A Case Study of a Replica Roman Bath

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Energy andBuildings63 (2013) 5966

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Energy and Buildings

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A computational investigation ofa room heated by subcutaneousconvectionA case study ofa replica Roman bath

Taylor Oetelaara,, CliftonJohnston a,b, David Wood a, Lisa Hughes c,John Humphreyc

a Department of Mechanical andManufacturing Engineering, Universityof Calgary, 2500UniversityDr NW, Calgary, AB,Canada T2N1N4b Department ofMechanical Engineering, DalhousieUniversity, 5269 MorrisStreet, Halifax, NS, CanadaB3H4R2c Department of Greek andRoman Studies, University of Calgary, 2500 University Dr NW, Calgary, AB,CanadaT2N 1N4

a r t i c l e i n f o

Article history:Received 1 May2012

Received in revised form 25March 2013

Accepted 26March 2013

Keywords:

Floor heating

Wall heating

Thermal comfort

Computational fluid dynamics

Romanbaths

a b s t r a c t

Floor and wall subcutaneous convective heating is a common and efficient supplementary system ofheating, ventilation, and air conditioning (HVAC) but the concept dates back nearly 2500 years to when

ancient Greeks and Romans used it towarm their bathing facilities. This paper explores the thermal envi-

ronment ofa replica Roman bath resulting from purely subcutaneous convective heating by modelling

the bath using computational fluid dynamics (CFD). Previous studies examining the interior ofbaths have

used either heat fluxes or lumped-mass thermodynamics, but neither approach possesses the detail of

CFD. Theaverage temperature in the 3m4mroommodelled is 35 C;however, the hottest air is trapped

in the high vault leaving the region inhabited by the patrons significantly cooler than the average. The

results also show that stratification is prominent and that the open doorway connecting to the next room

heavily influences the room temperature. The results also suggest a relative insensitivity to changes in

the convective heat transfer coefficient and addition ofhumidity to the model. Furthermore, this study

notonly provides further knowledge about an alternative HVAC system but enhances our understanding

ofancient Roman baths. In addition, it offers an insight to a unique thermal environment on the basis of

multi-phase and species modelling.

2013 Elsevier B.V. All rights reserved.

1. Introduction

Most modern HVAC systems rely on forced air to bring infresh air and heat or cool homes and buildings [1]. There hasbeen a move recently towards the use of in-floor radiant slab

heating to aid the standard HVAC forced air systems [1]. Whilethe use of in-floor heating is often seen as a modern advance-ment, the premise actually dates back nearly twenty-five hundredyears. The ancient Roman Empire made extensive use of subcu-

taneous convective floor heating in their public and private baths[2]. The premise behind the Roman heating system, known as thehypocaust (Fig. 1a), was simple but extremely effective. A fire in

a furnace (praefurnia) creates hot exhaust gases which circulatebetween the foundation floor and a suspended floor (suspensura)and upbox tubes (tubuli) inlaidin thewalls. The exhaust gasesgiveoff heat to the room before escaping to the atmosphere throughflues. Ourwork uses CFDto analyze the thermal environment, set-

tingasideairquality issues, ofa roomheatedusingonlya hypocaust

Corresponding author.

E-mail addresses: [email protected](T. Oetelaar),

[email protected] (C. Johnston), [email protected] (D.Wood),

[email protected] (L. Hughes), [email protected] (J. Humphrey).

system.The case study is thehotbathroomor caldariumofa replica

of an ancient Roman bath built for the PBS television series NOVAbya teamledbyYegl andCouch [3] locatedoutsideSardis,Turkey.TheCFDpackagethatweusedwas FLUENT6.3/ANSYSFLUENT13.0.BycomparisonwithmostRomanbaths, thebuildingis relatively

small (Fig. 1b), measuring 7.6m long by 6.4m wide by 2.8m highto the base of the vaulting, and has three rooms. The roomof inter-est, known as the caldarium, or hot bath room, is in the southwestcorner of the building. Its floor area is 2.84m by 3.02m and the

air volume is just over 42m3. The east wall has an open doorwaywhich connects to the next room called the tepidarium or roomwithwarmbathsandhasa clothdoor. The southwallhasan alcove

for a hot pool. The north,west, and eastwalls have the tubuli up tojust below the springing of the vault; these, in combination withthefloor, supplytheheat forthe room.Finally, thereare threesmallwindows, totalling 2m2, above the tubuli in the westwall.

2. Literature

The applicationofCFDto analyzebuildingsis rare because of the

long simulation time often required. The majority of analyses areconducted using building simulation. Most CFDmodels are of sin-glerooms, such as offices[48], or generic rooms [911] to analyzethermalcomfort,whichis a significantaspectofHVACdesign. There

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60 T. Oetelaar et al. / Energy and Buildings 63 (2013) 5966

Fig. 1. (a)Diagram of thehypocaust heating system. (b)Digital model of theNOVA

baths fromthe southwest looking northeast.

are some important exceptions. Some studies investigated ther-mal patterns and/or airquality issues in large open spaces [1218].Baloccos analysis [19] of the Salone dei Duecento di Palazzo Vec-chio (Hall of the Two Hundred of the Old Palace) in Florence

modelled the interior environment to help with tapestry preser-vation. Ayata andYildiz [20] proposed a newway of incorporatingnatural ventilation for buildings in Turkey through optimal place-ment ofwindows in the facade. Stavrakakis [21] demonstrated the

impact of cross-ventilation on thermal comfort by simulating asmall buildingwithtwodoors.While thesestudiesfocusedonmod-ernHVACsystemsand environments,theyall arepredicated ontheuse of, at least in part, forced air to control temperature. Our case

study predates, technologically-speaking, the advent of electricity

and,as such,the thermalenvironmentwillnecessarily bedifferent.In terms of bathing complexes, the useof numericalmethods is

veryuncommonandBasaranhas ledthe studies that haveused this

approach. In the first, Basaran and Ilken [22] did not use CFD butrather numerical heat transfer to investigate the heating systemof the Small Baths at Phaselis in Turkey. Their simulations sug-gested a number of key conclusions, including: (1) the bath only

had limited use in the winter; (2) the input heat was less than theheat lost; (3) the fuel requiredwasmassive. In thesecond, Basaranet al. [23] then used CFD to analyze the heating system of a bathhouse inMetropolis andfound that the hypocaustdesignwas inef-

ficient and the fuel requirements were substantial. The third andfinal [24], is, in essence, a summary of the first two andagain reit-erates the inefficiency of the heating system and high fuel costs.

There are, however, a number of analytical studies. Thatcher [25]

performed a very detailed sun study of the Terme del Foro at Ostiaand determined that it would have been possible to comfortably

bathe nude in the open rooms without glass in the windows. Ring[26], using thermodynamics, concluded that it was not feasible torely ontheheatfromthe sunand the hypocaustto reachanaccept-able temperature without the use of glazing. Jorio [27] provides

detailed information about the hypocausts of the Pompeian baths(Stabian, Forum, and Central) and then analyzed the heat lossesfrom four rooms (themens andwomens caldaria and tepidaria) inthe Stabian Baths. Rook [28] utilized thermodynamic equations to

estimate the fuel consumedby theWelwyn Romanbath as 13kg/hor 114 tonnes/yr. Yegl and Couch [3] also took measurements ofvarious parameterswhen they rantheirreplicamany ofwhichweused in our simulationsand performed a heat loss analysis. All of

these studies, though, deal in heat fluxes or average temperatures,which do not provide as detailed an analysis as CFD. CFD has theability to show how the temperature is distributed and the loca-tions of any drafts and hot spots that could dramatically affect our

understanding and interpretation ofcaldaria andhow people usedthem.

3. Methodology

3.1. Grid

We chose to start with an unstructured mesh combining tetra-hedral and hexahedral elements since the air volume is quitecomplex in shape. The initial mesh was 1,976,183 cells with no

cells above 80% skewness, meaning all cells were close to theirideal shape. This mesh was used to do preliminary set up, includ-ing contrasting turbulence models, density models and temporaldependency. A structured mesh was developed prior to includ-

ing the effects of theheated pool. To ensure continuity, the resultsfroma structuredmeshwithout the poolwere comparedwith theresults fromtheunstructuredmesh. After establishingcongruencybetween the results from thetwomesh types,weperformeda grid

refinement testwithdifferent cell sizes (100mm,50mm, 37.5mm,and 25mm with a corresponding change in the total number ofcells). We found that grid independencewas attained at a cell sizeof 37.5mm, with minor fluctuations near the window. Therefore,

thefinalstructuredmeshused 37.5mm cellswith 10mmcellsnearthewindowand had990,143 cells without the pool and1,164,501cells with the pool.

3.2. Sub-models

In this simulation there are five important sub-models: time-dependency, density, turbulence, multi-phase, and species. Thefirst run was done as steady-statebut subsequent runs were time-

dependent because this stabilized the multi-phase calculations.

The effect of time dependency appeared to be dramatic becausethe direction of the air velocity near the doorway to the tepidar-ium reversed when themodel was changed. Further investigation

revealed this as an anomaly for the reasons described below.Three density modelswere compared: the Boussinesq approx-

imation, the incompressible ideal gas law, and ideal gas law. Theresults of theBoussinesq approximationprovedverydependenton

thereference temperature. If thereference temperaturewasbelowthe bulk temperatures of the room the flow patterns in the roomvaried drastically from those of the two other models. Therefore,we rejected the Boussinesq approximation was rejected because

of this sensitivity to reference temperature. Therewere no differ-encesin any parameter betweenthe results of the twogas laws.Wechose the incompressible ideal gas law because it did not require

additional pressure calculations, which can slow the simulation.


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T. Oetelaar et al. / Energyand Buildings 63 (2013) 5966 61

Table 1

Theboundary conditions forthe wall sections.

Property Glazing External wall Heated floor Heated wall Connecting wall

Type Mixed Mixed Convective Convective Convective

Material Glass Custom Custom Custom Custom

Thickness (m) 0.005 0.40 0.20 0.06 0.40

Convectiveheat transfer coefficient (W/m2 K) 4 4 7 7 4

Free stream temperature (K) 288 288 363 363 300

External emissivity 0.49 0.94

External radiation temperature (K) 0 323

Four turbulence models were tested: RNG k, SST kT, andthose twowithviscousheating.(In thesedesignations,k represents

the turbulent kinetic energy, is the turbulent dissipation rate,

is the specific dissipation rate, RNGindicatesa renormalized grouptheory modification, and SST stands for shear stress transport. Formoreinformation, refer toWilcox [29].)We comparedresultswith

and without viscous heating for both turbulence models and theeffect of viscous heatingprovednegligible. Thedifference betweenthe RNG k-, and SST kTwas relatively small with the SST kTpro-ducingslightlywarmerresults (within 3 C) in theoccupied region

(the lower 2m of the roomheight). The results of Yegl and Couch[3] agreedwith the predictedwarmer temperature.As a result, we

adopted the SST kTmodel, however, either model was suitable.Only the implicit volume of fluid (VOF) and the Transport &

Reactionmodelswereapplicable formulti-phase andspecies sim-ulation, respectively.All othermulti-phase andspecies modelsdid

notmeetour requirements.However,the difficultpartis modellingthe evaporation of the water from the pool to the air. We used auser-defined function (UDF)to accomplish this. The UDF first iden-tifies the interfacebetween the two phases where the evaporation

Fig. 2. (a) The temperature distribution in thex-mid-planefor Case#1 (units: C).(b) Thetemperature distributionin thez-mid-planefor Case#1 (units: C). (c)The velocity

vectors in thex-mid-plane for Case #1 (units: m/s). (d)The velocity vectors in thez-mid-plane for Case #1 (units: m/s).


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Table 2

Casebreakdown.

Case Time-dependency Turbulence Multi-phase Species Heated wall CHTC (W/m2 K) Radiation model

#1 Base Unsteady SST k N/A N/A 2 N/A

#2 Unsteady SST k VOF S&T 2 N/A

#3 Unsteady SST k VOF S&T 7 N/A

#4 Unsteady SST k VOF S&T 7 S2S

is taking place through an area function and then calculates themass transfer rate on this interface. We also tested the effect ofincluding FLUENTs surface-to-surface (S2S) radiationmodel.

3.3. Boundary conditions

In this simulation there are a numberof key zones: the exteriorwalls, thewindowglass,the heated floor, the heatedwalls,thewall

connecting to the tepidarium, the doorway to the tepidarium, thewater inlet to the pool, the water outlet, and the walls that do nothave thermal significance (i.e., the door jamb).We gave the zones

withno thermalsignificance a zeroheat flux(insulating)condition.The conditions for the remaining walls are summarized in Table 1.Forthewall connected to the tepidarium themost suitable is the

convective boundary condition. This is because the heat transfer

is due to the natural convection of the air in the tepidarium andthe fact there is no separate radiation heat source. Once this typehas been selected, the next question concerns the convective heattransfer coefficient (CHTC). Since the wall is relatively large it can

be assumed to behave similarly to a vertical plate, on which thebehaviourof theCHTC iswell-known[30]. Fora verticalplateundernormalroomconditions, a good first estimate is 4W/m2 K [31]. Theemissivity for theglass came from a FLUENT tutorial [31] on HVAC

Fig. 3. (a) The temperaturedistribution in thex-mid-plane forthe Case #2 (units: C).(b) Thetemperaturedistributionin thez-mid-plane forthe Case #2 (units: C). (c) The

velocity vectors in thex-mid-plane forthe Case #2 (units: m/s). (d) Thevelocity vectors in thez-mid-plane forthe Case #2 (units: m/s).


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testing and we retrieved the emissivity for the external wall fromthe entry for rough concrete on the Engineering Toolbox website

[32].The heated wallspose an interesting problem. The most appro-

priate boundary condition is a convective one since that is theprinciplebehindthedesignhot air rising frombelow thesub-floor

and outthechimneys. The temperatureof thefreestreamis notdif-ficultto estimateas YeglandCouchgivevarious readings of theairinside the system [3]. The question then is what the CHTC shouldbe. For preliminary computer runs a value of 2W/m2 K was used

as the flueswere confined spaceswhich might indicate lower val-ues than normal. However, for thepenultimate simulation a moreaccurate assessment was necessary. The best way of determiningthis value was through experimentation. Based on these results

[33], the CHTC was set to 7W/m2 K. The free stream temperaturescame from the data in Ref. [3] and the external radiation tempera-ture came from Ref. [31]. We used themaximum recordedfluegastemperature for the heated surfaces.

The water inlets and outlets are uncomplicated. The watercomes in at 313K and an arbitrary low velocity of 0.1m/s andthe backflow temperature of the outlet is 312K. This is a commontemperature formany hot tub tests [34].

4. Results and discussion

There are three important cases to demonstrate the progres-sion of the simulation and are designated in Table 2. Displayingmeaningful results from a 3-D model is somewhat difficult as onecan only take flat slices or use iso-surfaces. For economy, only two

slices were chosen to display the temperature distributions andvelocity vectors: the mid-planes of both the x- and z-directions.These slices were chosen because they capture themajor featuresof the NOVA baththe hypocausted walls, the hypocausted floor,

thewindows, thepool,andthedoorwayto theadjoiningroomandthey represent the three Cartesiandirections.The temperature distribution and velocity vector profile of the

Case #1 are shown in Fig. 2ad. Overall, the temperature rangesfrom 27 C to 38 C and the velocity magnitudes are low withmost of the room being largely stagnant. The first thing that isimmediately apparent upon closer inspection of the temperaturedistributions is how, without a fan to stir the air, buoyancy drives

the movement as the stratification is pronounced. From a comfortperspective, however, this stratification has a drawback. It meansthattheregionoccupiedbythepatrons (i.e.,thevolumeof airbelowthe height of the door or 1.88m) is only between 30C and 35 C,

whichis only slightlywarmer than thetepidarium, which isawarmroom. Therefore,whilethe average temperature of theroommightbe30C,much of the heat from the hypocaust is lost to the vault.The other significant factorseen fromboth the temperatureand

velocity vector profiles is the impact of the doorway. The cooler

air from the tepidarium does not fully enter the room and thus ithas a limited effect on the overall temperature. The flow patternis unique and almost counter-intuitive because it is coming in the

topandleaving thebottom. Movingaway from the doorway, thereis a thin film of warm air above the floor and next to the heatedwalls showing the effect of these surfaces. The pool stand-in doesnot appear to havemuch impacton the overall temperaturedistri-

bution but there is a draft coming off the surface which indicatesthat it is perturbing the flow.With the addition of humidity and the pool the flow pattern

changes dramatically as seen in Fig. 3ad. It all, however, stems

from the reversal of the doorway flow. In Case #1, the air from thetepidarium came in from the topand exited out the bottomtherebylimiting the effect of its cooler nature. In Case #2, though, the air

entersat thebottomandexitsat thetop,whichmeansthecooler air

Fig. 4. The water vapour distribution in the z-mid-plane for the Case #2 (units:

kg/kg).

comes intothe roomfurther.This flowreversalcompletely changes

the environment within the room. The entire room is colder, par-ticularly the occupied region, and the velocities are higher in theroom. This pattern though ismore likelythan the onefromCase #1because of the more accurate modelling. The heating system has

the same effect: it creates an updraft and a layer of warm air nextto the walls.There are two new smaller drafts in Case#2. One fromthe win-

dows, which is due to an adjustment in the solar load calculator.Inadvertently, Case #1 did not include a feature that spread thesolar heating to adjacent cells. Without this feature enabled, thesolar heat would create unrealistic hot spots. We corrected thisoversight in Case #2. Themore significant draft is theone originat-

ingfromthe pool. InCase #1, thestand-in forthepool didnot affectthe flow regime greatly, but the addition of the water warmed thealcove by 10C and impeded the flow of cool air from the tepidar-ium.However,the temperatureeffectsof thepool remainslocalized

to thealcove, further showing the influence of the doorway.The humidity profile in Fig. 4 illustrates the effect of the pool

well. There is a definite stream of water vapour rising from thewater/air interface with the vapour culminating at the apex of the

alcove vault before dispersing into the room. The humidity itself

does not have a noticeable effect on the room temperature. Thisis not surprising since the room is dominated by the tepidariumdoor boundary condition which means most of the room is at the

tepidarium humidity.The only change with Case #3 was that the convective heat

transfer coefficient (CHTC)of the heated wallswas raised from theearly estimate of 2W/m2 K to the experimentally derived value

of 7W/m2 K [33]. The results (Fig. 5ad) illustrate the resultingchanges. A comparison ofFigs. 3b and 5b illustrates an increasein temperature along the heated wall from the 3035 C to the3540 C, indicating that the increased CHTC is generating more

heat. There is a similar trend with the z-mid-plane temperaturedistribution (Fig 5b). The cooling effect of the air coming in fromthe tepidarium is significantly reduced. These changes result in

the roombeing generally warmerwiththe experimentally derived


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Fig. 5. (a)The temperature distribution in thex-mid-planefor Case#3 (units: C). (b)The temperature distributionin thez-mid-planefor Case#3 (units: C). (c)The velocity


CHTC. However, the temperature has not increased significantlyin proportion to the increase in the CHTC. The value of the CHTCincreased 350% but the volume-averaged temperature in the room

onlyincreased 2 C (32.834.8 C),whichis less than sevenpercent.This suggests thatwhilethe CHTCof the heatedwalls isa drives thesimulation the temperature distribution in the room is relativelyinsensitive to changes in CHTC. In fact, the heat from the heated

wallsonly increasesbybetween139% and189%with an average of168% as seen in Table 3.

Part of this decreased response to CHTC is possibly due to theinsulating nature of the wall material. Because of its lower ther-mal conductivity, a ceramic wall such as this requiresmore heat to

make a set temperature increase than a metallic or modern com-positewall. This could be by design as a safety feature, but ismorelikelyaninherentbenefitof thematerialsavailabletoRomans.With90 C exhaust gases only 6 cm from the surface of the wall, some-

one leaning against it could be seriously burnedwithout this typeof wall.

Table 3

Comparison of heat fluxes calculatedby FLUENT.

Zone Case#2 input heat (W) Case #3 input heat (W) % I ncrease#2 to#3 Case#4 inputh eat (W) % Increase #3 to#4

Tubuli next to doorway 51.1 96.6 189.0 151.9 157.2

North Tubuli 460.7 787.4 170.9 1032.5 131.1

NE Tubuli 149.9 253.6 169.2 313.9 123.8

SE Tubuli 170.7 283.3 166.0 392.4 138.5

W Tubuli 535.6 934.0 174.4 1172.4 125.5

Top ofTubuli 70.2 97.6 139.0 195.2 200.0

Average 168.1 146.0


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Fig. 6. Thewatervapourdistribution in thez-mid-plane forCase #3 (units: kg/kg).

The velocity vector profiles are very similar. The velocities inCase #3 are slightly lower than the other cases. However, this is

only a marginal change. The main currents are almost identical inthe twocases.The water vapour (Fig. 6) reaches a higher concentration in the

corner of the alcove above the pool in the humidity distribution in

Case#3. It does not reach as far into the main room. This change isdue to the minor alteration in the air current above the pool.The addition of the radiation model in Case #4 (Fig. 7ad) does

notaffect theresultssignificantly, especially in theoccupiedregion.

The average temperatureby volumeonly differs by approximately0.1 C (34.8 C for Case#3versus34.7C for Case#4). The flow pat-terns are similar with the only important change at the top of thevault where the temperature breaches the next temperature con-

tour.Also, Table3 shows that the change in heat fluxes is less thanbetween Cases #2 and #3. It is also interesting to note that thelargest increase inheat flux came fromthe top of the tubuli; that is,above where the people are. The major zones only rose an average

of 30% and, while substantial, this, again, did not affect the over-all temperature of the room. Based on these data, we believe thatthechange resulting from additionof radiationmodel isnegligible.However, given the increase in heat flux, there might be a percep-

tual change in the thermal environment (i.e., itmight feel warmer)

but this is beyond the scope of the paper.Case #3 appears to compare well to the data from Yegl and

Couch [3]. The average temperatureof the caldarium given is 35C

Fig. 7. (a) The temperature distribution in thex-mid-planefor Case#4 (units: C).(b) Thetemperature distributionin thez-mid-planefor Case#4 (units: C). (c)The velocity



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and the volume-averaged temperature from the computationalmodel is 34.8C. However, one potential limitation of our simu-

lation is thatweused the maximum temperatureYegul and Couchlistedfor theexhaust gases.We feel that this is necessitated byourconsiderationof thedoorway to the tepidarium. We havemodelledthe door as anoutletwitha constant temperatureof 27C based on

the tepidarium temperature reported by Yegl and Couch. In actu-ality, the temperatureacross the length of the tworoomswill varysincethereis nowallseparatingthem.Theexchangebetweenthesetwo rooms shouldbe gradual. In fact, Yegl statesthat hedesigned

the baths so that the caldarium would heat, at least partially, thetepidarium. Nonetheless these three case studies still illustrate theeffectiveness of the heating system as well as the impact, or lackthere of, of the addition of humidity.

5. Conclusions

In this study, we have modelled a room heated by a subcuta-neous convective heating system rather than the modern mixing

of air through a simulation of a room inside a modern replica ofan ancient Roman bath built for the television series NOVA. With-out theconstant influx of new air thoughventilation, stratificationbecomes prominent and any opening in the envelope of the room

becomes extremely important to the air circulation patterns. Inthis case, the doorway to the tepidarium cools the occupied regionconsiderably which negates the heating system. The differencebetween a wall with the same thermal properties as water and a

simulated pool is remarkable. The pool hada much greater impacton the flow by creating a draft of warmer air. Interestingly, how-ever, the CHTC of the heated walls and floor has little impact onthe overall temperature. The volume-averaged temperature rose

by 2 C even thoughthe CHTC increasedby threehundred and fiftypercent from 2W/m2 K to 7W/m2 K. Finally, this study providesa methodological starting point for future CFD studies on Romanbaths. As the first application of CFD to the interior of a Roman

bath, we have shown that CFD can highlight previously untestedaspects.Heat fluxanalysesandlumped-mass thermodynamics, the

previous approaches, for example, do not take into account thestratification due to buoyancy which has a tremendous impact

on the thermal environment of the room. This methodology maystimulate different perspectives in terms of architectural or socialstudies.

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