Maximum Energy Dissipation Rate Research Articles

A characterization method for equivalent elastic modulus of rock based on elastic strain energy

Energy is an internal variable during rock deformation and failure, and its dissipation and conversion law can reflect the rock’s internal damage and deterioration state. Analysis of rock deformation and failure process from the perspective of energy is helpful to deeply understand the mechanism of rock damage, fracture and instability failure, and has important theoretical and practical significance for the stability evaluation and support control of surrounding rock. In this study, through single cyclic loading and unloading (SCLU) experiments, cyclic triaxial loading and unloading (CTLU) experiments and conventional triaxial compression (CTC) experiments, the equivalent elastic modulus method based on elastic strain energy is proposed to analyze the energy conversion of rock. The results show that the error of the elastic strain energy calculated by the strain energy formula method is generally higher than 10% with the secant and tangent modulus of the loading and unloading curve as input parameters. Taking the equivalent elastic modulus proposed in this study as an input parameter, more accurate elastic strain energy can be obtained by the strain energy formula. During the rock failure process, the equivalent elastic modulus shows a three-stage characteristic of increase, steady and decrease. The equivalent elastic modulus can be estimated by the quadratic function between the equivalent elastic modulus and confining pressure and axial strain. Under the same deformation and deviatoric stress, the elastic strain energy stored in rock increases with increasing confining pressure. The local maximum energy dissipation rate corresponds to stress drop, and the peak energy dissipation rate appears near the peak strength. High energy dissipation mainly occurs in a short time after peak strength, and energy release and dissipation are more sudden and severe under high confining pressure.

Estimation of overall droplet size distribution from a local droplet size distribution for a jet in crossflow: Experiment and multiphase large eddy simulations

• Experiment and multiphase large eddy simulations (LES) of oil jet in crossflow. • LES was coupled with the population balance model to compute local droplet size. • Maximum energy dissipation rate after 16 pipe diameters distance from the orifice was not sufficient to break the droplets injected at the orifice. • Plume DSD changed slightly after 15 pipe diameters distance from the orifice. • Overall plume DSD can be estimated from the measurement at a single point in the plume. A local droplet size distribution (DSD) from a jet in crossflow can overestimate or underestimate the overall DSD in the plume based on the measurement location. The overall DSD is crucial to evaluate the fate of oil droplets in the water column for a proper countermeasure following an oil spill. We present experimental results of a vertical oil jet in crossflow with a jet velocity of 2.4 m/s and a crossflow speed of 0.31 m/s, resulting jet-to-crossflow velocity ratio of 7.7 and a jet Reynolds number of 13,400. We measured the droplet size near the top and bottom boundaries of the plume while filming the whole plume. We conducted multiphase large eddy simulations coupled with a population balance model considering the relative velocity among the phases in the momentum and volume fraction equations. The computed plume boundaries and the DSD from the simulations agreed well with the measurements. The Sauter mean diameter and DSD considering all droplets across the plume cross-sections were found to be changing slightly beyond s/D ≈ 15. By considering different plume cross-sections for s/D> 15 and different droplet breakage rates, the overall DSD in a plume cross-section can be obtained locally near thevertical centerline of the plume cross-section (y/D = 0) at (58.8 ± 6.2)% of the plume cross-section height from the bottom boundary of the plume. The trajectory of the local DSD representing the overall DSD was found slightly below the plume trajectory.

Scale-up of an amoeba-based process for the production of the cannabinoid precursor olivetolic acid

BackgroundThe availability of new biological platform organisms to get access to innovative products and processes is fundamental for the progress in biotechnology and bioeconomy. The amoeba Dictyostelium discoideum represents a novel host system that has recently been employed for both the discovery of new natural products and as a cell factory for the production of bioactive compounds such as phytochemicals. However, an essential parameter to evaluate the potential of a new host system is the demonstration of its scalability to allow industrial applicability. Here, we aimed to develop a bioprocess for the production of olivetolic acid, the main precursor of cannabinoids synthesized by a recently engineered D. discoideum strain.ResultsIn this study, a sophisticated approach is described to scale-up an amoeba-based polyketide production process in stirred tank bioreactors. Due to the shear sensitivity of the cell wall lacking amoebae, the maximum local energy dissipation rate (εmax) was selected as a measure for the hydromechanical stress level among different scales. By performing 1.6-L scale batch fermentations with different stress conditions, we determined a maximum tolerable εmax of 3.9 W/kg for D. discoideum. Further, we used this parameter as scale-up criterion to develop a bioprocess for olivetolic acid production starting from a 7-L stirred tank reactor to the industrially relevant 300-L scale with a product concentration of 4.8 µg/L, a productivity of 0.04 µg/L/h and a yield of 0.56 µg/g glucose.ConclusionWe developed a robust and reliable scale-up strategy for amoeba-based bioprocesses and evaluated its applicability for the production of the cannabinoid precursor olivetolic acid. By determining the maximum tolerable hydromechanical stress level for D. discoideum, we were able to scale-up the process from shake flasks to the 300-L stirred tank reactor without any yield reduction from cell shearing. Hence, we showed the scalability and biotechnological exploitation of amoeba-based processes that can provide a reasonable alternative to chemical syntheses or extractions of phytochemicals from plant biomass.

Experimental and numerical study on dynamic response of concrete filled steel tubular pile subjected to oblique impact

To study the dynamic performance of concrete-filled steel tubular (CFST) piles under impact loads, the strain and displacement responses of the members were studied by oblique impact tests. Then the experimental process was simulated, and the simulation results are in good agreement with the test. Finally, parameter analysis based on numerical simulation is conducted to study the influence of the section stiffness and impact energy on the dynamic response of the members, as well as the energy absorption of the members are studied, and the response mode of the members is summarized. The results show that the response modes of CFST piles can be summarized as slight bruise at the impact point, dented damage at the impact point, bending deformation of the member, and failure of restrained end of the member. The displacement and energy absorption rate are sensitive to the variation of section stiffness, impact energy, impact height and angle. The impact force is sensitive to the change of section stiffness, impact energy and height, but not sensitive to the change of impact angle. The energy absorption rates are more than 50%, and the maximum energy dissipation rate reaches 91.3%.

Clear Air Turbulence Observed Across a Tropopause Fold Over the Drake Passage—A Case Study

AbstractAn aircraft turbulence encounter over the Drake Passage is investigated by combining unique high‐frequency flight level data, vertical profiles of a near‐simultaneous radiosonde profile and numerical results from global and regional numerical weather prediction (NWP) models. Meteorological analysis reveals an intense polar low propagating from the Bellinghausen Sea toward the Drake Passage. A small and deep stratospheric intrusion formed a tropopause fold that promoted strong upper‐level frontogenesis and enhanced shear and horizontal deformation of the upper tropospheric and lower stratospheric (UTLS) airflow. In this region, the Basic HALO Measurement and Sensor System (BAHAMAS) aboard the HALO research aircraft flying at FL450 detected large peak‐to‐peak variations in all meteorological parameters. The computed Energy dissipation rate (EDR) values (cubic root of the eddy dissipation rate) indicate moderate to severe turbulence. The location of this turbulence encounter was well‐predicted by the clear air turbulence (CAT) indices derived from the NWP results. The enhanced CAT indices emphasize the large shear and horizontal deformation of the airflow as the cause of the turbulence. Horizontal and vertical energy spectra calculated from the 10 Hz BAHAMAS data show a well‐defined energy cascade toward small scales with Kolmogorov scaling. Maximum EDR values of about 0.35 derived both from the spectra and structure functions for the wind speed agree quantitatively very well. In addition, the structure functions support the detection of turbulent atmospheric conditions with signatures of flow anisotropy generated by enhanced thermal stratification in the UTLS. The scales involved are between the buoyancy length scale LB ≈ 1,500 m and the Ozmidov scale LO ≈ 111 m.

On strain-induced degradation of the polymeric skeleton in poro-hyperelastic inflating vessels by a non-equilibrium thermodynamic framework

The present work develops the Poro-Hyperelasticity Theory (P-HT) into a fluid-saturated porous polymeric skeleton under Ogden-Hill material model with inhomogeneous properties resulting from bulk degradation. The only source of dissipation in the degradable skeleton is mechanical strain. To capture constitutive and evolution laws, P-HT and the principle of maximum energy dissipation rate are invoked in a non-equilibrium thermodynamic framework. The model is verified by available experimental data and the physical concept of consolidation. The degradation model is applied on a fluid-saturated pressurized polymeric vessel with the porosity-dependent permeability in the plane-strain case. To approximate the non-linear equations of degradable porous vessel, Standard Galerkin Finite Element Method (SGFEM) is implemented through programming in the FlexPDE commercial software. Contrary to the degradable hyperelastic polymers without fluid mechanical effects studied in the literature, the skeleton degradation initially starts with a non-maximum degradation rate. Degradation causes deformation-dependent porosity and permeability in the vessel to increase. The degradation leads to slower evolution of the pore pressure in the vessel. Pore pressure and stress can reach a time-independent flatted region in addition to the final time of coupled process, because of degradable skeleton. Energy dissipation and material softening rates are higher in the inner radius of the inflating vessel.

A study on deformation-induced degradation of the compressible polymeric pressurized vessel through a non-equilibrium thermodynamic framework

The present paper investigates the degradation of compressible polymers based on the proposed model on strain-induced degradation of incompressible polymers. In a non-equilibrium thermodynamic framework, constitutive equations and evolution laws are derived using the principle of maximum energy dissipation rate and specifying how energy can be stored and dissipated. As a computational model, the governing equations are applied to the pressurized polymeric vessel subjected to the Ogden–Hill compressible hyperelastic material model. To analyze the axisymmetric plane-strain degradable vessel, programming in ANSYS Parametric Design Language (APDL) and the Standard Galerkin Finite Element Method (SGFEM) are applied. The results show that the degradable compressible Ogden–Hill model can also predict the degradation of incompressible polymers subjected to the neo-Hookean model. Results also reveal that the highest dissipation rate and material softening occur at the inner radius of the inflated degradable vessel. Creep-like and stress-relaxation-like responses of the polymeric vessel with time-position-dependent material properties are examined. ANSYS coding indicates good accuracy and efficiency in studying the compressible vessel subjected to inhomogeneous degradation.

Multi-objective optimization of stepped spillway and stilling basin dimensions

Abstract In the present paper, an optimization procedure is proposed for stepped spillway design dimensions, which leads to maximum energy dissipation rate and minimum construction cost, considering independently the chute cost and stilling basin cost. Three independent objective functions are thus simultaneously satisfied. The procedure involves four main tools: the multi-objective particle swarm optimization method (MOPSO) to find Pareto solutions in one run, the K-means clustering algorithm to reduce the size of the obtained non-dominated solutions, the pseudo-weight vector approach (PWV) to facilitate the decision making and to select some adequate solutions, and finally, CFD simulations to analyze the retained optimal solutions. The suitability of the proposed procedure is tested through an example of application. As results, a set of 20 solutions with different satisfaction levels is found and compared to existing solutions. A multi-objective optimization problem may have many different solutions; the originality of the present work lies in the proposed procedure, which explores several possible solutions and reduces their number to give help to the decision making. Furthermore, an approximate expression of spillway total cost is also derived as a function of flow energy dissipation rate.

Numerical Simulation of Stepped Spillways with Front Step Deformation

In order to solve the flood discharge problem of both small- and medium-sized warping dams in the Loess Plateau, a stepped spillway scheme, based on an ecological bag, to achieve full-section water flow and energy dissipation has been proposed in this paper. The hydraulic and energy dissipation characteristics of a stepped spillway layout scheme were studied using 3D numerical simulation. As the height of the dams is low and the spillways are short, the research has shown that the traditional single-step layout scheme leads to a low overall energy dissipation rate due to the small amount of energy dissipated in the initial steps. As a result of this, this paper has put forward two kinds of step layout schemes such as the shunt type and the staggered type for the initial steps. Through analysis of the flow state, the pressure distribution, and the total energy dissipation rate, the results have shown that shunt type and staggered type with front step deformation produced an obvious mixing of the water flow, fewer negative pressure areas, and a higher energy dissipation rate. The optimal energy dissipation rate of the staggered type reached 87.75%, and the maximum energy dissipation rate was increased by 27.97%.

Experimental investigation of hydraulic characteristics and energy dissipation in a baffle-drop shaft.

The baffle-drop shaft structure is usually applied in deep tunnel drainage systems to transfer shallow storm water to underground tunnels. At present, the definition of the maximum operational capacity of baffle-drop shafts is lack of scientific and reasonable analysis, and the researches on hydraulic and energy dissipation characteristics have been insufficient. In this paper, a 1:25 scale hydraulic model test was conducted to observe the flow phenomena during the discharge process, analyze the relationship between the maximum inflow discharge and the baffle parameters, and calculate the energy dissipation rate of the shaft under different flow conditions. The results demonstrated that three kinds of flow regimes were presented in the discharge process: wall-impact confined flow, critical flow, and free-drop flow. The impact wave majorly brought about the energy dissipation of water on the baffle. The impingement and breakup of the inflow at the bottom of the drop shaft, as well as the reverse flow, resulted in the final energy loss. The time-averaged pressure value of the upper baffle was 1.5-3 times that of the central and lower baffles. The baffle with a design angle could effectively reduce the time-averaged pressure of the water flow acting on the baffle. The energy dissipation rate of the drop shaft decreased with the increase in the inflow discharge, and the energy dissipation rate was found to range from about 63.14% to 96.40%. The optimal size of the baffle-drop shaft with the maximum energy dissipation rate was d/B = 0.485 and θ = 10° (d, B, and θ are the baffle spacing, width, and angle, respectively).

Observation and simulation of mountain wave turbulence above Iceland: Turbulence intensification due to wave interference

AbstractThe High‐Altitude LOng Range research aircraft (HALO) encountered strong turbulence above Iceland at 13.8 km altitude on 13 October 2016. The generation of turbulence along the flight path is studied through numerical simulations in combination with the aircraft insitu observations. From the insitu observations, maximum energy dissipation rate values (cube root of the energy dissipation rate) of 0.39 m2/3 ·s−1 are obtained, which correspond to moderate to severe turbulence for a medium‐weight aircraft such as HALO. The turbulent region is characterized by observed large‐amplitude vertical wind fluctuations which coincide locally with a stagnation of the horizontal flow. The strong turbulence occurred downstream of and between the two Icelandic mountains Hofsjökull and Langjökull. High‐resolution numerical simulations, with realistic and idealized topography, show that the flow above these two nearby mountains is responsible for the observed turbulence. Vertically propagating hydrostatic mountain waves disperse horizontally in the region downstream and between Hofsjökull and Langjökull. There, both waves interfere and their superposition leads to enhanced amplitudes and, eventually, to convective instabilities. By comparing simulations with only one of the mountains to the simulation with both mountains, we infer that the wave interference can locally amplify the turbulence intensity by a factor of five and double the vertical extent of the turbulent region.

Influence of Impeller Geometry on Hydromechanical Stress in Stirred Liquid/Liquid Dispersions

Hydromechanical stress is a crucial parameter for a broad range of multiphase processes in the field of (bio)chemical engineering. The effect of impeller type and geometry on hydromechanical stress in stirred tanks is important. The present study aims at characterizing conventional and new impeller types in terms of particle stress. A two-phase liquid/liquid noncoalescing dispersion system is employed, and the drop breakage is monitored in-line in a stirred tank. The published effects of agitation on drop deformation are confirmed and expanded significantly for five modified new impeller types. Radial impellers are advantageous for applications where low shear conditions are desired. A modified propeller with a peripheral ring and the developed wave-ribbon impellers present remarkable results by producing significantly low and high hydromechanical stress, respectively. The results obtained are correlated in terms of mean and maximum energy dissipation rate, as well as circulation frequency in the impeller...

The use of computational fluid dynamics to predict the turbulent dissipation rate and droplet size in a stirred autoclave

The prediction of droplet sizes in emulsions is important for fields ranging from the chemical process industry to emergency planning in the event of an underwater oil release. Typically scale models have needed to be built and the results scaled up, but as computational resources have grown and turbulence models have matured it has become possible to use computational fluid dynamics (CFD) to simulate the behaviour of the fluid/s. While direct simulation of multiphase breakup at high Reynolds number is currently computationally impractical, this paper looks into the use of CFD along with a correlation function based on maximum turbulent kinetic energy dissipation rate to predict the Sauter mean diameter of droplets in a 1 in. baffle-and-vane type autoclave. The results show that using a RNG-k∊ turbulence model with a simplified 2D geometry gave droplet sizes within 26.2 μm of the Sauter mean diameter observed in experiments with no additional tuning of parameters. Correlating pipe and autoclave flows through the Reynolds number and the turbulent kinetic energy dissipation rate was also investigated. Using the traditional definitions of the Reynolds numbers the correlation is poor, the coefficient of determination of the linear fit to the log-log data is 0.64. The first modification replaced the diameter of the blade as characteristic length with the tip swept circumference which increased the coefficient of determination to 0.960. A further modification using data obtained from the turbulent fields of the simulation showed a significant improvement with the coefficient of determination increasing to 0.988.

Extremum characteristics of energy consumption in fluidization analyzed by using EMMS

This paper investigates the landscape of extremum characteristics for different energy consumption terms in gas-solid fluidization based on the Energy Minimization Multi-Scale (EMMS) model. The influence of typical cluster correlations on the extremum characteristics is also investigated to consolidate the results. The energy consumption terms are resolved into three types, i.e. suspension (“s”), transport (“t”) of the particles and pure dissipation (“d”) caused by their collisions and acceleration. Three regimes which are particle-dominated (PD), fluid-dominated (FD), and particle-fluid compromising (PFC) respectively subject to the extrema of ε = min, Wst = min and Nst = min, are investigated. Then the same procedure is extended to individual and combined terms (i.e. “s”, “t”, “d”, “s + t”, “t + d”, “d + s”) of energy consumption with respect to unit mass of particles (“N”) and to unit volume of bed (“W”). The study of extremum characteristics reveals an enclosure structure which features an upper voidage regime corresponding to minimum energy dissipation rate (MinED), a lower voidage regime to maximum energy dissipation rate (MaxED) and a so-called mesoregime in between. The landscape of extremum characteristics reveals that the stability condition must be constructed according to clear physical meaning, otherwise misleading may occur due to multiple contradictive extrema exist in specific regimes. Although the clustering effects on extremum characteristics exposed some limitations of current correlations, the above-mentioned characteristics are found to be insensitive to cluster diameter correlations, indicating that the findings are intrinsic to the EMMS model. Further work is still needed to explore the mesoscale structure and its relationship with extremum behavior as well as underlying physics in fluidization.

A non-equilibrium thermodynamic model for tumor extracellular matrix with enzymatic degradation

The extracellular matrix (ECM) of a solid tumor not only affords scaffolding to support tumor architecture and integrity but also plays an essential role in tumor growth, invasion, metastasis, and therapeutics. In this paper, a non-equilibrium thermodynamic theory is established to study the chemo-mechanical behaviors of tumor ECM, which is modeled as a poroelastic polyelectrolyte consisting of a collagen network and proteoglycans. By using the principle of maximum energy dissipation rate, we deduce a set of governing equations for drug transport and mechanosensitive enzymatic degradation in ECM. The results reveal that osmosis is primarily responsible for the compression resistance of ECM. It is suggested that a well-designed ECM degradation can effectively modify the tumor microenvironment for improved efficiency of cancer therapy. The theoretical predictions show a good agreement with relevant experimental observations. This study aimed to deepen our understanding of tumor ECM may be conducive to novel anticancer strategies.

Mesoscale modeling for turbulence based on EMMS principle

Turbulent flows in engineering are characterized by the coexistence of turbulent and non-turbulent fluids. Nonetheless, in traditional turbulence models, the laminar portion of the fluid flow is often neglected and constitutive laws are expressed to describe fully turbulent states within computational grids. This situation is perceived as a source of inaccuracies in modeling practical engineering flows. In this paper, a meso-scale turbulence model based on the principle of energy-minimization multi-scale model (EMMS) for improving the accuracy of turbulence modeling is presented. Then, the multi-scale structure and stability criterion originated from the compromise in competition between viscous and inertial control coordination mechanisms in turbulent flows are explored, and the physical basis of the models extension, the mathematical expression, the verification and the application are also analyzed. Furthermore, the contradiction between the hypothesis of minimum energy dissipation rate and that of maximum energy dissipation rate in hydraulics can be interpreted in a unified framework of the EMMS-based turbulence model. Finally, some problems and challenges in the EMMS-based turbulence model and the development of the turbulence-based meso-sciences are also discussed.

A numerical study on efficient recovery of fine-grained minerals with vortex generators in pipe flow unit of a cyclonic-static micro bubble flotation column

In the past decade, intensive research has proved that the cyclonic-static micro bubble flotation column (FCSMC) is an efficient flotation device which can be used to separate fine-grained minerals. The main way to strengthen the recovery of fine-grained minerals is further improvement of the highly-turbulent flow field of the pipe flow unit in the flotation column. With a decrease of fine-grained mineral diameter, the turbulence intensity in the pipe flow should be increased so as to strengthen the recovery of the fine-grained mineral. In this paper, the effect of vortex generators (VGs) on the turbulence kinetic energy and the turbulence dissipation rate in a pipe flow unit are primarily investigated by numerical simulations. The results showed that a staggered arrangement (S=20mm) exhibited the maximum volume-averaged turbulence kinetic energy and volume-averaged turbulence dissipation rate among different arrangements of VG arrays in the pipe flow unit. Streamwise vorticity was formed behind the VGs along the flow direction. With an increase of VG arrays from 0 to 5, the volume-averaged turbulence kinetic energy increased from 0.015m2/s2 to 0.05m2/s2. Similarly, with an increase of VG arrays from 0 to 5, the volume-averaged turbulence dissipation rate in the pipe flow unit increased from 1.99m2/s3 to 11.8m2/s3. A flotation experiment using coal slime was conducted by using different structures of pipe flow unit (including empty pipe and pipe with different VG arrays). The results showed that cumulative yield and combustible recovery were greatly improved due to the influence of VG arrays. The results of the study are equally beneficial in helping understand the recovery of fine-grained minerals in other separation equipment.

Acute hydrodynamic damage induced by SPLITT fractionation and centrifugation in red blood cells.

Though blood bank processing traditionally employs centrifugation, new separation techniques may be appealing for large scale processes. Split-flow fractionation (SPLITT) is a family of techniques that separates in absence of labelling and uses very low flow rates and force fields, and is therefore expected to minimize cell damage. However, the hydrodynamic stress and possible consequent damaging effects of SPLITT fractionation have not been yet examined. The aim of this study was to investigate the hydrodynamic damage of SPLITT fractionation to human red blood cells, and to compare these effects with those induced by centrifugation. Peripheral whole blood samples were collected from healthy volunteers. Samples were diluted in a buffered saline solution, and were exposed to SPLITT fractionation (flow rates 1-10 ml/min) or centrifugation (100-1500 g) for 10 min. Cell viability, shape, diameter, mean corpuscular hemoglobin, and membrane potential were measured. Under the operating conditions employed, both SPLITT and centrifugation maintained cell viability above 98%, but resulted in significant sublethal damage, including echinocyte formation, decreased cell diameter, decreased mean corpuscular hemoglobin, and membrane hyperpolarization which was inhibited by EGTA. Wall shear stress and maximum energy dissipation rate showed significant correlation with lethal and sublethal damage. Our data do not support the assumption that SPLITT fractionation induces very low shear stress and is innocuous to cell function. Some changes in SPLITT channel design are suggested to minimize cell damage. Measurement of membrane potential and cell diameter could provide a new, reliable and convenient basis for evaluation of hydrodynamic effects on different cell models, allowing identification of optimal operating conditions on different scales.

A novel active prevention technology for borehole instability under the influence of mining activities

Coal bed methane (CBM) drainage is an efficient method used to control gas hazards. Nevertheless, borehole instability is prone to occur under repeated disturbances by external stress from mining activities. Consequently, the collapsed coal blocks the gas-flow channel to further induce several gas drainage problems, including low gas concentration and flow, poor drainage result, etc. Due to these problems, screen pipes were installed in this work to provide active support in order to prevent borehole instability. Initially, the effect of mining activities on borehole stability was analysed. Subsequently, we explored the instability characteristics and corresponding acoustic emission (AE) properties of a non-supported borehole and a borehole stabilized by internal active support. These boreholes were drilled in the lab sample instead of the real coal sample. Moreover, the abilities of the holes to resist disturbances due to external stresses were compared. When the stress reached 10 MPa, the non-supported borehole was completely destroyed, whereas the actively supported borehole only slightly deformed. As the stress continuously increased to 14 MPa, a deformation of 15 mm was detected along the radial direction of the actively supported borehole. Additionally, an analysis of the dynamic changes in the strain on the screen pipe surface, the AE time–sequence parameter and location information indicated that the maximum AE event count and energy dissipation rate of the supported borehole at 14 MPa were 44% and 23% lower, respectively, than the corresponding values for the non-supported borehole at 10 MPa. Thus, the support increases the ability of the borehole to resist disturbance by at least 40%. Furthermore, the locating points and energy rate appeared to temporally cluster at coal-yielding or failure stage. Hence, the supporting effect of the screen pipe on the coal around boreholes at the crushing stage is significant. The internal support to the borehole provides a positive confining pressure for the coal in the fracture zone to improve the coal's residual strength. Depending on the support from the screen pipe, the coal can mesh to remain in place and thus prevent collapse, which improves the stability of the borehole.

The Relationship between Hurricane Potential Intensity and CAPE

Abstract The theoretical minimum eyewall pressure of tropical cyclones can be computed from convective available potential energy (CAPE) if the buoyancy in the CAPE is allowed to feed back on the surface pressure via hydrostatic balance. The relationship between this so-called hurricane CAPE and the surface pressure is exploited by a widely used algorithm for hurricane potential intensity (PI). For the observed atmosphere, the algorithm is shown to yield significantly weaker pressure intensity (20%–25%) and velocity intensity (5%–10%) than the most familiar analytical formulas. This discrepancy is found to come mostly from thermodynamic approximations in the formulas. The CAPE–PI algorithm makes a significant adjustment to the hurricane CAPE by subtracting the environmental CAPE. Most of the environmental profile becomes irrelevant as a result. Other steady-state theories retain the influence of the full environmental column. The impact of this choice on the pressure and velocity PI is analyzed. Another important choice—whether to allow the eyewall kinetic energy to contribute to the surface pressure perturbation—is also analyzed and quantified. The analytical formula for the velocity is updated with full moist thermodynamics and compared to the algorithm. The latter emerges as an excellent overall diagnostic of the underlying model. An exact algorithm for the velocity is also derived, based on its relationship to the radial derivative of hurricane CAPE. The thermodynamic efficiency often invoked to interpret velocity PI is identified as a marginal efficiency measured at the point of maximum energy dissipation rate and is contrasted with the global efficiency, which has a direct connection with the pressure intensity.