Thermal balance of a wall with PCM-enhanced thermal insulation

Transcription

1 Thermal balance of a wall with PCM-enhanced thermal inslation E. Kossecka Institte of Fndamental Technological esearch of the Polish Academy of Sciences, Warsaw, Poland J. Kośny Oak idge National aboratory; Bildings and Materials Grop, Oak idge, Tennessee, USA ABSTACT: PCM inslation mixtres fnction as lightweight thermal mass components. It is expected that these types of dynamic inslation systems will contribte to the objective of redcing energy se in bildings. In this paper, dynamic thermal properties of a material in which phase change occrs are analyzed, sing the temperatre-dependent specific heat model. Integral formla for the total heat flow in finite time interval, across the srface of a slab of the phase change material was derived. Simlations have been performed to analyze heat transfer throgh a light-weight wall assembly with PCM-enhanced inslation, in different external climate thermal conditions. eslts of simlations indicate that for cyclic processes, the effect of PCM in an inslation layer reslts in time shifting of the heat flx maxima and not in redction of the total heat flow. The heat gains maxima, reslting in high cooling loads, are shifted in time by abot two hors and redced p to % for not very high external sol-air temperatres. INTODUCTION esidential and commercial roofs and walls are crrently designed and tested sing steady-state criteria, with -vales based on the apparent thermal condctivity sed by bilding standards as an important measre of energy performance. Bilding envelope components, however, are sbject to dynamic environmental conditions. In an ON research team started working on fiber inslations blended with microencapslated PCMs (Phase Change Materials) [Kosny et al. 7a, b, 9a, b]. These PCM inslation mixtres fnction as lightweight thermal mass components. It is expected that these types of dynamic inslation systems will contribte to the objective of redcing energy se in bildings. This is a conseqence of this technology s ability to redce energy consmption for space conditioning and reshape peak-hor loads. Other anticipated advantages of PCMs inclde improvements towards occpant comfort, compatibility with traditional wood and steel framing technologies, and potential for application in retrofit projects. New PCM applications reqire carefl selection of materials, identification of PCM location, bonding thermal resistances, and specification of the amont of PCM to be sed. In this paper, dynamic thermal properties of a material in which phase change occrs are analyzed, sing the temperatre-dependent specific heat model. Theoretical considerations are illstrated with reslts of simlations, performed for a light-weight wall assembly with PCM-enhanced inslation, nder different external thermal excitations. MODE OF HEAT TANSFE IN THE PCM- ENHANCED INSUATION The heat storage capacity for a specific PCMenhanced prodct is a key indicator of its ftre dynamic thermal performance. A theoretical model of the material with temperatre-dependent specific heat can be sed to calclate phase change processes in most common materials [Heim & Clarke, Kissock & imas 6]. The one-dimensional heat transport eqation for sch a case is: T h t x x () where ρ and λ are the material density and thermal condctivity, T and h are temperatre and enthalpy per nit mass. Heat flx q is given by: T x, t qx, t () x 65

2 The enthalpy derivative over the temperatre (with consideration of constant pressre) represents the effective heat capacity, with phase change energy being one of the components: h ceff T. (3) T For most PCM materials, variations of enthalpy with temperatre depend to some extent on the direction of the process considered, and are different for melting and solidification. Therefore a model of the temperatre-dependent specific heat, represented by an niqe fnction of temperatre, is an approximation of a real material thermal capacitance. Figres and depict temperatre-dependent enthalpy differences and enthalpy crves for microencapslated PCM, generated dring differential scanning calorimeter testing. In this material, the melting takes place arond 7C and solidification arond 6oC. Total phase change enthalpy, H m, within temperatre interval [o, 9o] is kj/kg. ENTHAPY DIFFEENCE [J/gK] TEMPEATUE [ o C] melting solidification Figre Calorimetric data for the microencapslated PCM ENTHAPY [J/g] TEMPEATUE [ o C] melting solidification Figre Enthalpy crves for the microencapslated PCM Effective heat capacity, c eff, for a material which is a blend of inslation and PCM may be expressed as c c c, () eff ins effpcm where α denotes the percentage of PCM, c ins the specific heat of inslation withot PCM and c effpcm is effective heat capacity of PCM. In the liqid state, the effective heat capacity of PCM doesn t show temperatre dependence; it may be ths represented as the sm of two terms: c T c c T c, (5) effpcm l effpcm l where c l represents the temperatre independent specific heat in the liqid state. For a material to be sed as thermal inslation, thermal condctivity is the most important parameter, which determines its thermal performance in different thermal conditions. For celllose fiber inslation, linear dependence of condctivity on temperatre is to be observed (Kośny et al. 9a, : T T (6).3575;.3 Addition of microencapslated PCM does not reslt in a significant change in condctivity of the inslation. 3 THEMA BAANCE OF A WA WITH THE PCM-ENHANCED MATEIA Consider a plane wall of thickness, composed of layers of different materials, and assme that some of them are phase change materials. Bondary (linear) conditions at the internal (x = ), and external (x = ) srface of the wall have the form: q, t Ti t T, t (7) si q, t T, tte t (8) se where T i and T e are ambient temperatres and si, se, srface film resistances. Denote by i-x and x-e the resistances for heat transmission from the point x in the wall to the internal and external environment, respectively, and by the total resistance for heat transmission throgh the wall. With condctivity along the wall s thickness is represented by the fnction of λ(x), the resistances are given by: x dx i x si x (9) dx se () x x x e dx () x si se 66

3 On mltiplying Eq. () by the fnction x-e and integrating with respect to x over thickness of the wall we obtain the following formla: h T dx xe dx t x x xe x T T dx x x xe x se q e q T T () Temperatres T() and T() may be eliminated sing Eqs (7) and (8), which gives the following formla for the heat flx at internal srface: h xe q T i Te dx (3) t Analogos formla for q() is to be obtained on mltiplying Eqation () by i-x and integrating by parts. The effect of time variations of enthalpy h along thickness of the wall, on the heat flx across the srface x =, depends ths on the factor x-e /, which takes comparatively high vales, close to, in the vicinity of that srface and low vales, close to, in the vicinity of the opposite srface x =. This means that only time variations of enthalpy near the srface considered play an important role, whereas the effect of variations near the opposite srface may be small. Assme now that densities and condctivities are temperatre independent and ths constant in time. The last assmption shold be nderstood as an approximation; especially in the case of inslation materials (see Eq (6)). On performing now integration of Eq. (3) with respect to time, over the time interval [t, t ], and interchanging the integration order, one obtains: t,,, Q t t q t dt () t t t h Q t t T T dt dtdx t xe,, i e (5) t t Time integral in the second term represents the enthalpy difference Δh; it can be expressed as follows: t t,, eff, (6) t t T x, t T x, t h h T h x t t dt dt c x T dt t T t Integration of c eff (x,t) over temperatre can be condcted when the final temperatre distribtion in the slab is known. For particlar heat transfer processes, it is possible to determine the enthalpy difference Δh withot performing detailed simlations. Taking into accont Eq. (5), the total heat flow in time interval [t,t ] across the srface x = is given by: t Q, t, t Ti e tdt H s (7) t T t T t T t (8) ie i e xe H s t, t hx, t, t dx (9) ΔH s represents that part of the total enthalpy difference in a slab which is de to the heat flow across the srface x =. For cyclic processes, if time integration is over integral nmber of cycles, ΔH s =, and total heat flow depends on the mean ambient temperatre difference. TIME CONSTANT OF A PCM SAB Assme that the heat flx corse, q(t), across the nit srface area of the slab at the cold side, after a step fnction temperatre excitation at the opposite, hot side, as a fnction of time t may be approximately described as a simple relaxation process, with the time constant s : T t qt exp () s The total heat flow in time interval [, t] is given by: T t Qt t s exp () s For time t sfficiently long, as compared with s, the steady state of heat flow is attained, and Q(t) may be approximated by: T Qt t s () Comparison of (7) and () yields: H s s (3) T In earlier work of Kossecka and Kosny (8) a similar analysis was sed for estimating the time constants for conventional non-pcm assemblies, for prposes of the hot-box test measrements. However, in the case of a PCM specimen, the time constant is strongly dependent on its enthalpy difference within the temperatre interval taken into accont. Figre 3 depicts comparison of heat flxes across srfaces of inslation layer of thickness. m, with no PCM and 3% content of PCM, after the temperatre rapid jmp, from initial temperatre of oc to final temperatre of oc. (Inslation thermophysical properties as in Table, PCM enthalpy data as represented in Figre ). The time constant, τ s, estimated sing Eqs. (6), (9) and (3), was abot 56 min for pre inslation and 53 min for inslation with 3% PCM. 67

4 HEAT FUX [W/m ] % PCM 3% PCM Figre 3 Heat flxes across the srface of an inslation layer after temperatre jmp at the opposite srface 5 PEFOMANCE OF THE PCM-ENHANCED INSUATION IN DIFFEENT CIMATE CON- DITIONS Simlations have been carried ot to demonstrate the performance of a light-weight wall assembly with PCM-enhanced inslation in different external climate thermal conditions. The melting crve of Figre has been assmed as a model of the PCM effective heat capacity. Temperatre dependence of thermal condctivity was represented by Eq (6). Wall assembly similar to a typical cm (5.5 in) wood frame wall has been considered. Thermophysical properties of the wall s layers are listed in Table. Total resistance for heat transfer, inclding srface film resistances si =.3 m K/W and se =. m K/W, =. m K/W, and U-vale is. [W/m K]. PCM content of 3% in an inslation layer of thickness of. m and density of 33.6 kg/m 3 means abot. kg of PCM per sqare meter of a wall. Table Thermophysical properties of the wall s layers Material λ ρ c p m W/(m K kg/m 3 kj/(kg K ) ) Gypsm board Inslation Ins. 3% PCM c p (T) Plywood Wood siding One-dimensional heat transfer has been assmed and the effect of stds has been neglected. The idea was to analyse dynamic responses of a wall de to the external thermal excitation, T e, representing the dirnal temperatre swing and thermal peak, as one de to solar radiation incident on the external srface, dring the day-time. Internal temperatre, T i, has been set constant at the same time. In the linear model, when the heat flx de to solar radiation absorbed at the wall s srface, q s, is inclded, bondary condition (7) takes the form: q T Te qs T Tes () se Tes Te se qs (5) T es is the so called sol-air temperatre. With se =. m K/W, solar radiation flx of W/m increases T es by oc. The external (sol-air) temperatre profiles, assmed in simlations, were ths as follows. Dring night-time: t < 6 h or t > 8 h Tes Te A sin t 6 / Dring day-time: 6ºh t 8ºh Tes Te ( A A ) sin t 6 / o TEMPEATUE C] [ Ti Tes Tes Tes Figre Internal and external temperatre daily profiles (T i = 5oC) Two series of simlations have been performed for T i = oc, T e = oc and T i = 5oC, T e = oc, with amplitdes vales A = 5oC and A = oc, oc and 6oC, sbseqently. Simlation cycles have been repeated, to minimize the effect of initial conditions. To visalize dynamic effects, heat flxes for steady state, which represent the zero mass wall, were calclated, taking into accont dependence of inslation condctivity on temperatre. An accrate elementary soltion of the non-linear steady state heat transfer problem, in the case of linear dependence of condctivity on temperatre, may be obtained sing the Kirchoff transform method; see Kossecka (999). Figres 5 a,b,c represent comparison of dirnal heat flx profiles at internal srfaces of two walls; one containing plain fiber inslation layer, and another one containing 3% PCM enhanced inslation. The steady state heat flx profiles were added for comparison. se 68

5 HEAT FUX [W/m ] HEAT FUX [W/m ] % PCM 3% PCM steady state % PCM 3% PCM steady state HEAT FUX [W/m ] HEAT FUX [W/m ] % PCM 3% PCM steady state HEAT FUX [W/m ] - - % PCM 3% PCM steady state % PCM 3% PCM steady state Figre 5 a, b, c Comparison of the daily heat flx profiles at the internal srface of the wall containing. m thick inslation layer with % PCM and 3% PCM for T i = oc and A = oc(, oc( and 6oC( HEAT FUX [W/m ] % PCM 3% PCM steady state Figre 6 a, b, c Comparison of the daily heat flx profiles at the internal srface of the wall containing. m thick inslation layer with % PCM and 3% PCM for T i = 5oC and A = oc(, oc( and 6oC( Comparison of the plots and calclated daily heat flow vales indicates that for cyclic processes the effect of PCM in an inslation layer reslts in time shifting of the heat flx maxima and not in redction of the total heat flow. Heat losses corresponding to minimm external temperatres at midnight are shifted to morning time, at the same time large heat 69

6 gains from midday are shifted by abot two hors to the afternoon time. HEAT FUX [W/m ] HEAT FUX [W/m ] % PCM 3% PCM steady state % PCM 3% PCM steady state HEAT FUX [W/m ] HEAT FUX [W/m ] % PCM 3% PCM steady state % PCM 3% PCM steady state HEAT FUX [W/m ] HEAT FUX [W/m ] % PCM 3% PCM steady state % PCM 3% PCM steady state Figre 7 a, b, c Comparison of the daily heat flx profiles at the internal srface of the wall containing.3 m thick inslation layer with % PCM and 3% PCM for T i = oc and A = oc(, oc( and 6oC( Figre 8 a, b, c Comparison of the daily heat flx profiles at the internal srface of the wall containing.3 m thick inslation layer with % PCM and 3% PCM for T i = 5oC and A = oc(, oc( and 6oC( For T i = oc the heat gains maxima are redced by 8%, 8% and %, as external sol-air temperatre maxima increase from 5oC to 85oC, and for 7

7 T i = 5oC by 5%, 6% and 3% as those maxima increase from 5oC to 9oC. The effect of PCM in an inslation layer is ths positive, bt perhaps not as strong as one wold expect. An amont of the PCM in the inslation layer of abot. kg/m can not redce mch high negative heat flxes, reslting in cooling loads on the room space, for very high external sol-air temperatres. Simlations have been repeated for the wall containing the inslation layer of thickness.3 m. With PCM content of 3% and density of 33.6 kg/m 3 this means abot 3 kg of PCM per sqare meter of a wall. Figres 7 a,b,c represent, as before, comparison of dirnal heat flx profiles at internal srface of the wall, for different internal and external sol-air temperatre corses. edction of the heat gains maxima is now 8%, 5%, 5% for T i = oc, and 8%, 65%, % for T i = 5oC. CONCUSIONS eslts of simlations are consistent with reslts of theoretical considerations presented in section. Comparison of the plots and calclated daily heat flow vales indicates that for cyclic processes the effect of PCM in an inslation layer reslts in time shifting of the heat flx maxima and not in redction of the total heat flow. For inslation thickness of. m redction of the heat gains maxima, compared to plain celllose fiber inslation, is significant only when the external sol-air temperatre amplitde if not too high (p to 5oC); for very high external temperatre peaks its rather small. The sitation is mch better for very thick PCM enhanced inslation layer. In this case, redction of the heat gains maxima, compared to plain celllose fiber inslation, is abot 5% or more. Kosny J., Yarbrogh D., Miller W., Petrie T., Childs P., Syad A. 7b. Thermal Performance of PCM-Enhanced Bilding Envelope Systems, X Thermal Envelopes Conference. Kośny J., Yarbrogh D.W., Miller W.A., Wilkes K.E., ee E.S. 9a. Analysis of the dynamic thermal performance of fiberos inslations containing phase change materials, th International Conference on Thermal Energy Storage; Effstock 9 - Thermal Energy Storage for Energy Efficiency and Sstainability, Stockholm, Sweden. Kośny J., Yarbrogh D.W., Kossecka E. 9b. Use of a Heat- Flow Meter to Determine Active PCM Content in an Inslation. 3 th International Thermal Condctivity Conference, Pittsbrgh, PA USA. Kossecka E elationships between strctre factors, response factors and z-transfer fnction coefficients for mltilayer walls. ASHAE Transactions (),, Kossecka E Method of Averages to Determine Inslation Condctivity nder Transient Conditions, Jornal of Thermal Inslation and Bilding Science, Vol. 3, s Kossecka E. & Kośny J.. Inflence of inslation configration on heating and cooling loads in a continosly sed bilding, Energy & Bildings; Vol. 3, No., Kossecka E. & Kośny J. 8. Hot Box Testing of Bilding Envelope Assemblies; a Simplified Procedre for Estimation of Minimm Time of the Test; Jornal of Testing and Evalation, Vol. 36, Isse 3, 9. Kossecka E. & Kośny J. 9. Dynamic test method of PCM content in fiberos inslation [in Polish], XII Conference Bilding Physics in Theory and Practice, odz University, Poland. Zh N., Ma Z., Wang S. 9. Dynamic characteristics and energy performance of bildings sing phase change materials: A review. Energy Conversion and Management 5, EFEENCES Evers A.C., Medina M.A., Fang Y.. Evalation of the thermal performance of frame walls enhanced with paraffin and hydrated salt phase change materials sing a dynamic wall simlator, Bilding and Environment 5, Heim, D. & Clarke, J.A.. Nmerical modelling and thermal simlation of PCM-gypsm composites with ESP-r, Energy and Bilding, 36, Kissock K., imas S. 6. Dirnal load redction throgh phase-change bilding components. ASHAE Transactions (), Kosny J., Yarbrogh D, Petrie T.W., Syad A. 7a. Performance of Thermal Inslation Containing Microencapslated Phase Change Material, presented at 7 International Thermal Condctivity Conference. 7