Waltraud B. Buchenberg1, Florian Wassermann2, Sven Grundmann3, Jürgen Hennig1, and Bernd Jung4
1Radiology - Medical Physics, University Medical Center Freiburg, Freiburg, Germany, 2Center of Smart Interfaces, Technische Universität Darmstadt, Darmstadt, Germany, 3Institute of Fluid Mechanics, University of Rostock, Rostock, Germany, 4Interventional and Pediatric Radiology, University Hospital, Institute of Diagnostic, Bern, Switzerland
Synopsis
Since MR thermometry and MR velocimetry allow
non-invasive measurements of temperature fields and velocity fields, they are
widely applied to address medical questions; however, they are also suited to
investigate 3D fluid flow and heat transfer phenomena in technical devices.
This work investigates velocity fields and temperature distributions in a
countercurrent double pipe heat exchanger. 3D velocity and temperature measurements
were performed consecutively. A combination of forced convection (external pump providing laminar
flow) and free convection (heating) using MRI can add valuable new insights into
heat transfer processes.Purpose
Quantitative
monitoring of temperature changes, ∆T, can be achieved by MR thermometry (MRT)
based on proton resonance frequency (PRF) [1]. Additionally, MR velocimetry
(MRV) is a well-established method to quantitatively measure velocities. Measurements
of temperature and velocity fields are also of great interest to the
engineering community, e.g. for the optimization of heat transfer performance.
Conventional methods such as a combination of particle image velocimetry and
particle image thermometry are not capable to provide 3D data of flow and
temperature in macroscopic setups with one imaging modality and a single
measurement setup within a similar amount of time as MRI does. The combination
of MRT and MRV revealed promising results [2,3]; however, the capability of MRV
and MRT has not yet been widely investigated in fluid flow.
This work
aimed to investigate 3D velocity and temperature fields in a countercurrent
double pipe heat exchanger.
Methods
The heat exchanger consists of two separate closed flow
circuits, a copper pipe (outer diameter=15mm) inside a Plexiglass® pipe
(inner diameter=50mm, length of both pipes=320mm) oriented parallel to the
external magnetic field (Figure1). The inner hot
flow circuit (flow2) transferred heat to the surrounding non-heated flow
circuit (flow1=5l/min). The flow2 circuit was connected to a circulation
heater/cooler (Julabo FC1200T and SE, class III, Seelbach, Germany) providing
fluid temperatures of 21°C or 50°C with a constant flow rate. A detailed
description of the flow circuits and the model can be found in [4]. Velocity
and temperature fields were measured in flow1 when the temperature of flow2 was
increased. 3D data was acquired at a 3T MR system (Prisma, Siemens, Erlangen,
Germany) using a phase contrast GRE sequence for MRV and a velocity compensated
GRE sequence for PRF shift thermometry (imaging parameters listed in Table 1).
PRF data were acquired with 1.) both flow circuits at 21°C (heat off) and 2.)
flow1=21°C and flow2=50°C (heat on). The phase images of each acquisition were
subtracted and converted to $$\Delta T = \frac{\Delta \Phi}{2\pi \cdot f \cdot \alpha \cdot TE}$$ (f=123.2MHz, α
1%CuSO4=0.0097ppm/K). Reference phantoms filled with 5%Hydroxyethylcellulose+1%CuSO
4+dist. H
2O surrounded the
flow model to allow correction for field drift. For MRV a flow off scan was
acquired to correct for eddy currents.
Results
Figure 2 shows a
superposition of temperature maps (TMs) and velocity vector fields at different
cross-sectional views (distance 3cm) within the double pipe heat exchanger.
Heated fluid raises to the top of the outer pipe depicted as a localized thin
structure (plume). At the top, the heated fluid moves outwards forming side
lobes which are warmer than the surroundings. The velocity field clearly
represents the natural convection flow due to the temperature increase within
the fluid. In Figure 3 two streamlines starting at locations X and O are
superimposed on the color-encoded TMs. The distance between bullets represents the
velocity magnitude. In areas with no temperature change only forced convection
is present (represented by equally spaced bullets). In the heated area, a particle located
closely at the plume follows a 3D trajectory into the lobe as it is traveling
along Z. At the beginning, temperature and speed increase (wider spaced
bullets), in the side lobe the speed is slower (bullets are packaged).
Furthermore, it remains at a similar location when the forced convection
exceeds the natural convection.
Discussion & Conclusion
A combination of
forced convection (external pump providing laminar flow) and free convection
(heating) as investigated in this work using MRI can contribute valuable new
insights into heat transfer processes.
The coupling between
the successfully measured velocity and temperature fields can be clearly
observed. The temperature increase causes a decrease of density of the fluid.
Thus, the heated fluid rises (natural convection) in agreement with the
measured velocity. The observation of the plume due to natural convection has
been described in literature previously [5,6]. A detailed discussion on
possible sources of errors in the TMs and a comparison to thermocouple
measurements is given in [4].
The combination of
MRV and MRT is a very promising technique to examine thermo-fluidic questions
to gain a better understanding of devices such as heat exchangers. Currently,
no other modality provides a similar performance and speed. Additionally,
collaborations between fluid mechanical engineers and the MR community offer
great potentials to investigate heat transport processes via blood flow for
instance which occur during thermal treatment of tumors.
Acknowledgements
DFG-Grant
JU2687/10-1References
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