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The PHOENICS-Direct Simulation Scenario: TubeFlow

by Elena Pankova and Brian Spalding, February-April 2013

Click here for general information about Simulation Scenarios.

Contents

  1. Purpose
  2. Menu items
  3. How to save the menu settings
  4. How to run the TubeFlow simulation
  5. Inspecting the results
  6. The multi-run facility of PHOENICS-Direct
  7. Concluding remarks

1. Purpose

The TubeFlow scenario simulates steady flow of a fluid along a straight tube of circular cross-section, exchanging heat through a finite-thickness wall with an external environment.

Flow along tubes is frequently encountered in engineering practice; and it is often desired to determine the rate of heat transfer and also the pressure difference necessary to maintain the flow.

Engineers commonly deduce these quantities from formulae which connect:

Of these dimensionless numbers, the symbols and definitions are:

Name
symbol
definition
Nusselt
Nu
αD/λ
Reynolds
Re
ρUD/μ
Prandtl
Pr
cμ/λ
Grashof
Gr
D3ρ2gβΔT/μ2
friction coefficient
f
2 Δp/(ρU2 ) (L/D)- 1
Euler
Eu
2 Δp/(ρU2)

wherein the meanings of the symbols are:

Symbol
meaning
units
Symbol
meaning
units
c
specific heat
J/kg degC
D
tube diameter
m
U
velocity
m/s
αJheat-transfer coeffficientV
J/m2s
β
volumetric expansion coefficient
1/degC
Δp
pressure difference
N/m2
ΔT
temperature difference
degC
λ
thermal conductivity
J/degC m
μ
dynamic viscosity
kg/m s

For example, commonly accepted formulae are:

Conditions
Quantity
value
Fully-deveoped laminar flow
f
64.0 Re-1.0
ditto, uniform heat flux
Nu
3.66
ditto, uniform wall temperature
Nu
4.364
Fully-developed turbulent flow
Re > 2.e4
f
0.184 Re-0.2
ditto, uniform heat flux or
uniform wall temperature
Nu
0.023 Re0.8Pr0.333

However the values so deduced are of uncertain reliability because of factors which the formulae cannot correctly represent, including:

TubeFlow by contrast does take account of these factors by way of adjustable parameters arranged in several groups, as will now be explained.

Each simulation scenario (SimScene for short) opens with its 'top page' where information about each specific scenario and its interface is presented. The TubeFlow top page is displayed below.

on which access to the Menu structure is provided from the near-the-top tab: 'Inspect or modify input data'.

2. Menu items

Clicking on this allows the display and editing of all adjustable parameters, divided typically into ten groups, namely:
  1. General
  2. Geometry
  3. Variables solved
  4. Material properties
  5. Models
  6. Initial conditions
  7. Boundary conditions
  8. Output
  9. Computational grid
  10. Numerical

The number of groups among which the adjustable parameters are distributed need not be the typical ten; thus TubeFlow has the nine groups listed on the left-hand side of the following picture. The 'Initial Conditions' group is absent, because only steady-state processes are to be simulated.

2.1 General

This is the first image which is displayed when the 'inspect or modify input data' box is clicked. It is the 'general' menu as the blue colour of of the label on the left makes plain. Its sole use is to allow the selection of what is here called the 'flow formulation', the three available choices of which are revealed by clicking on the 'down' arrow by the side of the menu box.

The next image shows what is then revealed.