The purpose of this work was to generate validated CFD
predictions for:

• square-edged and knife-edged orifice plates, free of burrs and
other contaminants,

• circular, concentric orifices in circular pipes with identical
upstream and downstream cross-sectional areas,

• fully-developed flow conditions upstream and downstream of the
orifice,

•swirl-free, steady flow conditions with no cross-flow upstream
or downstream of the orifice plate and flow normal to the orifice
plate,

• laminar, transitional and turbulent flow regimes,

• single-phase, Newtonian liquids and gases in incompressible
flow (Mach number = 0.3 at the vena contracta plane).

The CFD validation studies covered the following geometrical
configurations and pipe Reynolds numbers:

• orifice to pipe diameter ratios: 0.3 = ß = 0.7; orifice
thickness to diameter ratios: 0.01 = t/d = 5.0.

• pipe Reynolds number: 10 = Re_D =
10⁵.

Based on the comparisons of the ESDU CFD predictions with the
experimental data in the literature, best practice guidelines are
provided for the modelling of the flow characteristics and pressure
loss in square-edge orifice plates.

In this Technical Note, the ESDU CFD validation studies are
presented for the prediction of friction losses and flow
characteristics in straight circular pipes with smooth walls.

Understanding of pipe friction and associated flow
characteristics in different flow regimes is fundamental to the
understanding of boundary layer development and turbulence
modelling in internal flow engineering applications such as viscous
drag and heat-transfer processes.

Typical industrial CFD applications of pipe flow include systems
where pipes are part of a more complex domain, such as aircraft
ducts, pipe fittings, heat exchangers, various components of power
generation plants, etc. In more general CFD applications, straight
long pipes are often used to set inlet and outlet boundary
conditions. At inlet boundaries, they are used as an artificial
extension of the inlet to the investigated flow domain to allow the
natural development of duct boundary layers. At outlet boundaries,
straight pipes are used as an artificial extension to the outlet of
the investigated flow domain to reduce the influence of the outlet
local fluid dynamics on the CFD predictions. In all such
applications, it is essential to reduce the sensitivity of CFD
predictions of friction losses to mesh density and distribution,
pipe length required for fully-developed flow, boundary conditions
and turbulence modelling.

Accurate prediction of the friction losses and flow
characteristics in straight pipes is one of the most challenging
problems in CFD. Although direct numerical simulation (DNS) and
large eddy simulation (LES) are used in research, in industry
Reynolds-averaged Navier-Stokes (RANS) methods are largely
used.

The purpose of this work is to provide guidance on the CFD
modelling of friction losses and flow characteristics in:

• straight circular pipes with smooth walls,

• laminar, transitional and turbulent flow regimes,

• swirl-free, uniform inlet velocity conditions,

• fully-developed exit flow conditions,

• steady-state flow conditions,

• incompressible flow of single-phase, Newtonian liquids
and gases.

• employing commercial CFD packages typically used in the
industry, i.e. finite volume RANS code with
low-Reynolds-number turbulence and transition correlation-based
‘bypass' modelling capabilities.

Extensions to rough pipes and to compressible flow will be
considered in future work.

Three types of meshes were considered: 2D-axisymmetric
hexahedral meshes, 3D purely tetrahedral meshes and 3D tetrahedral
meshes with prismatic layers. Pipes with different lengths were
tested in laminar, transitional and turbulent flow at Reynolds
numbers ranging 1 less than Re less than
10⁷.

Three different turbulence models were considered with different
near-wall treatments: the k – e with SCALABLE near-wall treatment,
k – ? with AUTOMATIC near-wall treatment and SST with AUTOMATIC
near-wall treatment. Three transition models were considered: the
SST specific-?, SST ? and SST ?-Re_? models.
Detailed CFD validation studies on transitional flow are presented
in ESDU TN 08009.

A brief description of the fundamental fluid mechanics in
straight pipes is given in Section 3. In this section,
correlations, measurements and DNS predictions in the literature
for friction losses and flow characteristics in straight pipes are
reviewed. The methodology used in the CFD predictions is described
in Section 4.

The ESDU CFD predictions for the different meshes, pipe lengths,
Reynolds number and turbulence models are discussed in Section 5
and compared to experimental data and correlations in Section 6.
Best Practice Guidelines on mesh density and distribution, setting
of boundary conditions and turbulence modelling are given in
Section 7. Overviews on the CFD modelling of turbulent and
transitional flows are given in Appendices A and B,
respectively.

The consistency of the data and the effects of non-standard
flow, operation and installation conditions are discussed. The main
emphasis of this Technical Note is on data for: (1) circular,
concentric orifices in circular pipes, (2) ducts with identical
downstream and upstream cross-sectional areas, (3) laminar,
transitional and turbulent flow regimes, (4) fully-developed,
swirl-free, steady flow conditions with no-cross flow upstream and
downstream of the orifice plate, and (5) single-phase, Newtonian
liquids and gases in incompressible flow. However, a brief review
on the data for cooling holes, annular and non-circular orifices,
and perforated plates is also presented.

The work is based on ESDU 83042 that gives a method for
estimating the location of spray patterns based, in part, on
research work at Bristol University using a spray-intensity probe
to obtain surveys of spray kinetic pressure behind a wheel running
in water. Further work at Bristol University, using a ‘force
measuring device' to find the force on a small plate in an attempt
to provide an understanding of the spray intensity probe results,
was also used.

The contribution arises because the fin induces an
antisymmetrical spanwise loading distribution across the tailplane
which generates a rolling moment about the tailplane centre-line
chord. The total contribution of the tail assembly of an aircraft
to the rolling moment derivative due to sideslip is obtained by
adding this contribution due to interference effect to the
contributions provided by the fin (using ESDU 82010 or Aero
C.01.01.01), and the tailplane planform and dihedral (obtained from
ESDU 80033 and Aero A.06.01.03 respectively).

The contribution due to the interference effect of a fin on a
tailplane is often small enough, when compared to the fin
contribution, for it to be ignored when estimating the rolling
moment derivative due to sideslip for an aircraft, but it is of
more importance structurally when considering bending moments at
the tailplane root.

The interaction between tyre, water, and ground is a complex example of a multi-phase flow. It is therefore not readily described in a simple, algebraic, engineering format. This Technical Memorandum presents a description of the simplified view of the way in which the footprint may be divided into three zones. In addition, an easily used model for the pressures in the zones is given.

At the concept and preliminary design stages, several different configurations may be considered as possible candidates to meet a given design specification. As more information becomes available, the range of configurations are reduced to a single choice. This Technical Memo gives an example of the use of rapid aerodynamic analysis tools at the concept and preliminary design stages applied, retrospectively, to three markedly different historical candidate designs to similar design specifications.