Richardson number

The Richardson number (after the British mathematician and meteorologist Lewis Fry Richardson ) is a dimensionless number . In fluid mechanics, it describes the relationship between potential and kinetic energy . ${\displaystyle Ri}$

definition

Liquids or gases in a gravitational field

For liquids or gases in a gravitational field , you can z. B. define

${\displaystyle Ri={\frac {g\cdot h}{u^{2}}}}$

With

• the gravitational acceleration  g
• a length  h typical for the problem (in the direction of the gravitational field)
• a typical speed  u .

In this definition, the reciprocal of the square root of the Richardson number is also called the Froude number :

${\displaystyle {\frac {1}{\sqrt {Ri}}}={\frac {u}{\sqrt {g\cdot h}}}={\mathit {Fr}}}$

In flight operations , the Richardson number gives z. B. Indications as to whether turbulence is occurring: the smaller the turbulence, the more likely it is - with typical Ri values ​​of 0.1 to 10. ${\displaystyle Ri}$

Thermal convection

The following definition is used in problems with thermal convection :

${\displaystyle {\mathit {Ri}}={\frac {g\cdot \gamma \cdot (T_{\text{Wand}}-T_{0})\cdot L}{u^{2}}}}$

is there

• ${\displaystyle \gamma }$the expansion coefficient
• ${\displaystyle T_{\text{Wand}}}$ the temperature of the heated wall
• ${\displaystyle T_{0}}$ a reference temperature
• ${\displaystyle L}$ a typical length of the problem.

This definition corresponds to an alternative definition of the Archimedes number and can also be written with the Grashof number and the Reynolds number as: ${\displaystyle Gr}$ ${\displaystyle Re}$

${\displaystyle Ri={\frac {Gr}{Re^{2}}}}$

Natural convection is negligible, forced convection is negligible. In the intermediate areas , both must be taken into account. ${\displaystyle Ri<0{,}1}$ ${\displaystyle Ri>10}$ ${\displaystyle (0{,}1<Ri<10)}$

Application example

District heating storage
to supply the city of Krems
with 50,000 m³ water content
and 2 GWh storage capacity

In particular, when designing heat storage systems , the Richardson number is used to dimension a proper temperature stratification in the storage system. The inflow into the reservoir must therefore be designed in such a way that the inflowing impulse does not destroy the reservoir stratification.

The end of 2007 was Europe's largest district heating storage with over 2 GWh storage capacity in the Theiss power station of EVN AG put into operation. It has a diameter of 50 meters and a height of a good 20 meters. Despite these geometrically unfavorable conditions, it has a perfect temperature stratification, as the inflow and outflow processes were calculated using the Richardson number and the inflow and outflow impulses were adjusted accordingly.

swell

1. ↑ Robert Huhn: Contribution to the thermodynamic analysis and evaluation of water heat storage in energy conversion chains . TUDpress, Dresden 2007, ISBN 978-3-940046-32-1 ; Andreas Oberhammer Europe's largest district heating storage system in combination with the optimal charging operation of a gas and steam turbine power plant (Lecture 2007)