Challenge

Steady Vs Unsteady flow over a cylinder

MMayank Raj30 Jun 2020

STEADY VS UNSTEADY FLOW OVER A CYLINDER:

PROBLEM STATEMNT:

The job here is to simulate the flow over a cylinder and explain the phenomenon of Karman Vortex Street for different Reynolds number

Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.
Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10,100,1000,10000 & 100000 all being run with the steady solver and the Discussing the effect of Reynolds number on the coefficient of drag.

1.2 DATA GIVEN:

The velocity here will be adjusted accordingly by keeping certain constants like viscosity and density same so that the Reynolds number keep on increasing in each case analysis from 10 to 100,1000,10000 and lastly 100000. This will be achieved by increasing the velocity ten times in every steps keeping the other constants same.

INTRODUCTION:

For many practical applications the external study of the flow of a fluid over any body is extensively been studied previously. Flow over a blunt body like circular cylinder, usually experiences boundary layer separation and very strong flow oscillations in the wake region behind the body can also be seen. For a certain Reynolds number range, a periodic flow motion will develop in the wake as a result of boundary layer vortices being shed alternatively from either side of the cylinder. This periodic pattern of the shedding of the vortex is called vortex Karman Street. It creates a wavering flow at a distinct frequency that is correlated to the Reynolds number of the flow. Here in this CFD analysis the distinct cases of various Reynolds number ranging from 10 to 100000 and the dependency of the vortex shedding has been shown in the observations below further. The instability of the flow on the basis of its velocity separation on the interaction to the wall and other monitoring points and the variation of different physical properties have been shown below by the plots charts and the contours to support the aim of this report.

AIM:

The project aims at comparing the study of flow for Re of 100 as per the steady state and unsteady state conditions and then comparing its drag and lift coefficients and the Strouhal number for the lift coefficients cases in the general and logarithmic form. Also the study of the various physical quantities and its variations depending upon the Re 10,100,1000,10000,100000 has to be studied in more analytic form.

THEORY OF VORTEX SHEDDING:

The boundary layer separates from the surface forms a free shear layer and is highly unstable. This shear layer will eventually roll into a discrete vortex and detach from the surface (a phenomenon called vortex shedding). Another type of flow instability emerges as the shear layer vortices shed from both the top and bottom surfaces interact with one another. They shed alternatively from the cylinder and generates a regular vortex pattern in the wake region behind the circular pattern on which the flow is going to interact directly here. Vortex shedding is a function of the Reynolds number. A general study shows that dimensionless frequency of the vortex shedding, the shedding Strouhal number, St = (f D/V) is approximately equal to 0.21 when the Reynolds number is greater than 1,000.

GEOMETRY, MODEL AND MESHING:

The model being drawn in ANSYS space claim shows the dimensions of the region for fluid flow where both the fluid interaction region and non-interaction region has been shown properly.

Fig: Model of the cylinder with hole in it

5.1 NAMED PARAMETERS:

A as Cylindrical wall
B as Outlet
C as inlet
D as Symmetry wall as along the length of the cylinder

Fig: Named parameter for the inputs, outputs interacting wall and symmetry

5.2 MESHING:

Fig: Meshing of the model

One body type geometric selection and the all Triangular mesh with the inflation layers added only at the cylindrical wall interaction region. The inflation layers details have been given above in table. Where the single element size is 0.25 m over the whole body. The below figure shows the magnified view of the inflation layers for the better analysis of the fluid solid interacting region here which matters a lot to study the nature of the wall geometry and its nature of interaction with the fluid.

Fig: Inflation layers of the cylindrical wall interacting region with fluid

5.2.1 MESHING DATA

Fig: Meshing details and data

TABLE: 1

Total Nodes	21479
Total Elements	41632
Inflation layers (cylinder wall)	6 layers
Growth rate (inflation layers)	1.2
Max Thickness	0.6 m

SOLVER, DESCRETISATION, PHYSICS & MODEL:

The Solver here is Pressure-Based with absolute velocity formulation for 2D space planar and steady time. Model here used is the laminar viscous model for both steady and unsteady flow with the operating condition as gauge pressure of 0 Pa. i.e. atmospheric pressure as 1bar.

Spatial Discretisation here used is:

Least square cell based Gradient
2^nd order Pressure
2^nd order upwind Momentum scheme

Solution method being used here is SIMPLE for pressure velocity coupling.

FLUID FLOW MATERIALS USED AND ITS PROPERTIES AND CASES FOR COMPARISION:

A user defined material is being used here with its properties being listed below:

TABLE: 2 (MATERIAL USED AS A FLUID)

Material	User-defined
Density	1 kg/m^3
Viscosity(dynamic)	0.1 kg/m-s

7.1 BOUNDARY CONDITIONS & CASES FOR COMPARISION:

TABLE: 3 (BOUNDARY CONDITIONS)

The fluid property like the viscosity and the density are bee kept constant throughout the study and observation and only velocity is been changed in each condition leading to the change in the Reynolds number. The left edge or boundary is been considered here the inlet and the right one as the out let and the above and the bottom walls are considered as the symmetry. The internal wall of the fluid flow model is considered as the wall only which is the interacting medium.

CASE	VISCOSITY(kg/m-s)	DENSITY(kg/m^3)	VELOCITY(m/s)	REYNOLDS NUMBER
1	0.1	1	0.5	10
PART I	0.1	1	5	100 (analysed in Part I for both steady and transient stares)
2	0.1	1	50	1000
3	0.1	1	500	10000
4	0.1	1	5000	100000

RESULTS AND DISCUSSION:

PART I: STEADY AND UNSTEADY STATE SIMULATION FOR REYNOLDS No- 100

8.1 STEADY STATE RESULTS:

The below plot shows that the value of the velocity starts oscillating for the monitoring point after certain iterations here after 150 iterations for the Reynolds number of 100 and the velocity of 5 m/s. This explains that there must be vortex shading in the monitor point region which later will be seen by the vortex plots

Fig: Vertex average of velocity for monitoring point

Fig: velocity contours for the steady flow for Re 100

The residuals have been shown to converge after a certain limit here. After the 250 around iterations the residuals plot is been seen to converge which shows that the other plots we got for the Cd, Cl and vertex velocity can be relied upon and are in the appropriate limits.

Fig: Residuals of the steady case

The coefficient of lift here starts oscillating around after 50 iterations only.

Fig: Coefficient of lift which oscillates at the monitoring point

The coefficient of drag plot here shows the constant value after certain number of iterations i.e. 25 iterations and thus converges after that and remains same for the monitoring point.

Fig: Coefficient of drag

8.1.1 VALUES FOR Cd, Cl and VERTEX VELOCITY OF MONITORING POINT (500 iter...)

Cd here is 1.3484070
Cl here is –0.057060
Vertex velocity here is 2.8920443
Force X (in x direction) 33.7102 N

8.1.2 STROUHAL No:

Below is the value of strouhal number (both general and logarithmic in Y) for the Cl (lift) which defines the local acceleration to the convective acceleration for the monitoring point here which is at 8m form the centre of the hole.

Fig: strouhal number for the lift at monitoring point

Fig: logarithmic plot of the strouhal number

8.1.3 VORTEX SHEDING CONTOURS:

Below contours shows the shedding of the flow just after the hole and the wake region after it. The pattern of the oscillation of the flow can easily be studied with the help of these contours

Fig: Vortex shedding contours

8.1.4 VELOCITY AND PRESSURE AT MONITORING POINT vs. WALL:

The velocity comparison and pressure comparison and its changes in Y direction at the cylindrical wall and monitoring point (8m away right to the centre of hole) for the lines given below is being shown in the chart below.

Fig: Lines representing the position of the wall and monitoring point

Fig: velocity comparison at the circular cylindrical wall and the monitoring point

Fig: Pressure comparison at the circular cylindrical wall and the monitoring point

Fig: Pressure contours for the steady state for Re 100

8.2 UNSTEADY STATE RESULTS:

The below plot shows that the value of the velocity starts oscillating for the monitoring point after certain iterations here after first 12 seconds(around 4000 iterations) of total time 50 sec after the start of the flow through inlet for the Reynolds number of 100 and the velocity of 5 m/s. This explains that there must be vortex shading in the monitor point region which later will be seen by the vortex plots.

Fig: Vertex average of velocity for monitoring point

Fig: velocity contours for the unsteady flow for Re 100

The coefficient of lift here starts oscillating around after 2^nd second itself and continues further

Fig: Coefficient of lift which oscillates at the monitoring point

The coefficient of drag plot here shows the constant value after certain number of iterations i.e. after first 7.5 second and thus converges after that and remains same for the monitoring point.

Fig: Coefficient of drag

8.2.1 VALUES FOR Cd, Cl and VERTEX VELOCITY OF MONITORING POINT (50 sec)

The time step here used was of 0.1 second and for total of 500 time steps. Also each time steps solves here till 20 iterations thus the total time is 50 sec till when the solution runs and thus total 10000 iterations have been performed for it.

Cd here is 1.2829
Cl here is -0.029826
Vertex velocity here is 0.6481m/s (after 50 sec)
Force X here is 32.0729 N

8.2.2 STROUHAL No:

Below is the value of strouhal number (both general and logarithmic in Y) for the Cl (lift) which defines the local acceleration to the convective acceleration for the monitoring point here which is at 8m form the centre of the hole.

Fig: strouhal number for the lift at monitoring point

Fig: strouhal number (in logarithmic Y) for the lift at monitoring point

8.2.3 VORTEX SHEDING CONTOURS:

Below contours shows the shedding of the flow just after the hole and the wake region after it. The pattern of the oscillation of the flow can easily be studied with the help of these contours

Fig: Vortex shedding contours

8.2.4 VELOCITY AND PRESSURE AT MONITORING POINT vs. WALL:

The velocity comparison and pressure comparison and its changes in Y direction at the cylindrical wall and monitoring point (8m away right to the centre of hole) along the vertical lines is being shown in the chart below.

Fig: velocity comparison at the circular cylindrical wall and the monitoring point

Fig: Pressure comparison at the circular cylindrical wall and the monitoring point

Fig: Pressure contours for the unsteady state for Re 100

PART I: CONCLUSION FOR STEADY & TRANSIENT STATE ANALYSIS FOR Re 100:

TABLE: 4

CASES

REY No

INLET VELOCITY(m/s)

MONITORING POINT VELOCITY(m/s)

STEADY

100

5 m/s

1.3484070

–0.057060

2.8920443

TRANSIENT

100

5 m/s

1.2829

-0.029826

0.6481m/s

For the above two cases it can be seen that in transient value of the velocity starts oscillating for the monitoring point after certain iterations here after first 12 seconds(around 4000 iterations) of total time 50 sec and the monitoring point velocity. Although if seen for the transient state as per the iteration terms then the velocity at monitoring point will be greater in case of transient case as compared to the steady state, but to get the convergence of solution and to observe whether or not the oscillations take place we need to do the total iterations of 10000 for transient case. Vortex shedding can been seen more in case for the steady state case as compared to the transient case. As per the normal forces at cylindrical wall are concerned both the cases gives almost same result.

PART II:

CASE 1: STEADY FLOW ANALYSIS WHEN REYNOLDS No is 10:

The below plot shows that the value of the velocity doesn’t oscillates for the monitoring point after ant number of iterations here even after 1000 iterations for the Reynolds number of 10 and the velocity of 0.5 m/s. This explains that there must not be vortex shading in the monitor point region which later will be seen by the vortex plots as a proof of the plot through the contours.

Fig: Vertex average of velocity for monitoring point

The coefficient of drag plot and coefficien

Fig: Coefficient of drag

Fig: Coefficient of lift which doesn’t oscillates at the monitoring point

VALUES FOR Cd, Cl and VERTEX VELOCITY OF MONITORING POINT (1000 iterations)

Cd here is 3.33357
Cl here is 0.001474
Vertex velocity here is 0.2109732m/s (after 1000 iterations)
Force X here is 0.833393 N

Fig: Values of the properties at monitoring point

Fig: velocity contours for the steady flow for Re 10

VORTEX SHEDING CONTOURS:

Below contours shows no shedding of the flow just after the hole and the wake region after it. The pattern of the oscillation of the flow can’t be seen with this much low value of Reynolds number as low as 10 and velocity =0.5 m/sec. Vortex shedding contours doesn’t seems to appear and just separation of boundary can be seen

Fig: Vortex contours

VELOCITY AND PRESSURE AT MONITORING POINT vs. WALL:

Fig: velocity comparison at the circular cylindrical wall and the monitoring point

Fig: Pressure comparison at the circular cylindrical wall and the monitoring point

CASE 2: STEADY FLOW ANALYSIS WHEN REYNOLDS No is 1000:

The below plot shows that the value of the velocity oscillates for the monitoring point after 100 number of iterations for the Reynolds number of 1000 and the velocity of 50 m/s. This explains that there must be vortex shading in the monitor point region which later will be seen by the vortex plots as a proof of the plot through the contours.

Fig: Vertex average of velocity for monitoring point

The coefficient of drag plot and coefficient of lift plot here shows the conversing value after certain number of iterations i.e. 120 iterations for Cd and only 60 iterations for oscillation of Cl and thus keeps oscillating after that for the monitoring point.

Fig: Coefficient of drag

Fig: Coefficient of lift which oscillates at the monitoring point

VALUES FOR Cd, Cl and VERTEX VELOCITY OF MONITORING POINT (500 iterations)

Cd here is 1.0809
Cl here is -0.5077
Vertex velocity here is 44.34m/s
Force X here is 2702.45 N

Fig: Values of the properties at monitoring point

Fig: velocity contours for the steady flow for Re 1000

VORTEX SHEDING CONTOURS:

Below contours shows shedding of the flow just after the hole and the wake region after it. The pattern of the oscillation of the flow can be seen with this value of Reynolds number at 1000 and velocity =50 m/sec. Vortex shedding contours seems to appear and separation of fluid from boundary can be seen

Fig: Vortex contours

VELOCITY AND PRESSURE AT MONITORING POINT vs. WALL:

Fig: velocity comparison at the circular cylindrical wall and the monitoring point

Fig: Pressure comparison at the circular cylindrical wall and the monitoring point

CASE 3: STEADY FLOW ANALYSIS WHEN REYNOLDS No is 10000:

The below plot shows that the value of the velocity do oscillates heavily for the monitoring point after around 100 number of iterations for the Reynolds number of 10000 and the velocity of 500 m/s. This explains that there must be vortex shading in the monitor point region which later will be seen by the vortex plots as a proof of the plot through the contours.

Fig: Vertex average of velocity for monitoring point

The coefficient of drag plot here shows the converging value after certain number of iterations i.e. 400 iterations for Cd and after 60 iterations for Cl and it starts oscillating after that and remains oscillating for the monitoring point.

Fig: Coefficient of drag

Fig: Coefficient of lift which oscillates at the monitoring point

VALUES FOR Cd, Cl and VERTEX VELOCITY OF MONITORING POINT (500 iterations)

Cd here is 1.1686411
Cl here is 0.48137257
Vertex velocity here is 344.2211 m/s
Force X here is 292160 N

Fig: Values of the properties at monitoring point

Fig: velocity contours for the steady flow for Re 10000

VORTEX SHEDING CONTOURS:

Below contours shows huge amount of shedding of the flow just after the hole and the wake region after it. The pattern of the oscillation of the flow can be seen with this much high value of Reynolds number as high as 10000 and velocity =500 m/sec. Vortex shedding contours seems to appear and large separation of boundary can be seen through vortex contours

Fig: Vortex contours

VELOCITY AND PRESSURE AT MONITORING POINT vs. WALL:

Fig: velocity comparison at the circular cylindrical wall and the monitoring point

Fig: Pressure comparison at the circular cylindrical wall and the monitoring point

CASE 4: STEADY FLOW ANALYSIS WHEN REYNOLDS No is 100000:

The below plot shows that the value of the velocity do oscillates more heavily as compared to the last case 3 for the monitoring point after around 100 number of iterations for the Reynolds number of 10000 and the velocity of 5000 m/s. This explains that there must be vortex shading in the monitor point region which later will be seen by the vortex plots as a proof of the plot through the contours.

Fig: Vertex average of velocity for monitoring point

The coefficient of drag plot here shows the a non-periodic varying value in the range of 0.6 to 2.25 after 50 iterations and after 60 iterations for Cl and it starts oscillating with greater magnitude after that and remains oscillating for the monitoring point.

Fig: Coefficient of drag

Fig: Coefficient of lift which oscillates at the monitoring point

VALUES FOR Cd, Cl and VERTEX VELOCITY OF MONITORING POINT (500 iterations)

Cd here is 1.5453034
Cl here is 0.9062512
Vertex velocity here is 4267.5059 m/s
Force X here is 86326e+07 N

Fig: Values of the properties at monitoring point

Fig: velocity contours for the steady flow for Re 100000

VORTEX SHEDING CONTOURS:

Below contours shows huge amount of shedding of the flow just after the hole and the wake region after it. The pattern of the oscillation of the flow can be seen with this much high value of Reynolds number as high as 100000 and velocity =5000 m/sec. Vortex shedding contours seems to appear more largely and separation of boundary can be seen through vortex contours

Fig: Vortex contours

VELOCITY AND PRESSURE AT MONITORING POINT vs. WALL:

Fig: velocity comparison at the circular cylindrical wall and the monitoring point

Fig: Pressure comparison at the circular cylindrical wall and the monitoring point

PART II: VORTEX SHEDDING CONTOURS COMPARISION FOR ALL CASES

The increase in the intensity of vortex shedding can easily be seen through these contours on the below distinct plots of vorticity on velocity contours. As the Re increases the separation of flow and swirling of flow and its disturbances from the continuity can be easily observed.

9.CONCLUSION:

9.1 STEADY & TRANSIENT STATE CONCLUSION FOR Re 100:

TABLE: 4

CASES

REY No

INLET VELOCITY(m/s)

MONITORING POINT VELOCITY(m/s)

STEADY

100

5 m/s

1.3484070

–0.057060

2.8920443

TRANSIENT

100

5 m/s

1.2829

-0.029826

0.6481m/s

9.2 CONCLUSION FOR CASE I, CASE II, CASE III & CASE IV:

Of all the cases the case with Reynolds number equals 10 is the one in which the vertex average velocity shows the constant value after some iterations and doesn’t shows any oscillations in its values and thus no any significant vortex shedding can be seen as given the cases here is with very low Reynolds number and low inlet velocity of around 0.5 m/seconds. The monitoring point velocity is significantly lesser that that of the inlet velocity and shows some losses of velocity by disruption in continuity due to vortex shedding.

The other cases are the ones where we can see the oscillating plot of the vertex velocity at monitoring point and this oscillation goes on increasing as we increase the velocity and thus the Reynolds number with it. Also the coefficient of lift keeps on oscillating with the further iterations and keeps oscillating further within certain limits which do shows that the solution is converged. The coefficient of drag plot also show distinct characteristics with the increase of the Reynolds number and from constant value to the converging but oscillating value can be seen for higher velocity and higher Reynolds number.

9.3 COEFFICIENT OF DRAG & LIFT COMPARISION FOR ALL CASES (STEADY STATE)

TABLE: 5

CASE	REYNOLDS No	Cd	Cl
1	10	3.3335	0.001474
2	100	1.3484	-0.05706
3	1000	1.08097	-0.50770
4	10000	1.1686	0.481372
5	100000	1.5453	0.906251

The above table shows that the value of lift coefficient keeps on increasing as we keep increasing the velocity and Re. The drag coefficient on the other hand is maximum for the lowest Reynolds No and goes on decreasing up to a certain extent and starts increasing for the Re 10000 and for Re 100000. Although the oscillations in the plot of Cl specifically shows that the value keeps fluctuating in periodic interval and the fluctuations magnitude goes on increasing as the velocity and Re increases. This couldn’t be seen in the case of Cd at initial lower Re which further after multiple times increase in Re do show a very slight oscillation when the plot starts to converge.

9.4 PREFERRED MATERIAL AND FEATURES FOR FLOW INSTABILITY REDUCTION:

The preferred method to check the intensity of the vortex shedding and for controlling the instability of the flow can be adding more smoothness to the layer of the interacting body with the fluid. Also adding and changing some aspects some aspects of the cylindrical wall by few means in which we no need to change even the material but just some additional changes which can be done to the surface of the interacting wall can also reduce the instability of flow among which are:

Helical strake
Shroud
Axial slats
Streamlined fairing
Splitter
Ribboned cable
Pivoted guiding vane
Spoiler plates.

As per the materialistic property point of view if the porosity in increased for the material then also the stability in the flow can be achieved but it just a relative term and which means the instability can be reduced up to some significant amount depending upon the material. Thus permeability plays a great role in deciding the stability of the flow and an optimum value of it can be decided by various experiments and analysis.

References from where the preferred material selection and other research of fluid flow over cylinder has been taken are: B. Pang and Fundamentals of vortex-induced vibration by C. Dalton.

Steady Vs Unsteady flow over a cylinder

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Ship work like this
in your own course.