The aimed experiments in the range of 200 to 1000P a could not be conducted due to the nucleation of bubbles in the inlet channel and the syringe. For further research it is recommended to solve this problem first. As discussed, these bubbles might be caused by a leakage, dissolved gas in the water and the boiling of water due to impurities. Possible improvements to remove these bubbles that have been considered are:
• The hose connections and the three way valve are not designed to be used under a high vacuum. These have to be replaced by a type that has been designed for low pressures.
Which is for example the use of Swagelok tubing and connections.
• The water has to be heated during the degasification process. This to speed up the process.
• The material of the tubing, valves and degasification vessel should be highly corrosive res-istance and be carefully cleaned. Even a small impurity can cause the water to boil.
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Appendices
Numerical model setup
A.1 Numerical model
A numerical model has been developed which will be used to interpret and discuss the experimental results. This model calculates a 1D temperature profile inside the setup (see Figure A.1). This has been done by solving the transient heat equation by finite differences with the appropriate boundary conditions. The general form of the problem can be described with the heat equation as follows:
In which T is the temperature, cpis the specific heat, ρ is the density, k is the heat conduction and ˙q is a source term. For the specification of the boundary conditions it is assumed that after a thin boundary layer the temperatures above the setup becomes the room temperature and at the bottom of the setup becomes the temperature of the ice water.
Equation A.1 is difficult to solve analytically because ρ(x)cp(x) and k(x) are discontinuous functions, which is caused by the different material layers. Therefore, both spacial dependency and time dependency will be solved with discredited steps.
A method to discretize the spacial dependency over a discretized domain,
x = [x0, x1, ..., xn−1, xn], is the central difference scheme. Which an appropriate scheme for a purely diffusive transport problem. The diffusive part of the transport equation,dxd(k(x)dTdx) = ˙q, has been discretized with the use of the central difference scheme:
1 which is a more appropriate form for solving it for the unknown variable T.
The transient term of the heat equation has been discretized with a backward Euler scheme.
which is a more stable method than the forward Euler scheme.
ρcpdT
dt = ρcpTik− Tik−1
∆t (A.5)
Which can be implemented in the steady state scheme ofA.4 ρcpTik− Tik−1
APPENDIX A. NUMERICAL MODEL SETUP Figure A.1: Domain of the numerical model
And be rewritten to:
This can be written as a linear system:
Ay=b (A.12)
This linear system has been implemented in a Matlab scrip which solves is per time step ’k’.
The discretized domain with it belonging material properties are depicted in FigureA.1.