Papers by Vlodek Tarnawski
International Journal of Thermophysics
The paper reveals the experimental procedure and thermo-physical characteristics of a coarse pyro... more The paper reveals the experimental procedure and thermo-physical characteristics of a coarse pyroclastic soil (Pozzolana), from the neighborhoods of Rome, Italy. The tested samples are comprised of 70.7 % sand, 25.9 % silt, and 3.4 % clay. Their mineral composition contained 38 % pyroxene, 33 % analcime, 20 % leucite, 6 % illite/muscovite, 3 % magnetite, and no quartz content was noted. The effective thermal conductivity of minerals was assessed to be about $$2.14\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}$$2.14W·m-1·K-1. A transient thermal probe method was applied to measure the thermal conductivity ($$\lambda $$λ) over a full range of the degree of saturation $$(S_{\mathrm{r}})$$(Sr), at two porosities (n) of 0.44 and 0.50, and at room temperature of about $$25\,^{\circ }\hbox {C}$$25∘C. The $$\lambda $$λ data obtained were consistent between tests and showed an increasing trend with increasing $$S_{\mathrm{r}}$$Sr and decreasing n. At full saturation ($$S_{\mathrm{r}}=1$$Sr=1), a nearly quintuple $$\lambda $$λ increase was observed with respect to full dryness ($$S_{\mathrm{r}}=0$$Sr=0). In general, the measured data closely followed the natural trend of $$\lambda $$λ versus $$S_{\mathrm{r}}$$Sr exhibited by published data at room temperature for other unsaturated soils and sands. The measured $$\lambda $$λ data had an average root-mean-squared error (RMSE) of $$0.007\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}$$0.007W·m-1·K-1 and $$0.008\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}$$0.008W·m-1·K-1 for n of 0.50 and 0.44, respectively, as well as an average relative standard deviation of the mean at the 95 % confidence level $$(\hbox {RSDM}_{0.95})$$(RSDM0.95) of 2.21 % and 2.72 % for n of 0.50 and 0.44, respectively.
International Journal of Thermophysics, 2016
An advanced geometric mean model for predicting the effective thermal conductivity ($$\lambda $$λ... more An advanced geometric mean model for predicting the effective thermal conductivity ($$\lambda $$λ) of unsaturated soils has been developed and successfully verified against an experimental $$\lambda $$λ database consisting of 40 Canadian soils, 15 American soils, 10 Chinese soils, four Japanese soils, three standard sands, and one pyroclasticsoil (Pozzolana) from Italy (a total of 667 experimental $$\lambda $$λ entries). Three soil structure-based parameters were used in the model, namely an inter-particle thermal contact resistance factor ($$\alpha $$α), the degree of saturation of a miniscule pore space $$(s_{\mathrm{r}})$$(sr), and the bulk thermal conductivity of soil solids $$(\lambda _{\mathrm{s}})$$(λs). The $$\alpha $$α factor strongly depended on the ratio of $$\lambda _{\mathrm{s}}$$λs to $$\lambda _{\mathrm{f}}$$λf (where $$\lambda _{\mathrm{f}}$$λf is the thermal conductivity of interfacial fluid) and an inter-particle contact coefficient ($$\varepsilon $$ε) whose value was obtained by reverse modeling of experimental $$\lambda $$λ data of 40 Canadian soils; the average values of $$\varepsilon $$ε varied between 0.988 and 0.994 for coarse and fine soils, respectively. In general, $$\varepsilon $$ε depends on soil compaction, soil specific surface area, and grain size distribution. The use of $$\alpha $$α was essential for close $$\lambda $$λ estimates of experimental data at a low range of degree of saturation $$(S_{\mathrm{r}})$$(Sr). For $$\lambda _{\mathrm{s}}$$λs estimates obtained from measured $$\lambda $$λ at soil saturation or a complete soil mineral composition data or experimental quartz content, 69 % of $$\lambda $$λ predictions were less than $$0.08\, \hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$0.08W·m-1·K-1, 15 % were between $$0.08\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$0.08W·m-1·K-1 and $$0.13\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$0.13W·m-1·K-1, and 13 % were between $$0.13\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$0.13W·m-1·K-1 and $$0.24\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$0.24W·m-1·K-1 with respect to experimental data $$(\lambda _{\mathrm{exp}})$$(λexp). The model gives close $$\lambda $$λ estimates with an average root-mean-square error (RMSE) of $$0.051\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$0.051W·m-1·K-1 for 22 Canadian fine soils and an average RMSE of $$0.092\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$0.092W·m-1·K-1 for 18 Canadian coarse soils. In general, better $$\lambda $$λ estimates were obtained for soils containing less content of quartz. Overall, the model estimates were good for all soils at dry state ($$\hbox {RMSE} = 0.050\, \hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$RMSE=0.050W·m-1·K-1; 22 % of the average $$\lambda _{\mathrm{exp}}$$λexp), saturated state ($$\hbox {RMSE} = 0.090\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$RMSE=0.090W·m-1·K-1; 5 % of the average $$\lambda _{\mathrm{exp}}$$λexp), soil field capacity ($$\hbox {RMSE} = 0.105\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$RMSE=0.105W·m-1·K-1; 9 % of the average $$\lambda _{\mathrm{exp}}$$λexp), and satisfactory near a critical degree of saturation, $$S_{\mathrm{r-cr}}$$Sr-cr ($$\hbox {RMSE} = 0.162\,\hbox {W} {\cdot } \hbox {m}^{-1} {\cdot } \hbox {K}^{-1}$$RMSE=0.162W·m-1·K-1; 26 % of the average $$\lambda _{\mathrm{exp}}$$λexp).
Encyclopedia of Earth Sciences Series, 2011
Journal of Plant Nutrition and Soil Science, 2004
ABSTRACT Eight pedotransfer functions (PTF) originally calibrated to soil data are used for evalu... more ABSTRACT Eight pedotransfer functions (PTF) originally calibrated to soil data are used for evaluation of hydraulic properties of soils and deeper sediments. Only PTFs are considered which had shown good results in previous investigations. Two data sets were used for this purpose: a data set of measured pressure heads vs. water contents of 347 soil horizons (802 measured pairs) from Bavaria (Southern Germany) and a data set of 39 undisturbed samples of tertiary sediments from deeper ground (down to 100 m depth) in the molasse basin north of the Alps, containing 840 measured water contents vs, pressure head and unsaturated hydraulic conductivity. A statistical analysis of the PTFs shows that their performance is quite similar with respect to predicting soil water contents. Less satisfactory results were obtained when the PTFs were applied to prediction of water content of sediments from deeper ground. The predicted unsaturated hydraulic conductivities show about the same uncertainty as for soils in a previous study. Systematic deviations of predicted values indicate that an adaptation of the PTFs to the specific conditions of deeper ground should be possible in order to improve predictions.
International Journal of Thermophysics, 2009
A comprehensive thermal conductivity (λ) database of three dry standard sands (Ottawa C-109, Otta... more A comprehensive thermal conductivity (λ) database of three dry standard sands (Ottawa C-109, Ottawa C-190, and Toyoura) was developed using a transient line heat source technique. The database contains λ data representing a variety of soil compactions and temperatures (T) ranging from 25 • C to 70 • C. The tested standard sands, due to their repeatable physical characteristics, can be used as reference materials for validation of thermal probes applied to similar dry granular materials. The measured data show an increasing trend of thermal conductivity at dryness (λ dry) against T in spite of declining quartz λ with T. The air content (porosity) controls the λ of dry sands by acting as a very effective thermal insulator around solid soil particles. As a result, a diminutive increase of λ dry with T is driven by increasing λ of air. The experimental λ data of dry sands were exceptionally well predicted by de Vries and Woodside-Messmer models, and also by a thermal conductance model, a product of λ of solids and the thermal conductance factor.
International Journal of Thermophysics, 2012
ABSTRACT The effective thermal conductivity of unsaturated soils was estimated by an enhanced ser... more ABSTRACT The effective thermal conductivity of unsaturated soils was estimated by an enhanced series-parallel model of conduction heat flow through a unit cell of soil. The cell is composed of three heat flow paths: solid contacts, solids + miniscule pores (filled with air and water, both parallel to heat flow direction), and a fluid path (water and air). The two basic characteristics of the soil cell, namely, the solid contact path volume fraction and the miniscule pore volume fraction, were estimated by simultaneously solving the model expressions at dryness and saturation with known measured thermal-conductivity data at these two states. In addition, the model utilized data on the thermal conductivity of soil solids and the degree of saturation of miniscule pores. The degree of saturation of miniscule pores was modeled as a function of the degree of saturation of the soil with a miniscule pore water retention factor. Water and air, in the fluid path, were modeled as being arranged in series or in parallel to the direction of heat flow. The model was calibrated using experimental thermal-conductivity data of five soils of different texture (coarse, medium, and fine). Then, empirical relations for all the model parameters were developed. The obtained thermal conductivity estimates of tested soils closely follow experimental data.
International Journal of Thermophysics, 2011
A non-stationary thermal probe technique was used to measure the thermal conductivity of three sa... more A non-stationary thermal probe technique was used to measure the thermal conductivity of three saturated standard sands (Ottawa sand C-109, Ottawa sand C-190, and Toyoura sand) in a range of soil porosities (n) from 0.32 to 0.42, and temperatures (T) from 25 • C to 70 • C. The sand thermal conductivities at full saturation (λ sat) increased with decreasing n (increasing compaction, 1 − n). In addition, a declining λ sat (T) n=const trend was observed. The peak λ sat values and highest decreasing rate of λ sat with T were observed at the heaviest compaction and lowest tested T. This trend gradually diminished with increasing T and expanding volume of water (larger n) due to the markedly lower ability of water to conduct heat than quartz. A series-parallel model, containing three parallel paths of heat flow (through continuous solids, continuous fluid, and solids plus fluid in series), was successfully applied to predicted λ dry and λ sat data. The model by de Vries, with new fitted grain shape values, also closely followed measured λ sat data. The corresponding square root of the relative mean squared errors varied from 2.9 % to 3.4 % for C-109, from 1.9 % to 3.0 % for C-190, and from 2.3 % to 2.4 % for Toyoura sand. The use of a weighted geometric mean model also provided good λ sat estimates with errors ranging from 3.1 % to 3.5 % for C-109 and C-190 and 8.3 % for Toyoura sand. This paper also discusses a successful attempt to model λ sat as a product of thermal conductivity of the solid fraction (quartz plus other minerals) and a thermal conductance factor of water.
International Journal of Refrigeration, 2005
Thermal conductivity models of frozen soils were analyzed and compared with similar models develo... more Thermal conductivity models of frozen soils were analyzed and compared with similar models developed for frozen foods. In total, eight thermal conductivity models and 54 model versions were tested against experimental data of 13 meat products in the temperature range from 0 to K40 8C. The model by deVries, with waterCice (wi) as the continuous phase, showed overall the best predictions. The use of wi leads generally to improved predictions in comparison to ice; water as the continuous phase is beneficial only to deVries model, mostly from K1 to K20 8C; fat is advantageous only to meats with high fat content. The results of this work suggest that the more sophisticated way of estimating the thermal conductivity for a disperse phase in the deVries model might be more appropriate than the use of basic multi-phase models (geometric mean, parallel, and series). Overall, relatively small differences in predictions were observed between the best model versions by deVries, Levy, Mascheroni, Maxwell or Gori as applied to frozen meats with low content of fat. These differences could also be generated by uncertainty in meat composition, temperature dependence of thermal conductivity of ice, measurement errors, and limitation of predictive models.
European Journal of Soil Science, 2021
Heat Pumps for Energy Efficiency and Environmental Progress, 1993
The measured mineral composition data (XRD/XRF) of 40 Canadian soils were modeled for the presenc... more The measured mineral composition data (XRD/XRF) of 40 Canadian soils were modeled for the presence of quartz as a function of soil texture. Preliminary mod-eling revealed a lack of strict correlation between quartz content and mass fraction of sand. For that reason, the occurrence of quartz content was modeled as dependent on a combined fraction of sand and silt, which produced an improved correlation for all tested soils. Then, all soils were modeled separately for five assigned provinces/regions of Canada and strong correlations of quartz versus combined sand and silt fractions were obtained. Estimates of quartz content and an average thermal conductivity of other minerals were also obtained by the reverse analysis of the weighted geometric mean model applied to the experimental thermal conductivity data of saturated soils. In general, quartz estimates followed XRD/XRF data sufficiently well. The thermal conductivity of the remaining soil minerals was about 2.13 W · m −1 · K −1 on average and did not depend on the soil texture.
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Papers by Vlodek Tarnawski