Dimensionless Factor Research Articles

Optimal design of annular thermoelectric generator with twisted tape for performance enhancement

The adaptation of annular thermoelectric generator (ATEG) to cylindrical heat sources exhibits a better performance compared to widely studied flat plate type thermoelectric generator (FTEG). To enhance heat transfer and improve the overall performance, a novel structure of the heat exchanger of the twisted-tape annular thermoelectric generator (TT-ATEG) is proposed in this paper. A three-dimensional finite element model of TT-ATEG is established for the first time. The net power gain coefficient and the efficiency gain coefficient are defined to quantify the performance of TT-ATEG, and the gain effects of the length, twist ratio and radius of the twisted tape are analyzed respectively. To maximize the comprehensive performance of TT-ATEG, the optimal weighting factor of net power and efficiency are determined, and the full-parameter optimization of the twisted tape is completed. The results reveal that the optimal performance of TT-ATEG is obtained if the weight ratio of net power and conversion efficiency is 1:4. In our case study, dimensionless factors radius ratio Rr, length ratio Lr and twist ratio of the twisted tape are 0.714, 0.479 and 136.84 respectively. Compared with the ATEG without twisted tape, the net power and efficiency are improved by 10.41% and 22.51%, respectively. The results demonstrate that the novel design of TT-ATEG could accelerate the heat transfer effectively and enhance the overall performance.

Darcy–Forchheimer MHD radiative flow through a porous space incorporating viscous dissipation, heat source, and chemical reaction effect across an exponentially stretched surface

AbstractThe impacts of viscous dissipation, Brownian motion, and the thermophoresis caused by temperature gradient on the steady two‐dimensional incompressible chemically reactive and radiative flow of traditional fluid through an exponentially stretched sheet embedded in a Darcy porous media are explored by approaching boundary layer analysis. A magnetic field effect is also addressed along the transverse direction of the horizontal stretched sheet. With the implementation of some suitable nondimensional quantities, the regulating nonlinear partial differential equations, which represent the flow geometry, are transformed into coupled nonlinear ordinary differential equations. To acquire the numerical findings from this set of equations, a three‐stage Lobatto IIIa, in‐built MATLAB scheme named, Bvp4c is used. The effects of the dimensionless physical factors on the flow, heat, and concentration profile, as well as on the coefficient of drag force and the rate of thermal and mass transit at the surface, are graphically and numerically depicted. The thermal profile, as well as the magnitude of the coefficient of the drag force and the Sherwood number, is found to be escalated with the Darcy–Forchheimer factor, but the depreciation in the value of temperature gradient at the wall is noticed for the same.

Analysis of Multifactor Influence Model on Energy Dissipation Rate of Rough-Strips Energy Dissipator in the Spillway Bend

The rough-strips energy dissipator (R-SED) is applied to the bottom of the spillway bend and can play the role of energy dissipation and flow stabilization. In this study, based on 18 sets of orthogonal tests and the principle of dimensional analysis, a multifactor influence model of R-SED’s energy dissipation rate was proposed. A dimensionless factor k was introduced, which can reflect the comprehensive characteristics of the geometric dimensions of R-SEDs. The multifactor influence model of the energy dissipation rate considered nine factors, including bend radius of curvature Rc, bend width B, flow velocity of the bend inlet v , R-SED’s average height hL, R-SED’s arrangement angle θ, R-SED’s arrangement spacing ∆L, fluid density ρ, dynamic viscosity coefficient μ, and gravitational acceleration g . The residual sum of squares of the model (RSS) was 6.6% and the correlation coefficient R was 83.2% (>80%), indicating the universality and feasibility of the model. The independent variables of the multifactor model of the energy dissipation rate were ranked according to the Pearson value in descending order: (ΔL/Rc) > (θ) > (B/Rc) > (hL/Rc) > (1/Fr2). This indicates that R-SEDs’ layout parameters showed larger effects on the multifactor model of the energy dissipation rate, compared with the engineering layout parameters of the spillway. The maximum relative error between the predicted value of the multifactor model and the measured value of the validation group was 6.28%, indicating good agreement. In the orthogonal tests, scenario 5 had the highest energy dissipation rate (44.83%) with k = 0.023; scenario 16 had the largest k value (0.043), with an energy dissipation rate of 40.78%. The multifactor influence model of R-SEDs’ energy dissipation rate proposed in this paper was a semi-theoretical and semi-empirical calculation formula, which can provide reference and support for similar practical engineering designs.

Experimental and numerical study on the bubble dynamics and flow field of a swirl flow microbubble generator with baffle internals

Microbubble generators have been widely applied in various fields. This paper explored the bubble generation performance and two-phase flow characteristics of a swirl flow microbubble generator with baffle internals. It showed that the bubble size evolution process in the generator was more sensitive to the liquid flow rate than the gas phase. A semi-empirical expression considering the dimensionless factors of gas-liquid flow rate ratio, Reynolds number, and Weber number predicted the Sauter mean diameter reasonably. Meanwhile, the hydrodynamic simulations were conducted for the generator by using various bubble breakage and aggregation kernels. The Lehr-Liao and Luo & Svendsen-turbulent model combinations were determined to predict the bubble dynamics performance well. The hydrodynamic simulations showed that the larger the liquid flow rate, the higher the turbulent dissipation rate, which resulted in a smaller bubble size. The work is helpful to the design and operation of the swirl flow microbubble generator.

Quality factor for zero-bias conductance peaks in Majorana nanowire

Despite recent experimental progress towards observing large zero-bias conductance peaks (ZBCPs) as signatures of Majorana modes, confusion remains about whether Majorana modes have been observed. This is in part due to the theoretical prediction of fine-tuned trivial (i.e., non-topological) zero-bias peaks that occur because of uncontrolled quantum dots or disorder potentials. While many aspects of the topological phase can be somewhat fine-tuned because the topological phase space is often small, the quantized height of the ZBCP associated with a Majorana mode is known to be robust at sufficiently low temperatures even as the tunnel barrier is pinched off to vanishingly small normal-state conductance. The key shortcoming of the existing experimental works is an acute lack of stability of the putative Majorana mode features, indicating the probable absence of a topological phase, and the current paper suggests specific experimentally accessible measures for a careful quantitative analysis of the measured ZBCP stability. In this paper, we study how the counter-intuitive robustness of the ZBCP height to the tunnel barrier strength can be used to distinguish Majorana modes from non-topological ZBCPs. To this end, we introduce a dimensionless quality factor $F$ to quantify the robustness of the ZBCP height based on the range of normal-state (i.e. above-gap) conductance (which depends crucially on the tunnel barrier height) over which the ZBCP height remains within a pre-specified range of quantization. By computing this quality factor $F$ together with the topological characteristics for a wide range of models and parameters, we find that Majoranas are significantly more robust (i.e., have a higher value of $F$) compared with non-topological ZBCPs in the ideal low-temperature limit. Even at a temperature as high as the experimentally used $20$ mK, we find that we can set a threshold value of $F\sim 2.5$ (for $\epsilon=0.1$) so that ZBCPs associated with a quality factor $F>2.5$ are likely topological and $F\ll 2.5$ are topologically trivial. More precisely, the value of $F$ is operationally related to the degree of separation of the Majorana modes in the system, although $F$ uses only the experimentally measured tunnel conductance properties. Finally, we discuss how the quality factor $F$ measured in a transport setup can help estimate the quality of topological qubits made from Majorana modes. In particular, we show that if the induced gap can be enhanced somehow beyond the currently available $\sim 30$ $\mu$eV in InAs/Al samples, large (small) values of $F$ could easily distinguish between stable topological (unstable trivial) ZBCPs with the quantum dot induced quasi-Majorana bound states occasionally behaving similar to topological Majorana modes in short wires.

Model III fracture analysis of a nanoscale elliptical hole with four cracks in one-dimensional hexagonal piezoelectric quasicrystals

When the defects are at the nanoscale, the failure characteristics of the piezoelectric quasicrystals are different from the macroscale case. The mode-III fracture problem of four nano-cracks emanating from a nanoscale elliptical hole in one-dimensional hexagonal piezoelectric quasicrystals was studied based on the Gurtin-Murdoch surface elasticity model. The analytical solutions of the electro-elastic field intensity factors and the energy release rate at the crack tip were obtained. The present solutions can be reduced to the existing results. The dimensionless electro-elastic field intensity factors show obvious size dependent effect. The influences of the defects size, the multi-cracks interaction, the phonon-phason field coupling coefficient and the applied electro-elastic loads on the fracture characteristics were discussed in detail.

Prediction of Mode I Fracture Toughness of Shale Specimens by Different Fracture Theories Considering Size Effect

In this study, mode I fracture tests on cracked straight-through Brazilian disc (CSTBD) and notched semi-circular bend (NSCB) shale specimens with different sizes were conducted to investigate the difference between maximum tangential stress fracture criterion and the size effect law (SEL) model in predicting apparent fracture toughness (Ka) of shale. In addition, the effects of specimen size and geometry on the Ka and the selection of fracture criterion on the prediction of the inherent fracture toughness (KIc) were also studied. The results show that the Ka increases with the increase of specimen size, and the difference between KIc of shale specimens with different sizes predicted by the fracture process zone length determined by the further improved maximum tangential stress (FIMTS) criterion is the smallest. For the prediction of Ka of NSCB specimen, the results predicted by the FIMTS criterion are the closest to the tested fracture toughness. However, the effect of SEL model applied to the prediction of Ka of NSCB specimens is poor. The effective establishment of SEL model requires high accuracy for test data, especially for the configuration with large variation of the dimensionless stress intensity factor (Y*) with normalized crack length (α).

Experimental study on synergistic effect of exhaust vent layout and exhaust rate on performance of ceiling central smoke extraction in road tunnel fires

In road tunnel fires, exhaust vent layout and smoke exhaust rate are two important parameters that affect the smoke exhaust performance of ceiling central smoke extraction. However, the synergistic effect between the two (cooperation of two factors) has not yet been quantitatively analysed. Reduced-scale (1:20) burning experiments were conducted in this study. Through variations in the vent area, vent width, and exhaust rate, the factors influencing the ventilation system efficiency VSE′ and ventilation system output VSO′ were analysed. It can be seen from the experimental results that for a constant vent width, the exhaust vent area has nearly no effect on VSE′ and VSO′. Furthermore, increasing the smoke exhaust rate can improve VSE′, but will reduce VSO′, whereas increasing the vent width can increase both VSE′ and VSO′. We also considered the effects of heat transfer at the tunnel wall and obtained a normalised VSE′ estimation correlation, which includes the aforementioned dimensionless influencing factors and the factor of distance between the exhaust vent and fire source. After verifying the correlation, we demonstrated its application value as a significantly useful reference for central smoke extraction design.

A 3D Monte Carlo Simulation of Convective Diffusional Deposition of Ultrafine Particles on Fiber Surfaces

The microscale simulation of ultrafine particle transport and deposition in fibrous filtration media was achieved with a novel particle tracking model using a 3D Monte Carlo model. The particle deposition process is governed by the convection–diffusion field. Simulations were performed by considering the fibrous filtration media as an array of identical parallel fibers, in which the flow field was accurately described by an analytical solution. The model of particle movement was described by the random probability distribution characterized by a dimensionless factor, the Peclet number (Pe), based on a convection–diffusive equation of particle transport in fluid. The influence of the particle Peclet number (Pe) on the particle deposition process and the resulting deposition morphology was investigated. The results were analyzed in terms of dust layer growth, particles’ trajectories and dust layer porosity for a vast range of Peclet numbers. The development of distinct deposition morphologies was found by varying the Peclet number (Pe). With a small Peclet number, diffusion dominated deposition and led to the formation of a more open and looser dust layer structure, while with larger Peclet numbers, convection dominated deposition and was found to form compact deposits. According to the change in the location of the packing densities along the dust layer height direction, the dust layer structure could be divided into three typical parts: the substructure, main profile and surface layer. In addition, the deposit morphologies observed for a high Pe were in good agreement with the experimental results found in the literature.

Heat transfer performance by forced convection of microencapsulated phase change material-latent functional thermal fluid flowing in a mini-channels heat sink

Conventional single-phase coolants have not been able to meet the high cooling requirements of electronic devices. Microencapsulated phase change material-latent functional thermal fluid (MPCM-LFTF), a solid–liquid two-phase cooling medium, has the dual advantages of active liquid cooling and passive phase change material cooling. However, it also increases the power consumption in the mini-channels, and the cooling efficiency of MPCM-LFTF in practical applications needs to be further studied. A new MPCM-LFTF was prepared by paraffin melamine resin MPCM and base fluid (absolute ethanol and deionized water) in this work. The heat transfer performance and hydrodynamic properties were investigated using the dimensionless wall temperature and friction factor, respectively. The efficiency factor was introduced to evaluate the cooling efficiency of MPCM-LFTF in mini-channels. The experimental results showed that the addition of MPCM increased the viscosity of MPCM-LFTF, which increased the friction factor. MPCM-LFTF with a mass fraction of 15 % had the best effect of temperature control and reduced the dimensionless wall temperature by 40.5 %. However, considering the characteristics of flow resistance and improved heat transfer, MPCM-LFTF with a mass fraction of 10 % had the highest cooling efficiency and the efficiency factor was 57.0 % higher than that of the base fluid.

Use of centrifugal systems for investigating water flow processes in unsaturated soils

Centrifugal modelling, both physical and numerical, has been used for studying groundwater flow and transport processes in the past. However, there was disagreement in previous studies whether numerical models can be used in simulating centrifugal systems under unsaturated flow condition. In the present study, a numerical model based on Richards’ equation was developed to predict one-dimensional unsaturated flow in centrifugal systems. The validity of the model was tested using data from physical models in four published benchmark problems. The ability of the numerical model to close mass balance was also tested. It was shown that the newly developed numerical model was able to recreate the four benchmark problems quite successfully, indicating that using such a model under unsaturated flow condition is feasible. The mass conservation result shows that the model is more sensitive to spatial grid resolution than to specified temporal step. Therefore, fine spatial discretization is suggested to ensure the simulation quality. Additionally, adaptive temporal time stepping method can be used to improve the computational efficiency. It was found that the dimensionless factors used for scaling physical dimensions by 1/N, seepage velocity by N, and temporal dimension by 1/N2 were useful parameters for scaling centrifugal systems.

Effect of rotational speed and flowrate on the startup characteristics of a pumps as turbine

The startup process of pump as turbine (PAT) is actually unavoidable. In order to reveal the transient behavior of a small centrifugal pump reversing as a turbine during an atypical startup, transient experiments are carried out on PAT test rig in the case of two valve openings and four rotational speeds so as to obtain the evolution characteristic of the external performance parameters over time. Meanwhile, three dimensionless parameters are also employed to deeply reveal the transient characteristics. It is found that the shock phenomena in static pressure are prevalent at the outlet of PAT, and that it tends to lag and weaken with increasing stable rotational speed. All three dimensionless factors have maximum values at the initial stage of PAT startup, whereafter they demonstrate the different evolution characteristics.

Modeling and experimentation for novel aerofoil embedded mesh disk-based partially submerged rotating reactor

A novel aerofoil embedded fiber mesh disk-based rotor has been proposed as an alternative to currently available rotating biological contactors. Specially designed aerofoil structures were incorporated into the rotor to increase its mass transfer performance and liquid hold capacity. The volumetric mass transfer coefficient and liquid hold-up for the novel rotor were determined at the rotational speeds of around 10, 15, 20, 25, 30, and 35 rpm under various submergence levels of 17.4, 21.7, 26.1, 27.8, 30.4, 34.8, 39.1, 43.5, and 50%. A dimensionless correlation for the dynamic liquid hold-up was proposed in terms of the Reynolds number, Froude number, and the submergence ratio. Another dimensionless term Oxygen transfer number (OT number) was proposed to characterize the mass transfer behavior of the reactor. The dependency of OT number was expressed in terms of Peclet number, Froude number, and dimensionless geometrical factor. The volumetric mass transfer coefficient and liquid hold-up were found to be strongly dependent on the rotation speed and submergence level.

An analytical description of the post-buckling behaviour of outstand plates in compression

A theoretical model describing the post-buckling behaviour of elastic outstand plates under uniaxial compression is presented in this study. The derivation is rooted in the Föppl-von Karman equations, which are further simplified by making a number of basic mechanical assumptions about the post-buckling stress field. An approximate solution to the emerging differential equation is obtained, which assumes a polynomial displacement profile in the transverse direction of the plate. This solution agrees eminently well with the results of finite element simulations, both for the case of a geometrically perfect plate and a plate containing an initial imperfection. By combining the obtained post-buckling stress profile with a failure criterion based on von Karman’s effective width concept, a closed-form strength equation for compressed outstand plates is derived, which is seen to be a sole function of the plate slenderness and a dimensionless imperfection factor. Based on this, a design equation is proposed which closely agrees with the available experimental data.

THERMAL PERFORMANCE ASSESSMENT OF WALL ASSEMBLIES: CRITERIA IMPORTANCE THEORY AND AHP APPROACH

The problem of the “best” choice in terms of the ecological, durable, cheap and energy-effective material of envelope construction has been considered in the paper. For the numerical assessment of the thermal performance, the MCDA techniques as Analytical Hierarchy Process (AHP) and Criteria Importance Theory (CIT) were used. There were proposed eight types of wall assemblies from a natural material, namely: Hempcrete, Adobe, Strawbale panel, Earthbag, Cordwood, SIP (plywood+ecofiber), Hempcrete+straw and Compositional building thermo-block. As a objective function for the search of the best alternative the integral index was proposed which consist of thermo-physical and economic criteria. As the thermo-physical criteria component of the index were taken the u-value of the envelope W/m2K, the dimensionless decrement factor of the envelope f and the internal areal heat capacity of the envelope k1, kJ/m2K according to ISO 13786:2017. As economic criteria of the integral index, the authors proposed the cost of the wall material Q, UAH/m2 and the mass of the wall m, kg/m2. The analysis of the conducted research has shown, that from the one hand there is no absolute “leader” in the ranking of the wall assemblies according to the proposed criteria and MCDA technique, but from the other hand by comparison of the results, there were revealed that the top three alternatives in both AHP and CIT technique are walls of “B”, “D” and “E” type with different point order, achieved in each MCDA calculation technique.

An analytical model for diffusion of chemicals under a thermal gradient in finite clayey soil

An analytical solution to non-isothermal diffusion of chemicals in finite porous medium with different combinations of boundary and initial conditions is presented. The average degree of diffusion was proposed to assess the contaminant removal efficiency from polluted soil with different initial contaminant concentration distribution conditions considering chemical and thermal diffusion. The dimensionless time factor for the average degree of diffusion U = 90% can be decreased by a factor of 8.4 in the case with rectangular initial solute concentration distribution considering thermal diffusion. An application of the model to study the effects of initial solute concentration distribution and adsorption on the average degree of diffusion show that both the adsorption performance of clayey soil to the contaminant and the initial solute concentration distribution have a significant effect on the average degree of diffusion. In the cases with rectangular and inverse triangular initial solute concentration distributions, when U = 50%, the times increase by factors of 2.2 and 5.3, respectively, compared to the case with triangular initial solute concentration distribution. An application of the model to study the effects of temperature on the average degree of diffusion of contaminant in polluted soil show that the temperature difference has a significant effect to promote the contaminant transport in clayey soil by increasing both of the thermal diffusion and chemical diffusion effect. It may be an effective method to remove contaminant from polluted soil by thermal diffusion.

Closed-form solution of oscillating Maxwell nano-fluid with heat and mass transfer

The primary goal of this article is to analyze the oscillating behavior of Maxwell Nano-fluid with regard to heat and mass transfer. Due to high thermal conductivity of engine oil is taken as a base fluid and graphene Nano-particles are introduced in it. Coupled partial differential equations are used to model the governing equations. To evaluate the given differential equations, certain dimensionless factors and Laplace transformations are used. The analytical solution is obtained for temperature, concentration and velocity. The temperature and concentration gradient are also finds to analyze the rate of heat and mass transfer. As a special case, the solution for Newtonian fluid is discussed. Finally, the behaviors of various physical factors are studied graphically for both sine and cosine oscillation and give physical meanings to the parameters.

An enriched improved complex variable element-free Galerkin method for efficient fracture analysis of orthotropic materials

The fracture problem of orthotropic materials has been widely concerned by researchers in the fields of mechanics and engineering. The meshless method using nodes to discrete the problem domain is an effective way to analyze cracked structures. In this paper, an enriched improved complex variable moving least squares (EICVMLS) approximation, in which a group of intrinsic enrichments is introduced into the conventional ICVMLS adopting a well-defined weighted complex variable error norm, is proposed for capturing the crack-tip fields in orthotropic media accurately. Then, an enriched improved complex variable element-free Galerkin (EICVEFG) method is developed to simulate fracture behavior in orthotropic media. The visibility criterion is used to model the discontinuity behavior around cracks and the M−integral is considered to evaluate stress intensity factor (SIF). The stress field and the displacement field at the crack tip, the SIF for different crack inclinations, and different directions of orthotropy axes are investigated to verify the validity of the proposed method. In addition, the effects of linear basis functions and enriched basis functions on the results are compared in this study. The numerical results reveal that the established EICVEFG approach can achieve higher accuracy than the extended finite element method (XFEM) and traditional meshless methods such as the element-free Galerkin (EFG) method and the meshless finite volume (MFV) method. Similarly, the EICVEFG method has been proved to offer a higher convergence rate by parameter studies (including dimensionless factor dmax, integral size, and the number of integral cells in M−integral).

Forecasting of saturated boiling heat transfer inside smooth helically coiled tubes using conventional and machine learning techniques

This study concerns to model the flow boiling heat transfer coefficient (HTC) in smooth helically coiled tubes. A dataset including 1035 samples was collected from 13 independent studies, enveloping a broad range of geometrical and operating conditions. The predictive capability of the earlier models was assessed for straight and coiled tubes by the analyzed database that they were not precise enough. Accordingly, a new empirical model based on the least square fitting method (LSFM) was constructed using seven input effective dimensionless factors. It was found that LSFM was not able to describe the complex and nonlinear nature of HTC in smooth helically coiled tubes. Furthermore, the intelligent method of genetic programming (GP) was utilized to obtain more accurate explicit correlation for HTC, which produced an acceptable average absolute relative error (AARE) of 17.35%. Finally, the machine learning approaches of multilayer perceptron (MLP), Gaussian process regression (GPR), radial basis function (RBF) was also implemented to model HTC in smooth coiled tubes. Although all intelligent based models provided excellent results, the GPR model outperformed the others with an average absolute relative error (AARE) of 5.93% for the tested dataset. In addition to the proposed models’ performance, the most influential factors in controlling the boiling HTC in coiled tubes were also detected.

Pullout capacity of circular multi-plate vertical anchors in sand – An experimental study

A multi-plate vertical anchor is a structural member designed to resist the horizontal pullout forces to provide stability to retaining structures inland and onshore. The tensile load of a structure is resisted by the multi-plate anchors using a number of plates connected axially along the central shaft. For a given embedment depth and placement ratio considered, the multi-plate vertical anchors generate higher pullout capacity than the single-plate vertical anchors. This paper presents a detailed experimental study to estimate the ultimate pullout capacity of circular multi-plate vertical anchors embedded in the sand. The plate anchors are placed at varying horizontal distances from the sidewall of the test tank. The pullout capacity of the single-plate vertical anchors was compared with the existing studies. The dimensionless breakout factors show that the multi-plate anchor can efficiently replace the existing single-plate anchors. The paper briefly discusses the scale effect, the effect of spacing, and the effect of anchors' placement ratio on pullout capacity. Results show an increase in pullout capacity of double-plate and triple-plate vertical anchors with an increase in embedment ratio and placement ratio. The results also show an increase in the breakout factor of multi-plate anchors with increased spacing between the plates.