Current Flow Field Research Articles

Noise Source Identification for the Unsteady Low-Pressure Turbine Flow Fields

Abstract The article presents a data processing methodology to identify the noise sources in low-pressure turbine (LPT) stages and their relative importance. Scale adaptive simulation (SAS) has been carried out on a geometry reproducing the midspan blade section of an entire LPT stage. The proper orthogonal decomposition (POD) is applied to data matrices constructed with the velocity and the pressure fields in order to distinctly extract the coherent structures responsible for velocity fluctuations and pressure waves (i.e., POD modes from the corresponding kernel), their temporal evolution and energies. The cross-correlation matrices of the pressure modes and the velocity modes reveal the degree of coupling between pressure and velocity oscillations, thus highlighting the modes linked to the same flow phenomena. The results show that the periodic vortex shedding at the stator trailing edge emits strong pressure waves, and the upstream-propagating waves reflect against the adjacent stator suction surface. The POD modes related to the rotor–stator interaction show peak amplitudes at the blade passing frequency and its harmonics and their shapes mimic the potential interaction in the stator domain and the migration of viscous wakes in the rotor domain. The POD modes with lower energy content correspond to the stochastic turbulent structures originated from the turbulent boundary layers as well as those carried by the vane and blade wakes. The biggest noise sources of the current flow fields are identified to be the von Karman vortex street downstream the stator trailing edge and the rotor–stator interaction.

Prediction model for self-starting of hypersonic inlets with soft critical unstart mode

The acceleration self-starting performance of hypersonic inlets is of critical importance for the stable operation of scramjet engines. The occurrence of soft unstart during the transition from hard unstart to start is an important flow state that has yet to be fully elucidated. The stability mechanism and corresponding self-starting characteristics of soft unstart remain poorly understood, and there is a pressing need for detailed modeling research in this area. This paper presents a rapid prediction model for the self-starting Mach number of two-dimensional hypersonic inlets with soft critical unstart mode, fully considering the influence of various geometric parameters and Reynolds number in the internal contraction section, and achieving a quantitative analysis of the two-dimensional soft unstart critical flow field. Given the incoming flow conditions and the inlet geometry, the prediction model is capable of accurately representing the actual viscous unstart flow field. It can fully map the unstart separation bubble and its surrounding critical wave structures, and calculate the minimum pressure rise required to maintain the current scale of the main separation bubble and the pressure rise exerted on the unstart separation bubble by the current actual flow field structure. Comparing the relative magnitude of these two pressures determines whether the inlet can transition from soft unstart to start. The proposed prediction model was validated using results from unsteady numerical simulations. The predicted results align well with the simulation results and are significantly better than previous prediction methods.

Supersonic combustion field evolution prediction in scramjet engine using a deblurring multi-scale attention network

Traditional deep learning technologies often overlook crucial spatiotemporal information when reconstructing supersonic combustion flow fields. These models can only reconstruct the current flow field, resulting in poor visual quality due to the atomization effect. This research introduces experimental studies on scramjet combustion flows with variable injection pressures at the inlet of a scramjet Mach 2.5, creating image datasets of flame evolution processes over different predicted time spans (5, 10, and 15 ms). It develops a multi-scale attention algorithm with deblurring (DB-MSAN) capabilities to predict the flame image after a certain period using the wall pressure signal from the previous moment. The algorithm employs two multi-head attention channels at different scales to extract timing information, encouraging the model to focus on the anisotropy of the input data and to identify more significant features. The DB module utilizes the adapted atmospheric scattering model to jointly estimate the transmission map and atmospheric light, achieving an exceptional defogging effect with a minimal computational expense. The model’s overall performance is assessed regarding efficiency and accuracy, comparing DB-MSAN’s performance differences with those of Chen’s and the ResNet16 models across multi-span, large-span, various test sets, and sparse wall measurement points. Experimental results indicated that, compared to other methods, DB-MSAN achieves a maximum peak signal-to-noise index improvement of 76.10 % and an SSIM index improvement of 155.26 % when predicting average-quality images. The prediction accuracy remains stable, even with sparse pressure input. In addition, DB-MSAN strikes an optimal balance between the number of parameters and model accuracy; it represents only 16.97 % of the volume compared to Chen’s model, which is 585 MB.

Large Eddy Simulation of a Turbulent Polydisperse Spray Flow: A Comparative Study of Subgrid Scale Models and Droplet Injection Models

Abstract This study performs an investigation of the effects of the subgrid-scale (SGS) and droplet injection models in the large eddy simulation (LES) of turbulent two-phase spray flows. Three LES SGS models (Smagorinsky, wall-adapting local eddy viscosity (WALE), and dynamic Smagorinsky) and two droplet injection models (cone nozzle injection and conditional droplet injection) are validated to the experimental measurements. For both gaseous and liquid phases, all SGS models provide comparable results, indicating that the current two-phase flow field does not exhibit a pronounced sensitivity to the LES SGS model. As for different droplet injection models and spray dispersion angles, minimal differences are observed in the prediction of the gaseous mean and root-mean-square (RMS) velocity profiles. However, for the result of liquid phase, CDIM (conditional droplet injection model) predictions of the droplet mean diameter and velocity are in better agreement with experiments, and less sensitive to spray dispersion angle settings. While the CNIM (cone nozzle injection model) prediction of droplet diameter is less accurate when increasing the dispersion angle. The study suggests that turbulent two-phase spray flows are more influenced by the spray boundary conditions rather than the LES SGS models.

Effect of multi-channel shape design on dynamic behavior of liquid water in PEMFC

A well-designed flow channel is crucial for effective water management in proton exchange membrane fuel cell. This study presents novel simulation investigation of the dynamic behavior of liquid water in three-dimensional multi-channels with various shape designs, including straight channel (SC), blocked channel (BC), wave channel (WC), and tapered channel (TC). The first, second, and third single channels are arranged in order from gas inlet in multi-channel. The results indicate that drainage rate of first channel in multi-channel is slower than that of second and third channel. Among the four designs, BC and TC reduced water ejection time by 7 ms and 6.5 ms respectively compared to SC, and reduced the time by 39 ms and 38.5 ms respectively compared to WC. In base case, drag reduction rate of TC compared to BC and WC increased by 4.12% and 20.98% respectively. However, WC has the smallest water coverage and average drag reduction ratio, while SC has a lower average gas flow resistance coefficient. This research offers innovative perspectives and theoretical foundations for current flow field design.

1.2-kV Low-Barrier 4H-SiC JBS Diodes by Virtue of P-Implants Across Dead Field of Current Flow

A low value of Schottky barrier height (SBH) ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi _{\textit{B}}\text{)}$</tex-math> </inline-formula> is highly desired to further reduce the power loss in 4H-SiC junction barrier Schottky (JBS) diodes; however, the reduced <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi _{\textit{B}}$</tex-math> </inline-formula> results in serious leakage current ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}_{\textit{R}}\text{)}$</tex-math> </inline-formula> when blocking high voltages. In this work, a tunable low <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi _{\textit{B}}$</tex-math> </inline-formula> of 0.92–0.98 eV with an ideal factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{n}$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$=$</tex-math> </inline-formula> 1.02–1.03 was first realized through effectual rapid thermal annealing (RTA) methods and combined with a trench-assisted stage-style p-type implants taking advantage of dead region for current flow to resolve the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}_{\text{R}}$</tex-math> </inline-formula> issue. Numerical simulation demonstrated the superiority of this promising strategy in alleviating the Schottky interface electric field ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{E}_{\text{S}}\text{)}$</tex-math> </inline-formula> and suppressing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}_{\textit{R}}$</tex-math> </inline-formula> without constraining the forward current flow. Based on this practical strategy, the fabricated device achieved one order of magnitude less <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{I}_{\textit{R}}$</tex-math> </inline-formula> at 25 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C and 220% enhancement of breakdown voltage ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{V}_{\textit{B}}\text{)}$</tex-math> </inline-formula> at 175 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{\circ}$</tex-math> </inline-formula> C in contrast to the conventional low-barrier one. In addition, benefiting from the low <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi _{\textit{B}}$</tex-math> </inline-formula> , the device achieved an ultralow turn-on voltage of 0.47 eV and a remarkable forward voltage drop ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textit{V}_{\textit{F}}\text{)}$</tex-math> </inline-formula> of 1.36 V extracted at 20 A, indicating 14% lower conduction loss than the titanium-based JBS diodes with the same device configuration. This novel device structure incorporating low-barrier Schottky contact metal and trench-assisted stage-style p-implants (SPs) in the dead region of current flow suggests a promising way to develop more advanced 4H-SiC JBS diodes in the future.

Assessment of groundwater salinization impact in coastal aquifers based on the shared socioeconomic pathways: An integrated modeling approach

Seawater intrusion (SWI) has become a significant threat to human health and sustainable economic development in coastal areas with the rapid pace of climate change. Therefore, it is crucial to determine the response of SWI to climate change. However, most studies cannot reflect the direct impact of future climate change on groundwater salinity. This study first established the SWAT-MODFLOW coupled model after unifying both spatiotemporal computational units. Streamflow, groundwater level observation data, etc., were used to calibrate and validate the coupled model. And then SEAWAT model was loaded into the coupled model to form a new integrated model. Finally, precipitation of six Global Climate Models (GCMs) under two shared socioeconomic pathways (1–2.6 and 5–8.5 scenarios) was imported into the above calibrated integrated model separately to make SWI prediction from December 30, 2020, to December 30, 2030. The results show that this integrated model accurately reflected the study area's current flow and concentration field distribution. Precipitation under different ssps had little effect on future SWI, while the uncertainty of SWI prediction was mainly derived from different GCMs. This study provides important implications for exploring the occurrence and the prediction of SWI in the coastal aquifer. It has specific reference significance for the optimal management of water resources in coastal areas and the effective mitigation of SWI.

Characterization of seawater intrusion based on machine learning and implications for offshore management under shared socioeconomic paths

With the increase of climate change and the risk of human activities, seawater intrusion has become an essential threat to human health and sustainable economic development in coastal areas. Therefore, identifying the critical features of seawater intrusion is significantly important, but the existing research on it is insufficient. Moreover, most of the work cannot reflect the direct impact of different shared socioeconomic paths on groundwater salinity in the future. To solve this problem, this study first established a numerical model of variable density flow for the Dagu River Basin based on SEAWAT to analyze the main aquifers' current flow field and concentration field distribution. Then two machine learning methods, random forest and mutual information methods, are introduced to identify critical features of seawater intrusion for the first time. Finally, taking the characteristics affected by climate are used as variables for selecting GCMs, the seawater intrusion in the study area is predicted by six GCMs under shared socioeconomic paths (ssp1-2.6 and ssp5-8.5) from 2020.12.30 to 2030.12.30. The findings indicate that regional precipitation and groundwater extraction exert significant influence on seawater intrusion, with the hydraulic conductivity of the primary aquifer also demonstrating crucial importance. Moreover, it is observed that the potential impact of different shared socioeconomic paths on future variations of seawater intrusion is negligible. This study verifies the effectiveness of machine learning in seawater intrusion analysis to a certain extent and has specific reference significance for the optimal management of water resources in coastal areas and the effective mitigation of seawater intrusion.

Multi-layer flow field mapping in a small-scale shallow water reservoir by coastal acoustic tomography

Long-term, high-precision and spatiotemporal observation of current structure in small-scale waters is important for underwater research and water resources management. In this paper, a reciprocal sound transmission experiment was conducted using three Coastal Acoustic tomography (CAT) systems within 300 m spacing in Huangcai reservoir, Hunan, China from 14 to 16, Sep 2020. The multi-arrival reciprocal paths between each pair of stations were identified with the help of ray simulation. 3-D CAT data which penetrated the full depth of water were obtained. The flow field along vertical slice were mapped and showed consistency with Acoustic Doppler Current Profiler (ADCP) and Temperature Depth (TD) data. A standard deviation of 0.73 m/s at the bottom layer were observed, indicating strong bottom flows in the reservoir. Furthermore, to visualize the strong bottom flow, the horizontal flow fields in the bottom layer were mapped by 3-D inversion technique. The feasibility of the technique was validated by three measures: 1) comparison between range average current and horizontal flow field; 2) Uncertainty analysis; 3) Check net volume transport. This work proves the CAT combined with 3-D inversion technique has the potentials to provide real-time 3-D current data for water researches.

Ensemble-Based Flow Field Estimation Using the Dynamic Wind Farm Model FLORIDyn

Wind farm control methods allow for a more flexible use of wind power plants over the baseline operation. They can be used to increase the power generated, to track a reference power signal or to reduce structural loads on a farm-wide level. Model-based control strategies have the advantage that prior knowledge can be included, for instance by simulating the current flow field state into the near future to take adequate control actions. This state needs to describe the real system as accurately as possible. This paper discusses what state estimation methods are suitable for wind farm flow field estimation and how they can be applied to the dynamic engineering model FLORIDyn. In particular, we derive an Ensemble Kalman Filter framework which can identify heterogeneous and changing wind speeds and wind directions across a wind farm. It does so based on the power generated by the turbines and wind direction measurements at the turbine locations. Next to the states, this framework quantifies uncertainty for the resulting state estimates. We also highlight challenges that arise when ensemble methods are applied to particle-based flow field simulations. The development of a flow field estimation framework for dynamic low-fidelity wind farm models is an essential step toward real-time dynamic model-based closed-loop wind farm control.

A high performance approach for solving the high voltage direct current ion flow field problem by tensor‐structured finite element method

A high performance approach for solving the high voltage direct current ion flow field problem by tensor‐structured finite element method

Deep neural network based reduced-order model for fluid–structure interaction system

Fluid–structure interaction analysis has high computing costs when using computational fluid dynamics. These costs become prohibitive when optimizing the fluid–structure interaction system because of the huge sample space of structural parameters. To overcome this realistic challenge, a deep neural network-based reduced-order model for the fluid–structure interaction system is developed to quickly and accurately predict the flow field in the fluid–structure interaction system. This deep neural network can predict the flow field at the next time step based on the current flow field and the structural motion conditions. A fluid–structure interaction model can be constructed by combining the deep neural network with a structural dynamic solver. Through learning the structure motion and fluid evolution in different fluid–structure interaction systems, the trained model can predict the fluid–structure interaction systems with different structural parameters only with initial flow field and structural motion conditions. Within the learned range of the parameters, the prediction accuracy of the fluid–structure interaction model is in good agreement with the numerical simulation results, which can meet the engineering needs. The simulation speed is increased by more than 20 times, which is helpful for the rapid analysis and optimal design of fluid–structure interaction systems.

Convolutional neural network analysis of radiography images for rapid water quantification in PEM fuel cell

Polymer electrolyte membrane (PEM) fuel cells produce water as a byproduct, which, if not properly managed, will cause electrode “flooding” and consequently performance loss. Nonintrusive methods, such as neutron or X-ray radiography, have been employed to obtain in-situ water images in PEM fuel cell. This study presents one of the first studies developing a machine learning approach to analyze neutron radiography images using the convolutional neural network (CNN), a deep learning model, to quantify liquid water content in PEM fuel cell. The CNN model is trained using the labeled radiography images constructed from the contour legend, which contains the information of the water areal mass density. Image enhancement is carried out to generate additional data for CNN training. The properly-trained CNN model is subsequently applied to the radiography images to obtain the average water areal mass densities under various current densities, relative humidity (RH), and flow fields. The results show that the water content can be significantly reduced by using low RH inlet flow and the counter-flow configuration renders the fuel cell a higher water content than the co-flow one. In addition, the quad-serpentine flow field increases the water content in the current density range of 0.4–0.8 A/cm2 compared with the single-serpentine one. The CNN model takes less than 0.1 s to analyze an image and its results agree well with the literature data from the conventional image processing method with an accuracy of 91%. The CNN method is applicable to other radiography methods and is suitable for the online/rapid monitoring of liquid water in PEM fuel cell.

Effect of pumping gas on temperature field and pressure in hollow tungsten arc

A hollow tungsten negative pressure arc (HTNA) is a heat source that controls the gas flow inside a tungsten electrode and optimizes the arc output. However, to ensure the widespread applicability of HTNAs, the factors affecting the temperature and pressure distribution of an HTNA should be studied. In this study, the effect of pumping gas on the temperature and pressure distribution of an HTNA is elucidated through experiments and numerical simulations. A double spectral line acquisition system with nine optical transmission fibers was used to obtain the arc light intensity for the temperature calculation and spatial reconstruction. Consequently, a unified numerical model was developed to quantitatively study the physical field distribution under the effect of pumping gas. It was observed that the maximum temperature of the traditional gas tungsten arc (GTA) and hollow tungsten arc (HTA) decreased more than that of the HTNA owing to the effects of pumping gas. By analyzing the current density and flow field, it was concluded that convective heat transfer owing to pumping gas is the primary cause of the temperature difference between the arcs rather than Joule heat. Compared with the effect of the Lorenz force, the arc flow had a more significant effect on the pressure difference between the inner and outer tungsten electrodes. The gas in the arc region flowing into tungsten also affected the arc pressure on the base metal surface. The results of this study are expected to provide guidance for controlling the energy output of the welding arcs.

Multi-input convolutional network for ultrafast simulation of field evolvement

SummaryThere is a compelling need for the regression capability of mapping the initial field and applied conditions to the evolved field, e.g., given current flow field and fluid properties predicting next-step flow field. Such a capability can provide a maximum to full substitute of a physics-based model, enabling fast simulation of various field evolvements. We propose a conceptually simple, lightweight, but powerful multi-input convolutional network (ConvNet), yNet, that merges multi-input signals by manipulating high-level encodings of field/image input. yNet can significantly reduce the model size compared with its ConvNet counterpart (e.g., to only one-tenth for main architecture of 38-layer depth) and is as much as six orders of magnitude faster than a physics-based model. yNet is applied for data-driven modeling of fluid dynamics, porosity evolution in sintering, stress field development, and grain growth. It consistently shows great extrapolative prediction beyond training datasets in terms of temporal ranges, spatial domains, and geometrical shapes.

Three-dimensional unsteady model of arc heater plasma flow

Arc jets are unique facilities used to evaluate the performance of Thermal Protection Systems (TPS) for hypersonic vehicles. They produce high pressure and high enthalpy plasma flow to simulate the extreme heat encountered during atmospheric entry. The constricted arc heater part of an arc jet increases the test gas temperature by Joule heating. This study details the development of the three-dimensional unsteady plasma flow analysis tool, ARCHeS (ARC Heater Simulator). Coupled Navier-Stokes, radiative transfer and Maxwell equations yield current density, magnetism, radiation, and flow field solutions. The present work constitutes the first demonstration of an unsteady three-dimensional plasma flow simulation of high pressure and high enthalpy arc heater that captures kink instabilities of the electric arc. It is found that the arc attachment is mainly driven by upstream arc instabilities.

EXPERIMENTAL AND NUMERICAL STUDY OF THE EFFECT OF A PIER ON SHIP TRAJECTORIES IN CURRENTS

A study is presented of the effect of a pier on ship trajectories in currents. The current flow field around the pier is investigated. Experiments on ship manoeuvring and drift motion in the vicinity of a rectangular pier were carried out in a tank. Different current velocities and current angles were taken into account. The characteristics of the deviations of the ship trajectories from the initial course around the pier are investigated. Experimental findings indicate that the minimum required distance for safety navigation becomes larger with an increase of the current velocity. To obtain the details of continuous three-dimensional flow field around a pier, numerical simulation based on CFD calculations is conducted. The validity of the numerical simulation is demonstrated by comparison with experimental results.

Strain-driven radial vortex core reversal in geometric confined multiferroic heterostructures

The magnetic radial vortex is a nanoscale magnetization configuration that is typically stabilized by the interfacial Dzyaloshinskii–Moriya interaction (i-DMI). The existing control methods for the radial vortex core polarity rely on the use of current flow or magnetic fields, which may cause long consumption times or limit device miniaturization. Here, we investigate a repeated reversal of a radial vortex that can be driven by strain from a piezoelectric substrate using micromagnetic simulations. A phase diagram for the representative regions against perpendicular anisotropy, i-DMI, and the applied strain was obtained. The derived phase diagram was used to associate the mechanism of the core reversal with edge magnetization rotation during core magnetization switching, which exhibits a relationship by transforming a quasi-Bloch wall into a Néel wall. The existence of the i-DMI effect causes the core polarity and radial chirality of the radial vortex to be reversed simultaneously without resulting in larger core movements. These results offer an alternative and efficient way to achieve core reversal, which is expected to stimulate the radial vortex application in magnetoresistive memory devices.

Characteristic current flow through a stocked conical sea-cage with permeable lice shielding skirt

The characteristic current flow field around a 55 m deep full-scale stocked conical Atlantic salmon sea-cage equipped with a 10 m permeable skirt was studied experimentally using acoustic Doppler velocimeters and profilers. The weakest current speed was inside the cage at 6 m depth and the highest reduction downstream was recorded behind the shielded volume. Downstream of the cage the reduction in speed became little to non-existing at 22 m depth, probably due to the decreasing diameter of the cage with depth. To reduction in current speed through the cage was compared with estimated reduction from theoretical expressions. The results compared reasonably well downstream of the shielded cage, while the reduction inside the cage was higher than the estimates. The difference in current flow field behind a conical cage compared with a cylindrical cage may have implications for the dispersal of waste, feed pellets and microorganisms from the cage influencing the benthic impact of the farm.

Influence of Structural Defects on the Resistivity and Current Flow Field in Conductive Thin Layers

The paper presents an analysis of the influence of microcracks in textronic conductive layers on their conductive properties. The tested structures were created in the physical vacuum deposition process. The paper presents the results of computer simulations of the current flow field in thin conductive stripes with defects distributed along a line perpendicular to the stripe axis and randomly placed on its entire surface. It was found, inter alia, that a larger number of shorter collinear defects may have many times lower resistance than a small number of longer defects of the same total length (e.g., with 40 collinear cracks with a total length of 90% of the strip width, the sheet resistance is only about 3% greater compared to a track without cracks). It was found that the percolation threshold of the tested models with square proportions and randomly selected defects is close to the value of 0.5. This is consistent with the theoretical calculations for analogous discrete models with infinite sizes. It was also found that the sheet resistance of the conductive strip with randomly distributed defects clearly depends on its length when the defect concentration exceeds 20%. The simulations were carried out on the basis of the integral equation method, with the solution presented in the form of double layer potentials.