PWR Accumulator Modeling¶
Overview¶
This section provides guidance on how to model a typical PWR accumulator and its discharge line in TRACE. The guidance applies to the following commercial PWR designs:
- Westinghouse 2-loop PWR
- Westinghouse 3-loop PWR
- Westinghouse 4-loop PWR
- Combustion Engineering 2-loop PWR
- Babcock and Wilcox PWR
The guidance is written assuming the analyst is building the model in SNAP, but the corresponding ASCII input variable names are also referenced.
Source
This page is extracted from TRACE PWR Modeling Guidance, Revision 1 (February 2015), Section 12 — PWR Accumulator Modeling Guidance and Appendix A.12 — Accumulators.
Component Function¶
The accumulator is a passive ECCS component. It contains borated water held under pressure by a non-condensable gas cushion (typically nitrogen) and discharges automatically through a check valve when primary system pressure drops below the accumulator gas pressure — as during a LOCA.
Required Inputs¶
Before building the model, obtain the following plant-specific information:
Required Plant Data Checklist
- Accumulator fluid temperature
- Accumulator gas temperature
- Accumulator pressure
- Accumulator fluid volume
- Accumulator boron concentration
- Accumulator geometry (total volume)
- Accumulator material properties
- Accumulator wall roughness
- Discharge line wall roughness
- Discharge line loss coefficients
- Discharge line material
- Discharge line dimensions (length, ID, wall thickness)
- Discharge line initial conditions (pressure, temperature)
- Accumulator check valve geometry
- Accumulator check valve open/close time
Component Selection¶
| System Element | TRACE Component | Rationale |
|---|---|---|
| Accumulator tank | PIPE (PIPETYPE IACC = 2) |
Non-spherical accumulator with interface sharpener and level tracking |
| Discharge line with check valve | VALVE (IVTY = 9, check valve) |
Allows flow-area-controlled discharge on reverse ΔP |
Why IACC = 2?
TRACE provides specialized PIPE types for accumulators. PIPETYPE = 2
includes a specialized discharge model for non-spherical accumulators, an
interface sharpener at the accumulator exit, and a level-tracking model
that prevents gaseous discharge until all liquid is gone. Because the
level-tracking model requires the second junction (PIPE outlet) to be the
accumulator outlet, the tank is oriented downward (gas at the top,
discharge at the bottom).
Accumulator PIPE Component¶
A typical accumulator PIPE has 6 cells and 7 edges.
Component Initialization (SNAP)¶
| Input | Value |
|---|---|
| Total Length | Accumulator height (\(H_{accum}\)) |
| Hydraulic Diameter (HD) | Accumulator diameter (overwritten per edge below) |
| Number of Cells (NCELLS) | 6 |
| Number of Pipes (NPIPES) | 1 |
| Orientation | Vertical |
Naming conventions:
- Component Name (
CTITLE):Loop # - Accumulator— orLoop # - Accumulator A/Bfor plants with two accumulators per loop. - Component Number (
NUM):(Loop number) * 100 + 1040(single or Accumulator A);(Loop number) * 100 + 1070(Accumulator B). - Description: Reference the source of the design information.
Geometry Inputs¶
The guidance assumes the accumulator tank is cylindrical with hemispherical caps on top and bottom. In SNAP, select the "Area" radio button on the Cells tab so that SNAP calculates the volume-averaged flow area while the analyst enters cell volumes, lengths, and the edge flow areas separately.
Cell Length (DX)¶
Cell Volume (VOL)¶
If detailed tank geometry is available, compute exact per-cell volumes. Otherwise use the closed-form expressions below (cylinder with hemispherical caps). Verify the cell volumes sum to the total accumulator volume and adjust as needed.
10:1 Volume Ratio Check
After computing cell volumes, verify that adjacent-cell volumes do not exceed the 10:1 volume-ratio guidance. If they do, adjust DX values accordingly. Also compare the SNAP-computed volume-averaged FA to the analyst-computed edge FA for cells with no flow-area change — they should be approximately equal.
Edge Flow Area (FA)¶
Edge Hydraulic Diameter (HD)¶
Do not select "Calculate Hydraulic Diam." in SNAP — enter these values explicitly.
Edge CCFL Model¶
CCFL is not expected in the accumulator. Do not activate the CCFL model:
Orientation, Angle (θ), and GRAV¶
The accumulator is vertical. If plant-specific orientation information is available, use it; otherwise use the typical PWR values:
| Parameter | Value (edges 1–7) |
|---|---|
| Orientation | Vertical |
| Angle \(\theta\) | \(-1.571\) rad |
| GRAV = \(\sin\theta\) | \(-1.0\) |
Initial Conditions¶
Accumulator ICs should be a reasonable estimate of plant steady-state conditions. The steady-state run will refine the values used to initialize the transient.
Thermodynamic Consistency
Initial pressures and temperatures must be thermodynamically consistent.
Cell ICs¶
| Variable | Value |
|---|---|
| \(P_{cells\,1-6}\) | Nominal accumulator pressure |
| \(TL_{cells\,1-6}\) | Nominal accumulator water temperature |
| \(TV_{cells\,1-6}\) | Nominal accumulator water temperature |
Gas Volume Fraction (ALPN) — Transition Cell Method¶
The "transition cell" (cell \(t\)) is the cell containing the liquid–gas interface. Cells below \(t\) are all liquid; cells above \(t\) are all gas.
-
Locate the transition cell:
- If \(VOL_{AccumWater} < VOL_{cell\,6}\), then \(t = 6\).
- If \(VOL_{cell\,6} < VOL_{AccumWater} < VOL_{cell\,6} + VOL_{cell\,5}\), then \(t = 5\).
- If \(VOL_{AccumWater} > VOL_{cell\,6} + VOL_{cell\,5}\), compute the transition height from the bottom of the tank:
\[ H_{transition} = IR + \frac{VOL_{AccumWater} - \tfrac{2}{3}\pi \, IR^{3}}{\pi \, IR^{2}} \] -
Then set:
\[ \begin{aligned} ALPN_{cells\,1\,\ldots\,(t-1)} &= 1.0 \\ ALPN_{cell\,t} &= 1 - \frac{VOL_{AccumWater} - VOL_{cells\,(t+1)\,\ldots\,6}}{VOL_{cell\,t}} \\ ALPN_{cells\,(t+1)\,\ldots\,6} &= 0.0 \end{aligned} \]
Non-Condensable Partial Pressure (PA)¶
Edge ICs¶
Accumulator flow is zero at steady state:
Friction Inputs¶
Friction Factor Correlation (NFF)¶
Nodalization Criterion
Section 1.5 of the Rev 1 guidance defines a nodalization criterion that
must be checked for cells adjacent to edges where NFF = 0. For the
accumulator, verify the cells adjacent to edge 7.
Forward Loss Coefficient (KFAC)¶
KFAC is only modeled at edges where flow area or direction changes. A small
non-zero placeholder (1.0E-10) is entered at a few edges with area changes
that are already accounted for at edge 7 — this suppresses a SNAP/TRACE
warning for the unaccounted area change.
Reference: Crane TP-410 (Reference 4 in the Rev 1 guide), page 2-11.
Reverse Loss Coefficient (KFACR)¶
Choked Flow Model (ICFLG)¶
Choked flow is not expected within the accumulator:
General Inputs¶
| Input | SNAP setting / Value | Notes |
|---|---|---|
Solute in coolant (ICONC) |
Per Section 1.6 | — |
Initial boron concentration (CONC) |
Nominal tank value (ppm) | If ICONC = 1 |
Fluid power option (IPOW) |
0 (Not modeled) |
No direct fluid power in the tank |
Wall roughness (EPSW) |
Plant value, or \(4.572 \times 10^{-5}\) m (1.5E-4 ft) for commercial steel | — |
Cross-flow connections (NSIDES) |
0 |
No side junctions |
PIPETYPE (IACC) |
2 |
Non-spherical accumulator with level tracking |
| Leak paths | 0 |
Do not use TRACE internally spawned leak paths |
| Pipe wall & wall power | Per Section 1.7 | — |
Accumulator Discharge Line (VALVE Component)¶
A typical discharge-line VALVE has 5 cells and 6 edges. The nodalization is generic; if the plant geometry differs significantly, adjust the DX and orientation to represent the actual pipe bends.
Component Initialization (SNAP)¶
| Input | Value |
|---|---|
| Total Length | Discharge line length |
| Hydraulic Diameter (HD) | \(ID_{AccumDischargeLine}\) |
| Number of Cells (NCELLS) | 5 |
| Orientation | Horizontal |
Naming conventions:
- Component Name:
Loop # - Accumulator Discharge Line— or suffixA/Bas appropriate. - Component Number:
(Loop number) * 100 + 1045(single / A);(Loop number) * 100 + 1075(B).
Geometry Inputs¶
Cell Length / Volume¶
Five equal-length cells covering the entire line from accumulator exit to cold leg entrance. Adjust lengths as needed to place elbows and the check valve appropriately.
Check the 10:1 volume-ratio guidance as before.
Edge Flow Area (FA)¶
Edge Hydraulic Diameter (HD)¶
CCFL¶
Orientation, Angle, and GRAV¶
| Edges | Orientation | Angle (rad) | GRAV |
|---|---|---|---|
| 1, 2 | Vertical | \(-1.571\) | \(-1.0\) |
| 3 | Angled (−45°) | \(-0.7855\) | \(-0.707\) |
| 4, 5, 6 | Horizontal | \(0.0\) | \(0.0\) |
Initial Conditions¶
Cell ICs¶
| Variable | Cells 1–3 | Cells 4–5 |
|---|---|---|
Pressure (P) |
Nominal accumulator pressure | Plant-specific SS pressure, else primary system nominal |
Liquid temp (TL) |
Nominal accumulator water temperature | Plant-specific SS temperature, else RV inlet temperature |
Vapor temp (TV) |
Nominal accumulator water temperature | Plant-specific SS temperature, else RV inlet temperature |
Gas volume fraction (ALPN) |
0.0 | 0.0 |
Non-condensable partial pressure (PA) |
0.0 | 0.0 |
Edge velocities are zero at steady state:
Friction Inputs¶
Nodalization Criterion
Check the cells adjacent to edges 1 and 6 against the nodalization
criterion in Section 1.5 because these edges use NFF = 0.
Check-Valve Edge Special Case
If the valve's fully-opened flow area is much smaller than the pipe area (\(FA_{pipe} > 2 \, FA_{valve}\)), set \(NFF_{edge\,4} = 0\) and add an appropriate \(KFAC\) / \(KFACR\) at edge 4. This is not expected in typical designs but should be checked.
Loss Coefficients¶
Loss coefficients are modeled at edges 1 (contraction from accumulator), 3 (pipe bends), 4 (check valve), and 6 (expansion into cold leg).
Define \(\beta_{1} = ID_{AccumDischargeLine} / ID_{Accumulator}\) and \(\beta_{6} = ID_{AccumDischargeLine} / ID_{ColdLeg}\). The Darcy friction factor \(f_{T}\) is taken from the smooth-commercial-steel-pipe table in Crane TP-410 (Reference 4).
| Edge | Feature | KFAC (forward) | KFACR (reverse) |
|---|---|---|---|
| 1 | Contraction from tank | \(0.5\,(1-\beta_{1}^{2})\) | \((1-\beta_{1}^{2})^{2}\) |
| 2 | Straight pipe | 0.0 | 0.0 |
| 3 | Two 45° elbows | \(32\,f_{T}\) | \(32\,f_{T}\) |
| 4 | Swing check valve | \(50\,f_{T}\) | \(50\,f_{T}\) |
| 5 | Straight pipe | 0.0 | 0.0 |
| 6 | Expansion into cold leg | \((1-\beta_{6}^{2})^{2}\) | \(0.5\,(1-\beta_{6}^{2})\) |
Bend Loss Coefficients
The edge-3 value of \(32\,f_{T}\) represents two 45° standard elbows (\(2 \times 16\,f_{T}\)). For other bend angles, derive the appropriate coefficient — for example, a 90° standard elbow is \(30\,f_{T}\).
TRACE will automatically apply an adjusted loss coefficient across the valve
edge to account for the valve flow-area fraction (per Equation 2-127 of the
Theory Manual) when INTLOSSOFF = 0.
Choked Flow Model (ICFLG)¶
Choking is only expected at the discharge-line exit into the cold leg:
General and Valve Inputs¶
| Input | Value | Notes |
|---|---|---|
Solute in coolant (ICONC) |
Per Section 1.6 | — |
Initial boron (CONC), cells 1–3 |
Nominal accumulator value (ppm) | — |
Initial boron (CONC), cells 4–5 |
Primary system nominal (ppm) | — |
Valve type (IVTY) |
9 — Check Valve |
— |
Fluid power (IPOW) |
0 |
Not modeled |
Wall roughness (EPSW) |
\(4.572 \times 10^{-5}\) m if unknown | — |
Valve interface edge (IVPS) |
Edge 4 of 6 | Valve flow area adjusted here |
Flow-area adjustment type (IVTYOV) |
0 — Flow Area Fraction / sec |
— |
Internal loss model (INTLOSSOFF) |
0 — On |
See rationale below |
Max valve rate (RVMX) |
\(1 / t_{open/close}\) | — |
Off-adjustment rate (RVOV) |
\(1 / t_{open/close}\) | — |
Min/max position (FMINOV / FMAXOV) |
0.0 / 1.0 | Fully closed / fully open |
Valve flow area (AVLVE) |
Fully-opened check-valve flow area | — |
Valve hydraulic diameter (HVLVE) |
Fully-opened check-valve HD | — |
Initial valve fraction (FAVLVE) |
0.0 | Check valves start closed |
Initial stem position (XPOS) |
0.0 | Consistent with FAVLVE |
Check-valve type (HYSTER) |
0 — Static Pressure / Flow with Hysteresis |
— |
Open delta pressure (ADDDP) |
Spring-loading ΔP of the plant valve | — |
Leak area ratio (LEAKARAT) |
Leak area / open area (or 0 if none) | — |
Latch option (LATCHOPT) |
0 — Open/Close Repeatedly |
Required for reclosure behavior |
| Leak paths | 0 |
No TRACE internally spawned leak paths |
Signal variable (IVSV) |
0 |
Not used for check valves |
Override trip (IVTROV) |
0 |
Not used for check valves |
| Pipe wall & wall power | Per Section 1.7 | — |
Why the Internal Loss Model is Used Here
For most PWR valves, TRACE's internal additive flow-loss model is not used because manufacturer-tested loss coefficients are readily available. Accumulator check valves are an exception: they operate across a wide range of conditions and flapper positions, so their loss coefficients are more uncertain. NRC staff engineering judgment is to apply the internal loss model here to correct for the unknowns.
Geometry Input Summary¶
Accumulator PIPE (Table 12.5-1)¶
| Node | DX | VOL | Edge | FA | HD | GRAV | KFAC | KFACR | NFF | ICFLG |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | \(IR_{hemi}\) | \(\tfrac{2}{3}\pi IR^{3}_{hemi}\) | 1 | 0.0 | \(1.0 \times 10^{10}\) † | −1.0 | 0.0 | 0.0 | 0 | 0 |
| 2 | \((H_{accu}-2IR_{hemi})/3\) | \(DX_{2}\cdot FA_{2}\) | 2 | \(\pi ID_{2}^{2}/4\) | pipe \(ID_{2}\) | −1.0 | 1.0E-10 | 1.0E-10 | 0 | 0 |
| 3 | \((H_{accu}-2IR_{hemi})/3\) | \(DX_{3}\cdot FA_{3}\) | 3 | \(\pi ID_{3}^{2}/4\) | pipe \(ID_{3}\) | −1.0 | 0.0 | 0.0 | 1 | 0 |
| 4 | \((H_{accu}-2IR_{hemi})/3\) | \(DX_{4}\cdot FA_{4}\) | 4 | \(\pi ID_{4}^{2}/4\) | pipe \(ID_{4}\) | −1.0 | 0.0 | 0.0 | 1 | 0 |
| 5 | \(IR_{hemi}/2\) | \(VOL_{1}-VOL_{6}\) | 5 | \(\pi ID_{5}^{2}/4\) | pipe \(ID_{5}\) | −1.0 | 1.0E-10 | 1.0E-10 | 0 | 0 |
| 6 | \(IR_{hemi}/2\) | \(\tfrac{\pi DX_{6}}{6}(3IR^{2}_{hemi}-2DX^{2}_{6})\) | 6 | \(\pi(IR^{2}_{hemi}-DX^{2}_{6})\) | \(2\sqrt{IR^{2}_{hemi}-DX^{2}_{6}}\) | −1.0 | 1.0E-10 | 1.0E-10 | 0 | 0 |
| 7 | \(\pi ID^{2}_{acculine}/4\) | \(ID_{7}\) discharge line | −1.0 | \(0.5(1-\beta^{2})\) | \((1-\beta^{2})^{2}\) | 0 | 0 |
\(EPSW\) = known value, else \(4.572 \times 10^{-5}\) m. \(\beta = ID_{edge\,7} / ID_{edge\,5}\). CCFL not activated on any edge. † TRACE requires HD > 0.
Accumulator Discharge Line VALVE (Table 12.5-2)¶
| Node | DX | VOL | Edge | FA | HD | GRAV | KFAC | KFACR | NFF | ICFLG |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | \(L_{tot}/5\) | \(DX_{1}\cdot FA_{1}\) | 1 | \(\pi ID_{1}^{2}/4\) | pipe \(ID_{1}\) | −1.0 | \(0.5(1-\beta_{1}^{2})\) | \((1-\beta_{1}^{2})^{2}\) | 0 | 0 |
| 2 | \(L_{tot}/5\) | \(DX_{2}\cdot FA_{2}\) | 2 | \(\pi ID_{2}^{2}/4\) | pipe \(ID_{2}\) | −1.0 | 0.0 | 0.0 | 1 | 0 |
| 3 | \(L_{tot}/5\) | \(DX_{3}\cdot FA_{3}\) | 3 | \(\pi ID_{3}^{2}/4\) | pipe \(ID_{3}\) | \(\sin(-45°)\) | \(32 f_{T}\) | \(32 f_{T}\) | 1 | 0 |
| 4 | \(L_{tot}/5\) | \(DX_{4}\cdot FA_{5}\) | 4 (check valve ‡) | \(\pi ID^{2}_{openvalve}/4\) | \(ID_{4}\) fully open | 0.0 | \(50 f_{T}\) ‡‡ | \(50 f_{T}\) ‡‡ | 1 ‡‡ | 0 |
| 5 | \(L_{tot}/5\) | \(DX_{5}\cdot FA_{5}\) | 5 | \(\pi ID_{5}^{2}/4\) | pipe \(ID_{5}\) | 0.0 | 0.0 | 0.0 | 1 | 0 |
| 6 | \(\pi ID_{6}^{2}/4\) | pipe \(ID_{6}\) | 0.0 | \((1-\beta_{6}^{2})^{2}\) | \(0.5(1-\beta_{6}^{2})\) | 0 | 1 |
\(\beta_{1} = ID_{edge\,1} / ID_{Accumulator}\). \(\beta_{6} = ID_{edge\,6} / ID_{ColdLeg}\). \(L_{tot}\) = discharge line total length. \(f_{T}\) is from Table 1.5-1 of the Rev 1 guide. ‡ IVTY = 9; see valve inputs above. ‡‡ If \(FA_{pipe} > 2 \, FA_{valve}\), set \(NFF_{edge\,4} = 0\) and add appropriate \(KFAC/KFACR\) at edge 4.
Steady-State Initialization Criteria¶
For model-to-plant comparisons during steady-state initialization, the Rev 1 guidance (Section 29.x, PWR Steady-State Initialization) recommends the following tolerances for accumulator parameters:
| Parameter | Acceptance Criterion |
|---|---|
| Accumulator liquid temperature | Target Value ± 0.007 MPa (1 psi equivalent) |
| Accumulator pressure | Target Value ± 1 K (1.8 °F) |
| Accumulator liquid level | Target Value ± 1% |
Modeling Basis (Appendix A.12)¶
The rationale behind the recommended approach:
Why this nodalization
TRACE provides specialized accumulator PIPE types; PIPETYPE = 2 is
recommended because it includes specialized discharge models for
non-spherical accumulators, an interface sharpener at the exit, and a
level-tracking model that prevents gaseous discharge until all liquid is
gone. The level-tracking model requires the second junction (PIPE outlet)
to be the accumulator outlet — so the tank is oriented downward.
The tank is modeled as a cylinder with hemispherical caps. The nodalization was developed from LOCA-analysis modeling experience to adequately capture the key thermal-hydraulic phenomena documented in the applicable PIRTs, without unnecessary increase in computational cost. The tank is connected via a conical-frustum nozzle to the discharge line, which is a simple cylindrical pipe with several bends and a check valve. Because exact bend geometry varies by plant, the analyst is responsible for verifying the actual configuration.
Non-condensable gas
Accumulators typically contain nitrogen to pressurize the liquid. The gas can be specified as nitrogen (Section 1, subsection 1), but modeling experience has shown that TRACE's default non-condensable (air) is an adequate substitute in most analyses. When deciding whether to change to nitrogen, consider the presence of other non-condensable gases in the system — especially in any CONTAN components in the model.
Why the internal loss model is applied to the check valve
TRACE's internal additive loss model is not typically used for PWR valves because manufacturer-tested loss coefficients are readily available. Accumulator check valves are an exception: they operate across a wide range of conditions and flapper positions, so the appropriate loss coefficient is more uncertain. It is NRC staff engineering judgment that applying the internal loss model is appropriate here.
Check-valve placement
The check valve is deliberately placed at edge 4 (rather than immediately adjacent to the cold leg) to help reduce chattering and associated numerical problems. Check-valve operation is controlled by the pressure difference between the volumes adjacent to the valve edge, and pressure fluctuations are more likely on the cold-leg side — so the valve is positioned so that the adjacent volume is "insulated" from the cold leg by one additional cell. Recent versions of TRACE have improved check-valve stability, which may allow relocation of the valve for specific applications if there is a justifiable reason; absent a compelling reason, follow the recommended placement.
See Appendix A.23 of the Rev 1 guide for further discussion generic to all thermal-hydraulic components.
References¶
- TRACE PWR Modeling Guidance, Revision 1, U.S. NRC, February 2015 — Section 12 and Appendix A.12.
- TRACE V5.0 Theory Manual, U.S. NRC, ADAMS ML120060218 — Equation 2-127 (internal valve loss model).
- TRACE V5.0 User's Manual, Volume 2: Modeling Guidelines, U.S. NRC, ADAMS ML120060402.
- Crane Technical Paper No. 410, Flow of Fluids Through Valves, Fittings, and Pipe (loss-coefficient tables for sudden contractions/expansions, elbows, and check valves).
Related Topics¶
Extracted from TRACE PWR Modeling Guidance, Rev 1 (Feb 2015), §12 and App. A.12. No discrepancies were found between the PDF and the corresponding component-level Word source (Historical-Rev_1/Accum.docx).