Qlosses,day )/ηconv]] = ηconv (1/(1 + Qlosses,day / Qload,day ) = ηconv [1/(1 + UAtotal∆Tset-env ∆tday/Mdaycp∆Tout-in )]

Danger: Math slide!

33

Derivation of the Tankless Draw Efficiency Model

Assume Tuse = Tset (i.e., if Tout,TWH < Tset, “wasted H2O/Q”) This assumption makes derivation simple, but can be relaxed

Given: Tankless: ηconv, UA, C, τdecay (= C/UA) Draw statistics: ∆tlast-draw, ∆tdraw, mdot,draw

Temperatures: Tmains, Tset, Tenv

Basis of the model: Solution of the one-node energy balance (exponential)

Do both during decay, charge ramp, and stead state


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Derivation of the Tankless Draw Efficiency Model, cont.

1. Calculate T@start of draw Tstart = Tenv + (Tset – Tenv)e-∆t_lastdraw/τ_decay

2. Calculate ∆tcharge Calc T∞ = (ηconvQdot,gas,max + mdot,drawcpTmains + UATenv )/D, where D = mdot,drawcp + UA ∆tcharge = -τdecayln[(Tset – T∞)/(Tstart – T∞)]

3. Calculate Qwaste Qwaste = mdot,draw∆tcharge

4. Calculate useful Qdraw Qdraw = mdot,drawcp(Tset – Tmains), Mdraw = mdot,draw ∆tdraw

5. Calculate draw efficiency: ηdraw = Qdraw/(Qdraw + Qwaste/ηconv) = ηconv[1/(1 = ηconvQwaste/Qdraw)


Danger: Math slide!

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Using Ratings Data to Predict Field Performance of ...apps1.eere.energy.gov/buildings/publications/pdfs/building_america/... · Using Ratings Data to Predict Field Performance of