Fluid Flow:
Steady Flow
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Section 5 – Fluid Flow
Objectives
Module 4: Steady Flow
Page 2

Understand steady flow.

Identify the types of steady flow.

Examine the considerations for steady flow.

Study the Navier-Stokes Equation for steady flow.

Learn from two examples:
 CFD Analysis of Couette Flow
 Flow between two fixed parallel plates
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Section 5 – Fluid Flow
Steady Flow
Module 4: Steady Flow
Page 3
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A steady flow is one in which the conditions (velocity, pressure and
cross-section) may differ from point to point but DO NOT change
with time.
In steady flow, all time derivatives in the governing equations are
removed.
Compared to unsteady flow, steady flow is computationally less
expensive and therefore much faster to solve.
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Section 5 – Fluid Flow
Steady Flow Types
Module 4: Steady Flow
Page 4

Steady flow can be further classified into steady uniform flow and
steady non-uniform flow.

Steady uniform flow:


Conditions do not change with position in the stream or with time. An
example is the flow of water in a pipe of constant diameter at constant
velocity.
Steady non-uniform flow:

Conditions change from point to point in the stream but do not change with
time. An example is flow in a tapering pipe with constant velocity at the inlet.
Velocity changes as fluid moves along the length of the pipe toward the exit.
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Section 5 – Fluid Flow
Considerations for Steady Flow
Module 4: Steady Flow
Page 5
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For all steady state flow cases, the total amount of flow entering into
the system must have an outlet boundary that would allow the same
amount of fluid out.
If this is not done, the solution will either fail to converge or
circulation will occur at the inlet boundary.
Mass flow conservation as well as energy conservation should be
ensured for the domain.
Flow out
Flow in
Flow out
Flow out
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Section 5 – Fluid Flow
Navier–Stokes Equation for Steady Flow
Module 4: Steady Flow
Page 6
0
The time derivative is set to zero, thus simplifying the calculation.
The most simplified cases of CFD are incompressible steady
state flow with no body forces, as the terms inside the
Navier–Stokes Equation are reduced.
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Video Example: CFD Analysis of Couette Flow
(Steady State)

The CFD analysis of Couette flow using
Autodesk Simulation Multiphysics has
been described in a two-part video:

Section 5 – Fluid Flow
Module 4: Steady Flow
Page 7
Y
u0
Moving Plate
The first part explains the problem, setting up
of the flow domain, meshing and application
of boundary conditions.
Stationary Plate

X
The second part explains the analysis and post
processing, covering the details of equation
solving in the background and display of the
analysis results.
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Additional Example:
Flow Between Two Fixed Parallel Plates
Section 5 – Fluid Flow
Module 4: Steady Flow
Page 8
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Setting up geometry and walls can be fixed
Y
Distance between the plates is 2Y
The velocity can be defined as:
u 

y
Flow between two fixed parallel plates
Couette flow case can be used
 pY
2
2
y 2

1

(
)

Y 

x
Exact Solution
Maximum Velocity will occur at the
center, i.e., at y =0
u max 
© 2011 Autodesk
 pY
2
These two exact solution equations can be
used by students to verify results from CFD.
2
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Section 5 – Fluid Flow
Summary
Module 4: Steady Flow
Page 9

Steady flow is when flow behavior (velocity, pressure) does not
change with the passage of time.

Many real life studies are carried out assuming steady flow.

Even when studying unsteady flow, it is a common practice to carry
out a steady state analysis first.
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Section 5 – Fluid Flow
Summary
Module 4: Steady Flow
Page 10

For example, study of flow across a vehicle is carried out in steady
state to evaluate the drag coefficient.

It is important that the boundary conditions are set up for steady
flow such that the continuity is maintained and changes with time
inside the domain are zero.

Otherwise, the numerical analysis may diverge.
© 2011 Autodesk
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that content has been modified from the original, and must attribute source content to Autodesk.
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