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The various concepts involved in the mathematical modeling of the fluid–solid interactions (FSIs) of catalytic combustion processes occurring within a porous burner are presented and discussed in this paper. The following aspects of them are addressed: (a) the relevant physical and chemical phenomena appearing at the interface between the gas and the catalytic surface; (b) a comparison of mathematical models; (c) a proposal of a hybrid two/three-field model, (d) an estimation of the interphase transfer coefficients; (e) a discussion of the proper constitutive equations and the closure relations; and (f) a generalization of the Terzaghi concept of stresses. Selected examples of application of the models are then presented and described. Finally, a numerical verification example is presented and discussed to demonstrate the application of the proposed model.

This paper presents an improvement in the Huber–Mises–Hencky (HMH) material effort hypothesis proposed by Burzyński. Unlike the HMH hypothesis, it differentiates the plastic effort between compression and tensile load states, and links shear with tensile limit. Furthermore, it considers the fact that construction materials do not have infinite resistance in the pure tensile hydrostatic load state, which was proved by the static load experiment performed on St12T heat-resistant steel. The asymmetry between tensile and compressive loads is captured by the elastic region asymmetry coefficient ϰ, which was established by experiment for St12T steel in the temperature range between 20 °C and 800 °C.

The cooling technology of hot turbine components has been a subject of continuous improvement for decades. In high-pressure turbine blades, the regions most affected by the excessive corrosion are the leading and trailing edges. In addition, high Kt regions at the hot gas path are exposed to cracking due to the low and high cycle fatigue failure modes. Especially in the case of a nozzle guide vane, the ability to predict thermally driven loads is crucial to assess its life and robustness. The difficulties in measuring thermal properties in hot conditions considerably limit the number of experimental results available in the literature. One of the most popular test cases is a NASA C3X vane, but coolant temperature is not explicitly revealed in the test report. As a result of that, numerous scientific works validated against that vane are potentially inconsistent. To address that ambiguity, the presented work was performed on a fully structural and a very fine mesh assuming room inlet temperature on every cooling channel. Special attention was paid to the options of the k−ω SST (shear-stress transport) viscosity model, such as Viscous heating (VH), Curvature correction (CC), Production Kato-Launder (KT), and Production limiter (PL). The strongest impact was from the Viscous heating, as it increases local vane temperature by as much as 40 deg. The significance of turbulent Prandtl number impact was also investigated. The default option used in the commercial CFD code is set to 0.85. Presented study modifies that value using equations proposed by Wassel/Catton and Kays/Crawford. Additionally, the comparison between four, two, and one-equation viscosity models was performed.

In the classical approaches, used in Central Europe in practice, cutting forces and cutting power in sawing processes of timber are commonly computed by means of the specific cutting resistance kc. It needs to be highlighted that accessible sources in handbooks and the scientific literature do not provide any data about wood provenance, nor about cutting conditions, in which cutting resistance has been empirically determined. In the analyses of sawing processes, the use of a model with elements of fracture mechanics involved is an alternative way. In this work, predictions of the newly developed model (FRAC_MOD) for the circular sawing machine are presented. Thanks to this modern approach, it was possible to reveal the usefulness of the FRAC_MOD, using experimental results data on fracture toughness and shear yield stresses of both Polish pine (Pinus sylvestris L.) and Czech beech wood (Fagus sylvatica L.). The achieved results were compared to the forecasted values obtained with classical models (CLAS_PL and CLAS_CZ), which are commonly applied in Central European sawmills. The carried out analyses allowed us to discover undesired effects in the form of underestimation of cutting power when applying the CLAS_PL and CLAS_CZ models. For that reason, the FRAC_MOD cutting model could be suggested for the prediction of energetic effects in cases of dynamical analyses and even unsteady cases.

Wood drying is an important stage in the woodworking process. After drying, wood is subject to a re-sawing process, for which a high quality surface, low material loss, and high efficiency are often required. In this paper, forecasted values were presented of cutting power for the re-sawing process of pine and beech wood that were dried with four different methods. Forecasting of cutting power for an industrial band saw machine that works daily in a Polish sawmill was determined. Values of cutting power were forecasted for a full range of feed speeds of the analyzed band saw machine. The achieved results allowed the observation of noticeable changes in the forecasted cutting power for a given sawing process as a function of the wood drying method applied. Significant changes were observed for pine wood, especially between air-dried pine wood and wood dried with warm air-steam mixture, and between pine wood dried in a conventional kiln and with warm air-steam mixture.

The modern wood converting processes consists of several stages and material drying belongs to the most influencing future performances of products. The procedure of drying wood is usually realized between subsequent sawing operations, affecting significantly cutting conditions and general properties of material. An alternative methodology for determination of mechanical properties (fracture toughness and shear yield stress) based on cutting process analysis is presented here. Two wood species (pine and beech) representing soft and hard woods were investigated with respect to four diverse drying methods used in industry. Fracture toughness and shear yield stress were determined directly from the cutting power signal that was recorded while frame sawing. An original procedure for compensation of the wood density variation is proposed to generalize mechanical properties of wood and allow direct comparison between species and drying methods. Noticeable differences of fracture toughness and shear yield stress values were found among all drying techniques and for both species, but only for beech wood the differences were statistically significant. These observations provide a new highlight on the understanding of the effect of thermo-hydro modification of wood on mechanical performance of structures. It can be also highly useful to optimize woodworking machines by properly adjusting cutting power requirements.

The cutting force is an energetic effect of splitting material, and might be considered from a point of view of modern fracture mechanics. Forecasting of the shear plane angle in cutting broaden possibilities for modelling of the cutting process even for thin uncut chips. Such mathematical model has been developed here for description of the orthotropic materials' cutting on the base of fracture theory, and includes work of separation (fracture toughness) in addition to the material plasticity and friction. The original methodology of simultane- ous determination of the fracture toughness and the shear yield strength on the basis of wood cutting forces (or cutting power) is also presented in this paper. The set of data nec- essary for computation can be easily obtained while cutting wood with common rotating tools, such as a circular saw or a router bit. The results generated include both fracture toughness and shear yield stresses in the shear plane, separately for two anatomical direc- tions of wood. The simplicity and reliability of this method provides wide range of practical applications.

The article analyzes the cutting process of hard bars. Investigations conducted in industrial conditions demonstrated the presence of surface errors in the machined workpieces in the form of washboard patterns. The purpose of this study was to analyze the results of cutting on band sawing machines with different band saw blades. The cutting processes were conducted on three different horizontal band sawing machine types. Analyzed material was an alloy steel &Oslash, 40 mm rod with a hardened surface covered with a thin layer of chromium. The hardness of the outer layer was 547 HV with a core hardness of 180 HV. The surface topography measurements of the processed workpieces were carried out with the 3D Optical Profiler, which supplied information on the irregularities of the processed material texture. In each of the analyzed cases, a corrugated surface was obtained after sawing, which is the effect of the occurrence of the washboarding phenomenon, despite the fact that the teeth of each band saw had variable pitches. The washboarding phenomenon when cutting rods with hard surfaces is caused by the phenomenon of wave regeneration. Despite the use of variable pitch saw blades, the cutting process results in rippling of the sawn surface, which is caused by the high hardness of the outer layer of the workpiece, as well as by the type of tool with spring setting of teeth.

In the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specifi c cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, the cutting forces (power) problem may be tackled with an innovative, up-to-date fundamental analysis of the mechanics of sawing based on modern fracture mechanics. This line of attack is an improvement on traditional approaches for cutting forces and power, many of which are empirical and based upon limited information. Such formulae do not permit generalisation to new conditions of operation of sawmills, such as e.g. the use of narrow-kerf blades. The presented algebraic model, for cutting power determination while sawing, in addition to timber ‘strength’ and friction between tool and workpiece, takes into account the property called ‘fracture toughness’ (resistance to cracking), which is a vital ingredient. Furthermore, forecasting of the shear plane angle with this model is achievable even for small values of uncut chips. Moreover, the mentioned model is a universal one, and useful for determination of energetic effects of sawing of every kinematics such as: frame sawing machines, bandsawing machines and circular sawing machines.

Knowledge on the fracture properties of materials is essential to assure structural integrity and proper design of mechanical connections in timber constructions. Measurement of this property is, however, a very challenging task. The linear fracture mechanics is usually used for its assessment assisted with experimental data acquired by means of various techniques, usually of destructive nature. The cutting force is an energetic effect of splitting material, and might be therefore considered from a point of view of modern fracture mechanics. The original methodology of simultaneous determination of the fracture toughness and of the shear yield strength on the basis of cutting forces was adopted here for timber characterisation. The set of experimental data was generated in a simple cutting test by using slightly modified out-the-shelf instrumentation. The resulting data are the slope and intercept of linear regression function of cutting forces versus chip thickness estimated for five European wood species. Both parameters are usable for computation of fracture toughness and shear yield strength in the shear plane, separately for two anatomical directions of wood. The simplicity and reliability of this method provides wide range of practical applications, including structural health assessment of the timber structures.

In the classical approach, cutting forces and cutting power in sawing processes of orthotropic materials such as wood are generally calculated on the basis of the specific cutting resistance kc (cutting force per unit area of cut). For every type of sawing kinematics (frame saws, band saws and circular sawing machines) different empirical values of specific cutting resistance kc have to be applied. It should be emphasised that sources in the scientific literature and handbooks do not provide any information about wood provenance, nor about cutting conditions in which cutting resistance had been determined. In analyses of sawing processes in which the offcut is formed by shear, Atkins’s ideas that all cutting forms a branch of elastoplastic fracture mechanics can be applied. Thanks to this modern approach it was possible to reveal, using experimental results data of fracture toughness and shear yield stresses of Polish pine (Pinus sylvestris), the significant effect of the raw material provenance (source of wood) on cutting power. In the common model for circular sawing machine kinematics, which is similar to metal milling, the sum of all uncut chip thicknesses of the all the teeth simultaneously engaged represented the mean uncut chip thickness. In this work predictions of the newly-developed model for the circular sawing machine are presented. In the model, beside uncut chip thicknesses changes, appropriate changes in shear yield stress and toughness with tooth/grain orientation have been taken into account. The conducted analyses have demonstrated that values of RMS of cutting power obtained with the new developed model are slightly larger than experimental values. On the other hand computed values of cutting power with the use of the mean uncut chip thicknesses in the model are a bit lower from the empirical one.

In the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specifi c cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, the cutting forces (power) problem may be tackled with an innovative, up-to-date fundamental analysis of the mechanics of sawing based on modern fracture mechanics. This line of attack is an improvement on traditional approaches for cutting forces and power, many of which are empirical and based upon limited information. Such formulae do not permit generalisation to new conditions of operation of sawmills, such as e.g. the use of narrow-kerf blades. The presented algebraic model, for cutting power determination while sawing, in addition to timber ‘strength’ and friction between tool and workpiece, takes into account the property called ‘fracture toughness’ (resistance to cracking), which is a vital ingredient. Furthermore, forecasting of the shear plane angle with this model is achievable even for small values of uncut chips. Moreover, the mentioned model is a universal one, and useful for determination of energetic effects of sawing of every kinematics such as: frame sawing machines, bandsawing machines and circular sawing machines., U klasičnom pristupu energijske se veličine (sile rezanja i snaga rezanja) tijekom procesa piljenja drva obično izračunavaju na temelju specifi čnog otpora rezanja, koji je pri rezanju drva funkcija više ili manje važnih čimbenika. Nasuprot tomu, problem određivanja sila rezanja i snage rezanja može se riješiti inovativnim pristupom uz primjenu temeljne analize mehanike piljenja koja se temelji na modernoj mehanici loma. Taj način pristupa određivanju sila rezanja i snage rezanja poboljšanje je s obzirom na tradicionalne metode, od kojih su mnoge empirijske i utemeljene na ograničenim podacima. Takve empirijske formule ne dopuštaju poopćenje prema novim uvjetima rada pilane, kao što je primjena tankih pila s malom širinom propiljka. Predstavljeni algebarski model za određivanje snage rezanja tijekom piljenja osim čvrstoće drva i trenja između alata i obratka uzima u obzir i svojstvo pod nazivom lomna žilavost (otpornost na pucanje), koje je ključni utjecajni čimbenik na snagu cutrezanja. Nadalje, predviđanje kuta smicanja ravnine opisanim modelom ostvarivo je čak i za male vrijednosti debljine strugotine. Osim toga, model je univerzalan i primijenjiv za određivanje energijskih veličina pri različitim kinematikama rezanja kao što su piljenje pilom jarmačom, tračnom pilom i kružnom pilom.

In the classical approach, energetic effects (cutting forces and cutting power) of wood sawing process are generally calculated on the basis of the specific cutting resistance, which is in the case of wood cutting the function of more or less important factors. On the other hand, cutting forces (or power—more interesting from energetic point of view) could be considered from a point of view of modern fracture mechanics. Cutting forces may be employed to determine not only toughness but also shear yield strength, which are then applied in the models. Furthermore, forecasting of the shear plane angle for the cutting models, which include fracture toughness in addition to plasticity and friction, broadens possibilities of energetic effects modelling of the sawing process even for small values of the uncut chip. Mentioned models are useful for estimation of energetic effects of sawing of every kinematics. However, for band saws and circular sawing machines, the chip acceleration power variation as a function of mass flow and tool velocity ought to be included in analysis of sawing at larger cutting speeds.