# Condenser

Under construction.

## Performance

The following performance calculations are available on condenser instances:

 Calculation Reference Output Tags CWDP .c2.dP.use CWR ASME PTC 12.2(6.9) .c2.dT.use LMTD ASME PTC 12.2(6.9) .LMTD.use Heat Transfer .c2.dQ.use Heat Transfer Coefficient .heatTransferCoefficient.use TTD ASME PTC 12.2(6.9) .ttd.use CF .condenserCleanliness.use Sub .subCooling.use

LMTD

The LMTD (Log Mean Temperature Difference) describes the mean temperature difference between cooling water and condensing steam (PTC 12.2 5.1.2).

$$LMTD_{cond} = \frac{T_{cwout} - T_{cwin}}{In\frac{T_{satsteamin} - T_{cwin}}{T_{satsteamin} - T_{cwout}}}$$

Where:

• $T_{cwout}$ = Hot cooling water temperature (^{o}C)
• $T_{cwin}$ = Cold cooling water temperature (^{o}C)
• $T_{satsteamin}$ = Saturation temperature of condenser back pressure $(^{o}C)$

In CAS terms:

$$cond.LMTD.use = \frac{cond.c2.dT.use}{In\frac{cond.c1in.prop.satTemp.use - cond.c2in.prop.temp.use}{cond.c1in.prop.satTemp.use - cond.c2out.prop.temp.use}}$$

TTD

The TTD (Terminal Temperature Difference) describes the heat transfer and the cleanliness of the heat exchange area.

$$TTD_{cond} = T_{satsteamin} - T_{cwout}$$

Where:

• $TTD_{cond}$ = TTD condenser $(^{o}C)$

In CAS terms (where ”.” represents a condenser):

$$.ttd.use = .c1in.prop.satTemp.use - .c2out.prop.temp.use$$

Heat Transfer Coefficient

The condenser heat transfer coefficient is:

$$HTC = \frac{Q_{stm}}{LMTD}$$

Where:

• $Q_{stm}$ = Heat flow from condensing steam (kW)
• $LMTD$ = Log mean temperature difference $(^{o}C)$
• $HTC$ = heat transfer coefficient $(kW/^{o}C)$

In CAS terms:

$$cond.heatTransferCoefficient.use = \frac{cond.c1.dQ.use}{cond.lmtd.use}$$

Condenser Cleanliness

The condenser cleanliness is determined by comparing the design Heat Transfer Co-efficient to the actual heat transfer co-efficient.

The actual heat transfer co-efficient (from water side) can be determined by (where ob = cond, PTC 12.2 5.1.2):

$$U_{meas} = \frac{Q_{cw}}{LMTD \times N_{tubes} \times L_{tubes} \times \pi \times D_{tube}}$$

Where:

• $U_{meas}$ = Actual heat transfer co-efficient: $\frac {kW}{(m^2)(^{o})C}$
• $Q_{cw}$ = Heat transfer from cooling water (kW)
• $N_{tubes}$ = Number of tubes not plugged due to condenser leaks
• $L_{tubes}$ = Length of tubes (m)
• $D_{tube}$ = Outside diameter of tube (m)

In CAS terms:

$$cond.heatTransferCoefficient.use = \frac{cond.c2.dQ.use}{cond.LMTD.use \times cond.numberOfTubes.use \times cond.tubeLength.use \times \pi \times cond.od.use}$$

The Design Heat Transfer (cond.heatTransferCoefficient.design) can be determined from HEI Steam Surface Condensers, Table 1):

$$Udesign = C1 \times C_{t} \times C_{m} \times C_{f}$$

Where:

• $Udesign$ = Design heat transfer co-efficient: $\frac {kW}{m^2)}$
• $C1$ = Uncorrected heat transfer co-efficient: $\frac {kW}{(m^2)(^{o})C}$
• $C_{t}$ = Cooling water inlet temperature correction factor $(^{o}C)$
• $C_{m}$ = Tube metal correction factor $(^{o} C)$
• $C_{f}$ = Design condenser cleanliness factor

In CAS terms (where ”.” is condenser):

$$cond.heatTransferCoefficient.design = .heatTransferCoefficient.uncorr \times .coldWaterCorrection.use \times .tubeWallCorrection.use$$

From (HEI Steam Surface Condensers, Table 1), the uncorrected Heat Transfer Co-efficient is defined as:

$$C1 = f(V_{tube})$$

Where:

• $V_{tube}$ = Velocity of condenser tubes $(m/s)$

Condenser Tube Velocity:

$$V_{tube} = \frac{VolFlow}{\pi\left ( \frac{ID}{2} \right )^{2} \times N_{tubes}}$$

Where:

• $VolFlow$ = Volumetric flowrate of cooling water (m^{3}/s)
• $ID$ = Inner diameter of tubes $(m)$
• $N_{tubes}$ = Number of tubes

In CAS terms (where ”.” is a condenser):

$$.tubeVelocity.use = \frac{.c2in.volFlow.use}{\pi \times (\frac{.diameter.use}{2})^{2} \times .numberOfTubes.design}$$

The inlet temperature correction (cond.coldWaterCorrection.use) can be approximated by the following function (interpolation from PTC):

$$C_{t} = A0 + T \times A1 + T^{2} \times A2 + T^{3} \times A3 + T^{4} \times A4 + T^{5} \times A5$$

Where:

• $T$ = Cooling water inlet temperature $(^{o}C)$
• $A0$ = 0.57497
• $A1$ = 2.126449E-02
• $A2$ = 6.906916E-04
• $A3$ = 5.824107E-05
• $A4$ = 1.265904Q-06
• $A5$ = -9.136189E-09

A correction factor ($C_{t}$, cond.tupeWallCorrection Factor.use) for the tube wall thickness and material construction is required and a table of corrections is shown below (from HEI Steam Surface Condensers - Table 3).

 Condenser Tube Wall Guage 25 24 23 22 20 18 16 14 12 Tube Materials Admiralty Metal 1.03 1.03 1.02 1.02 1.01 1 0.98 0.96 0.93 Arsenical Copper 1.04 1.04 1.04 1.03 1.03 1.02 1.01 1.00 0.98 Copper Iron 194 1.04 1.04 1.04 1.04 1.03 1.03 1.02 1.01 1.00 Aluminum Brass 1.03 1.02 1.02 1.02 1.01 0.99 0.97 0.95 0.92 Aluminum Bronze 1.02 1.02 1.01 1.01 1.00 0.98 0.96 0.93 0.89 90-10 Cu-Ni 1.00 0.99 0.99 0.98 0.96 0.93 0.89 0.85 0.80 70-30 Cu-Ni 0.97 0.97 0.96 0.95 0.92 0.88 0.83 0.78 0.71 Cold Rolled LCS 1.00 1.00 0.99 0.98 0.97 0.93 0.89 0.85 0.80 300 Series SS 0.91 0.90 0.88 0.86 0.82 0.75 0.69 0.62 0.54 Titanium 0.95 0.94 0.92 0.91 0.88 0.82 0.77 0.71 0.63 UNS N08367 0.90 0.89 0.87 0.85 0.81 0.74 0.67 0.60 0.52 UNS S43035 0.95 0.94 0.92 0.91 0.88 0.82 0.77 0.71 0.63 UNS S44735 0.93 0.91 0.90 0.88 0.85 0.78 0.72 0.65 0.57 UNS S44660 0.93 0.91 0.90 0.88 0.85 0.78 0.72 0.65 0.57

TUBE GAGE TO THICKNESS

 Guage Thickness (in) Thickness (mm) 00 0.380 9.652 0 0.340 8.636 1 0.300 7.62 2 0.284 7.2136 3 0.259 6.5786 4 0.238 6.0452 5 0.220 5.588 6 0.203 5.1562 7 0.180 4.572 8 0.165 4.191 9 0.148 3.7592 10 0.134 3.4036 11 0.120 3.048 12 0.109 2.7686 13 0.095 2.413 14 0.083 2.1082 15 0.072 1.8288 16 0.065 1.651 17 0.058 1.4732 18 0.049 1.2446 19 0.042 1.0668 20 0.035 0.889 21 0.032 0.8128 22 0.028 0.7112 23 0.025 0.635 24 0.022 0.5588

Diametric Tube Constant

 OD inch mm C (BTU/(F.ft**2.hr)/(ft/s)^0.5 C (kW/(K.m^2))/(m/s)^0.5 5/8 15.875 267 2.7459805034262077 3/4 19.05 267 2.7459805034262077 7/8 22.225 263 2.7049724701564823 1 25.400 263 2.7049724701564823 1 1/8 28.575 259 2.6637108536421561 1 1/4 31.750 259 2.6637108536421561 1 3/8 34.925 255 2.6225760287501299 1 1/2 38.100 255 2.6225760287501299 1 5/8 41.275 251 2.5814230907692042 1 3/4 44.450 251 2.5814230907692042 1 7/8 47.625 247 2.5402882658771784 2 50.800 247 2.5402882658771784
• There are 29920
• Tubes are OD 7/8 inch, 22.225 mm
• Guage 22, thickness 0.028 inch, 0.71 mm
• Correction Factor = 0.84
• There are 2080
• Tubes are 7/8 inch, 22.225 mm
• Guage 19.5, 0.0393, 1 mm
• Correction Factor = 0.79

Figure 1: Condenser Tube Construction Correction Factors (FM)

$$U_{design} = C1 \times C_{t} \times C_{m}$$

In CAS terms (where ”.” is condenser):

Cleanliness Factor is the ratio of the condenser heat transfer co-efficient to the clean (design) heat transfer co-efficient:

$$\frac{U_{meas}}{U_{design}}$$

Where:

• $U_{meas}$ = Heat transfer co-efficient from cooling water heat flow $(kW/m^{2})$

In CAS terms (where ”.” is condenser):

$$.cleanlinessFactor.use = 100 \times \frac{.heatTransferCoefficient.use}{.heatTransferCoefficient.design}$$

Cooling Water Range

The cooling water range is the temperature rise in the condenser cooling water and is defined as:

$$T_{r} = T_{out} - T_{in}$$

Where:

• $T_{r}$ = Cooling water range $(^{o}C)$
• $T_{out}$ = Condenser cooling water outlet temperature $(^{o}C)$
• $T_{in}$ = Condenser cooling water inlet temperature $(^{o}C)$

In CAS terms:

$$cond.c2.dT.use = c2out.prop.temp.use - cond.c2in.prop.temp.use$$

Condenser Sub Cooling

Condenser sub-cooling is the difference between the saturated steam temperature of the condenser back-pressure and the temperature of the hotwell. It is an indication of too much cooling in the condenser defined as:

$$T_{s} = T_{sat} - T_{hw}$$

Where:

• $T_{s}$ = Sub cooling temperature $(^{o}C)$
• $T_{sat}$ = Saturation steam temperature at condenser back pressure $(^{o}C)$
• $T_{hw}$ = Hotwell temperature $(^{o}C)$

In CAS terms:

$$cond.subCooling.use = cond.c1in.prop.satTemp.use - cond.c1out.prop.temp.use$$

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