Flow Solution Research Articles

Electrochemical Polishing Method for Titanium Alloys with a Microgroove Structure

TI–6AL–4V alloys are widely used in various fields owing to their excellent corrosion resistance, high-temperature resistance, and low-temperature toughness. Herein, a microgroove fixture was used to simulate the microgrooves in a titanium alloy with different aspect ratios to study the influence of the electrolyte flow rate on the polishing effect. The optimization of the electrochemical polishing parameters was conducted using experiments and simulations. The effects of process parameters, such as the concentration of sodium chloride (NaCl) and zinc chloride (ZnCl2), polishing time, and processing voltage, on the quality of the post-polished surface were studied. Experiments were conducted on microgrooves with different aspect ratios under the optimized polishing process parameters. Changes in the surface elements of the microgrooves after polishing were detected. The experimental results indicated that the optimal electrochemical polishing solution flow rate, NaCl concentration, ZnCl2 concentration, polishing time, and processing voltage were 0.2 m/s, 4.0 wt.%, 0.4 wt.%, 8 min, and 90 V, respectively. After 8 min of electrochemical polishing, a TiO2 passivation film was formed on the surface of the microgroove. The surface roughness of the notch and bottom of the microgroove decreased from 250 nm to below 40 nm, with a minimum of 24.5 nm.

Modal stability analysis of toroidal pipe flow approaching zero curvature

The present study investigates the modal stability of the steady incompressible flow inside a toroidal pipe for values of the curvature $\delta$ (ratio between pipe and torus radii) approaching zero, i.e. the limit of a straight pipe. The global neutral stability curve for $10^{-7} \leq \delta \leq ~10^{-2}$ is traced using a continuation algorithm. Two different families of unstable eigenmodes are identified. For curvatures below $1.5 \times 10^{-6}$ , the critical Reynolds number ${{Re}}_{cr}$ is proportional to $\delta ^{-1/2}$ . Hence, the critical Dean number is constant, ${{De}}_{cr} = 2\,{{Re}}_{cr}\,\sqrt {\delta } \approx 113$ . This behaviour confirms that the Hagen–Poiseuille flow is stable to infinitesimal perturbations for any Reynolds number and suggests that a continuous transition from the curved to the straight pipe takes place as far as it regards the stability properties. For low values of the curvature, an approximate self-similar solution for the steady base flow can be obtained at a fixed Dean number. Exploiting the proposed semi-analytic scaling in the stability analysis provides satisfactory results.

An Analytical Study on the influence of Magnetic Field-Dependent Viscosity on Viscous and Ohmic Dissipative Second-Grade Fluid Boundary Layers

Abstract The article aims to investigate the magnetohydrodynamic (MHD) boundary layer flow of a second-grade non-Newtonian fluid over a horizontally stretching sheet, considering magnetic field-dependent (MFD) viscosity, as well as viscous and Ohmic dissipations. Analytical solutions for previously unexplored momentum and heat transfer equations involving MFD viscosity are derived. Two boundary conditions, namely Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF), are taken into account. Governing dimensional partial differential equations (PDEs) are transformed into non-dimensional ordinary differential equations (ODEs) using similarity transformations. Closed-form analytical solutions for flow are derived, considering stretching velocity, MFD viscosity, second-grade fluid properties, and suction impacts. Heat transfer equations are transformed into Gauss-hypergeometric form, yielding solutions in terms of confluent hypergeometric functions. Analytical expressions for skin friction, local Nusselt number, and non-dimensional wall temperature are derived. A unique solution is obtained for the flow equation. It is found that both second-grade and magnetic viscosity parameters expand the momentum boundary layer, while the magnetic parameter reduces thickness. Thermal boundary layer thickness increases with a higher second-grade parameter, magnetic viscosity, and Eckert number. Moreover, analytical solutions are validated against published results for a special case.

Well-Balanced conservative central upwind scheme for solving the dam-break flow problem over erodible bed

This work deals with the numerical solution of dam-break flow over an erodible bed. The mathematical model is a combination of the shallow water, the transport diffusion and the bed morphology change equations. The system is solved by a well-Balanced central upwind scheme with conservative property. Several tests are illustrated in order to validate the accuracy and the performance of the model. A comparison of central upwind scheme and Roe scheme is presented.

Fabrication of 3D Polycaprolactone Macrostructures by 3D Electrospinning.

Building 3D electrospun macrostructures and monitoring the biological activities inside them are challenging. In this study, 3D fibrous polycaprolactone (PCL) macrostructures were successfully fabricated using in-house 3D electrospinning. The main factors supporting the 3D self-assembled nanofiber fabrication are the H3PO4 additives, flow rate, and initial distance. The effects of solution concentration, solvent, H3PO4 concentration, flow rate, initial distance, voltage, and nozzle speed on the 3D macrostructures were examined. The optimal conditions of 4 mL/h flow rate, 4 cm initial nozzle-collector distance, 14 kV voltage, and 1 mm/s nozzle speed provided a rapid buildup of cylinder macrostructures with 6 cm of diameter, reaching a final height of 16.18 ± 2.58 mm and a wall thickness of 3.98 ± 1.01 mm on one perimeter with uniform diameter across different sections (1.40 ± 1.10 μm average). Oxygen plasma treatment with 30-50 W for 5 min significantly improved the hydrophilicity of the PCL macrostructures, proving a suitable scaffold for in vitro cell cultures. Additionally, 3D images obtained by synchrotron radiation X-ray tomographic microscopy (SRXTM) presented cell penetration and cell growth within the scaffolds. This breakthrough in 3D electrospinning surpasses current scaffold fabrication limitations, opening new possibilities in various fields.

Chaotic-quasi-oppositional-phasor based multi populations gorilla troop optimizer for optimal power flow solution

This paper proposes an efficient modified Gorilla Troops Optimizer (MGTO) to address the problem of prone to local optima and stagnation possibility in the standard Gorilla Troops Optimizer (GTO). The proposed MGTO is based on multiple strategies including chaotic initialization, quasi-oppositional based learning, phasor motion, and multi-populations strategy. The proposed MGTO is applied to resolve the non-convex single objectives optimal power flow (OPF) problem to reduce the fuel cost without and with vple, the emissions, the fuel cost considering prohibted zones (POZs) and piecewise functions, while for multiple objective cases the fuel cost is optimized with the power losses, the voltage deviation and the emissions. To validate the effectiveness of the proposed optimizer, it is tested on IEEE 30-bus and 57-bus systems, as well as 23 standard benchmark functions and the obtained outcomes are compared with the other seven well-known optimization techniques such as SCSO, GWO, WOA, SCA, PF, BWO and GTO. The simulation results verified that the proposed MGTO provides a remarkable and robust solution for the OPF problem solution compared to the other state-of-the-arts algorithms.

Network equivalent-based VQ Curve method and its application in a novel real-time voltage stability assessment methodology

The PV and VQ curves have been widely accepted tools for monitoring voltage stability. Although these curves have been used in offline studies, their online applications are not trivial, involving specific issues and complexities concerning real-time environment. The literature presents some approaches to determine quantities related to voltage stability limit in real-time analysis of the PV curve. However, it does not occur with the corresponding quantities for the VQ curve, making it difficult to analyze these curves jointly. This work presents two significant innovative contributions, based on the use of real-time network equivalents estimated through measurement data. The first is a technique suitable for real-time applications to calculate the complete VQ curve, called Network Equivalent-based VQ Curve. The second is a methodology for determining voltage stability margins using information from both PV and VQ curves. Simulations were carried out in RVS Test System, and 9, 14, 30 and 118 Bus Test Cases available in MATPOWER. The results of Network Equivalent-based VQ Curve application were validated by power flow solution. The voltage stability assessment methodology proposed in this paper represents a significant advance, going beyond the traditional approaches.

Parametric analysis of the performance of the SPH solutions of unsteady free-surface flow

ABSTRACT In this article, the performances of the SPH method to solve Shallow Water Equations SWEs with three investigation parameters were studied, such as the type of kernel functions, namely: cubic spline, Gaussian and quintic spline kernels, the number of particles used and the stabilization terms injected, specifically: Lax Friedrichs flux, artificial viscosity and two shocks Riemann solver. Three benchmarking tests make the subject of unsteady free surface flow in this study. It is 1D typical dam-break on wet and dry bottom; 2D partial dam-break on a dry floodplain and 2D partial dam-break on channel with 90° bend. The analysis of the different errors between the numerical and analytical solutions and/or the experimental data shows that the SPH method gives reliable values with the selected optimal parameters which are the cubic kernel function and the artificial viscosity term. The increase in the number of particles increases the precision but also the calculation time.

Modification of deglycerolization procedure improves processing and post-thaw quality of cryopreserved sickle trait red cell concentrates

Red blood cell (RBC) transfusion is a critical therapy for those with sickle cell disease (SCD). Alloimmunization is frequent for those with SCD and may limit the availability of matched RBC. Cryopreserved RBCs, from family members or donors with a similar RBC antigen profile could provide a viable alternative to avoid further alloimmunization and prevent hemolytic transfusion-related events. However, cryopreserved SCD and Sickle Cell trait (S-trait) donor RBC units suffer from reduced recovery following deglycerolization. This study proposes and tests a modified deglycerolization protocol using an automated cell processor to mitigate RBC loss. Six red cell concentrates (RCC) from donors with S-trait and six control RCCs were glycerolized, frozen (<−65 °C) and deglycerolized on the ACP 215 using modified parameters (decreased hypertonic solution flow rate (100 mL/min) and hypertonic equilibration delay (120 s), and increased NaCl dilution volumes (500 mL). Quality testing included: hematocrit (HCT), hemolysis, indices, extracellular potassium, morphology, osmotic fragility, osmotic gradient ektacytometry, hemoglobin (HGB), and recovery. Canadian standards (CS) indicate that acceptable deglycerolized units for transfusion require a HCT ≤0.80 L/L, HGB ≥35 g/unit, and hemolysis <0.8 % in 90 % of units tested. No significant differences in HGB or RBC recovery were observed between study groups. Significant differences between study groups were identified in osmotic fragility and osmotic gradient ektacytometry parameters. Of the 6 S-trait RCCs, 3/6 units were within the HCT, HGB and hemolysis thresholds set by the CS. The modified deglycerolization protocol provides a path for the routine cryopreservation of S-trait RBCs.

Nonlinear Stability of Equilibria in Hamiltonian Systems with Multiple Resonances without Interactions

In this work, we advance in the study of the Lyapunov stability and instability of equilibrium solutions of Hamiltonian flows. More precisely, we study the nonlinear stability in the Lyapunov sense of equilibrium solutions in autonomous Hamiltonian systems with n-degrees of freedom, assuming the existence of two resonance vectors k1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{k}^1$$\\end{document} and k2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extbf{k}^2$$\\end{document} without interaction (|k1|≤|k2|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\ extbf{k}^1|\\le |\ extbf{k}^2|$$\\end{document}). We provide conditions to obtain a type of formal stability, called Lie stability. In particular, we need to normalize the Hamiltonian function to any arbitrary order, and our results take into account the sign of the components of the resonance vectors. Subsequently, we guarantee some sufficient conditions to obtain exponential stability in the sense of Nekhoroshev for Lie stable systems. In addition, we give sufficient conditions for the instability in the Lyapunov sense of the full system. For this, it is necessary to normalize the Hamiltonian function to an adequate order, and assuming that the components of at least one resonance vector change of sign.

Generalized Solution for Double-Porosity Flow Through a Graded Excavation Damaged Zone

Generalized Solution for Double-Porosity Flow Through a Graded Excavation Damaged Zone

Graph‐based solution for smart grid real‐time operation and control

AbstractUnder the envisioned smart grid paradigm, there is an increasing demand for a fast, accurate, and efficient power flow solution for distribution system operation and control. Various solution techniques have been proposed, each with its own unique formulation, solution methodology, advantages, and drawbacks. Motivated by challenges associated with the integration of renewable distributed energy resources and electric vehicles into distribution systems and further by the speed and convergence limitations of existing tools, this paper presents a novel graph‐based power flow solution for smart grid's real‐time operation and control, named Flow‐AugmentationPF algorithm. The proposed method formulates a power flow problem as a network‐flow problem and solves it by using a maximum‐flow algorithm, inspired by the push‐relabel max‐flow technique. The performance of the proposed algorithm is tested and validated using several benchmark networks of different sizes, topologies, and parameters and compared against the most commonly used solution techniques and commercial software packages, namely PSS/E and PSCAD. The proposed formulation is simple, accurate, fast, yet computationally efficient, as it is based on matrix‐vector multiplication, and is also scalable, considering the formulation works as a graph‐based method, which, inherently, allows for parallel computation for added computational speed.

Pressure-dependent large-scale seismic anisotropy induced by non-Newtonian mantle flow

Summary Observations of large-scale seismic anisotropy can be used as a marker for past and current deformation in the Earth’s mantle. Nonetheless, global features such as the decrease of the strength of anisotropy between ∼150–410 km in the upper mantle and weaker anisotropy observations in the transition zone remain ill-understood. Here, we report a proof of concept method that can help understand anisotropy observations by integrating pressure-dependent microscopic flow properties in mantle minerals particularly olivine and wadsleyite into geodynamic simulations. The model is built against a plate-driven semi-analytical corner flow solution underneath the oceanic plate in a subduction setting spanning down to 660 km depth with a non-Newtonian n = 3 rheology. We then compute the crystallographic preferred orientation (CPO) of olivine aggregates in the upper mantle (UM), and wadsleyite aggregates in the upper transition zone (UTZ) using a viscoplastic self-consistent (VPSC) method, with the lower transition zone (LTZ, below 520 km) assumed isotropic. Finally, we apply a tomographic filter that accounts for finite-frequency seismic data using a fast-Fourier homogenization algorithm, with the aim of providing mantle models comparable with seismic tomography observations. Our results show that anisotropy observations in the UM can be well understood by introducing gradual shifts in strain accommodation mechanism with increasing depths induced by a pressure-dependent plasticity model in olivine, in contrast with simple A-type olivine fabric that fails to reproduce the decrease in anisotropy strength observed in the UM. Across the UTZ, recent mineral physics studies highlight the strong effect of water content on both wadsleyite plastic and elastic properties. Both dry and hydrous wadsleyite models predict reasonably low anisotropy in the UTZ, in agreement with observations, with a slightly better match for the dry wadsleyite models. Our calculations show that, despite the relatively primitive geodynamic setup, models of plate-driven corner flows can be sufficient in explaining first-order observations of mantle seismic anisotropy. This requires, however, incorporating the effect of pressure on mineralogy and mineral plasticity models.

Power Flow Calculation for AC/DC Power Systems with Line-Commutated Converter–Modular Multilevel Converter (LCC-MMC) Hybrid High-Voltage Direct Current (HVDC) Based on the Holomorphic Embedding Method

To harness the strengths and mitigate the limitations of line-commutated converter (LCC) and modular multilevel converter (MMC) HVDC systems, the LCC-MMC hybrid HVDC system has been developed. This paper proposes a holomorphic embedding (HE)-based power flow calculation method for AC/DC power systems with the LCC-MMC hybrid HVDC system. Firstly, the methodology involves establishing the mathematical model of the LCC-MMC hybrid HVDC system and its control modes. Subsequently, the HE formulation for the constructed LCC-MMC model is derived using the HE method. The proposed method simplifies the HE formulation using substitute variables, making it adaptable to various control modes. The designed HE formulation facilitates the derivation of the germ solution and the calculation of high-order power series coefficients. A sequential solution flow chart compatible with AC power flow algorithms is constructed to enhance the practicality of the HE method for real-world large-scale systems. The accuracy and effectiveness of the proposed method are verified through numerical tests on the modified IEEE 14-bus, IEEE 57-bus, and large 2383-bus system. The proposed method provides a reliable and efficient solution for power flow analysis in hybrid HVDC systems.

Effect and mechanism of solution flow rate during interfacial polymerization on morphology and performance of hollow fiber membranes

Interfacial polymerization (IP) using m-phenylenediamine and trimesoyl chloride (TMC) is an essential method for producing thin-film composite (TFC) membranes. Nevertheless, IP is highly sensitive to changes in process parameters, especially the TMC solutions flow rate during inside-out TFC hollow fibers (HF) production. Research on the impact of flow conditions (i.e., laminar vs. turbulent flows) of these organic solutions on the final membrane characteristics and corresponding mechanism is still lacking. This research tested different TMC flow rates (0.1–2 mL/min) to produce inside-out TFC HF. With a TMC flow rate increase, (i) the leaf-like structures of the polyamide (PA) layer decreased in size, (ii) the thickness of the PA layer slightly increased, and (iii) the pure water permeability decreased. However, the elemental composition, chemical bonds, and NaCl rejection remained stable. Different fluid regimes are considered to affect the performance of HF membranes by affecting the heat dissipation process during IP reaction. A TMC flow rate in the laminar flow state (i.e., low flow rates) is recommended for synthesizing HFs. The current research provides new insights into the IP reaction mechanism of HF membrane, thus offering valuable guidance to optimize and produce membrane products with better performance.

Approximate closed‐form solution of free convection flow past a vertical cone

AbstractThis paper presents a technique to find the closed‐form solution of the boundary‐value problem representing free convection flow past a vertical cone. Partial differential equations that govern the flow are converted into nonlinear ordinary differential equations with the aid of similarity transformations. First, a numerical solution is obtained with the help of the bvp4c package of MATLAB, and then utilizing the numerical solution, the closed‐form solution is obtained. The accuracy of the closed‐form solution is analyzed by the residual technique. Graphs of the residuals of the governing equations indicate that our approximate closed‐form solution closely matches the exact solution.

Novel nanostructure approach for antibiotic decomposition in a spinning disc photocatalytic reactor

Conventional wastewater treatment processes are often unable to remove antibiotics with resistant compounds and low biological degradation. The need for advanced and sustainable technologies to remove antibiotics from water sources seems essential. In this regard, the effectiveness of a spinning disc photocatalytic reactor (SDPR) equipped with a visible light-activated Fe3O4@SiO2-NH2@CuO/ZnO core–shell (FSNCZ CS) thin film photocatalyst was investigated for the decomposition of amoxicillin (AMX), a representative antibiotic. Various characterization techniques, such as TEM, FESEM, EDX, AFM, XRD, and UV–Vis-DRS, were employed to study the surface morphology, optoelectronic properties, and nanostructure of the FSNCZ CS. Key operating parameters such as irradiation time, pH, initial AMX concentration, rotational speed, and solution flow rate were fine-tuned for optimization. The results indicated that the highest AMX decomposition (98.7%) was attained under optimal conditions of 60 min of irradiation time, a rotational speed of 350 rpm, a solution flow rate of 0.9 L/min, pH of 5, and an initial AMX concentration of 20 mg/L. Moreover, during the 60 min irradiation time, more than 69.95% of chemical oxygen demand and 61.2% of total organic carbon were removed. After the photocatalytic decomposition of AMX, there is a substantial increase in the average oxidation state and carbon oxidation state in SDPR from 1.33 to 1.94 and 3.2, respectively. Active species tests confirmed that ·OH and ·O2− played a dominant role in AMX decomposition. The developed SDPR, which incorporates a reusable and robust FSNCZ CS photocatalyst, demonstrates promising potential for the decomposition of organic compounds.

Advanced Computational Framework to Analyze the Stability of Non-Newtonian Fluid Flow through a Wedge with Non-Linear Thermal Radiation and Chemical Reactions

The main idea of this investigation is to introduce an integrated intelligence approach that investigates the chemically reacting flow of non-Newtonian fluid with a backpropagation neural network (LMS-BPNN). The AI-based LMS-BPNN approach is utilized to obtain the optimal solution of an MHD flow of Eyring–Powell over a porous shrinking wedge with a heat source and nonlinear thermal radiation (Rd). The partial differential equations (PDEs) that define flow problems are transformed into a system of ordinary differential equations (ODEs) through efficient similarity variables. The reference solution is obtained with the bvp4c function by changing parameters as displayed in Scenarios 1–7. The label data are divided into three portions, i.e., 80% for training, 10% for testing, and 10% for validation. The label data are used to obtain the approximate solution using the activation function in LMS-BPNN within the MATLAB built-in command ‘nftool’. The consistency and uniformity of LMS-BPNN are supported by fitness curves based on the MSE, correlation index (R), regression analysis, and function fit. The best validation performance of LMS-BPNN is obtained at 462, 369, 642, 542, 215, 209, and 286 epochs with MSE values of 8.67 × 10−10, 1.64 × 10−9, 1.03 × 10−9, 302 9.35 × 10−10, 8.56 × 10−10, 1.08 × 10−9, and 6.97 × 10−10, respectively. It is noted that f′(η), θ(η), and ϕ(η) satisfy the boundary conditions asymptotically for Scenarios 1–7 with LMS-BPNN. The dual solutions for flow performance outcomes (Cfx, Nux, and Shx) are investigated with LMS-BPNN. It is concluded that when the magnetohydrodynamics increase (M=0.01, 0.05, 0.1), then the solution bifurcates at different critical values, i.e., λc=−1.06329,−1.097,−1.17694. The stability analysis is conducted using an LMS-BPNN approximation, involving the computation of eigenvalues for the flow problem. The deduction drawn is that the upper (first) branch solution remains stable, while the lower branch solution causes a disturbance in the flow and leads to instability. It is observed that the boundary layer thickness for the lower branch (second) solution is greater than the first solution. A comparison of numerical results and predicted solutions with LMS-BPNN is provided and they are found to be in good agreement.

Numerical study of binary mixture and thermophoretic analysis near a solar radiative heat transfer

The main focus of the current article is to investigate the two-dimensional boundary layer flow of non-Newtonian fluid induced by a linear stretching surface in the streamwise direction. The flow features of non-Newtonian fluid (i.e. shear-thinning and thickening nature of the fluids) are explored with Carreau fluid model. In addition, thermophoresis, Brownian motion, thermal radiation (with Rosseland approximation), binary mixture and activation enthalpy are also incorporated in fluid model for better analysis of thermal and solutal properties. The mathematical modelling of under consider physical problem yields nonlinear partial differential system. The governing mathematical system is first simplified with scaling transformations for the high Reynolds number and then transformed into non-dimensional ordinary differential system by using the similarity variables. Since the governing mathematical system comprised on nonlinear boundary value problem, thus shooting method is utilized for the numerical solution of the fluid flow governing equations. The obtained results followed the qualitative manners of the previously reported data. The computed results for important physical quantities (i.e. velocity, temperature, and concentration) are presented through graphs and then interpreted physically. It is observed that the boundary layer thickness increased for shear thickening fluids (n>1) while it is reduced for shear thinning fluids (n<1). Also, the temperature of shear thinning fluid is higher than shear thickening fluid. In addition, heat generation and thermal radiations enhance the thermal boundary layer. Thermophoretic viscosity effect reduces the concentration profile significantly in the flow domain.

Risk Assessment of Radial Distribution Systems using Modified Jelly Fish Search Algorithm to analyse the Performance Indices

One of the essential techniques for figuring out Power Distribution System performance is reliability evaluation. With time, the range of methods for assessing reliability has grown, and the distribution system's evolution has also become more intricate. The likelihood of a network failing grows with time once it begins to function, especially if it is used for an extended period. Reliability indices have been evaluated using different algorithms such as Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and various modified versions of algorithms. The Jelly Fish Search Algorithm has been used in various power system applications such as to determine the most cost-effective way to dispatch generating units' loads, integrate Distributed Generation (DG) units, track the maximum power of photovoltaic systems, and determine optimal power flow solutions, among other uses. The performance indices for the Radial Distribution System (RDS) have not been evaluated using JFSA.Variation of performance indices with respect to unavailability has not been discussed in the literature. Here an attempt is made to analyse the variation of the indices with the unavailability. The proposed algorithm is evaluated first on 3 load point radial distribution system and the computations are performed on the popular IEEE-RBTS Bus2 test system. Based on the output it is observed that for the both the systems the behaviour of the indices with respect to the unavailability is in similar fashion. The equations are derived for the performance indices using the Minitab. With the equations obtained the Performance indices values can be predicted for the given unavailability value. It is the better appropriate method for the assessing the performance indices of Radia Distribution System.