======Sudden Pipe Expansion======
=====Experiments by Szczepura=====

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====Description====

Flow of water in a sudden pipe expansion.  One of the aims of the experiment was to 
provide results which shed light upon the limitations of the standard 
\(k\)-\(\varepsilon\) model for turbulent flows.

2D axisymmetric flow with constant temperature.

===Geometry===

<imgcaption cas13-geom| Pipe expansion geometry>{{ figs:case013:cas13-geom1.png | Pipe expansion geometry}}</imgcaption>

The experiments were performed in a specially designed facility.  The axisymmetric pipe
expansion (<imgref cas13-geom>) forms part of a water-filled loop which is described below.  The water circuit is
illustrated in <imgref cas13-exp1>.

<imgcaption cas13-exp1| Water circuit and details of the plenum>{{ figs:case013:cas13-exp1.png | Water circuit}}</imgcaption>

To avoid corrosion products the rig was constructed of stainless steel and ABS plastic throughout.  
Demineralised water was used with an anti-fungicide additive to prevent algae growth.  An HMD glandless pump, fitted with a 
Fluidrive fluid coupling, was used to provide a controllable mass flow. Fine control was 
achieved by using a bypass loop.  The pump is of a rotating impeller design, so the 
outflow is very asymmetric. This asymmetry was removed by the plenum illustrated in <imgref cas13-exp1>.

The design of the 'top hat' was critical and the final version consisted of thirty-seven 25mm diameter
holes providing radial jets which mix before reaching the side wall of the plenum.  The flow then enters a 
straight pipe of internal diameter \(d = 78.3\) mm and length of \(47d\).  The circularity of this pipe was to within 
+/- 0.4%.  The actual measurement region is in a sudden expansion to a pipe of internal diameter \(D = 152.4\) mm. 
This was constructed of a stainless steel, sharp edged backstep and a glass cylinder of length \(4.2D\) and 
circularity +/- 0.2%.  Spigotted and O-ring sealed joints were used throughout to ensure the squareness of 
the measurement region, backstep and inlet pipe. The glass cylinder, which was surrounded by a water-filled 
square section box to minimise refraction of the laser beams, was matched into a stainless steel tube giving 
an overall straight length downstream from the backstep of \(8.0D\). The mass flow rate in the rig was measured 
by an orifice plate installed according to BS1042 requirements giving an absolute accuracy of 1.5%.  The 
circuit includes a free surface tank in which any entrained air can escape.

===Flow Characteristics===

The flow can be divided into three distinct regions, a core, a shear layer and a reverse 
flow, as illustrated in <imgref cas13-flow>.

<imgcaption cas13-flow| Flow regions>{{ figs:case013:13fig4.jpg | Flow regions}}</imgcaption>

These regions reflect the features of the flow observable in contour plots.  
An annular shear layer grows from the step edge, merging on the centreline at 
\(x/D = 1.5\) and reaching the wall at \(x/D = 2.3\).  The 
shear stress has an elongated peak extending from \(x/D = 1.4\) to \(2.2\).

In the core region, which is monotonically reduced in size by the shear layer growth, upstream
pipe conditions persist.  The ratio of centreline velocity to bulk velocity was 1.18, the expected value
for a pipe Reynolds number of \(4 \times 10^5\). The shear stress 
\(\overline{u_1u_2}\) had a pronounced curvature which indicates a non-developed flow.

The reverse flow region is of particular interest since previous experiments 
have failed to detect secondary recirculation.  The evidence is that this secondary 
recirculation extends to \(x/D = 0.35\), and covers a significant 
portion of the backstep. If this reverse flow is viewed as a wall jet flowing into a 
corner then a recirculation is not very surprising.  A minimum in the Nusselt number at 
about one step height downstream is interpreted as a counter-rotating secondary vortex.


===Flow Parameters===

  * The fluid used in this experiment was water.
  * Outlet pipe Reynolds number based on bulk velocity: \(Re = 2\times 10^5\).

===Inflow Conditions===

At \(x/D = -0.25\), in the inlet pipe, the flow is fully developed and the following measurements are 
provided along a radius for \(r/D\) ranging from 0 to 0.257 (in file {{cdata:case013:tape-part4.dat|tape-part4.dat}}:

Profiles of:

  * First order moments: \(U\), \(V\)
  * Turbulent kinetic energy: \(k\)
  * Turbulent viscosity \(\nu_t\)

====Experimental Details====

Velocity measurements using a two-channel LDV system.

The turbulent kinetic energy dissipation rate \(\varepsilon\) has been 
estimated from spectral measurements, and the turbulent viscosity \(\nu_t\) has
been derived from both values of \(\varepsilon\) and \(k\).

The friction velocity is defined as: \(U^* = (\tau_w/\rho)^{1/2}\)
where \(\tau_w\) is the wall shear stress. The wall shear stress has been derived from
experimental velocity measurements at \(r/D = 0.4771\) by fitting to an empirical logarithmic law.

===The LDA System===

The LDA system consists of modular units manufactured by Thermo Systems incorporated (TSI). These were 
assembled as in <imgref cas13-lda> to give three separate beams which co-incidentally cross in the measurement region.

<imgcaption cas13-lda| The LDA system>{{ figs:case013:13fig5.jpg | LDA system}}</imgcaption>

The system is operated with the top beam (the reference beam) plane polarized at an angle \(0^o\), and the other 
beams at \(+45^o\) and \(-45^o\).  This gives two sets of fringes in the control volume which are orthogonal and at 
\(45^o\) to the major axis of the measurement region.  The 40MHz Bragg cell frequency shifts the reference beam, so both sets of
fringes are moving.  This ensures that results can be correctly interpreted in regions of reversing flow.  The circuit was initially 
cleaned using the bypass filter fitted with 2 \(\mu\)m elements.  After
cleaning, no Doppler signal could be obtained.  Then 2.95 \(\mu\)m latex spheres were introduced as
scattering particles.  This size was chosen to optimise the signal to noise of the system, the fringe spacing being 
4.5 \(\mu\)m.  The photomultiplier outputs were downmixed to frequencies
comparable with the Doppler frequency (in the lMHz range), band-pass filtered to remove the pedestal and then 
processed by two trackers.  The tracker outputs, which consists of a voltage proportional to the incoming frequency, were digitised using an 
in-house manufactured multiplexing analogue-to-digital convertor.  The multiplexing rate was 15 kHz compared with a
typical Kolmogorov frequency in the experiment of l0 kHz (see Szczepura 1985),  so the signals can be treated as having been taken simultaneously.  
These digitised pairs were read by a PDP-8 computer.  The time interval between reading of pairs was roughly 1 ms and was governed by the
computer and not by particle arrivals in the control volume.  This procedure ensures that there is no bias in the data collection 
towards higher velocities.

===Measurement Errors===

| \(\delta(U)\)   |  \(\pm 0.56\%\)  |
| \(\delta(V)\)   |  \(\pm 3.3\%\)   |
| \(\delta(u')\)  |  \(\pm 2.2\%\)   |
| \(\delta(v')\)  |  \(\pm 3.4\%\)   |
| \(\delta(w')\)  |  \(\pm 3.0\%\)   |
| \(\delta(\overline{uv})\)  |   \(\pm 3.2\%\) |

       
====Available Measurements====

The data can be downloaded as compressed archives from the links
below, or as individual files.

  * {{cdata:case013:pipx-allfiles.zip|pipx-allfiles.zip}}
  * {{cdata:case013:pipx-allfiles.tar.gz|pipx-allfiles.tar.gz}}

[[case013-plots|Sample plots]] of selected quantities are available.


At \(x/D = 0.05\), profiles for \(r/D\) ranging from 0 to 0.5 are provided (in file {{cdata:case013:tape-part1.dat|tape-part1.dat}}) of:

  * First order moments: \(U\), \(V\)
  * Second order moments: \(\overline{u^2}\), \(\overline{v^2}\), \(\overline{w^2}\), \(\overline{uv}\)
  * Turbulent kinetic energy: \(k\)
  * Profile of turbulent viscosity: \(\nu_t\)

At several \(x/D\) positions ranging from 0.05 to 2.95 with an increment of 0.1, 
the following profiles are provided for \(r/D\) ranging from 0 to 0.5 (in file {{cdata:case013:tape-part2.dat|tape-part2.dat}}):

  * Profile of turbulent viscosity: \(\nu_t\)
  * Profile of turbulent length scale

The friction velocity along the wall (\(u^*\)) for \(x/D\) ranging from 0.05 to 2.95 is provided in
file {{cdata:case013:tape-part3.dat|tape-part3.dat}}.

At \(x/D = -0.25\), in the inlet pipe, profiles are provided for \(r/D\) ranging from 0 to 0.257 of (in file {{cdata:case013:tape-part4.dat|tape-part4.dat}}:

  * First order moments: \(U\), \(V\)
  * Turbulent kinetic energy: \(k\)
  * Turbulent viscosity \(\nu_t\)


====Reference====

  - Szczepura, R.T. (1985). Flow characteristics of an axisymmetric sudden pipe expansion - results obtained from the turbulence studies rig. Part 1 mean and turbulence velocity results. //CEGB Berkeley TPRD/B/0702/N85//.

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Indexed data:
<data dbcase confined_flow>
case       : 013
title      : Sudden Pipe Expansion
author*    : Szczepura
year       : 1985
type       : EXP
flow_tag*  : 3d, axisymmetric, separated, varying_cross_section
</data>