# CFD Modeling of Laminar and Turbulent Flow  Over a Circular Cylinder

## Flow Over a Cylinder

• Flow over a cylinder is important in many industrial application like cooling of iron  or cylindrical pipe
• Circular pipes have more application in heat exchanger. High temperature flue gases flow over a circular cylinder in a cross flow.
• Depending on flow rate, fluid properties and size of cylinder, the flow can be laminar, transition and turbulent  • Larger vortexes are found at  lower Reynolds number. ## Geometry for CFD Simulation

• Geometry and Computational domain for cross flow over a circular cylinder inside the pipe ## Computational Grid (Mesh Model)

• Structured and body fitted mesh used for CFD simulations using ANSYS GAMBIT
• High mesh density used around the cylinder to numerically resolve boundary layers for turbulent flow
• Various Mesh Models of used in this study is shown below
• Mesh 1 • Mesh 2 • Mesh3: Fine Mesh Model for flow over a circular cylinder • Fine mesh region around the cylinder ## Physical Properties

• Constant thermo physical properties used for the present numerical simulation
• The physical properties for a dummy fluid  assumed to be constant with density (ρ) of 1 kg/m3 and viscosity 1 kg/m-s.

## Governing Equation for Laminar and Turbulent Flow

• In the present study, the flow is assumed to be two-dimensional and incompressible. The effects of body forces and viscous dissipation are neglected in this study.
• The thermo-physical properties for a dummy fluid are assumed to be constant
• Both laminar and turbulent flows are considered in this study. In the following subsections, the governing equations are given for laminar and turbulent flows.

### Laminar Flow

• Continuity equation • Momentum  equations In the above equations, u, v , w are the velocity in x, y and z directions p is the pressure ρ, and ν are density and kinematic viscosity of the fluid.

## Turbulent Flow Modeling

### Standard k-ε Model

The governing equations in unsteady turbulent flow for 2 equation Standard k-ε Model is given below. For 2D turbulent flow in a X-Y plane, all the gradients w.r.t. Z-directions are zero.

Turbulent Kinetic Energy Equation (k): Dissipation of TKE (ε): Pk denotes the rate of shear production of k ### Standard Wall Functions

The standard wall functions for the mean stream-wise velocity and turbulence kinetic energy are given as ### Turbulence Model : Reynolds Stress Model (RSM)

• Transport equation for the Reynolds stress tensor τij after some adjustments can be written as Where,

Pressure strain rate in the Reynolds stress transport equation: Dissipation term in the Reynolds stress transport equation: Turbulent Transport in the Reynolds stress transport equation: • For Reynolds stress modeling (RSM), 7 equations used to model the anisotropic turbulent flow

## Initial and Boundary condition

In the present study, the flow is unsteady and periodic. The results must be taken only after the periodic flow is established.

Initial Condition: t he velocity is initialized as At t = 0 u = 0, v = 0 (10)

### Boundary conditions:

• Inlet: A uniform velocity and constant free stream temperature are assumed at the inlet boundary

u = U∞, v = 0 (11)

• Outlet: Outflow (zero gradient) condition  used at the outlet.
• Symmetry: Since the problem considered is a 2-D problem, symmetry boundary conditions are imposed for both top and bottom boundaries
• Wall: The cylinder surface and side walls ae considered as wall with no slip condition

### Lift coefficient

To represent the results and characterize the combined heat transfer problem, the following non-dimensional variables and parameters are defined.

The lift  coefficients are computed from the following expressions Where, D is the cylinder diameter, Fx and Fy are the force components resolved in the directions x and y.

• If τs is shear stress at wall and y is distance from it, then the non-dimensional term in turbulent flow is given as

## Numerical Details in ANSYS FLUENT

ANSYS GAMBIT used for  mesh generation and meshing. Tthe numerical simulation carried out by using a commercial finite volume method solver (ANSYS FLUENT).

• Solver Setting
• Steady Incompressible Solver at Re=1
• Unsteady, second order Implicit Incompressible solver at Re=272, 2902
• Physical Model:
• Viscous-laminar Model for Re=1 and 272
• Turbulent Models; standard k-ε and RSM Models for Re=2902
• Velocity Boundary Conditions
• For inlet a fixed uniform velocity of 0.0005 m/s used such that, Reynolds number

(Re =ρ U D/μ ) are 1,272, and 2902 based on different velocities (U), 1, 272 and 2902 m/s at inlet with cylinder diameter (D), 1 m.

• Turbulent Parameters  at inlet: Turbulent Intensity 1 % and Hydraulic diameter, D (1m)
• Pressure Boundary: The operating pressure 101325 Pa used at inlet.

Pabsolute = Pgauge +P operating, assumed zero gauge pressure at inlet

Ptotal = Pstatic + 1/2ρu2 for incompressible flow

• Pressure Velocity Coupling – Semi –implicit Method for Pressure Linked Equation (SIMPLE)
• Discretization Scheme or Spatial Interpolation
• Pressure – Standard
• Momentum – QUICK (Quadratic Upwind interpolation for Convective Kinetics)
• Turbulent Kinetic Energy.: QUICK
• Turbulent Dissipation rate :- QUICK
• Reynolds Stresses: QUICK
• Time Step (Δt) :
• Δt=1e-3 S for laminar flow is less than the time period of vortex shedding , 0.021second.
• Δt=1e-5 second used for turbulent, Standard k-e models, it is less than time period of vortex shedding , 0.0018 seconds.
• Δt=1e-6 second used for turbulent, RSM models, it is less than time period of vortex shedding , 0.00018 seconds.
• Convergence Criteria: Convergence criteria for all flow variable kept 1e-7
• Convergence for laminar flow at Red = 1 • Residuals for turbulent flow ## Grid Independence Study

Effect of different meshes on CFD results have been studied at Re = 272

Grid Sensitive studies for Velocities contours at Re=272

• Mesh 1  • Velocity Contours for Mesh 2 • Velocity Contours for Mesh 3 • From above grid sensitive studies for different gird sizes, it shows that the velocity contours around the cylinders for Grid3 are properly calculated, this grid is used for laminar flow and turbulent flow evaluation

## Results for Laminar Flow

### Coefficients of Lift (CL)

• Coefficients of Lift Vs Flow time for laminar flow over the cylinder, Re=272 ### Velocity Distribution at Re=272

• Velocity Contours over a cylinder • Stream lines around the cylinder •  Velocity profile around the cylinder
• Velocity in wake region of the cylinder is low compared to other regions ### Pressure Distribution (PStatic) at Re=272

• High pressure is front side of cylinder and low pressure in the rear portion of cylinder ## CFD Results for Turbulent flow

### Turbulent Flow and Pressure Field using Standard k-ε Model

• Velocity Contours and vectors in turbulent flow over a cylinder, Re=2902
• Velocity Contours over a cylinder is shown below • Velocity profile in wake region of the cylinder • Pressure fields in turbulent flow over a cylinder  • Coefficients of Lift Vs Flow time for turbulent flow over the cylinder, Re=2902 • Wall Y-plus for turbulent flow over the cylinder, Re=2902
• As expected Y-plus around the cylinder is less than 5 means and fine mesh used for turbulent study is acceptable at Re=2902 ### Results for RSM turbulent Model

• Velocity Contours and vectors in turbulent flow over a cylinder, RSM-Model at Re=2902 • Stream lines for CFD simulation using the RSM turbulence model is shown below #### Velocity Contours over a cylinder • Velocity profile in wake region of the cylinder • Pressure fields in turbulent flow over a cylinder • Coefficients of Lift Vs Flow time for turbulent flow over the cylinder, Re=2902 • Wall Y-plus for RSM turbulent flow over the cylinder, Re=2902 ## Comparison of flow Laminar and Turbulent Flow

• ### Velocity vector for flow over a cylinder at Re=1, 272 and 2902

(a) Re=1

• Flow pattern is symmetrical above and below of the cylinder.
• The size of wake region is small (b) Re=272

• At this Reynolds number, flow around the cylinder is laminar and the boundary layer region around the cylinder is significant up to an angle of 100 degree from stagnation point
• With an increase in Reynolds number, the size of wake region behind the cylinder increases (c) Re=2902

• At this Reynolds number, flow around the cylinder is turbulent and the boundary layer region around the cylinder is significant up to an angle of 120 degree from stagnation point
• Compare to laminar flow, the size of wake region behind the cylinder is higher for turbulent flow
• Velocity vectors for Turbulent flow over a cylinder is presented as below ### Velocity Contours for flow over a cylinder at Re=1, 272 and 2902

• Flow at Low Reynolds Number (Re=1)
• Velocity contours around the cylinder  symmetrical  • Flow at Intermediate Reynolds Number (Re=272)
• Velocity contours around the cylinder  is not symmetrical
• Unsteady (Von karman) vortexes are observed behind the cylinder  • Flow at High Reynolds Number (Re=2902)
• Velocity contours around the cylinder  is not symmetrical
• Unsteady vortexes of small sizes are observed behind the cylinder  ### Vortex Shedding Frequency and Stroul Number

 Reynolds Number, ReD Velocity, U (m/s) Time Period, T (S) Frequency (T-1) St=f D/U ΔSt* 272 (Laminar flow) 272 0.0201 49.75 0.1829 -1E-04 2902 ( Turbulent flow) 2902 0.0018 555.556 0.191 +0.0080

Note: * The correlation for a circular cylinder, f*D/U=0.183, it is compared with numerical values

## Concluding Remark

• CFD analysis of laminar and turbulent flow over a circular cylinder has been carried out for different Reynolds number. Coefficients of lift, contours of velocity and pressures are discussed in details.
• At low Reynolds number (Re=1) flow is steady, and streamline are  symmetrical about Y-axis of cylinder
• With increasing in Reynolds number, the  flow becomes unsteady, flow pattern shows periodic flow of vortex shedding in the wake region of the cylinder which is called the von Kaman vortex
• At a higher Reynolds number,   flow around the cylinder becomes irregular. The increased inertia forces break the vortex generated behind the cylinder, with a higher frequency of vortex shedding than that in laminar flow