.TransiEnt.Components.Boundaries.Ambient.UndergroundTemperature

Information

1. Purpose of model

Gives the underground temperature at the specified depth and simulated time as a sinusoidally oscillation with an oscillating period of one year.

2. Level of detail, physical effects considered, and physical insight

As stated in [1] the underground temperature is not effected by hourly up to couple of days fluctuations of the ambient temperature. Therefore, the annual course of the ambient temperature can be approximated as a sinusoidally temperature oscillation, which describes the course of the monthly average temperatures very well (s. eq. (2)). The non disturbed underground temperature in the specified depth followes the ambient temperature with time delay. For the temperature boundary condition of 3rd kind Grigull and Sandner [2] derived eq. (2) with the help of the Laplace transformation.

3. Limits of validity

Equation (2) is only valid for heat transfer coefficients towards infinity at the earth's surface. The full equation with heat transfer coefficient can be found in [1] where it is also shown that the impact of the heat transfer coefficient is negligible.

4. Interfaces

Real output of underground temperature in K.

5. Nomenclature

T_amb_avg: Annual average temperature

dT_amb_month: Amplitude of annual monthly averaged temperature course

t_0: Oscillation period (one year in seconds)

t_Tmax: Second of the year when maximal temperature occurs

z: Depth at which T_underground is calculated

6. Governing Equations

Sinusoidally ambient temperature of monthly means (z=0):

(1)

with the phase displacement of the maximal temperature compared to the beginning of the year

.

Sinusoidally underground temperature as function of z and t:

(2)

with taking into account the depth in the underground, the soil transport characteristics and the oscillation period:

with a as thermal diffusivity defined as

.

Find transport characteristica of different soil material in [3].

7. Remarks for Usage

The oscillation period of the temperature is normally one year. Be sure to change the soil transport characteritica according to the depth.

8. Validation

Tested in check model "TestUndergroundTemperature"

9. References

[1] Ramming, Klaus: Bewertung und Optimierung oberflächennaher Erdwärmekollektoren für verschiedene Lastfälle, Technical University Dresden, 2007

[2] Grigull, Ulrich ; Sandner, Heinrich: Wärmeleitung, Wärme- und Stoffübertragung. Berlin, Heidelberg : Springer Berlin Heidelberg, 1990 — ISBN 978-3-540-52315-4

[3] VDI 4640 Blatt 1: Thermische Nutzung des Untergrunds - Grundlagen, Genehmigungen, Umweltaspekte. In: Verein Deutscher Ingenieure e.V. Düsseldorf (2010)

10. Version History

Model created by Lisa Andresen (andresen@tuhh.de), Dec 2016

Contents

Name	Description
Material	Material in the ground