Semi-theoretical Model Research Articles

Characteristics of wave loading and viscous energy loss of a bottom-sitting U-OWC wave energy device: A validated numerical perspective

This study involves numerical simulations of regular waves interacting with a bottom-sitting circular OWC wave energy converter with a U-shaped duct (circular U-OWC). A numerical wave tank is built based on the RANS equation and is validated against experiments. The effect of water depth and the height of the outer tube of the U-shaped duct on capture efficiency, wave loading, and viscous energy loss is investigated numerically. Results show that the height of the outer tube of the U-shaped duct has a significant effect on the capture efficiency of the device. Wave loading analysis reveals a critical mode of stability that may threaten the operation safety of the device. It is found that increasing the height of the U-shaped duct opening increases the viscous energy loss inside the U-shaped duct. A semi-theoretical model between work done by waves to the device and the viscous energy loss in the U-shaped duct is established, numerical data indicates that a significant amount of work done by waves to the device is lost in viscous effects. This suggests that certain optimization for reducing wave loading could possibly also reduce viscous energy loss, thus improving the overall efficiency of the device.

Model of bores interaction in the swash

This paper examines the impact of wave interactions in the inner-surf zone, including the swash, on shoreline excursion dynamics. Specifically, the study focuses on how the time lag between consecutive waves and the slope of the beachface affect shoreline dynamics. To investigate this, a laboratory experimental setup is developed to study the behaviour of two consecutive bore-type waves travelling over a fluid layer with constant depth, representing an idealized inner-surf zone, before impacting an inclined solid plane with slope β, representing the beachface. Bore waves are generated using two dam-break flow devices, with a controlled time lag Δt between them. This simplified physical model allows for the assessment of semi-theoretical predictive models based on shallow water approximation, resulting in ballistic-type models for shoreline motion. By combining these approaches, the study characterizes different flow regimes in the (Δt,β) parameter space. It is observed that varying Δt at a fixed β distinguishes four interaction regimes, either wave–wave interaction in the inner-surf zone or wave-swash interaction in the swash, with possibilities of merging or collision depending on wave orientation. In particular, increasing Δt leads to either bore–bore merging in the inner-surf, bore-runup merging in the swash, bore-backwash collision in the swash or bore–bore collision in the inner-surf. Bore–bore merging and bore-runup merging enhance runup, peaking when Δt is such that merging occurs near the transition from the inner-surf to the swash. On the contrary, bore-backwash collision results in additional dissipation of the second bore’s dynamics, leading to a reduced shoreline extension compared to that induced by the first bore. All processes within the swash, including the transition between bore-runup and bore-backwash regimes, as well as the enhancement and extra dissipation of the second bore’s swash excursion, exhibit some level of dependence on β. Overall, the results from this physical model help characterize and explain local mechanisms triggered by wave interaction near the shoreline. Validating this model’s relevance warrants specific attention through comparisons with field data. As an initial validation attempt, field data extracted from the literature are compared to the physical model, showing promising agreement.

Spray characteristics of different regions downstream of a swirl cup

The spray characteristics of different regions downstream of swirl cups play a critical role in cold start and re-ignition of gas turbines. The spray measurements were performed at the fuel pressures of 0.5, 0.8, 1.0, 1.5, and 2.0 MPa and the fuel temperatures of −23, −13, −3, 7, 17 and 27 ℃, respectively. The droplet size, droplet velocity, droplet number, and instantaneous spatial spray image of sprays from an aviation kerosene Jet-A were measured using a two-component phase Doppler particle analyzer and a digital off-axis holography system. As the fuel pressure and temperature increase, the Sauter Mean Diameter (SMD) and spray non-uniformity of the Spray Shear Layer (SSL) gradually decrease. As the fuel pressure increases, the SMD and spray non-uniformity of the Central Toroidal Recirculation Zone (CTRZ) gradually decrease, and the slopes of these curves both decrease. As the fuel pressure increases, the SMD and spray non-uniformity of the CTRZ rapidly decrease at the fuel temperature of −23 ℃, while slightly decrease at the fuel temperature of 27 ℃. The droplets in the CTRZ come from 3 different sources: simplex nozzle, venturi, and outside the CTRZ. As the fuel pressure increases, the proportion of droplets recirculated from outside the CTRZ decreases. This study proposed the concept of the “pressure critical point” for the swirl cups. As the fuel temperature decreases, the proportion of droplets recirculated from outside the CTRZ increases below the critical pressure, while decreases above the critical pressure. In addition, through the models of liquid film formation and breakup on the curved cylindrical wall, a semi-theoretical model was established to predict the SMD of SSL for swirl cups. The prediction uncertainty of this model is less than 6% for all 14 conditions in this paper.

Semi-theoretical compression model of wet fiber web for the prediction of airflow rate in vacuum dewatering process of papermaking

This study expands the investigation of a mathematical method for predicting the airflow rate during the vacuum dewatering process of papermaking based on our previous research. By integrating poroelastic theory and initial saturation thickness, based on experimental data with a range of 20–60 kPa pressure difference and 20-200 g · m − 2 basis weight, a mathematical method with a semi-theoretical model for compression characteristics of the wet fiber web, the poroelastic porosity model (PEPM), was developed to support and expand on our previously established empirical model for porosity variations in wet fiber web, the variable porosity model (VPM). The accuracy of the mathematical method with the PEPM in predicting the airflow mass flux passing through the wet fiber web was validated using experimental data with a range of 0–60 kPa pressure difference and 20-200 g · m − 2 basis weight. The mean relative errors with the PEPM within the pressure difference range of 0-20 kPa and 0-60 kPa were 7.68% and 8.80%, respectively, compared to 17.44% and 11.67% for those with the VPM, demonstrating the improved applicability and generalization of the mathematical method, particularly in the zone of low pressure difference exceeding the range of the modeling experimental data. The PEPM effectively revealed the strain hardening behavior during the compression process and the diminishing returns of energy in the vacuum dewatering process with an increasing pressure difference. The developed mathematical method with the PEPM for the compression characteristics of the wet fiber web provides an effective and accurate way to predict the airflow rate during the vacuum dewatering process of papermaking.

Improved semi-theoretical correlation to predict the Sauter mean diameter of swirl cups

The spray downstream of swirl cups involves complex two-phase flow. Comprehensively, understanding the flow physics of the spray to accurately predict the characteristics of the swirl spray is crucial for developing next-generation low-emission gas turbine combustors. The Sauter mean diameter (SMD) of the spray is an important design parameter in a gas turbine combustor, and the semi-theoretical method is among the most widely used approaches for predicting the SMD of atomizers. Of the available semi-theoretical models for predicting the SMD of prefilming-type atomizers, Shin's phenomenological three-step atomization (PTSA) model is a physics-based correlation. The PTSA model comprises three submodels: those of the pressure-swirl spray, impingement and film formation, and aerodynamic breakup. Based on similar physical mechanisms, the PTSA model can effectively predict the SMD for the spray shear layer of swirl cups. In this study, a new model, called the PTSA-V model, is proposed by introducing the viscosity of the liquid to the three submodels of PTSA. Additionally, the submodel of impingement and film formation was reconstructed, using a simplified model of a round water jet impinging on a cylindrical wall to predict the thickness of the liquid film on the Venturi surface. Experiments were carried out on a swirl cup under different pressures and temperatures of fuel as well as varying pressure drops in the air by using a two-component phase Doppler particle analyzer. The resulting uncertainty in predictions of the PTSA-V model was lower than ±7.4% under the 26 operating conditions considered here, compared with an uncertainty of ±20% in the outcomes of PTSA. Uncertainty in predictions of PTSA-V was lower than ±15% when it was applied to SMD data downstream of the swirl cup from the literature.

Tensile properties and constitutive model of cost-effective multiscale hybrid fiber reinforced strain hardening cementitious composites

To enhance the mechanical properties and cost-effectiveness of conventional polyvinyl alcohol fiber reinforced strain hardening cementitious composite (PVA-SHCC), a modified version called multiscale hybrid fiber reinforced SHCC (MsHySHCC) was developed. This new composite incorporates a combination of steel fiber, PVA fiber and calcium carbonate (CaCO3) whisker. Uniaxial direct tensile behaviors (stress-strain relationship, tensile strength, tensile deformation capacity and tensile toughness) of designed MsHySHCCs were investigated and evaluated. The results show that the PVA fibers dominate the ductile behavior and the steel fibers and CaCO3 whiskers effectively affect the strength of MsHySHCCs. The PVA fibers can be partially replaced by CaCO3 whisker and steel fiber, along with an increase in tensile strength and ductility of designed composites. The findings suggest that the configuration of MsHySHCC proves to be a viable approach in simultaneously enhancing the strength and ductility of PVA-SHCC. A semi-theoretical prediction model for tensile constitutive relationship was derived. The comparison of the theoretical results with the experimental data shows that this semi-theoretical model is applicable for determining the tensile constitutive relationship of PVA-SHCCs and MsHySHCCs.

In vitro photoinactivation of Pseudomonas aeruginosa and Staphylococcus aureus biofilm by a novel multi-dose LED-based illumination method

Significancerecently, an aerosolized light source has been proposed to photo-inactivate pathogens responsible for multidrug-resistant chronic lung infections. To maximize the light source in vivo photokilling efficacy, its emission spectrum was predicted by a semi-theoretical model. To confirm and upgrade the model with experiments, biofilm photoinactivation studies were performed. Approachin vitro biofilms of P. aeruginosa and S. aureus (reference and clinical strains) were photo-inactivated by LED sources at 415, 445, 525 and 623nm. Non-uniform illumination protocol was employed to deliver different doses (10 to 110 J/cm2) in a single experiment. Photokilling efficacy was quantified by CFU counting. Results415nm-peaked light was associated with the maximum photokilling efficacy for all the considered strains. Other wavelengths have a minor or scant effect. Conclusionsbiofilm photoinactivation was studied as a function of both dose and illumination wavelength. Results are compatible with expected presence of endogenous photosensitizers (porphyrins) in the bacteria.

Drying kinetics and mathematical modeling of seeds of two mango varieties at different temperatures and with different pretreatments

AbstractIncreasing global waste generation is not only a threat but also an opportunity to address energy insecurity and pollution using green valorization techniques. However, this requires pretreatment of waste and byproducts and optimization of drying to obtain high‐quality biofuels. Hence, this study aims to analyze the performance of currently used drying models, the influence of different drying temperatures, drying time, and seed pretreatment on the drying kinetics of two varieties of mango seed. Accordingly, whole seeds and crushed seeds were exposed to five drying temperatures (313–353 K) in a heating furnace. Weight loss was recorded systematically, converted into moisture ratio, and then fitted to four semitheoretical mathematical models, namely: (i) Lewis, (ii) Henderson and Pabis, (iii) Page, and (iv) Avhad and Marchetti models. The fitness of these models was compared using statistical parameters, such as R2, X2, root mean square error (RMSE), mean bias error (MBE), and mean absolute error (MAE). The results showed that seed pretreatment and increasing the drying temperature led to an increase in the rate of moisture evaporation and reduced the time required for drying. Among all models, the Avhad and Marchetti model provided higher R2 values of 0.9994 and 0.9991 for local and hybrid mango at 313 K, and 0.9977, and 0.9970 for local and hybrid crushed mango seeds at 353 K and 313 K, respectively; hence, it showed the best performance. The activation energy (Ea) showed a slight differences for both varieties of mango seed and among pretreatments in all mathematical models. The mean Ea values for local and hybrid mango seeds were 41.18 kJ mol−1 and 46.21 kJ mol−1, respectively. For whole and crushed local and hybrid mango varieties, the mean Ea values were 31.37 kJ mol−1, 40.80 kJ mol−1, 50.99 kJ mol−1, and 51.61 kJ mol−1. The likely reason for this variation might be differences in variety, chemical composition, growing conditions, and cellular structure of the seed varieties.

A mathematical model for predicting crystallization fouling in narrow rectangle channel incorporating crystal growth effect

Crystallization fouling is an ongoing concern for many heat transfer systems, and simulating fouling formation under various flow and heat transfer conditions is crucial for predicting fouling resistance and improving energy efficiency. This paper proposes a mesoscopic model for predicting crystallization fouling in narrow rectangle channels accounting for the realistic crystal growth. A hybrid lattice Boltzmann and finite difference model is established to predict the coupled process of fluid flow, heat transfer, concentration diffusion and crystallization fouling. The second-order mass deposition rate is solved and transformed to the surface-reaction boundary condition in lattice Boltzmann (LB) scheme, and the volume of pixel (VOP) method is employed to simulate the dynamic crystal growth. The scheme and the sub-models are verified systematically by the analytical solution of a linear diffusion-reaction problem, the semi-theoretical fouling models, and the experimental data. The results indicate that the present model can effectively predict the crystallization fouling controlled by either surface integration or mass transfer, and show its capability to simulate the non-uniform fouling growth process in heat transfer channels, providing insight towards full understanding and mitigation design of crystallization fouling.

Correlating multicomponent surface tension data with Padé approximants. Part I. Surface tension

Eberhardt (1966), Connors and Wright (1989), Piñeiro et al. (2001), Das and Bhattacharyya (2003) and Belda (2009) all proposed successful mixture models for correlating the surface tension data for binary liquid mixtures. Rational extensions of these semi-theoretical and empirical models are derived in order to cater for multicomponent mixtures. It is shown that a canonical Padé approximant emanates from the Piñeiro et al. (2001) and Das et al. (2003) proposals:σ=∑iβiixiσi∑jκijxj/∑i∑jβijxixjWhere the σi’s are the surface tensions of the pure components as a function of temperature. The βij and κij are adjustable model constants (with κii = 1) and they carry some physical meaning. The other models are special cases that are obtained by the application of different combining rules. For example, when the Extended Langmuir model developed by Piñeiro et al. (2001) holds, one obtains βij=βiiβjj; on the other hand, it reduces to the Connors and Wright (1989) model if βij=βii+βjj/2. The theories underpinning these models, suggest that the parameters βij and κij might be temperature dependent. However, Shardt and Elliott (2017) found that, for binary systems they can be assumed constant, i.e. that the temperature dependence is carried solely by the pure component surface tensions. This premise was confirmed for the seven ternary systems which were used to validate the proposed multicomponent canonical Padé approximant.

Experimental investigation for enhancement of heat and mass transfer during regeneration of zeolite 13X-water pair

The effect of adding metal pieces in the adsorbent bed for enhancing the effective thermal conductivity and drying kinetics is investigated for the Zeolite 13X bed. Aluminum, stainless-steel pieces ranging in size from 1.5 cm to 2 cm, and aluminum oxide nanoparticles are chosen, and the total weight added to the bed is approximately 2 % of the adsorbent weight. The different semi-theoretical drying models like Lewis, Page, Logarithmic, Henderson, and Pabis and empirical models like Weibull and Gaussian model are used for the analysis. Adsorption and desorption of Zeolite 13X-water integrated with various metal pieces revealed a decrease in the adsorption capacity of adsorbents with metal pieces and increased bed moisture content for powdered aluminum oxide. It can be noticed that the desorption process was improved by including the metal pieces in the adsorbent bed.; Desorption rates range from 19.54 % for the bed mixed with straight aluminum pieces and 21.43 % for the bed filled with stainless steel. The desorption rates for the bed containing nanoparticles of aluminum oxide and spiral aluminum pieces are 20.48 % and 22.21 %, respectively. The experimental investigation on efficiency enhancement revealed that the desorption process of an adsorbent bed with straight aluminum pieces increased efficiency by 12.38 %, while the bed with aluminum oxide and stainless steel increased efficiency by 17.75 % and 23.20 %, respectively. The effectiveness of an adsorbent bed with spiral aluminum pieces is enhanced by 27.68 %. The drying kinetics analysis of zeolite 13x regeneration using semi-theoretical and empirical models which showed good agreement with experimental results.

Biaxial bending moments calculation model based on stress distribution for H-section steel members under different loading paths

To explore the biaxial bending development mechanism of H-section steel members under different cyclic loading paths, we conducted a parametric analysis involving various axial force ratios, plate width-to-thickness ratios, and loading angles. Three loading paths were considered, including linear, rectangular, and triangular loading paths. Finite element models were established in ABAQUS and validated for accuracy using existing experimental data. Based on the finite element analysis results, a methodology for determining the form of normal stress distribution was derived by analyzing the mechanism of biaxial interactions in H-section steel members. By establishing a relationship between the normal stress distribution and the biaxial bending moments, a semi-empirical semi-theoretical calculational model was developed to simulate the entire process of biaxial bending and compression loading at reverse point in H-section steel members under different loading paths. The validity of this model was confirmed, as it demonstrated effective prediction of the complete development trends of biaxial bending moments for H-section steel members. This model establishes the basis for seismic design of H-section steel members subjected to biaxial loading conditions.

Convective drying of black rice grains (Oryza sativa L.): new mathematical modeling insights and thermodynamic properties

The aim of this study was to investigate the thin layer drying of brown rice grains at different temperatures (35-75 °C), exploring its kinetics and thermodynamic properties. Black rice grains (30% b.u.) were subjected to convective drying, and the experimental data were subjected to analysis of theoretical, semi-theoretical and empirical drying models, and thermodynamic parameters were calculated. Increasing temperature accelerated drying, shortening the time required to reach moisture balance. The modified Page model modified by Cavalcanti-Mata showed excellent fit to the experimental data, standing out for its simplicity and effectiveness in describing the relationship between water content and drying time. The analysis of thermodynamic properties revealed that the activation energy increased with temperature, evidencing its influence on moisture removal. The observed variations in thermodynamic properties reinforce the importance of considering energy factors in drying. The results offer insights to optimize the black rice grain drying process, contributing to advances in the food industry and providing a basis for future research in the processing of agricultural products.

Flow field characteristics and energy loss model of the effective upstream flow region of orifice in liquid jet

Orifice jets commonly adhere to the thick-walled orifice jet mechanism or the thin-walled one, where the difference between the two orifice jet mechanisms is generally considered to be caused after the fluid enters the orifice. However, ignoring the energy loss before entering the orifice could be inaccurate and even misleading. Therefore, we studied the flow behavior in the upstream flow region of thick-walled orifices (small orifices) and thin-walled ones (large ones). Firstly, the concept of the effective upstream flow region of orifice was proposed based on the film theory. It can be simplified into an approximate hemispherical multi-channel parallel contractive flow field. Then, the experiments of the effective upstream flow region were conducted by the streamlined contractive orifices with equivalent energy loss. The proportion of the energy loss before the fluid enters the orifice to the total energy loss was obtained. In addition, the maximum impact range of the effective upstream flow region was remarked by theoretical derivation, and local resistance coefficient functions were established based on the CFD simulation results. Finally, a semi-theoretical model of energy loss in this region was developed. It can quantitatively measure the proportion of increased energy consumption caused by the sucked air inside orifice, well verifying the eddy energy consumption, which provides a scientific exclusion method for predicting the complex form resistance.

Constitutive Model of Bond-Slip between Rubber Granule–Basalt Fiber Composite Modified Concrete and Rebar

The bonding properties between rubber granule–basalt fiber composite modified concrete (RBFC) and rebar greatly impact the load-carrying capacity, stiffness, and crack development of RBFC structures. In this paper, the effects of rebar diameter, bonding length, and concrete type on the bonding properties between RBFC and rebar were investigated using center pull-out tests. The bond stress–slip curve as well as the bond strength and its influencing factors were discussed in detail, and a semi-theoretical and semi-empirical model of RBFC with rebar was established. According to the findings, when rubber granules were added to concrete, its bond strength with rebar decreased. At a dosage of 5%, the bond strength was reduced by approximately 4% compared to ordinary concrete (OC) under the same conditions. It was shown that the addition of small amounts of rubber granules did not significantly reduce the bond strength. On the other hand, the incorporation of an appropriate amount of basalt fibers had a positive effect on the bond strength. An admixture of 4.56 Kg/m3 of fibers increased the bond strength by 3% compared to OC under the same conditions. The bond strength of RBFC with these two additions was improved by approximately 2% compared to OC under the same conditions. When the bonding length was 60 to 100 mm, the ultimate bond strength decreased with increasing bonding lengths. The bond strength decreased by 13.91–16.72% for every 20 mm increase in bonding length. When the rebar diameter was 12 to 16 mm, the ultimate bond stress decreased as the rebar diameter increased. The bond strength decreased by 3.96–5.94% for every 2 mm increase in rebar diameter. The segmental bond–slip constitutive model between RBFC and rebar, established using the results of the center pull-out test, can provide a reference basis for engineering applications of RBFC.

Methods to Improve the Accuracy and Robustness of Satellite-Derived Bathymetry through Processing of Optically Deep Waters

Selecting a representative optical deep-water area is crucial for accurate satellite-derived bathymetry (SDB) based on semi-theoretical and semi-empirical models. This study proposed a deep-water area selection method where potential areas were identified by integrating remote sensing imagery with existing global bathymetric data. Specifically, the effects of sun glint correction for deep-water areas on SDB estimation were investigated. The results indicated that the computed SDB had significant instabilities when different optical deep-water areas without sun glint correction were used for model training. In comparison, when sun glint correction was applied, the SDB results from different deep-water areas had greater consistency. We generated bathymetric maps for the Langhua Reef in the South China Sea and Buck Island near the U.S. Virgin Islands using Sentinel-2 multispectral images and 70% of the Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) bathymetry data. Additionally, 30% of the ICESat-2 bathymetry data and NOAA NGS Topo-bathy Lidar data served as the validation data to evaluate the qualities of the computed SDB, respectively. The results showed that the average quality of the SDB significantly improved with sun glint correction application by a magnitude of 0.60 m in terms of the root mean square error (RMSE) for two study areas. Moreover, an evaluation of the SDB data computed from different deep-water areas showed more consistent results, with RMSEs of approximately 0.4 and 1.4 m over the Langhua Reef and Buck Island, respectively. These values were consistently below 9% of the maximum depth. In addition, the effects of the optical image selection on SDB inversion were investigated, and the SDB calculated from the images over different time periods demonstrated similar results after applying sun glint correction. The results showed that this approach for optical deep-water area selection and correction could be used for improving the SDB, particularly in challenging scenarios, thereby enhancing the accuracy and robustness of SDB.

A New Approach of Solidification Analysis in Modular Latent Thermal Energy Storage Unit Based on Image Processing

The solidification process of RT18HC in a cylindrical shell and tube storage unit has been studied using a new methodology based on image processing. The main idea of the algorithm is to label the region of solidification and use statistical functions to calculate the dimensions of the solidification front over time. Said analysis includes two methods. The first method is to measure the solid fraction changes during solidification. The novelty of this method, as compared to other literature findings, is that pre-processing and calculation process occurs automatically via a calculation algorithm. This method is used to calculate the solid fraction of RT18HC which is reported to be a bit fast at the beginning that 40 % of its volume solidified in 1000 s while the rest of the process is completed in almost 6500 s. The second method is used to measure and calculate the thickness of the solid front by using image processing. This method’s error is calculated to be less than 7% throughout the entire process. The second method also acts as an experimental database of front thickness to use in a novel, simplified, semi-theoretical model proposed to calculate the solid front thickness as a function of time in this paper. It is also worth presenting solution extended by a general definition of thermal resistance for a cylindrical partition. The above study will enable the development of an enhanced and optimized model for complex geometries based on image processing techniques in the future. It will also allow the investigation of both processes i.e. solidification and melting alongside other influencing parameters such as the geometry of the storage unit in future.

A thick-layer drying kinetic model and drying characteristics of moisture-containing porous materials

The thick-layer drying kinetics of moisture-containing porous material (honeysuckle) at constant temperature and humidity are experimentally investigated, and the drying characteristics under variable temperature and humidity conditions are analyzed in this paper. The results show that the drying rate is constant and linearly/positively corrected with the moisture content under constant temperature and humidity conditions, and the corresponding slope (drying rate constant) decreases exponentially with the increase in the number of stacked layers because of the increased flow resistance and diminished convective migration of water vapor. The migration of saturated water vapor changes from convection-dominated to diffusion-dominated after the thickness of the stacked materials exceeds a critical value. Based on the experimental data, a new semi-theoretical drying model was proposed for thin-layer and thick-layer drying of moisture-containing stacked porous materials, and it was experimentally verified with a coefficient of determination greater than 0.92. The relative humidity of the drying medium is a key factor in determining the drying rate, and reducing the relative humidity of the drying medium at a constant temperature is suitable for drying heat-sensitive materials. This paper can contribute to the development of drying kinetics and provide a theoretical basis for the drying of moisture-containing porous material.

Mathematical Modeling of Thin-Layer Drying Kinetics of Tomato Peels: Influence of Drying Temperature on the Energy Requirements and Extracts Quality.

Tomato drying implies high energy consumption due to the high moisture content, and limiting drying temperatures is necessary to avoid carotenoid degradation. To explain the mechanism of moisture transport through the material and to scale up the drying process, drying experiments are needed and supported by mathematical modeling. For the Rila tomato peel drying process, ten thin-layer mathematical models were formulated based on experimental data for six temperatures (50-75 °C) and validated by statistical analysis. Considering the slab geometry of the peels sample and Fick's second law of diffusion model, the calculated effective moisture diffusivity coefficient values Deff varied between 1.01 × 10-9-1.53 × 10-9 m2/s with R2 higher than 0.9432. From the semi-theoretical models, Two-term presents the best prediction of moisture ratio with the highest R2 and lowest χ2 and RMSE values. Using the experimental data on extract quality (carotenoid content), two degradation models were formulated. Increasing the drying temperature from 50 °C to 110 °C, a degradation of 94% for lycopene and 83% for β-carotene were predicted. From the energy analysis, a specific energy consumption of 56.60 ± 0.51 kWh is necessary for hot-air drying of 1 kg of Rila tomato peel at 50 °C to avoid carotenoid degradation.

Effect of temperature step on selection strategy of deposition head lift height and manufacturing stability during the direct laser deposition process

Based on the layer by layer cladding characteristics of the direct laser deposition (DLD), the optimal selection strategy of deposition head lift height is one of the effective methods to maintain the manufacturing process stability, improve product quality, and reduce complex post-process. However, owing to the temperature step caused by changeable layer residual temperature, the selection of deposition head lift height becomes extremely complex. In this paper, to clearly analyze the effect of temperature step on selection strategy of deposition head lift height for the DLD multilayer deposition process with a 1.85 kW fiber laser and a coupled coaxial four-channel nozzle, a semi-theoretical model considering the main physical phenomena involved in DLD process is proposed, validated, and applied. Here, working plane position, deposition head lift height, and step of residual and preheating temperature are considered as input process variables while manufacturing stability and error are determined as process responses. Results show that without considering the temperature influence, the final manufacturing stability can be achieved by ensuring that the distance between the deposition head and the initial working plane is less than the maximum relative distance corresponding to the selected deposition head lift height. When the layer residual temperature is considered, the single-layer cladding height steps positively, which makes the extreme working plane position positively migrated, and the manufacturing stability is also further enhanced. However, due to the migration of the finally stable working plane position, the manufacturing errors are also conditionally changed. Finally, in order to obtain an optimal manufacturing process, for any DLD process where the initial working plane position has been determined, the deposition head lift height should be selected slightly smaller than the single-layer height corresponding to that determined plane under residual temperature condition (hTr,Si), otherwise the manufacturing process will gradually lose stability and lead to fabrication failure.