department of flow, heat and combustion mechanics – ghent university – ugent linear stability...
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Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University – UGent
Linear stability analysis of a supercritical loop
C. T’Joen, M. Rohde*, M. De Paepe
* Delft University of Technology
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Introduction: supercritical fluids
• Raising cycle temperature and pressure increases the thermal efficiency (Carnot efficiency)
• T and p above critical condition: ‘supercritical fluid’
• Current applications: supercritical water boilers (up to 320 bar) for coal fired plants, supercritical extraction, dyeing of fabrics…
• Future target applications:‣Supercritical Water Nuclear Reactor (SCWR)‣Supercritical Organic Rankine Cycle: heat recovery
‣Transcritical cooling cycles (CO2)
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Supercritical fluid properties
• Very strong variation of fluid properties close to the critical point• Behaviour ranges from liquidlike at low temperatures to gaslike at high
temperatures. • Strong peak of specific heat
capacity: large enthalpy raisewith small temperature increase
• Large impact on the fluid flow:onset of buoyancy, mixed convection conditions…
• Large density difference: potential for natural circulation?
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Natural circulation loops
• Extensive research has been published on ‘subcritical’ natural circulation loops: single and two-phase loops
• Instability can occur: ‣Static: Ledinegg excursions, flow excursion ‣Dynamic: ‘density wave oscillations’: triggered by the density
differences in the loop and the interaction with the pressure drop
• Limited research available on supercritical natural circulation loops:‣Do these phenomena also occur? Instabilities?‣Numerical research conducted here
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Numerical rectangular testloop
• Rectangular test loop: 2m high 0.5m wide• Uniform flux heating (bottom) and cooling (top)• 1D time dependent conservation equations• Equation of state
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Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Numerical rectangular testloop
• Fluid: supercritical R23 (CHF3), scaling fluid for H2O• Pressure: 5.7 MPa• Pseudo-critical temperature: 33°C• Friction modeling:
‣Bends: K-factor 0.5‣Wall friction: Haaland equation (surface roughness)
• Non-dimensional properties:‣Subcooling number
‣Pseudo phase change number pcin
hPCH hAG
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pc
inpcSUB h
hhN
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Numerical implementation
• Comsol multiphysics software is used: finite element solver
• The conservation equations are recast into G (mass flux), P (total pressure) and h (enthalpy)
• Equation of state implemented as a series of splines (based on REFPROP), care is needed to define proper derivatives from tabular data
• Natural circulation: through boundary condition: static pressure inlet = static pressure exit
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Numerical implementation and verification
• Stability: studied through eigenvalue analysis of the linearised system‣Solve the steady state problem (UMFPACK methods)‣Linearise the matrix around this solution‣Determine the eigenvalues (LAPACK methods)‣if any have a real part > 0 unstable system
• Grid independence verified: good agreement between 74, 102, 208 and 500 cells for steady state and stability predictions
• Convergence criterion: 1e-8
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Model validation
• Comparison with steady state data from open literature:‣Jain and Uddin (supercritical CO2), Chatoorgoon (supercritical water)‣Good agreement found for both systems
• Stability: only 5 points by Jain and Uddin: good agreement
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Results: steady state flow
• Strong impact of the heater inlet temperature: a lower temperature increases the driving force
• Two regimes:‣Gravity dominated: increasing
the heater power raises the flow rate (left side) as the driving forceincreases more than the friction‣Friction dominated regime:
further increases of the powerresult in a net reduction of the flow rate due to a stronger raiseof the friction
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Results: stability map
• Similar trends to the stability boundary of a boiling system: 2 types of instabilities (low and high frequency), but also differences!
• Grid independent stability map
• Clear ‘bump’ in the map at low subcooling numbers (highinlet temperature) and at highNPCH (high power): potentialinteresting operating point
• Red zone: undefined properties
Impossible to reach for a boiling system
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Results: stability map
• Similar trends to the stability boundary of a boiling system: 2 types of instabilities (low and high frequency), but also differences!
• Grid independent stability map
• Clear ‘bump’ in the map at low subcooling numbers (highinlet temperature) and at highNPCH (high power): potentialinteresting operating point
• Red zone: undefined properties
Impossible to reach for a boiling system
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Results: stability map
• Similar trends to the stability boundary of a boiling system: 2 types of instabilities (low and high frequency), but also differences!
• Frequency plot shows suddenjumps as one follows the neutralstability boundary?
• Stability plane is build up fromdifferent modes each with anotherfrequency spectrum!
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Results: stability map: mode analysis
• First mode: low frequencies, forming the entire left branch of the stability plot
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Results: stability map: mode analysis
• First mode: low frequencies, forming the entire left branch of the stability plot
• Second mode: higher frequencycuts off the tip of the bump
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Results: stability map: mode analysis
• First mode: low frequencies, forming the entire left branch of the stability plot
• Second mode: higher frequencycuts off the tip of the bump
• Third mode: forms the highfrequency branch of the neutralstability boundary
Department of Flow, Heat and Combustion Mechanics – www.FloHeaCom.UGent.beGhent University-UGent
Conclusions
• The stability of a natural circulation loop with a supercritical fluid (R23) was investigated
• A numerical tool was developed in Comsol, and validated based on existing numerical data for steady state and stability behaviour
• Results indicate similarities between the boiling loop behaviour (well known) and that of a supercritical natural circulation loop: multimodal behaviour
• 3 modes detected with varying frequency that build up the stability boundary