Heat transfer optimization of pulsating flow in orrugated hannel

Overview

Heat exchangers are engineered to maximize efficiency by optimizing the surface area between two fluids while minimizing flow resistance and material costs Enhancements such as corrugations or fins can increase the heat exchange surface area and promote fluid turbulence, thereby improving performance Engineers and researchers face the critical challenge of designing more effective and compact heat transfer systems To boost the heat transfer rate, three primary techniques are employed: active, passive, and a compound approach that integrates both active and passive methods.

Recent research has focused on using pulsating flow to enhance convective heat transfer Elsafei et al conducted experiments on pulsating turbulence flow in smooth pipes, revealing that the thermal performance factor can increase by 9% and decrease by 12%, influenced by Reynolds number and frequency Similarly, Habib et al (2002) explored convective heat transfer in a tube with uniform heat flux under laminar pulsating flows, finding that heat transfer coefficients can improve by up to 30% at frequencies between 1-4.1 Hz and by 9% at 18-22 Hz However, they also noted significant reductions in heat transfer coefficients, with decreases of up to 40% at frequencies between 4.1-18 Hz and 20% at frequencies above 22 Hz.

Researchers have conducted extensive studies on corrugated channels to enhance heat transfer and thermal performance Ali and Ramadhyani [4] experimentally compared the heat transfer efficiency of a corrugated channel with that of a parallel plate channel using water as the working fluid Their findings revealed that optimal heat enhancement occurs at Reynolds numbers between 1750 and 2000.

The performance of corrugated channels declines for Reynolds numbers greater than 2000, as demonstrated by Islamoglu and Parmaksizoglu, who conducted experimental tests within a Reynolds number range of 800-4000 Their findings revealed that increasing channel height enhances both the Nusselt number and friction factor, but negatively impacts overall thermal performance Additionally, Islamoglu and Kurt utilized artificial neural networks (ANNs) to predict heat transfer in corrugated channels, achieving accuracy within 4% of experimental results Ghaddar and El-Hajj's numerical study highlighted a 120% increase in heat transfer for corrugated channels at a Reynolds number of 375 compared to parallel channels, identifying a height-length ratio of 0.35 as optimal for thermal performance Comini et al investigated the aspect ratio's influence on heat transfer and pressure loss, finding that a decrease in aspect ratio leads to increased Nusselt numbers and friction factors Hwang et al observed that Görtler vortices appear at Reynolds numbers below 1000, but vanish as the flow transitions from laminar to turbulent at higher Reynolds numbers, with optimal thermal performance occurring at a Reynolds number of 1000 before slightly declining Naphon's experiments confirmed that both heat transfer and pressure drop increase in corrugated channels compared to parallel plates Overall, research in this field has predominantly focused on sharp and sinusoidal corrugated channels, with this study specifically examining the impact of sharp corrugated channels on heat transfer rates.

Figure 1 The distribution of investigated channels' percentage

Research on the compound method is limited due to the complexities involved in setting up experimental and numerical studies Akdag et al [12] conducted a numerical analysis of a 2D sinusoidal channel with varying amplitudes and frequencies under fully laminar flow conditions, revealing that the convective rate of pulsating flow increases with higher amplitudes compared to steady flow Similarly, Nandi et al [13] utilized a numerical approach to examine 2D wave channels under pulsating flow at the inlet, testing different amplitudes (0.2, 0.5, 0.8) and frequencies (1, 5, 10) as sinusoidal velocity inlet boundary conditions, and discovered enhanced heat transfer performance in comparison to steady flow.

Recent surveys indicate that corrugated channels and pulsating flow are the preferred methods for enhancing heat transfer, attracting researchers globally to explore both experimental and numerical approaches Most publications have focused on the impact of geometric configurations on heat transfer and the effects of pulsating flow in smooth tubes.

This study employs a compound method to investigate the impact of pulsating flow on corrugated channels under both transient and turbulent regimes However, the turbulence characteristics remain unclear and are not thoroughly described.

This study employs Large Eddy Simulation with the advanced wall-adapting local eddy-viscosity (WALE) model to investigate the impact of V-shaped corrugated channels and pulsating flow on turbulence characteristics, heat convection rates, and overall thermal performance in 3D corrugated channels While numerous researchers have focused on the height of the channels, this research specifically examines how pulsating flow affects existing corrugated channels.

Application

Heat exchangers play a crucial role in various engineering applications, spanning from household systems to industrial uses They are essential in heating and air conditioning systems, the automotive and aerospace industries, as well as in ocean thermal energy conversion technology.

Researchers and companies are actively developing heat exchangers to maximize energy extraction from the ocean Ocean thermal energy conversion (OTEC) utilizes the temperature difference between cold deep ocean water and warm tropical surface waters to generate electricity OTEC plants pump significant volumes of deep cold and surface seawater to operate a power cycle, providing a reliable, clean, and sustainable energy source This technology is particularly beneficial for tropical countries like Vietnam, where abundant sunlight and numerous islands lack reliable power supplies.

The diagram in Fig 1 illustrates the Ocean Thermal Energy Conversion (OTEC) system and its operational mechanics A key component for enhancing the efficiency of this system is the heat exchanger This study introduces a groundbreaking method aimed at improving heat transfer within the heat exchanger, significantly boosting overall system performance.

In the aviation industry, heat exchangers play a vital role in modern airplanes These devices function by initially storing heat from the primary medium in a reservoir, which is then regenerated for use.

The heat exchanger in air conditioners for airplanes must be compact and highly efficient to minimize size and weight, as illustrated in Figure 2, which features a modern heat exchanger produced by JAMCO Various fin shapes, including sharp fins, wave fins, rectangular fins, and arc fins, are utilized in these systems to enhance performance.

Figure 3 The heat exchanger used for aviation industry and different ﬁn

Simulation domain setup

The present investigation analyzes a model with specific boundary conditions, illustrated in Fig 4 The geometry features two opposite corrugated plates, as depicted in Fig 5(b), each consisting of 11 crests spaced 27 mm apart The overall dimensions of the corrugated plates are 361 mm in length and 130 mm in width, with a 41 mm straight section at the channel inlet, equivalent to 1.5L, ensuring fully developed flow before entering the heated segment Additionally, there is a 20 mm straight section at the outlet, corresponding to 0.75L, and the channel height measures 20 mm, with a wave height of 5 mm and a corrugated angle of 20°.

The boundary conditions used for validation in this study, depicted in Fig 6(b), are consistent with the experimental setup conducted by Naphon [11] Air serves as the working fluid, with two plates of the corrugated channel subjected to a constant heat flux of 590 W/m², while the remaining walls are treated as adiabatic The inlet flow temperature is maintained at 296.89 K, and the inlet velocity magnitude is defined by a sinusoidal function, as illustrated in Fig 1(b).

Where is the amplitude and is the frequency For reference case, the amplitude A=0.8 and the frequency is select to comparison with steady flow inside corrugated channel

Figure 4 Geometry parameter and computational domain

Im portant parameters

The reference velocity magnitude was calculated by the hydraulic diameter and Reynolds number which deﬁned as:

Uniform wall heat flux Adiabatic wall

(a) Geometry parameter of corrugated channel

The heat enhancement rate is a crucial parameter for evaluating the effectiveness of surface modifications on heat transfer This article compares the heat enhancement achieved through a compound method versus a passive method between two corrugated plates, utilizing the heat enhancement term for analysis.

Where the and represent for pulsating ﬂow and steady ﬂow respectively

Heat transfer enhancement techniques aim to reduce thermal resistance by either increasing the effective heat transfer surface area or generating turbulence, although these methods may also lead to higher pumping power requirements and costs The effectiveness of these techniques is measured by the Thermal Performance Factor (TPF), which compares the change in heat transfer rate to the change in friction factor Various inserts are utilized in heat transfer enhancement devices, with geometrical parameters such as width, length, twist ratio, and twist direction significantly influencing heat transfer performance To assess the overall efficiency of energy systems, modifications like pulsatile flow or corrugated channels are evaluated using the TPF, which is essential for determining the balance between heat transfer rates and friction factors.

Where Nusselt number, Nu and friction factor f in this research is identical as [11,14]:

The parameter (7) represents half the height of the channel and measures the distance from the leading edge of the corrugated plate along its surface Additionally, it indicates the thermal conductivity of air Pressure loss is defined as the difference in average pressure between the channel's inlet and outlet.

Governing equations

In a corrugated channel characterized by a very low Mach number and minimal temperature fluctuations, the flow field can be effectively described using the incompressible assumption The governing equations for this scenario are formulated accordingly.

Where represents the Cartesian coordinates ( , is the air density, stands for static temperature, is static pressure and is uniform kinematic viscosity Under thermal conditions, the above equation have been

The analysis assumes constant fluid properties, including thermal conductivity, specific heat capacity, and air density Additionally, it considers viscous dissipation effects to be negligible in comparison to the convective heat transfer rate, leading to the exclusion of the dissipation function term from the full energy equation.

Heat flux is given by:

This study employs the Large Eddy Simulation (LES) method, which is particularly effective for analyzing complex turbulent flows, such as those found in pulsating corrugated flow, where turbulence significantly impacts heat transfer and fluid properties LES resolves large-scale turbulent structures while modeling the smaller sub-grid scales By utilizing the box-filter, commonly applied in LES, the continuity, momentum, and energy conservation equations are addressed, leading to the formulation of the filtered Navier-Stokes equations.

The filtered velocity component is represented in the specified direction, alongside the filtered pressure and temperature The influence of small scales is captured in the sub-grid scale (SGS) stress term, which will be modeled accordingly.

Sub -grid scale model

Applying the eddy-viscosity assumption to model the sub-grid scale tensor:

Where is Kronecker symbol if and zero otherwise), is eddy viscosity and

(17) is the strain rate tensor of the resolved scales

This study focuses on the WALE model introduced by Nicoud and Ducros, which is grounded in the square of the velocity gradient tensor The model effectively incorporates both the shear stress tensor and the rotation tensor to enhance its accuracy in fluid dynamics analysis.

Where is deﬁned in this work, is same as

Eq.17 and is defined as:

CFD solver setup

This study utilizes OpenFOAM, a high-quality C++ library, to solve Large Eddy Simulation (LES) equations OpenFOAM leverages Object-Oriented Programming (OOP) principles to address computational continuum mechanics challenges It offers a variety of applications designed to tackle a broad spectrum of problems, particularly in fluid dynamics.

12 this study, OpenFOAM help model and solve unsteady ﬂow with LES equations and heat transfer equations

In this section, I will describe the mesh generation utility, blockMesh, supplied with OpenFOAM

The blockMesh utility is designed to create parametric meshes featuring grading and curved edges by decomposing the domain geometry into one or more three-dimensional hexahedral blocks The edges of these blocks can be defined as straight lines, arcs, or splines, with the mesh specified by the number of cells in each block direction, allowing blockMesh to effectively generate the necessary mesh data The code facilitates control over all geometry parameters, resulting in the generation of 11 blocks that establish a heated region and parallel ducts at the head and tail, ensuring stable flow before entering the critical area.

Figure 5 BlockMesh control parameter code

The structured hexahedral mesh system for this study was created using blockMesh As illustrated in Fig 2-2, the grid system incorporates a bias command to manage mesh density near the heated corrugated plates, gradually decreasing the mesh size near the walls to accommodate the high-velocity gradient.

Figure 6 Structure of the grid system

The boundary setup file, found in the 0 file, includes essential parameters such as temperature, velocity, and pressure conditions, as illustrated in Fig 2-3 These boundary conditions are configured to align with the experimental setup conducted by Naphon [11].

Figure 7 Boundary condition setup ﬁles

The Large Eddy Simulation (LES) governing equation, integrated with a proposed sub-grid scale model, was implemented in OpenFOAM-v7 The PISO algorithm effectively solves the governing differential equations based on the principles of mass, momentum, and energy conservation A second-order approximation is employed to discretize the advection terms within these equations, ensuring accurate results Finally, the output results are averaged for comprehensive post-processing analysis.

14 which is really important with the pulsatile state, a script is created to collect data and calculated the Nusselt number, fanning friction factor, overall thermal performance factor

All simulation cases are executed on a High Performance Computer (HPC) featuring dual Xeon E5 processors and utilizing 48 parallel processors To maintain accuracy, the non-dimensional time between each time step is configured to keep the Courant number below one Each simulation for a single configuration requires approximately 50 to 60 hours of computation on this machine.

Grid dependency test and validation

To assess the sensitivity of the mesh on numerical results, a mesh validation test was conducted using six different configurations ranging from 1.52 to 7.95 million cells The grid resolutions, which are clustered near the heated surfaces, are illustrated in Fig 3-1 The first mesh layer adjacent to the heated walls is maximized for accuracy The average wall temperature results are also presented in Fig 3-1 Based on these findings and the simulated cost analysis, the optimal configuration is determined to be 5.6 million cells.

The Large Eddy Simulation (LES) utilizing the WALE sub-grid scale model is an effective technique for accurately predicting flow behavior in corrugated channels Notably, the WALE model excels at forecasting flow dynamics in proximity to solid walls, making it a valuable tool in fluid dynamics research.

Number of cells (million) Avergare Plate Temperature Mesh # No of elements

The sharp corrugated channel analyzed by Naphon requires validation of its numerical results A comparison is made between the average Nusselt number and the average temperature of the heated plate, as illustrated in Figure 4.

Figure 9 Validation of numerical results with experimental data the compassion between the average plate temperature measured by Naphon

The present study includes experimental tests and numerical results that demonstrate a strong correlation between the average plate temperature and experimental data Additionally, Figure 4 illustrates a comparison of the average Nusselt number from numerical simulations with those from Naphon's experimental work, revealing reasonable agreement between the two sets of data.

Steady ﬂow inside the corrugated channel

In this study, the steady ﬂow inside the corrugated channel is analysis ﬁrst to see the details of the vorticity properties created by the sharp corrugated channels

To understand the flow field behavior in a corrugated channel, it is essential to identify the structures that develop throughout the channel Initial experiments reveal significant insights into these flow dynamics.

Numerous analyses have explored the flow regime in wavy channels, highlighting the challenges of identifying 3D behavior experimentally To investigate the mechanisms of instability growth and the transition from laminar to turbulent flow, the authors employed various techniques for vortex identification These methods primarily focus on local clustering of vortex lines, elongated low-pressure regions, and the second invariant of the velocity gradient tensor, all of which effectively capture vortex signatures In this study, the Q-criterion was utilized to describe vorticity, as illustrated in Figure 10, which presents the 3D iso-surface distribution of the Q-criterion across different Reynolds numbers.

Figure 10 3D iso-surface of Q-criterion with regard to different Reynolds numbers

At ﬁrst glance, the vortex structures developed in the wavy channel ﬂow are significantly dependent on the Reynolds number and wavy period considered For

At a Reynolds number (Re) of 2371, various vortex topologies have been identified, with high vortex intensity first emerging after the flow passes the crests The vortex development along the channel indicates that the flow field becomes unsteady starting from period 3 Similarly, at Reynolds numbers of 3967 and 5379, a consistent trend is observed: as the Reynolds number increases, vortices appear earlier in the flow.

Figure 11 Instantaneous contour of spanwise temperature and vorticity of steady ﬂow

The analysis of flow field fluctuations reveals that the vorticity magnitude is more pronounced at the crests due to the narrowing of the channels, which increases the local Reynolds number As the Reynolds number rises, significant vortices emerge, leading to the disruption and reforming of the thermal layer near the heat walls, thereby enhancing the heat transfer rate Figure 11(c) illustrates that higher Reynolds numbers correlate with stronger heat fluctuations Additionally, the bulk thermal layer close to the heat walls diminishes as the Reynolds number increases, consistent with experimental observations.

Figure 12 Instantaneous contour of heat plate temperature of steady ﬂow

Fig 12 show the instantaneous temperature of heat plate at different Reynolds number range from 2371 to 5379, it is clearly seen that at higher

At high Reynolds numbers, the flow becomes more turbulent, leading to an increased swirl flow that effectively enhances heat removal from heated surfaces, resulting in a decrease in surface temperature.

The effect of pulsating flow

To assess the impact of pulsating inlet flow on overall heat flow characteristics, pulsation was introduced at the inlet The unsteady conditions are regulated by the amplitude of the pulsation and its frequency, which varies accordingly.

The study explores frequency ranges from 0 to 1 Hz and 0 to 25 Hz, which were deliberately constrained to prevent reverse motion in heat exchanger pipes, with a maximum amplitude of 1 chosen for stability Frequencies exceeding 25 Hz require significant power for oscillations The focus of this analysis is not on optimizing amplitude and frequency parameters but rather on illustrating the overall behavior, supported by a series of CFD simulations.

The impact of pulsating flow on flow properties and heat transfer rates was analyzed using a reference case with an amplitude of A=0.8 and frequency f Hz As illustrated in Fig 13, the Nusselt number at steady state in the corrugated channel rises with an increasing Reynolds number Notably, the Nusselt number in corrugated channels consistently surpasses that of straight channels across all phase shift values Furthermore, the enhancement in heat transfer percentage increases as the Reynolds number rises.

Higher Reynolds numbers lead to increased swirl flow intensity and enhanced turbulent intensity in corrugated channels compared to conventional channels In pulsating flow conditions, the average Nusselt number significantly exceeds that of steady flow, although the difference between pulsating and steady flow diminishes slightly as the Reynolds number increases Notably, at a Reynolds number of 2371, the Nusselt number in the corrugated channel is approximately 86% higher, and in the smooth channel, it is about 250% higher.

Figure 13 Variation of Nusselt number with Reynolds number

When designing a heat exchanger, it is crucial to account for pressure drop, which significantly impacts performance The friction factor plays a key role in this consideration, and its relationship with the Reynolds number in various corrugated channels is illustrated in Fig 14.

Figure 14 Variation of fraction factor with Reynolds number

Average Nusselt Number Nu[-] Corrugated channel - Pulsating (A0.8 - f10Hz)

Corrugated channel - Steady Parallel channel - Steady

Corrugated channel - Pulsating (A0.8 - f10Hz) Corrugated channel - Steady

Figure 15 3D iso-surface of Q-criterion with different time state at Reynolds of 2371

The friction factor in parallel channels decreases with increasing Reynolds number, while in corrugated channels, it initially rises sharply from Re 2371 to Re 3370 and only slightly increases beyond Re 370 due to drag forces and turbulence enhancement caused by the corrugated surface In pulsating flow conditions, the friction factor is significantly higher than that of both corrugated and smooth channels, particularly at a Reynolds number of 2371 Overall, the friction factor for smooth channels is several times lower than that of pulsating and corrugated channels.

To clearly depict the effect of pulsating ﬂow, four states of ﬂow at Reynolds equal 2371 need to be demonstrated in three-dimensional iso-contours

Ve lo ci ty 4Time

In the analysis of the Q-criterion, the vortex structures in the pulsating wavy channel flow exhibit notable changes throughout the velocity cycle Initially, during state 1, the vortex structures are relatively small as the velocity magnitude begins to rise from a stagnation point, resulting in a swift flow that primarily generates vortices near the crests As the velocity reaches its peak in state 2, turbulence rapidly develops, particularly in the areas around and beyond the crests In state 3, as the inlet velocity decreases from its maximum, the flow maintains significant momentum, leading to strong turbulence almost immediately upon entering the corrugated section Finally, in the last state, where the inlet velocity is at its minimum, the flow approaches stagnation; however, the residual momentum within the corrugated section continues to mix the boundary layer and core fluid regions.

Figure 16 Comparing instantaneous streamwise velocity for Reynolds of 2371

To compare the influent of pulsating flow and steady flow, the instantaneous velocity, vorticity, and temperature had shown and clearly depicted in Fig 16, 17,

18 As seen in Fig 16 and Fig 17, the ﬂow passes through to the diverging section

In a corrugated channel, the boundary layer separates from both the upper and lower walls due to an adverse pressure gradient This occurs because the momentum of the fluid layer near the wall is insufficient to counteract the pressure recovery in the diverging section of the channel, leading to the formation of recirculation bubbles that interact with the core flow region.

Figure 17 illustrates the vorticity and temperature contours in the midplane (y=0) at four distinct time steps during pulsating flow conditions for A = 0.8 and fp Hz The reference case, without pulsation, shows consistent U main velocity behavior up to the 5th corrugation period, after which the U-contour indicates increased unsteadiness and acceleration regions due to flow and structure development Vorticity contours highlight this structural evolution starting from the 5th corrugation period, which eventually transitions to turbulent flow by the 8th period Pulsating conditions at the inlet enhance flow organization, leading to spatial velocity heterogeneities that generate vortex structures along the channel The pulsation promotes structure formation from the 1st corrugation and induces oscillations over time, contributing to flow destabilization At t=t1, vorticities emerge at the diverging corrugation's edge during acceleration, with structures forming and being shed in the core flow by t=t2 The main flow's deceleration at t=t4 disrupts these structures, coinciding with the flow's lowest velocity, resulting in their dissipation Overall, the pulsating motion at the inlet accelerates transitions by facilitating the creation and dissipation of vortices.

As fluid flows through a corrugated channel, the momentum predominates over pressure recovery in the converging section, causing the boundary layer to adhere to the wall This flow behavior facilitates entrainment between the core flow and recirculation bubbles, along with the shear layer However, instabilities in the shear layer between the core flow and recirculation region promote heat, mass, and momentum exchanges, enhancing heat transfer but also leading to a pressure drop Additionally, the presence of recirculating bubbles contributes to thermal insulation, resulting in lower overall efficiency.

Figure 17 Comparing instantaneous streamwise vorticity for Reynolds of 2371

In a diverging-converging channel, fluid velocity near the wall is significantly lower than in the core flow region, leading to a dramatic decrease in heat transfer rates This flow behavior is consistently observed in each diverging-converging section of the corrugated channel under steady-state conditions, as illustrated in Fig 16.

In pulsating flow conditions, the behavior of velocity vectors changes significantly, leading to enhanced mechanisms for heat, mass, and momentum transfer This phenomenon is illustrated in Figures 16-18, which depict the four distinct states present during pulsating flow.

The digits 1, 2, 3, and 4 illustrate the pulsation period, with the number 1 indicating the start of this cycle The final frames capture the point of lowest velocity within the pulsation Throughout each pulsation period, the spatial structure of the recirculating regions in the diverging and converging sections of the corrugated channel experiences disruption.

In a study of flow dynamics within a corrugated channel, it was observed that recirculating flows at a Reynolds number of 2371 are effectively ejected into the core flow region as high-momentum fluid passes through the channel's minimum cross-section This process facilitates the transfer of high-temperature air into the core flow, while fresh fluid continuously enters the diverging-converging sections to create new recirculating flow bubbles Consequently, this fluid mixing occurs repeatedly during each pulsating period The interaction between the core and recirculating flow regions, along with intense shear layers, significantly influences heat transfer As illustrated in Figure 18, the pulsating flow enhances thermal performance by reducing the thermal boundary layer, unlike the steady-state condition where the core region and heated walls are separated by circulation flow due to the corrugated geometry.

Figure 19 3D comparing instantaneous streamwise vorticity for Reynolds of 2371

Figure 19 presents a 3D comparison of instantaneous streamwise vorticity at a Reynolds number of 2371 This visualization clearly demonstrates that the pulsating flow significantly lowers the temperature of the heated walls, particularly in the affected regions.

The effect of amplitude of pulsating flow

The study investigates the impact of varying amplitude magnitudes, ranging from 0 to 1, on heat transfer performance at a fixed frequency of 10Hz Results indicate that heat transfer efficiency increases, peaking at an amplitude of 0.8 before declining This phenomenon is attributed to enhanced convective effects in the flow field, leading to stronger vortices in the grooves and improved mixing with the mainstream fluid Consequently, the temperature gradient near the wall rises with increasing amplitude, emphasizing the significant role of pulsating amplitude on the heat transfer rate compared to other flow parameters.

Table 1 Effect of amplitude of pulsating ﬂow

Pulsating flow applications primarily aim to enhance heat transfer; however, the impact of pressure drops in such conditions is a crucial aspect in wavy channels Traditional wavy channels significantly increase pressure drops due to the convergent and divergent sections of the flow passages, which inhibit flow transition and lead to higher pressure losses To assess these pressure drops, a dimensionless friction factor is utilized, with Δp representing the average pressure drops of the pulsating nanofluid flow within the wavy channel The relative Fanning friction values are essential for this evaluation.

The impact of pulsating flow amplitude on the friction factor at a constant Reynolds number of 2371 and a frequency of 10Hz is depicted in the figure Notably, the friction factor shows a significant increase with higher pulsating amplitudes The findings indicate that the friction factor reaches its minimum at a specific amplitude level.

The analysis reveals that the heat transfer enhancement in the wavy channel is significantly greater than the associated friction factor penalty, indicating an effective balance between improved heat transfer and pressure drop.

Amplitude AAAAA AverageNuNuNuNuNuNusselt Number Nusselt number

Heat transfer enhancement techniques aim to reduce thermal resistance by either increasing the effective heat transfer surface area or generating turbulence in the fluid flow However, these improvements often lead to increased pumping power, which can raise costs The effectiveness of these techniques is assessed using the Thermal Performance Factor (TPF), a metric that compares the change in heat transfer rate to the change in friction factor To provide an objective selection method, TPF values were estimated, and the heat and pressure loss efficiency of pulsating versus non-pulsating cases were compared to classical parallel wall configurations A TPF value greater than one indicates that the flat wall configuration is more advantageous.

The influence of amplitude on the thermal performance factor (TPF) is significant, as illustrated in Fig 27 At a steady flow with an amplitude of 0, the heat exchange rate doubles (Fig 20); however, this results in a 10% decrease in overall efficiency due to pressure loss As the pulsating amplitude rises, both the heat transfer rate and pressure loss increase, leading to enhanced heat exchange efficiency.

Figure 21 Thermal performance factor for Re#71 at constant frequency 10Hz

The effect of frequency of pulsating flow

This study investigates the impact of frequency on heat transfer, examining six different frequency magnitudes ranging from 0 to 25 while maintaining a constant Reynolds number of 2371 and an amplitude of 0.8 The findings, detailed in Table 2, indicate a consistent increase in the average Nusselt number from 9.581981 to 25.14528 Similarly, the friction factor exhibits a parallel trend, rising from 0.909945 to 2.214732 The thermal performance factor serves as the overall metric for evaluating system efficiency.

2, the maximum heat transfer rate increases 160% compared with the non- pulsating ﬂow, and the overall performance increase 76% compared with the parallel non-pulsating channel

Table 2 Effect of frequency of pulsating ﬂow

Figure 21 demonstrates that increasing the frequency of pulsating flow enhances both the average Nusselt number and the friction factor This increase is attributed to the heightened turbulence caused by higher frequencies, leading to improved heat transfer rates.

At a frequency of 25 Hz, the friction factor significantly influences the pulsating effect in this type of channel, impacting both heat transfer rate and pressure loss Notably, the average Nusselt number, which indicates heat transfer efficiency, increases at a faster rate than the friction factor, particularly in the vicinity of 25 Hz.

Figure 22 Effect of frequency of pulsating ﬂow at ﬁxed Reynolds number of 2371 and amplitude of 0.8

Fig 22 depicts the 3D iso-surface of Q criterion at amplitude = 0.8 and frequency -

= 25 for Reynolds of 2371 Compared with the result of the case of frequency of

In a channel with a frequency of 25 and an amplitude of 0.8, the flow exhibits increased turbulence Initially, at time t = t1, the inlet velocity begins to rise, causing vorticities to move towards the outlet By time t = t2, as the inlet velocity peaks, turbulence is expelled from the channel; however, new, intense turbulence forms after the flow navigates the crests of the corrugated channel This process generates vorticity within the channel, and as time progresses to t = t3, the velocity decreases, allowing vorticity to develop further in the divergent-convergent sections of the corrugated channel.

At time t = t4, the inlet velocity is at its lowest, leading to significant turbulence in the channel's divergent-convergent sections This turbulence facilitates optimal mixing between the air layer adjacent to the heated wall and the core flow By controlling the frequency, vorticity is effectively managed, resulting in a substantial increase in the heat transfer rate.

Figure 23 3D iso-surface of Q-criterion at amplitude = 0.8 and frequency = 25 for

Figures 23 and 24 depict the instantaneous velocity and vorticity at a Reynolds number of 2371, with a frequency of 25 Hz and an amplitude of 0.8 Notably, as frequency increases, the time required for velocity to transition from its peak to its lowest point decreases.

23 Moreover, the velocity change continuously helps us control the occurrence of turbulence at specific positions (Figure 24) At time t = t1 to time t = t2, as the

As the velocity increases, the local Reynolds number rises, leading to intensified flow velocity at the crests However, when the velocity decreases, turbulence becomes trapped in the divergent-convergent sections of the corrugated channel, affecting the heat exchange duration with the hot wall.

Figure 24 Instantaneous streamwise velocity for Reynolds of 2371 frequency 25

Figure 25 Instantaneous streamwise vorticity for Reynolds of 2371 frequency 25

Here is a rewritten paragraph that captures the meaning of the original content, complying with SEO rules:"Optimizing heat transfer efficiency can be achieved by setting the Hz frequency to 0.8 amplitude, resulting in a longer and more efficient process By employing the forced convection method, turbulence is generated, creating a robust convection zone that facilitates enhanced heat exchange between the hot wall surface and the core flow, mirroring the expected behavior."

Stirring a glass of hot water significantly accelerates its cooling process, while an unstirred glass retains heat for a longer duration.

Figure 26 Instantaneous streamwise temperature for Reynolds of 2371 frequency

The method of forced convection is illustrated through the temperature distribution shown in Figures 25 and 26 The frequency effectively regulates areas of strong vorticity, leading to enhanced convection in divergent-convergent positions As a result, the temperature in the near head zone is significantly lower compared to a non-pulsating flow.

The influence of frequency on the thermal performance factor (TPF) is significant, particularly when compared to amplitude effects With a fixed amplitude of 0.8, it is observed that TPF increases most rapidly at frequencies below 15Hz Beyond this threshold, the rate of increase in TPF diminishes, reaching its peak at 25Hz This indicates that frequency plays a more crucial role in enhancing thermal performance than amplitude.

Figure 27 3D instantaneous temperature with 4 different time state at Reynolds of 2371 frequency 25 Hz amplitude 0

Figure 28 Thermal performance factor for Re#71 at constant amplitude A=0.8

This study employs a 3D numerical analysis using the LES turbulence model to explore heat transfer performance in a corrugated channel, comparing pulsating and steady flow cases across a frequency range of 0 to 25 and Reynolds numbers from 2000 to 6000 Additionally, the research thoroughly examines the 3D iso-surface of the Q-criterion, which illustrates turbulence properties and enhances heat transfer Key conclusions highlight the significant findings of this investigation.

The heat enhancement factor (TPF) reaches a maximum value of 1.76 in a corrugated channel, observed at a Reynolds number of Re#71, with a frequency of 25 and an amplitude of 0.8.

Here is a rewritten paragraph that captures the essence of the original content, optimized for SEO:"In steady flow cases, the flow phenomenon, characterized by the interruption of the thermal boundary layer, flow separation, and entrainment between the separated region and the main flow through the shear layer, enhances the heat transfer rate However, this phenomenon comes at a cost, as the thermal performance factor decreases by 10%."

The average heat transfer rate enhances up to a certain level with increasing the frequency of pulsation The frequency controls the strong convection position for boost heat transfer rate

[1] N Kurtulmuş, B Sahin, A review of hydrodynamics and heat transfer through corrugated channels, Int Commun Heat Mass Transf 108 (2019) https://doi.org/10.1016/j.icheatmasstransfer.2019.104307

[2] E.A.M Elshafei, M Safwat Mohamed, H Mansour, M Sakr, Experimental study of heat transfer in pulsating turbulent flow in a pipe, Int J Heat Fluid

Flow 29 (2008) 1029 1038 – https://doi.org/10.1016/j.ĳheatfluidflow.2008.03.018.

[3] M.A Habib, A.M Attya, A.I Eid, A.Z Aly, Convective heat transfer characteristics of laminar pulsating pipe air flow, Heat Mass Transf Und

[4] M.M Ali, S Ramadhyani, Experiments on convective heat transfer in corrugated channels, Exp Heat Transf 5 (1992) 175–193 https://doi.org/10.1080/08916159208946440

[5] Y Islamoglu, C Parmaksizoglu, Numerical investigation of convective heat transfer and pressure drop in a corrugated heat exchanger channel, Appl

Therm Eng 24 (2004) 141 147 – https://doi.org/10.1016/j.applthermaleng.2003.07.004

[6] Y Islamoglu, A Kurt, Heat transfer analysis using ANNs with experimental data for air ﬂowing in corrugated channels, Int J Heat Mass Transf (2004) https://doi.org/10.1016/j.ĳheatmasstransfer.2003.07.031

[7] N Ghaddar, A El-Hajj, Numerical study of heat transfer augmentation of viscous ﬂow in corrugated channels, Heat Transf Eng 21 (2000) 35 46– https://doi.org/10.1080/01457630050127937

[8] G Comini, C №nino, S Savino, Effect of aspect ratio on convection enhancement in wavy channels, Numer Heat Transf Part A Appl 44 (2003)

[9] S.D Hwang, I.H Jang, H.H Cho, Experimental study on ﬂow and local heat/mass transfer characteristics inside corrugated duct, Int J Heat Fluid

Flow 27 (2006) 21 32 – https://doi.org/10.1016/j.ĳheatﬂuidﬂow.2005.07.001

[10] P Naphon, Laminar convective heat transfer and pressure drop in the corrugated channels, Int Commun Heat Mass Transf 34 (2007) 62–71 https://doi.org/10.1016/j.icheatmasstransfer.2006.09.003

[11] P Naphon, Heat transfer characteristics and pressure drop in channel with

V corrugated upper and lower plates, Energy Convers Manag 48 (2007)

[12] U Akdag, S Akcay, D Demiral, Heat transfer enhancement with laminar pulsating nanoﬂuid ﬂow in a wavy channel, Int Commun Heat Mass

Transf 59 (2014) 17 23 – https://doi.org/10.1016/j.icheatmasstransfer.2014.10.008

[13] T.K Nandi, H Chattopadhyay, Numerical investigations of simultaneously developing ﬂow in wavy microchannels under pulsating inlet ﬂow condition, Int Commun Heat Mass Transf 47 (2013) 27 31 – https://doi.org/10.1016/j.icheatmasstransfer.2013.06.008

[14] M Sakr, Convective heat transfer and pressure drop in V-corrugated channel with different phase shifts, Heat Mass Transf Und Stoffuebertragung 51

[15] P Naphon, K Kornkumjayrit, Numerical analysis on the ﬂuid ﬂow and heat transfer in the channel with V-shaped wavy lower plate, Int Commun Heat

Mass Transf 35 (2008) 839 843 – https://doi.org/10.1016/j.icheatmasstransfer.2008.03.010

[16] C Maradiya, J Vadher, R Agarwal, The heat transfer enhancement techniques and their Thermal Performance Factor, Beni-Suef Univ J Basic Appl Sci 7 (2018) 1–21 https://doi.org/10.1016/j.bjbas.2017.10.001

[17] M V Pham, F Plourde, S.K Doan, Turbulent heat and mass transfer in

41 sinusoidal wavy channels, Int J Heat Fluid Flow 29 (2008) 1240–1257 https://doi.org/10.1016/j.ĳheatﬂuidﬂow.2008.04.002

[18] F Nicoud, F Ducros, Subgrid-scale stress modelling based on the square of the velocity gradient tensor, Flow, Turbul Combust 62 (1999) 183 200 – https://doi.org/10.1023/A:1009995426001

[19] T.O Foundation, The OpenFOAM 7 User Guide, (2014) 212.

[20] O Ben-Nasr, A Hadjadj, A Chaudhuri, M.S Shadloo, Assessment of subgrid-scale modeling for large-eddy simulation of a spatially-evolving compressible turbulent boundary layer, Comput Fluids 151 (2017) 144–

The article titled "Investigation of Subgrid-Scale Models in Large Eddy Simulation on the Unsteady Flow Around a Hydrofoil Using OpenFOAM" by A Bel Hadj Taher et al explores the application of subgrid-scale models in large eddy simulations It focuses on analyzing the unsteady flow dynamics around a hydrofoil, utilizing OpenFOAM as a computational tool This research contributes to the understanding of fluid dynamics in engineering applications, particularly in the context of hydrofoil performance.

[22] M Weickert, G Teike, O Schmidt, M Sommerfeld, Investigation of the LES WALE turbulence model within the lattice Boltzmann framework, Comput Math with Appl 59 (2010) 2200 2214 – https://doi.org/10.1016/j.camwa.2009.08.060

[23] E.A.M Elshafei, M.M Awad, E El-Negiry, A.G Ali, Heat transfer and pressure drop in corrugated channels, Energy 35 (2010) 101 110 – https://doi.org/10.1016/j.energy.2009.08.031

[24] H Pehlivan, I Taymaz, Y Islamoǧlu, Experimental study of forced convective heat transfer in a different arranged corrugated channel, Int Commun Heat Mass Transf 46 (2013) 106–111 https://doi.org/10.1016/j.icheatmasstransfer.2013.05.016

[25] N Tokgoz, B Sahin, Experimental studies of ﬂow characteristics in corrugated ducts, Int Commun Heat Mass Transf 104 (2019) 41–50 https://doi.org/10.1016/j.icheatmasstransfer.2019.03.003

[26] N Kurtulmuş, B Sahin, Experimental investigation of pulsating flow

42 structures and heat transfer characteristics in sinusoidal channels, Int J Mech Sci 167 (2020) https://doi.org/10.1016/j.ĳmecsci.2019.105268

\\ / F ield | OpenFOAM: The Open Source CFD Toolbox

\\ / O peration | Website: https://openfoam.org

{ version 2.0; format ascii; class dictionary; object blockMeshDict;

P 0.02727; // Length of distant/pitch h 0.005; // Height of the wavy

H 0.015; // Mean hight of the channel

W 0.13; // width of the channel halfP #calc "($P/2)";

Hi #calc "($H-$h)"; gridx 28; // number of cells in x direction gridy 140; // number of cells in y direction gridz 60; // Number of cells in z direction

// head block hex (92 0 3 93 94 4 7 95) ($gridx $gridy $gridz) simpleGrading

//tail block hex (88 96 97 89 90 98 99 91) ($gridx $gridy $gridz) simpleGrading

) hex (0 1 2 3 4 5 6 7) ($gridx $gridy $gridz) simpleGrading

) //(1 10 0.1) hex (1 8 9 2 5 10 11 6) ($gridx $gridy $gridz) simpleGrading

48 hex (16 20 21 17 18 22 23 19) ($gridx $gridy $gridz) simpleGrading

{ version 2.0; format ascii; class dictionary; location "constant"; object turbulenceProperties;

LESModel WALE; turbulence on; printCoeffs on; delta cubeRootVol; dynamicKEqnCoeffs

{ version 2.0; format ascii; class dictionary; location "system"; object fvSchemes;

{ default none; div(phi,U) Gauss linearUpwind grad(U);

Tiêu đề	Heat Transfer Optimization Of Pulsating Flow In Corrugated Channel
Tác giả	Hoang Van Quan
Người hướng dẫn	PhD. Dinh Cong Truong
Trường học	Hanoi University of Science and Technology
Chuyên ngành	Mechanical Engineering
Thể loại	master thesis
Năm xuất bản	2020
Thành phố	Ha Noi

Định dạng
Số trang	70
Dung lượng	10,87 MB