Rec = 4 and β = 0.2, (b) blockage ratio for Rec = 4 and left cylinder rotation direction and (c) rotational cylinder Reynolds number for β = 0.05 and right cylinder rotation direction on the pressure contours. Rec = 10 and β = 0.1, (b) blockage ratio for Rec = 10 and CW direction of cylinder rotation and (c) rotational Reynolds number of the cylinder for β = 0.1 and CW direction of cylinder rotation on the flow surfaces.
Natural Convection
Forced Convection
Mixed Convection
Forced Convection Inside Channel
Laminar Flow
Turbulent Flow
Most of the kinetic energy of turbulent motion appeared in the region of large structures. For example, the largest integral length scale of a pipe flow problem is equal to the pipe diameter.
Direct Numerical Simulation
Although it is possible to find some specific solutions of the Navier-Stokes equations using the fluid motion, all such solutions are unable to find finite perturbations at large Reynolds numbers. There are no useful analytical solutions of turbulent flow in geometries of engineering interest although statistical theories of turbulent flow have provided a better understanding of the scaling laws in various flow regimes.
Turbulence Modelling
- Algebraic yPlus Model
- Spalart-Allmaras Model
- k-ε Model
- k-ω Model
- Low Reynolds Number k-ε Model
- Shear Stress Transport (SST) Model
- v2-f Model
Its convergence is much more difficult and is quite sensitive to the initial guess of the solution. To combine the overall behavior of the k-ω model at the near-wall region with the entirety of the k-ε model, Menter et.
Turbulent Channel Flow and Heat Transfer
Motivation of the Present Study
Main Objectives of the Thesis
Outline of the Thesis
The flow past a stationary cylinder in a channel with the cylinder symmetrically placed in the center of the channel was studied by Chen et al. Huang and Feng (1995) also investigated the numerical flow over a circular cylinder confined between two parallel plates.
Laminar Flow and Heat Transfer over a Rotating Cylinder
2018) investigated the flow over a circular cylinder embedded in different spherical and cylindrical surfaces at a fixed Reynolds number of 100 and found that the effect of surface curvature is insignificant on the drag coefficient, lift coefficient and Strouhal number. 2002) numerically investigated two-dimensional laminar flow over a circular cylinder rotating at a fixed angular velocity and found that the average drag decreases with increasing circumferential velocity of the cylinder. Lam (2009) investigated vorticity for flow past a rotating circular cylinder with different Reynolds number and rotation speed. After that, Snagmo Kang (2006) and Sojoudi and Saha (2013) studied numerically uniform shear or shear thinning and thickening on a rotating circular cylinder. 2011) experimentally investigated the flow past a rotating circular cylinder and showed that Strouhal number measurements and global wake patterns agree well with previous work.
1989) also studied the stable and unsteady flows past a circular cylinder rotating with constant angular velocity and translating with constant linear velocity. In addition to fluid flow, Paramane and Sharma (2009), Paramane and Sharma (2010) numerically investigated the heat transfer across a rotating circular cylinder maintained at a constant temperature and uniform heat flow respectively to determine flow patterns, Nusselt numbers for different Reynolds numbers and blocking ratios to observe. . 2011) extended the similar work to analyze the combined effect of channel confinement and cylinder rotation on the flow and heat transfer through a cylinder for different blocking ratios, rotational speed and Reynolds number. Similarly, the effects of Prandtl number on the heat transfer characteristics of an unconfined rotating circular cylinder are investigated for varying rotational speed for different Reynolds numbers and Prandtl numbers are investigated by Sharma and Dhiman. They also investigated the temperature distribution and heat transfer for a uniform wall temperature for flowing past a rotating cylinder.
Turbulent Flow and Heat Transfer over a Confined Cylinder
They concluded that the values of the steady-state lift, drag and moment coefficients of the two methods are found to be in good agreement. Tabata and Fujima (1991) then numerically studied the flow past a circular cylinder using the finite element method and discussed the effect of the subdivision of the boundary layer on flow patterns and drag coefficients. The roughness effects on the flow past a circular cylinder were investigated numerically by Rodriguez et al. 2016) investigated high Reynolds number flow around a cylindrical bluff body and concluded that the k-ω (SST) model is superior to other two-equation RANS models and is able to capture the effects of surface roughness .
Then, turbulent flow characteristics around a circular cylinder were studied by Yao et al. 2019) to show the effect on drag coefficient, lift coefficient and wind pressure distribution. Then, the superhydrophobicity of the flow past a circular cylinder in different flow regimes is investigated using particle image velocity-based experiments. These were studied by Sooraj et al. Using the technique of large eddy simulation flow over a circular cylinder at Reynolds number 3900 is studied numerically by Kravchenko and Moin (2000).
Turbulent Flow and Heat Transfer over a Rotating Cylinder
Sanjital and Goldstein (2004) studied the forced convection heat transfer from a circular cylinder for a wide range of Reynolds numbers and Prandtl numbers. They had found that strain coefficients were inversely proportional to Reynolds number for most of the rotational speeds studied. Then, Mgaidi et al. 2019) analyzed the flow around a rotating circular cylinder at subcritical regime of Reynolds number by both experimental and.
The computational domain is presented in Cartesian coordinate with its origin at the center of the cylinder. The cylinder rotates at an angular speed of ω in either clockwise (CW) or counterclockwise (CCW) direction and the surface of the cylinder is kept at a high temperature Th. Three different diameters of the cylinder are chosen and thus the blocking ratio (β) is varied as β = d/D and 0.2 respectively.
Mathematical Modelling
Laminar Flow Governing Equations
The working fluid in the duct is considered to be air and the thermophysical properties of air are considered to be constant. The radiation and its effects on buoyancy, together with the viscous dissipation, are neglected in this study. The radiant heat transfer in this case is very negligible than the convective heat transfer.
And since air is used as working fluid in our smaller cylinder study, so we can ignore the effect of motion as well as viscous dissipation. Where, x and y are the dimensional Cartesian coordinates, u and v are the dimensional velocity components in the x and y directions respectively, p is the dimensional pressure, T is the dimensional temperature, ρ is the fluid density and μ is the dynamic viscosity and Cp is the capacitance of heat at constant pressure.
Boundary Conditions
Dimensional Analysis for Laminar Flow
Non- dimensional Scales
5.1 (a) reveal the fact that the direction of rotation of the cylinder has little effect on the thermal fields. The thermal fields downstream of the channel strongly depend on the blockage ratio and the rotational Reynolds number of the cylinder at low Re. So the pattern below changes significantly due to the increasing size of the cylinder.
57] Parnaudeau P., Carlier J., Heitz D. and Lamballais E., "Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900", Phys. 61] Daneshi M., “Numerical investigation of fluid flow around and along a circular cylinder by Ansys Simulation”, Int. 77] Catalano P., Wang M., Iaccarino G. and Moin P., "Numerical simulation of the flow around a circular cylinder at high Reynolds numbers", Int.
Non-dimensional Governing Parameters
Non-dimensional Boundary Conditions
Boundary conditions for the present problem in the non-dimensional form are presented in table 3.2. From the dimensional boundary conditions presented in §3.2.2 and by using scales (see §3.3.1), these non-dimensional boundary conditions are obtained.
Turbulent Flow Governing Equations
Turbulent Models
- k - є Model
- k – ω Model
- SST Model
- Low Reynolds Number k - є Model
The SST model is a combination of the k-ε model in the free stream and the k-ω model near the walls [105]. Low Reynolds number refers to the region close to the wall where the viscous effect dominates. The low Reynolds number k-ε model is similar to the k-ε model but does not need wall functions: it can solve for the flow everywhere [106].
It is a logical extension of the k-ε model and shares many of its advantages, but generally requires a denser network; not only on walls, but everywhere, the low Reynolds number properties come into effect and dampen the turbulence. The low Reynolds number k-ε model can calculate lift and drag forces and heat fluxes can be modeled with higher accuracy compared to the k-ε model.
Dimensional Analysis for Turbulent Flow
Non-dimensional Boundary Conditions
Non-dimensional Turbulent Models
- k - є Model
- k – ω Model
- SST Model
- Low Reynolds Number k - є Model
These equations can be simplified by removing the viscous terms to give Euler's equations. Finally, for small perturbations in subsonic and supersonic flows (not transonic or hypersonic), these equations can be linearized to obtain linearized potential equations. Various types of numerical solution procedures are available, among which finite difference, finite element, finite volume, and spectral element methods are very popular.
However, a proper choice of method can shorten the calculation time and ensure better numerical accuracy. Although finite element methods have certain limitations, advanced techniques are applied to overcome these limitations and keep the numerical error within reasonable limits. The numerical solution techniques are becoming more popular day by day due to their attractive features.
Finite Element Method
Advantages of Finite Element Method
Numerical Formulation
Discretization of Equations
Calculation of Performance Parameters
Mesh Generation
Model Validation
Grid Independence Test
Turbulence Modelling
- Model Validation for Turbulent Model
- Isosurface Plots
- Streamline Plots
- Pressure Contour
- Variations of Performance Parameters
Only the blocking ratio of the cylinder thus plays a dominant role on the thermofluid properties within the channel. 9], which in turn leads to the formation of the eddies at the downstream of the cylinder. The decreasing trend of the variation of CD and the increasing trend of Nu is observed with increasing mean flow Reynolds number.
Furthermore, the absolute values of CL remain the same but with the opposite sign due to the change in the direction of rotation of the cylinder. The rotation of the cylinder can affect the drag coefficient which decreases with increasing Re. This causes the pressure drag coefficient to decrease with a further increase in rotational speed [46].
Turbulent Flow
- Isosurface Plots
- Streamline Plots
- Pressure Contours
- Variations of Performance Parameters
Because, flow restriction and hot surface area increases as cylinder size increases. There is no significant difference in the thermal fields for the direction of rotation of the cylinder, because the average velocity of the fluid flow is large enough to overcome the effect of the rotational velocity. The pressure field changes significantly with increasing blockage ratios, especially downstream.
Increasing Re by keeping the rotation speed constant increases the upward disruption of the stagnation point. This is probably due to the higher average flow inlet velocity compared to the relatively lower rotational velocity of the cylinder which cancels out the effect of rotational velocity. Thermal fields and pressure fields at the downstream of the channel also depend significantly on the blockage ratio.
Effect of Mean Fluid Velocity
Effect of Rotational Direction of the Cylinder
Effect of Cylinder Speed
Future Research Scopes
18] Mehdi H., Namdev V., Kumar P., and Tyagi A., "Numerical Analysis of Fluid Flow around a Circular Cylinder at Low Reynolds Number," J. 32] Stojković D., Breuer M., and Durst F. ., “Effect of high rotational speeds on the laminar flow around a circular cylinder,” Phys. 33] Stojković D., Schön P., Breuer M., and Durst F., “On the new vortex shedding mode past a rotating circular cylinder,” Phys.
66] Rodríguez I., Lehmkuhl O., Piomelli U., Chiva J., Borrell R., and Oliva A., "Numerical simulation of roughness effects on the flow past a circular cylinder," J. 78] Rodríguez I., Lehmkuhl O., Chiva J., Borrell R., and Oliva A., “ On the flow past a circular cylinder from critical to supercritical Reynolds numbers: Wake topology and vortex shedding ,” Int. 79] Sidebottom W., Ooi A., and Jones D., “A parametric study of turbulent flow past a circular cylinder using large eddy simulation,” J .
Previous studies of laminar fluid flow in confined channel
Previous work of laminar flow over a rotating cylinder
Previous work of turbulent flow over a circular cylinder in a confined
Previous work of turbulent flow over a rotating cylinder
Boundary conditions of the present model in dimensional form
Non-dimensional boundary conditions of the present problem
Non-dimensional boundary conditions of the present problem for turbulent
Some of the main mesh parameters
Grid independence test for laminar flow
Variation of drag and lift coefficients with experimental study
Comparison of Nu with experimental study
