Turbulent Kinetic Energy Levels Research Articles

Cut-cell method based large-eddy simulation of tip-leakage flow

The turbulent low Mach number flow through an axial fan at a Reynolds number of 9.36 × 105 based on the outer casing diameter is investigated by large-eddy simulation. A finite-volume flow solver in an unstructured hierarchical Cartesian setup for the compressible Navier-Stokes equations is used. To account for sharp edges, a fully conservative cut-cell approach is applied. A newly developed rotational periodic boundary condition for Cartesian meshes is introduced such that the simulations are performed just for a 72° segment, i.e., the flow field over one out of five axial blades is resolved. The focus of this numerical analysis is on the development of the vortical flow structures in the tip-gap region. A detailed grid convergence study is performed on four computational grids with 50 × 106, 250 × 106, 1 × 109, and 1.6 × 109 cells. Results of the instantaneous and the mean fan flow field are thoroughly analyzed based on the solution with 1 × 109 cells. High levels of turbulent kinetic energy and pressure fluctuations are generated by a tip-gap vortex upstream of the blade, the separating vortices inside the tip gap, and a counter-rotating vortex on the outer casing wall. An intermittent interaction of the turbulent wake, generated by the tip-gap vortex, with the downstream blade, leads to a cyclic transition with high pressure fluctuations on the suction side of the blade and a decay of the tip-gap vortex. The disturbance of the tip-gap vortex results in an unsteady behavior of the turbulent wake causing the intermittent interaction. For this interaction and the cyclic transition, two dominant frequencies are identified which perfectly match with the characteristic frequencies in the experimental sound power level and therefore explain their physical origin.

Experimental study of the turbulent field behind a perforated vortex generator

The influence of the wake vortex arising behind a perforated tab on the mixing process in heat exchangers and chemical reactors is analyzed. The preliminary step of this study, i.e., investigation of the turbulent field generated by a single perforated tab, is presented here. For this aim, laser Doppler velocimetry measurements are conducted downstream from a perforated trapezoidal vortex generator placed in a wind tunnel. It is shown that two shear layers are generated by the tab. The first shear layer is located at the upper edge of the tab, and the other is ejected from the perforation edges. These shear layers are characterized by high turbulent kinetic energy levels, which are profitable for meso-mixing enhancement. Finally, a spectral study shows that the turbulent macro-scale is nearly the same for typical locations in the shear layers shed from the tab and perforation edges.

Thermal mixing enhancement of a free-cooling system with a fractal orifice plate

The downstream hydrodynamic and thermal mixing performance of control and fractal orifice plates is numerically investigated. Each insert is positioned following a T-duct. Four blockage ratio plates σ=0.5, namely, square orifice (SO), circular orifice (CO), square fractal orifice (SFO), and the Koch snowflake orifice (KSFO), are employed to promote thermal mixing. In particular, orifice configuration effects that induced transverse and horizontal thermal convergence, turbulence kinetic energy, and pressure gradient changes are discussed. Numerical validations reveal good agreement between the experimental and numerical results for centerline velocity and temperature distributions along the channel. The results show that KSFO outperforms the rest with respect to effective hydrodynamic and thermal mixing. It is critical to note that the maximum cross-sectional temperature difference Δθ for KSFO is the lowest and decreases further downstream. Clearly, such low Δθ values along the channel ensure temperature uniformity. Furthermore, KSFO generated area-averaged turbulence kinetic energy levels approximately 37%, 48%, 371%, and 1454% higher than those of CO, SO, SFO, and the smooth channel without an insert, respectively, at x/H=1.04. It is also important to note that the studied fractal orifice pressure gradients are lower than those of CO and SO. These pressure drop observations are consistent with those of Nicolleau et al. (2011). Overall, the complex KSFO geometry forms a prominent balance between the pressure coefficient and thermal mixing at a Reynolds number of Reh=1.94×104. Most importantly, this finding may help guide the long-term sustainable development of heating, ventilation and free-cooling air conditioning systems.

Prediction of the Broadband Noise Radiated from a Fan Rotor of a High-Bypass Ratio Turbofan Engine: Take-off Condition

The purpose of this study is to predict the broadband noise generated by the fan rotor of a high bypass ratio turbofan engine at take-off condition. A numerical investigation of the unsteady aerodynamics of a fan rotor was described, with emphasis on acoustics. Three case studies were examined; namely, design point, a choked point and a near surge point. It was found that the dominant broadband noise mechanisms are due to interaction of turbulence of the incoming flow with the engine casing and nose, interaction of the turbulent boundary layers on the rotor blades with their trailing edges, and interaction of the rotating blade with the turbulence in the incoming flow. The most important noise source was the interaction of the turbulent boundary layers on the rotor blades with their trailing edges. Choked case scored the highest noise level as it has the maximum turbulent kinetic energy levels, maximum mass flow rate and thus maximum relative Mach number. Near-surge case has the lowest noise level except at the lower part of the suction side of the rotor where the reverse flow and vortices caused higher levels of noise.

VERTICAL STRUCTURE OF WAVE INDUCED CURRENTS, ORBITAL VELOCITY AND TURBULENCE OBSERVED IN NATURAL VEGETATION

Vertical structures of hydrodynamics under wave conditions were investigated using live plants in a large-scale wave flume. The effect of vegetation on hydrodynamics were analyzed for regular wave cases. The interaction of waves and emergent vegetation under regular waves significantly affect wave-induced motion and turbulence intensity. Coastal vegetation motion affected the water particle kinematics so that the vertical distribution of water particle velocity showed a large deviation from linear wave theory. Also, the vegetation motion increased turbulence intensity in the middle of water column and this caused a different vertical distribution of turbulent kinetic energy compard to the control case with no vegetation. In addition to the turbulence kinetic energy level, the vegetation changed the anisotropy characteristics of turbulence, decreasing vertical turbulent component.

Effects of incoming surface wind conditions on the wake characteristics and dynamic wind loads acting on a wind turbine model

An experimental investigation was conducted to examine the effects of incoming surface wind conditions on the wake characteristics and dynamic wind loads acting on a wind turbine model. The experimental study was performed in a large-scale wind tunnel with a scaled three-blade Horizontal Axial Wind Turbine model placed in two different types of Atmospheric Boundary Layer (ABL) winds with distinct mean and turbulence characteristics. In addition to measuring dynamic wind loads acting on the model turbine by using a force-moment sensor, a high-resolution Particle Image Velocimetry system was used to achieve detailed flow field measurements to characterize the turbulent wake flows behind the model turbine. The measurement results reveal clearly that the discrepancies in the incoming surface winds would affect the wake characteristics and dynamic wind loads acting on the model turbine dramatically. The dynamic wind loads acting on the model turbine were found to fluctuate much more significantly, thereby, much larger fatigue loads, for the case with the wind turbine model sited in the incoming ABL wind with higher turbulence intensity levels. The turbulent kinetic energy and Reynolds stress levels in the wake behind the model turbine were also found to be significantly higher for the high turbulence inflow case, in comparison to those of the low turbulence inflow case. The flow characteristics in the turbine wake were found to be dominated by the formation, shedding, and breakdown of various unsteady wake vortices. In comparison with the case with relatively low turbulence intensities in the incoming ABL wind, much more turbulent and randomly shedding, faster dissipation, and earlier breakdown of the wake vortices were observed for the high turbulence inflow case, which would promote the vertical transport of kinetic energy by entraining more high-speed airflow from above to re-charge the wake flow and result in a much faster recovery of the velocity deficits in the turbine wake.

Unsteady aerodynamics and aeroacoustics of a fan rotor of a high-bypass ratio turbofan engine

The purpose of this study is to predict the broadband noise generated by the fan rotor of a high bypass ratio turbofan engine. A numerical investigation of the unsteady aerodynamics of a fan rotor is described, with emphasis on acoustics. Two flight conditions are discussed: cruise and takeoff. For each case, three case studies are examined: namely, operating point, a choked point and a near surge point. It is found that the dominant broadband noise mechanisms are due to interaction of turbulence of the incoming flow with the engine casing and nose, interaction of the turbulent boundary layers on the rotor blades with their trailing edges and interaction of the rotating blade with the turbulence in the incoming flow. The most important noise source is the interaction of the turbulent boundary layers on the rotor blades with their trailing edges. Choked case exhibits the highest noise level as it has the maximum turbulent kinetic energy levels, maximum mass flow rate and thus maximum relative Mach number. Near-surge case has the lowest noise level except at the lower part of the suction side of the rotor where the reverse flow and vortices causes higher levels of noise.

Computational study of the influence of in-cylinder flow on spark ignition–controlled auto-ignition hybrid combustion in a gasoline engine

In this research, computational fluid dynamics simulations were performed to investigate the effect of in-cylinder flow motion on the in-cylinder conditions and spark ignition–controlled auto-ignition hybrid combustion. It is proved in this study that asymmetric intake valve events could be used to generate the swirl-dominated flow motion. However, the macroscopic flows, such as the swirl and tumble, show very weak correlations with zone-to-zone conditions and hybrid combustion process. The detailed investigation on the in-cylinder zone-to-zone conditions indicates that the in-cylinder turbulent kinetic energy level and the mean flow velocity (Vm) around the spark plug would directly affect the early flame propagation process, which in turn affect the subsequent auto-ignition process through changing the heat transfer between central burned gas and end-gas. In addition, the increased temperature inhomogeneity of the spherical zones caused by the in-cylinder flow motion would prolong the auto-ignition combustion. The structures of the flame front and auto-ignition sites also demonstrate the significant impact of in-cylinder motion on the combustion process. It is found that the combustion mode transition is very sensitive to the in-cylinder turbulent kinetic energy, Vm, and temperature and its inhomogeneity, indicating that these flow and thermal conditions could be used to optimize the hybrid combustion mode operation. It also proves the fluctuations of the in-cylinder flow, and thermal conditions could be the reasons leading to significant cycle-to-cycle variations in spark ignition–controlled auto-ignition hybrid combustion.

Mixing Enhancement of Compressible Planar Mixing Layer Impinged by Oblique Shock Waves

This paper presents the mixing enhancements of a spatially developing planar mixing layer interacting with an oblique shock wave by means of large-eddy simulation. The large-scale coherent vortices are found to be modulated by the oblique shock, which results in enhanced vorticity of the vortices. The thickness of the mixing layer impinged by oblique shock waves first decreases due to the increased compressibility effects of the shock wave, but then it increases and finally exceeds that of the shock-free mixing layer because of an accelerating growth rate larger than 0.05. The fluctuating levels of velocities and turbulent kinetic energy are strengthened in the shock–mixing-layer flows. The production term in the Reynolds stress transport equation dominates the increase of the transverse component of the Reynolds normal stresses, whereas the pressure–strain term decreases them and redistributes the energy to the streamwise component in shock–mixing layers, which then leads to the mixing enhancement between two streams. With the increase of shock wave strength, the thickness and mixing efficiency both increase in the shock–mixing layer. When the incident position of the shock wave moves upstream, the thickness of the shock–mixing layer increases much more and the mixing is realized faster. The present conclusions are helpful to further propose flow control strategy for mixing enhancement of supersonic flows.

A DNS study of jet control with microjets using an immersed boundary method

In this work, a microjet arrangement to control a turbulent jet is studied by means of direct numerical simulation. A customised numerical strategy was developed to investigate the interactions between the microjets and the turbulent jet. This approach is based on an improved immersed boundary method in order to reproduce realistically the control device while being compatible with the accuracy and the parallel strategy of the in-house code Incompact3d. The 16 converging microjets, so-called fluidevrons, lead to an increase of the turbulent kinetic energy in the near-nozzle region through an excitation at small scale caused by the interaction between the fluidevrons and the main jet. As a consequence, very intense unstable ejections are produced from the centre of the jet toward its surrounding. Further downstream, the turbulent kinetic energy levels are lower with a lengthening of the potential core compared to a natural jet, in agreement with experimental results.

Numerical and experimental investigations of a nonslender delta wing with leading-edge vortex flap

The aim of this paper is to numerically and experimentally evaluate the control efficiency of a series of leading-edge vortex flaps for a nonslender delta wing at a moderate Reynolds number. Both downward and upward deflected leading-edge vortex flaps are examined by experimental measurements and numerical simulations. It has been found in the wind tunnel experiments that the upward deflected vortex flap increases the vortex lift at low angles of attack due to the enhancement of the vortex strength while at high angles of attack the aerodynamic performances are significantly deteriorated due to a premature flow stall. Meanwhile the flap deflected downward has an excellent performance at high angles of attack, especially with a flap deflection angle of −70°. Consequently, numerical simulations of this optimal configuration are conducted to explore the mechanism of aerodynamic performance improvement and the vortical structures. A recently modified turbulence model has been demonstrated to be suitable to capture the complex vortex structures in this type of flow. In addition, the numerical results are in good agreement with those of the PIV data. Obviously the lift enhancement is due to the fact that the stall phenomenon of the baseline wing is significantly delayed by the vortex flap. This has been proved by the comparisons of vortical topologies, mean pressure coefficients and the limiting streamlines between the experimental measurements and the numerical simulations. Besides, the drag coefficient is reduced by an additional vortex system generated at the leeside of the flap. Furthermore, our simulations are capable of discerning the classical dominant frequencies of helical mode instability, Kelvin–Helmholtz instability and vortex wandering. Correspondingly some unsteady phenomena encountered in the two cases are investigated by the distributions of high levels of turbulent kinetic energy.

Direct numerical simulation of a turbulent flow in a rotating channel with a sudden expansion

AbstractThe effects of spanwise rotation on the channel flow across a symmetric sudden expansion are investigated using direct numerical simulation. Four rotation regimes are considered with the same Reynolds number$\mathit{Re}=5000$and expansion ratio$\mathit{Er}=3/2$. Upstream from the expansion, inflow turbulent conditions are generated realistically for each rotation rate through a very simple and efficient technique of recycling without the need for any precursor calculation. As the rotation is increased, the flow becomes progressively asymmetric with stabilization (destabilization) effects on the cyclonic (anticyclonic) side, respectively. These rotation effects, already present in the upstream channel, lead further downstream to an increase (reduction) of the separation size behind the cyclonic (anticyclonic) step. In the cyclonic separation, the free-shear layer created behind the step corner leads to the formation of large-scale spanwise vortices that become increasingly two-dimensional as the rotation is increased. Conversely, in the anticyclonic region, the turbulent structures in the separated layer are more elongated in the streamwise direction and also more active in promoting reattachment. For the highest rotation rate, a secondary separation is observed further downstream in the anticyclonic region, leading to the establishment of an elongated recirculation bubble that deflects the main flow towards the cyclonic wall. The highest level of turbulent kinetic energy is obtained at high rotation near the cyclonic reattachment in a region where stabilization effects are expected. The phenomenological model of absolute vortex stretching is found to be useful in understanding how the rotation influences the dynamics in the various regions of the flow.

On the onset of wake meandering for an axial flow turbine in a turbulent open channel flow

AbstractLaboratory experiments have yielded evidence suggestive of large-scale meandering motions in the wake of an axial flow hydrokinetic turbine in a turbulent open channel flow (Chamorro et al., J. Fluid Mech., vol. 716, 2013, pp. 658–670). We carry out a large-eddy simulation (LES) of the experimental flow to investigate the structure of turbulence in the wake of the turbine and elucidate the mechanism that gives rise to wake meandering. All geometrical details of the turbine structure are taken into account in the simulation using the curvilinear immersed boundary LES method with wall modelling (Kang et al., Adv. Water Resour., vol. 34(1), 2011, pp. 98–113). The simulated flow fields are in good agreement with the experimental measurements and confirm the theoretical model of turbine wakes (Joukowski, Tr. Otdel. Fizich. Nauk Obshch. Lyub. Estestv., vol. 16, 1912, no. 1), yielding a near-turbine wake that consists of two layers: the tip vortex (or outer) shear layer that rotates in the same direction as the rotor; and the inner layer counter-rotating hub vortex. Analysis of the calculated instantaneous flow fields reveals that the hub vortex undergoes spiral vortex breakdown and precesses slowly in the direction opposite to the turbine rotation. The precessing vortex core remains coherent for three to four rotor diameters, expands radially outwards, and intercepts the outer shear layer at approximately the location where wake meandering is initiated. The wake meandering manifests itself in terms of an elongated region of increased turbulence kinetic energy and Reynolds shear stress across the top tip wake boundary. The interaction of the outer region of the flow with the precessing hub vortex also causes the rotational component of the wake to decay completely at approximately the location where the wake begins to meander (four rotor diameters downstream of the turbine). To further investigate the importance of turbine geometry on far-wake dynamics, we carry out LES under the same flow conditions but using actuator disk and actuator line parametrizations of the turbine. While both actuator approaches yield a meandering wake, the actuator line model yields results that are in better overall agreement with the measurements. However, comparisons between the actuator line and the turbine-resolving LES reveal significant differences. Namely, in the actuator line LES model: (i) the hub vortex does not develop spiral instability and remains stable and columnar without ever intercepting the outer shear layer; (ii) wake rotation persists for much longer distance downstream than in the turbine-resolving LES; and (iii) the level of turbulence kinetic energy within and the overall size of the far-wake meandering region are considerably smaller (this discrepancy is even more pronounced for the actuator disk LES case) compared with the turbine-resolving LES. Our results identify for the first time the instability mechanism that amplified wake meandering in the experiment of Chamorro et al., show that computational models that do not take into account the geometrical details of the turbine cannot capture such phenomena, and point to the potential significance of the near-hub rotor design as a means for suppressing the instability of the hub vortex and diminishing the extent and intensity of the far-wake meandering region.

Prediction of the Broadband Noise Radiated from a Fan Rotor of a High-Bypass Ratio Turbofan Engine: Cruise Condition

The purpose of this study is the prediction of the broadband noise generated by the fan rotor of a high bypass ratio turbofan engine at cruise condition. A numerical investigation of the unsteady aerodynamics of a fan rotor was described, with emphasis on acoustics. Three case studies were examined; namely, design point, a chocked point, and a near surge point. It was found that, the dominant broadband noise mechanisms are due to, interaction of turbulence of the incoming flow with the engine casing and nose, interaction of the turbulent boundary layers on the rotor blades with their trailing edges, and interaction of the rotating blade with the turbulence in the incoming flow. The most important noise source was the interaction of the turbulent boundary layers on the rotor blades with their trailing edges. Chocked case scored the highest noise level as it has the maximum turbulent kinetic energy levels, maximum mass flow rate and thus maximum relative Mach number. Near-surge case has the lowest noise level except at the lower part of the suction side of the rotor where the reverse flow and vortices caused higher levels of noise.

Variation Of Airflow Pattern Through Dissimilar Valve Lift In A Spark Ignition Engine

Bi-fuel conversions are a common alternative fuelling option for mono-fuel gasoline SI vehicles because of the minor vehicle modifications required. In Malaysia, most bi-fuel vehicles are fuelled with compressed natural gas (CNG) and gasoline. However, CNG flame speed is lower than gasoline reducing the power and range of the vehicle when operating on CNG. This situation can be improved by increasing the flame speed via higher swirl generation. A Computational fluid dynamics model is used to analyse swirl generated by dissimilar valve lift (DVL) profiles on the intake valve. A three-dimensional engine simulation shows differences in swirl motion and turbulence between the original symmetric valve lift profile and the DVL. The higher swirl number reduces the turbulence kinetic energy level slightly. The best case profile is selected for further experimental testing.

Numerical simulation of turbulent reacting flow in porous media using two macroscopic turbulence models

This paper presents two dimensional simulations of air/methane combustion in cylindrical porous burner using models that explicitly consider the intra-pore levels of turbulent kinetic energy. Two most used turbulence models in porous media, proposed by Pedras and de Lemos (P–dL) and Nakayama and Kuwahara (N–K), have been used in the present study. Results of two macroscopic turbulence models are presented and compared for different Reynolds numbers and several flame locations. The values of turbulent kinetic energy and eddy viscosity calculated by two models are quite different due to the difference between the terms proposed for internal generation in turbulent kinetic energy and dissipation rate equations. It is found that P–dL model more accurately predicts the characteristics of reacting flow in porous media such as turbulent kinetic energy and eddy viscosity. Also, it is shown that the effects of turbulence in porous media are more significant when the flame stabilizes at the downstream of burner. Due to enhancement of heat and species diffusion, the preheating of reactants increases and the flame moves closer to the burner entrance when turbulence models are applied.

Turbulence modeling in a parallel flow moving porous bed

This paper deals with numerical simulation of turbulence in a parallel flow moving bed, in which turbulence is considered in the void spaces occupied by the fluid phase. Volume averaging techniques are applied to both time-mean and statistical flow fields. The set of resulting governing equations is discretized via the control-volume method and the resulting algebraic equation set is solved via the SIMPLE method. Results indicate that for lower values of slip ratio, Darcy number and bed porosity, higher levels of turbulence kinetic energy are computed.

Particle image velocimetry study of parameter influence for synthetic-jet application

Flow separation control of a circular cylinder using a synthetic jet positioned at the front stagnation point is experimentally investigated by the particle image velocimetry (PIV) technique. The control results for different excitation parameters, including the stroke length, the excitation frequency, and the momentum coefficient, are compared to distill the essential control parameters, and the influence of the cylinder Reynolds number on the control effect is discussed. The separation control mechanism for the present control configuration is also revealed. It is suggested that the effective control ability of the synthetic jet is attributed to the increment of the turbulent kinetic energy (TKE) and the dissipation rate surrounding the circular cylinder. High level of TKE enhances the dynamics of the fluids and thus flow around the leeward surface is endured a considerable vertical acceleration pointing to the centerline from both sides, which is more resistant to flow separation.

Interactions Between Benthic Predators and Zooplanktonic Prey are Affected by Turbulent Waves

Predators capture prey in complex and variable environments. In the ocean, bottom-dwelling (benthic) organisms are subjected to water currents, waves, and turbulent eddies. For benthic predators that feed on small animals carried in the water (zooplankton), flow not only delivers prey, but can also shape predator-prey interactions. Benthic passive suspension feeders collect prey delivered by movement of ambient water onto capture-surfaces, whereas motile benthic predators, such as burrow-dwelling fish, dart out to catch passing zooplankton. How does the flow of ambient water affect these contrasting modes of predation by benthic zooplanktivores? We studied the effects of turbulent, wavy flow on the encounter, capture, and retention of motile zooplanktonic prey (copepods, Acartia spp.) by passive benthic suspension feeders (sea anemones, Anthopleura elegantissima). Predator-prey interactions were video-recorded in a wave-generating flume under two regimes of oscillating flow with different peak wave velocities and levels of turbulent kinetic energy ("weak" and "strong" waves). Rates of encounter (number of prey passing through a sea anemone's capture zone per time), capture (prey contacting and sticking to tentacles per time), and retention (prey retained on tentacles, without struggling free or washing off, per time) were measured at both strengths of waves. Strong waves enhanced encounter rates both for dead copepods and for actively swimming copepods, but there was so much variability in the behavior of the live prey that the effect of wave strength on encounter rates was not significant. Trapping efficiency (number of prey retained per number encountered) was the same in both flow regimes because, although fewer prey executed maneuvers to escape capture in strong waves, more of the captured prey was washed off the predators' tentacles. Although peak water velocities and turbulence of waves did not affect feeding rates of passive suspension-feeding sea anemones, increases in these aspects of flow have been shown to enhance feeding rates and efficiency of motile benthic fish that lunge out of their burrows to catch zooplankton. Faster, more turbulent flow interferes with the ability of prey to detect predators and execute escape maneuvers, and thus enhances capture rates both for passive suspension-feeding predators and for actively swimming predators. However, prey captured in the mouths of fish are not washed away by ambient flow, whereas prey captured on the tentacles of suspension feeders can be swept off before they are ingested. Therefore, the effects of flowing water on predation on zooplankton by benthic animals depend on the feeding mode of the predator.

Numerical and experimental assessment of turbulent kinetic energy in an aortic coarctation

The turbulent blood flow through an aortic coarctation in a 63-year old female patient was studied experimentally using magnetic resonance imaging (MRI), and numerically using computational fluid dynamics (CFD), before and after catheter intervention. Turbulent kinetic energy (TKE) was computed in the numerical model using large eddy simulation and compared with direct in vivo MRI measurements. Despite the two totally different methods to obtain TKE values, both quantitative and qualitative results agreed very well. The results showed that even though both blood flow rate and Reynolds number increased after intervention, total turbulent kinetic energy levels decreased in the coarctation. Therefore, the use of the Reynolds number alone as a measure of turbulence in cardiovascular flows should be used with caution. Furthermore, the change in flow field and kinetic energy were assessed, and it was found that before intervention a jet formed in the throat of the coarctation, which impacted the arterial wall just downstream the constriction. After intervention the jet was significantly weaker and broke up almost immediately, presumably resulting in less stress on the wall. As there was a good agreement between measurements and numerical results (the increase and decrease of integrated TKE matched measurements almost perfectly while peak values differed by approximately 1mJ), the CFD results confirmed the MRI measurements while at the same time providing high-resolution details about the flow. Thus, this preliminary study indicates that MR-based TKE measurements might be useful as a diagnostic tool when evaluating intervention outcome, while the detailed numerical results might be useful for further understanding of the flow for treatment planning.