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BURIED PIPE SYSTEMS WITH SENSIBLE AND LATENT HEAT EXCHANGE : VALIDATION OF NUMERICAL SIMULATION AGAINST ANALYTICAL SOLUTION AND LONG-TERM MONITORING

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Aepted for 9th Conferene of International Building erformane Simulation Assoiation August , Eole polytehnique de Montréal BURIED IE SYSTEMS WITH SENSIBLE AND LATENT HEAT EXCHANGE : VALIDATION OF
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Aepted for 9th Conferene of International Building erformane Simulation Assoiation August , Eole polytehnique de Montréal BURIED IE SYSTEMS WITH SENSIBLE AND LATENT HEAT EXCHANGE : VALIDATION OF NUMERICAL SIMULATION AGAINST ANALYTICAL SOLUTION AND LONG-TERM MONITORING ierre Hollmuller and Bernard Lahal Centre universite d étude des problèmes de l énergie (CUEE) Université de Genève, Switzerland ABSTRACT A finite differenes numerial model for buried pipe systems is presented, aounting for sensible as well as for latent heat exhanges, so as for fully three dimensional heat diffusion in soil and flexible border onditions. After desription of the algorithm, extensive validation against an analytial solution as well as against several long-term monitored real sale installations will be disussed. INTRODUCTION Laking better tools, most authors (Athienitis et al. 2; Bansal et al. 1983; Chen et al. 1983; Elmer and Shiller 1981; Levit et al. 1989; Rodriguez et al. 1988; Santamouris and Lefas 1986; Shiller 1982; Seroa da Motta and Young 198; Serres et al. 1997; Tiwari et al. 1993; Tzaferis et al. 1992) are dimensioning /soil heat exhangers by way of simple stati exhange models, simple to handle but for whih estimation of the fundamental parameters (/soil heat exhange oeffiient and effetive soil temperature) isn't evident at all, espeially in transient regime. As an alternative, some analytial models expliitly treat heat diffusion in the soil. One of them (Claesson and Dunand 1983) onerns periodi heat diffusion from a ylindrial pipe embedded in a semi-infinite medium (with onstant temperature at upper free surfae). The indued effet on the longitudinal temperature of the flow has been treated apart (Sawhney and Mahajan 1994), appropriate physial interpretation and operational presentation of the results unfortunately not being arried out. A similar problem inludes the interferene of neighboring pipes (Kabashnikov et al. 22) but onerns deeply buried pipes, without interferene of upper border onditions. As a last ase, a ylindrial model (Hollmuller 23) treats the ase of a pipe subjet to isothermal or adiabati boundary ondition at finite radial distane (limitation of available soil layer). Apart from yielding expliit understanding of the heat diffusion phenomenon (in terms of the natural temperature penetration depth) latter model also puts forward the theoretial possibility, under ertain onditions, to ompletely phase-shift the periodi input while barely dampening its amplitude, a phenomenon apparently unexploited up to now. Although they might give important insight in the physial heat exhange and storage phenomenon whih are at work, preeding analytial models are obviously limited to onstant flow rates and rather simple geometries and border onditions. As an alternative, several numerial simulation models based on finite differenes have also ontributed to haraterize diffusive heat exhangers. Some of them are limited to desription of one only typial pipe (Boji et al. 1997; Huber and Remund 1996; Mihalakakou et al. 1994). Other ones allow for the desription of several parallel running pipes, with or without possibility to treat more ompliated ases than steady flow rate, homogenous and laterally adiabati soils, or sole sensible heat exhange (Boulard et al. 1989; De aepe 22; Gauthier et al. 1997; Gygli and Fort 1994). However, when validation against monitoring is ever arried out, latter in all ases remains limited to a few hours or s and does generally not onern real sale installations, thereby not providing neessary proof of robustness one would expet. Corroboration against an analytial solution is furthermore never given, exept for the last one of these models and for the trivial ase of one-dimensional heat diffusion without flow. As a response to preeding state of the art, we will present a flexible, finite differenes numerial model, allowing for desription of sensible as well as latent heat exhanges. After desription of the algorithm, extensive validation against an analytial solution as well as against several long-term monitored real sale installations will be disussed. NUMERICAL MODEL The simulation tool developed here bases on a previously developed finite element model, whih already aounted for simultaneous sensible and latent heat exhange between and es, as well as fully tree dimensional heat diffusion in soil (Boulard et al. 1989). The original model has been ompletely revised, so as to allow for various geometries, soil properties and border onditions, as well as to inlude fritional losses, possible water infiltration and ontrol of flow diretion. With partiular are on flexible definition of in- and outputs, the model was adapted to TRNSYS, a modular environment for transient simulation of energy systems, allowing for links to other preexisting modules like buildings. z y Meteo Zone 2 (isothermal) Surf 3 Surf 1 Zone 1 (free floating) Buried pipe system (Type 26) Multizone building (Type 6) Surf 3 Meteo Tube Soil 1 Soil 2 Figure 1 : Shemati example of model geometry and TRNSYS-link to multizone building. diff soil onv e and water sbl diff lat diff onv flow saturated diff Figure 2 : Energy and mass transfer in a pipe node. Hypothesis Following hypothesis, options and onstraints have been adopted (Fig. 1 and 2) : So as to be flexible, the orthogonal meshing allows for variable node widths in all three dimensions. Cirular es are represented by way of equivalent square setions, lateral exhange surfae being omputed by way of an adequate orretive fator. Thermal heat diffusion is fully three dimensional. Soil harateristis may be inhomogeneous but are onstant in time. Border onditions, whih may be various on the same fae, are either adiabati or driven by a transient input. Latter an be defined in terms of temperature or heat load, with possibility to inlude an additional surfae resistane. As for most other model and oherent with analytial approah developed in parallel (Hollmuller 23), temperature and veloity are onsidered to be uniform within a pipe setion. Heat exhange with pipe is treated by means of an overall onvetive whih depends on veloity, but not on temperature. The thermal effet of the harge losses, omputed in funtion of a frition fator, the e surfae and the veloity, is evenly distributed along the es. Eventual singular harge losses have to be treated apart. Transient water infiltration, if any, ours on a predefined part of the es, where it adds to possible ondensed water. Algorithm The model s kernel bases on the energy and mass exhanges between the flow and the pipe (Fig. 2). They are omputed iteratively for eah pipe node, from inlet to outlet, and omprise : The sensible heat lost by the flow : sbl S h ( T T ) omputed for the lateral surfae, with a onvetive exhange oeffiient whih depends on the veloity : h h + h v v as a simplified but quite aurate form of more refined formulations in terms of Reynolds and randtl numbers, with typial values of 3 W/K.m 2 for h and 2. W/K.m 2 per m/s for h v (Hollmuller 22). The latent heat, determined by the Lewis analogy, whih atually onsiders former sensible heat to result from a onvetive exhange between the flow and a superfiial layer at pipe s temperature, the analogy implying following onvetive exhange rate : onv sbl ( T T ) Considering the layer to be saturated in humidity, this exhange also indues a water vapor exhange, whih is determined by the differene in humidity ratios of main flow and superfiial layer : m & lat ( W W ) onv where, aording to perfet gases : W W ( ) H rsat T Mwat r M 1% r ( T ) M r M sat wat When positive, this vapor transfer orresponds to ondensation, when negative to evaporation. In latter ase it is further limited by the free water ontent in the onsidered node, as well as by the maximum humidity (saturation pressure) whih an be absorbed by the flow. With these definitions, the assoiated latent heat finally writes as : lat lat lat The heat diffusion from the 4 lateral soil nodes and the 2 preeding and following pipe nodes : ( Tsoil, i, t 1 T ) + Siki ( T, i, t T ) diff Siki 1 soil e The saturation pressure being non-linear in terms of temperature, the value of T as well as preeding heat rates are being determined by iterative resolution of the energy balane : ( ) + + int sbl lat diff where the apaitive gains of the pipe and the free water are given by : ( m + m ) ( T T ) wat wat, t 1, t 1 int t The assoiated hydri balane on its turn allows to determine the new water ontent of the node : ( ) m m, 1 + inf t wat wat t lat Charge losses are taken in aount by way of a frition oeffiient f, for whih typial values are to be found on a Moody diagram (ASHRAE, Ch.2, 1989) : 2 l v fri f d 2 Finally, preeding energy and mass balanes yield the input onditions of the next pipe node : T, i W, i T W + fri sbl ( + vap W ) lat where omputation repeats in the same manner. After ompleting this alulation for all e nodes, omputation treats diffusion of heat into soil nodes, taking into aount user-speified border onditions. VALIDATION AGAINST AN ANALYTICAL MODEL First validation of the model as well as illustration of different onfigurations for preheating or ooling of buildings by way of suh systems onerns a unique pipe, embedded in a soil ylinder of finite radius and with perfetly adiabati border onditions (orresponding to one out of a multi-layer array of parallel running pipes, eah having a limited available soil layer, in absene of other border onditions), for whih a omplete analytial solution in periodi mode has been developed (Hollmuller 23). The simulated system is omposed of a pipe of 2 m diameter, a homogenous sandy and weakly saturated soil (ondution and apaity of 1.9 W/K.m and 1.9 MJ/K.m 3, yielding a 17 m penetration depth around the pipe for the daily temperature osillation, respetively a 3.2 m penetration depth for the annual osillation, see Hollmuller 23), and is subjet to a onstant 2 kg/h flow, with an hourly input as given by the standard annual meteorologial temperature for Geneva (Meteonorm 199). For the rest, simulation onerns a set of 3 different geometri onfigurations (Fig. 3) : A m pipe length and a 2 m soil radius, enabling annual heat diffusion to expand almost fully over its natural penetration depth, and annual amplitude thus to be dampened down (as is neessary for winter preheating of fresh ); A m pipe length and a.6 m soil radius, not enabling annual heat diffusion to expand over its natural penetration depth any more, so that only daily amplitude is being dampened down (as an be suffiient for summer ooling of buildings in Mid-European limates); A 4 m pipe length and a.6 m soil radius, whih doesn t dampen the annual osillation muh more than in previous ase, but allows its phase-shifting over some 6 months. Although suh a onfiguration remains quite theoretial (in partiular regarding the perfetly adiabati border ondition), it onstitutes yet another good test ase for ross validation of analytial and numerial model. In the ase of the numerial model, retangular meshing was hosen so as to yield equivalent ylindrial setions as the analytial problem (at pipe as well as soil level). It was laterally submitted to adiabati boundary ondition and longitudinally segmented in 1 m piees. In the ase of the analytial model, Fourier analysis of the input temperature into a omplete sum of harmonis (from yearly up to hourly frequeny) allows for diret reonstrution of the orresponding output. Despite the retangular approximation of the numerial model, an exellent orrespondene with the analytial approah is manifest (Fig. 3), with a mean bias in all ases below. K and a standard deviation below.2 K C soil radius : 2 m pipe length : m 2 2 numerial [ C] analytial [ C] C soil radius :.6 m pipe length : m 2 2 numerial [ C] analytial [ C] C soil radius :.6 m pipe length : 4 m 2 2 numerial [ C] analytial [ C] input min/max output min/max hourly values Figure 3 : Numerial simulation results for different onfigurations of single buried pipe with ylindrial heat diffusion and adiabati border onditions : daily minimum and maximum input and output values (left) and hourly omparison with analytial model (right). VALIDATION AGAINST IN-SITU MONITORED SYSTEMS reheating and ooling of in ontrolled ventilation : Shwerzenbaherhof building Loated near Zürih (CH), this buried pipe system is part of the Shwerzenbaherhof ommerial and administrative building (144 MJ/m 2 heating demand for 8 m2 heated surfae), seleted for the IEA Low Energy Cooling Subtask (Zimmermann and Andersson 1998). The system onsists of 43 pipes (2 m external diameter, 23 m length, 116 m mean axial distane, 9 m 2 total exhange surfae, inluding distribution and olletor pipes) running at 7 m beneath the seond basement of the building (~ 6 m beneath ground surfae). The system is used as well for winter preheating of fresh (12' m 3 /hr,.6 ah), in onjuntion with heat reovery on exhaust, as for summer ooling of building with slightly enhaned flow (18' m 3 /hr,.7 ah), in onjuntion with diret night ventilation. almost independent of water infiltration being turned on or off, although later ase best fits the annual balane (4% over-estimate on summer harge, 1% under-estimate on winter disharge). Latent heat exhanges, ompletely absent without water infiltration (no spontaneous ondensation and evaporation), are relatively well reprodued when later is turned on (14% under-estimate on summer evaporation, 22% over-estimate on winter evaporation). Note presented here, heat diffusion from the basement of the building (as roughly estimated by three loal temperature ouples and 7 m above the pipe array) is quite well reprodued when water infiltration is set to zero, but rises when later is turned on, so as to ompensate additional evaporation energy. Not so for heat diffusion to the deep ground, whih is quite independent of water infiltration and subsequent evaporation to be at work or not. Short term heat storage of exess solar gains in agriultural greenhouses : Geoser projet Realized in Sion (CH), the Geoser projet aimed at omparing three idential agriultural greenhouses submitted to a ommon agronomial program, of whih two were equipped with storage systems of the diurnal solar exesses : the first one in the soil, via a set of buried pipes, the seond one in a water tank, via aero-onvetors (Hollmuller et al. 22). With some hundred sensors, a very omplete monitoring ampaign over 17 months in minute steps (very nervous dynami of the greenhouses, due to small thermal apaity) allowed to haraterize the systems very preisely and to furnish omplete omparative energy balanes. Figure 4 : Shwerzenbaherhof building and buried pipe system. Extensive monitoring over a one year period, handed out by the Federal offie of energy, indiates evaporation all year around without any ondensation ever. ossibly due to some monitoring problem, latter evaporation ould also result from water infiltration into the pipes, as already observed on similar systems. In this ontext, omparison with two different simulation runs, with and without water infiltration (defined by the daily quantity of water apparently evaporated, evenly distributed over 24 hours), allows for some insight in the importane suh a phenomenon an have, as well as for further validation of the numerial model (Fig. 6) : Sensible heat exhanges are very well reprodued as well in hourly as in weekly dynami and are Figure : Geoser greenhouse with buried pipe system. The buried pipe system onsists of 24 VC pipes (16 m diameter, 11 m length, 33 m axial distane, 132 m 2 exhange surfae) running at 8 m below the greenhouse. A variable and reversible fan ( 6' m 3 /h) provides for diurnal storage as well as nightly disharge, in losed loop with the greenhouse. Again important latent exhanges are being observed, in this ase as well in the form of ondensation (during first hour of diurnal storage, when the flow is quite humid) as in the form of evaporation (during following diurnal hours or during nightly disharge). However, an important mass defiit again indiates that some kind of water infiltration has been at work (evaporation and water drainage at pipe being muh more important than assoiated ondensation). Latter learly seems to result from the automati fog system in the greenhouse, the fine water droplets possibly being swept into the pipes by the flow, hypothesis whih is ompatible with alulation on the time needed for suh droplets to evaporate (Hollmuller et al. 22). Comparison with numerial simulation, again with and without water infiltration (defined by the apparent monitored daily water defiit, evenly distributed over 24 hours), yields similar results as before (Fig. 7) : Sensible heat exhanges are very well reprodued, as well in hourly as in weekly dynami, and are almost independent of water infiltration being turned on or off. Later ase however fits the annual balane best (1% underestimate on annual harge, 3% under-estimate on annual disharge). Evaporation, almost inexistent without water infiltration, is very well reprodued when later is turned on (1% under-estimate on annual integral). Not so for ondensation however, whih remains way too low (91% under-estimate on annual integral). Heat diffusion to and from the greenhouse also is more important with than without water infiltration (ompensating for evaporation and ondensation energy), with annual integrals loser to the monitored data (orroborating the hypothesis of suh an infiltration atually to have been at work). CONCLUSION We developed a finite differenes numerial model for buried pipe systems, aounting for sensible as well as for latent heat exhanges, so as for fully three dimensional heat diffusion in soil and flexible border onditions. An extensive validation ampaign yields following results : Comparison with a omplete analytial solution in ylindrial symmetry, without latent exhanges, yields perfet reprodution of temperature outputs, for a variety of analyzed onfigurations. Comparison with two long-term in-situ monitored systems, both with important latent exhanges, yields very good reprodution of sensible as well as latent heat exhanges, provided the monitored water defiit is given as water infiltration. NOMENCLATURE Symbols orrespond to node and time step under onsideration, unless marked with i (neighbor node) or t-1 (preeding time step). lat J/kg latent heat of water J/K.kg speifi heat of vap J/K.kg speifi heat of vapor wat J/K.kg speifi heat of water J/K.kg speifi heat of e d m e diameter f frition fator h W/K.m 2 onvetive heat oeffiient H % relative humidity k W/K.m 2 ondutive heat oeffiient l m e length M kg/mol molar mass of M wat kg/mol molar mass of water m kg mass of e m wat kg mass of free water kg/s flow onv kg/s /e onvetive exhange &m inf kg/s water infiltration &m lat kg/s ondensation/evaporation diff W heat diffusion fri W fritional losses int W internal heat gain lat W latent heat exhange sbl W sensible heat exhange r a pressure of r sat a pressure of saturated S m 2 lateral node surfae S m 2 e surfae t s time step T C temperature of T soil C temperature of soil T C temperature of e v m/s veloity of W kg water / kg humidity ratio of W kg water / kg humidity ratio at e surfae Hourly dynami over one week (May 27 th June 2 nd ) disharge kw harge evaporation kw ondensation sensible / 28/ 29/ 3/ 31/ 1/6 2/6 3/6 1 latent / 28/ 29/ 3/ 31/ 1/6 2/6 3/6 Weekly dynami over one year (January Deember) disharge kwh harge evaporation kwh ondensation sensible w eek latent w eek monitoring simulation w ith infiltration simulation w ithout infiltration. Figure 6 : Shwerzenbaherhof, omparison of monitoring and numerial simulation. Hourly dynami over one week (May 6 th May 12 th ) disharge kw harge evaporation kw ondensation sensible 6/ 7/ 8/ 9/ 1/ 11/ 12/ 13/ latent 6/ 7/ 8/ 9/ 1/ 11/ 12/ 13/ Weekly dynami over one year (April Marh) disharge kwh harge evaporation kwh ondensation sensible w eek latent week monitoring simulation w ith infiltration s
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