Mechanical Energy Balance Research Articles

Analytical model of small- and large-amplitude drop oscillation dynamics

The mechanical energy balance over a bulk of fluid that oscillates between prolate and oblate shapes in another immiscible fluid is solved using a general spheroidal coordinate system. The drop shape is described by a unique parameter that may continuously vary over the time, making the implementation of the model rather simple. Potential flow is assumed, and inertial and viscous effects are accounted for in both the inner and outer flow fields. The characteristics of drop oscillation for small and large amplitudes are studied, and the results are compared with theoretical, experimental, and numerical data from the open literature. The rather satisfactory validation of the model over a large variety of operating conditions allows its extension to include other physical phenomenon, like evaporation and its effect on drop oscillation.

Energy Dissipation during Wenzel Wetting via Roughness Scale Interface Dynamics.

A numerical method is proposed to simulate the roughness scale interface dynamics of a slow-moving fluid interface as it advances over a chemically homogeneous rough surface. Analysis of the governing augmented Navier-Stokes and Young's boundary condition equations shows how the local interface behavior can be represented via a series of incrementally advanced equilibrium interfacial morphologies. Combined with a roughness scale mechanical energy balance [Harvie, D. J. E. Contact-angle hysteresis on rough surfaces: mechanical energy balance framework. J. Fluid Mech. 2024, 986, A17], the simulations are used to calculate the energy dissipation associated with a surface decorated with a periodic array of round-edge square pillars. This dissipation is used to predict static contact angle hysteresis (CAH) from knowledge of just the surface roughness topography and equilibrium contact angle. We show that the energy dissipated varies approximately as ϕln ϕ (with ϕ being the area fraction), becoming zero as ϕ → 0. The CAH predicted by our method is in good agreement with the experimental results of Forsberg et al. [Forsberg, P. S.; Priest, C.; Brinkmann, M.; Sedev, R.; Ralston, J. Contact line pinning on microstructured surfaces for liquids in the Wenzel state. Langmuir 2010, 26, 860-865], thereby demonstrating that our numerical method of simulating interfacial dynamics adequately captures the real interface motion, as well as illustrating how far-field contact angle and energy dissipation approaches are consistent for this surface. We also compute CAH for an interface moving at 45° to the surface periodicity direction to show that the experimental measurements are bracketed by the 0° and 45° advance direction results. The proposed method opens up the field to quantitative analysis, surface functionalization, and design for different specific applications.

Contact-angle hysteresis on rough surfaces: mechanical energy balance framework

Using as a starting point conservation of momentum, a multiphase mechanical energy balance equation is derived that accounts for multiple material phases and interfaces present within a moving control volume. This balance is applied to a control volume that is anchored to a three-phase contact line as it advances continuously over the surface of a rough and chemically homogeneous and inert solid. Using semi-quantitative models for the material behaviour occurring within the control volume, an order of magnitude analysis is performed to neglect insignificant terms, producing an equation for predicting contact-angle hysteresis from a knowledge of the interface dynamics occurring around the three-phase contact line. It is shown that the viscous energy dissipation that occurs during the ‘stick–slip’ motion of the three-phase contact line, being the cause of contact-angle hysteresis on rough surfaces, can be calculated from changes in intermediate equilibrium interface states. The balance is applied to the Wenzel, Cassie–Baxter and Fakir (super-hydrophobic) wetting states, showing for the Fakir case that significant dissipation occurs during both interface advance and recede, and relating these dissipations to interfacial area changes that occur around the ‘stick–slip’ events.

Viscoelastic flow with slip in a hyperbolic channel

We study theoretically the steady viscoelastic flow in confined and symmetric hyperbolic channels considering slip along the walls. Under the lubrication approximation and a variety of constitutive models, a high-order perturbation solution with respect to the Deborah number is calculated. The solution for all the field variables (velocity, pressure, and extra-stress) is found analytically up to eighth order and is used along with proper acceleration techniques to achieve convergence up to order one Deborah number. We reveal that even in the presence of slip, the pressure drop decreases monotonically with increasing the fluid elasticity. We evaluate the influence of slip in terms arising from two different decompositions of the pressure drop obtained with the aid of the total force balance and the mechanical energy balance of the flow system. In contrast to the nonslip Newtonian flow, our analysis also showed that the fluid slip along the walls introduces variations in the strain rate at the midplane with the distance from the inlet. However, these are small, and an effective strain rate can be well-represented using a previously developed formula [Housiadas, K. D., and A. N. Beris, Phys. Fluids 36(2), 021702 (2024)]. We also show that when the solution for the midplane velocity is used in the general formula for the Trouton ratio, instead of the Newtonian lubrication solution, there are no appreciable changes, thus confirming the validity and accuracy of our previously reported results [Housiadas, K. D., and A. N. Beris, J. Rheol. 68(3), 327–339 (2024)].

Role of induced elastic deformations at the Mg/MgH2 transformation

The kinetics of magnesium hydride formation depends on many factors such as thermodynamic conditions, the presence/absence of additives and the mechanical treatments applied to the starting material. As a result, the impact on the reaction of the material is complex. Additionally, during repeated hydrogenation/dehydrogenation cycles, the microstructure of the material becomes significantly different from the original one. In such case, it is not so simple to order the relative importance of the different experimental contributions. In fact limited research efforts have been devoted to the impact of elastic deformation and its direct consequences on the hydride nucleation process. This motivates the present theoretical analysis of the mechanical energy balance between the Mg and MgH2 entities. Here the formation and interaction of a hydride nucleus with structural defects as a pore or a free surface is carried out in the Mg-MgH2 system.The present work evidences that calculation makes it possible to underline and unequivocally analyze the importance of a single parameter among a set of multiple factors that potentially have an impact on the kinetic processes. It is demonstrated here that due solely to the change in volume during hydride nucleation, conditions develops in the magnesium matrix for predominant release of hydride onto free surfaces, including pores.The calculation of the energy balance made it possible to classify the local impact on the nuclei for different typical configurations such as the vicinity of a free surface, a boundary and the vicinity of low rigidity defects (e.g. pores, vacancies, etc.). Hydride formation near a surface (external or internal, a twin plane or a grain boundary, etc.) results in a reduction in mechanical energy terms, which favors the easy nucleation step in magnesium. Nucleation occurs primarily on free surfaces rather than in bulk.

Linear instability and weakly nonlinear effects in eastward dipoles

The linear instability and weakly nonlinear dynamics of eastward-propagating, steady-state Larichev–Reznik vortex dipoles are explored in terms of two-dimensional normal-mode analysis. To extract the fastest growing normal modes, we apply both breeding methodology based on solving the initial-value problem, as well as a direct-solution approach through the full-spectrum eigenproblem involving large matrices. We find that the amplification rate of dipole instability decreases with respect to increase in dipole intensity. In our study, both approaches yield consistent results and are systematically compared to provide guidance for further studies of vortex structures.We consider nonlinear self-interaction of the fastest growing mode, along with the induced eddy fluxes, their divergence and mechanical energy balance. Through this analysis, we find that the unstable mode leads to weakening of the dipole by extracting its energy and exchanging potential vorticity content in the down-gradient sense, thus, providing a nonlinear physical mechanism for the dipole destruction. In particular, we highlight the fundamental importance of the west-east asymmetry of the normal mode for destruction to be realized. In summary, we consider this work to be a foundational demonstration of useful methodology for future studies of dynamics and stability of isolated vortices without simplifying spatial symmetries, such as ubiquitous vortices in geophysical fluids.

Duct flow with leakage

The effect of wall leakage on the traditional duct flow equations based of the balance of mass, momentum and mechanical energy applied on a duct section is considered. Application of the momentum balance produces a Bernoulli equation type form, where the multiplier 1/2 in the dynamic pressure is however replaced by the value 1. Some relevant literature references are discussed. As an application, a nozzle duct flow problem is treated.

On the generalized Bézier-based integration approach for co-simulation applications

This paper investigates the efficiency of a recently developed numerical approach for the integration of the dynamics of co-simulation subsystems. In this regard, a robust Bézier-based multi-step integration approach is implemented in the subsystem solvers instead of conventional approaches, like the Euler method. Although such simplistic integration formulas proved to be accurate and easy to incorporate, they often suffer from instability when using large step sizes, particularly in solving stiff differential equations. On the other side, multistep methods can show better accuracy and convergence properties, which make them proper candidates for the solution of co-simulated dynamics. This paper puts forward the use of the Bézier integration formulas in the integration of Multibody system (MBS) dynamics, with a particular focus on co-simulation algorithms. To evaluate the proposed method efficiency, some straightforward benchmark problems are considered as case studies, such as a linear oscillator and two nonlinear hydraulic cranes. This study reveals the ability of the Bézier formula to keep the mechanical energy balance of the overall system. As a consequence, the stability of co-simulation results is improved. Furthermore, implementing the Bézier formulas minimizes the residual energy, which consequently reduces the energy errors in the co-simulation environment.

A novel method for preventing technical challenge during drilled cuttings/produced water reinjection: An injection rate management tool

Drilled cuttings reinjection (DCRI) is arguably the most cost-effective technique for disposing of drilling wastes, especially under the zero-discharge policy. However, there are many failed operations due to technical issues related to surface pumps and annular pressure. Currently, there is no sophisticated model for predicting an optimum injection rate that prevents technical failure during DCRI. The practice of using an arbitrary rate is not based on sound engineering principles and may be unable to prevent annular or pump failure. This is because operators do not relate the injection rate to the Maximum Allowable Surface Pressure (MASP) and/or the Maximum Allowable Annular Surface Pressure (MAASP). Due to these limitations, operators seek to find new methods to handle DCRI through the annulus. Thus, this study was carried out to derive a model systematically for the optimum injection rate to prevent technical challenges during DCRI. The components combined include the mechanical energy balance (MEB) and the model for hydraulic horsepower (HHP). The MEB between the wellhead and the annulus was used to derive a model for the annular pressure. Mechanical equilibrium between the STP and the MASP was used to generate another equation, based on the HHP. Then, the new expression was substituted into the annular pressure model. Lastly, the optimum rate was derived based on mathematical principles. The results applied to Well B of the Niger Delta showed a value (2.95 Bbl/min or 675.37 m3/day) that is consistent with the existing field database, and outperformed other related models for flow rate. Simulation results showed that the annular size (78.8%), rheological parameters (12.4%), and MASP (2.9%) were the main factors that affected the optimum injection rate. Thus, we can apply a higher injection rate in larger annuli compared to smaller ones, and to maintain annular pressure simply ensure uniform annulus devoid of erosion/thermal effects.

Total mechanical energy budget in open-channel transitions with turbulent flows

Abstract The issue of mechanical energy budget has received a lot of attention in open-channel flows which are frequently turbulent. Turbulent motions play a major role in the total mechanical energy of the flow field. It is difficult to evaluate total mechanical energy balance and energy loss for 3-D turbulent flows in irregular open channels due to the formation of vortices and the presence of secondary currents. In 3-D turbulent flows, the effect of these phenomena has often been considered as the empirical coefficient of energy loss. In this study, these details in the total mechanical energy budget are investigated through theoretical analysis and numerical simulation, a new form of the total mechanical energy equation and a relationship for the energy loss in 3-D turbulent flows are derived, and their applications are examined in open-channel transitions. For this purpose, the Navier-Stokes equations are solved numerically, and the results are used to obtain the various terms in the total mechanical energy balance equation and analyze the details. The relationships derived in this study generally support the concept of the total mechanical energy budget to comprehend the turbulence parameters affecting the mechanical energy balance in various open-channel flows.

The High-resolution Soft X-Ray Spectrum of Nova Delphini 2013

We present the high-resolution soft X-ray spectrum of Nova Delphini 2013. Two spectra were taken with the Low Energy Transmission Grating Spectrometer on the Chandra X-ray Observatory, on 2013 November 9 and 2013 December 6, 87 and 114 days after the nova eruption, respectively. The spectra are of very high statistical quality, and reveal clear spectral evolution between the two observations. The source is bright enough on the two occasions that the third spectral order, with resolving power up to ∼3000, can easily be seen. We observe the photospheric emission spectrum of the hot white dwarf, which exhibits a rich absorption line spectrum from an atmosphere of effective temperature likely near T eff ∼ 640,000 K, and complex chemical abundances. Superimposed on this photospheric spectrum, we detect the absorption spectrum of a shell of highly ionized gas, comprising absorption by the K-shell ions of C and N, blueshifted (outflowing) by ∼1400 km s−1, and with a velocity width of ∼1000 km s−1. The abundance ratio C/N is clearly very nonsolar, and indicative of thermonuclear fusion by the CNO cycle. We discuss the physical properties (kinematics, ionization balance, radiative transfer, mechanical energy balance, chemical abundances) of this hot shell, in the context of the physics of nova eruptions.

Heat Exchanger 5 Leak Analysis in PPSDM Migas

PPSDM Migas has an oil refinery with a capacity of 600 m3 per day where the crude oil produced will produce various products, such as pertasol CA, pertasol CB, pertasol CC, naphtha, diesel, and residue. One of the operating units used in this production process is a heat exchanger which aims to minimize the use of fuel in the furnace heating process. Of the five heat exchangers in the field, one of the heat exchangers was damaged, namely HE-05. Therefore, an analysis of the causes of damage to HE-05 was carried out with research methods in the form of field studies and literature studies, such as data collection on operating conditions in the Distributed Control System (DCS) and directly in the field using the Piping & Instrumentation Diagram (P&ID) so that it can calculate overall mechanical energy balance. Based on the results of the analysis, it can be concluded that the water content in crude oil exceeds the threshold (< 0.7%) of 5.5%. High water content will affect the steam fraction of crude oil which results in an increase in operating pressure. Then, the safety valve on the stabilizer did not work so that the gasket of the HE-5 was unable to withstand the high pressure in this incident. In addition, inaccurate pressure and temperature sensor readings cause operator delays in dealing with these incidents.   Keywords: Crude oil, heat exchanger, water content

A 6-components mechanistic model of cutting forces and moments in milling

Most of the cutting models developed in the literature attest only to the presence of cutting forces in the balance of mechanical energy resulting from cutting. However, several studies [1–4] have highlighted the presence of cutting moments during machining, and particularly for milling. From a theoretical point of view, a complete energy balance must integrate all the components of the mechanical actions (forces and moments). The predictive model of this study proposes to characterize the evolution of the moments in the cutting zone for milling. The objective is to determine a model similar to the cutting forces which expresses a relationship with the chip section define by the Kc coefficient but by integrating the specific behavior of the moments. This work gives perspectives from an energetic point of view for which the part of moments in the energy balance could be substantial for specific configurations as small-radius tools or high-speed milling.

Analysis of the details of total mechanical energy balance and turbulent flow characteristics in irregular open-channels

Analysis of the details of total mechanical energy balance and turbulent flow characteristics in irregular open-channels

Analytical and numerical investigation of mechanical energy balance and energy loss of three-dimensional steady turbulent flows in open-channels

Abstract Study about the mechanical energy balance and the energy loss of 3-D turbulent flows in open-channels has its own complexities. The governing equation of the mechanical energy in turbulent flows has been previously known and includes turbulence parameters that their calculations or measurements are not easy. In this study, a form of the total mechanical energy equation that leads to a number of significant physical insights is analytically investigated, from which analytical relationships for the energy loss estimation in 3-D turbulent flows are defined. The effect of different turbulence parameters is reflected on the new relationships and analyzed by equalizations replacing unknown correlations with closure approximations using the numerical turbulence simulation. In order to investigate the application of the analytical relationships, numerical simulations are performed by using OpenFOAM software to solve the Navier-Stokes equations with the RSM turbulence model in open-channels with different geometries. Then, the contribution of the turbulence parameters to the total mechanical energy balance is evaluated in uniform and nonuniform turbulent flows and their difference is analyzed, that leads to identify the parameters affecting the friction and local losses. The results demonstrate that the magnitudes of the turbulent diffusion, the work done by the viscous stresses pertaining to the mean motion and the viscous diffusion of the turbulence energy are substantially smaller than the other terms of the total energy equation for turbulent flows in open-channels with different geometries, while the effect of the variations of the turbulence kinetic energy and the work done by the turbulence stresses, that has not been considered in the previous mechanical energy equations, is more important in complex flows. From a practical viewpoint, in order to study the details of the total mechanical energy balance and the energy loss in 3-D turbulent flows with the presence of the secondary currents, the proposed method can be useful.

The Dutch connection of Bob de Vogel

This contribution to the journal issue commemorating Professor Robert Byron Bird focuses on his Dutch connection, which dates back to as early as 1950. Bird twice spent a semester-long period at (the current) Delft University of Technology. The development over time of two different schools of teaching transport phenomena and their mutual influencing are reviewed in quite some detail. The cornerstone in both schools is the analogy between the transport modes for mass, momentum, and energy. However, the role of fluid mechanics and its treatment is different. In addition, the didactic concepts underpinning the textbooks from the two schools are rather different as well, both having their pros and cons. This is illustrated for the mechanical energy balance and its derivation.

Modeling and simulations of plate and frame pervaporative module for the production of low sulfur containing FCC gasoline

Pervaporation is now reorganized as one of the most suitable processes for removing aromatic sulfur-containing compounds (thiophenes) from FCC gasoline, which are otherwise difficult to remove by other traditional processes. Industrial-scale membrane-based separation operations require membrane modules to treat large volumes of feed. Most of the pervaporative membranes used for desulfurization are crosslinked flat sheet membranes, for which plate and frame modules are most suitable. The design of industrial-scale desulfurization units requires the development of mathematical models to predict the module's performance.In this study, a mathematical model is developed to predict plate and frame pervaporative module performance for desulfurization by performing microscopic material and thermal energy balance at the feed side and material and mechanical energy balance at permeate side. A binary mixture of n-heptane/thiophene is taken as the model gasoline. For more realistic simulations, transport properties of membrane were taken from the experimental results reported from literature. Simulations showed that feed temperature and the permeate pressure have profound effects on the module performance and thus may be considered the main operating parameters. Lower permeate pressure and higher feed temperature were found suitable operating parameters to increase the fluxes.On the other hand, lower permeate pressure and lower feed temperature improved the enrichment factor of thiophene. The performance of the plate and frame module were different from the performance of the membrane test cell in all simulations. Moreover, enrichment factors with varying permeate pressure for plate and frame module and test cell were inversed. These results confirm the importance of the developed model over available local mass transport models.

Effects of high oil viscosity on oil‐gas downward flow in deviated pipes. Part 2: Holdup and pressure gradient

AbstractIn Part 1 of this work, new experimental data on high viscosity oil‐gas flow in inclined downward flow were presented. Flow patterns transitions were identified and analyzed, and the performance of some flow pattern prediction models was validated. This study uses the same experimental data set generated for a mixture of air‐oil (with a viscosity of 213 mPa · s) flowing in a 50.8 mm internal diameter pipe with inclination angles of −45°, −60°, −70°, −80°, −85° for a ranges 0.05 m/s‐0.7 m/s and 0.7 m/s‐7 m/s of superficial liquid and gas velocities, respectively, to investigate holdup and pressure gradient behaviour. The holdup and pressure recovery effects are explained in terms of the predominant transport mechanism through phase slippage and the mechanical energy balance. For a constant superficial liquid velocity, the average‐liquid holdup results show a discernible behaviour dependent on the relative velocity between phases (slip velocity). Consistently, results show a switch between the gravity or shear forces transport mechanism, that coincides with the switch of a sign of the total pressure gradient (pressure recovery effect). Performance analysis of the available mechanistic models has been presented. The results are not satisfactory, which justifies the need for a detailed study of the effects of viscosity and the inclination of the pipe in liquid‐gas mixtures.

Sweeping by sessile drop coalescence

During coalescence of liquid drops contacting a solid, the liquid sweeps wetted and solid-projected areas. The extent of sweeping dictates the performance of devices such as self-cleaning surfaces, anti-frost coatings, water harvesters, and dropwise condensers. For these applications, weakly- and non-wetting solid substrates are preferred as they enhance drop dynamical behavior. Accordingly, our coalescence studies here are restricted to drops with contact angle 90{\deg} $\le \theta_{0} \le$ 180{\deg}. Binary sessile drop coalescence is the focus, with volume of fluid simulations employed as the primary tool. The simulations, which incorporate a Kistler dynamic contact angle model, are first validated against three different experimental substrate systems and then used to study the influence of solid wettability on sweeping by modifying $\theta_{0}$. With increasing $\theta_{0}$ up to 150{\deg}, wetted and projected swept areas both increase as drop center of mass heightens. For $\theta_{0} \ge$ 150{\deg}, coalescence-induced drop jumping occurs owing to the decreasing wettability of the substrate and a focusing of liquid momentum due to the symmetry-breaking solid. In this regime, projected swept area continues to increase with $\theta_0$ while wetted swept area reaches a maximum and then decreases. The sweeping results are interpreted using the mechanical energy balance from hydrodynamic theory and also compared to free drop coalescence.

Frictional internal work of damped limbs oscillation in human locomotion.

Joint friction has never previously been considered in the computation of mechanical and metabolic energy balance of human and animal (loco)motion, which heretofore included just muscle work to move the body centre of mass (external work) and body segments with respect to it. This happened mainly because, having been previously measured ex vivo, friction was considered to be almost negligible. Present evidences of in vivo damping of limb oscillations, motion captured and processed by a suited mathematical model, show that: (a) the time course is exponential, suggesting a viscous friction operated by the all biological tissues involved; (b) during the swing phase, upper limbs report a friction close to one-sixth of the lower limbs; (c) when lower limbs are loaded, in an upside-down body posture allowing to investigate the hip joint subjected to compressive forces as during the stance phase, friction is much higher and load dependent; and (d) the friction of the four limbs during locomotion leads to an additional internal work that is a remarkable fraction of the mechanical external work. These unprecedented results redefine the partitioning of the energy balance of locomotion, the internal work components, muscle and transmission efficiency, and potentially readjust the mechanical paradigm of the different gaits.