a project report on turbulent flows

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Turbulent Flow-M.Sc Computational Mechanics Project Summer Semester 2013

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A PROJECT REPORT ON

DETERMINATION OF TURBULENT FLOW IN

PIPE USING ANSYS CFX

Guided By:- Prof. Dr. Andreas Kempf

&

M.Sc Andreas Rittler

BY

NISHANT KUMAR

Matrikelnummer :-ES0227948700

M.Sc (Computational Mechanics)


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Introduction to Turbulent Flows

In fluid mechanics the type of flow through any device is quite important for

determination of various physical properties.Turbulent flow,type offluid (gas orliquid) flow in which the fluid undergoes irregular fluctuations, or mixing, in contrast

to laminar flow, in which the fluid moves in smooth paths or layers. In turbulent flow the

speed of the fluid at a point is continuously undergoing changes in both magnitude and

direction. The flow of wind and rivers is generally turbulent in this sense, even if the currents

are gentle. The air or water swirls and eddies while its overall bulk moves along a specific

direction. Turbulent flow is characterized by unsteady eddying motions that are in constant

motion with respect to each other. At any point in the flow, the eddies produce fluctuations in

the flow velocity and pressure.

Most kinds offluid flow are turbulent, except for laminar flow at the leading edge of

solids moving relative to fluids or extremely close to solid surfaces, such as the inside wall of

a pipe, or in cases of fluids of high viscosity (relatively great sluggishness) flowing slowly

through small channels. Common examples of turbulent flow are blood flow in arteries, oil

transport in pipelines, lava flow, atmosphere and ocean currents, the flow through pumps and

turbines, and the flow in boat wakes and around aircraft-wing tips.

The nature of flow could be mathematically determined by Reynoldss Number.Re

is the Reynolds number, named after Osborne Reynolds who did systematic experiments, of a

similar type to those described above, one hundred years ago. If V or d (or both) are small

and the viscosity is large, Re will be small. For this case the flow will be laminar. Increase d

or V or decrease the viscosity, and Re will increase.

The Reynoldss Equation is given by;

The type of turbulence & nature of flow of turbulence can be computed by Navier

Stokes equation.The Navier-Stokes equations are based on the principles of conservation of

mass, momentum and energy.The Navier-Stokes equations may be obtained by using

infinitesimal or finite control volume approaches, and the governing equations can be

expressed in differential or integral forms.
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The above equation represents the significance of each term & its effects on the flow of fluid.

The Navier Stokes equations has various forms for different nature of fluids which could be

simply elaborated with the help of following tree diagram;


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Turbulence Models

The Reynolds-averaged equations and their reduced forms cannot be solved without

information about the various correlations. Terms that make up the stress tensor, and the

same is true for the energy equation. It is well known that these terms, which represent

turbulent diffusion, are much larger than those corresponding to laminar diffusion except in

the

immediate vicinity of a wall, and in turbulent wall boundary layers, wakes, jets

and more complex flows, these turbulent diffusion terms are of similar magnitude

to the convective terms. Hence a need for modelling of Turbulence models is felt. Types of

turbulence models are;

1. Zero-Equation Models:-The zero-equation, often referred to as algebraic eddy viscosity and/or mixing

length models, are used to model the Reynolds shear stress term in the momentum

equations. 0-equation models describe the Reynolds-stress-tensor directly by

means of the known terms from the conservation equation for momentum.

Such models can be obtained from:

a. Dimensional analysis

b. Phenomenological consideration

2. One - Equation Models:-This method employs a single transport equation for eddy viscosity, is popular for

wall boundary-layer and free-shear flows and is used in both boundary-layer and

Navier-Stokes methods.In 1-equation models, in addition to the conservationequation for mean momentum, the equation for the turbulent kinetic energy kissolved.

3. Two-Equation Models:-There are several two-equation models. Three of the more popular, accurate and

widely used models are the k-e model of Jones and Launder , the k-model of Wilcox

and the SST model of Menter which blends the k-w modelling the outer region and k-emodel in the near wall region. All three models can be used for a range of flow

problems with good accuracy.In 2-equation models, two further transport equations are solved.

a) One equation for the turbulent kinetic energy k

b) One additional equation for a length scale or time scale (mixing length)

(Since already yields the velocity scale.)

Some important points about Two-equation models;

The Reynolds-stress-tensor is a function of the tensor for the mean

velocity and a function of the turbulent kinetic energy.Equilibrium turbulence ( is

determined through the time scales and length scales of large eddies).Satisfying

simulations of several types of flow. Usage of a set of constants, often modified

constants and additional terms are needed.


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Problem statement & approach to problem

Air flows through the pipe having Reylonds number Re=1,00,000 with a ratio of R/r=0.682.

Determine Turbulence with help of Turbulence model K-omega & SST.

Also a simulation for both fine & coarse mesh had to be done.

Assumed Data:-

Properties of Air;

Temp. (C)= 1000C, Density (Kg/m3)=0.946 kg/m3,

Viscosity (Pa-s) = 2.17 x 10-5 Pa-sec, Kinematic Viscosity(m2/s)= 2.30 10-5 m2/sec

Gas Constant (J/kgK) = 287.

Analytical Approach to Problem:-

Assuming Length of 1000 mm with diameter =100mm of pipe

Re= *V*L/

V=Re* / *L

=2.17*1,00,000/0.946*1

=2.293 m/sec

With sides of cube =2*r

=2*25

= 50 mm


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Simulation in Ansys CFX

A. For Coarse mesha) SST model:-

Pressure results

a. From the simulation results the maximum pressure is observed on theinlet face of the cube. Its indicated by smallest of arrows.b. While the back pressure is observed in the region between the face ofcube & walls of pipe. Indicated by medium size arrow.

c. While longest of arrows denote the negative pressure developed at theoutlet side of the cube.

d. The points b & c lead to turbulence in the system.

a

b

c


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Velocity results

a. This region shows a start of nearly zero velocity regions at the inlet side of the cube.b. A highly turbulent region could be observed in this region due to sudden increase in

the velocity which is due to sudden compression of the air causing shock waves &

also due to sudden drop in pressure.

c. Again a zero velocity region is observed due to decrease in pressure.d. A fully developed turbulence region is observed in the region.

b

cd

a


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Velocity Streamlines

b) K-omega model:-

Pressure results


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Velocity results

B. For Fine Mesh:-a) SST model

Pressure Results

a

b

c

d


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a. Maximum pressure in this region.b. Sudden drop in pressure, negative pressure region. A back flow of fluid is observed.c. Pressure increases from negative to positive region, turbulence could be observed in

this region.

d.

A constant pressure region is observed after the turbulent behaviour of the fluid.

Velocity Results

a. This region shows a start of nearly zero velocity regions at the inlet side of the cube.b. A highly turbulent region could be observed in this region due to sudden increase in

the velocity which is due to sudden compression of the air causing shock waves &

also due to sudden drop in pressure.

c. Again a zero velocity region is observed due to decrease in pressure.d. A fully developed turbulence region is observed in the region.


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Velocity Vector Result

b) K-omega model:-

Total Pressure Results


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Velocity Results

Velocity Vector Results


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Conclusion

1. The cube is placed at a distance which is close to inlet of the fluid pipe,which causes generation of shock waves in Air as its due to sudden

compression of the air near the walls & then contraction.

The longer arrow indicates the region where the air is contracted, while

the smaller arrow indicates the region having expansion of the air.

2. In both the methods of modelling, K-omega & SST models we couldobserve a prominent turbulent region towards the end of the surface of

cube.

3. There is not much difference between the results obtained from bothmodels K-omega & SST models but SST models gives a finer results near

the walls of the pipe.

4. The quality of mesh could also increase the accuracy of the simulation.


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Reference

1. Fluid Mechanics-Frank. M. White2. Wikipedia3. Properties of Air-Google

a project report on turbulent flows

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