blr102 flow calculations

Flow CalculationsBLR 102 Lunch & Learn Course

Flow CalculationsBLR 102 Lunch & Learn Course

November 2009

Flow CalculationsFlow Calculations

Flow Measurement Apparatus:– dP Type– Variable Area Type (Rotameter)– Turbine Flow Meters– Magnetic Flow Meters


Most Common Flow Measurement Apparatus: dP Type– Operate on the principle that dP is proportional to the

flow rate squared.– Consist of dP cells installed across some pressure

drop in the flow system.– dP needed to sense flow is deliberately created by the

insertion of a flow restriction such as a flow orifice, nozzle, or venture tube.


Flow Orifice Plate– A thin metal disc clamped between gaskets in a flanged

piping joint.– A circular hole smaller than the internal piping diameter is at

the center of the metal disc.– Create the largest pressure loss.– Least expensive– Easiest to replace.


Flow Nozzle– A metal cone clamped between gaskets in a flanged piping

joint so that the cone tapers in the direction of fluid flow.– Sides of the nozzle converge as fluid flows through the

nozzle.– Nozzle ends in a cylindrical throat.– Less pressure reduction than orifice because the entrance

cone guides flow into the constricted throat section, reducing the amount of turbulence and energy loss.


Venturi Tube– Consist of entrance and exit cones that guide flow into and

out of the constricted throat area.– Minimum turbulence and fluid energy loss.– Most efficient and accurate flow resistors.– Most expensive.– Most difficult to replace.


dP Elbow Type– Use pressure drop across a piping elbow to obtain the

required dP.– Suitable for pipes of very large diameters containing sharp

bends (90 degree).– dP from centrifugal effect is proportional to flow rate

squared.


Variable Area Flow Meter (Rotameter)– A float (or weight) is allowed to move freely inside a

vertically positioned tapered tube.– As flow increases, the dP across the annulus would rise and

produce more force pushing up the bottom of the float.– Float will rise until it opens up sufficient annular area to

hold dP constant to accommodate the higher flow.– The height of the float within the tapered tube is linearly

proportional to flow.


Turbine Flow Meter– Momentum of flowing fluid is transferred to vanes of a

turbine wheel.– Turbine wheel speed is sensed magnetically by a pickup

coil.– Pulse frequency is proportional to flow.


Magnetic Flow Meter– A voltage is induced in the meter fluid as it flows.– Fluid serves as an electrical conductor.– Electric coils mounted on the outside of the pipe establish a

magnetic field perpendicular to the direction of fluid flow.– Voltage electromagnetically induced in the fluid is

proportional to flow.– Advantages: no moving parts and no flow obstructions.


Two Simplified “dP Type” Flow Equations to Remember:

1. Mass Flow Equation.

2. Volumetric Flow Equation.

– They work for subcooled liquid flow, saturated steam flow, superheated steam flow, and gas flow.

– Only the density (or specific volume) term changes based on the type of flow.


Simplified Mass Flow Equation (dP Type):

where

= flow constant [(klbm-ft1.5)/(hr-lbm0.5-psi0.5)]

= pressure loss [psid]

= mass flow [klbm/hr]

= average density of fluid [lbm/ft3]

CdPW

dPCW


Simplified Volumetric Flow Equation (dP Type):

where

= flow constant [(kft3-lbm0.5)/(hr-ft1.5-psi0.5)]


= volumetric flow [kft3/hr]

= average density of fluid [lbm/ft3]

volC

dP

volW

dP

CW volvol


Why is Mass Flow important in Power Plants?– Mass Airflow is preferred because it correlates to

Fuel Flow in the combustion process. – Mass Liquid Flow is preferred because it can be

used easily for energy balance (conservation of energy). Also, the conservation of mass principle can be followed.

– Percent Fuel Flow is a percentage of energy flow (MBTU/hr), not a percentage of mass flow (Klbm/hr).


Constant Density Mass Flow– Assume density is constant in flow equation.– Suitable only for liquid flow.– Ovation’s SQUAREROOT algorithm has the GAIN

inside the square root.

where

= flow constant [(klbm2)/(hr2-psi)]



dPCW 1

1C

dP

W


Tips for Calculating Constant Density Mass Flow in Ovation:– Delimit dP to 0 using GAINBIAS algorithm.– SMOOTH dP signal to eliminate noise.– Use SQUAREROOT algorithm to compute mass

flow in engineering units based on dP; then use a GAINBIAS algorithm to convert engineering units to percent.

– DO NOT compute % mass flow directly using SQUAREROOT algorithm based on dP.


Variable Density Liquid Mass Flow

– Specific volume v is a function of P and T for subcooled or

compressed liquid flow.– Specific volume v can be looked up from Superheated

Steam and Compressed Water Steam Table based on Pressure and Temperature (Ref: ASME Steam Tables).

– In Steam Tables, P is in psia and T is in degF.– In SI Unit Steam Tables, P is in MN/m2 and T is in degC.

v

dPCdPCW


Liquid Specific Volume - Steam Table Look-up– In Steam Tables, specific volume (v) is shown, not density.– To look up specific volume v (ft3/lbm) based on P (2654.7 psia) and T (455

degF), use 2-D interpolation technique.– From Superheated Steam and Compressed Water Steam Table (ASME):

P (psia) - 2600 2700

T (460 degF) - 0.01927 0.01926

T (450 degF) - 0.01911 0.01909– STEP 1: Compute specific volumes for 455 degF at 2600 psia and 2700 psia

using linear interpolation.

P (psia) - 2600 2700

T (455 degF) - 0.01919 0.019175– STEP 2: Compute specific volume for 2654.7 psia using linear interpolation.

P (2654.7 psia) – 0.01918– STEP 3: Invert specific volume to obtain density.


Variable Density Liquid Mass Flow (WDPF Implementation)

where

= flow constant [(klbm2)/(hr2-psi)]


= specific volume of fluid flow [ft3/lbm]

= base specific volume of fluid flow; a constant [ft3/lbm]


2C

dP

v

basev

W

dPv

vC W

base* 2


Variable Density Liquid Mass Flow (WDPF Implementation) – Cont.– Specific volume v is assumed to be saturation liquid state

(vf) and is based on temperature T only.– For subcooled flow, specific volume of saturated liquid (vf)

is very closed to the subcooled specific volume (v).– Since vf is based on T only, use 1-D interpolation from

Saturated Steam Table to obtain the approximated specific volume.

– Density compensation is done using a specific volume factor (vbase / vf). The factor is looked up using a F(X) based on temperature T.

– Use SQUAREROOT algorithm to calculate flow; notice the GAIN is inside the SQUAREROOT.

– Please refer to example calculations in handout.


Variable Density Liquid Mass Flow (Ovation Implementation)

where

= flow constant [klbm/(hr-psi0.5)]





dPv

vCW base *3

3C

dP

v

basev

W


Variable Density Liquid Mass Flow (Ovation Implementation) – Cont.– Use compressed liquid algorithm VCLTP to look up Specific

Volume v based on P and T.– P and T should be near the location of the transmitter.– If P is not available, use saturated liquid algorithm VSLT to look

up an approximated Specific Volume vf based on T only.– If T is not available, use saturated liquid algorithm TSLP to look

up saturation temperature T based on P. Then use saturated liquid algorithm VSLT to look up specific volume vf based on T. There are no direct Ovation steam table algorithms to look up specific volume vf based on P.

– Input v and dP to STEAMFLOW algorithm to determine compressed or subcooled liquid flow; notice that the GAIN of STEAMFLOW algorithm is outside of the SQUAREROOT.


Tips for Variable Density Liquid Mass Flow in Ovation:– SMOOTH dP signal to eliminate noise.– Delimit dP to 0 using a GAINBIAS algorithm.– Add a GAINBIAS algorithm immediately after the VCLTP (or

VSLT) steam table algorithm to turn quality propagation OFF and to delimit the specific volume range.

– If P, T, or the output of VCLTP algorithm is in bad quality, transfer in the Base specific volume immediately after the GAINBIAS algorithm.

– Use STEAMFLOW algorithm to compute mass flow in engineering units based on dP; then use a GAINBIAS algorithm to convert engineering units to percent.

– DO NOT compute % mass flow directly using STEAMFLOW algorithm based on dP.


Saturated or Superheated Steam Flow:Saturated Steam can be found at:– Wet steam from Drum, before any superheating.– Turbine exhaust.– Inside Drum, Condenser, Feedwater Heaters, and Deaerator.– Desuperheater Outlet Header (if over-spraying).

Superheated Steam can be found at:– After Superheaters; and after Reheaters.

P is about the same, but with increased specific enthalpy h due to heat input from flue gas.

– After throttling turbine Governor Valve; or after a flow restricting orifice.

Specific enthalpy h is about the same, but with decreased P.


Saturated Steam Mass Flow (WDPF Implementation)– Saturated Steam Mass Flow – specific volume is

based on 1 state variable such as P or T.

where = flow constant [(klbm2)/(hr2-psi)]





dPv

vCW base *2

2C

dPvbasev

W


Saturated Steam Mass Flow (WDPF Implementation) – Cont.– Specific volume is assumed to be saturation vapor

state vg and is based on temperature T only.– Since specific volume of saturated vapor vg is based

on T only, use 1-D interpolation from Saturated Steam Table to obtain the specific volume.

– Density compensation is done using a specific volume factor (vbase / vg). The factor is looked up using a F(X) based on temperature T.

– Use SQUAREROOT algorithm to calculate flow; notice the GAIN is inside the SQUAREROOT.


Saturated Steam Mass Flow (Ovation Implementation)

where






dPv

vCW base *3

3C

dP

v

basev

W


Saturated Steam Mass Flow (Ovation Implementation) – Cont.

– If P is available, use saturated vapor algorithm HSTVSVP to look up specific volume vg based on P.

– If T is available, use saturated liquid algorithm PSLT to look up P based on T. Use saturated vapor algorithm HSTVSVP to look up specific volume vg based on P. There are no direct Ovation steam tables to look up vg based on T.

– P or T should be near the location of the transmitter.– Input vg and dP to STEAMFLOW algorithm to determine

saturated steam flow; notice that the GAIN of STEAMFLOW algorithm is outside of the SQUAREROOT.


Superheated Steam Mass Flow (WDPF Implementation)– Specific volume is based on 2 state variables

such as P and T.

where= flow constant [(klbm2)/(hr2-psi)]





dPv

v

v

vCW T

baseP

base *|*|2

2C

dP

vbasev

W


Superheated Steam Mass Flow (WDPF Implementation) – Cont.– Density compensation is done by multiplying two

specific volume factors. – One specific volume factor is based on varying T

at constant (base) P from Superheat Steam Table. – One specific volume factor is based on varying P

at constant (base) T from Superheat Steam Table.– Use SQUAREROOT algorithm to calculate flow;

notice the GAIN is inside the SQUAREROOT.– Please refer to sample calculations in handout.


Superheated Steam Mass Flow (Ovation Implementation)

where






dPv

vCW base *3

3C

dP

v

basev

W


Superheated Steam Mass Flow (Ovation Implementation) – Cont.– Must have 2 state variables such as P and T to

look up specific volume of superheated steam.– Cannot use 1 state variable for superheated steam

table lookup.– Use superheated steam algorithm HSVSSTP to

look up specific volume v based on P and T.– Input v and dP to STEAMFLOW algorithm to

determine superheated steam flow; notice that the GAIN of STEAMFLOW algorithm is outside of the SQUAREROOT.


Tips for Variable Density Steam Mass Flow in Ovation:– SMOOTH dP signal to eliminate noise.– Delimit dP to 0 using a GAINBIAS algorithm.– Add a GAINBIAS algorithm immediately after the steam table

algorithm to turn quality propagation OFF and to delimit the specific volume range.

– If P, T, or the output of steam table algorithm is in bad quality, transfer in the Base specific volume immediately after the GAINBIAS algorithm.

– Use STEAMFLOW algorithm to compute mass flow in engineering units based on dP; then use a GAINBIAS algorithm to convert engineering units to percent.

– DO NOT compute % mass flow directly using STEAMFLOW algorithm based on dP.


Turbine Steam Mass Flow 1. Calculated based on SQRT of dP, from flow transmitter;

use vg for saturated steam and v for superheated steam.

2. Steam mass flow is proportional to HP Turbine first stage pressure.

3. Steam mass flow is proportional to first stage pressure with temperature compensation; formula supplied by customer or turbine vendor. Do not compensate steam flow using Throttle Pressure.

4. Other turbine steam flow calculations as supplied by customer or turbine vendor. Please refer to attached examples for turbine steam flow calculations.

Flow CalculationsFlow CalculationsGas Mass Flow (GASFLOW Algorithm)

– Gas density based on Ideal Gas Law.– P is in absolute pressure (psia); T is in absolute temperature (degR).– Notice that the GAIN is outside of the SQUAREROOT in GASFLOW

algorithm.

where= base gas pressure [psia]

= base gas temperature [oR]

= flow constant [(klbm -ft1.5)/(hr-lbm0.5-psi0.5)]




= gas pressure [psia]

= gas constant [air = 0.37 (psia-ft3)/(lbm-oR)]

= gas temperature [oR]

= gas mass flow [klbm/hr]

dPCW

dPT

C

C

PCdP

TR

PCW tb

pbgasgasgas

''

pbC

tbC

gasC''gasC

dPPRTgasW

C


Gas Volumetric Flow (GASFLOW Algorithm)– Gas density based on Ideal Gas Law.– P is in absolute pressure (psia); T is in absolute temperature (degR).– Notice that the GAIN is outside of the SQUAREROOT in GASFLOW

algorithm.

where= base gas pressure [psia]

= base gas temperature [oR]

= flow constant [(kft3-ft1.5)/(hr-lbm0.5-psi0.5)]

= flow constant [kft3/(hr-psi0.5)]


= gas pressure [psia]

= gas temperature [oR]

= gas volumetric flow [kft3/hr]

dP

CW volvol

dPC

T

P

CCdP

P

TRCW

tb

pbvolvolvol

''

pbC

tbC

volC''volC

dP

PTvolW


Tips for using GASFLOW algorithm in Ovation:– SMOOTH dP and P signals to eliminate noise.– Delimit dP to 0 using a GAINBIAS algorithm.– If P is not available, set P to -1 to normalize the P ratio to

1.– If T is not available, set T to -1 to normalize the T ratio to

1.– If P is in bad quality, set P to base P value.– If T is in bad quality, set T to base T value.– Use GASFLOW algorithm to calculate flow in engineering

units first. Then use a GAINBIAS algorithm to compute % flow off the engineering unit flow.


Gas Fuel Flow:– Although Gas Fuel Flow is expressed in ft3/hr or kft3/hr,

do not use volumetric flow equation; instead use mass flow equation.

– Multiplying mass flow (kft3/hr) by gas heat content (BTU/ft3) will yield energy flow (MBTU/hr).

– Power plant’s existing Gas Fuel Flow formula looks like the following:

dPT

C

C

PCdP

TR

PCW tb

pbgasgasgas

''

dPPCW gasgas

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