CFD Analysis of Fluid Flow and Heat Transfer in Ducts with Different Geometries

Introduction

Fluid flow and heat transfer analysis in ducts with various geometries is crucial for numerous engineering applications, ranging from HVAC systems to industrial processes. Understanding the behavior of fluid flow and heat transfer in different duct shapes is essential for optimizing system performance and efficiency. In this study, computational fluid dynamics (CFD) is employed to investigate fluid flow and heat transfer characteristics in circular, rectangular, and square ducts. By utilizing CFD simulations, insights into the impact of geometry on flow patterns, pressure distribution, and heat transfer rates can be obtained.

This analysis aims to provide valuable insights for the design and optimization of duct systems in engineering applications.

Geometry Size

The experiment would be repeated using different geometry which are circular ducts, rectangular ducts and square ducts. All of the geometry would shared the same length which are 3 m as well as the same hydraulic diameter. The cross-sectional area for square ducts would be 0.01m x 0.01m and the hydraulic diameter of square ducts could be determined as Equation 13 and 14 below (Tekir, Arslan and Ekiciler, 2017).

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Hydraulic Diameter of Non-Circular Tube:

D_H=4A/P Eq 13

Hydraulic Diameter of Circular Tube:

D_H=(4πR^2)/2πR=2R=D Eq 14

Therefore, the hydraulic diameter for square and rectangular ducts would be 0.01m while the diameter of circular ducts would be 0.01m as well. The cross-section area for the rectangular duct would be 0.02m x 0.00667 m.

Governing Equation

The governing equation that used by CFD software ANSYS 19.1 to perform calculation is shown. The incompressible and steady state flow, continuity, momentum and energy equation are shown in Equation 15, 16 and 17.

(∇ ⃗ ) v ⃗=0 Eq 15

ρ (Dv /Dt=-∆p+ μ∇^2 v ⃗ Eq 16

ρCp DT/Dt=k∇^2 T Eq 17

The selected Reynolds Number for turbulent flow would around 10000-100000. Hence, the ƙ-ɛ turbulence model was chose for this simulation to perform numerical calculation. The kinetic energy, ƙ and dissipation rate, ɛ is calculated using transport equation by ANSYS FLUENT using Equation 18 and 19.

∂/∂x (ρƙ)+∂y/(∂x_i ) (ρku_i )=∂y/(∂x_j ) ((μ+μ_t/σ_ƙ ) ∂k/(∂x_j ))+G_k+G_b-ρε-Y_M+S_k Eq 18

∂/∂x (ρε)+∂y/(∂x_i ) (ρεu_i )=∂y/(∂x_j ) ((μ+μ_t/σ_ϵ ) ∂ϵ/(∂x_j ))+C_1ε ε/ƙ (G_k+C_3ε G_b )-C_2ε ρ ε^2/ƙ-S_ε Eq 19

The Eddy viscosity, μE and turbulent intensity, I of fluid are calculated using Equation 20 and 21.

μ_E=ρC_μ ƙ^2/ε Eq 20

I=0.16(Re)_D^(-1/8) Eq 21

Referred to Equation 15 to 21, turbulent kinetic energy generation due to mean velocity gradient is expressed as Gk while turbulent kinetic energy generation due to buoyancy is expressed as Gb. The contribution of fluctuating dilation in Compressible Turbulence to the overall dissipation rate is expressed as YM. The constant, C used for the transport equation is 1.44 for C 1ɛ , 1.92 for C 2ɛ and 0.09 for Cμ. The σƙ is the turbulent Prandtl Number for kinetic energy, ƙ while σɛ is the turbulent Prandtl Number for dissipation rate, ɛ. The user defined source term is expressed as Sƙ and Sɛ. (Tekir, Arslan and Ekiciler, 2017).

Properties Equation

The thermal properties thermal conductivity of hybrid nanofluid are determine using Equation 22 and 23 whereas base fluid or water is represent by bf, hybrid nanofluid is represent by hnf and single-particle nanofluid is represent by nf (Tekir, Arslan and Ekiciler, 2017).

k_nf/k_f =[(k_np+2k_bf-2φ(k_bf-k_np ))/(k_np+2k_bf+φ(k_bf-k_np ) )] Eq 22

k_hnf/k_f =[((φ_Cu k_Cu+φ_((Al)_2 O_3 ) k_((Al)_2 O_3 ))/φ+2k_bf+2(φ_Cu k_Cu+φ_((Al)_2 O_3 ) k_((Al)_2 O_3 ) )-2(φ)(k_bf))/((φ_Cu k_Cu+φ_((Al)_2 O_3 ) k_((Al)_2 O_3 ))/φ+2k_bf-(φ_Cu k_Cu+φ_((Al)_2 O_3 ) k_((Al)_2 O_3 ) )+(φ)(k_bf))] Eq 23

Density, ρ, specific heat capacity, Cp and volume fraction, ϕ of Hybird Nanofluid, Al2O3-Cu/water are calculated using Equation 24 to 28 as listed.

φ=φ_Cu+φ_((Al)_2 O_3 ) Eq 24

ρ_nf=(1-φ)ρ_bf+φρ_np Eq 25

ρ_hnf=(1-φ) ρ_bf+φ_Cu ρ_Cu+φ_((Al)_2 O_3 ) ρ_((Al_)_2 O_3 ) Eq 26

((ρCp))_nf=(1-φ) ((ρCp))_bf+φ((ρCp))_np Eq 27

((ρCp))_hnf=(1-φ) ((ρCp))_bf+φ_Cu ((ρCp))_Cu+φ_((Al)_2 O_3 ) ((ρCp))_((Al)_2 O_3 ) Eq 28

Moreover, the dynamic viscosity, μ of Hybird Nanofluid, Al2O3-Cu/water determined using Equation 29 and 30.

μ_nf=μ_bf/)(1-φ)_^2.5 Eq 29

μ_hnf=μ_bf/((1-(φ_Cu+φ_((Al)_2 O_3 ))))^2.5 Eq 30

Boundary Condition

The temperature of inlet flow is 300K with uniform axial velocity,vo calculated based on the Reynold Number at turbulent region from 10000-100000. The flow is assumed to be in single phase where the velocity of particle is assumed to be identical to the velocity of base fluid. At the outlet, the pressure is assumed atmospheric while the velocity is yet to be determined. For the wall of ducts, no-slip condition was applied and constant heat flux was imposed with value by 20kW/m2 . The length of tube is set for 3 m in order to achieve hydrodynamically and thermally fully developed flow fulfilling the constant axial velocity condition at ducts inlet (Behroyan et.al, 2016).

Numerical Technique

ANSYS 19.1 employs finite-volume methods to solve the governing equations along with boundary conditions. The iteration continues until convergence is achieved, with a residual limit set at 10−510−5. Hexahedral mesh is applied for all ducts, and mesh intensity is increased near the wall to ensure accurate simulation of thermal convection and flow in the viscous layer.

These equations and techniques provide a comprehensive framework for simulating fluid flow and heat transfer in ducts of various geometries, facilitating the analysis of complex systems.