Thermal Penetration Depth Research Articles

Numerical analysis on thermoacoustic prime mover

A two-dimensional numerical model based on compressible SIMPLE algorithm was developed to simulate the evolution process of self-excited oscillation in a thermoacoustic engine at two different heating conditions. Moreover, the performance analysis of the thermoacoustic engine was researched. On one hand, the influence of stack parameters and charge pressure on the onset temperature of self-excited thermoacoustic oscillation was exhibited and analyzed. On the other hand, the impact of different gas types on the onset temperature difference was investigated. The results indicated that the self-excited thermoacoustic oscillation happened with the same performance for both two heating conditions. The minimum onset temperature difference can be achieved when the dimensionless stack length and position are Lr = 0.055–0.06 and Xr = 0.14–0.16, respectively. For a detail, the optimal stack plate thickness is 33% of the stack channel width when the computational width is 3 times as large as the thermal penetration depth of the working gas. Furthermore, the onset temperature difference increased with the increasing of the charge pressure in prime mover. For different working gas, the onset temperature difference was the highest for argon, which was followed by helium and nitrogen. Finally, the performance was improved with the increase of the temperature difference between the two exchangers in the prime mover.

Comprehensive performance improvement of standing wave thermoacoustic engine with converging stack: Thermodynamic analysis and optimization

In a thermoacoustic engine, the ratio of the plate spacing to the thermal penetration depth crucial to the performance and efficiency of thermoacoustic conversion. However, the temperature gradient in the regenerator or stack causes the non-uniform distribution of the thermal penetration depth. In this paper, the thermoacoustic stack comprised of converging channels has been put forward and applied in a standing wave thermoacoustic engine. The influence of the ratio of the plate spacing to the thermal penetration depth at the cold end of the stack, yc/δkc, on the performance parameters of different models is investigated in detail. Results show that suitable value of yc/δkc in parallel and converging stack models can improve the acoustic power and efficiency. It is also found that the converging stack can basically replace the parallel stack with the same yc/δkc and reduce the cost of consumptive materials. A dimensionless parameter β is defined to evaluate the comprehensive performance of thermoacoustic engine and used to guide the design of the stack.

Effect of Stack Spacing on the Performance of Thermoacoustic Refrigerators Using Helium and Air as Working Substances

This paper deals with the design of thermoacoustic refrigerators using linear thermoacoustic theory. The refrigerator components are designed at 3% drive ratio by considering the practical limitations of providing sufficient spacing for attaching the loudspeaker to the resonator tube and accommodating instrumentation. The effects of spiral stack spacing in terms of thermal penetration depth on the theoretical performance of refrigerator using helium and air as working substances are discussed. The quarter-wavelength resonator designs with taper and divergent section terminated with hemispherical end are optimized with helium and air for better performance. Theoretical results are validated with DeltaEC software results and are in agreement with each other. Helium shows better performance compared to air but lacks power density. The DeltaEC predicts COP 0.514 at the cold heat exchanger temperature of [Formula: see text]C with helium compared to air (COP 0.616 at [Formula: see text]C) for the 50[Formula: see text]W cooling power 100[Formula: see text]mm diameter quarter-wavelength resonator designs.

Optimization of the Design Parameter for Standing Wave Thermoacoustic Refrigerator using Genetic Algorithm

Standing wave thermoacoustic refrigerator has a potential of replacing conventional vapor compression refrigeration system due to several factors. Firstly, this green technology does not contain any harmful chemicals or ozone depletion refrigerant. In fact, it uses the sound wave to generate the cooling effect. Thus, it is friendly to the environment. Besides, this technology is affordable, lightweight and easy to be constructed too. However, it has a low coefficient of performance compared to conventional refrigerator with the same cooling capacity. Recently, there is no noticeable breakthrough in the research of this technology. In this study, genetic algorithm is used to optimize the design parameters of the standing wave thermoacoustic refrigerator system to achieve the highest coefficient of performance. Multi-Objective Genetic Algorithm is used to provide the performance trend of a standing wave thermoacoustic refrigerator system. There are five normalized parameters which will undergo optimization using genetic algorithm, namely normalized stack length, normalized stack center position, blockage ratio, drive ratio and normalized gas thermal penetration depth. The results show that the highest COP that can be achieved by a thermoacoustic refrigerator system (working gas = air, temperature = 300 K and pressure = 1 atm) is 4.8904. The coefficient of performance is about 120.3 % higher than the previously published data. A standing wave thermoacoustic refrigerator prototype is built based on the optimized results obtained from genetic algorithm, whereby the system is operating under no load condition. It is found that the experimental results agree well with the optimization results.

Investigating the effects of hybrid nanoparticles on solid-liquid phase change process in a Y-shaped fin-assisted LHTESS by means of FEM

The Latent Heat Thermal Energy Storage Systems (LHTESS) are widely used in different applications to make a balance between the energy requirement and energy supply. In this study, the effect of dispersing hybrid nanoparticles into the pure Phase Change Material (PCM) and making Hybrid Nano-Enhanced Phase Change Material (HNEPCM) on the solidification process in a LHTESS enhanced with Y-shaped fins is investigated. In order to enhance the thermal conductivity of system, TiO2 − Cu nanoparticles are added to water which is considered as PCM. Moreover, Y-shaped fins are attached to inner wall to enhance the thermal penetration depth. The effect of geometric parameters of Y-shaped fins including the bifurcation angle and fin length on the solidification process is investigated. The Finite Element Method (FEM) is applied to simulate the unsteady heat and mass transfer during the solidification process. Moreover, Response Surface Method (RSM) is applied to obtain a correlation for full solidification time as a function of nanoparticle shape factor, fin bifurcation angle and fin length. Results illustrated that by enhancing the fin length and fin bifurcation angle, the average temperature and total energy of the system experience lower values, while the solid fraction increases.

Experimental investigation on thermal stratification induced by steam direct contact condensation with non-condensable gas

Thermal stratification induced by steam direct contact condensation is a significant technical concern to consider in the energy industry. Thirty experiments have been performed to investigate the effect of steam mass flux, bulk water temperature and air mass fraction on temperature distribution in the water pool. The condensation behavior and time evolution of temperature distribution are recorded and analyzed. Two condensation regimes of chugging and bubbling are observed. Three flow patterns, namely chugging-induced synthetic jets, steam-driven negative buoyancy jets and plume, are discussed. Three thermal patterns of mixing, stratification and re-mixing are identified. A small amount of air (1–2%) could make stratification pattern occur earlier and severer. The maximum vertical temperature difference is about 30 °C in pure steam experiments and 60 °C in mixture gas experiments. Re-mixing pattern occurs when the bulk water temperature is close to 80 °C. In addition, thermal penetration depth, the velocity of thermocline moving down and the thickness of thermocline are estimated through temperature data.

Traveling and standing thermoacoustic waves in solid media

The most attractive application of fluid-based thermoacoustic (TA) energy conversion involves traveling wave devices due to their low onset temperature ratios and high growth rates. Recently, theoretical and numerical studies have shown that thermoacoustic effects can exist also in solids. However, these initial studies only focus on standing waves. This paper presents a numerical study investigating the existence of self-sustained thermoelastic oscillations associated with traveling wave modes in a looped solid rod under the effect of a localized thermal gradient. Configurations having different ratios of the rod radius R to the thermal penetration depth δk were explored and the traveling wave component (TWC) was found to become dominant as R approaches δk. The growth-rate-to-frequency ratio of the traveling TA wave is found to be significantly larger than that of the standing wave counterpart for the same wavelength. The perturbation energy budgets are analytically formulated and closed, shedding light onto the energy conversion processes of solid-state thermoacoustic (SSTA) engines and highlighting differences with fluids. Efficiency is also quantified based on the thermoacoustic production and dissipation rates evaluated from the energy budgets.

Selective laser broiling of Atlantic salmon

Selective laser broiling is a novel food processing technique that utilizes a 2-axis mirror galvanometer system to direct laser power to cook raw food. Unlike conventional cooking processes, laser cooking benefits from the high spatial and temporal precision of power delivery. In this investigation, we use a trochoidal scanning pattern to optimize the cooking of Atlantic salmon (Salmo salar), which is used as a model food system. We vary geometry of the trochoidal cooking pattern (circle diameter, circle density, and period) as well as the heat flux (2.71 MW/m2 and 0.73 MW/m2) and power (2 W and 5 W) of the blue laser and measure the internal temperature and depth of heat penetration via color analysis. Heat generated by blue laser operating at 445 nm has a thermal penetration depth nearing 2 mm in salmon and provide sufficient protein denaturation for cooking thin food layers. We achieve food safe cooking temperatures (>62.8 °C) in the salmon fillets and desirable color and textural changes through the use of high speeds and repetitive exposure. Ultimately, the goal of this study is to explore laser cooking of meat with an eye to applications both in food printing as well as an augmentation of conventional oven cooking.

A correction of porous media model for active magnetic regenerator based on a finite thermal penetration depth

A sphere-packed regenerator is often used in the active magnetic regenerator (AMR) of a magnetic refrigerator. When simulating such a regenerator, porous media instead of the practical sphere geometry is assumed and the solid refrigerants are assumed to be homogeneous in temperature. In fact, the temperature is inhomogeneous and determined by the ratio between sphere radius and thermal penetration depth. A method was used here that evaluates the influence of inhomogeneous temperature distribution inside the spheres on the cooling capacityand a correction factor was proposed to modify the porous media model under different particle diameters, frequencies and mass flow rates. Simulation results showed that the relative deviation of cooling capacity increased in the porous media AMR model with the increase of the ratio between sphere radius and thermal penetration depth. With a frequency below 3 Hz, when the particle radius was approximately 0.8 times the thermal penetration depth, the relative deviation of cooling capacity can be controlled within 5%. Comprehensively considering the pumping work and the heat transfer, a smaller diameter was selected to obtain the maximum COP value, at which the influence of thermal penetration depth can be ignored.

Characterization of CO2 laser browning of dough

Abstract We study the application of laser-heating technology to browning dough, due to its potential for high-resolution spatial and surface color control. An important component of this process is the identification of how laser parameters affect browning and baking and whether desirable results can be achieved. In this study, we analyze the performance of a carbon dioxide (CO2) mid-infrared laser (operating at 10.6 μm wavelength) during the browning of dough. Dough samples—consisting of flour and water—were exposed to the infrared laser at different laser power, beam diameter, and sample exposure time. At a laser energy flux of 0.32 MW m−2 (beam diameter of 5.7 mm) and sample exposure time of 180 s we observe a maximum thermal penetration of 0.77 mm and satisfactory dough browning. These results suggest that a CO2 laser is ideal for browning thin goods as well as for food layered manufacture. Industrial relevance A CO2 laser that operates at a wavelength of 10.6 μm (IR) was used as an alternative method for browning dough. The high-power flux of the laser and the high energy absorption of food at this wavelength allow for rapid surface browning; however, the high absorption limits thermal penetration depth. Nevertheless, accuracy of the laser beam enables high resolution spatial and thermal control of the non-enzymatic browning process. This high precision cooking makes laser-browning particularly ideal for food layered manufacture (FLM), a food processing technique that has gained increased attention in recent years. Using FLM, one can adjust the printed layer height to match cooking penetration depth. As a digital manufacturing technology, laser-browning could also enable manufacture of highly complex and customized food geometries and textures.

Structural capacity in fire of laminated timber elements in compartments with exposed timber surfaces

In compartment fires with boundaries consisting of exposed mass timber surfaces – for example in compartments with exposed cross-laminated timber (CLT) walls or floors – the thermal penetration depth, i.e. the depth of timber heated to temperatures significantly above ambient behind the char-timber interface, during fire exposure may have a significant influence on the load bearing capacity of structural mass timber buildings, particularly in the decay phase of a real fire. This paper presents in-depth timber temperature measurements obtained during a series of full-scale fire experiments in compartments with partially exposed CLT boundaries, including decay phases. During experiments in which the timber surfaces achieved auto-extinction after consumption of the compartment fuel load, the thermal penetration depth continued to increase for more than one hour, whilst the progression of the in-depth charring front effectively halted at extinction. A simple calculation model is presented to demonstrate that this ongoing progression of thermal penetration continues to reduce the structural load bearing capacity of the CLT elements, thereby increasing the potential for structural collapse during the decay phase of the fire. This issue is considered to be most important for timber compression elements. Currently utilised structural fire design methods for mass timber generally assume a fixed ‘zero strength layer’ depth to account for thermally affected timber behind the char line; however they make no explicit attempt to account for these decay-phase effects.

Radiant Heat Conduction in the Heat Insulating Lightweight Materials

An evaluation of scattering and absorbing abilities of light heat insulating materials in the IR spectrum range is given. The generalized form of Fourier equation application to such materials with taking into account radiant environment heat conduction is shown. Convectionless measurements of material specimen thermal resistance of different thickness are performed. Theoretical substantiations and ideas concerning heatprotective material properties are reliably confirmed. Exact values of total material heat conduction are obtained, and values of material radiant heat conduction, as well as of thermal radiation penetration depth into them are estimated.

Monocoque shell and tube heat exchanger for thermoacoustics

Heat exchangers can be a limiting factor to thermoacoustic power density. They can also be difficult to construct because of a tendency toward many small parts due to the small size of the thermal penetration depth. We present a heat exchanger that consists of around five pieces and yet has very small feature size and is easy to construct in large numbers. A sacrificial mandrel, consisting of a sheet with a lattice of specially shaped holes, is formed by casting in a mold with a lattice of specially shaped pins. The mandrel is plated with nickel, electroless nickel, or other metal. The mandrel is then removed by melting or dissolving, leaving a monocoque tube bundle. A screen mesh may be joined to one or both faces of the monocoque to act as fins to improve thermal contact to the working fluid that flows through the tubes. Coolant flows around the tubes within the monocoque shell. For a typical device, we find that without a mesh on the monocoque, lost work is minimized with tubes on the order of 8 mm long and spaced by 0.4 mm, but with a 100-mesh copper screen on both faces, the tubes can be a more manageable 3 mm long spaced by 4 mm.

Performance optimization of the regenerator of a looped thermoacoustic engine powered by low-grade heat

This paper focuses on the influence of regenerator on the performance of a single-stage looped thermoacoustic engine. Numerical simulation has firstly been carried out to investigate how the regenerator efficiency, generated acoustic power, and acoustic field in the regenerator are affected by the cross-sectional area, regenerator length, and mesh number. Based on the numerical optimization, an experimental setup with a normalized cross-sectional area of 14.5 and a normalized regenerator length of 0.0036 has been established, and the influence of the hydraulic radius of regenerator (determined by regenerator mesh number) on the onset process and the stable oscillation of the system has been studied. The results show that the ratio of the hydraulic radius of regenerator over thermal penetration depth should be in the range of 0.2 to 0.3, in order to achieve a low onset temperature difference and a high thermal efficiency. In the experiments, an onset temperature difference of 84°C and a thermal efficiency above 4% at a temperature difference of about 200°C were obtained, showing the potential to recover low-grade heat.

Stethoscope-type 3ω independent detector for fast measurement of material thermal conductivity.

As one of the most basic properties of materials, thermal conductivity is a key parameter to investigate the analysis and design of the particular thermal process, such as the analysis of the thermal/cool energy storage and release process, the thermal/cool energy storage system design, and so on. Also, it is the foundation of energy technology development. In order to overcome the problem that the measurement frequency of a polyimide substrate independent detector is lower and the measurement time is longer, based on the relationship among 3ω detection frequency, thermal wave penetration depth, and thermal properties of the substrate material, this paper developed a stethoscope-type 3ω independent detector based on a sapphire substrate for fast measurement of material thermal conductivity. Nickel, with a high resistance temperature coefficient, was used as the metal detector. The influence of the width of the nickel metal detector and the thickness of the sapphire substrate on the measurement accuracy was analyzed by introducing an effective heat flow ratio. The sapphire substrate independent detector was calibrated by using copper, aluminum, 304 stainless steel, quartz glass, ethylene glycol, and plexiglass with known thermal conductivities. The experiment shows that the measurement frequency of the stethoscope detector can be ten times higher than that of a Kapton film independent detector. Its measurement time is only one tenth of that of the Kapton film independent detector.

Non-invasive measurement of effective thermal conductivity of human skin with a guard-heated thermistor probe

This paper describes a non-invasive method for measurement of the effective thermal conductivity of human skin with a guard-heated thermistor probe. The guard-heated thermistor probe makes it possible to accurately measure the absolute surface temperature of a material at temperatures higher than the ambient temperature. In this study, the probe was used for a non-invasive measurement of the effective thermal conductivity of human skin by measuring skin surface temperature response for a short time. The effective thermal conductivity of human skin was measured at different body locations, such as cheeks, forearms, and heels, on five healthy volunteers. The measured values reflect the effects of multi-layered skin structure and biological processes, such as blood perfusion and metabolism beneath the skin. The results reveal a correlation between the effective thermal conductivity and the skin structure. A numerical simulation was performed to assess the effects of the epidermis thickness and the thermal conductivities of skin layers on the effective thermal conductivity of human skin. The results show that the thickness of the epidermis has a large impact on the effective thermal conductivity measured with a guard-heated thermistor probe. This is because the measured effective thermal conductivity is a function of the thermal conductivities of both the epidermis and dermis, depending on the thermal penetration depth during measurement. At locations on the body with a thicker epidermis, such as the heel, the epidermal thermal conductivity dominates over the effective thermal conductivity. At locations on the body with a thinner epidermis, such as the cheek and forearm, the dermal thermal conductivity dominates over the effective thermal conductivity. The influences of physiological conditions, such as blood perfusion beneath the skin and metabolism, on the effective thermal conductivity of human skin, were also analyzed numerically. Variations in the blood perfusion rate and metabolic heat generation rate of the dermis layer were found to have a slight impact on the effective thermal conductivity; however, only the blood perfusion rate and the arterial blood temperature were found to influence the skin surface temperature.

Influence of thermal contact on heat transfer from glowing firebrands

The influence of thermal contact between a glowing firebrand and the target fuel bed on the resultant heat transfer into the fuel bed was investigated in this study. A zero dimensional (0-D) model for the firebrand coupled to a transient two dimensional (2-D) explicit finite difference model for the fuel bed were used simulate transient heat transfer from a firebrand deposited on a fuel bed. Two firebrand shapes, a disk shaped firebrand in contact with the fuel bed and a cylinder shaped firebrand with a protruding node in contact with fuel bed, were considered. A model was proposed to estimate the thermal contact resistance between the firebrand and the target fuel bed. Heat transfer from a cylinder shaped firebrand with two contact points was also investigated. The model developed in this study provided detailed information on the temperature distribution and thermal penetration depth in the target fuel bed. Predictions made by the model were in qualitative agreement with experimental data reported in the literature. The firebrand thermal contact resistance model presented in this study can be a useful tool to account for variations in firebrand shape and surface irregularities in both the firebrand and the target fuel bed.

Depth-resolved sample composition analysis using laser-induced ablation-quadrupole mass spectrometry and laser-induced breakdown spectroscopy

Monitoring a sample's material composition became more and more important over the last years for both - industrial process control as well as for post mortem analysis in research and industrial development. Although material composition identification as well as a comparison with standard samples works fine, there is a lack of diagnostics which can provide quantitative information with depth resolution without any standard samples.We present a novel method utilizing a residual gas analysis with quadrupole mass spectrometry after picosecond laser-induced ablation and release of volatile species. In the present experiment, well characterized multilayer thin film solar cells (μc-Si:H and a-Si:D as p-i-n-junctions on ZnO:Al electrodes) are used as a set of well characterized material samples to demonstrate the capabilities of the new method.The linearity of the spectrometer signal to gas pressure simplifies its calibration and reduces its uncertainties in comparison with other analysis techniques, although high vacuum conditions (10−6hPa to 10−7hPa) are required to reach high sensitivity better than the percent-range. Moreover, the laser-ablation based sample analysis requires no preparation of the sample and is flexible regarding ablation rates. The application of a picosecond laser pulse ensures that the thermal penetration depth of the laser is in the same order of magnitude as the ablation rate, which enables to achieve depth resolutions in the order of 100 nm and avoids matrix mixing effects at the edge of the laser-induced crater in the sample.

Depth of thermal penetration in straight grinding

Unlike the usual numerical FEM approach to determine the thermally affected layer during the grinding process, we propose a simple analytical approach to estimate the depth of thermal penetration. For this purpose, the one-dimensional definition of depth of thermal penetration is applied to the two-dimensional heat transfer models of straight grinding. A method for computing the depth of thermal penetration in these two-dimensional models is derived and compared to the one-dimensional approximation. For dry grinding, it turns out that the one-dimensional approximation is quite accurate when we consider a moderate percentage in the temperature fall beneath the surface, regardless the type of heat flux profile entering into the workpiece (i.e., constant, linear, triangular, or parabolic). In wet grinding, the latter is true if we consider a constant heat flux profile and a high Peclet number, i.e., Pe > 5. Finally, the one- and two-dimensional approaches calculating analytically the depth of thermal penetration have been compared to the temperature field numerically evaluated by a three-dimensional FEM simulation given in the literature, obtaining a quite good agreement.

Spatial Behavior of the Steady State Vibrations in a Dual-Phase-Lag Rigid Conductor

This paper studies the spatial behavior of the steady state vibrations in a cylinder made of a dual-phase-lag anisotropic rigid conductor material. We analyze the influence of the lagging model upon the spatial behavior of the amplitude of vibration along the axis of the cylinder, providing the explicit expressions of the decay rate and of the corresponding critical frequency in terms of the coefficients of the considered constitutive equation (or delay times). In fact, for the amplitude of the harmonic vibrations we obtain some exponential decay estimates of Saint-Venant type, provided the frequency of vibration is lower than a critical value. This gives information on the thermal penetration depth of the steady state vibrations describing the heat affected zone. Illustrative examples are given for the class of lagging behavior models that are thermodynamically compatible.