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Experimental study on the unsteady laminar heat transfer downstream of a backwards facing step
... Current researches suggest that single-phase pulsating flow is beneficial for the application of industry and medicine [9,[19][20][21][22][23][24][25]. The investigation of single-phase pulsating flow involves many aspects, including laminar pulsating flow in different kind of channels , pulsating cross-flow through a cylinder or other objects , pulsating flow through porous media in pipes [104][105][106][107][108][109][110][111][112][113][114][115], single-phase nanofluid pulsating flow [130][131][132][133][134][135][136][137][138][139][140][141][142][143], and pulsating flow around ribs [144][145][146][147]. Fig. 4 shows different typical single-phase pulsating flows that have been studied. These studies are carried out by theoretical, numerical and experimental methods. ...
... The method of heat transfer enhancement by pulsating flow of nanofluids has been adopted by many scholars. The present studies are focus on the effect of different shaped particles, different volume fraction and different geometry to pulsating flow heat transfer [130][131][132][133][134][135][136][137][138][139][140][141][142][143]. Heat transfer enhancement is achieved ideally by using this kind of composite method. ...
... Terhaar et al. [138] conducted an experimental study on the oscillatory heat transfer downstream of the backward step in laminar flow pulsations. The experimental Reynolds number is 300. ...
This paper introduced the research status of pulsating flow, including different types of pulsating flow and their enhancement of heat transfer, as well as the enhancement effects of composite heat transfer technology which is synergized with other heat transfer technologies. Firstly, the most widely studied single-phase laminar pulsating flow was introduced, it suggested that the performance of reciprocating flow is more stable than unidirectional flow. Then the research status of two-phase pulsating flow was presented, high frequency two-phase pulsating flow is beneficial for heat transfer. Finally, the research status of intermittent jet was introduced, jet impingement may be a better approach collaborate with pulsation. Different research teams have studied the effects of different parameters on the enhancement of flow and heat transfer, including the direction, waveform, amplitude, frequency of the pulsating flow, and other parameters, such as heat transfer coefficient, porous medium type, volume fraction of nanofluid, CHF, etc. And it is pointed out that the mechanism of pulsating flow has not been fully revealed. There is also a need for further research to investigate parameters that influence pulsating flow and the effect of heat transfer.
... Other examples in which flow pulsation makes no difference have been reported by Mackley and Stonestreet [8], Chattopadhyay et al. [9], and Liu et al. [10]. Yet, other examples in which pulsation enhances heat transfer but its extent depends on the pulsation frequency and/or amplitude have been presented by Velazquez et al. [11], Velazquez et al. [12], Terhaar et al [13], Moo et al. [14], Suksangpanonrung et al. [15], Al-Sumaily and Thompson [16], Ji et al. [17], Selimefendigil and Oztop [18], Wantha [19], Akdag et al. [20], Dey et al. [21], Mulcahey et al. [22], and Yu et al. [23]. In these 13 last references [11][12][13][14][15][16][17][18][19][20][21][22][23], it is worth noting two important aspects. ...
... Yet, other examples in which pulsation enhances heat transfer but its extent depends on the pulsation frequency and/or amplitude have been presented by Velazquez et al. [11], Velazquez et al. [12], Terhaar et al [13], Moo et al. [14], Suksangpanonrung et al. [15], Al-Sumaily and Thompson [16], Ji et al. [17], Selimefendigil and Oztop [18], Wantha [19], Akdag et al. [20], Dey et al. [21], Mulcahey et al. [22], and Yu et al. [23]. In these 13 last references [11][12][13][14][15][16][17][18][19][20][21][22][23], it is worth noting two important aspects. First: flows with large separation regions were involved in a number of them, which suggests that flow pulsation may, on the spatial and temporal average, decrease the size of the low velocity separated flow regions; thereby increasing heat transfer. ...
... 13 show the different temperature field regions. Of special interest are the regions surrounding the prism and close to the channel walls. ...
This 3D study deals with the effect that a low Reynolds number (Re) pulsating water flow has on both the heat transfer to the walls of a square section channel in which a square section prism was located, and the associated pumping power. The prism blockage ratio was 2.5/1. Re, based on the prism cross-section height, varied from 100 up to 200. The inflow velocity profile was sinusoidal. Taking St0 as the Strouhal number of the vortex shedding downstream of the prism at Re 100, the inflow Strouhal of the pulsating cases varied between 0.125 St0 and 4 St0. The results show that, for this particular geometry and parametric space, flow pulsation generally enhances heat transfer although its extent depends on Re and pulsation frequency. In the most favorable case, heat transfer doubles as compared to the clean channel case at the expense of tripling the pumping power.
... In another study, experimental measurements of Terhaar et al. [14] proved that superimposing pulsation on the mean flow can enhance the heat exchange in a backward-facing step as compared to an equivalent steady-state case. ...
... Meanwhile, the incoming fluid temperature and the flow Reynolds number are 303 K and 300, respectively. The results of this problem in terms of time evolution of pressure for f = 10 Hz are compared with experimental evidences of Terhaar et al. [14] in Fig. 5. Attention to this figure expresses that the results of the Eulerian-Eulerian approach in unsteady conditions are in good agreement with the experimental data. ...
... Comparing the results of the Eulerian-Eulerian model with the those of Kherbeet et al.[7] in a backward-facing step. Comparing the results of the Eulerian-Eulerian model with experimental evidences of Terhaar et al.[14] for pulsating water flow downstream of a backward-facing step. ...
In this paper, unsteady flow and heat transfer of water flow in a backward-facing step under pulsating nanofluid blowing are studied numerically. Attention is focused to examine the impact of this type of blowing and its pertinent parameters on the heat transfer performance and to detect possible non-equilibrium between the base fluid and the nanoparticles inside the flow field. To this aim, the Eulerian-Eulerian two-phase model is adopted. This approach consists of separate equation sets for the base fluid and the nanoparticles. So, it provides details of the flow field for each of the constituents, separately. Computations are undertaken for different cases and the consequences of the frequency, amplitude, and the mean velocity of the pulsating blowing as well as the type, diameter, and the volume fraction of the nanoparticles therein on the heat transfer characteristics are analyzed. It is found that in addition to thermal conductivity of the blown nanoparticles, their penetration into the water flow is an important trait that has a momentous role on the heat transfer rate. In the current Eulerian-Eulerian simulation, temperature distributions of the base fluid and the nanoparticles are similar but the corresponding velocity fields are quite distinct. This reveals a kind of non-equilibrium between the base fluid and the nanoparticles inside the flow that invalidates equilibrium approaches (e.g., the single-phase model or the two-phase mixture model) for the description of the problem.
... Certain heat transfer devices, such as those used to cool reactors and electronic components, cooling channels, combustion chambers, and many other heat transfer surfaces, can be optimized by taking into account the friction coefficient near the shoulder, which is common for flows through backward-facing steps [6][7][8][9][10][11]. Yaseen et al. [12] reported on the heat transfer of a heated cylinder into a backward-step channel through mixed convection and fluid-structure interaction (FSI). ...
... Nonetheless, the recirculation zone is extended if the inserts are short and highly porous. Terhaar et al. [13] experimentally investigated pulsating laminar unsteady heat transfer through a backward-facing channel. They found a rise in the Nusselt number up to a certain value of Strouhal numbers and degradation with the increase in the frequency of pulsation. ...
Many engineering device, including nuclear reactors, heat exchangers, and electronic circuit boards, exhibit flow separation and reattachment. To reduce thermal stress impacts, the components of these devices, which resemble stepped channel designs and are susceptible to high heat flux, must be properly cooled. The present work numerically investigates the fluid flow and heat transfer characteristics through a double backward-facing step with elliptic obstacles located after each step. For this purpose, equations governing fluid flow and heat transfer are solved in a Cartesian framework using an in-house code based on streamline upwind/Petrov-Galerkin finite element method. The effect of various parameters (axis ratios (0.25, 0.5, 0.75, 1), vertical location of obstacles (0.38, 0.577, 0.769), Reynolds number (300, 500, 800, 1000)) on fluid flow and heat transfer characteristics in the channel with and without obstacles are compared and quantified. The recirculation region length of the double backward-facing stepped channel with obstacles decreases after the first and second steps when compared with no obstacles. The local Nusselt number distribution along the corner regions of the stepped wall is enhanced due to obstacles. The axis ratio of obstacles has less influence on the convective heat transfer enhancement than the vertical location of the obstacles.
... His results indicated that the influence of both Reynolds number and the expansion ratio on entropy generation was certain. Terhaar et al. [6] were concluded experimentally an increasing in the Nusselt number of the laminar heat transfer in a Backward facing step horizontal channel. ...
The current work focuses on the experimental research of a vapor compression cycle using Polyol
Oil Ester (POE) with nano copper oxide (CuO) and a fluidized bed for condenser cooling to
enhance its performance. The efficiencies of the modified and normal systems using only POE oil
have been compared to present the actions of using nano CuO and a fluidized bed. Three volume
fractions of CuO 0.1%, 0.3%, and 0.5% have been used. The fluidized bed contained a uniform
particle size (0.5 mm) to sink heat from the condenser, where the bed height was 2.5 mm to get
good mixing of particles. The experiment outcomes indicated that adding nanoparticles to the
lubricant and using a fluidized bed for condenser cooling improves the refrigeration system’s
performance. The results demonstrated that employing nano-lubricant (POE oil+0.5% CuO)
rather than just POE oil boosted the coefficient of performance of the system by approximately
15.96% while reducing power consumption by 50%. Also, the refrigeration impact was raised,
and the compressor’s performance was reduced with the volume fractions of CuO rising.
... His results indicated that the influence of both Reynolds number and the expansion ratio on entropy generation was certain. Terhaar et al. [6] were concluded experimentally an increasing in the Nusselt number of the laminar heat transfer in a Backward facing step horizontal channel. ...
Convective of hybrid nanofluids heat transfer flow over backward facing step in a heated rectangular duct under laminar flow is performed experimentally. It is used mixing of Al2O3 and TiO2 solid nanoparticles suspended in pure water. The preparation process of hybrid nanofluid for 1%, 2% and 3% mass fraction has been conducted. The test rig of this experimental study has been fabricated then both temperature and pressure drop along the duct have been measured. The duct is heated from the bottom by using an electrical heater and the other walls are being insulated. Results of heat transfer enhancement and pressure drop are indicated. It was observed that Nusselt number increases with increase of Reynolds number and mass fraction while, friction factor decreases as decrease of Reynolds number and increase of mass fraction. It is concluded that significant using the hybrid nanofluid through facing step. The enhancement of heat transfer and pressure drop are approximately 14% and 4% respectively.
... A review of the literature suggests that the pulsating flow on the backward-facing step has also been of interest to some researchers. Terhaar et al. [125] investigated the effect of the pulsating flow on a backward-facing step. Their analysis showed that applying the pulsating inlet flow can improve the heat exchange efficiency compared with the steady-state conditions. ...
In this review, an overview of pulsating flows with and without heat transfer is done. In addition to conventional fluids, the effects of using nanofluids are investigated. Using nanofluids instead of conventional fluids and application of pulsating flows instead of steady flows are two efficient approaches in increasing heat transfer. The impact of parameters such as nanofluid volume fraction, nanofluid type, pulsating frequency and amplitude, and Reynolds number on thermal and hydraulic attributes of pulsating flows are reviewed. The studies performed reveal a promising view to reach superior thermohydraulic characteristics by combining pulsating flows and nanofluids. With increasing the Reynolds number, the axial velocity increases, and thus, nanofluid mixing intensifies. This augments the mixing of hot fluid adjacent to walls and inlet cold fluid, and therefore, the rate of heat transfer improves. The researchers have used nanofluids in the form of metal oxide nanoparticles/water more than other nanofluids in this area. According to the fact that agglomeration of the nanoparticles has often been a serious problem in using nanofluids, employing pulsation in flows can significantly reduce occurrence of this problem and improve the stability of nanofluids. The existing challenges are introduced and future research requirements are recognized and projected.
... Laminar and turbulent flow in a backward-facing step channel have been extensively investigated using experimental [4][5][6][7] and numerical methods [8][9][10][11][12][13][14]. Additionally, threedimensional backward-facing step flow has become a popular field of study in fluid dynamics since Armaly et al. proposed the advancement of this method [4]. ...
In this study, the forced convection characteristics of transitional fluid flow and heat transfer enhancement in a two-dimensional, backward-facing step channel by inserting an adiabatic cylinder were numerically investigated. The computational fluid dynamics simulations were performed using finite volume method in the commercial package Ansys Fluent. The effects of various streamwise positions (X C /S = 0.6, 0.9, 1.2, and 1.5) and cross-stream positions (Y C /S = 0.5, 1.0, and 1.5) of the cylinder were examined for a fixed diameter of the inserted cylinder (d/S = 0.4). As per the results, a 114% enhancement of the overall heat transfer on the bottom wall could be achieved by inserting an adiabatic cylinder at X C /S = 0.6 and Y C /S = 1.0 as compared with the case without the cylinder. Additionally, the insertion of a cylinder significantly diminishes the deterioration of heat transfer in the primary recirculation zone.
... A harmonically varying pressure gradient is imposed and it was observed that the unsteady part of Nusselt number varies with higher values of dimensionless frequencies. In the experimental work of Terhaar et al. [6], unsteady heat transfer characteristics with pulsed inflow was examined for a backward facing step geometry. It was observed that the Nu number versus frequency of pulsation shows a resonant type behavior. ...
In this study, performance assessment of a thermoelectric generator module located in between two channels where carbon-nanotube/water nanofluid streams flow is studied with combined effects of nanoparticle inclusion and flow pulsations. The finite element method is used to solve the 3D unsteady coupled fluid flow, heat transfer and electric field equations. Different pertinent parameters effects such as Reynolds number (between 250 and 1000), nanoparticle volume fraction (between 0 and 0.04), pulsating flow frequency (Strouhal number between 0.01 and 0.1) and amplitude (between 0.25 and 0.95) on the power generation are examined. It is observed that flow pulsation changes the dynamic features of thermoelectric power generated in the device. Higher power values are obtained when Reynolds number, flow pulsation amplitude and nanoparticle solid volume fraction rise. However, the effect is reverse for higher pulsation frequencies. Including nano sized particles further enhances the performance of the device with flow pulsation. It is also observed that 24.4% enhancement in the power are achieved for nanofluid with flow pulsation when lowest and highest pulsation amplitudes are compared. At lowest pulsation frequency and highest amplitude 14.2% enhancement in power is obtained for water as compared to steady flow case while this amount rises to 31% for carbon nanotube nanofluid at the highest solid volume fraction. System identification method is used to obtain dynamic lower order model of the system for different pulsation amplitudes to predict the time dependent power generated in the thermoelectric generator device.
... The outcomes showed an increase in the heat transfer coefficient at the separation zone and a decrease in pressure drop. In another investigation by Terhaar et al. [8], pulsating laminar heat transfer through a BFS channel was studied experimentally. They found a rise in the Nusselt number at specific Strouhal numbers. ...
This paper reports a numerical study on heat transfer improvement in a double backward-facing expanding channel using different convectional fluids. A finite volume method with the k-ε standard model is used to investigate the effects of step, Reynolds number and type of liquid on heat transfer enhancement. Three types of conventional fluids (water, ammonia liquid and ethylene glycol) with Reynolds numbers varying from 98.5 to 512 and three cases for different step heights at a constant heat flux (q = 2000 W/m2) are examined. The top wall of the passage and the bottom wall of the upstream section are adiabatic, while the walls of both the first and second steps downstream are heated. The results show that the local Nusselt number rises with the augmentation of the Reynolds number, and the critical effects are seen in the entrance area of the first and second steps. The maximum average Nusselt number, which represents the thermal performance, can be seen clearly in case 1 for EG in comparison to water and ammonia. Due to the expanding of the passage, separation flow is generated, which causes a rapid increment in the local skin friction coefficient, especially at the first and second steps of the downstream section for water, ammonia liquid and EG. The maximum skin friction coefficient is detected in case 1 for water with Re = 512. Trends of velocities for positions (X/H1 = 2.01, X/H2 = 2.51) at the first and second steps for all the studied cases with different types of convectional fluids are indicated in this paper. The presented findings also include the contour of velocity, which shows the recirculation zones at the first and second steps to demonstrate the improvement in the thermal performance.
... Forced convection over facing steps is used in many studies to represent the flow separation and its subsequent reattachment features. There are many experimental, numerical and analytical studies available in the literature dedicated to identify the essential features of fluid flow and convective heat transfer for flow over step geometry [1][2][3][4][5][6][7][8] . In the work of Abu-Mulaweh [9] , review for the applications of laminar mixed convection for flow over facing step geometry in various configurations is presented. ...
In this study, a novel method for convective heat transfer control of flow past a double backward facing step with combined effects of oriented magnetic field, rotating tube bundle and inclusion of highly conductive CNT nanoparticles in the base fluid is offered. Hydro-thermal performance assessment of double backward facing step is numerically performed with finite volume method in laminar flow regime. Effects of Reynolds number, rotational Reynolds number, circular cylinder arrangement and horizontal local of the tube bundle, distance between the steps and magnetic field strength on the fluid flow, heat transfer, pressure drop and hydro-thermal performance coefficient variation are examined. The rotation of the cylinder, arrangement and location were found to alter hydro-thermal performance while the average Nu is enhanced with higher Reynolds and Hartmann numbers. The presence of the upper vortex location resulted in higher deflection of the main stream toward the hot bottom wall which resulted in higher local heat transfer rates. This is especially the case for clockwise direction rotation at the height speed and local Nu value increment is 244% as compared to non-rotating cylinder case. Best performance coefficient is obtained with MHD flow at Hartmann number of 5 while performance increase is 13% as compared to non-magnetic field configuration. The vertical size and location of the upper vortex changes with the horizontal location of the tube bundle and spacing between the steps. As compared to reference configurations, variations in the hydrothermal performance coefficients are 15% and 20% when varying the horizontal location and distance between the steps. The CNT nanoparticles inclusion in the base fluid resulted in performance coefficient enhancement of 52% at the highest solid volume fraction. As flow separation and subsequent attachments are encountered in a variety of heat transfer engineering applications, the results of the present work will be helpful in the design and optimization of various thermal engineering systems.
... In the study by [2] an experimental analysis for the flow over a BFS geometry was performed by using Laser-Doppler measurement and distribution of velocity and reattachment length were reported for the two dimensional configuration.In the experimental work of Terhaar et al. [3] flow pulsation effects are investigated for two dimensional laminar case for the Reynolds number of 300 and Strouhal number up to 1.2. A resonant type behavior for the average Nusselt number versus Strouhal number is obtained. ...
In this study, local curvature effects of upper wall on the separated flow and heat transfer features are numerically examined for a layered channel which contains porous and nanofluid (CNT-water) layers with sudden area expansion under the magnetic field effects. Finite volume method was used for the numerical simulations and impact of different pertinent parameters such as Reynolds number (between 100 and 400), Hartmann number (between 0 and 20), local curvature of the upper wall (r1 between 2H and 10H, r2 between 0 and 2H), porous medium Darcy number (between 10−4 and 5×10−2), size of the porous layer (between H and 20H) on the convective heat transfer features are numerically analyzed. A novel multi-domain POD approach was used for estimation of flow variables and heat transfer rate. It was observed that the heat transfer rate is enhanced with higher values of Reynolds number, Hartmann number and Darcy number. The peak value and the average value of Nusselt number increase by about 12.86% and 22.48% magnetic field effects at Ha=20 when compared to case without magnetic field.There is slight impact of the porous layer size on the fluid flow and heat transfer. However, impact of the curvature of the upper wall on the convective heat transfer feature is significant. The maximum value of local Nusselt number increases up to 4.76 times and therefore it can be used an excellent tool for convective heat transfer control.
... Two methods have been chosen for periodical pulsation of flow rate: an electrical method and a mechanical one. The electrical method means to use a frequency converter to change the rotation speed of the centrifugal pump in a regular way [5,18,19,22]. The mechanical method means to use a piston equipment to force the flow rate change periodically [12,13,23,24]. ...
An experimental research was conducted to study the effects of non-reversing pulsating flow on subcooled boiling heat transfer performance on a chip using FC-72 in a horizontal rectangular narrow channel with a hydraulic diameter of 8.57 mm. The associated bubble characteristics were also analyzed. In the experiment, the pulsating period varied from 3 s to 20 s with the pulsating amplitude changing from 20% to 50% for the inlet liquid subcooling of 35 K. The result indicates that time-average boiling curves under pulsating flow overlapped with that under steady flow, and the heat transfer coefficient was not affected by flow pulsation. The critical heat flux (CHF)decreased compared with that under time-average steady flow, and the decrease would be further aggravated with the increases of the pulsating amplitude or the decrease of the pulsating period. The CHF under pulsating flow was limited by the lowest flow rate. Bubble behavior changed periodically with the flow rate, and bubble accumulation effect under pulsating flow was found. There was no slide process during bubble growth, and the bubbles near the CHF tended to be bigger and more round-like with no obvious deformation. This phenomenon was caused by the virtual mass force acting on the bubble due to fluid acceleration.
... The flow separation and its subsequent reattachment appear clearly in case of the flow over a backward facing or forward facing step. Massive amount of numerical and experimental research work has been considered [30][31][32][33][34][35][36][37]. In addition, Yılmaz and Öztop [38] studied numerically using the commercial code FLUENT, the turbulent heat transfer by forced convection in double forward facing step flow. ...
In this paper, the unsteady magnetohydrodynamic forced convection of -water ferrofluids inside the backward facing step benchmark is investigated. A rotating cylinder with fixed dimensions is located inside the flow domain and one phase model is used to simulate the ferrofluid. The dimensionless governing equations are discretized using the Galerkin finite element method in space and the Crank-Nicolson scheme in time. The discrete system of equations in each time level is treated with the help of Newton's method and the resulting linearized problems are computed using multigrid approach. Wide ranges of the governing parameters are considered such as the Hartmann number , the magnetic field inclination angle , the angular velocity , the Reynolds number and the nanoparticle volume fraction . It is observed that the average Nusselt number and lift coefficient are enhanced by the increase in either nanoparticle volume fraction or Reynolds number, while the drag coefficient takes its minimum in case of the fixed cylinder (). In addition, the lift coefficient takes its minimum at value of the magnetic field inclination angle equals . Moreover, the electromagnetic force slowdown the ferrofluid flow but the drag coefficient is enhanced. Also, the average Nusselt number decreases with ratio 53.12\% as the Hartmann number increases from 0 to 100.
... A vast amount of literature is dedicated to that subject either numerically [6,7,16,30,32,33] or experimentally [2,4,37,39]. 3D linear stability analysis of flow over a backwardfacing step for Reynolds numbers between 450 and 1050 was studied in [7]. Velocity distribution and reattachment length using Laser-Doppler measurement for flow downstream of a backward facing step in a two-dimensional channel was reported in [4]. ...
In the current study, numerical investigation of pulsating magnetohydrodynamic mixed convection over a backward facing step is carried out for the range of parameters; Reynolds number (25 ≤ Re ≤ 100), Hartmann number (0 ≤ Ha ≤ 60), Strouhal number (0:1 ≤ St ≤ 1) and Gr number is kept at Gr = 104. The governing equations are solved with a general purpose finite element based solver. The effects of various parameters on the fluid flow and heat transfer characteristics are numerically studied. It is observed that the flow field and heat transfer rate are influenced by the variations of Reynolds, Hartmann and Strouhal numbers. Furthermore, recurrence plot analysis is applied for the analysis of the time series (spatial averaged Nusselt number along the bottom wall downstream of the step) and for a combination of different parameters, the systems are identified using recurrence quantification analysis parameters including recurrence rate, laminarity, determinism, trapping time and entropy.
... A numerical study of 3D linear stability analysis of flow over a backward-facing step for Reynolds numbers between 450 and 1050 was presented in Ref. [8]. Experimental studies have also been conducted for the flow over a backward-facing or forward-facing step [9][10][11][12][13]. When pulsations are applied to the flow system, heat transfer may be enhanced due to the change of the thickness of the boundary layer and thus the thermal resistance [14][15][16][17]. ...
In the present study, laminar pulsating flow over a backward-facing step in the presence of a square obstacle placed behind the step is numerically studied to control the heat transfer and fluid flow. The working fluid is air with a Prandtl number of 0.71 and the Reynolds number is varied from 10 and 200. The study is performed for three different vertical positions of the square obstacle and different forcing frequencies at the inlet position. Navier-Stokes and energy equation for a 2D laminar flow are solved using a finite-volume-based commercial code. It is observed that by properly locating the square obstacle the length and intensity of the recirculation zone behind the step are considerably affected, and hence, it can be used as a passive control element for heat transfer augmentation. Enhancements in the maximum values of the Nusselt number of 228% and 197% are obtained for two different vertical locations of the obstacle. On the other hand, in the pulsating flow case at Reynolds number of 200, two locations of the square obstacle are effective for heat transfer enhancement with pulsation compared to the case without obstacle.
... Their results showed that with increasing step height, the transverse velocity fluctuation and temperature fluctuations downstream of the forward-facing step increased. Terhaar et al. [6] experimentally studied laminar unsteady heat transfer over a backward-facing step for pulsating flow at Reynolds number 300 and observed enhancement of Nusselt number up to a certain Strouhal number followed by degradation when the pulsation frequency increased. Kumar and Dhiman [7] numerically investigated the effect of insertion of an adiabatic circular cylinder on heat transfer enhancement in laminar forced convection flow over a backward-facing step. ...
Laminar forced convection of nano-encapsulated phase change material (NEPCM) slurry over a 2D horizontal backward-facing step is numerically investigated using a finite volume method based on a collocated grid. The slurry consists of water as base fluid and n-octadecane NEPCM particles with an average diameter of 100 nm. Uniform heat flux boundary condition is imposed to the downstream wall while the step and upstream walls are subjected to adiabatic boundary condition. The effects of Reynolds number ranging from 20 to 80, volume fractions of nanoparticles ranging from 0% to 30%, as well as heat flux ranging from 500 to 2,500 W/m2 are studied. In order to understand the physics of flow and heat transfer of slurry over the backward-facing step, the streamlines and isotherms of the flow were studied. An enhancement in heat transfer coefficient up to 67% using slurry as working fluid compared with pure water can be observed. However, because of the higher viscosity of mixture compared with pure water, the slurry can cause a higher pressure drop in the system. Furthermore, as wall heat flux and Reynolds number increase, the heat transfer coefficient of the bottom wall increases until a critical heat flux is reached and heat transfer performance becomes independent of heat flux.
... Reattachment flow appeared after the separation flow and these flow phenomena are addressed in several experimental and numerical studies [2][3][4][5]. With developments in computational fluid dynamics (CFD) software and access to accurate equipment, some investigations have looked into separation and reattachment zones [6][7][8][9]. Addad et al. [10] utilized large eddy simulation (LES) to study fluid flow over a forwardbackward facing step and found the separation length and reattachment offset to be 1.2 and 0.6 step height, respectively. Turbulent heat transfer and fluid flow of air over a double forward-facing step were analyzed by Yılmaz and Ö ztop [11], whose results revealed that compared to length ratio, step ratio has considerable influence on heat transfer rate. ...
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... Reattachment flow appeared after the separation flow and these flow phenomena are addressed in several experimental and numerical studies [2][3][4][5]. With developments in computational fluid dynamics (CFD) software and access to accurate equipment, some investigations have looked into separation and reattachment zones [6][7][8][9]. Addad et al. [10] utilized large eddy simulation (LES) to study fluid flow over a forwardbackward facing step and found the separation length and reattachment offset to be 1.2 and 0.6 step height, respectively. Turbulent heat transfer and fluid flow of air over a double forward-facing step were analyzed by Yılmaz and Ö ztop [11], whose results revealed that compared to length ratio, step ratio has considerable influence on heat transfer rate. ...
The turbulent forced convection heat transfer of water/functionalized multi-walled carbon
nanotube (FMWCNT) nanofluids over a forward-facing step was studied in this work.
Turbulence was modeled using the shear stress transport K-x model. Simulations were
performed for Reynolds numbers ranging from 10,000 to 40,000, heat fluxes from 1,000 to
10,000W/m2, and nanoparticle volume fractions of 0.00% to 0.25%. The two-dimensional
governing equations were discretized with the finite volume method. The effects of nanoparticle
concentration, shear force, heat flux, contraction, and turbulence on the hydraulics
and thermal behavior of nanofluid flow were studied. The model predictions were found
to be in good agreement with previous experimental and numerical studies. The results
indicate that the Reynolds number and FMWCNT volume fraction considerably affect the
heat transfer coefficient; a rise in local heat transfer coefficient was noted when both Reynolds
number and FMWCNT volume fraction were increased for all cases. Moreover, the contraction
of the channel passage leads to the formation of two recirculation regions with augmented
local heat transfer coefficient value
... It was found that adding the baffle on the upper wall has significant effect on the magnitude of the normal velocity component. A numerical investigation of laminar flow over a backward-facing step was presented by Chiang et al. [16][17][18][19][20] At t = 1 vortex form was produced at the upper corner of the step due to the sudden change in stream wise velocity. ...
The effects of two dimensional laminar and turbulent combined convection nanofluids flows over backward facing step in a channel having a blockage are numerically investigated. The continuity, momentum and energy equations are solved using finite volume method (FVM) with the SIMPLE algorithm scheme. The duct has a step height of 0.01, and an expansion ratio of 2. The Reynolds number was in the range of 100-1900 (laminar flow) and in the range of 4000-10000 (turbulent flow). The effect of the blockage shape (circular, square and triangular) on the flow and heat transfer characteristics is examined. The effects of various types of nanoparticles such as Al2O3, SiO2, CuO, and ZnO dispersed in a base fluid (water), volume fraction of nanoparticles in the range of 1% to 4% and nanoparticle diameter in the range of 25 nm to 80 nm are also studied. It is inferred that the circular blockage has the highest Nusselt number compared to other two shapes. The reattachment point is found to move downstream far from the step as Reynolds number increases. Nanofluid of SiO2 is observed to have the highest Nusselt number and skin friction coefficient among other nanofluids types, while nanofluid of CuO nanoparticles has the lowest Nusselt number and skin friction coefficient.
... Three-dimensional instability in flow over a backward-facing step with Reynolds number between 450 to 1050 numerically studied by Barkley et al. [5]. Terhaar et al. [6] presented study of unsteady heat transfer to laminar flow over backward facing step for pulsating flow at Reynolds number of 300. The results showed increase in Nusselt number up to certain Stouhal number then reduces at increases in frequency of the pulsating. ...
Heat transfer and laminar air flow over a double backward-facing step numerically studied in this paper. The simulations was performed by using ANSYS ICEM for meshing process and using ANSYS fluent 14 (CFD) for solving. The k-ɛ standard model adopted with Reynolds number varied between 98.5 to 512 and three step height at constant heat flux (q=2000 W/m2). The top of wall and bottom of upstream are insulated with bottom of downstream is heated. The results show increase in Nusselt number with increases of Reynolds number for all cases and the maximum of Nusselt number happens at the first step in compared to the second step. Due to increase of cross section area of downstream to generate sudden expansion then Nusselt number decrease but the profile of Nusselt number keep same trend for all cases where increase after the first and second steps. Recirculation region after the first and second steps are denoted by contour of streamline velocity. The higher augmentation of heat transfer rate observed for case 1 at Reynolds number of 512 and heat flux q=2000 W/m 2 .
... The developing turbulent boundary layer separates as air passes over the step and reattaches downstream of the step, resulting in a turbulent recirculating flow region behind the step, as illustrated in Fig. 8. The resulting flow has been studied extensively [35,36] as a model problem for numerical simulations [37,38] and experiments [39]. It is conventional in these problems to characterise the size of the turbulent recirculation region behind the step by the step height H, and to characterise the flows by a Reynolds number Re based on the free-stream velocity U ∞ and by the step height H, Re H = U ∞ H/ν, with ν f the kinematic viscosity of the fluid. ...
Many energy conversion and other thermal-fluid systems exhibit unsteady convective heat exchange. In such systems, generic spatiotemporal variations in the flow give rise to variations in the heat flux for a given fluid–solid temperature difference, which can be interpreted as spatiotemporal fluctuations of the instantaneous heat transfer coefficient. These variations can lead to unsteady conjugate heat transfer, in which the exchanged heat flux arises from an interaction between the bulk fluid temperature and the temperature in the solid. Further, the nonlinear coupling between the fluctuating temperature differences and the heat transfer coefficient can lead to an effect we refer to as augmentation, which quantitatively describes the ability of a particular arrangement to have a different time-mean heat flux from the product between the mean heat transfer coefficient and the mean temperature difference across the fluid. It is important to be able to understand and to model in a simple framework the effects of the material properties, the geometry and the character of the heat transfer coefficient on the thermal response of the fluid–solid system, and consequently to predict the overall heat transfer performance of these systems.
... 33 The flow over the backward facing step with heat transfer is 34 well documented with experimental data for different geometry 35 configuration, e.g., Refs. [3][4][5][6][7][8]. Experimental data of Vogel and 36 Eaton [3] are used for validation. ...
An accurate prediction of the flow and the thermal boundary layer is required to properly simulate gas to wall heat transfer in a turbulent flow. This is studied with a view to application to gas turbine combustors. A typical gas turbine combustion chamber flow presents similarities with the well-studied case of turbulent flow over a backward facing step, especially in the near wall regions where the heat transfer phenomena take place. However, the combustion flow in a gas turbine engine is often of a dynamic nature and enclosed by a vibrating liner. Therefore apart from steady state situations, cases with an oscillatory inlet flow and vibrating walls are investigated. Results of steady state and transient calculations for the flow field, friction coefficient and heat transfer coefficient, with the use of various turbulence models, are compared with literature data. It has been observed that variations in the excitation frequency of the inlet flow and wall vibrations have an influence on the instantaneous heat transfer coefficient profile. However, significant effect on the time mean value and position of the heat transfer peak is only visible for the inlet velocity profile fluctuations with frequency approximately equal to the turbulence bursting frequency.
Since high heat generation is one of the main factors that limits the ability of electrical appliances, in this paper investigated the effect of step height and duct angle on flow and heat transfer characteristics in a reverse step model. The paper presents a numerical simulation of 10 variants of the main problem with two different step heights (2.4 and 4.8 mm) and different slope angles (0° < γ < 180°). Al2O3/H2O nanofluid with a concentration of 1% was chosen as the medium. The nanofluid entered the channel 360 mm long at Re = 100. The bottom wall behind the stage maintained a constant heat flux q = 200W/m2. The upper wall maintained a temperature of 293 K. A comparative analysis of the results of velocity profiles u and v, temperature and Nusselt number was carried out. The used mathematical model and numerical algorithm were validated on the test problem of other authors.
This paper presents the computational results of heat transfer for a 2D laminar flow with different channel tilts with forward facing step and backward facing step, taking into account buoyancy forces for various bottom wall lengths. The inclination angle influence on the distribution of velocity and temperature is investigated. The validated numerical algorithm was used to the problem forward and backward facing steps with buoyancy force and at various tilt angles. From the obtained numerical results, it can be noticed that the length of the lower part of the channel has a very strong effect on the flow fluctuation and temperature distribution over the entire channel. It should be noticed that the tilt angle also has a very strong effect on the distribution of flow and temperature. Thus, taking into account the buoyancy force changes the shape of the main recirculation region, but at the same time, regardless of the different tilt angles, the number of vortices does not change, but only the size of the vortices changes. It should also be noticed that when the buoyancy force is taken into account, cooling occurs more efficiently in the middle of the channel.
An experimental research was conducted to study the effects of high-frequency reciprocating flow on subcooled boiling heat transfer performance on a chip using FC-72 in a horizontal rectangular narrow channel with a hydraulic diameter of 7.5 mm. In the experiments, the flow velocity varied from 0.25 to 0.95 m/s for the inlet liquid subcooling of 35 °C, and the frequency was from 0 to 10 Hz. The result indicates that the flow reciprocation can improve heat transfer performance in the low and high heat flux regions, but has limited effect under medium heat flux. The CHF of reciprocating flow has a tendency to increase with the increase of Reynolds number and Strouhal number. The maximum improvement of CHF is 42.3% with the flow velocity of 0.5 m/s and the frequency of 10 Hz. Photographic studies showed that bubbles under reciprocating flow are much smaller because of the limited growth time and the alternative variation of the flow field.
Purpose
The purpose of this study is to numerically analyze the convective heat transfer features for cooling of an isothermal surface with a cavity-like portion by using CuO-water nano jet. Jet impingement cooling of curved surfaces plays an important role in practical applications. As compared to flat surfaces, fluid flow and convective heat transfer features with jet impingement cooling of a curved surface becomes more complex with additional formation of the vortices and their interaction in the jet wall region. As flow separation and reattachment may appear in a wide range of thermal engineering applications such as electronic cooling, combustors and solar power, jet impingement cooling of a surface which has a geometry with potential separation regions is important from the practical point of view.
Design/methodology/approach
Numerical simulations were performed with a finite volume-based solver. The study was performed for various values of the Reynolds number (between 100 and 400), length of the cavity (between 5 w and 40 w), height of the cavity (between w and 5w) and solid nano-particle volume fraction (between 0 and 4 per cent). Artificial neural network modeling was used to obtain a correlation for the average Nusselt number, which can be used to obtain fast and accurate predictions.
Findings
It was observed that cavity geometrical parameters of the cooling surface can be adjusted to change the flow field and convective heat transfer features. When the cavity length is low, significant contribution of the inclined wall of the cavity on the average Nusselt number is achieved. As the cavity length and height increase, the average Nusselt number, respectively, reduce and slightly enhance. At the highest value of cavity height, significant changes in the convective flow features are obtained. By using nanofluids instead of water, enhancement of average heat transfer in the range of 35-46 per cent is obtained at the highest particle volume fraction.
Originality/value
In this study, jet impingement cooling of an isothermal surface which has a cavity-like portion was considered with nanofluids. Addition of this portion to the impingement surface has the potential to produce additional vortices which affects the fluid flow and convective features in the jet impingement heat transfer. This geometry has the forward-facing step for the wall jet region with flow separation reattachment in the region. Based on the above literature survey and to the best of the authors’ knowledge, jet impingement cooling for such a geometry has never been reported in the literature despite its importance in practical thermal engineering applications. The results of this study may be useful for design and optimization of such systems and to obtain best performance in terms of fluid flow and heat transfer characteristics.
Study of turbulent forced convection heat transfer to functionalized multi-walled carbon nanotube nanofluids over a forward-facing step of circular tube has been presented in this paper. Shear stress transport k-ω model was considered as the turbulence model. With the finite volume method, the two-dimensional governing equations were discretized. The effects of Reynolds number, heat fluxes, nanoparticles volume fraction, step height, turbulence on the hydraulics and thermal conductivity of nanofluids on heat transfer to the flowing suspensions were studied. It is noted that the increase in volume concentration of FMWCNT nanofluids or Reynolds number increases the heat transfer coefficient. Use of FMWCNT nanofluids enhances heat transfer significantly compared to the pure water. It has observed that the increase of step height increases the local heat transfer coefficient after contraction. The numerical results were validated closely by the experimental available data.
In this study, numerical analysis of mixed convection of CuO-water nanofluid in a cavity with inlet and outlet ports is performed under the effects of inclined magnetic field and step like corrugated elastic walls. The numerical simulation results are obtained by using finite element method. The Arbitrary-Lagrangian–Eulerian method is utilized for the description of the fluid motion with the elastic wall in the fluid-structure interaction model. In the current study, multiple step like corrugation of the wall is considered and it is made elastic which adds additional flexibility for the control of convective heat transfer features of the vented cavity. Effects of various pertinent parameters such as Reynolds number (between 100 and 500), Hartmann number (between 0 and 40), magnetic inclination angle (between 0° and 90°), elastic modulus of the flexible wall (between 5 × 10⁴ and 10⁸), number of step-like corrugation (between 1 and 8) and nanoparticle volume fraction (between 0 and 3%) on the fluid flow and heat transfer characteristics are numerically examined. It is observed that for higher value of Reynolds number, local Nusselt number both deteriorates and enhances in various locations along the hot wall whereas the changes in the local Nusselt number are marginal for lower value of Reynolds number. The multiple vortices in the vented cavity are influenced by the variation of magnetic field parameters and number of step like corrugation of the wall while the effects are not significant for the change of magnetic inclination angle. When the value of Hartmann number augments, the average heat transfer reduces until Hartmann number of 30 and increases for the highest value of Hartmann number. The average Nusselt number increment are in the range of 9-9.5% with the nanoparticle addition at the highest volume fraction in the absence and presence of magnetic field. Even though significant changes in the local Nusselt number are observed when the number of step like corrugation increases, it has a deterioration effect on the average heat transfer generally and 5.5% reduction in the average Nusselt number is obtained when the value is increased from 1 to 8.
Purpose
Numerical study of nanofluid forced convection within a branching channel was performed under the influence of a uniform magnetic field. The purpose of this study is to enhance the heat transfer performance of the separated flow at the branching channel with the use of magnetic field and nanofluid. The use of magnetic field and enhancement in both the thermal conductivity and electrical conductivity with the inclusion of the nanoparticles provides favorable thermophysical properties of the nanofluid when it used as a heat transfer fluid in a branching channel. The results of this study may be used to control the thermal performance in a branching channel and further optimization studies in the presence of magnetic field.
Design/methodology/approach
Galerkin weighted residual finite element method was used for the simulations. The numerical simulation results are performed by changing the inclination angle of the lower branching channel (between 0° and 90°), thermophysical properties of the fluid via inclusion of nanoparticles (between 0 and 0.04), Reynolds number (between 100 and 400) and magnetic field strength (Hartmann number changes between 0 and 15).
Findings
It was observed that the recirculation zones and reattachment length of the upper and lower branching channels are affected by the variation of those parameters. Reattachment lengths increase with the augmentation of the Reynolds number and deterioration of the Hartmann number. Average Nusselt number becomes higher for higher values of Hartmann number and solid particle volume fraction. Inclusion of the nanoparticle to the base fluid is very effective for the configuration with higher values of Hartmann number. An optimum value of the inclination angle of the lower branching channel is observed, beyond which heat transfer rate is significantly reduced due to the establishment of a large vortex in the upper branching channel and restriction of the fluid motion.
Originality/value
In this study, forced convection of nanofluid flow in a branching channel under the effect of magnetic field was numerically studied. Magnetic field effects with nanoparticle inclusion to the base fluid on the convective heat transfer was analyzed for various inclination angles of the lower branching channel. Flow separation at the junction of the channels and thus convective heat transfer rate are influenced by the variation of these parameters. There are many studies related to application of the magnetic field with nanofluids, and a few of them are related to configurations with separated flows. To the best of the authors’ knowledge, there exist no studies for the application of nanofluids and magnetic field for the convective heat transfer in a branching channel. This topic is of importance as there are many engineering applications of the branching channels.
In this study, mixed convection of pulsating ferrofluid flow over a backward-facing step under the effect of a magnetic source is performed. Heat transfer and fluid flow characteristics for a range of flow parameters were identified in terms of streamlines, isotherms and local and averaged Nusselt number plots. Finite element method was used to solve the resulting governing equations. The effects of the Richardson number (), strength of the magnetic dipole (), horizontal and vertical locations of the magnetic dipole (), amplitude and non-dimensional frequency of flow pulsation () on the fluid flow and heat transfer enhancement were numerically investigated in detail. It was observed that the magnetic dipole parameters effect is different in pulsating flow compared to steady flow simulation results. The flow pulsation was found to enhance the average heat transfer which is about 17.5% in the absence of magnetic dipole source. When magnetic dipole source was used, up to 32% in the average heat transfer was obtained with flow pulsation. The primary recirculation zone behind the step is deteriorated by the presence of the magnetic source, and an addition vortex which is restricted to a very small region near the step is formed. The magnetic dipole source can be combined with flow pulsation to control the mixed convective flow over the backward-facing step.
Numerical simulations are presented for a 2-D, incompressible, crossed Poiseuille flow over a circular cylinder confined in a sudden expansion channel. The SIMPLE algorithm with the QUICK scheme is employed. The simulations are carried out for Reynolds number, Re, varying from 10 to 300, the expansion ratio of the channel, Er, ranging from 1 to 4, and the position of the circular cylinder, Xc, ranging from 1 to 15. The results show that the heat transfer mechanism is a complex function of Re, Er and Xc. Steady-state, periodical oscillating and chaotic solutions are obtained and the route of flow state from steady state to chaotic oscillation is not unique. For the fixed Er and Xc, the time-averaged Nusselt number, Nut¯, is an increasing function of Re. For the fixed Re, the heat transfer intensity depends on the flow pattern decided by both Er and Xc.
In this study, a direct numerical simulation of the fluid flow and heat transfer characteristics of separation and reattachment flow at a backward-facing step is presented. A computer program of FORTRAN code is used to solve the governing equations according to finite volume method. The effects of the Reynolds number and expansion ratio on the fluid flow and heat transfer characteristics are investigated. The size of the primary recirculation zone increases with the reduction of expansion ratio and the fluctuation of isotherms increased with the increase of Reynolds number. The periodic characteristics and the dissimilarity between Nu and Cf appear in the transitional flow regime. The rotating fluids in the reattachment region increase the flow instability and the interchange of the hot and cold fluids increases heat transfer instability. The combined effects of flow instability and heat transfer instability play an important role in the formation of the dissimilarity between Nu and Cf.
In this numerical study, the effect of suction and blowing with constant mass fluxes on heat transfer enhancement and flow separation behind a backward facing step in a sufficiently long channel is investigated. The simulations have been carried out by a laminar, incompressible, unsteady open-source flow solver (OpenFoam). Using the constant Reynolds number for the base-flow, a systematic investigation of ejections and suctions is performed. The jet-mass flow rate is constant and the flow control is carried out either by suction and blowing from three slots located on the upper, lower wall of the channel and on the vertical step wall. The representative flow fields and the reattachment lengths are reported in an effort to optimize the operation parameters. The velocity and temperature profiles extracted downstream of the slots are then obtained to show that the recirculation zone behind the backward facing step has reduced significantly and the heat transfer is enhanced through better mixing. Based on the friction coe fficient and the Nusselt number variation along the bottom wall of the channel, the optimum operating conditions are defined.
In the present study, results obtained from three-dimensional incompressible flow over backward-facing step in a
rectangular duct using Realizable k- turbulence model are reported. Effects of step inclination angle have been investigated for =30, 45, 90 while upper wall of duct kept parallel to the bottom wall and then rose to =6. Reynolds number based on freestream velocity and step height is examined by varying its magnitude in the range of 15,000-64,000. Simulated results are presented for revealing the general flow features and reattachment lengths after a successful validation of the present work with the experimental data of Driver and Seegmiller (1985). It is found that turbulence kinetic energy increases suddenly after the step for both straight and raised upper walls and reaches its maximum at x/h=5 that consistent with the published literature. The size of reattachment lengths increases with the step inclination angle, i.e., maximum reattachment length occurs at 90 for both straight and raised upper walls. It is seen that raising the upper wall leads to longer reattachment lengths.
In this study, numerical analysis of the heat transfer enhancement and fluid flow characteristics of a rotating cylinder under the influence of magnetic dipole in the backward facing step geometry is conducted. The governing equations are solved with a finite element based commercial solver. The effects of Reynolds number (10⩽Re⩽20010⩽Re⩽200), cylinder rotation angle (-75⩽Ω⩽75-75⩽Ω⩽75) and strength of the magnetic dipole (0⩽γ⩽160⩽γ⩽16) on the heat transfer characteristics are studied for backward facing step flow. It is observed that the length and size of the recirculation zones can be controlled with magnetic dipole strength and cylinder rotation angles. As the Reynolds number increases, local Nusselt number increases and number of peaks in the presence of the magnetic field decreases. The effect of cylinder rotation on the local Nusselt number distribution is more pronounced at low Reynolds number.
This paper explores the possibility of using the Moire-Fourier deflectometry for measuring the local heat transfer coefficient inside small confined flows (micro-channels) and their relevance for checking theoretical models. This optical technique, supplemented with a digital image processing method of fringes, is applied for studying the local heat transfer over a backward facing step. The experimental results are compared with numerical results obtained from a commercial code, which has been contrasted with relevant solutions from the literature and bulk fluid temperature measurements at the inlet and outlet sections. In order to show the possibilities of the experimental technique, the influence of assuming an adiabatic wall on the numerical heat-transfer model is examined and the degree of agreement is discussed. As a result, the paper shows that the proposed Moiré-Fourier technique is a simple experimental setup suitable for temperature measurements with an accuracy similar to the thermocouples but with a spatial resolution near 0.01 mm.
The effect of an upper wall mounted adiabatic thin fin on laminar pulsating flow in a backward facing step has been investigated numerically. Study is performed for different Reynolds numbers (based on the step height) in the range of 10 and 200 and for the expansion ratio of 2. The working fluid is air with the Prandtl number of 0.71. The governing equations are solved with a general purpose finite volume based solver, FLUENT. The effects of various pertinent parameters, Reynolds number, fin length and pulsating frequency on the fluid flow and heat transfer characteristics are numerically studied. It is observed that fin alters the flow field and thermal characteristics. In the steady flow case, heat transfer enhancement is obtained with the installation of the fin on the upper wall and increases with increasing fin length and increasing Reynolds number. Heat transfer enhancement of 188% is obtained for fin length of Lf = 1.5H at Reynolds number of 200. In the pulsating flow case, time-spatial averaged Nusselt number along the bottom wall downstream of the step normalized with spatial averaged Nusselt number in the steady flow case versus excitation Strouhal number shows a resonant type behavior; first an increase in the value is seen up to St = 0.05, then a decrease is seen with the increasing values of the frequency of the pulsation for the case without fin. Adding a fin shifts the maximum value of the normalized Nusselt number from St = 0.05 to St = 0.1. Compared to steady flow with no-fin case, adding a fin is not advantageous for heat transfer enhancement in pulsating flow.
In the present study, the application of the system identification method for forecasting the thermal performance of forced pulsating flow at a backward facing step with a stationary cylinder subjected to nanofluid is presented. The governing equations are solved with a finite volume based code. The effects of various parameter frequencies (0.25 Hz-8 Hz), Reynolds number (50-200), nanoparticle volume fraction (0.00-0.06) on the fluid flow and heat transfer characteristics are numerically studied. Nonlinear system identification toolbox of Matlab is utilized to obtain nonlinear dynamic models of data sets corresponding to different nanoparticle volume fractions at frequencies of 1, 4 and 8 Hz. It is observed that heat transfer is enhanced with increasing the frequency of the oscillation, nanoparticle volume fraction and Reynolds number. The level of the nonlinearity (distortion from a pure sinusoid) decreases with increasing phi and with decreasing Reynolds number. It is also shown that nonlinear dynamic models obtained from system identification toolbox could produce thermal output (length averaged Nusselt number) as close to as output from a high fidelity CFD simulation.
La aparición de maquinas de pequeño tamaño, de tan solo micras y aun menores, y cada vez más complejas, crea la necesidad del desarrollo de técnicas de estudio que permitan obtener conclusiones efectivas para el diseño de estos dispositivos que les permita ser eficientes en su aplicación. En particular los códigos comerciales de técnicas computacionales para tratar la dinámica de fluidos, como el programa Fluent, que además permiten un estudio de los efectos térmicos en el fluido, pueden ser valiosos a la hora de analizar el funcionamiento de estas maquinas bajo estos criterios. En este proyecto se trata de una aplicación concreta de este tipo de MEMS que pretende la evacuación de calor para la refrigeración de una pequeña pared a 80 grados centígrados mediante la circulación de agua a 20 grados en un conducto que se haya en contacto con la pared. Se pretende analizar lo idóneo de Fluent para esta tarea y la validez de los resultados, así como efectuar un análisis del campo térmico y fluido resultante tanto en el caso estacionario como el caso pulsado. Se analiza también la influencia del pulso en la trasferencia de calor a través del número de Nusselt promedio en la zona de estudio, y la relación de acoplamiento entre la dinámica del fluido y los efectos térmicos. Ingeniería Técnica en Mecánica
Laser-Doppler measurements of velocity distribution and reattachment length are reported downstream of a single backward-facing step mounted in a two-dimensional channel. Results are presented for laminar, transitional and turbulent flow of air in a Reynolds-number range of 70 < Re < 8000. The experimental results show that the various flow regimes are characterized by typical variations of the separation length with Reynolds number. The reported laser-Doppler measurements do not only yield the expected primary zone of recirculating flow attached to the backward-facing step but also show additional regions of flow separation downstream of the step and on both sides of the channel test section. These additional separation regions have not been previously reported in the literature.
The incompressible laminar flow of air and heat transfer in a channel with a backward-facing step is studied for steady cases
and for pulsatile inlet conditions. For steady flows the influence of the inlet velocity profile, the height of the step and
the Reynolds number on the reattachment length is investigated. A parabolic entrance profile was used for pulsatile flow.
It was found with amplitude of oscillation of one by Re=100 that the primary vortex breakdown through one pulsatile cycle. The wall shear rate in the separation zone varied markedly
with pulsatile flows and the wall heat transfer remained relatively constant. The time-average pulsatile heat transfer at
the walls was greater as with steady flow with the same mean Reynolds number.
Es wird eine zweidimensionale numerische Untersuchung des instationären Wärmeübergangs und Druckverlustes im laminar durchströmten
Spaltkanal mit einer plötzlichen Kanalerweiterung dargelegt und zwar für stationäre und periodische Geschwindigkeitsprofile
am Eintritt des Kanals. Für stationäre Strömungen wurden die Form des Eintrittsprofils, die Reynoldszahl und die Kanalerweiterung
variiert. Als Lösung der Navier/Stokes-und der Energiegleichungen mit periodischen Randbedingungen resultiert eine oszillierende
Strömung, die das Aufplatzen des Primärwirbels in einer Schwingungsperiode zur Folge hat. Der Einfluß dieser Oszillation auf
den Wärmeübergang und den Strömungsverlust wurde für die maximale Amplitude und für Re=100 eingehend untersucht.
This paper deals with the study of 2-D, laminar, pulsating flow inside a heated rectangular cavity with different aspect ratios. The cooling liquid (water with temperature dependent viscosity and thermal conductivity) comes and leaves the cavity via inlet and outlet ports. The flow topology is characterised by the large recirculation regions that exist at inner corners of the cavity. These low velocity regions cause the heat transfer to be small when compared, for instance, to that of a straight channel. We study the effect that a prescribed pulsation at the inlet port has on the cavity heat transfer. This pulsating boundary condition, of the unsteady Poiseuille type, is described by its frequency and the amplitude of the pressure gradient. The time averaged Reynolds number of the flow, based on the hydraulic diameter of the inlet channel, is 100 and we consider that the dimensionless pulsation frequency (Strouhal number) varies in the range from 0.0 to 0.4. We show that the prescribed pulsation enhances heat transfer in the cavity and that the mechanism that causes this enhancement appears to be the periodic change in the recirculation flow pattern generated by the pulsation. Regarding the quantitative extent of heat transfer recovery, we find that appropriate selection of the pulsation parameters allows for the cavity to behave like a straight channel that is the configuration with the highest Nusselt number.
This study is motivated by the need to devise means to enhance heat transfer in configurations, like the back step, that appear in certain types of MEMS that involve fluid flow and that are not very efficient from the thermal transfer point of view. In particular, the work described in this paper studies the effect that a prescribed flow pulsation (defined by two control parameters: velocity pulsation frequency and pressure gradient amplitude at the inlet section) has on the heat transfer rate behind a backward facing step in the unsteady laminar 2-D regime. The working fluid that we have considered is water with temperature dependent viscosity and thermal conductivity. We have found that, for inlet pressure gradients that avoid flow reversal at both the upstream and downstream boundary conditions, the time-averaged Nusselt number behind the step depends on the two above mentioned control parameters and is always larger than in the steady-state case. At Reynolds 100 and pulsating at the resonance frequency, the maximum time-averaged Nusselt number in the horizontal wall region located behind the step whose length is four times the step height is 55% larger than in the steady-case. Away from the resonant pulsation frequency, the time-averaged Nusselt number smoothly decreases and approaches its steady-state value.
Results are reported from a three-dimensional computational stability analysis of flow over a backward-facing step with an expansion ratio (outlet to inlet height) of 2 at Reynolds numbers between 450 and 1050. The analysis shows that the first absolute linear instability of the steady two-dimensional flow is a steady three-dimensional bifurcation at a critical Reynolds number of 748. The critical eigenmode is localized to the primary separation bubble and has a flat roll structure with a spanwise wavelength of 6.9 step heights. The system is further shown to be absolutely stable to two-dimensional perturbations up to a Reynolds number of 1500. Stability spectra and visualizations of the global modes of the system are presented for representative Reynolds numbers.
this paper and the Reynolds number which applies to the downstream channel)
The problem of heat transfer from a cylindrical pipe is formulated for a case where the flow inside the pepe consists of a periodic motion imposed on a fully developed steady laminar flow. It is shown that the velocity pulsations induce harmonic oscillations in temperature thus breaking the temperature field into a steady mean part and a harmonic part. The interaction between the velocity and temperature oscillations introduces an extra term in the energy equation which reflects the effect of pulsations in producing higher heat transfer rates.
Results of experimental and numerical investigations of air flows over a two-dimensional backward-facing step are presented. The lengths of separation and reattachment on the upper and lower walls were measured nonintrusively using closely spaced, multi-element hot-film sensor arrays for Re≤3000 and expansion ratios of 1·17 and 2·0. The hot-film sensor measurements are in good agreement with the present as well as previous numerical predictions. It is anticipated that this measurement capability will provide a practical means for the study of unsteady flow phenomena with flow separation as well.
Combined heat transfer and fluid dynamic measurements in a separated and reattaching boundary layer, with emphasis on the near-wall region, are presented. A constant heat-flux surface behind a single-sided sudden expansion is used to obtain Stanton number profiles as a function of Reynolds number and boundary-layer thickness at separation. Fluctuating skin-friction and temperature profiles demonstrate the importance of the near-wall region in controlling the heat transfer rate. The fluctuating skin friction controls the heat transfer rate near reattachment, while the conventional Reynolds analogy applies in the redeveloping boundary layer beginning two or three step heights downstream of reattachment.
Heat transfer in a laminar air flow past a heated backstep is investigated experimentally in the 20 x 15 x 61-cm working section of a low-speed wind-tunnel of contraction ratio 12.5:1 by Mach-Zehnder interferometry. Top-wall steps with channel-expansion ratios 1.06, 1.03, and 1.02 are examined, and additional pressure, temperature, velocity, and (smoke-injection) reattachment-point determinations are obtained. Typical interferograms are given, and the results are presented in graphs and tables. Heat transfer downstream of the step is found to increase monotonically in the streamwise direction but to remain less than the flat-plate value (at most 56 percent for the 1.06-expansion-ratio step), as predicted by the cavity theory of Chapman et al. (1958). Smaller steps are shown to give smaller values of heat transfer, and an expression for the average transfer is derived.
Pulsating laminar convection heat transfer in a circular tube with constant wall heat flux is investigated analytically. The results show that both the temperature profile and the Nusselt number fluctuate periodically about the solution for steady laminar convection, with the fluctuation amplitude depending on the dimensionless pulsation frequency, ω*, the amplitude, γ, and the Prandtl number, Pr. It is also shown that pulsation has no effect on the time-average Nusselt numbers for pulsating convection heat transfer in a circular tube with constant wall heat flux.
The problem of pulsatile flow in a tube with constant heat flux at the wall is considered analytically to determine how pulsation affects the rate of heat transfer and how the phenomenon depends on the Prandtl number and on pulsation frequency. The results indicate that in a range of moderate values of the frequency there is a positive peak in the effect of pulsation whereby the bulk temperature of the fluid and the Nusselt number are increased, but the effect is reversed when the frequency is outside this range. The peaks are higher at lower Prandtl numbers.
This paper presents results of numerical studies of the impulsively starting backward-facing step flow with the step mounted in a plane, two-dimensional duct. The numerical prediction procedure employed in the study is described, and the initial and boundary conditions are given. Results are presented for Reynolds numbers of 10, 368, and 648. For time going to infinity, the results are compared with predictions obtained with a computer program for steady flows and also with results obtained by laser-Doppler anemometry.
Pulsation effect on heat transfer in laminar incompressible flow, which led to contradictory results in previous studies, is theoretically investigated in this work starting from basic principles in an attempt to eliminate existing confusion at various levels. First, the analytical solution of the fully developed thermal and hydraulic profiles under constant wall heat flux is obtained. It eliminates the confusion resulting from a previously published erroneous solution. The physical implications of the solution are discussed. Also, a new time average heat transfer coefficient for pulsating flow is carefully defined such as to produce results that are both useful from the engineering point of view, and compliant with the energy balance. This rationally derived average is compared with intuitive averages used in the literature. New results are numerically obtained for the thermally developing region with a fully developed velocity profile. Different types of thermal boundary conditions are considered, including the effect of wall thermal inertia. The effects of Reynold and Prandtl numbers, as well as pulsation amplitude and frequency on heat transfer are investigated. The mechanism by which pulsation affects the developing region, by creating damped oscillations along the tube length of the time average Nusselt number, is explained.
Laser-Doppler velocity measurements adjacent to the bounding walls of three-dimensional (3-D) backward-facing step flow are performed for the purpose of mapping the boundaries of the reverse flow regions that develop in this geometry (adjacent to the sidewalls, the flat wall and the stepped wall) as a function of the Reynolds number. The back-ward-facing step geometry is configured by a step height (S) of 1 cm, which is mounted in a rectangular duct having an aspect ratio (AR) of 8:1 and an expansion ratio (ER) of 2.02:1. Results are presented for a Reynolds number range between 100 and 8000, thus covering the laminar, transitional and turbulent flow regimes. The boundaries of the reverse flow regions are identified by locating the streamwise coordinates on a plane adjacent to the bounding walls where the mean streamwise velocity component is zero. The size of the reverse flow regions increases and moves further down-stream in the laminar flow regime; decreases and moves upstream in the transitional flow regime; and remains almost constant or diminishes in the turbulent flow regime; as the Reynolds number increases. The spanwise distribution of the boundary line for the reverse flow region adjacent to the stepped wall develops a minimum near the sidewall in the laminar flow regime, but that minimum in the distribution disappears in the turbulent flow regime. Predictions agree well with measurements in the laminar flow regime and reasonably well in the turbulent flow regime.
Numerical studies of flow and heat transfer in a circular tube under pulsating flow condition were carried out in the laminar regime. The flow at the inlet consists of a fixed part and a pulsating component, which varies sinusoidally in time. The flow was both thermally and hydrodynamically developing while the tube wall was kept at a uniform temperature. The solution of two-dimensional Navier–Stokes equation was performed using the SIMPLE algorithm with the momentum interpolation technique of Rhie and Chow. By analysing the data generated from the simulation, it is observed that in the range of present study (frequency: 0–20 Hz; amplitude: < 1.0), pulsation has no effect on time-averaged heat transfer, although the Nu distribution varies in time in the near-entry region of the pipe.
Effect of the backward-facing step heights on turbulent mixed convection flow along a vertical flat plate is examined experimentally. The step geometry consists of an adiabatic backward-facing step, an upstream wall and a downstream wall. Both the upstream and downstream walls are heated to a uniform and constant temperature. Laser–Doppler velocimeter and cold wire anemometer were used, respectively, to measure simultaneously the time-mean velocity and temperature distributions and their turbulent fluctuations. The experiment was carried out for step heights of 0, 11, and 22 mm, at a free stream air velocity, u∞, of 0.41 m/s, and a temperature difference, ΔT, of 30 °C between the heated walls and the free stream air. The present results reveal that the turbulence intensity of the streamwise and transverse velocity fluctuations and the intensity of temperature fluctuations downstream of the step increase as the step height increases. Also, it was found that both the reattachment length and the heat transfer rate from the downstream heated wall increase with increasing step height.
The effect of highly varying thermal boundary conditions on the convective heat transfer in a backward-facing step flow was investigated in a two-dimensional (2D) boundary-layer tunnel in air. A modified form of the transient heat transfer technique was used that allowed variable surface temperature distributions to be imposed by heating the test surface with a radiative lamp prior to cooling. The experiments were restricted to axial variations in surface temperature. Surface temperatures were measured with both cement-on foil thermocouples and thermochromic liquid crystal thermography. A semianalytic superposition technique was developed that was capable of predicting the heat transfer for any arbitrary axial surface temperature distribution, given the general solution or “Green's” function. The Green's function was measured to a limited spatial resolution by solving a simultaneous set of equations using data from 30 experiments. The techniques were developed and tested in a 2-D flat-plate boundary layer with Reδ2 of 3500 at the leading edge and qualified against a well-verified boundary-layer code. The Green's function and inverse Green's function were then measured in a turbulent backward-facing step flow with Re based on step height of 26,000. In the separated flow, it was found that the effect of localized heating extended only a short distance upstream and downstream, and that the heat transfer was less sensitive to temperature boundary conditions than would be expected from attached flow behavior. This corroborates the conclusion of previous workers that the primary resistance to the heat transfer is localized near the wall. This localized behavior, and the spatial insensitivity of the Green's function, suggest that with proper scaling, the results could be extended to other separated flows.
This paper presents a comprehensive review of the flow and heat transfer results of single-phase laminar mixed convection flow over vertical, horizontal and inclined backward- and forward-facing steps that have been reported in several studies in the open literature. The purpose of this paper is to give a detailed summary of the effect of several parameters such as step height, Reynolds number, Prandtl number, inclination angle, expansion ratio, temperature difference between the heated wall and the free stream, and buoyancy force (assisting and opposing) on the flow and thermal fields downstream of the step. Several correlation equations that were reported in many of these studies to predict the reattachment lengths of the recirculation regions that may develop upstream and/or downstream of the step are also summarized in this review.
Flow and thermal control downstream of a backward-facing step has been performed in order to achieve heat transfer enhancement by introducing small disturbance with electromagnetic flap actuators on the step edge. Flap oscillation frequency and amplitude were both changed variously under the laminar flow condition. As the flap oscillation frequency increases, heat deterioration area just behind the step rapidly decreases its size until the oscillation Strouhal number Sr equals up to 0.35, but increases once and then intensively decreases again. Thus, the largest heat transfer enhancement is obtained at the highest oscillation frequency Sr=4.0 within the studied frequency ranges, though sub-optimum frequency around 0.2<Sr<0.35 is also obtained. From velocity measurements by PIV, it was found that intensifications of two different fluid motions, i.e., a large-scale unsteady vortex and a downward high-speed flow, are the main cause to enhance the heat transfer in the sub-optimum and in the high-frequency conditions, respectively.
We report experimental data on the heat transfer performance of a periodically baffled tube subject to both steady (net) flow and oscillatory flow. The data show that, in particular, at a low net flow Reynolds number, significant heat transfer enhancement can be achieved with the superposition of fluid oscillations. A general correlation is derived for the measured Nusselt number as a function of both net flow and oscillatory Reynolds number. Dynamic pressure drop data for oscillatory flow are also reported, and estimates of energy efficiency for obtaining heat transfer enhancement made from these measurements are compared with smooth wall turbulent flow equations. For large amplitudes of oscillation (equivalent to half the tube diameter) the overall power dissipation follows the quasi-steady theory. At smaller amplitudes of oscillation the power dissipation was larger than predicted by the quasi-steady theory, indicating an increased eddy interaction.