Coaxial Pipe Research Articles

Impacts of thermally stratified medium on transient convective heat transfer between co‐axial horizontal fixed pipes: Applications of the thermal stratification

AbstractThermal stratification improves coaxial pipe systems’ efficiency and stability. Thermal stratification enables accurate temperature maintenance, reduces thermal stress, optimizes heat transmission performance, and minimizes usage of energy to guarantee the system's long‐term performance. The main aim of the current study is to investigate the impacts of thermal stratification on buoyancy force flow and thermal transmission between coaxial fixed pipes. In the present research, the applications of thermally stratified medium on transient convective heat transfer between two coaxial fixed pipes are studied. A two‐dimensional mathematical formulation in terms of mutually nonlinear partial differential equations is used to analyze the unsteady flow and temperature field between the co‐axial pipes, when the internal pipe is uniformly heated and the outer wall of the external pipe is placed at infinity from the surface of the inner fixed pipe. Flow is assumed along the axial direction of the internal pipe and stationary boundary condition is assumed at the surface of the inner pipe. The coupled equations of the simulated model are solved numerically by applying the Implicit Finite Difference Technique. The computed outcomes in the form of geometrical interpretation are highlighted by using the technically advanced software TECHPLOT‐360. Comprehensive detail of the obtained results for the non‐dimensional parameters included in the flow formulation is predicted for steady state velocity, temperature distribution, time‐dependent surface shearness and time‐dependent energy shearness in results and discussion section of the manuscript. The emphasis is placed on the thermal stratification parameter in the above mentioned chief quantities. From the obtained results, it is predicted that the fluid flow pattern and thermal distribution are both reduced for rising values of the thermal stratification parameter S = 0.001, 0.03, 0.05, and 0.07. Minimum flow and thermal profile are observed at S = 0.07. Further, the amplitude of the time‐dependent surface shearness is uniformly distributed throughout the medium and the amplitude of the time‐dependent energy shearness is reduced effectively for S = 1.0, 5.0, and 10.0.

A novel coaxial heat pipe with an inner vapor tube for cooling high power electronic devices

Improving heat transfer limit of heat pipe is important for their application in high-power equipment system. Shear stress at the liquid–vapor interface affects the heat transfer capacity of heat pipe. In this study, a novel coaxial heat pipe is designed to eliminate vapor entrainment from interfacial shear stress for the first time. An inner thin-walled tube is sintered with the powder wick in the adiabatic section by one-step sintering process. The effects of filling ratio and powder size of sintered wick on the thermal performance of coaxial heat pipe are investigated experimentally. The results indicate that the optimal powder size range for the sintered wick of coaxial heat pipe is 106–125 μm, while the optimal filling ratio is about 125 %. It means that the sintered wick with 106–125 μm powder can achieve better trade-off between capillary performance and permeability. The coaxial heat pipe can operate at heat loads of 70 ∼ 140 W with the total thermal resistance less than 0.06 °C /W. Moreover, compared with the normal heat pipe, the heat transfer capacity of coaxial heat pipe is increased by 57 %, while the evaporation temperature is decreased by 9.6 ∼ 19.1 °C and the total thermal resistance is decreased by 41 %∼320 %. The inner tube can improve the replenishment efficiency of working liquid by eliminating interfacial shear stress, resulting in the significant heat transfer improvement. The design of coaxial heat pipe is an effective and low-cost solution to improve the thermal performance of heat pipe.

Analyzing the thermal performance of transient heat transfer mechanism due to the combined effects of solar energy and variable surface temperature: Growing applications of solar energy in co-axial pipes

The current analysis is carried out to study the laminar convective heat transfer characteristics that change with time in the co-axial pipes along the impact of heat radiation and variable surface temperature. The flow is assumed along the axial direction of the pipe, and variable boundary condition is assumed at the surface of the pipe due to the variable surface temperature. A two-dimensional mathematical model made up of non-linear partial differential equations is solved using the implicit finite difference method. The project involves predicting the thermal efficiency of a pipe's time dependent flow across a number of flow model-relevant parameter ranges. Graphical representations highlighted the derived predictions. After separating the numerical solutions into the time independent and the time dependent components, the time dependent energy and surface shearness were found using the data from the time independent component. Comprehensive detail of the obtained results for the non-dimensional parameters included in the flow formulation is predicted for steady state velocity, temperature distribution, time dependent surface sheerness, and time dependent energy sheerness, which is given in results and discussion section of the manuscript. Major focus is given on the influence of the radiation parameter on the above-mentioned primary measures. Furthermore, it is concluded that in all cases, the steady state flow is as R→∞ and velocity profile as U→1 and θ→0, which ensured the accuracy of the obtained results by satisfying the boundary conditions. For various values of the fluid's absorption parameter D = 1.0, 3.0, 5.0, and 10.0, the flow profile is increased and U→1 as R→∞. Simultaneously, thermal distribution also increases and θ→0 as R→∞.

Numerical Investigation of the Coaxial Geothermal Heat Exchanger Performance

Space heating and cooling using geothermal heat exchangers is a promising environmentally friendly green energy solution. Modeling these energy storage systems is crucial for optimizing their design and operation. In this context, the present study consists of numerically investigating the effects of various physical properties, including thermal conductivity, density, and specific heat capacity of each material, as well as flow velocity, on the process of heat transfer in vertical geothermal heat exchangers using coaxial pipes to optimize their energy performance. Numerical simulations were carried out using Gambit-Fluent software. Different materials that make up the coaxial heat exchanger structure studied were tested to highlight their effects on the progress of heat flux and temperature. Thermal and fluid mechanics aspects were also studied. At the end of this study, a comparative analysis was carried out using the U-tube geothermal heat exchanger. The results indicate that the heat exchanger using a coaxial tube demonstrates superior thermal efficiency compared to the U-tube configuration. It has been found that using a low velocity with an appropriate selection of tube, grout, and soil materials results in enhanced dynamic exchanges, thereby enhancing the thermal efficiency of the geothermal exchanger.

Novel hybrid coaxial-U-shaped closed-loop geothermal system for enhanced energy extraction: a numerical analysis

ABSTRACT Insulated U-shaped closed-loop geothermal system (UCLGS) is an efficient and environmentally friendly method of harnessing geothermal energy. However, heat available in the rock surrounding the insulated production pipe has not been extracted yet. Therefore, this study proposed a novel hybrid coaxial-U-shaped CLGS (HCLGS) to enhance the overall thermal performance of CLGS. The HCLGS comprises an insulated UCLGS for harnessing energy from the reservoir rock, alongside a coaxial double pipe system designed to extract additional thermal energy from the rock enveloping the insulated production pipe of the UCLGS. Further, the study explored the thermal feasibility of the proposed HCLGS in various rock formations for geothermal energy extraction at different depths. The results showed that the HCLGS installed in the pyroxenite rock produced primary hot fluid with a maximum temperature of 94°C and secondary hot fluid at a temperature of 38.5°C for the base case, achieving a COP of 1.15. The proposed HCLGS can extract up to 18% higher thermal power than the insulated UCLGS, with a COP ranging from 1.11 to 1.16. Finally, the proposed hybrid system significantly harnessed the additional heat available in the rock encompassing the insulated production pipe of UCLGS.

Thermofluid-dynamic and thermal–structural assessment of the EU-DEMO WCLL “double bundle” Breeding Blanket concept left outboard segment

As part of the activities performed by the DEMO Central Team (DCT) to study alternative configurations of the Water-Cooled Lead Lithium (WCLL) Breeding Blanket (BB), to overcome the open issues that emerged at the end of the Pre-Conceptual Design phase, a new concept, the WCLL BB “double bundle” (db), was developed. This concept adopts an array of db tubes poloidally distributed inside the breeding zone, mimicking the arrangement inside heat exchangers. These are coaxial pipes the gap between which is filled with PbBi (or alternatively with gas and fins), which avoids direct contact between PbLi and water in case of in-box LOCA events. Similarly, the First Wall channel cooling water is separated from the PbLi. The use of PbBi as an inert fluid makes the Segment Box (SB) sizing less stringent: in the case of an in-box LOCA due to a break of the water cooling circuit inside the BB SB, the pressurized volume is only the PbBi one, instead of the whole SB volume as in the reference WCLL design configuration. Consequently, the total amount of steel inside the BB can be reduced, with benefits in terms of increased tritium breeding ratio. Within this framework, University of Palermo, in support of the DCT and under the EUROfusion action, preliminarily analysed the steady-state thermal, thermo-hydraulic and normal and off-normal thermo-mechanical performances of this concept, following a theoretical-numerical approach based on finite volume and finite element methods, and adopting the ANSYS CFX and ANSYS Mechanical codes. The analyses carried out allowed a preliminary optimization of the design, improving the thermal and thermo-mechanical performances of the WCLL-db BB, in compliance with the design requirements, while reducing the total steel amount. Models, assumptions and main results are herewith reported and critically discussed.

Numerical simulation of the thermal response of seabed sediments to geothermal cycles in Suvilahti, Finland

Renewable thermal energy from seabed sediment is used for heating and cooling houses in Suvilahti, Vaasa, Finland. Innovative coaxial polyethylene pipes (Refla) filled with heat collection fluid are laid horizontally in the sediment layer. This study aims to evaluate the adequacy and possible overuse of this shallow geothermal energy. This entailed a numerical analysis of the heat relations of a “coaxial closed-loop geothermal system (CCGS)" to investigate the thermal behavior of the sediment. The numerical model was developed in Midas GTS NX software with a thermal analysis module. The objective was to understand temperature fluctuation in the sediment, which is influenced not only by geothermal energy exploitation, but also by seasonal weather. The numerical model, due to its design, provided information mainly about changes in sediment temperature due to the geothermal energy exploitation during the different seasons. The results show that in the first third of the total length of the Refla pipes, the sediment environment is significantly affected by energy exploitation's temperature loading. It is advisable to exclude the first third from an analysis of total geothermal energy reserves. The remaining two-thirds of the length shows potential to provide sustainable, long-term geothermal energy (GE) exploitation at the current rate.

Investigating Reynolds number effects in turbulent concentric coaxial pipe flow using stochastic one‐dimensional turbulence modeling

AbstractThe present study numerically investigates turbulent momentum transfer in concentric coaxial (annular) pipe flow with small radius ratios . To model the flow, a stochastic one‐dimensional turbulence (ODT) model formulated for cylindrical geometry is used that provides full‐scale resolution along a representative radial coordinate. The present investigation extends the model validation by Tsai et al. (PAMM, 22:e202200272, 2023), to radius ratios smaller than 0.1 and addresses boundary layers with strong spanwise curvature effects. The focus is on the assessment and analysis of statistical flow features in the vicinity of the inner cylinder wall, particularly in cases with small radius ratios. Following Boersma & Breugem (Flow Turbul. Combust., 86:113–127, 2011), classical boundary‐layer and mixing‐length theory is utilized to analyze the model predictions. The results demonstrate that the ODT model captures leading‐order curvature and mixing‐length effects by its physics‐compatible construction. Utilizing the model for extrapolation to high Reynolds numbers inaccessible to conventional high‐fidelity numerical approaches shows that curvature effects persist and nonlocally affect the entire boundary layer. The model results provide support for a spanwise‐curvature‐modified wall function.

Use of a residential building’s foundation as Energy Geo-Structures: A case study in the Mediterranean environment

Geothermal energy, a type of renewable energy obtained from the Earth, can be used by Ground Source Heat Pumps (GSHPs) for space heating and cooling. GSHP systems extract/reject heat from/into the earth via a network of pipes or tubes known as Ground Heat Exchangers (GHEs),. GHEs can be horizontal or vertical and come in a variety of forms, including slinky loops and vertical spiral loops for horizontal configurations, and single U-tube, double U-tube in series or parallel, coaxial pipe, and spiral/helical pipe for vertical configurations. Although GSHPs exhibit a higher performance than conventional Air Source Heat Pumps (ASHPs), the systems are less appealing as investments due to their longer payback times and greater upfront costs. A competent design of the GSHP system with the appropriate GHE sizing, including the case of employing the GHEs in the structures foundations, can minimize the initial cost. Such structures are referred to as Thermo-Active Structure systems or Energy Geo-Structures (EGS), which have already found applications as energy piles, barrette piles, diaphragm walls, shallow foundations, retaining walls, embankments, and tunnel linings [1, 2, 3].
 Residential buildings in Cyprus have a higher cooling than heating demand, with an extended payback period for the investment, especially if the system is solely utilized for heating [4]. EGS coupled with a GSHP could offer a substitute to reduce the system’s initial expenses and make it more attractive as an investment. EGS have not yet seen applications in Cyprus, therefore an initial computational analysis utilizing the COMSOL software and relevant data is taken into consideration. To determine the heating and cooling loads, a three-bedroom, two-storey house with a total floor space of 190 m2, with nearly Zero Energy Building (nZEB) characteristics, is used as the typical case for a single detached residential building in Cyprus. The TRNSYS software was used to calculate the heating and cooling loads. In order to analyze the rejected/absorbed energy from the earth, typical foundations were constructed as full sized models in COMSOL (Figure 1). With the exception of pipes, where a 1D solution is employed, the convection diffusion equation for heat transfer is utilized with 3D conservation of heat transfer for an incompressible fluid. A detailed methodology can be found in Aresti et al. [5].
 For the COMSOL compuations, the site ground temperature characteristics and the local ambient temperature were taken into account. Based on the provided loads, the inlet and outlet temperatures were hourly calculated for the highest demand months: February for winter – heating, and July for summer – cooling.
 To assess the potential of using the foundation bed as an alternative to energy piles, a comparison on the performance of the two cases is presented in Figure 2 for both summer and winter conditions. The foundation bed is seen to work in a steady manner, which is highly desired in a system. However, it performs less well, with a lower COP than the energy piles system, which exhibits greater COP values than the foundation bed system both in winter and summer. It remains that both systems exhibit high enough COPs and nearly steady conditions. The COPs vary between 4.4 and 4.8. A yearly simulation (not shown here) yielded a lowest COP value of 4.5.
 The systems were also assessed economically by being compared to a convectional ASHP system. The economic study demonstrated that the suggested foundation systems had relatively short payback times, making them a plausible alternative. More detailed discussion on the results can be found in Aresti et al. [5]. As a future objective, an environmental and Life Cycle Analysis investigation, similar to the one performed by Aresti et al. [6], could provide a deeper insight of the plausibility of using the building foundation as EGS.

SIMULATION OF HEAT EXCHANGE PROCESSES IN THE “THERMAL CORE” FILLED WITH HEAT ACCUMULATION MATERIAL

The presented article proposes an analytical method for modeling heat exchange processes inside the “thermal core”, which is a coaxial cylinder filled with heat storage material with a phase change material. The equation for heating the cooled phase change material inside the “thermal core” is derived, taking into account the radial transfer of heat in any i-th zone and in the first and last ring zones, separately. The dependence of the heat capacity of the phase change material on the temperature was studied, taking into account the change in the heat capacity according to the cosine law. Also, a comparison of the analytical data of the mathematical modeling with the results obtained experimentally in previous studies is presented and obtained a high degree of similarity, which indicates the reliability of the proposed analytical methodology. Recommendations are provided for the practical implementation of the research results, namely the use of a coaxial pipe “thermal core” filled with a pre-selected material with a phase change material in the construction of storage batteries used in the thermal power industry. As a result, capacitive batteries with a “thermal core” filled with ceresin are used in mobile thermal batteries MTA-0,5MW. Bibl. 14, Fig. 4, Tab. 2.

A discussion of internal flow characteristics and performance of super long gravity heat pipes for deep geothermal energy extraction

Super long gravity heat pipe (SLGHP) provides a novel way for harvesting thermal energy from a deep geothermal reservoir. Previous research has demonstrated the feasibility of this innovative technique, most studies have focused on the overall performance of the heat extraction system, whereas detailed investigations into the internal flow characteristics remains ambiguous. This hampers the application and further advancement of SLGHPs. In this study, a preliminary analysis of the internal flow resistance characteristics is carried out using of the homogeneous model for two SLGHPs, a regular one and a modified one with an inner coaxial pipe. It indicates that the regular SLGHP has higher flow resistance under the same thermal condition of the reservoir. Specifically, the regular SLGHP experiences approximately 1.75 times larger flow resistance than the modified SLGHP (average temperature of the evaporation section and condenser is 95.6 °C and 55 °C, respectively, with water as the working fluid). While on the other hand, the heat transfer capability of the modified SLGHP was improved 29.73%∼77.77% at various condensation temperature compared with the regular SLGHP. The dominant factor contributing to pressure drop in the regular SLGHP is the frictional loss resulting from the counter-current flow of rising vapor and falling liquid film. Conversely, the SLGHP with a coaxial pipe effectively separates the vapor and condensate flows, reducing frictional resistance and improving heat transfer performance. It is speculated that explosive nucleate pool boiling may occur in the liquid pool at the bottom of the SLGHP, enhancing heat transfer from the liquid bulk to the upward-flowing vapor.

Axisymmetric Stress State of an Adhesive Joint of Two Coaxial Pipes. An Improved Theory

Axisymmetric Stress State of an Adhesive Joint of Two Coaxial Pipes. An Improved Theory

Напружено-деформований стан клейового з’єднання, що має поздовжній дефект

In adhesive joints, one has to face the phenomenon of non-adhesive. It is known that non-adhesive reduces the strength of such joints. Analytical models known today for calculating the stress-strain state of adhesive joints have certain defects that appear as a result of simplification (one-dimensional models), and the realization of numerical methods requires a large resource of computing equipment. The subject of study in this article is a mathematical model of the stress-strain state of an adhesive joint of two plates. The purpose of this research is to study the stress-strain state of an adhesive joint with non-adhesives and to develop methods for studying the stress state of adhesive lap joints. Methods: a simplified two-dimensional analytical model of the stress state of the adhesive joint was used to construct an analytical solution to the problem of the stress state of the joint, which contains a defect in the adhesive layer along the side edge of the bonding area. The simplification of the model consists of the fact that the transverse displacements of the base layers are considered to be zero. This assumption can be interpreted as the presence of base layers of high stiffness in the transverse direction, and it allows reducing the problem of the stressed state of the joint to a system of two partial differential equations with respect to the longitudinal movements of the base layers and obtaining the solution of the problem in an analytical form. The obtained solution is written in the form of functional series. The eigenfunctions are not orthogonal. Using the least squares method, the solution of the problem is reduced to a system of linear equations. The model problem for joining two aluminum plates of the same size has been solved. The results showed that the presence of non-adhesive area can significantly increase the stress near the edge of the adhesive layer. Corner points in the adhesive layer are especially dangerous from the strength point of view. The results were compared with the results of finite element modeling. The comparison showed that the proposed mathematical model has high accuracy for engineering calculations. This model can be developed to solve similar problems, for example, to study the stress state of the joint of coaxial pipes, which has defects in the adhesive layer.

Acoustic wave radiation from a coaxial pipe with partial lining and inner perforated screen

In this study, the analysis of sound waves from a coaxial pipe with a perforated screen and a partial acoustic absorbing lining is investigated. The geometry under consideration consists of an infinite pipe placed in a semi-infinite cylindrical pipe such that the inner surface of the outer pipe is covered with a partial acoustic absorbing lining. Because of the partial lining, the solution is obtained with both the Jones’ method and the Mode-Matching method. The effects of the problem parameters such as perforated screen and partial lining on the radiation phenomenon are presented.

Studying the effect of the force convection boundary condition and radius magnetic field on fluid flow and heat transfer between coaxial pipes

AbstractAn investigation of the heat transfer of Newtonian fluid flow through coaxial two pipes with variable radius ratio has been conducted with the boundary conditions of forced convection on the inner pipe walls and a radius magnetic field. This paper presents an exact analytical solution to the momentum equation and a novel semi‐analytic collocation method for solving the full‐term energy equation that takes Joule heating into account as well as viscous dissipation. Based on the results of the numerical fourth‐order Runge–Kutta method, it was found that increasing the magnetic parameter decreased the amount of friction on the surface of the pipe walls and the rate of heat transfer. As the radius ratio of the two pipes increases, so does the skin friction and heat transfer rate on the internal pipe walls. As Eckert (Ec) and Prandtl (Pr) numbers increase, the mean temperature as well as the dimensionless temperature between the two pipes increases. The increase in Biot number (Bi) has the opposite impact on the mean temperature. As Ec, Pr, and Bi increase, so does the rate of heat transfer on the inner wall of the pipe.

Experimental investigation on a diffusion jet flame performance using a developed flame holder supplied with air from a concentric pipe

In this study, a diffusion jet flame consisting of a newly developed flame holder with three coaxial pipes to transfer air and fuel to the combustion zone, is investigated experimentally to simulate the ramjet effect. The flame holder is a double cone with three fuel ports on the top cone to improve the mixing of fuel and air. The inner pipe transfer fuel and is connected to the flame holder (which serves as a fuel injection point) and the middle pipe transfer primary air and the outer pipe transfer secondary air to the combustion zone (to investigate the impact of removing still air from around the flame as in ramjet applications). The flame holder and the primary air exit were at fixed positions (Datum Z4= 0) while the secondary air exit position changed many times below and above the datum line. The results showed that the secondary air exit location had an effect on the flame temperature distribution, flame shape, flame length, and flame width. The optimum position of the secondary air pipe was found above the datum line at Z5 = 7.5 mm, where the flame temperature and length are considered relatively high compared to other secondary air pipe positions.

Thermal performance assessment of the coaxial pipe evacuated tube solar air heater in Bilaspur climatic conditions

The present era finds the implementation of small-scale solar thermal applications to overcome emissions caused by fossil fuels. In this connection, a forced convection co-axial pipe evacuated tube solar air heater is fabricated and examined under various operating parameters and in Bilaspur Chhattisgarh climatic conditions in the months from October 2021 to March 2022. The performance parameters under consideration were outlet air temperature, collector efficiency, exergy efficiency, and overall system efficiency. The experiments have been performed for different mass flow rates 9.36, 15.84, 18.36, 22.32, and 26.28 kg/h of air. The ambient air temperature varied in the range of 20.8 °C to 41.6 °C. The air temperature at the inlet of the heater varies from 28.4 °C to 66.7 °C. The maximum outlet air temperature and temperature rise recorded were 82.9 °C and 37.2 °C in the month of March and February, respectively, for the low mass flow rate of 9.36 kg/h. It was observed that the maximum collector efficiency, exergy efficiency, and overall system efficiency were achieved as 82.95%, 6.4%, and 81.92%, respectively, for a moderate mass flow rate of 15.84 kg/h. All the performance parameters seem to be strongly dependent on the solar intensity and were found to be highest when the intensity was at its peak value. It is found that the increase in mass flow rates beyond 15.84 kg/h tends to decrease the temperature rise as well as the efficiency of the solar heater. No significant temperature rise is observed for a mass flow rate beyond 26.28 kg/h. The study finds that the fabricated setup can effectively produce a low to moderate temperature range (40 °C–80 °C) and can be used for domestic as well as small-scale industrial applications.

Development and application of a novel pre-drilling thermal probe in-situ testing equipment

At present, the in-situ testing equipment used for measuring the thermophysical properties of rock and soil is scarce. Based on the working principle of the pressuremeter and ground heat exchanger, a pre-drilling thermal probe in-situ testing equipment is developed. This novel developed pre-drilling thermal probe in-situ testing equipment includes thermal probe, pressure control system, temperature control system, integrated conversion control device, and coaxial pressure pipe connection pipeline. A three-dimensional heat transfer model was established to simulate the heat transfer between the thermal probe and surrounding ground. Based on the principle of the temperature dissipation and numerical simulation, a calculation method for the thermal conductivity of rock and soil with pre-drilling thermal probe is proposed. Laboratory model tests of the sand under dry and saturated conditions were conducted. The deviation values for the thermal conductivities of sand under dry and saturated conditions measured by the designed pre-drilling thermal probe and thermal conductivity tester are 0.037 and 0.026 W/m·°C, respectively. Thus, the reliability of utilizing the new pre-drilling thermal probe testing equipment to measure the thermal conductivity of the soil is confirmed. The field test of utilizing this new pre-drilling thermal probe testing equipment to measure the thermal properties of the soil was performed. The results show that because the soil layers are in undisturbed state during the test process, the pre-drilling thermal probe testing equipment can truly reflect the inherent thermal properties of different soil layers.

Axisymmetric Stress State of Adhesive Joint of a Circular Patch with a Plate Weakened by a Circular Cut-out

Adhesive lap joints are widely used in modern structures. Known analytical mathematical models of the stress state of lap joints describe the joints of straight beams or cylindrical coaxial pipes. It is assumed that the stress state of these structures depends on only one coordinate. The study of the stress state of plates with defects, which are reinforced by patches, in most cases requires the use of at least two-dimensional mathematical models. In this work, it is shown that the axial symmetry of the plate, the cut-out, the patch, and the applied load makes it possible to reduce the problem to a one-dimensional problem in the polar coordinate system. An adhesive lap joint with circular symmetry is considered for the first time. The stress-strain state of the structure is described in an analytical form. Comparison of the results of calculating the stress state of the joint with the results of finite element modelling showed good adequacy of the proposed mathematical model.

Numerical simulation of pressure loss in a classifier with coaxial pipes

Numerical simulation of pressure loss in a classifier with coaxial pipes