2. Reference solution#

2.1. Calculation method#

2.1.1. Calculating vapour pressure from temperature#

We assume the linear saturation curve. So it is written:

eq 2.1.1-1

[R7.01.11 éq 3.2.1-2] then give:

Eq 2.1.1-2

We write that the total mass of water is preserved (because there is no water flow at the edge) and we get:

Eq 2.1.1-3

[R7.01.11 éq 4.4-1] also gives

Eq 2.1.1-4

The coupling of equations [éq 2.1.1-3] and [éq 2.1.1-4], to which must be added the ideal gas equation for steam, is a highly non-linear system that we will solve in a small disturbance, which allows it to be linearized.

All calculations done, we get:

Eq 2.1.1-5

2.1.2. Temperature calculation#

[R7.01.11 éq 3.2.4.3-1] gives:

Eq 2.1.2-1

(since the other expansion coefficients are zero).

[éq 3.2.4.3-2] gives:

eq 2.1.2-2

So we get:

Eq 2.1.2-3

In this problem,

is nothing but the heat provided per unit volume.

By calling

the total volume of the room and

its lateral surface and

the application time of the flows:

Eq 2.1.2-4

2.1.3. System to be solved#

Eq 2.1.3-1

2.2. Benchmark results#

We give the value of the temperature, liquid pressure and vapor pressure, solution of the system [éq 2.1.3-1] with the data summarized in paragraphs [§1.2] and recalled below. To calculate the calorific capacities, the following relationships are used:

, the latter relationship being true because the grain expansion coefficient is zero.

					(calculated)



5,00E-01	-1,00E-12	3,00E+02	3,70E+03	2.50E+06	2,67E-02	1.00E+03

		(calculated)		l		(calculated)



2.20E+03	3,00E-01	2,93E+03	1.05E+03	4,18E+03	1.90E+03	2.78E+06





1.00E+06	1000	400	1.00E+04