U-Tube Steam Generator (UTSG) Modeling¶

Source

Rev 1 Modeling Guidance, §4 — SG Primary Side (U-Tube SGs); §13 — SG Secondary Side (U-Tube SGs); Appendix A.4 — SG Primary Side Bases; Appendix A.13 — SG Secondary Side Bases.

Overview¶

This section provides guidance on modeling the primary and secondary sides of U-tube steam generators (UTSGs) in TRACE. The guidance is applicable to:

Westinghouse 2-loop, 3-loop, and 4-loop PWRs
Combustion Engineering 2-loop PWRs

This guidance is not applicable to once-through steam generators (OTSGs) used in Babcock & Wilcox plants — see the OTSG Modeling page — or to helical coil SGs proposed for some SMRs.

Required Inputs¶

Primary Side¶

Reactor vessel outlet and inlet fluid temperatures
Primary loop nominal system pressure
SG primary side pressure drop
SG inlet and outlet plena geometry (ID, height, total volume)
SG plenum material properties
SG U-tube geometry (ID, length, average bend radius)
SG U-tube material properties
Number of SG U-tubes
% Steam generator tube plugging (SGTP)
Loss coefficients for fittings, nozzles, etc.
SG plenum and U-tube wall roughness

Secondary Side¶

Nominal SG steam dome pressure
Nominal feedwater and steam outlet flow
Main steam line diameter
SG secondary side geometry (boiler region ID, shell OD, shroud dimensions)
SG U-tube geometry (OD, pitch)
Primary separator geometry (riser cylinder dimensions, swirl vane inlet location, outer drainage cylinder dimensions, total height)
Secondary separator geometry (height, total volume, inlet/outlet flow areas)
SG separator carryover and carryunder
Nominal SG separator inlet quality
Loss coefficients for tube support plates and SG separators
Flow path geometry for downcomer-to-boiler region connection

Primary Side¶

The SG primary side is modeled as three PIPE components: inlet plenum, U-tubes, and outlet plenum.

SG Inlet Plenum — PIPE (1 cell, 2 edges)¶

Figure 4.2-1: Typical U-tube SG inlet plenum nodalization.

Component setup:

Total Length = SG plenum height
NCELLS = 1
NPIPES = 1
Orientation = Vertical
Component Number = (Loop Number) × 100 + 1005

Geometry¶

Parameter	Value
DX_cell1	SG plenum height
VOL_cell1	½ volume of cap = π · DX₁² · (3 · IR_plenum − DX₁) / 6
FA_edge1	π · ID²_{inlet nozzle} / 4
FA_edge2	NPIPES × π · ID²_U-tube / 4 (set by U-tube component)
HD_edge1	ID_{inlet nozzle}
HD_edge2	ID_{one U-tube}
CCFL	None at either edge
GRAV_edge1	sin(45°) = 0.707 if angle unknown
GRAV_edge2	1.0 (vertical)

Plenum Volume

If measured SG primary volumes are available from the NSSS vendor, use those values. Otherwise, calculate using the half-spherical-cap formula above. The plenum hydraulic diameter is HD = (4 · FA / π)^0.5. If the inner diameter is not explicitly known, it may be assumed equal to the ID of the SG boiler region.

Friction¶

Edge	NFF	KFAC	KFACR	ICFLG
1	0	16 f_T (standard elbow, 45°)	16 f_T	0
2	0	0.5 · (1 − β²) sudden contraction	(1 − β²)² sudden expansion	0

β = ID_{one U-tube} / HD_{inlet plenum}
f_T = Darcy friction factor for smooth commercial steel pipe (Table 1.5-1)

Initial Conditions¶

P = plant-specific or nominal primary system pressure
TL = plant-specific or reactor vessel outlet temperature
TV = reactor vessel outlet temperature
ALPN = 0.0 (all liquid)
PA = 0.0 (no non-condensables)
VL, VV = plant-specific or 0.0

General Inputs¶

ICONC: per §1.6; CONC = nominal boron concentration (ppm)
IPOW = 0 (no fluid power)
EPSW = plant-specific or 4.572 × 10⁻⁵ m (commercial steel)
NSIDES = 0, IACC = 0, JUNLK ≠ 0
Use Pipewall = False (use manually attached HTSTR components)

SG U-Tubes — PIPE (19 cells, 20 edges)¶

Figure 4.2-2: Typical U-tube SG tube nodalization (19 cells, 20 edges).

Component setup:

Total Length = average U-tube length + 2 × tubesheet thickness
NCELLS = 19
NPIPES = total U-tubes (or adjusted for SGTP: [1 − SGTP%/100] × total)
HD = ID_{one SG tube}
Component Number = (Loop Number) × 100 + 1010

Tube Plugging

NPIPES accounts for SG tube plugging. If NPIPES is changed, the flow area for the upper edges of the SG plena must also be updated. SNAP will adjust automatically if changes are made through the GUI.

Cell Layout¶

Cells	DX	Description
1, 19	Tubesheet thickness	Tubesheet flow path
2–7	L_straight / 10	Hot-side straight tubes (finer mesh)
8–9	L_straight / 5	Hot-side upper straight section
10–13	2π · IR_{avg U-bend} / 8	U-bend region (¼ circle each)
14–18	L_straight / 5	Cold-side straight tubes

Basis — Appendix A.4

"The part of the U-tube nearest to the inlet plenum (and thus carrying hotter fluid) is more finely nodalized than the remaining U-tube section. This helps capture the steeper temperature gradients due to higher heat transfer in this region."

Edge Geometry¶

FA_{all edges} = π · ID²_{one U-tube} / 4
HD_{all edges} = ID_{one U-tube}
VOL_cells = FA × DX (cylindrical tubes)

CCFL at Tubesheet Inlet (Edge 2)¶

CCFL is applied at the SG tubesheet inlet interface (edge 2 only) for reflux-condensation scenarios during SBLOCAs:

Parameter	Value
CBETA	0.0 (Wallis correlation)
CCFLM	1.0
CCFLC	0.8

Basis — Appendix A.4

"A CCFL model is necessary at the tubesheet inlet interface, since during SBLOCAs, reflux-condensation transients may occur, leading to countercurrent flow in the hot leg. The CCFL model is based on recommended values from available publications bolstered by assessments based on tests at the Bethsy, ROSA-IV, and LOFT test facilities."

Orientation¶

Edges	Angle	GRAV
1–10 (ascending hot side)	+π/2	+1.0
11 (entering U-bend)	+π/4 (or known)	+0.707
12 (U-bend apex)	0.0	0.0
13 (leaving U-bend)	−π/4 (or known)	−0.707
14–20 (descending cold side)	−π/2	−1.0

Basis — Appendix A.4

"The U-bend is simply approximated by the use of four nodes with 45-degree changes in direction for each successive edge. Therefore, the exact average elevation for the SG U-tubes is not perfectly modeled. It is the current position of NRC staff that this modeling is adequate to account for most, if not all analysis scenarios of interest."

Friction¶

Edge	NFF	KFAC	KFACR
1	0	0.5 · (1 − β²) contraction	(1 − β²)² expansion
2–11, 13–19	1	0.0	0.0
12 (U-bend)	1	50 f_T (close-pattern return bend)	50 f_T
20	0	(1 − β²)² expansion	0.5 · (1 − β²) contraction

Edge 1: β = HD_edge1 / HD_{inlet plenum}
Edge 12: f_T from Table 1.5-1 (this is a rough estimate; verify via primary-side ΔP)
Edge 20: β = ID_{one U-tube} / HD_{outlet plenum}
ICFLG = 0 at all edges

General Inputs¶

EPSW = plant-specific or 1.524 × 10⁻⁶ m (drawn piping — note: different from plenum roughness)
NSIDES = 0, IACC = 0, IPOW = 0
Use Pipewall = False (HTSTR components attached manually for SG tube heat transfer)

SG Outlet Plenum — PIPE (1 cell, 2 edges)¶

Figure 4.2-3: Outlet plenum (single intermediate leg).

Figure 4.2-4: Outlet plenum (two intermediate legs — use side junctions).

Component setup:

Total Length = SG plenum height
NCELLS = 1, NPIPES = 1
Component Number = (Loop Number) × 100 + 1015

Geometry¶

Parameter	Single IL	Two ILs
FA_edge1	NPIPES × π · ID²_U-tube / 4	Same
FA_edge2	π · ID²_{outlet nozzle} / 4	0.0 (use side junctions)
HD_edge2	ID_{outlet nozzle}	1.0 × 10¹⁰ (TRACE requires HD > 0)
NSIDES	0	2 (side junctions at 135°)

Basis — Appendix A.4

"For two-cold-leg loops, the recommendation is to connect both intermediate legs via side junctions with an appropriate angle (consistent with the orientation of the SG outlet nozzles). This will ensure that both legs are treated equally by the code and analyst."

Figure 4.5-1: Side junction angle configuration for outlet plenum.

Friction¶

Edge	KFAC	KFACR
1	(1 − β²)² expansion	0.5 · (1 − β²) contraction
2 (single IL)	16 f_T (standard elbow)	16 f_T
2 (two ILs)	0.0	0.0

Primary Side Geometry Summary¶

Figure 4.6-1: Typical U-tube SG primary side nodalization summary.

Table 4.6-1: Primary Side Geometry Input Summary (click to expand)

Region	Node	DX	Edge	FA	HD	CCFL	GRAV	KFAC	KFACR	NFF
Inlet plenum →	—	—	1 inlet	π·ID²_nozzle/4	ID_nozzle	None	sin(45°)	16f_T	16f_T	0
Inlet plenum	1	Plenum height	—	VOL/DX	(4·FA/π)^0.5	—	—	—	—	—
Plenum → tube	—	—	2 inlet	NPIPES·π·ID²_tube/4	ID_tube	None	1.0	0.5(1−β²)	(1−β²)²	0
Tubesheet	1	Thickness	1 tube	π·ID²_tube/4	ID_tube	None	1.0	—	—	—
			2 tube	Same	Same	CCFL	1.0	0.0	0.0	1
Hot side	2–7	L_str/10	3–10	Same	Same	None	1.0	0.0	0.0	1
Hot side upper	8–9	L_str/5	11	Same	Same	None	sin(45°)	0.0	0.0	1
U-bend	10–13	2π·R_avg/8	12	Same	Same	None	0.0	50f_T	50f_T	1
Cold side upper	14–18	L_str/5	13	Same	Same	None	sin(−45°)	0.0	0.0	1
Tubesheet	19	Thickness	14–19	Same	Same	None	−1.0	0.0	0.0	1
Tube → plenum	—	—	20	Same	Same	None	−1.0	(1−β²)²	0.5(1−β²)	0
Outlet plenum	1	Plenum height	—	VOL/DX	(4·FA/π)^0.5	—	—	—	—	—
Outlet plenum →	—	—	2 outlet	π·ID²_nozzle/4	ID_nozzle	None	sin(−45°)	16f_T	16f_T	0

Notes: NPIPES = number of active U-tubes. EPSW_plenum = 4.572×10⁻⁵ m, EPSW_tubes = 1.524×10⁻⁶ m. β values use plenum HD calculated from FA.

Secondary Side¶

The SG secondary side is modeled as three PIPE components (boiler region, downcomer, steam dome), one SEPD component (separator), and one SJC (downcomer-to-boiler flow path).

SG Boiler Region — PIPE (10 cells, 11 edges)¶

Component Number = (Loop Number) × 100 + 1410

Cell Layout¶

The boiler region is nodalized consistently with the primary side U-tube component for heat structure thermal coupling. Cells 1 and 19 of the U-tube component are in the tubesheet and do not extend into the boiler region.

Cells	DX	Description
1	H_{downcomer-to-boiler flow path}	Bottom (flow path height)
2	DX_cell2,U-tube − H_{flow path}	Remainder coupled to U-tube cell 2
3–9	DX_{cells3-9,U-tube}	Coupled to primary cells
10	H_boiler − Σ DX_1-9	Top to transition cone

Volume — Account for U-tube Displacement¶

\[ \text{VOL}_{cells\ 1-9} = \left(\frac{\pi}{4} \cdot ID_{boiler}^2 - 2 \cdot N_{tubes} \cdot \frac{\pi}{4} \cdot OD_{tube}^2\right) \cdot DX \]

\[ \text{VOL}_{cell\ 10} = \frac{\pi}{4} \cdot ID_{boiler}^2 \cdot DX_{10} - N_{tubes} \cdot \frac{\pi}{4} \cdot OD_{tube}^2 \cdot \pi \cdot R_{avg\ U-bend} \]

where N_tubes = total number of U-tubes (includes both blocked and unblocked).

Edge Geometry¶

Edge	FA	HD
1	0.0 (no flow — SJC provides flow path)	0.0
2–10	π/4 · ID²_boiler − 2·N_tubes · π/4 · OD²_tube	4 · FA_{unit cell} / (π · OD_tube)
11	π/4 · ID²_boiler	ID_boiler

Basis — Appendix A.13

"The hydraulic diameter is calculated based on a unit cell of the SG tube lattice rather than basing it on the total flow area and wetted perimeter across an axial cross section area of the SG. In PWRs, the local conditions on the secondary side of most SG tubes are most accurately defined by the unit cell of the tube lattices."

Friction¶

NFF_edges1,11 = 0; NFF_edges2-10 = 1
KFAC_edge1 = 0
KFAC_edges2-10 = k_{tube support plates} (if known or approximated)
KFAC_edge11 = k_tubebank + k_expansion
- k_tubebank ≈ 2.0 × (average number of rows crossed), based on staggered tube bank with typical pitch/OD ratio of 1.28
- k_expansion = (1 − FA_edge10 / FA_edge11)²

Initial Conditions¶

P = nominal SG pressure
TL, TV = saturation temperature at SG pressure
ALPN = plant-specific void distribution, or 0.50 if unknown
PA = 0.0

Liquid velocity estimate:

\[ VL_{edges\ 2-11} = \frac{\dot{m}_{FW} / x_{in}}{[\left(\rho_l - \rho_g\right) \cdot (1 - ALPN) + \rho_g] \cdot FA} \]

where x_in = nominal separator inlet quality, ṁ_FW = nominal feedwater flow.

General Inputs¶

NSIDES = 1 (for SJC connection); THETA = 90°; IENTRN = 0
IACC = 0, IPOW = 0
Use Pipewall = False (HTSTR for U-tube and shroud heat transfer)

SG Downcomer — PIPE (13 cells, 14 edges)¶

Component Number = (Loop Number) × 100 + 1400

The downcomer extends from below the boiler region to the top of the primary separators. It includes the annular region between the SG shell and shroud, plus the volume surrounding the separators.

Basis — Appendix A.13

"The primary consideration in modeling the downcomer was the way that the boiler and separator regions were nodalized, because the heat structure representing the shroud and the separators needs to connect these regions."

The downcomer nodalization is consistent with the boiler region and separator for heat structure coupling. Feedwater injects at the cell including the appropriate elevation (typically near primary separators).

The downcomer connects to:

Boiler region via SJC (bottom)
Separator via SEPD side pipe (liquid return)
Steam dome via side junction (vapor displacement path)

SG Separator — SEPD (4 cells, 6 edges)¶

Component Number = (Loop Number) × 100 + 1415

Figure 13.4-1: Upper part of a typical U-tube steam generator showing separator regions.

The SEPD component models the upper plenum (transition cone), primary separator, and liquid return path. Phase separation occurs at the secondary separator location.

Cell Layout¶

Cell	DX	Description
1 (main)	H_{primary sep bottom} − H_{transition cone bottom}	Transition cone
2 (main)	H_separators − 2 · H_{swirl vane to top}	Lower primary separator
3 (main)	2 · H_{swirl vane to top}	Upper primary separator (separation point)
4 (side)	½ H_separators − H_{swirl vane to top}	Liquid return arm

Volume Formulas¶

VOL_cell1 = π/12 · DX₁ · (ID²_{lower cone} + ID²_{upper cone} + ID_lower · ID_upper) — conical frustum
VOL_cell2 = N_risers · DX₂ · π/4 · ID²_riser
VOL_cell3 = N_risers · (DX₃ · π/4 · ID²_riser − VOL_{swirl vanes})
VOL_cell4 = π/4 · (OD²_{riser opening} − ID²_{riser opening}) · DX₄ — annular

Edge Geometry¶

Edge	FA	HD
1	π/4 · ID²_boiler	ID_boiler
2–4	N_risers · π/4 · ID²_riser	ID_riser
5–6 (side)	π/4 · (OD²_{riser opening} − ID²_{riser opening})	(OD² − ID²) / (OD + ID)

Separator Parameters¶

Parameter	Value
ISTAGE	0 (ideal separator with constant carryover/carryunder)
JCELL	3 (side tube connects at cell 3 — secondary separator location)
NSEPS	1 (separators lumped as one)
NDRYR	0 (dryers not modeled separately)
XCO (carryover)	Plant-specific, or 1.0 × 10⁻³
XCU (carryunder)	Plant-specific, or 5.0 × 10⁻³
ALPSMN	0.05 (minimum barrel void — avoids oscillation)
ALPSMX	0.9 (maximum barrel void)
IENTRN	0 (offtake model off)

Basis — Appendix A.13

"The SEPD component is preferred because it allows for greater control over certain aspects of separator performance such as carryover and carryunder. It also avoids use of non-physical modeling artifacts to artificially force the separation of liquid from vapor, such as very high liquid loss coefficients."

"The steam flowing into the main steam line is typically expected to be at least 99.9% vapor, so the carryover is set to a corresponding value (0.001). The phase separation that occurs in the secondary separator is very small compared to the primary separator."

Friction¶

NFF_{all edges} = 0 (no friction factors — complicated separator geometry)
KFAC_edge4 = facility-specified or initially 1.0 (vapor phase through separator)
KFAC_edge6 = facility-specified or initially 1.0 (liquid phase through side arm)
Adjust during steady-state initialization to match target SG pressure drops

SG Steam Dome — PIPE (2 cells, 3 edges)¶

Component Number = (Loop Number) × 100 + 1420

Cell	DX	VOL
1	Top of primary separator → top of secondary separator	π/4 · ID²_{upper shell} · DX₁ − VOL_{secondary separator}
2	Top of secondary separator → SG outlet	4π/3 · ID²_{upper shell} · DX₂ (ellipsoid)

Edge	FA	HD
1	N_risers · π/4 · ID²_riser	ID_riser
2	π/4 · ID²_{upper shell}	ID_{upper shell} or secondary separator HD
3	π/4 · ID²_{SG outlet}	ID_{SG outlet}

Basis — Appendix A.13

"There is a side junction connecting the bottom cell of the steam dome region to the upper part of the downcomer to allow for vapor displacement. This side junction is what necessitated the modeling of the steam dome as a separate component, because TRACE does not currently have the capability to model side junctions connecting to any cells in the SEPD component."

Initial Conditions¶

P = nominal SG pressure
TL, TV = saturation temperature at SG pressure
ALPN_cell1 = 0.50 or plant-specific; ALPN_cell2 = 1.0 (all vapor)
PA = 0.0

SJC — Downcomer-to-Boiler Flow Path¶

Component Number = (Loop Number) × 100 + 1405

The SJC models the flow path from the bottom of the downcomer to the bottom of the boiler region. Both junction angles should be set to 90°. The offtake model (IENTRN) should be off.

Basis — Appendix A.13

"A SJC component is connected between the two cells via side junctions with the offtake model deactivated. The SJC component can then be used to define the flow path characteristics (flow area, hydraulic diameter, K loss coefficients). The offtake model is not used because the flow path from the downcomer to the boiler region is not consistent with the internal assumption by TRACE that side junctions are cylindrical."

Steady-State Checklist¶

Steady-State Verification

Cross-References¶

OTSG Modeling — Once-through SG guidance for B&W plants
Primary Loop — Hot leg, intermediate leg, RCP connections
Pressurizer — Pressure control
Heat Structures — SG tube and shroud HTSTR guidance (§17)

This page faithfully extracts U-tube SG modeling guidance from Rev 1 §4 (primary side) and §13 (secondary side), with associated bases from Appendix A.4 and A.13. The guidance does not consider economizer regions incorporated in more recent SG designs due to relatively limited modeling/assessment experience.