Simultaneous 3D velocity and temperature mapping in fluid flow using MRI
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, α1%CuSO4=0.0097ppm/K). Reference phantoms filled with 5%Hydroxyethylcellulose+1%CuSO4+dist. H2O 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 JU2687/10-1

References

[1] Rieke, V and Pauly, KB. MR Thermometry. JMRI 2008;27:376-390

[2] Elkins et al. Full-field velocity and temperature measurements using magnetic resonance imaging in turbulent complex internal flows. Heat&Fluid Flow 2004;25:702-710

[3] Ogawa et al. Simultaneous measurement of temperature and velocity maps by inversion recovery tagging method. MRI 2000;18:209-216

[4] Buchenberg et al. Acquisition of 3D temperature distributions in fluid flow using proton resonance frequency thermometry. MRM 2015;DOI 10.1002/mrm.25874

[5] van Dyke. An album of fluid motion. Paraboli Press 1982;4th ed.:121-122

[6] Togun et al. A review of studies on forced, natural and mixed heat transfer to fluid and nanofluid flow in an annular passage. Renewable and Sustainable Energy Reviews 2014;39:835-856

Figures

Table 1: Imaging parameters.

Figure 1: Double pipe heat exchanger.

Figure 2: Cross-sectional TMs and superimposed velocity fields. Temperature changes in flow1 are localized to a thin region directly above flow2, and a larger region at the top of the Plexiglass® pipe. Flow2 is not MR visible since it is inside the copper tube.

Figure 3: Cross-sectional TMs and superimposed streamlines starting at locations X and O. The distance between the bullets represents the speed (the larger the distance the faster a particle moves).



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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