OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 Numerical Simulation Approach ANSYS Fluent was used for the simulations. The governing equations were the 3D Navier-Stokes equations (Eqs. 1–6), which incorporate eddy viscosity (μt), strain rate (Eij), and velocity components (ui). Energy transport was governed by Eq. (7). The friction factor and theoretical Nusselt number (Nu) were determined using Eq. (8) and the Dittus-Boelter correlation (Eq. 9) [38–41]. 0 ( ) ( ) ( ) p u v w t x y z ∂ ∂ ρ ∂ ρ ∂ ρ + + + = ∂ ∂ ∂ ∂ (1) 2 2 2 2 2 2 1 u u u p u u u u v w x y z x x y z ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + = − + µ + + ∂ ∂ ∂ ρ ∂ ∂ ∂ ∂ (2) 2 2 2 2 2 2 1 v v v p v v v u v w x y z y x y z ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + = − + µ + + ∂ ∂ ∂ ρ ∂ ∂ ∂ ∂ (3) 2 2 2 2 2 2 1 w w w p w w w u v w x y z z x y z ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + = − + µ + + ∂ ∂ ∂ ρ ∂ ∂ ∂ ∂ (4) 2 ( ) ( ) i t t ij ij i j k j ku p k k E E t x x x ∂ ρ µ ∂ ρ ∂ ∂ + = + µ − ρε ∂ ∂ ∂ σ ∂ (5) 2 1 2 2 ( ) ( ) i t s t ij ij s i j s j u p k C E E C t x x x k k ∂ ρε µ ∂ ρ ε ∂ ∂ε ε ε + = + µ − ρ ∂ ∂ ∂ σ ∂ (6) v p T T T T k k k q C x x y y z z t ∂ ∂ ∂ ∂ ∂ ∂ ∂ + + + = ρ ∂ ∂ ∂ ∂ ∂ ∂ ∂ (7) 2 2 4 2 ; ( / ) / P m f V L D V D ∆ = = ρ ρπ (8) Nu = 0.023Re0.8Pr0.4 (9) Mesh Generation Mesh quality significantly impacts accuracy. A near-orthogonal grid with y⁺ = 0.5 (spacing y = 1.3628×10−5) ensures accurate wall resolution [42]. The structured mesh consisted of 1,283,136 nodes. Fig. 3 shows a cross-sectional view of the mesh. Velocity inlet conditions included a constant uniform profile for validation and a sinusoidal pulsing profile for dynamic cases, as defined by V = U₀[1 + A sin(2πft)], where A denotes amplitude, f frequency, t time, and U₀ mean velocity. A heat flux was applied at the wall, and a pressure outlet condition was established at the pipe exit. Boundary Conditions The following boundary conditions were applied: 1. A pulsating velocity profile was imposed at the inlet using a userFig. 3. Meshing at the cross section defined function for sinusoidal velocity input.
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