Laminar Flow Element Theory of Operations
Internally Compensated Laminar
One methodology for an ICL unit is based on the physics of the Poiseuille Equation.
First an internal restriction is created. This restriction is known as a Laminar Flow Element (LFE).
The LFE forces the gas molecules to move in parallel paths along the length of the passage, nearly eliminating flow turbulence (Figure 1).
The differential pressure drop is measured within the laminar region.
The Poiseuille Equation quantifies the relationship between pressure drop and flow as:
Q = (P1 - P2)π r4 / 8ηL
Where:
Q = Volumetric Flow Rate
P1 = Static pressure at the inlet
P2 = Static pressure at the outlet
r = Hydraulic Radius of the restriction
η = (eta) absolute viscosity of the fluid
L = Length of the restriction
Since π, r and L are constant, the equation can be rewritten as:
Q = K(Δ P/η)
In this equation, K is a constant factor determined by the geometry of the restriction. It shows the linear relationship between
volumetric flow rate (Q), differential pressure (ΔP), and absolute viscosity (η) in a simpler form.
Changes in gas temperature affect the absolute viscosity of the gas. This requires a temperature measurement
to determine the value of η. For most DP devices this is done by manually
referencing charts that indicate the viscosity properties of the gas at
given temperatures. In an ICL device this reference is performed
internally through the use of a discrete temperature sensor and a
microprocessor.
At this point only the volumetric flow rate has
been determined. For an ICL device to address the range limitations of
thermal devices, additional measurements must be taken to determine the
actual mass flow rate of the gas. The relationship between volume flow and
mass flow is:
Mass = Volume * Density Correction
Factor
Ideal gas laws show us that the density of a gas is affected
by its temperature and absolute pressure. Using ideal gas laws, the effect
of temperature on density is:
ρa /
ρs = Ts /
Ta
Where:
ρa = Density @
Flow Condition
Ta = Absolute Temperature @ Flow
Condition in Kelvin
ρs = Density @ Standard
Condition
Ts = Absolute Temperature @ Standard
Condition in Kelvin
°K = °C +273.15 (to find
Kelvin)
And the effect of absolute pressure on density
is:
ρa / ρs = Pa /
Ps
Where:
ρa = Density @
Flow Condition
Pa = Flow Absolute
Pressure
ρs = Density @ Standard
Condition
Ps = Absolute Pressure @ Standard
Condition
Therefore, in order to determine the mass flow rate (M),
two correction factors must be applied to volumetric flow rate:
temperature effect on density, and absolute pressure effect on density.
This can be written as:
M = Q(Ts /
Ta)( Pa / Ps)
In an ICL flow meter
a discrete absolute pressure sensor is also placed in the laminar region
of the flow stream. This information is sent to the microprocessor and is
combined with the data from the discrete absolute temperature sensor for
the appropriate calculations to determine mass flow.
Performing
these calculations requires reference to some standard temperature and
pressure (STP) as indicated by variables ?s, Ts and Ps. STP is usually
defined at sea level conditions, but no single standard exists for this
convention. Examples of common reference conditions
include:
0 °C and 14.696 PSIA
25 °C and
14.696 PSIA
0 °C and 760 torr (mmHG)
It is relevant
to note, while the correct units for mass are expressed in grams,
kilograms, etc., it has become standard that the mass flow rate is
specified in SLPM (standard litres per minute), SCCM (standard cubic
centimetres per minute) or SCFH (standard cubic feet per hour). By knowing
the STP calibration of the device and the density of a particular gas at
that STP, it is possible to determine the flow rate in grams per minute,
kilograms per hour, etc. For example:
Given:
Gas =
Helium
M = 250 SCCM
STP = 25 °C and 14.696 PSIA
Gas Density =
0.166 Grams per Litre
True Mass Flow = M * Gas Density at
STP
True Mass Flow = (250 SCCM)(1 litre per 1000 CC)(0.1636 grams per
litre)
True Mass Flow = 0.0409 Grams per Minute of
Helium
|
