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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