INVESTIGATION OF THERMAL PROPERTIES OF SOIL BY IMPULSE METHOD Juraj Veselský

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1 THERMOPHYSICS 6 October 6 5 INVESTIGATION OF THERMAL PROPERTIES OF SOIL BY IMPULSE METHOD Jurj Veselský Fculty of Civil Engineering STU Brtislv, Rdlinského, 8 68 Brtislv Abstrct The therl properties of soils is needed to study in building industry in reltion to the het loss fro underground hot wter pipes, het loss fro building foundtions nd underground constructions nd reltion to the effect of frost on rod nd irfield pveents. In wide rnge of tepertures there is needed to study the therl properties of soils in reltion to ppliction of rtificil soil freezing technology. Moisture nd teperture re iportnt preters which effect soil therl properties. The trnsient ethod with the line ipulse het source ws used to esure the therl properties of the soil in dependence on teperture nd oisture. This ethod enbles to esure the therl diffusivity, the therl conductivity λ, s well s the voluetric het cpcity cρ. INTRODUCTION The overll het trnsfer in soils nd other porous terils is relized by three odes: conduction, convection nd rdition. It is very difficult to evlute unbiguously the contributions of prticulr echniss of het trnsfer. In ddition, het trnsfer depends lso upon the prticle nd pore size nd their rrngeent. Therefore het trnsfer in soils nd other porous terils is very often described only by het conduction. In this cse the therl properties contin lso contribution of other two het trnsfer echniss. Then such therl preters re designted s effective, for exple the effective therl conductivity. Different ethods re used to the therl properties of soils esureents, stedy- -stte nd qusi-stedy-stte or non-stedy-stte (trnsient ethods). Stedy-stte ethods re used reltively rre, becuse the ppliction of the teperture grdient for long period of tie restricts their ppliction for esureent of dry or frozen soils only. More often the trnsient ethods re used nd fro these the ethods with line het source ctuting in for of unit jup or ipulse. Needle probes in which is exploited ny fro entioned dynic ethods re used very often [e.g.,, ].. Principle of the esureent ethod EXPERIMENT The trnsient ethod with the line ipulse het source ws used to esure the therl properties of the soil in this study. The ethod enbles to esure the therl diffusivity, the therl conductivity λ, s well s the voluetric het cpcity cρ, where ρ is the bulk density nd c is specific het. In ddition, the ethod is possible to cobine with the qusi- -stedy-stte ethod in cylindricl rrngeent nd with the trnsient ethod, which use line step

2 THERMOPHYSICS 6 October 6 6 chnge het source [, 4]. The coprison of esureents by different ethod provided the stisfying greeent. The het ipulse in used esuring ethod is generted by pssing of n electricl current during n pproprite tie intervl t through the resistnce wire. At esureent we record the tie response of teperture t certin, properly selected, esuring point in sple on het ipulse of source. Fro point of view of evlution of esuring, the coordintes (t nd T ) of U l Trt (,) r Teperture t T I xiu of tie dependence of teperture re very iportnt. The teperture function, i.e. the function describing the teperture field in tested sple tht respond to ction of the liner het ipulse source under idel propgtion of het through the sple, hs for Q ( ) = r l T r, t T exp. Φ () 4π λt 4t 4 t where T is teperture in tie t t point of the sple (Fig. ), which is distnt r fro the het source, T initil teperture of the sple, Q het generted per length unit of the het source, λ coefficient of therl conductivity, therl diffusivity of the sple, l length of liner het source nd Φ ( x) error function. l When >, the vlue of Φ l nd teperture function () will be sipler 4 t 4 t Q ( ) r T r, t = exp + T 4π λt 4t () This function hs xiu (Fig. b). By solving eqution ( r, ) = therl diffusivity ) b) Tie Fig.. ) Principle of the ipulse ethod, b) The teperture response on the het ipulse. T t t we get reltion for

3 THERMOPHYSICS 6 October 6 7 nd for coefficient of therl conductivity where t is tie when teperture reches xiu vlue, i.e. T. The voluetric het cpcity cρ is deterined by the expression. Experientl pprtus r = () 4t Q λ =. (4) 4πe t T λ cρ = (5) The pprtus used to esure therl conductivity of soils is shown in Fig.. A sple of soil is plced in cylindricl continer de of durluin. The het source is situted in xis of the continer nd is fstened t either end. The heting wire running through the box is connected to COMPENSATOR PREAMPLIFIER THERMOCOUPLES DATA A/C UNIT HEAT SOURCE SAMPLE CONTAINER CONTROLLER CURRENT PULSE SOURCE Fig.. Schetic digr of the experientl pprtus. current pulse source tht het it. The therocouples tht scn the response on het ipulse re inserted in distnce r nd r fro the het source. The third therocouple scns teperture (T ) of the sple before ppliction of het ipulse. The therocouples re ttched to dt A/C unit. Chnge of sple teperture is chieved by inserting of sple continer to Dewr vessel with liquid nitrogen.. Experientl results nd discussion In this prt we present experientl dt, which we cquired by esureent of the therl preters of fine silic snd in rnge fro indoor teperture to teperture of boiling point of nitrogen (96 C) t different oisture.

4 THERMOPHYSICS 6 October 6 8 Therl conductivity. The experientl results of the therl conductivity λ re presented in Fig.. It is difficult to nlyze the teperture dependence of the effective therl conductivity of Therl conductivity (W.. K ) Moisture -, % - 9,9 % -,7 % -,4 % -, % Teperture ( C) Fig.. Therl conductivity vs. teperture for fine silic snd. snds nd other coposite terils. So, we will try to explin esured teperture dependence of the therl conductivity λ t lest qulittively. In dry stte the snd consists of solid nd gseous coponents. The contct therl resistnce the therl resistnce t contct of different coponents hs the gret effect on the therl conductivity. It is bigger, when there re ore different elstic properties of contcting coponents. For tht reson nd fro ide tht in the dry stte the solid prticles re rndoly distributed in continuous gseous ediu (ir), it is possible to ssue, tht tendency of the teperture dependence of λ of snd will be given by behviour of the teperture dependence of the therl conductivity of gs, i.e. with decresing teperture the therl conductivity of the snd will be lso decresing. When we will be grdully supplying ir by wter, the contct therl resistnce will be decresing. In ddition, wter which supply ir hs the therl conductivity higher then ir. Consequently the therl conductivity of the coposite teril will be grdully incresing up to vlue, which is deterined only by the therl conductivity of the solid nd liquid coponents. If gin we pply ide tht solid prticles re diffused in the continuous liquid coponent, behviour of teperture dependence of the therl conductivity of snd will be inly deterined by the teperture dependence of the therl conductivity of wter. The therl conductivity of snd bove teperture C will be incresing, if teperture will be incresing. This ide is experientlly confired in pper [5]. At tepertures below C wter is in solid stte, wht result in dditionl reduction of the contct therl resistnce nd, of course, lso in the chnge of the therl properties of the sturtion tter. In this cse we cn tret snd s non-idel crystl nd then its therl conductivity will be incresing nd showing pek t soe teperture if teperture will be decresing. Such vision bout behviour of the therl dependence of the therl conductivity well grees with the experientl dependence (Fig. ). Therl diffusivity. The experientl teperture dependence of the therl diffusivity (Fig. 4) shows t ll contents of wter, s well s for dry sple the increse in vlues with decresing teperture. This trend we cn explin by reltion

5 THERMOPHYSICS 6 October 6 9 Therl diffusivity (.s ) -6 4 Moisture -, % - 9,9 % -,7 % -,4 % -, % Teperture ( C) Fig. 4. Therl diffusivity vs. teperture for fine silic snd. - Voluetric het cpcity (J/. K ) Moisture -, % - 9,9 % -,7 % -,4 % -, % Teperture ( C) Fig. 5. Voluetric het cpcity vs. teperture for fine silic snd. = vf lf (6) Although snd is ulti-coponent teril, we cn predict tht verge speed of phonons v f is independent on teperture, nd tht the en free pth of phonons l f will be incresing consequently the wne of phonon-phonon scttering, when teperture will be decresing. In ddition, with growing content of wter the therl contct on the interfce of the coponents will be iproving nd so the growth of the therl diffusivity should be steeper with decresing teperture t the speciens with high content of wter. Voluetric het cpcity. The experientl teperture dependence of the voluetric het cpcity cρ (Fig. 5) is decresing with decresing teperture. Such dependence grees with

6 THERMOPHYSICS 6 October 6 predictions, which Debye`s theory of the het cpcity of solids provides. Debye`s teperture of the bsic eleent of snds, nely siliciu is T DSi = 65 K. The teperture intervl, in which we esured dependence, lies below this teperture nd so the specific het ust with decresing teperture decrese too. Therl conductivity dependence on content of wter. In next text our i will be focused on dependence therl conductivity of fine silic snd on content of wter. Coprison of our experientl therl conductivity λ dependence on degree of sturtion S of soil by wter with soe odels is shown in Fig. 6. Fro figure we cn see, tht the odels of prllel nd series rrngeent of coponents deterine the re of possible vlues of the effective therl conductivity of soil. The other cobin-tions of the "resistnce" odels provide the therl conductivity lying in this re. Fro two ore coplicted odels, the odel presented in pper [] better pproxites whole experientl depen-dence. We cn see tht none resistnce odel is not ble to explin s-profile of experientl dependence. Therefore we look for the other pos-sibility of experientl dt explntion. We proposed sei-epiricl odel, which will be described in following section. This odel hs soe initil ides s bridge odel used in work [5] but it is essentilly different in physicl inter-prettion. The odel is bsed on the following ides: How the content of wter in soil grdully growths, wter tht hs higher therl conductivity s ir, tred out ir fro pores nd supply it. The olecules of wter re bounded on surfce of the solid prticles nd crete wter lyer round the. When thickness H of wter lyer reches hlf of the chrcteristic size L of pore, the pore is copletely filled by wter. We predict tht the representtive pore sizes l re distributed ccording norl distribution lw. Next, the increse of the therl conductivity λ will be proportionl to probbility tht the pores, which hve representtive size L less s l re filled by wter nd resultnt therl conductivity we cn express s ( L < ) k.f ( l) Δλ = k.p = (7) l + Δλ = + k. F Fig. 6. Coprison of our experientl dt with soe odels: experientl dt ( ), siple odel of prllel pores (---), siple odel of series pores ( ), Woodside, Messer`s odel ( ) [], Chundhri, Bhndri`s odel ( ) [6]. ( l) λ = λ λ (8) where λ is therl conductivity of the dry sple of soil, k constnt of proportionlity, F () l = P( L < l) distributive function. Probbility P ( L < l) is equl probbility P ( H < h) tht thickness pprent wter lyer H < h = l. However the sickness of the wter lyer is proportionl to degree of sturtion S nd we cn write Therl conductivity (W..K ),,8,4,,4,6,8, Degree of sturtion ( - )

7 THERMOPHYSICS 6 October 6 F l h S = ( l) = F ( h) = F ( S) = f ( l) dl = f ( h) dh f ( S) ds where functions F i re the distributive functions nd functions f i re corresponding density functions of the norl distribution. The reltion (8) we cn rewrite s ( S) λ = λ + k.f () The constnt k we deterine by following wy: When degree of sturtion is equl to the rithetic en of degree of sturtion S (when the content of wter strt to hve n effect on therl conductivity) nd S b (when the content of wter in soil stop to hve significnt effect on λ ), thus S + Sb S = () P S < S = F S =,. When degree of sturtion hs vlue S, the therl conductivity is probbility ( ) ( ) 5 nd for k we hve ( S ) λ = λ + k.f () ( S ) (9) λ λ k = () F So s we could clculte the vlues of distribution function F ( S) for different S, we need to know stndrd devition σ tht we deterine in this nner: The therl conductivity λ t degree of sturtion S is where By substitution F S ( S ) = σ. π ( S ) λ = λ + k.f (4) z exp - ( S S ) σ the norl distribution trnsfors to stndrd norl distribution ds (5) S S = (6) σ or generlly for vrious S Φ z = (7) π ( z ) exp - dz z Φ z z = (8) π () z exp - dz

8 THERMOPHYSICS 6 October 6 The density function nd the distribution function of this distribution re in for of tbles or the stndrd progrs exist for their deterintion. Therl conductivity (W.. K ),,4,6,8, Degree of sturtion (-) Fig. 7. Coprison of experientl dt with clculted dt (continul lines) by sei-epiricl odel. Tble. No. S z ( z) λ F W. -.K,5,68,58,75,,74,95,48,5,467,477,457 4, -,7559,48,5 5,5 -,465,9,66 6, -,744,48,7 7,5,6,546,88 8,4,47,658,896 9,5,9885,885,,6,57,948,4,7,55,984,77,8,7,9968,87,,8959,,9 λ t = C Input preters =, W.. K λ =,8 W..K λ =,76 W..K λ b =,4 W..K S S S = 6, = = 6, b, Fro the reltion (4) we know vlue of distribution function F ( S ) to which we bind set stndrd vrible z nd by reltion (6) we clculte stndrd devition σ.

9 THERMOPHYSICS 6 October 6 Then the therl conductivity corresponding to degree of sturtion S we clculte ccording ter (). We clculte the vlue F ( S) by known stndrd vrible z, which we deterine fro reltion S S z =. (9) σ The vlues λ, λ, λ, λb, S, S, Sb re obtined fro experient. In this wy were fitted experientlly obtined dependencies of the therl conductivity of fine silic snd on degree of sturtion by wter t tepertures C, -5 C, C, 5 C nd 96 C. Grphicl output is in Fig. 7 nd the exple of clcultion results nd vlues of input preters for teperture C re in Tble. Picture confirs good greeent of clculted nd esured vlues. CONCLUSION Investigtion of the therl properties of soils nd other porous terils is still ctul proble not only fro interest of building prctice, but lso fro point of view better understnding of het trnsfer in these terils. A lot of odels of coposite terils, which re trying to explin het trnsfer through tht ones were creted. However, ll these odels re ore or less successful in soe liits only. The sei-epiricl odel proposed in this work very good fit experientl dt. However this odel, s follow fro its ne, tkes input preters fro experient. Tht is wekness of the odel. ACKNOWLEDGEMENT The uthors would like to thnk the Grnt Agency APVV (grnt No. 5 74) for funding this reserch. REFERENCES [] Woodside, W., Messer, J. H.: J. Appl. Phys., 96,, 688 [] Lncini, A. et l.: High Tepertures-High Pressures, ETPC Proceedings 99,, p. 5 [] Krepský, J.: Mernie terofyzikálnych veličín. Brtislv, VEDA SAV 969. [4] Kubičár, Ľ.: Pulse Method of Mesuring Bsic Therophysicl Preters, Aster-d, Elsevier Science 99. [5] Mtsuoto, J., Okubo, T.: Technology Reports Tohoku University 4, 978, p. 5 [6] Chundhri D. R., Bhndri R. C.: Brit. J. Appl. Phys. D 9, 968, p..

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