Thermal Expansion Effects Research Articles

Burnup and neutronic parameter analysis of GAMA molten salt reactor (GAMA-MSR)

The GAMA molten salt reactor (GAMA-MSR) is a small modular MSR design developed by the Nuclear Reactor Research Team of the Department of Nuclear Engineering and Engineering Physics, Universitas Gadjah Mada. In the GAMA-MSR design, the reactor core is placed above the primary heat exchanger. The primary heat exchanger is partially filled with fuel in normal operation, allowing room to be filled with the fuel drained from the reactor. Thus, in addition to control rods, the design of GAMA-MSR provides unique reactivity control through the balance of fuel salt fuel from the reactor core to the primary heat exchanger vice versa by adjusting fuel pump capacity. This design allows to shutdown the reactor by switching off the fuel pump. The reactor is initially fueled with 7LiF-ThF4-UF4 with 75: 20.1: 4.9 mol composition. The uranium has 19.75 % U-235 mol fraction. The reactor criticality and nuclide composition in the reactor fuel are calculated using OpenMC code during the reactor operation lifetime, with periodic adjustments to the fuel composition to simulate the effects of the fissile and fertile additions to the fuel and the extraction of actinides and fission products from the fuel. The calculated reactor thermal power is 60 MWth in this paper. The reactor is operated until it achieves a burnup value of 34,000 MWd/tHM. At this burnup value, the U-235 inventory is consumed and the amount is reduced from 794 kg to 250 kg. The U-233, Pu-239 and Pu-241 are produced with the amount are 246 kg, 24 kg and 8 kg respectively at the end of reactor operation. The effects of temperature, fuel density change, and fission product neutron poisons are also calculated. The average temperature reactivity coefficient value is approximately -4.4395×10-5Δk/k per °C. The effect of thermal expansion has been included in the calculation of this temperature reactivity coefficient value. The average value of the void reactivity coefficient is +1.2606×10-3Δk/k per % of void fraction for the void fraction value range up to 50 %. However, molten salt fuel suffers only small changes in density during operation. The negative value of the temperature reactivity coefficient will be dominant; thus, the GAMA-MSR becomes inherently safe. The GAMA-MSR is designed for a 30-year operation time. The effect of the fission product to the reactor reactivity is -1.4597×10-2Δk/k. Full draining of the fuel to primary heat exchanger brings the reactor to shutdown condition with the reactivity of −0.20525. Results showed that this reactor has an inherently safe characteristic and has an effective shutdown system, especially due to the fuel draining system.

Fully bonded iron-based shape memory alloy for retrofitting large-scale bridge girders: Thermal and mechanical behavior

This study presents a prestressed retrofitting solution for addressing fatigue issues in large-scale steel girders, employing iron-based shape memory alloy (Fe-SMA) strips and adhesive bonding. A comprehensive study encompassing design, experimental tests, and numerical analysis is conducted to develop and validate the proposed solution. A 4200×100×1.5 mm Fe-SMA strip is fully bonded along its entire surface using a two-component epoxy adhesive to a 5300 mm span steel girder. An activation strategy to prestress the Fe-SMA strip is formulated based on a series of finite element (FE) analyses, entailing successive block-by-block heating using a gas torch. Experimental and numerical studies illuminate the full-range thermal and mechanical behavior of the retrofitted girder throughout the activation process. A FE heat transfer analysis with experimental validation reveals the temperature developments and distributions during activation, highlighting a 160 ℃/mm temperature gradient along the adhesive thickness and longitudinal distributions with localized high temperatures. The mechanical behavior during activation, encompassing the effects of thermal expansion, Fe-SMA prestress, and adhesive softening and re-hardening, is interpreted based on experimental and numerical results, showing the evolutions and distributions of deflections, strains, and Fe-SMA prestresses. Static tests and a high-cycle fatigue test up to 3 million load cycles demonstrate the effectiveness and structural integrity of the proposed retrofitting solution.

Zero Thermal Expansion Effect and Enhanced Magnetocaloric Effect Induced by Fe Vacancies in Fe2Hf0.80Nb0.20 Laves Phase Alloys

Zero Thermal Expansion Effect and Enhanced Magnetocaloric Effect Induced by Fe Vacancies in Fe₂Hf_0.80Nb_0.20 Laves Phase Alloys

Behavior of hybrid R.C. columns under the effect of fire furnace (experimental and numerical study)

ABSTRACT When fire exposes the hybrid reinforced concrete R.C. columns, it seriously damages the mechanical qualities of steel bars, concrete, and glass fiber reinforced polymer G.F.R.P. bars. This study focused on hybrid reinforced concrete R.C. columns’ behaviour and failure modes that were eccentrically and concentrically loaded during the fire until a failure. The behaviour of these R.C. columns will be quantified by demonstrating and going over the load-displacement relationships, failure mechanisms, crack patterns, strain distribution at failure, ductility, and stiffness. The number and width of cracks in the columns heated to 300 ºC, 500 ºC, and 700 ºC were significantly more than in the unheated columns. When the specimen is exposed to high temperatures, less force is needed to cause a first crack, and the ultimate strength decreases as the applied load and eccentricity ratio values increase. Hence, all specimens’ axial and lateral displacement values increase. This can be explained by two factors: the depth of the practical section because of the thermal expansion effect and the cracking expansion of concrete when subjected to high temperatures, and heating causes a loss in stiffness of column because the elasticity of concrete’s modulus of elasticity drops.

Effect of Negative Thermal Expansion on the Zero-Phonon Line of Implanted Silicon Vacancy Color Centers in Diamond

Effect of Negative Thermal Expansion on the Zero-Phonon Line of Implanted Silicon Vacancy Color Centers in Diamond

Optical fiber sensor for curvature and temperature simultaneous measurement based on an anti-resonance mechanism

Based on an anti-resonance mechanism, we propose and experimentally demonstrate an optical fiber sensor for simultaneous measurement of curvature and temperature. The sensor structure consists of a hollow fiber and a twisted graded index multimode fiber spliced between two single-mode fibers. By using the twisted graded index multimode fiber to change the energy distribution of the mode field, not only improve the coupling efficiency of the sensor but also the sensitivity of the curvature measurement. The experimental results show that the intensity of the resonance peak based on the anti-resonance mechanism decreases with the increase of curvature, while the resonance peak wavelength is insensitive to curvature. In addition, due to the thermal expansion and thermo-optic effect of the fiber, the wavelength of the resonance peak is red-shifted with increasing temperature, and the intensity of the resonance peak is insensitive to temperature. Therefore, the intensity and wavelength signals of the resonance peak are monitored separately, and the simultaneous measurement of displacement and temperature is realized. The maximum sensitivity of the proposed curvature sensor can reach −2.84 dB/m−1, the dynamic range of curvature is 0 m−1 to 20.18 m−1, and the temperature sensitivity of 20 pm/∘C is realized. The proposed sensor has a compact structure, simple preparation, high coupling efficiency, and good repeatability, making it an ideal choice for simultaneous measurement of curvature and temperature in structural monitoring, mechanical manufacturing, and other fields.

Thermal expansion, lattice vibration, and isotope effect on hydrogen diffusion in BCC Fe, Cr, and W from first-principles calculations.

Fe, Cr, and W are important elements in the alloys of in-reactor materials and operate in high-temperature environments with thermal expansion. Their tritium-impeding abilities are crucial to the radiation safety of various nuclear reactors. In this study, first-principles density functional theory is combined with quasi-harmonic approximation to evaluate factors that can affect the interstitial formation energy and diffusion coefficient of hydrogen isotopes in body-centered cubic (BCC) Fe, Cr, and W, including thermal expansion, metal host lattice vibrations, phonon density-of-states (pDOS) coupling diffusing atoms, and isotope effects. Calculation results indicate that the interstitial formation energy decreases as lattice expansion increases, whereas the jump barriers remain almost constant. Thermal expansion, host lattice vibration, and pDOS coupling minimally affect the diffusion coefficients of hydrogen isotopes in Fe, Cr, and W. The diffusion coefficient ratios between hydrogen isotopes are higher than the inverse ratio of the square root of the isotope mass at low temperatures. However, they decrease to the inverse ratio of the square root of the isotope mass at temperatures exceeding 800K. This study comprehensively investigates factors that affect the diffusion coefficients of hydrogen isotopes in BCC Fe, Cr, and W, thus providing a firm theoretical foundation for predicting the diffusion coefficients of tritium at different temperatures using protium/deuterium diffusion coefficients.

Incorporation of self-heating effect into a thermo-mechanical coupled constitutive modelling for elastomeric polyurethane

Elastomeric polyurethane (EPU) is characterised by distinctive mechanical properties, including high toughness, low glass transition temperature, and high impact resistance, that render it indispensable in diverse engineering applications from soft robotics to anti-collision devices. This study presents a thermo-mechanically coupled constitutive model for EPU, systematically incorporating hyperelasticity, viscoelasticity, thermal expansion, and self-heating effect in a thermodynamically consistent manner. Experimental data, obtained from previous studies, are then used for parameter identification and model validation, including iterative updates for temperature parameters considering the self-heating effect. Subsequently, the validated model is integrated into finite element codes, i.e., user subroutine to define a material’s mechanical behaviour (UMAT) based on the commercial finite element software ABAQUS, for the computation of three-dimensional stress-strain states, facilitating the analysis of the structural response to various mechanical loads and boundary conditions. The results obtained from simulations are compared with analytical solutions to confirm the precision of Finite Element Method (FEM) implementation. The self-heating effect is further analysed under different strain rates and temperatures. To validate the engineering significance of the FEM implementation, a plate with a hole structure is also simulated. In conclusion, this research provides a robust tool for engineers and researchers working with soft materials, enhancing their understanding and predictive capabilities, notably addressing the self-heating effect in thermo-mechanical behaviours.

Numerical study on thermal-hydraulic characteristics of streamwise-interrupted flying-wing finned tubes

To improve the thermal-hydraulic performance, this study conducted numerical studies on streamwise-interrupted flying-wing finned tubes utilising both single- and double-channel interruption modes. The interruptions varied in width from 0.5 to 10 mm and were strategically positioned in nine distinct locations along the flow direction. The RNG k-ε turbulence model was applied for viscous flow simulation. The findings reveal that fin interruptions create a “breakpoint thermal expansion effect” at specific locations, enhancing heat transfer downstream while diminishing it upstream. For the single-channel interruption mode with a centrally positioned interruption channel, a 5–6 mm width is optimal at a low air velocity (150 Pa total pressure drop and a Reynolds number of 1282.31 for the continuous flying-wing finned tubes). However, at high air velocities (550 Pa total pressure drop and a Reynolds number of 2944.91), interruption is unnecessary. In both modes, standardising the interruption channel width to 2 mm is more effective when the interruptions are placed closer to the downstream end, as opposed to an even distribution. This study provides valuable insights for enhancing the thermal-hydraulic performance of flying-wing finned tubes and similar continuous-finned designs through strategic flow-channel interruptions.

Bowtie design for thermal expansion mimicry and mitigation

A geometric bowtie design for the purpose of mimicking (matching) and/or mitigating (reducing) the thermal expansion effects between two laterally opposing structures is investigated. A bowtie design is that of two opposing overlapping triangles with farthest sides parallel. This design embodies thermal centering concepts which utilize the relationships of the trigonometric identity known as the law of sines for a triangle from which beneficial thermal properties can be engineered. For validation. The bowtie design is embodied using two separated Zerodur plane mirrors, symmetrically opposed, and each seated in Maxwell-style kinematic couplings of spheres and vee-groves. The vee-grooves form a wheel-like pattern on an aluminum baseplate. The intersection of the vee-grooves is the common overlapping thermal center of both mirror mounts. The refractive-index corrected interferometric measurement of the displacement between these two mirrors shows that even during non-isothermal non-equilibrium transitions and states, the nominal ∼90 μm thermally induced (13 °C) expansion of an aluminum baseplate can be mitigated, being reduced more than 98 % to ∼1.4 μm by mimicking the thermal expansion properties of the mirrors’ structural material. Engineering thermally-invariant kinematic bowtie designs using materials having higher thermal expansion coefficients is also described.

A Micro-Mach–Zehnder Interferometer Temperature Sensing Design Based on a Single Mode–Coreless–Multimode–Coreless–Single Mode Fiber Cascaded Structure

In this paper, a temperature sensing scheme with a miniature MZI structure based on the principle of inter-mode interference is proposed. The sensing structure mainly comprises single mode–coreless–multimode–coreless–single mode fibers (SCMCSs), which have been welded together, with different core diameters. The light beam has been expanded after passing through the coreless optical fiber and is then coupled into a multimode optical fiber. Due to the light passing through the cladding and core mode of the multimode optical fiber with different optical paths, a Mach–Zehnder interferometer is formed. Moreover, due to the thermo-optic and thermal expansion effects of optical fibers, the inter-mode interference spectrum of a multimode fiber shifts when the external temperature changes. Through theoretical analysis, it is found that the change in the length of the sensing fiber during temperature detection has less of an effect on the sensitivity of the sensing structure. During the experiment, temperature changes between 20 and 100 °C are measured at sensing fiber lengths of 1.5 cm, 2.0 cm, 2.5 cm, 3.0 cm, 3.5 cm, and 4.0 cm, respectively, and the corresponding sensitivities are 65.98 pm/°C, 72.70 pm/°C, 67.75 pm/°C, 66.63 pm/°C, 74.80 pm/°C, and 72.07 pm/°C, respectively. All the corresponding correlation coefficients are above 0.9965. The experimental results indicate that in the case of a significant change in the length of the sensing fiber, the sensitivity of the sensing structure changes slightly, which is consistent with the theory that the temperature sensitivity is minimally affected by a change in the length of the sensing fiber. Therefore, the effect of the length on sensitivity in a cascade-based fiber structure is well solved. The sensing scheme has an extensive detection range, small size, good linearity, simple structure, low cost, and high sensitivity. It has a good development prospect in some detection-related application fields.

Study on the evolution law of physical mechanics and abrasion characteristics of granite under high temperature-water cooling treatment

During deep geothermal resource development, the estimation of drilling efficiency and tool wear in extremely hard rocks relies primarily on CAI testing. However, the degradation of rocks caused by high-temperature water cooling conditions leads to unpredictable changes in CAI. To address this issue, this study conducted P-wave velocity, hardness, thermal conductivity testing, BTS experiments, CAI testing, and NMR testing on granite samples subjected to water cooling at different temperatures (25–600 °C). The study analyzed the degradation mechanisms of granites under high temperature-water cooling conditions, the relationship between various parameters and the CAI index, and established a dual-parameter fitting model. The results indicate that the degradation of rocks under hightemperature-water cooling conditions is primarily attributed to mineral thermal reactions, thermal expansion effects at high temperatures, and rapid cooling-induced thermal contraction effects. Once the degradation effects exceed the skeleton constraint limit, macroscopic cracks gradually form within the granite. The formation of macroscopic cracks has a mitigating effect on abrasivity. The research findings on the correlation between CAI and various parameters can provide important theoretical support for the application of high-temperature rock breaking engineering.

A Sealability Study on Bismuth-Tin Alloys for Plugging and Abandonment of Wells

Summary The use of bismuth alloys as a barrier material for plugging and abandonment (P&A) has gained traction in the literature due to the large number of wells scheduled to be plugged and abandoned. In addition, many questions have been raised regarding the sealing efficiency of cement in the long run. Within this context, this work performs a thorough study of the sealability of plugs made with the eutectic bismuth-tin alloy. This effort is divided into three fronts: laboratory tests to verify the pressure resistance and leakage rate of these plugs, microscopy analyses to corroborate the tests’ insights through observations of the alloy microstructure, and numerical simulations to capture and model the involved phenomena aiming to reproduce real well scenarios in the future. Results show that bismuth-tin plugs exhibit better pressure resistance and lesser leakage rates than cement plugs, which indicates that this material is a suitable candidate. Better sealing properties are achieved when the plugs are set under higher curing pressures than the atmospheric pressure, an observation that is confirmed when observing the microstructures formed. Finally, a suitable material model that captures the expansion upon solidification is proposed, and the effect of thermal expansion on the plug and pipe assembly is observed.

Effects of Thermal Expansion and Pressure on Far-Field Fluctuations of Heterogeneous Propellants

In this work, we carry out three-dimensional mesoscale simulations of heterogeneous solid propellant combustion. We solve the reactive low-Mach-number equations in the gas phase with complete coupling to the solid phase. The model takes into account thermal expansion and deformation in the solid phase by using a hypoelastic law in the quasi-static limit. To account for morphology, we select two different propellant formulations with different particle size distributions and present the results as a function of pressure. The thermomechanical behavior is accessed by examining quantities such as strain and stress in the propellant as a function of pressure and propellant morphology. We also show that temperature and velocity fluctuations exist in the far field above the propellant surface and that these fluctuations can be significant. To better understand the nature of these fluctuations, we vary the pressure and make relevant plots of normal velocity and temperature probability density functions, as well as time autocorrelations. Such descriptions are necessary to account for the coupling between the mesoscale and the macroscale, where the fluctuations at the mesoscale can affect quantities at the macroscale, such as head-end pressure, trigger parietal vortex shedding, and aeroacoustics.

Temperature-transferable tight-binding model using a hybrid-orbital basis.

Finite-temperature calculations are relevant for rationalizing material properties, yet they are computationally expensive because large system sizes or long simulation times are typically required. Circumventing the need for performing many explicit first-principles calculations, tight-binding and machine-learning models for the electronic structure emerged as promising alternatives, but transferability of such methods to elevated temperatures in a data-efficient way remains a great challenge. In this work, we suggest a tight-binding model for efficient and accurate calculations of temperature-dependent properties of semiconductors. Our approach utilizes physics-informed modeling of the electronic structure in the form of hybrid-orbital basis functions and numerically integrating atomic orbitals for the distance dependence of matrix elements. We show that these design choices lead to a tight-binding model with a minimal amount of parameters that are straightforwardly optimized using density functional theory or alternative electronic-structure methods. The temperature transferability of our model is tested by applying it to existing molecular-dynamics trajectories without explicitly fitting temperature-dependent data and comparison with density functional theory. We utilize it together with machine-learning molecular dynamics and hybrid density functional theory for the prototypical semiconductor gallium arsenide. We find that including the effects of thermal expansion on the onsite terms of the tight-binding model is important in order to accurately describe electronic properties at elevated temperatures in comparison with experiment.

Study of the Influence of Doping Efficiency of CeO2 Ceramics with a Stabilizing Additive Y2O3 on Changes in the Strength and Thermophysical Parameters of Ceramics under High-Temperature Irradiation with Heavy Ions

The article outlines findings from a comparative analysis of the effectiveness of doping CeO2 ceramics with a stabilizing additive Y2O3 on alterations in the strength and thermophysical parameters of ceramics under high-temperature irradiation with heavy ions comparable in energy to fission fragments of nuclear fuel, which allows, during high-temperature irradiation, to simulate radiation damage that is as similar as possible to the fission processes of nuclear fuel. During the studies, it was found that the addition of a stabilizing additive Y2O3 to the composition of CeO2 ceramics in the case of high-temperature irradiation causes an increase in stability to swelling and softening because of a decrease in the thermal expansion of the crystal lattice by 3–8 times in comparison with unstabilized CeO2 ceramics. It has been determined that the addition of a stabilizing additive Y2O3 leads not only to a rise in the resistance of the crystal structure to deformation distortions and swelling, but also to a decrease in the effect of thermal expansion of the crystal structure, which has an adverse effect on the structural ordering of CeO2 ceramics exposed to irradiation at high temperatures.

Impact of Lanthanide (Nd3+, Gd3+, and Yb3+) Ionic Field Strength on the Structure and Thermal Expansion of Phosphate Glasses.

Phosphate glasses containing Nd3+, Gd3+, and Yb3+ as lanthanide ions are attractive for applications in laser materials, phototherapy lamps, and solar spectral converters. The composition-structure-property relation in this type of glass system is thus of interest from fundamental and applied perspectives. In this work, the impact of the differing ionic radius of Nd3+, Gd3+, and Yb3+ and consequent field strength on the physical properties of phosphate glasses is investigated, focusing ultimately on thermal expansion effects. The glasses were made by melting with a fixed concentration of the lanthanide ions having 50P2O5-46BaO-4Ln2O3 nominal compositions (mol %) with Ln = Nd, Gd, and Yb. The investigation encompassed measurements by X-ray diffraction (XRD), optical spectroscopy, density, X-ray photoelectron spectroscopy (XPS), Raman spectroscopy, and dilatometry. XRD supported the amorphous nature of the glasses, whereas absorption and photoluminescence spectra showed the optical features of the Nd3+, Gd3+, and Yb3+ ions in the glasses. Oxygen speciation by XPS indicated an increase in nonbridging oxygens for the larger radii Nd3+ and Gd3+ ions relative to the host, contrasting with Yb3+. Phosphorus XPS analysis further supported the hypothesis that the P 2p binding energies of the glasses increased with the cation field strength of the lanthanides. The Raman spectra were interpreted based on glass depolymerization effects and the impact of Ln3+ ions with high field strength. Particularly, the band position of the symmetric out-of-chain nonbridging oxygen stretch, νs(PO2-), shifted to higher frequencies correlating with the Ln3+ field strength. Dilatometry ultimately revealed a steady decrease in the coefficient of thermal expansion for the glasses, which correlated linearly with Ln3+ field strengths and thus indicated to sustain increased glass rigidities. The various analyses performed thus illuminated the structural foundation of the thermomechanical behavior of the glasses connected with changes in the Ln3+ field strengths.

Effect of thermal expansion to the coupling efficiency of (1 + 1) long distance side pumping fiber

With the same fiber preform, two long distance side pumping fibers were fabricated and measured based on a master oscillator power structure. The residual pump power tendency of the two fibers were obtained in experiment. It was found the residual pump power would arise rapidly when the power reached turning point, which was defined by derivative value of residual pump power to pump power equal to 2.5%. Numerical analysis reveals that the thermal expansion of low refractive polymer between signal and pump fibers, will increase the distance between fibers, deteriorate the coupling efficiency, and lead to an exponential increasing of the residual pump power.

Experimental investigation on the effects of transverse injection distribution scheme on dual flame dynamics subjected to flow disturbances

Combustion instability has become a major problem in low-emission annular gas turbine combustors. It is of practical importance to investigate the effects of transverse nozzle distribution scheme on multi-flame dynamics subjected to external acoustic perturbations. In this study, the responses of heat release rate perturbations from dual propane/air laminar premixed flames to axial acoustic perturbations have been experimentally measured. Specifically, the velocity disturbance upstream the flame base has been measured by two-microphone method and the flame heat release rate perturbation is obtained by the photomultiplier tube with CH* filter lens. The dynamic evolution of dual flames is captured by the high-speed camera and then analyzed with the proper orthogonal decomposition (POD) method. Results indicate that there is a critical distribution distance, where the peak gain of the dual flame transfer function is the largest. And the direct injection dual flame transfer function can behave as the low-pass filter. Furthermore, the dual flame transfer function behaves nonlinearly with the increase of the injection angle. The dual flame transfer function for large injection angle can behave as the hybrid mode of the low-pass filter and the band-pass filter. The POD analysis reveals that the coupling effect of gas thermal expansion and stretch effect would contribute to the interaction between dual flame front dynamics. The transverse injection distribution scheme (dual flame distance and injection angle) has a significant effect on the dual flame front dynamics, which in turn affects the flame heat release rate disturbance. The bulk mean flow velocity can enhance the interaction effect between dual flame front dynamics.

Investigation on damage-permeability model of dual-porosity coal under thermal-mechanical coupling effect

Understanding the permeability characteristics of coal under mining disturbance is crucial for ensuring coal mine safety and efficient gas extraction. Coal is a dual porosity medium consisting of matrix and fracture, and there are some differences in mechanics and permeability between matrix pores and fracture. However, research on the damage and gas seepage characteristics of dual-porosity coal is limited. In this paper, a coupled damage-permeability model considering matrix pores and fractures in coal is established, incorporating the influences of effective stress, gas adsorption, thermal expansion, and thermal cracking. And the reliability of the newly developed model was verified using experimental data of temperature and pressure variations under different stress boundary conditions. The results indicate that during the elastic stage, the total permeability and fracture permeability of coal exhibit a trend of decreasing and then increasing with pore pressure, while matrix permeability gradually increases. In the full stress-strain stage, the overall damage-permeability and fracture damage-permeability of coal exhibit an “S"-shaped variation trend with axial strain, while matrix damage-permeability shows a slow increasing trend. To accurately characterize the evolution of gas seepage in coal, contributions from matrix pores and fractures must be comprehensively considered, and the effects of gas adsorption, effective stress, thermal cracking, and thermal expansion on permeability cannot be ignored. Furthermore, through parameter sensitivity analysis, it is found that during the elastic stage, coal permeability decreases with an increase in the adsorption sensitivity coefficient and thermal expansion coefficient. In the full stress-strain process, coal permeability increases with an increase in the damage-permeability coefficient. The results of this study are of great significance for predicting the evolution of coal permeability in the working face ahead under mining disturbance.