Securing offshore resources development:A mathematical investigation into gas leakage in long-distance flexible pipes

Gas flexible pipes are critical multi-layered equipment for offshore oil and gas development.Under high pressure conditions,small molecular components of natural gas dissolve into the polymer inner liner of the flexible pipes and further diffuse into the annular space,incurring annular pressure build-up and/or production of acidic environment,which poses serious challenges to the structure and integrity of the flexible pipes.Gas permeation in pipes is a complex phenomenon governed by various factors such as internal pressure and temperature,annular structure,external temperature.In a long-distance gas flexible pipe,moreover,gas permeation exhibits non-uniform features,and the gas permeated into the annular space flows along the metal gap.To assess the complex gas transport behavior in long-distance gas flexible pipes,a mathematical model is established in this paper considering the multiphase flow phenomena inside the flexible pipes,the diffusion of gas in the inner liner,and the gas seepage in the annular space under varying permeable properties of the annulus.In addition,the effect of a variable temperature is accounted.A numerical calculation method is accordingly constructed to solve the coupling mathematical equations.The annular permeability was shown to significantly influence the distribution of annular pressure.As permeability increases,the annular pressure tends to become more uniform,and the annular pressure at the wellhead rises more rapidly.After annular pressure relief followed by shut-in,the pressure increase follows a convex function.By simulating the pressure recovery pattern after pressure relief and comparing it with test results,we deduce that the annular permeability lies between 123 and 512 m D.The results help shed light upon assessing the annular pressure in long distance gas flexible pipes and thus ensure the security of gas transport in the emerging development of offshore resources.

Experimental Analyses of Flow Pattern and Heat Transfer in a Horizontally Oriented Polymer Pulsating Heat Pipe withMerged Liquid Slugs

Extended experiments were conducted on the oscillation characteristics of merged liquid slugs in a horizontally oriented polymer pulsating heat pipe(PHP).The PHP’s serpentine channel comprised 14 parallel channels with a width of 1.3 mm and a height of 1.1 mm.The evaporator and condenser sections were 25 and 50 mm long,respectively,and the adiabatic section in between was 75mmlong.Using a plastic 3D printer and semi-transparent filament made from acrylonitrile butadiene styrene,the serpentine channel was printed directly onto a thin polycarbonate sheet to form the PHP.The PHP was charged with hydrofluoroether-7100.In the experiments,the evaporator section was heated,and the condenser section was cooled using high-temperature and low-temperature thermostatic baths,respectively.Flow patterns of the working fluid were obtained with temperature distributions of the PHP.A mathematical model was developed to analyze the flow patterns.Themerged liquid slugs were observed in every two channels,and their oscillation characteristics were found to be approximately the same in time and space.It was also found that the oscillations of the merged liquid slugs became slower,but the heat transfer rate of the PHP increased with a decrease in the filling ratio of the working fluid.This is because vapor condensation was enhanced in vapor plugs as the filling ratio decreased.However,the filling ratio had a lower limit,and the heat transfer rate was maximum when the filling ratio was 40.6%in the present experimental range.

Numerical Investigations on Fluid Flow and Heat Transfer Characteristics of an Ultra-Thin Heat Pipe with Separated Wick Structures

Thermal and fluid-flow characteristics were numerically analyzed for ultra-thin heat pipes.Many studies have been conducted for ultra-thin heat pipes with a centered wick structure,but this study focused on separated wick structures to increase the evaporation/condensation surface areas within the heat pipe and to reduce the concentration of heat flux within the wick structure.A mathematical heat-pipe model was made in the threedimensional coordinate system,and the model consisted of three regions:a vapor channel,liquid-wick,and container wall regions.The conservation equations for mass,momentum,and energy were solved numerically with boundary conditions by using a code developed by one of the authors.The numerical results with the separated wick structures were compared with those with the centered,which confirmed the effectiveness of the separation of the wick structure.However,the effectiveness of the separation was affected by the position of the separated wick structure.A simple equation was presented to determine the optimum position of the separated wick structures.Numerical analyses were also conducted when the width of the heat pipe was increased with the cooled section,which clarified that the increase in the cooled-section width with the addition of wick structures wasmore effective than the increase in the cooled-section length.A 44%reduction in the total temperature difference of the heat pipe was obtained under the present numerical conditions.Furthermore,a comparison wasmade between experimental results and numerical results.

A Novel Integrated Photovoltaic System with a Three-Dimensional Pulsating Heat Pipe

Solar energy is a valuable renewable energy source,and photovoltaic(PV)systems are a practical approach to harnessing this energy.Nevertheless,low energy efficiency is considered a major setback of the system.Moreover,high cell temperature and reflection of solar irradiance from the panel are considered chief culprits in this regard.Employing pulsating heat pipes(PHPs)is an innovative and useful approach to improving solar panel performance.This study presents the results of the power performance of a PV panel attached to a newly designed spiral pulsating heat pipe,while graphene oxide nanofluid with three different concentrations was used as a working fluid to maximize the efficacy of the solar panel.The study proved that the cooling method delivered high efficiency by reducing the temperature,especially in the middle of the day.Using nanofluid graphene oxide at concentrations of 0.2,0.4,and 0.8 gr/lit as the working fluid can reduce the thermal resistance of PHPs by over 30%,24%,and 15%,respectively.This,in turn,enhances the system’s electrical power output by approximately 9%,7%,and 6%,respectively.

Optimization of Finned-Tube Heat Exchanger in a Gravity-Assisted Separated Heat Pipe

Finned-tube heat exchanger(FTHE)is often used as an evaporator in commercial products of separated heat pipe(SHP).The working conditions of FTHE in gravity-assisted SHP are significantly different from those working in refrigerators and air conditioners.Although FTHE is widely used in commercial products of SHP,previous research on its characteristics is very limited.In this paper,a mathematical model for a SHP with FTHE as the evaporator and plate heat exchanger as the condenser is established and verified with experiments.Parametric analyses are carried out to investigate the influences of evaporator design parameters:air inlet velocity,number of tube rows,tube diameter,and fin pitch.With the increasing of air velocity,number of tube rows and tube diameter,and the decreasing of fin pitch,the heat transfer rate increases,while the energy efficiency ratio(EER)decreases monotonically.Using the total cost of the ten-year life cycle as the performance index,the structure parameters of the evaporator with a given heat transfer rate are optimized by the method of orthogonal experimental design.It is found that the total cost can differ as large as nearly ten times between groups.Among the three factors investigated,the number of tube rows has a significant impact on the total cost of the evaporator.With more tube rows,the total cost will be less.The impacts of fin pitch and tube diameter are insignificant.These results are of practical importance for the engineering design of FTHE in gravity-assisted SHP.

Flow Patterns and Heat Transfer Characteristics of a Polymer Pulsating Heat Pipe Filled with Hydrofluoroether

Visualization experiments were conducted to clarify the operational characteristics of a polymer pulsating heat pipe(PHP).Hydrofluoroether(HFE)-7100 was used as a working fluid,and its filling ratio was 50%of the entire PHP channel.A semi-transparent PHP was fabricated using a transparent polycarbonate sheet and a plastic 3D printer,and the movements of liquid slugs and vapor plugs of the working fluid were captured with a high-speed camera.The video images were then analyzed to obtain the flow patterns in the PHP.The heat transfer characteristics of the PHPwere discussed based on the flowpatterns and temperature distributions obtainedwith thermocouples.Before starting heating,because of high wettability,large liquid slugs positioned at the evaporator section of the PHP.After starting heating,since the occurrence of boiling divided the large liquid slugs,oscillatory flowof smaller liquid slugs and vapor plugs was found in the PHP.Clear circulation flow of liquid slugs and vapor plugs was observed when the power input to the PHP was larger than 12.0 W.The flow patterns and temperature distributions confirmed that the circulation flow enhanced the heat transfer from the evaporator section to the condenser section of the PHP.In the circulation flow mode,large growth and contraction of vapor plugs were found one after another in all even-numbered PHP channels.However,the analysis of flow patterns clarified that the phase-change heat transfer rate by large growth and contraction of vapor plugs was 19%of the total heat transfer rate of the PHP.Although the generation of large vapor plugs was found in the PHP,most of the heat was transferred by the sensible heat of the working fluid.

Decoupled thermal–hydraulic analysis of an air-cooled separated heat pipe for spent fuel pools under natural convection

An investigation of the decoupled thermal–hydraulic analysis of a separated heat pipe spent fuel pool passive cooling system(SFS)is essential for practical engineering applications.Based on the principles of thermal and mass balance,this study decoupled the heat transfer processes in the SFS.In accordance with the decoupling conditions,we modeled the spent fuel pool of the CAP1400 pressurized water reactor in Weihai and used computational fluid dynamics to explore the heat dissipation capacity of the SFS under different air temperatures and wind speeds.The results show that the air-cooled separated heat pipe radiator achieved optimal performance at an air temperature of 10℃ or wind speed of 8 m/s.Fitted equations for the equivalent thermal conductivity of the separated heat pipes with the wind speed and air temperature we obtained according to the thermal resistance network model.This study is instructive for the actual operation of an SFS.

Analysis of Heat Transfer Performance of Oscillating Heat Pipes Based on a Central Composite Design

Oscillating heat pipes (OHPs) are very promising cooling devices. Their heat transfer performance is af- fected by many factors, and the form of the relationship between the performance and the factors is complex and non-linear. In this paper, the effects of charging ratio, inclination angle, and heat input and their interaction effects on heat transfer performance of a looped copper-water OHP are analyzed. First, suppose that the relationship between the response and the variables approximates a second-order model. And use the central composite design to arrange the ex- periment. Then, the method of least squares is used to estimate the parameters in the second-order model. Finally, multi- variate variance analysis is used to analyze the model. The results show that the assumption is right, that is to say, the re- lationship is well modeled by a second-order function. Among the three main effect variables, the effect of inclination angle is the most significant, but their interaction effects are not significant. In the range of the considered factors, both the optimum charging ratio and the optimum inclination angle increase as the heating water flow rate increases.

FEM Simulation of Large Diameter Pipe Bending Using Local Heating

With the aid of elastic plastic large deformation finite element method （FEM）, an elastic plastic and cou pling thermo-mechanical model was built to calculate the bending process of the bent pipe, combining with local heating or cooling of the bent pipe. Based on the FEM simulation, the metal deformation during the bending process was analyzed in detail. The thinning and thickening ratio of the pipe wall thickness, the ovality of the cross section of the pipe and the spring back angle, etc. , are presented.

A review on application of nanofluid in various types of heat pipes

Nanotechnology is widely used in heat transfer devices to improve thermal performance.Nanofluids can be applied in heat pipes to decrease thermal resistance and achieve a higher heat transfer capability.In the present article,a comprehensive literature review is performed on the nanofluids’ applications in heat pipes.Based on reviewed studies,nanofluids have a high capacity to boost the thermal behavior of various types of heat pipes such as conventional heat pipes,pulsating heat pipes,and thermosyphons.Besides,it is observed that there must be a selected amount of concentration for the high-performance utilization of nanoparticles;high concentration of nanoparticles causes a higher thermal resistance which is mainly attributed to increment in the dynamic viscosity and the higher possibility of particles’ agglomeration.Enhancement in heat transfer performance is the result of increasing in nucleation sites and the intrinsically greater nanofluids’ thermal conductivity.

Experimental Investigation on Cooling/Heating Characteristics of Ultra-Thin Micro Heat Pipe for Electric Vehicle Battery Thermal Management

Due to the heat pipes’ transient conduction,phase change and fluid dynamics during cooling/heating with high frequency charging/discharging of batteries,it is crucial to investigate in depth the experimental dynamic thermal characteristics in such complex heat transfer processes for more accurate thermal analysis and design of a BTMS. In this paper,the use of ultra?thin micro heat pipe(UMHP) for thermal management of a lithium?ion battery pack in EVs is explored by experiments to reveal the cooling/heating characteristics of the UMHP pack. The cooling performance is evaluated under di erent constant discharging and transient heat inputs conditions. And the heating e ciency is assessed under several sub?zero temperatures through heating films with/without UMHPs. Results show that the pro?posed UMHP BTMS with forced convection can keep the maximum temperature of the pack below 40 °C under 1 ~ 3 C discharging,and e ectively reduced the instant temperature increases and minimize the temperature fluctuation of the pack during transient federal urban driving schedule(FUDS) road conditions. Experimental data also indicate that heating films stuck on the fins of UMHPs brought about adequate high heating e ciency comparing with that stuck on the surface of cells under the same heating power,but has more convenient maintenance and less cost for the BTMS. The experimental dynamic temperature characteristics of UMHP which is found to be a high?e cient and low?energy consumption cooling/heating method for BTMSs,can be performed to guide thermal analysis and optimiza?tion of heat pipe BTMSs.

Numerical investigation on the startup performance of high-temperature heat pipes for heat pipe cooled reactor application

A suitable model for high-temperature heat pipe startup is a prerequisite to realizing the numerical simula-tion for the heat pipe cooled reactor startup from the cold state.It is required that this model not only describes the transient behavior during the startup period,but also reduces the computing resources of the heat pipe cooled reactor simulation in the simplest way.In this study,a simplified model that integrates the two-zone and network models is proposed.In this model,vapor flow in the vapor space,evaporation,and condensation in the vapor–liquid interface are decoupled with heat conduction to achieve a fast calculation of the transient characteristics of the heat pipe.An experimental system for a high-temperature heat pipe was developed to validate the proposed model.A potassium heat pipe was utilized as the experimental material.Startup experiments were performed with differ-ent heating powers.Compared with the experimental results,the accuracy of the proposed model was verified.Moreover,the proposed model can predict the vapor flow,pressure drop,and temperature drop in the vapor space.As indicated by the analysis results,the essential requirements for successful startup are also determined.The heat pipe cannot achieve a successful startup until the heating power satisfies these requirements.All the discussions indicate the capability of the proposed model for the simulation of a high-temperature heat pipe startup from the frozen state;hence,can act as a basic tool for the heat pipe cooled reactor simulation.

Effect of the Arrangement of a New-Type of Turbulator Inserts on Heat Pipe Exchanger Performances

This research tests the effect of introducing turbulators of a new type into a circular tube heat exchanger under a constant and uniform longitudinal heatflux condition.A 45 mm diameter copper tube with a length of 1,350 mm is utilized with a solid disk being inserted inside the tube,which consists of three sections,each one containing two slots.The slot is cut at a 45 degree angle toward the inner tube surface,which results in diverging theflow toward the inner hot tube surface in order to enhance the heat transfer process.Air is considered as the workingfluid with Prandtl number 0.71.The Reynolds number spans the interval from 6,000–13,500,which indicates that the consideredflow is turbulent.The heat exchanger performance is studied and analyzed in terms of average Nusselt number.The experimental results show that the Nusselt number value is directly proportional to the increase of the Reynolds number,and the number of turbulators inserts.With the use of three novel turbulators,the heat transfer was about 3.15 times higher than that in the smooth tube and the friction factor was about 1.11.

Capillary force of a novel skew-grooved wick structure for micro heat pipes

In order to improve the capillary force of grooved wick, a novel skew-grooved wick structure was proposed for micro heat pipes. Risen meniscus experiments were carried out to research the capillary force of the skew-grooved and rectangle-grooved wick and a comparison of capillarity between the two wick structures was explored. A theoretical capillary force model of skew-grooved wick structure was also developed to calculate its effective capillary radius by comparing with the rectangle-grooved wick. From the experimental results, the maximum capillary force of the skewed-grooved wick is 8.62% larger than that of the rectangle-grooved wick. From the theoretical analysis, because the skewed-grooved wick has a smaller effective capillary radius, its maximum capillary force is 8.64% larger than that of the rectangle-grooved wick. The results indicate that the skew-grooved wick provides larger capillary force than the rectangle-grooved wick.

The Study of Condensation Processes in the Low-Temperature Short Heat Pipes with a Nozzle-Shaped Vapour Channel

The results of researches of condensation processes in the vapour channel similar to the Laval nozzle of short linear heat pipes are presented. Capacitive sensors are additionally installed in cooled top covers of the heat pipes, and electromagnetic pulses were supplied to them from the external generator. At heating the heat pipe evaporator, starting from a certain thermal power threshold value, electromagnetic pulses became modulated. It is related with the formations of the boiling process in the capillary-porous evaporator and large amount of vapour over it. Boiling process results in rapid increase of the pressure under which the average temperature of the evaporator occurs to be less than the boiling temperature of the working fluid under increased pressure. Considering condensation of excess vapour, this leads to repeated initiation and extinction of the boiling process in the evaporator, which reflects in pressure pulsations in the vapour channel. Pressure pulsations cause modulating effect on electromagnetic impulses. Pulsations frequencies are measured as well as their dependence from overheating of the evaporator. Using the capacitive sensors and a special electronic equipment we measured the local thickness of the working fluid at the condensing surface inside the heat pipes. Time-averaged values of the condensate film thickness are measured, depending on the heat load on the capillary-porous evaporator. The measurement error does not exceed 2 × 10–3 mm. It is demonstrated that the condensate film thickness lessens sharply with the increase of the heat load on the evaporator of a Laval-like low-temperature heat pipe, while the heat resistance of the film on the condensing surface reaches 60% of the total heat resistance of heat pipe with the capillary-porous evaporator.

Experimental and Simulation Studies on Cold Welding Sealing Process of Heat Pipes

Sealing quality strongly affects heat pipe performance, but few studies focus on the process of heat pipe sealing. Cold welding sealing technology based on a stamping process is applied for heat pipe sealing. The bonding mechanism of the cold welding sealing process （CWSP） is investigated and compared with the experimental results obtained from the bonding interface analysis. An orthogonal experiment is conducted to observe the effects of various parameters, including the sealing gap, sealing length, sealing diameter, and sealing velocity on bonding strength. A method with the utilization of saturated vapor pressure inside a copper tube is proposed to evaluate bonding strength. A corresponding finite element model is developed to investigate the effects of sealing gap and sealing velocity on plastic deformation during the cold welding process. Effects of various parameters on the bonding strength are determined and it is found that the sealing gap is the most critical factor and that the sealing velocity contributes the least effect. The best parameter combination （AIB3CID3, with a 0.5 mm sealing gap, 6 mm sealing length, 3.8 mm sealing diameter, and 50 mm/s sealing velocity） is derived within the experimental parameters. Plastic deformation results derived from the finite element model are consistent with those from the experiment. The instruction for the CWSP of heat pipes and the design of sealing dies of heat pipes are provided.

Localized Theoretical Analysis of Thermal Performance of Individually Finned Heat Pipe Heat Exchanger for Air Conditioning with Freon R404A as Working Fluid

This work contributes to the improvement of energy-saving in air conditioning systems. The objective is to apply the thermal efficiency of heat exchangers for localized determination of the thermal performance of heat exchangers with individually finned heat pipes. The fundamental parameters used for performance analysis were the number of fins per heat pipe, the number of heat pipes, the inlet temperatures, and the flow rates of hot and cold fluids. The heat exchanger under analysis uses Freon 404A as a working fluid in an air conditioning system for cooling in the Evaporator and energy recovery in the Condenser. The theoretical model is localized and applied individually to the Evaporator, Condenser, and heat exchanger regions. The results obtained through the simulation are compared with experimental results that use a global approach for the heat exchanger. The thermal quantities obtained through the theoretical model in the mentioned regions are air velocity, Nusselt number, thermal effectiveness, heat transfer rate, and outlet temperature. The comparisons made with global experimental results are in excellent agreement, demonstrating that the localized theoretical approach developed is consistent and can be used as a comprehensive analysis tool for heat exchangers using heat pipes.

Parametric Influence on Thermal Performance of Flat Plate Closed Loop Pulsating Heat Pipes

This paper presents an experimental study on a flat plate closed loop pulsating heat pipes. It consisted of total 40 channels with square cross section （2 × 2 mm^2, 165 mm long） machined directly on an aluminum plate（180×120×3 nm^2）, which was covered by a transparent plate. The working fluid employed was ethanol. As the results, the influence parameters of thermal performance were investigated, such as filling ratio, heat load and operational orientations etc. Filling ratio was found to be a critical parameter, and its effect was rather complicated. According to its values the PHP plate could have four distinct working zones with different operational characteristics and heat transfer performance. The effect of heat load on thermal performance was found to be positive, and in general, iucrcasing the heat load would improve heat transfer performance. In order to analyze the effect of gravity on thermal performance, three different heat modes and total seven tilt angles were tested and compared. Successful operation at all orientations with respect to gravity was also achieved.

Visual Study on Flow and Operational Characteristics of Flat Plate Closed Loop Pulsating Heat Pipes

This paper presents an experimental study including visualization on a flat plate closed loop pulsating heat pipes.It consists of a total of 40 channels with square cross section(2 mm×2 mm,165 mm long) machined directly on an aluminum plate(180 mm×120 mm×3 mm) covered by a transparent plate.The working fluid employed is ethanol.As a result,various flow patterns and their transitions are observed and found to be related to the fluid fill ratio,input heat load and the device orientation.Also the operational characteristics and working mechanism are discussed.

A Numerical Investigation of the Thermal Performances of an Array of Heat Pipes for Battery Thermal Management

A comparative numerical study has been conducted on the thermal performance of a heat pipe cooling system considering several influential factors such as the coolant flow rate,the coolant inlet temperature,and the input power.A comparison between numerical data and results available in the literature has demonstrated that our numerical procedure could successfully predict the heat transfer performance of the considered heat pipe cooling system for a battery.Specific indicators such as temperature,heat flux,and pressure loss were extracted to describe the characteristics of such a system.On the basis of the distributions of the temperature ratio of the battery surface,together with the heat flux and the streamlines around the heat pipe condenser,we conclude that the low disturbance of the coolant is the cause of the temperature gradient along the fluid flow direction.