There are very few standards available for use when making fluid flow calculations.
Piping Systems FluidFlow makes use of the latest standards and guides where possible.
For calculating pressure losses across control valves for liquid and gas flow the
software uses the following guide: ANSI/ISA-75,01.01-2002 - Flow Equations for Sizing
Control Valves.
For predicting all physical properties of water we use the IFC-97 formulations
developed by the International Association for the Properties of Water and Steam.
For calculation of liquid or gas flow pressure losses across orifice plates we use the
publication from the International Organisation for Standardisation - ISO 5167-1:2003
Part 1. Measurement of fluid flow by means of pressure differential devices inserted in
circular cross-section conduits running full.
For calculation of liquid or gas pressure losses through nozzles we use ISO 5167-
1:2003 Part 3.
Liquid Pressure Loss Calculations
For calculating liquid friction losses in a physical pipe of any material, we use the Darcy
Weisbach equation and the Haaland formula for calculating friction factor. (Haaland, SE
(1983). "Simple and Explicit Formulas for the Friction Factor in Turbulent Flow". Trans.
ASIVIE, J. of Fluids Engineering 103: 89–90.)
It is possible to configure the software to use the Hazen-Williams method for
predicting friction loss, this may be useful for designing fire protection and irrigation
systems. It is not recommended that users use this method for substances other than
water. Overall fire sprinkler system design guidelines, are provided by the National Fire
Protection Association (NFPA) 13, (NFPA) 13D, and (NFPA) 13R.
Pressure losses through sprinklers can use the K method or the user can enter data
directly from a specific manufacturer.
For the calculation of pressure losses through bends, tee and cross junction the user
can select from one of 4 available relationships:
Using relationships and data found in the Handbook of Hydraulic Resistance - 3rd Ed
- I.E. Idelchik.
Using relationships and data found in Internal Flow Systems - 2nd Ed - D.S. Miller
Using relationships and data found in Flow of Fluids through Valves Fittings and Pipe
- Crane Technical Paper 410
Using relationships and data found in AIR1168/1 - Thermodynamics of Incompressible
and Compressible Fluid Flow
Performance data for centrifugal pumps, positive displacement pumps are usually taken
from manufacturers data. We have developed utility software that can read and
convert data directly from manufacturers catalogues.
Pressure Losses through valves can be calculated from generic relationships found in
the Miller and Idelchik references above. Additionally, the software can use
relationships based on Cv or Kv values which the user can enter.
Pressure losses through check valves use the K method.
Gas Pressure Loss Calculations
For accurately calculating pressure losses in gas pipes there is no simple formula, as is
the case for liquids. This is because the specific fluid physical properties of density,
temperature and enthalpy do not remain constant over the pipe length.
The FluidFlow gas calculation routines are rigorous calculations which allow for the
increase in kinetic energy and changing physical properties that occur as gas
accelerates with pressure loss. The calculations allow for the changing non-ideal
behaviour of the gas as it flows by using an equation of state to describe the changes
in gas physical properties.
There are three equations of state (EOS) available within the software (Benedict Webb
Rubin with Hans Starling modifications; Lee Kesler and Peng Robinson), it is possible to
select the most appropriate EOS for each physical property. Using the EOS the gas
thermophysical properties such as enthalpy and density are calculated as the gas
accelerates. An analytical solution to the EOS, energy and momentum equations is not
possible and FluidFlow solves these equations numerically. FluidFlow make no
assumptions of gas ideality or adiabatic flowing conditions.
Our algorithm dynamically splits the pipe into segments based on an incremental
density change. For each segment, upstream conditions of flow, static pressure, static
density and static enthalpy are known and these are used to calculate downstream
static temperature and density. From these values it is possible to backsolve the EOS
to obtain downstream static pressure. The energy equation and momentum equations
can now be solved for each segment. The method is a development of a paper
originally published in The Chemical Engineer - Relief Line Sizing for Gases Part1 and 2.
Dec 1979 - HA Duxbury.
For pressure loss calculations across other fluid equipment items refer to the liquids
section.
Non-newtonian Fluid Pressure Loss Calculations
Piping Systems FluidFlow provides the user with the option of selecting one of 4
possible calculation methods for determining pressure loss for Non-Newtonian fluids
flowing within a pipe system.
The available calculation methods are based on the relationships used to describe the
fluid rheology data. It is recommended that the user obtains fluid rheology data prior
to making a Non-Newtonian calculation.
The available rheology models are:
- Power Law with the friction factors calculated according to the relationships
provided by Ron Darby - Chemical Engineering Fluid Mechanics
- Bingham Plastic with friction factors calculated according to the relationships
provided in Darby together with the solution of Buckingham Reiner equation
- Hershel-Bulkley with friction factors calculated according to the method of Dodge
and Metzner
- Casson with friction factors calculated according to the method of Wilson Thomas
- For calculation of pressure losses across other fluid equipment items the K factor
method is used. K factors are adjusted at low Reynolds numbers as recommended by Steffe - Non-Newtonian Flows in the Food Industry
Settling Slurry Pressure Loss Calculations
Piping Systems FluidFlow provides the user with the option of selecting one of 3
possible calculation methods for determining pressure loss for the flow of settling
slurries through a piping system.
For settling slurries, i.e., a “carrier fluid” conveying
solid particles, the calculation is considerably more complicated than a liquid
calculation, due to the wide range of variables involved, viz particle size and size
distribution, solids density and shape, percent solids, mixture velocity etc.
The accepted approach is to determine the ‘solids effect’, the extra friction loss
caused by the solids content over that for an equivalent flow of the carrier fluid alone.
The carrier fluid may be clean water if the solids are relatively coarse with no fraction
below about 0.4mm but solids smaller than 0.4mm can be held in suspension and
create a ‘homogeneous’ carrier fluid, the friction characteristics of which needs to be
determined.
A number of inter-related factors influence the excess pressure drop in a pipeline over
the pressure loss for water alone (or the carrier fluid if a fine particle fraction exists).
The two main factors are the solids characteristics and the velocity of flow of the
mixture but pipe inclination is also important.
The design method is highly empirical. “Slurry Transport Using Centrifugal Pumps”, by
KC Wilson, GR Addie, A Sellgren and R Clift provides the best reference with a
synthesis of the authors’ many papers together with “Introduction to Practical Fluid
Flow” by R.P. King providing some useful additions.
These two references, and a considerable amount of literature research, provided the
basis for the development of the FluidFlow3 Slurry simulator.
FluidFlow simulates heterogeneous settling slurries according to five correlations:
- Durand-Condolios-Worster
- Wilson-Addie-Sellgren-Clift
- WASP
- 4-Component Model
- Liu Dezhong method
Two Phase Pressure Loss Calculations
When two-phase liquid gas flow occurs in pipes, many different flow patterns are
created, depending on fluid properties, the relative rates of each fluid and the pipe
inclination. There are large differences in flow behavior between horizontal, inclined
and vertical pipe flow. The pressure gradient (pressure loss per unit length) is flow
pattern dependant. For a rigorous estimation of two-phase pressure drop we also need
to split the pipe into segmental lengths, similar to the approach used in gas pipe
calculations.
Our pressure loss algorithm dynamically splits the pipe into segments based on an
incremental pressure change.
The user can select from any one of 7 available models:
Whalley Criteria (uses Friedel, Chisholm or Lockhart Martinelli, selection of method is
made by FluidFlow according to the criteria of Whalley)
- Drift Flux Model (2007 correlations)
- Beggs and Brill (Extended Regions)
- Friedel
- Muller Steinhagen Heck
- Chisolm Baroczy
- Lockhart Martinelli
Physical Property Estimation Methods
Piping Systems FluidFlow can use any of the following thermophysical properties during
flow calculations. Density, Specific Heat, Thermal Conductivity, Viscosity, Heat of
Vaporisation, Enthalpy, Melting Point, Vapour Pressure and Surface Tension.
The physical properties are often complex functions of pressure, temperature and
phase state. Data needed to evaluate these properties at phase states, pressures and
temperatures in the physical world are stored in a physical property database that
contains over 900 fluids.
The user can select any one of the following estimation methods:
For Liquid Density Prediction:
- A single fixed Value
- Yamada Gunn method with a reference density
- Spencer Danner method
- Yamada Gunn method without a reference density
- Interpolation from a table of values
- Peng Robinson Equation of State
- Benedict Webb Rubin Equation of State
- Lee Kesler law of Corresponding States
For Liquid Specific Heat Capacity Prediction:
- A single fixed Value
- A polynomial approximation
- Bondi estimation method
- Lee Kesler
- Interpolation from a table of values
For Liquid Specific Heat Capacity Prediction:
- A single fixed Value
- A polynomial approximation
- Latini estimation method
- Sato Riedel estimation method
- A log power law approximation method
- Interpolation from a table of values
For Liquid Viscosity Prediction:
- A single fixed Value
- A log polynomial approximation
- A natural log series
- Interpolation from a table of values
- Andrade method
- Przezdziecki estimation method
For Vapour Pressure Prediction:
- A log polynomial approximation
- Interpolation from a table of values
- Wagner estimation
- Antoine estimation
For Gas Density Prediction:
- Peng Robinson Equation of State
- Benedict Webb Rubin Equation of State
- Lee Kesler law of Corresponding States
For Gas Specific Heat Capacity Prediction:
- A polynomial based on ideal gas constants
- Lee Kesler law of Corresponding States
For Gas Thermal Conductivity Prediction:
- A polynomial approximation
- Chung estimation method
- Interpolation from a table of values
For Gas Viscosity Prediction:
- A polynomial approximation
- Chung estimation method
- Interpolation from a table of values
- Lucas corresponding states estimation
For Heat of Vaporisation Prediction:
- A single fixed Value which is adjusted by the software as a function of temperature
- An estimation method based on critical properties
For Liquid Surface Tension Prediction:
- A linear approximation
- An estimation method based on critical properties
Relief Valves and Bursting Disks:
- Relief Valves and Bursting Disks can automatically size according to the International
- Standards of API 520 Part 1 or ISO 4126.
- Sizing for liquid, critical gas and non-critical gas flow are available for both standards.
- Sizing of 2-Phase flow systems only uses API 520 guidelines.
There are two calculation methods available in FluidFlow for predicting the pressure loss through relief valves, API RP 520 & ISO 4126. API RP 520 caters for Newtonian liquids, steam, gas/vapors and two-phase flow. ISO 4126 caters for liquid and gas flow only.