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Selected Problems in Fluid Flow and Heat Transfer

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Nguyễn Gia Hào

Academic year: 2023

Chia sẻ "Selected Problems in Fluid Flow and Heat Transfer"

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Numerical study on lightweight design of PTC heater for electric vehicle heating system. Energies. Numerical study of magnetic field effect on ferromagnetic fluid flow and heat transfer in a square porous cavity. Energies.

Analysis of Different POD Processing Methods for SPIV-Measurements in Compressor Cascade Tip

Introduction

Unfortunately, there is a lack of use of the POD method to analyze the unsteady peak leakage current. In this paper, the effects of different decomposition regions and decomposition dimensionalities on POD decomposition and peak flow reconstruction are clarified.

Apparatus and Techniques

In the compressor cascade, the main factor contributing to the type B uncertainty of the time average velocity(UB,uij) is the time average of the instantaneous velocity deviation shown in Equation (2). Thus, the combined standard relative uncertainty of the time-averaged velocity in the u component can be given as:

Figure 3. Velocity profiles at the hub and tip walls. Note that the y-axis is the vertical distance of test points to the wall.
Figure 3. Velocity profiles at the hub and tip walls. Note that the y-axis is the vertical distance of test points to the wall.

Results

The x-axis in the figure is the distance between the center of the TLV core and the suction surface of the blade. Together, they demonstrate the geometric and kinematic characteristics of the TLV in the reconstructed flow field.

Figure 8. Combined maps of time-averaged SPIV measurement results in the blade passage
Figure 8. Combined maps of time-averaged SPIV measurement results in the blade passage

Conclusions

Effect of spatial wander on experimental laser velocity measurements of endwall vortices in an axial flow pump. Exp. Quantitative evaluation of the unsteady behaviors of the tip flow vortex in a subsonic axial compressor rotor. Exp.

Unsteadiness of Tip Leakage Flow in

  • Methodology 1. Testing Case
  • DES Results 1. Validation
  • Discussion
  • Conclusions

Detailed tip leakage current structures closely related to operating conditions were captured. Numerical investigation of unsteady flow tip leakage and the onset of rotating stall in a transonic compressor.J.

Figure 1. Schematic structure of the 1.5-stage compressor.
Figure 1. Schematic structure of the 1.5-stage compressor.

Effect of Rotor Thrust on the Average Tower Drag of Downwind Turbines

  • Methodology
  • Wind Tunnel Test 1. Outline
  • Analysis 1. Outline
  • Validation
  • Conclusions

In case the rotor thrust effect occurs, the wind speed at the tower position is reduced. The thrust value at the top of the tower was used as the rotor thrust.

Figure 1. Top view of a downwind turbine. U 0 , free stream wind speed, D T , tower diameter.
Figure 1. Top view of a downwind turbine. U 0 , free stream wind speed, D T , tower diameter.

POD Analysis of Entropy Generation in a Laminar Separation Boundary Layer

Experimental Facility

The turbulence of the water tunnel is less than 1%, and the Reynolds number is based on the total length of the flat plate and the inlet velocity is about 3×104. The flat plate is mounted horizontally in the middle of the water tunnel to ensure zero leakage incidence. The total length of the flat plate is 390 mm and the geometric structure of the leading edge is an ellipse with a ratio of 3:1 to the length of the semi-minor axis, as Figure 2 shows.

The distance from the first window to the front edge of the flat plate is 30 mm, and the distance between each window is 40 mm.

Dara Processing Method 1. POD Method

A more detailed investigation of uncertainty in the turbulent boundary layer can be found in [25]. In order to investigate the effect of the size of the decomposition zone on the POD results, different sizes of the decomposition zone were investigated. This is mainly because POD extracts a coherent structure with respect to the total kinetic energy of the flow field.

The first-order mode captures more than 99% of the energy at W5 and W6, as shown in Figure 4; the higher-order modes naturally capture a very low energy.

Figure 3. The third-order mode of the streamwsie velocity with different spanwise decomposition region size: (a) H = 20 mm; (b) H = 25 mm; (c) H = 30 mm; and (d) H = 35 mm.
Figure 3. The third-order mode of the streamwsie velocity with different spanwise decomposition region size: (a) H = 20 mm; (b) H = 25 mm; (c) H = 30 mm; and (d) H = 35 mm.

Results and Discussion 1. Time-Mean Flow Field

The first-order mode flow structure is consistent with the time-averaged flow field. Figure 12 shows the variation of the integrated entropy generation at the boundary along the flow. In the laminar region (W1–3), the entropy generation of the laminar boundary layer is at a very low level.

The entropy generation of POD-extracted coherent structures can be calculated using Equations (2)–(5) and (10).

Figure 6 shows the normalized velocity pattern of the boundary layer along the streamwise
Figure 6 shows the normalized velocity pattern of the boundary layer along the streamwise

Experiment Setup

The pitot tube and propeller probes were placed 1 m in front of the T-section prism. In a word, it could be ensured that the incoming flow in the swing range of the prism was a uniform flow. The linear motion of the prism was transferred to the rotary motion of the rotor.

First, free decay tests [35] were performed with different spring stiffness values ​​in air to obtain the natural frequency (fn) of the experimental system.

Figure 1. Recirculating water channel system.
Figure 1. Recirculating water channel system.

Results and Discussion 1. Vibration Characteristic Analysis

It can be concluded that the oscillatory responses of the T-section prism were similar to those of the triangular prism and the PTC round cylinder. The energy conversion efficiency of the galloping branch was found to be much higher than that of the VIV branches for the T-section prism. This indicated that the stability of the output power was good on the upper branch of the VIV.

D The width of the projection of the prism in the direction of the incoming flow H The height of the cross-section of the prism of the T-section.

Figure 9. High galloping (HG) oscillation characteristics 8 Ω ≤ R L ≤ 13 Ω (0.208 ≤ ζ ≤ 0.305):
Figure 9. High galloping (HG) oscillation characteristics 8 Ω ≤ R L ≤ 13 Ω (0.208 ≤ ζ ≤ 0.305):

Flow Structure and Heat Transfer of Jet Impingement on a Rib-Roughened Flat Plate

Numerical Methodology

At low Reynolds numbers, there will be no difference in the value of the Nusselt number. Figure 3 shows the geometry and meshing strategy used in the case of a rough flat plate. A very fine mesh in the direction normal to the heated surface was used, as well as roughness elements to ensure the correct functionality of the turbulence model, especially the low Reynolds numbers that required a dimensionless distance between the wall and the first node less than unity.

The cell growth rate near the heated surface, where all the heat transfer takes place, was no greater than 1.2 in the direction normal to the heated surface.

Figure 1. Geometry and computational domain.
Figure 1. Geometry and computational domain.

Results and Discussion 1. Simulation Characteristics

Depending on the velocity gradients, the location of the fins can have a different impact on the flow physics and heat transfer rate. For e≥1 mm, another Nupeak occurs just ahead of the rib, due to recirculation of the flow ahead of the rib that increases the heat transfer rate in this region. It is argued that the maximum increase in the heat transfer rate was achieved when the fin was installed at a location close to the boundary between the stagnation region and the wall current region, at R/D = 2.

Experimental investigation of impinging heat transfer on a flat plate with depressions with different cross-flow schemes. International

Figure 4. Nusselt number distribution for three mesh grids, jet-to-target distance H/D = 6, R e = 10,000.
Figure 4. Nusselt number distribution for three mesh grids, jet-to-target distance H/D = 6, R e = 10,000.

Numerical Study on Thermal Hydraulic Performance of Supercritical LNG in Zigzag-Type Channel PCHEs

Numerical Approach

In this study, the thermal hydraulic performance of supercritical LNG in zigzag PCHE is investigated. In this paper, we only study the performance of supercritical LNG in the cold channel. Therefore, as shown in Figure 2 , the thermal properties of supercritical LNG were approximated as piecewise-polynomial functions of temperature.

The effect of grid numbers on the convection heat transfer coefficient is shown in Table 4.

Figure 1. Schematic diagram of the physical model: (a) Schematic diagram of cross flow printed circuit heat exchanger (PCHE) model; (b) The computational single channel and boundary conditions; (c) Top view of zigzag channel.
Figure 1. Schematic diagram of the physical model: (a) Schematic diagram of cross flow printed circuit heat exchanger (PCHE) model; (b) The computational single channel and boundary conditions; (c) Top view of zigzag channel.

Results and Discussion

As shown in Figure 11 , the local convection heat transfer coefficient and pressure drop increase significantly when the mass flow increases due to the increase in turbulent flow. When the mass flow increases by 2 times, the local heat transfer coefficient increases by 1.4 times, while the pressure drop increases by 3.3 times. Therefore, the local convection heat transfer coefficient decreases with decreasing inlet pressure along the flow direction.

When the mass flow increases by 2 times, the local heat transfer coefficient increases by 1.4 times, and the pressure drop increases by 3.3 times.

Figure 6. Local convection heat transfer coefficient and bulk temperature at different bend angles along the streamwise direction.
Figure 6. Local convection heat transfer coefficient and bulk temperature at different bend angles along the streamwise direction.

A Machine Learning Approach to Correlation Development Applied to Fin-Tube Bundle

Method

The validation set consists of 30 CFD simulations selected by sampling the Latin hypercube of the design space as shown in Figure 1. A database of published experimental work was previously established at the Norwegian University of Science and Technology [17]. The database contains data for 248 different finned tube bundles from 21 publications, including plain and serrated fin geometries. This makes it easy to interpret the correlation as consisting of one velocity-dependent term multiplied by many "geometry correction" terms.

The accuracy of the correlation was evaluated based on the coefficient of determination (R2) and root mean square error (RMSE) values ​​on an independent CFD-sampled data set (N=30).

Results and Discussion 1. Correlation Development

The remaining free variables and limits were equal to the design variables and limits in Table 2, with the lower limit of the fin thickness set to 0.5 mm andws. This phenomenon has been more thoroughly discussed in [27] but ultimately requires a different modeling approach than the present one due to the large non-linearity involved. The predictive accuracy for the reference correlations (Holfeld [17], Escoa [18] and PFR [26]) are generally poor due to the severe extrapolation induced by the design space definition.

The PFR correlation for Eu has a relatively high coefficient of determination compared to the Escoa and Holfeld correlations, indicating that the hydraulic diameter (which is the unique feature of the PFR Eu correlation) may be a stronger length scale than the pipe diameter.

ESCOA

The Euler number shows a high sensitivity to the flow rate and fine aperture compared to the other four variables (Figures 5 and 7). The Nusselt number is primarily a function of the flow rate and pipe diameter (Figures 6 and 8). However, the sensitivity to the design variables close to the optimal point for the case study is exaggerated for some variables.

The Nusselt number is relatively insensitive to all design parameters except flow velocity and pipe diameter (i.e., Reynolds number) around the design points studied.

A Numerical Study on the Light-Weight Design of PTC Heater for an Electric Vehicle Heating System

CFD Model Details 1. Physical Model

The open area ratio was the ratio of the inlet area of ​​a model to the radiating cross-sectional area of ​​the electric heater. Based on the experimental data, curve fitting was performed to obtain the resistance-temperature curve for PTC elements, as shown in Figure 4. Based on these considerations, Model B was selected as the most appropriate option as a result of the simulation.

This also implies that the non-uniformity of the mass flow rate depends on the location of the heater.

Experimental Results for the Electric Heater

The inlet/outlet air temperature of the electric heater in the winding tunnel was measured with 25 T-type thermocouples with an error rate of ±0.1◦C. As shown in Figure 11, the test results of the electric heater prototype show the difference in heating performance according to the heat dissipation location of the heater. Variations in heating capacity with flow rates at the whole heater level ranged from 3% to 22% in the analysis and experiment, respectively.

The correlation between the simulation results and the heating performance results of the prototype according to the inlet flow rate showed that the error rate between the performance variations was about 4%.

Unsteady Simulation of a Full-Scale CANDU-6 Moderator with OpenFOAM

Simulation Method 1. Open Source Code

The realizable leak-εturbulence model is also applied for the low Reynolds number turbulent flow in the moderator. A realizable model, which is better for rotational flow, is used for the simulation of turbulent flow. The energy equation to get the temperature field for the calculation afV in Equation (2) is.

The initial temperature of the entire computational domain is 47.3◦C, and the flow is assumed stationary at the beginning of the calculation.

Result and Discussion

The temperature of the two outlets are slightly different from each other due to the asymmetry from the flow instability. The hot water maintains the temperature balance in the upper region of the tube bundles due to the movement in the momentum transfer. The buoyancy term in the incompressible Navier-Stokes equation is considered with the Boussinesq approximation of temperature variation.

In Proceedings of the 10th Annual Conference of the Canadian Nuclear Society, Ottawa, ON, Canada, 4–7 juni 1989.

Visualization Study on Thermo-Hydrodynamic Behaviors of a Flat Two-Phase Thermosyphon

Description of Experiment 1. Experimental Apparatus

The top of the copper column is in close contact with the evaporator surface of the flat two-phase thermosiphon. The constant temperature water bath supplies cooling water with a constant temperature (±0.1◦C temperature swing) for the condenser section of the two-phase flat thermosyphon. This definition characterizes the resistance of heat transfer from the evaporator surface to the condenser surface, and smaller thermal resistance means better heat transfer performance of the flat two-phase thermosiphon.

Therefore, these complex thermohydrodynamic behaviors play an important role in the operation and heat transfer of a planar two-phase thermosyphon.

Hình ảnh

Figure 9. (a) Statistics of identified TLV time-averaged parameters; (b) Schematic of TLV core trajectory.
Figure 14. Mode 1 energy fraction at different decomposition region sizes and different chord position.
Figure 17 reflects the relative contribution of the modes to the fluctuation energy of the flow field.
Figure 23. Statistics of instantaneous reconstructed flow field using first 10 modes at L/c = 1.1.
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