Dimensionless Parameters Research Articles

Optimization Analysis of the Arrangement of the Submerged Floating Tunnel Subjected to Waves

The motion responses, mooring tensions, and submergence depth are the dominant factors for the arrangement of the Submerged Floating Tunnel (SFT) subjected to waves. Generally, the maximum values of motion responses, mooring tensions, and absolute submergence depth are mainly focused on. In the present study, experiments are implemented to measure the motion responses and mooring tensions of the SFT with different mooring patterns and submergence depths under waves with different characteristic wave heights and periods. In order to evaluate the arrangement of the SFT more effectively and comprehensively, besides the maximum values, several new characteristic parameters are introduced. Such parameters account for the motion responses in the frequency domain, the uniformity of the tension distribution, the length of time during which the cable reaches a relaxed condition during wave action, the KC number, the dimensionless period, the wave height, and the submergence depth. The results from the optimization analysis show the following: according to the characteristic values of motion responses and mooring tensions, the pattern of diagonal cables is better than that of diagonal cables + vertical cables; and within the range of the present experiments, there are optimal dimensionless parameters—the dimensionless submergence depth d0/LP ≥ 0.15, the KC number ≤ 0.8, or the dimensionless wave height Hs/d0 ≤ 0.10—for the condition of which the dynamic responses and mooring tensions vary slightly.

Particle fracture regimes from impact simulations.

We introduce an approach to particle breakage, wherein the particle is modeled as an aggregate of polyhedral cells with their common surfaces governed by the Griffith criterion of fracture. This model is implemented within a discrete element code to simulate and analyze the breakage behavior of a single particle impacting a rigid plane. We find that fracture dynamics involves three distinct regimes as a function of the normalized impact energy ω. At low values of ω, the particle undergoes elastic rebound and no cracks occur inside the particle. In the intermediate range, the particle is damaged by nucleation and propagation of cracks, and the effective restitution coefficient declines without breakup of the particle. Finally, for values of ω beyond a well-defined threshold, the particle breaks into fragments and the restitution coefficient increases with ω due to kinetic energy carried away by the fragments. We show that particle damage, restitution coefficient, and fracture efficiency (the amount of energy input consumed for particle fracture) collapse well as a function of dimensionless scaling parameters. Our data are also sufficiently accurate to scale fragment size and shape distributions. It is found that fragment masses (volumes) follow a power-law distribution with an exponent decreasing with fracture energy. Interestingly, the average elongation and flatness of fragments are very close to those observed in experiments and lunar samples at the optimal fracture efficiency.

A supervised approach for improving the dimensionless frequency estimation for time‐domain simulations of building structures on embedded foundations

AbstractThe analysis of soil–structure interaction (SSI) problems has been established successfully in recent decades. In particular, the solution in the frequency domain provides an exact and efficient method for computing the response of the coupled system. Despite this, the state of practice as a first attempt to incentivize time domain analyses compatible with standard finite element packages introduces the so‐called dimensionless flexible‐base frequency. This frequency, which depends solely on the structure‐to‐soil‐period ratio, allows transforming the frequency domain analyses into time domain analyses using frequency‐independent soil impedance values. However, if such frequency exists for the combined system, it must depend on several physical variables. In this work, we propose a supervised approach to obtain the flexible‐base dimensionless frequency at which the frequency‐independent soil impedance should be used. The analysis is carried out using five dimensionless parameters, and the importance of each one to the estimation of the dimensionless flexible‐base frequency is investigated. We use an inverse problem based on ensemble Kalman inversion (EnKI) to obtain the optimal frequency of the interaction. The data obtained are then employed in a machine‐learning framework to map a set of dimensionless parameters to such a frequency. The generated mapping is finally verified, and a significant improvement in time‐domain simulations is shown compared to the state of practice.

Analysis of ECCC cross-weld creep test data on grade 92 steel

ABSTRACT The UK High Temperature Power Plant Forum have completed a long term cross-weld creep test programme on a Grade 92 steel pipe. This paper describes an analysis of the creep test data. The weld strength factor (WSF), i.e. the ratio of cross-weld strength to base material strength for a specified rupture time and temperature, is shown to be a unique function of a dimensionless parameter S, the creep test stress divided by ultimate tensile strength at the test temperature. The key practical finding is that, since a single universal cross-weld creep life parametric is applicable to all temperatures, long-term behaviour at service temperatures should reliably be predictable from short-term tests at accelerated temperatures.

3D numerical simulations of mixed convective heat transfer and correlation development for a thermal manikin head

The head represents 10 % of the body's total surface area. Unprotected, it accounts for a significant portion of overall heat loss when exposed to cold conditions. This study was motivated by a need to clarify how the human head interacts with its environment in terms of heat exchange. Accurate estimations of heat transfer coefficients on the human head are essential for conducting thermal comfort and safety analyses in buildings. In this study, a thermal head resembling a real male human head is utilized to investigate heat transfer between the body and the surrounding environment. A three-dimensional computational fluid dynamics (CFD) model is proposed to simulate steady-state dry heat loss from the human head within a chamber. This model provides predictions for heat flux, temperature, and velocity distribution surrounding the head. A straightforward correlation, derived from numerical and experimental findings, is introduced to forecast the average Nusselt number for the head under combined natural and forced convection. This correlation, relying on dimensionless parameters (Grashof, Reynolds, and Prandtl numbers), offers enhanced accuracy, simplicity, and fewer terms. The predicted average Nusselt numbers from the proposed correlation for mixed convection closely match CFD and experimental results, with relative percentage differences within ±2 %, signifying excellent accuracy across a broader range of flow conditions, including temperature differences and air velocities. Additionally, the study explores the impact of head diameter on overall heat transfer.

Experimental Study on Two-Phase Countercurrent Flow Limitation in Horizontal Circular Pipes

The two-phase countercurrent flow limitation (CCFL) in horizontal channels is important in relation to nuclear reactor safety. In this study, we aim to investigate the CCFL characteristics and the flow behaviors in horizontal circular pipes with small diameters. The effects of pipe diameter and the water head in the upper plenum on CCFL characteristics are experimentally studied. An image-processing technique and statistical treatments are implemented to analyze the horizontal countercurrent flow. The results show that the CCFL characteristics for the horizontal circular pipes with small diameters can be well correlated using the dimensionless parameters, which are based on adding fluid viscosity to the Wallis parameters. The CCFL characteristics are significantly affected by the pipe diameter and are slightly affected by the water head above the horizontal pipe. The gas–liquid interface fluctuates with certain periods, and flow pattern transitions happen in the horizontal air–water countercurrent flow. As the air flow rate increases, the occurrence location of the liquid slug appears to shift towards the water entrance. In addition, the further away from the water entrance, the lower the average of liquid holdup.

R2 corrections on screening length

We study finite-coupling corrections on the screening length of a heavy quark-antiquark (QQ¯) pair moving in strongly coupled Super Yang-Mills plasma. We performed the analysis by computing the Wilson loop in a general AdS5 space with curvature-squared (R2) corrections and the Gauss-Bonnet (GB) background, respectively. For the general case, it is shown that the screening length with R2 corrections can be larger or smaller than that without R2 corrections depending on the correction coefficients, and these effects are more pronounced for the perpendicular case compared with parallel case. For the GB case, it turns out that increasing λGB (a dimensionless parameter in GB gravity) leads to decreasing the screening length thus reducing the binding energy of QQ¯ pair. In addition, we discuss how the screening length changes with the ratio of shear viscosity to entropy density at strong coupling under GB corrections.

Heat transfer analysis of subcooled flow boiling in copper foam helical coiled heat exchanger – A pore-scale numerical study

High performance thermal energy systems are crucial in fulfilling the growing demand of thermal energy. Consequently, numerous heat transfer enhancements have been proposed. Some of the promising methods are boiling flow heat transfer, helical coiled tube and metal foam insert. Although the performance of each strategy has been extensively studied, based on our literature review, the effectiveness of combining these strategies has not been investigated. This missing information may impede further development of efficient heat transfer systems. This study is therefore performed to investigate subcooled flow boiling heat transfer in helical tube with copper foam insert. A high-resolution three-dimensional pore scale model that considers the shape, porosity and pore density of the metal foam is developed and validated against the published experimental results. Using the model, the effect of inlet temperature, mass flux, wall heat flux, porosity, pore density and half-filled metal foam are studied. The results suggest that operating parameters have mild effects on the heat transfer performance. In contrast, porosity and pore density show significant influence in heat transfer coefficient and pressure drop. It has also been found that total heat transfer surface area and base area are better in characterizing heat transfer in pore-scale level than porosity and pore density at pore-scale level. Moreover, implementing metal foam at outer half of the tube is observed to offer slightly better heat transfer than implementing it at the inner side by around 4.8%. Overall, this study indicates that helical metal foam tubes offer the best performance at mass flux of 200 kg/m2∙s with performance index of 0.72, while straight tubes with 0.90 porosity has the highest performance index of 0.66. Empirical correlations to relate dimensionless parameters to the Nusselt number and friction factor is generated. Finally, the model developed in this study can serve to provide guidelines for the upcoming studies in boiling in metal foam structure and assist in designing metal foam heat exchangers.

Experimental studies on the effect of Al2O3 + water nanofluid concentrations on dimensionless heat transfer parameters in a cleanroom air handling unit

Nanofluid, a colloidal suspension of nonmetallic or metallic nanoparticles into conventional base fluid and used for heat transfer characteristics enhancement for many industrial applications. Cleanrooms are essential at various industries for controlling airborne contamination and environmental parameters. In this article, heat transfer properties of nanofluid (Al2O3 + water) at various nanoparticle concentrations (1%, 2%, and 3%) on a prototype cleanroom air handling chiller unit was investigated experimentally in laminar flow zone. Thermal conductivity ratio, Nusselt number, Peclet number, and pressure drop were obtained for above nanoparticle concentrations. Experimental investigations indicate the heat transfer properties improvement in a prototype cleanroom air handling chiller unit by using nanoparticle at base fluid. Experimental investigation on varying Al2O3 + water nanofluid concentrations in a cleanroom air handling chiller unit heat exchanger revealed a notable increase in heat transfer by reducing nanoparticle size from 50 to 10 nm and increasing concentration from 1% to 3% volume, resulting in a 17.70% rise in thermal conductivity ratio and a significant 9.23% increase in Nusselt number at higher Peclet numbers. However, this improvement in heat transfer was accompanied by a substantial 72.5% increase in pressure drops, particularly with increased Reynolds number and particle concentration. Manipulating nanoparticle characteristics resulted in substantial improvements in Nusselt number across a wide range of Reynolds numbers, with smaller particle sizes and higher volume concentrations yielding more significant heat transfer improvements. The novelty of this research lies in its investigation of the influence of variable Al2O3 + water nanofluid concentrations, encompassing different nanoparticle sizes, and volume concentrations, on dimensionless heat transfer parameters within a cleanroom air handling unit, offering valuable insights into optimizing heat transfer efficiency in a controlled and critical environment, addressing a significant research gap in the field.

Study on the Ionic Transport Properties of 3D Printed Concrete

Three-dimensional printed concrete (3DPC) is an anisotropic heterogeneous material composed of a concrete matrix and the interfaces between layers and filaments that form during printing. The overall ion transport properties can be characterized by the equivalent diffusion coefficient. This paper first establishes a theoretical model to calculate the equivalent diffusion coefficient of 3DPC. Verification through numerical calculations shows that this theoretical model is highly precise. Based on this, the model was used to analyze the effects of dimensionless interface parameters on the equivalent diffusion coefficients in different directions of 3DPC. Finally, the dynamic ionic transport properties of 3DPC were investigated through finite element numerical simulation. The results of the dynamic study indicate that interfaces have a significant impact on the ion distribution and its evolution within 3DPC. The product of the interface diffusion coefficient and interface size can represent the ionic transport capacity of an interface. The stronger the ionic transport capacity of an interface, the higher the ion concentration at that interface. Due to the “drainage” effect of lateral interfaces, the ion concentration in the middle of 3DPC with a smaller equivalent diffusion coefficient is higher than that in 3DPC with a larger equivalent diffusion coefficient.

Hybrid Nanofluids Flow over a Vertical Cylinder with Heat Source/Sink and Prescribed Surface Heat Flux

This work presents the steady mixed convection in Al2O3-Cu/water hybrid nanofluids along a vertically stretching/shrinking cylinder with the prescribed surface heat flux and the effects of heat source/sink. The governing hybrid nanofluids model was simplified using a similarity transformation. The bvp4c solver in MATLAB software is used to solve the hybrid nanofluids flow problem numerically. It is observed that two outcomes are feasible for the assisting and opposing flow regions as well as stretching and shrinking cases . Besides that, the effects of the dimensionless parameters are analyzed graphically and tabularly. In particular, the critical point is reduced by 3% when the curvature parameter goes from 0 to 0.1 and from 0.1 to 0.2 when the cylinder is stretched. This means that the higher curvature parameter could delay the process of separating the boundary layer. It is noted that the positive heat source will decrease the fluid motions and reduce the shear stress on the surface. Moreover, Al2O3-Cu/water hybrid nanofluids have better performance in heat transfer and velocity of fluid flow than Al2O3/water nanofluids.

Resonant detectors of gravitational wave in the linear and quadratic generalized uncertainty principle framework

In this work, we consider a resonant bar detector of gravitational waves in the generalized uncertainty principle (GUP) framework with linear and quadratic momentum uncertainties. The phonon modes in these detectors vibrate due to the interaction with the incoming gravitational wave. In this uncertainty principle framework, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors. We observe that the energy eigenstates and the eigenvalues get modified by the GUP parameters. We also observe non-vanishing transition probabilities between two adjacent energy levels due to the existence of the linear order momentum correction in the generalized uncertainty relation which was not present in the quadratic GUP analysis (Class Quantum Gravity 37:195006, 2020). We finally obtain bounds on the dimensionless GUP parameters using the form of the transition rates obtained during this analysis.

Exploring the nonlinear behavior of flow through cracked concrete by water permeability test

This study investigates the nonlinear behavior of flow passing through 28 crack topographies in concrete at various pressure gradients using water permeability test. Artificial cracks were generated and quantified by point-cloud matching technique. Results indicate Darcy's law becomes biased for calculating an apparent transmissivity of cracked concrete at a high Reynolds number. As an alternative, Forchheimer's parabolic equation is employed to model the flow rates at different pressure gradients, constructing an equivalent energy conversion model to calculate inertial and viscous pressure gradients and determine intrinsic transmissivity. A numerical model is proposed in which transport efficiency is represented as a function of dimensionless parameter J of pressure gradient. The model is validated by experimental data and further used to explore the onset of nonlinear flow. It is observed that the flow exhibits a significant nonlinear behavior once the transport efficiency reaches 0.9305. This threshold is utilized to delimit the flow regimes and construct a Moody chart for permeability assessment of concrete in practice. It provides an effective way to characterize the behaviors of water flow in concrete and evaluate its transport properties.

Experimental study on flame interaction, gas temperature distribution, and radiative heat flux from two rectangular burning propane sources

This work experimentally investigates the flame interaction (flame merging and flame height), gas temperature distribution, and radiative heat flux from two rectangular propane burners by varying total heat release rate (80–360 kW) and burner spacing (0–1.28 m). The results show that the dominant mechanism of air entrainment rate changes from spacing to heat release rate with increasing spacing, making two flames from fully merging to non-merging. A method for predicting the flame height is proposed in terms of air entrainment mechanism, which is proportional to the 2/3 power of the group dimensionless parameter (Q˙total*,Q˙total*=Q˙totalρ0CpT0g1/2LP3/2). With the decrease of spacing, gas temperature in the additional region is distributed in an inverted U-shaped manner in the horizontal direction, reaching its extreme value at the center of the two burners. The vertical gas temperature can be employed to estimate the critical flame merging, which depends on the dimensionless parameters of Q˙total* and S/W. When S/W < 51 Q˙total*, two flames are merged; otherwise, the two flames are separated. For two rectangular fires with different burner spacings, the radiative heat flux received by the external targets is accurately predicted using the Richardson Number (Rix, Rix=gβ(Tf−T0)xU2).

Experimental Study on Double Jet Flames with Different Nozzle Diameters

Double jet flames are commonly observed in the energy industry. A facility consisting of a double jet flames apparatus, was designed to experimentally simulate the interaction of double jet fires with different spaces and nozzle diameters. It has been found that the exit momentum, nozzle diameters and nozzle spacing significantly affect the flame behavior. The experimental results show that the flame merging probability (Pm) of double jet fires with different nozzle diameters can be fitted with dimensionless parameters that couple the Froude number(Fr) and the distance between fire sources. Additionally, it has been observed that the difference in height between the two flames can be used as a parameter to determine the correlation between flame height and the distance to the nozzle center.

Weakly nonlinear models of stochastic wave propagation in two-layer hydrodynamic systems

The paper discusses three-dimensional models of the propagation of stochastic internal waves in hydrodynamic systems: ’half-space - half-space’, ’half-space - layer with rigid lid’, and ’layer with solid bottom - layer with rigid lid’. In constructing the models, the layers are considered to be ideal fluids separated by a contact surface. The main objective of the modeling is to obtain a dynamic equation for the stochastic amplitude of surface waves. A comparative analysis of the obtained results has been conducted. In order to control the contribution of nonlinear terms, a dimensionless non-numerical parameter has been introduced. The models are distinguished by boundary conditions that determine the general form of solutions. As a result, a dynamic equation for the stochastic amplitude of internal waves has been derived. After ensemble averaging of the amplitudes, the dynamic equation is formulated in integral form using Fourier-Stieltjes integrals. The dynamic equation reveals two-wave and three-wave interactions, as well as the contribution of dispersion to wave dynamics. An investigation of the boundary case of the transition of internal waves in the ’half-space - half-space’ system to surface waves in the absence of an upper liquid layer confirms the validity of the results.

Unsteady flow of bubble liquid in hydraulic systems of aircraft and helicopters

The subject of this work is the phenomenon of a water hammer in a liquid that contains a small volume of gas bubbles. Historically, this phenomenon began to be studied as the dynamics of gas bubbles (Rayleigh-Pleset equation). Today, thanks to progress in computer technology, this phenomenon is studied at the level of bubble deformation during hydraulic shock. Another approach is to consider the dynamics of a multiphase (two-phase) medium in the form of a bubbly liquid. After several assumptions, the main one being a relatively small gas content in the liquid, the model consists of two differential equations with respect to the shock wave propagation speed and the resulting pressure perturbations. The specified system of equations differs from the corresponding classical water hammer equations: they consider the convection of the velocity field. In addition, the friction of the liquid against the wall according to the Weisbach-Darcy model is considered. Because of the small content of gas bubbles, the Weissbach-Darcy friction is approximated in the same way as in a homogeneous liquid, i.e., in a certain sense, greater than the real friction. Maybe that is why more or less physical results are obtained only for small values of the dimensionless parameter responsible for the friction of the liquid against the wall. It concerns the non-contradiction of the assumptions and the results obtained on their basis. Thus, in the front region of the shock pulse, where the pressure increases, the radial velocity of the bubbles is negative; however, for relatively large values of the friction parameter, the maximum pressure disturbance moves from the center of the shock pulse. This contradicts the assumption about compression: after passing the maximum pressure, gas bubbles expand due to a decrease in pressure. The graphical dependence obtained in this study are compared with the results related to a homogeneous liquid. They agree, but the shock pulse in a bubbly liquid is not as concentrated in space as that in a homogeneous liquid. Its length is 10-12 times greater than the corresponding value in a homogeneous liquid. Research methods are purely theoretical. The well-known bubble liquid model is used as a single-speed model continuum. Differential equations are solved analytically, approximately (series expansion), and numerically. In addition, the original approach of obtaining an analytical solution of an autonomous system is used-finding the function of pressure disturbances from the velocity of propagation of the shock pulse (and vice versa). Conclusions. A simple one-dimensional hydraulic model of shock wave (impulse) propagation in a bubbly liquid is proposed. In contrast to classical ideas (solutions) about a water hammer, which consists of two waves of opposite directions of propagation, a shock pulse is a region of pressure disturbances in which the speed of motion of fluid particles is also variable – from the maximum value to almost zero.

Safe Operating Conditions of isoperiodic Homogeneous Semi-Batch Reaction Based on Parameter Uncertainties Analysis

Proper operating conditions have a significant impact on the process state of semi-batch reaction. However, various error and bias lead to the uncertainties of parameter, which affect process safety of the semi-batch reaction. In this work, the effect of dimensionless parameters dimensionless adiabatic temperature rise (), Westerterp number (Wt), , dimensionless activation energy (γ), volumetric heat capacity ratio (RH) and relative volume increase (ε) on the temperature of the isoperiodic homogeneous semi-batch reaction are investigated by local sensitivity analysis. The sensitivity of the dimensionless maximum temperature to global parameters is analyzed using the scatter plot method based on Monte-Carlo sampling. Parameter sensitivity results are further quantitatively calculated by the eFAST method. The results indicate that there is a strong linear relationship between the maximum reaction temperature and △τad,0, which exhibits the highest sensitivity index compared to the other parameters. The safety boundary diagram and adiabatic temperature diagram are constructed by considering parameter uncertainty and the effect of parameter uncertainty on the critical criteria is analyzed.

Development of a New Correlation for Saturated Flow Boiling Heat Transfer in a Helically Coiled Tube

We have developed a heat transfer correlation for saturated flow boiling of water in a helically coiled tube. Initially, we collected experimental data encompassing a broad spectrum of thermal-hydraulic conditions and geometric configurations, and examined the influences of key dimensionless parameters, such as the convection number and the boiling number. The data analysis showed that the observed trend aligns with previous studies on boiling heat transfer within a straight tube. Also, we investigated the influence of centrifugal force acting on the fluid in a helically coiled tube and confirmed its significant impact on boiling heat transfer. Based on our findings, we propose a new heat transfer correlation that incorporates a dimensionless number of the centrifugal force divided by gravitational force. The basic structure of this correlation was adapted from the Kandlikar correlation for saturated flow boiling. The new correlation demonstrated enhanced accuracy compared to existing ones. Additionally, we showed its applicability to boiling heat transfer within a straight tube as well.

Numerical investigation in effects of refrigerants’ thermodynamic properties on performance of supersonic ejector

ABSTRACT Using zeotropic mixtures with unique temperature glide characteristics as the working medium in heat-driven ejector refrigeration system will potentially reduce the irreversible losses in heat exchange process. However, the intrinsic link between the pure/mixture refrigerants’ thermophysical properties and the entrainment performance of supersonic ejector has not yet been elucidated. In this study, a novel ejector CFD model is established by coupling the real-gas thermodynamic equation and species transport equation, then the relationships between thermophysical properties of pure/mixture refrigerants and ejector’s dimensionless operational parameters were thoroughly investigated. The results indicated that the ejector expansion ratio rises as primary flow inlet temperature or refrigerant’s normal boiling point increases, while the dimensionless parameters of primary nozzle are relatively insensitive to the variation of primary flow inlet temperature and refrigerant’s boiling point, resulted in changes of supersonic jet expansion behaviour. Moreover, the specific volume and adiabatic index change characteristics resulted in minor fluctuations of primary nozzle’s dimensionless parameters. When the bubble point temperature is fixed at 30℃ in the condenser, the saturated vapor/liquid phase pressure glide characteristics of R600a/R1234ze mixture may lead to an increasement of ejector’s compression ratio.