Natural Circulation

Natural Circulation

Natural Circulation - schema
Natural circulation in a closed loop

Natural circulation is the circulation of fluid within piping systems or open pools that is due to the density changes caused by temperature differences. Natural circulation does not require any mechanical devices to maintain flow.

This phenomenon have similar nature as natural convection, but in this case the heat transfer coefficient is not an object of study. In this case, the bulk flow through the loop is the object of study. This phenomenon is rather a hydraulic problem than a heat transfer problem, although in result natural circulation removes heat from source and transports it to the heat sink and is of the highest importance in reactor safety.

 
What is Natural Convection
Natural convection, known also as free convection is a mechanism, or type of mass and heat transport, in which the fluid motion is generated only by density differences in the fluid occurring due to temperature gradients, not by any external source (like a pump, fan, suction device, etc.).

In natural convection, fluid surrounding a heat source receives heat and by thermal expansion becomes less dense and rises. Thermal expansion of the fluid plays a crucial role. In other words, heavier (more dense) components will fall, while lighter (less dense) components rise, leading to bulk fluid movement. Natural convection can only occur in a gravitational field or in the presence of another proper acceleration, such as:

  • acceleration
  • centrifugal force
  • Coriolis force

Natural convection essentially does not operate in the orbit of Earth. For example, in the orbiting International Space Station, other heat transfer mechanisms are required to prevent electronic components from overheating.

Conditions Required for Natural Circulation

Similarly as for natural convection, natural circulation essentially does not operate in the orbit of Earth. Natural circulation occurs in a loop only under specific conditions. Even after natural circulation has begun, removal of any one of these conditions will cause the natural circulation to stop. The conditions for natural circulation are as follows:

  • Presence of proper acceleration. Natural circulation can only occur in a gravitational field or in the presence of another proper acceleration, such as acceleration, centrifugal force.
  • Presence of heat source and heat sink. Heat source and heat sink are required, because natural circulation is generated by density difference in the fluid occurring due to temperature difference. Fluid entering a heat source receives heat and by thermal expansion becomes less dense and rises. Thermal expansion of the fluid plays a crucial role. Process in a heat sing is opposite, the heat sing receives heat and the fluid becomes denser. The density difference is the driving force for natural circulation flow. The difference in temperature must be maintained for the natural circulation to continue. Addition of heat by a heat source must exist at the high temperature area. Continuous removal of heat by a heat sink must exist at the low temperature area. Otherwise the temperatures would eventually equalize, and no further circulation would occur.
  • Proper geometry. The presence and magnitude of natural circulation also depend on the geometry of the problem. The presence of a fluid density gradient in a gravitational field does not ensure the existence of natural convection currents. Natural circulation in a fluid filled closed loop is established by locating a heat sink in the loop at an elevation that is higher than the heat source. The circulating fluid removes heat from source and transports it to the sink. The flow can be single phase or two phase wherein vapor flows alongside the liquid. The difference in temperature must be maintained for the natural circulation to continue. Addition of heat by a heat source must exist at the high temperature area. Continuous removal of heat by a heat sink must exist at the low temperature area. Otherwise the temperatures would eventually equalize, and no further circulation would occur. It is possible to have natural circulation take place in two-phase flow, but it is usually more difficult to maintain flow.
  • Fluids in contact. The two areas must be in contact so that flow between the areas is possible. If the flow path is obstructed or blocked, then natural circulation cannot occur.

Natural Circulation – Flow Rate

Natural circulation flow rate in the loop, under steady state condition is determined from the balance between the driving and the resisting forces. Driving force results from density difference between hot leg and cold leg of the loop. The head required to compensate for the head losses is created by density gradients and elevation changes.

Thermal Driving Head

Thermal driving head is the force that causes natural circulation to take place. It is caused by the difference in density between two bodies or areas of fluid. Consider two equal volumes of the same type of fluid. If the two volumes are not at the same temperature, then the volume with the higher temperature will also have a lower density and, therefore, less mass. It is known that the density of gases and liquids depends on temperature, generally decreasing (due to fluid expansion) with increasing temperature. Since the volume at the higher temperature will have a lower mass, it will also have less force exerted on it by gravity. This difference in the force of gravity exerted on the fluid will tend to cause the hotter fluid to rise and the colder fluid to sink. Thermal driving head can be simply calculated using the difference in hydrostatic pressures:

thermal driving head - equation

As can be seen, the greater the temperature difference between the hot and cold areas of fluid, the greater the thermal driving head and the resulting flow rate.

 
Density of water as a function of temperature
Chart - density - water - temperature

Density of water as a function of temperature

Hydraulic Resisting Force

PLC - Pressure loss coefficient - equationsAs was written, natural circulation flow rate, V, in the loop, under steady state condition is determined from the balance between the driving head and the resisting forces. Like pipe friction, the overall pressure losses are proportional to the square of the flow rate and therefore they can be easily integrated into the Darcy-Weisbach equation. Engineers often use the pressure loss coefficient, PLC. It is noted K or ξ (pronounced “xi”). This coefficient characterizes pressure loss of a certain hydraulic system or of a part of a hydraulic system. It can be easily measured in hydraulic loops. The pressure loss coefficient can be defined or measured for both straight pipes and especially for local (minor) losses. Since the Darcy friction factor is a function of velocity (in Reynolds number), then the calculation of the pressure loss coefficient is an iterative process.

Natural Circulation in Reactor Engineering

Natural Circulation - schema
Natural circulation in a closed loop

In reactor engineering, natural circulation is very desired phenomenon, since it is capable to provide reactor core cooling after the loss of RCPs (e.g. after loss of offsite power – LOOP). In PWRs, plant design provides an elevation difference, h, of approximately 12 meters between the centerline of the steam generator and the centerline of the reactor core. The layout of the system must ensure natural circulation capability following a loss of flow to permit cooldown without overheating the core. Moreover, the interconnecting piping from the reactor pressure vessel to the steam generators must be intact, free from obstructions such as non-condensable gasses (e.g. steam pockets). In this way, natural circulation will ensure that the fluid will continue to flow as long as the reactor is hotter than the heat sink, even when power cannot be supplied to the pumps.

RCPs are not usually “safety system”, as defined. After the loss of RCPs (e.g. after loss of offsite power – LOOP) the reactor must be shutdown immediately, since RCPs slowly coast down to zero flow rate. Sufficient and safe residual heat removal is then ensured by a natural circulation flow through the reactor. With no forced flow, the coolant in the core begins to heat up. The increase in coolant temperature causes a reduction in coolant density, which in turn moves the coolant into the steam generator. It must be noted, natural circulation is not sufficient to remove the heat being generated when the reactor is at power.

Modern reactor designs use natural circulation a very important safety feature. Many passive safety systems in modern reactor designs operate without using any pumps, which creates increased design safety, integrity, and reliability, while simultaneously reducing overall reactor cost.

Indicators of Natural Circulation

In PWRs, various parameters can be used to indicate or verify natural circulation is occurring. This is dependent on plant type and plant systems. For instance for a PWR selected parameters that can be used are as follows:

  • Ideally, the flow rate can be measured in each of loops.
  • ΔT (THot – TCold). The temperature difference between hot legs and cold legs should be 25-80% of the full power value and either steady or slowly decreasing. This indicates that the decay heat is being removed from the system at an adequate rate to maintain or reduce core temperatures.
  • Hot and cold leg temperatures should be steady or slowly decreasing. Again, this indicates that heat is being removed and the decay heat load is decreasing as expected.
  • Steam generator steam pressure (secondary side pressure) should be following reactor coolant system temperature. This verifies that the steam generator is removing heat from the RCS coolant.

Special Reference: Natural circulation in water cooled nuclear power plants, IAEA-TECDOC-1474. IAEA, 2005. ISBN 92–0–110605–X.

 
References:
Heat Transfer:
  1. Fundamentals of Heat and Mass Transfer, 7th Edition. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. John Wiley & Sons, Incorporated, 2011. ISBN: 9781118137253.
  2. Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866.
  3. U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow. DOE Fundamentals Handbook, Volume 2 of 3. May 2016.

Nuclear and Reactor Physics:

  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
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  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
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  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
  9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2.
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Natural Convection