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Research Papers

On Some Relevant Effects in the Simulation of Flow Stability With Fluids at Supercritical Pressure

[+] Author and Article Information
Walter Ambrosini

Dipartimento di Ingegneria Civile e Industriale,
Università di Pisa,
Largo Lucio Lazzarino 2, Pisa 56126, Italy
e-mail: walter.ambrosini@ing.unipi.it

1Corresponding author.

Manuscript received August 7, 2015; final manuscript received January 24, 2016; published online June 17, 2016. Assoc. Editor: Guanghui Su.

ASME J of Nuclear Rad Sci 2(3), 031005 (Jun 17, 2016) (13 pages) Paper No: NERS-15-1174; doi: 10.1115/1.4032595 History: Received August 07, 2015; Accepted January 24, 2016

The paper collects and discusses findings emerging from the analysis of systems operating with fluids at supercritical pressure, with reference to flow stability. In particular, the influence of heating structures and numerical diffusion on the predicted dynamic behavior is highlighted, clarifying that results obtained paying little attention to the presence of these effects should be reconsidered for a better realistic prediction of stability characteristics. Examples of applications in which truncation error and the presence of heating structures play an important role are reported, in order to warn about a tendency to underestimate these effects on the basis of the knowledge of similar phenomena (e.g., in two-phase flow) or system configurations in which they might play a lesser role. The use of a computational fluid dynamics (CFD) code in the analysis of a simple single-tube stability problem shows that models more complex than the usual one-dimensional (1D) ones also show similar effects. The results obtained by 1D numerical tools developed for the analysis of natural circulation with supercritical pressure fluids, equipped with the capability to simulate linear and nonlinear stability with first- and second-order explicit schemes, are then reported. The discussion of the eigenvalues and the eigenvectors calculated for an existing natural circulation loop and a single channel highlight interesting aspects that can be helpful in understanding the results of stability analyses. The CFD code analysis adds additional aspects of interest for the discussion.

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Figures

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Fig. 1

Typical instability observed in the BARC loop by varying power (from [9])

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Fig. 2

Effect of the heat structures density on BARC loop unstable behavior (from [20])

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Fig. 3

Discretization adopted for the BARC loop

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Fig. 4

Effect of the heat structures heat capacity on unstable behavior for the BARC loop with CO2 (8.6 MPa, low-diffusion numerical scheme). Heat-transfer correlation by Jackson [35]: (a) full-structure heat capacity, (b) 1/2-reduced structure heat capacity, (c) 1/5-reduced structure heat capacity, and (d) 1/10-reduced structure heat capacity.

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Fig. 5

Eigenvalues of the matrix representing the linear dynamics of the BARC loop: effect of the structure heat capacity (heating power = 1400 W, secondary HTC=1000  W/m2 K, pressure = 8.6 MPa, low-diffusion numerical scheme): (a) overall distribution and (b) detail.

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Fig. 6

Reconstructed and most amplified eigenvector for the case with 1/10 structure heat capacity (BARC loop, heating power 1400 W, secondary HTC=1000  W/m2 K, pressure = 8.6 MPa): (a) normalized pressure, (b) normalized specific Enthalpy, (c) normalized flow rate, and (d) normalized wall temperature.

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Fig. 7

Stability maps for the BARC loop with two different numerical schemes (pressure = 8.6 MPa, 1/10 structure heat capacity): (a) low-diffusion numerical scheme and (b) first-order numerical scheme.

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Fig. 8

Schematic configuration of the heated channel

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Fig. 9

Time trend of NTPC obtained by RELAP5 calculations with 1 mm thick wall and different values of the volumetric heat capacity (from [22]).

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Fig. 10

Time trend of NTPC obtained by RELAP5 calculations for ρCp=4.2×103  J/m3 K, 1 mm thickness, and two numerical schemes (from [22]).

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Fig. 11

Effect of the heat capacity of a 1 mm thick structure on unstable behavior for the heated channel with H2O (25 MPa): (a) full-heat capacity, (b) 1/2-reduced heat capacity, (c) 1/5-reduced heat capacity, and (d) 1/10-reduced heat capacity.

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Fig. 12

Eigenvalues of the matrix representing the linear dynamics of the heated channel effect of the structure heat capacity (heating power = 105 kW, inlet temperature = 553.15 K, pressure = 25 MPa, low-diffusion numerical scheme): (a) overall view and (b) detail.

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Fig. 13

Reconstructed and most amplified eigenvector for the case with 1/10 structure heat capacity: (a) normalized pressure, (b) normalized specific Enthalpy, (c) normalized flow rate, and (d) normalized wall temperature.

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Fig. 14

Stability maps for the single heated channel with two different numerical schemes (pressure = 25 MPa, 1/10 structure heat capacity): (a) low-diffusion numerical scheme and (b) first-order numerical scheme.

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Fig. 15

Transient behavior of NTPC for the 2D heated channel with different assumptions for wall heat capacity and the numerical scheme (inlet temperature = 553.15 K and pressure = 25 MPa).

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