Time-averaged Reynolds Number Research Articles

Numerical investigation of the physical-thermal-chemical behaviours of particles during coal combustion and desulfurization processes in a CFB combustor

The desulfurization process has been practised for the clean utilization of coal in chemical engineering fields, yet the physical, thermal, and chemical characteristics of particles are still lacking understanding. In this work, a comprehensive numerical model based on the Eulerian-Lagrangian framework was established to study the particle behaviours during coal combustion and desulfurization processes in a pilot-scale circulating fluidized bed (CFB) combustor. After model validation, the effects of several crucial operation parameters (e.g., excess air ratio, calcium to sulphur ratio, and calcium oxide size) on particle behaviours are illuminated. The results show that density-induced segregation causes coal particles to accumulate in the upper part of the riser. The sand, coal, and CaO particles have time-averaged Reynolds numbers of 15, 6.5, and 0.5, respectively. The particle temperature is higher in areas with lower solid concentrations. Increasing excess air ratio (ϕg) decreases the temperature of sand particles but elevates that of coal and CaO particles. The average particle heat transfer coefficients (HTCs) for sand, coal, and CaO particles are 205 W/m2·K, 172 W/m2·K, and 275 W/m2·K, respectively. With the increase in ϕg, the HTC of sand particles increases but that of CaO particles remains unchanged, additionally, the mass of coal particles decreases and the mass of carbon in coal particles decreases along with the riser. The influence of the Ca/S ratio and CaO size on the axial distribution of coal particle mass and carbon mass fraction is negligible. For each particle species, the axial dispersion coefficient (Dz) is two orders of magnitude greater than the radial ones (Dx, Dy), indicating that the vertical introduction of the fluidizing gas dominates the dense gas-solid flow in the riser.

Experimental study on the control of temperature oscillation in power electronics via pulsating jet impingement

Thermal oscillations in power electronics due to transient load conditions present a significant challenge. This experimental study investigates the application of intermittent jet impingement, coupled with transient heat flux boundary conditions of 100 W, 200 W, and 300 W, to a thermal test chip at a frequency of 0.5 Hz (70 % duty cycle), to assess its effectiveness in minimizing junction temperature fluctuations. Temperature oscillations were recorded to compare the advantages of intermittent pulsation over steady jet flow. The results demonstrate reduced hot spot temperature oscillations of 10 %, 12.5 %, and 16.7 % at 100 W, 200 W, and 300 W, respectively, at a Reynolds number of 8850. Remarkably, even during the pulsation off-period, the minimum temperature limit was maintained at the inlet temperature of the jet, attributed to the formation of strong vorticity rings at the end of the jet pulse, inducing a cooling effect and reducing the junction temperature. Pulsating jets exhibit superior control over temperature fluctuation compared to steady jets, with the reduction being more pronounced at Reynolds numbers closer to 2000 and diminishing as Reynolds number increases to 17000. Moreover, the heat transfer coefficient and the Nusselt number enhanced by 18 % due to pulsating jet impingement. An enhancement factor is introduced to quantify the benefits of using pulsating jets, revealing a higher reduction in temperature oscillation compared to steady jets at the same time-averaged Reynolds number, valid within the Reynolds number range of 2000–14000. Additionally, a correlation is proposed to calculate the enhancement factor for pulsating jets. Finally, the pulsating jet impingement proves to reduce the exergy destruction by 30 % compared to steady jet.

Impact of jet intermittency on surface-structured heat sinks for electronics liquid cooling

The boosting heat generation rate of high-performance processors is challenging the conventional cooling techniques. Passive surface structure designs no longer satisfy the heat dissipation requirement. The present work proposes the combined design of active jet intermittency and passive surface modification in heat sinks, and evaluates the heat transfer enhancement through numerical and experimental approaches. The trapezoidal-waveform flow rate at the inlet has constant time-averaged Reynolds number of 763 and the Strouhal number ranges from 0.01 to 0.04. The surface geometry includes cylindrical groove and hemispherical dimple with different arrangements. The underlying physics of thermal performance improvement is explained by complex flow circulation that disrupts the thermal boundary layer growth and dynamic vortex motion that promotes mixing between near-wall fluid and mainstream coolant. Higher pulsation frequency and smaller duty cycle are beneficial for cooling enhancement while the percentage improvement of dimple structure is higher than groove structure, which agrees with the experimental results. Compared to the steady-flow flat heat sink, a maximum enhancement of 45% is obtained by adopting intermittent jet at grooved surface.

Energy buffer mechanism for heat transfer enhancement in grooved channel cooling with flow intermittency

Driven by the ever-growing heat load in industrial applications such as fast charging electrical vehicle batteries and high-performance processors, advanced cooling technologies for efficient thermal management are urgently needed. This numerical work demonstrates the great potential of flow intermittency in grooved channels for thermal performance improvement at laminar condition, and aims to reveal the underlying mechanism that governs the heat transfer enhancement. The open-source computational fluid dynamics code OpenFOAM is employed to resolve the intermittent channel flow with triangular surface grooves. The time-averaged Reynolds number Re m = 100 and the Strouhal number St = 0.2 are maintained, while the close time ratio γ ranges from 0.1 to 0.9. The thermal performance improvement is attributed to the “energy buffer” mechanism by cavity vortices, which induces strong near-wall reverse flow and promotes effective mainstream-boundary flow mixing. The results indicate that the averaged surface Nusselt number consistently increases with the close time ratio and at γ = 0.9 reaches 1.9 times of the steady-flow value. Particularly the heat transfer performance inside grooves is remarkably improved by a maximum of 175%. This novel concept of synergizing flow intermittency and surface structure achieves notable heat transfer enhancement under constant coolant consumption, and shows ample design space for further optimization.

The effect of modulated driving on non-rotating and rotating turbulent plane Couette flow

Direct numerical simulations of turbulent non-rotating and rotating plane Couette flow with a periodically modulated plate velocity are conducted to study the effect of modulated forcing on turbulent shear flows. The time-averaged shear Reynolds number is fixed at $Re_S = 3 \times 10^4$ , which results in a frictional Reynolds number of approximately $Re_\tau \approx 400$ . The modulating frequency is varied in the range $Wo\in (20,200)$ , while the modulating amplitude is kept fixed at $10\,\%$ of the shear velocity except to demonstrate that varying this parameter has minimal effect. The resulting shear at the plates is found to be independent of the forcing frequency, and equal to the non-modulated baseline. For the non-rotating simulations, two clear flow regions can be seen: a near-wall region that follows Stokes’ theoretical solution, and a bulk region that behaves similar to Stokes’ solutions but with an increased effective viscosity. For high driving frequencies, the amplitude response follows the scaling laws for modulated turbulence of von der Heydt et al. (Phys. Rev. E, vol. 67, 2003, 046308). Cyclonic rotation is not found to modify the system's behaviour in a substantial way, but anti-cyclonic rotation changes significantly the system's response to periodic forcing. We find that the persistent axial inhomogeneities introduced by mild anti-cyclonic rotation make it impossible to measure the propagation of the modulation adequately, while stronger anti-cyclonic rotation creates regions where the modulation travels instantaneously.

Two-dimensional shear rate field and flow structures of a pseudoplastic fluid in a stirred tank using particle image velocimetry

For non-Newtonian fluids, an accurate determination of the shear rate is essential to optimize process parameters, which can lead to the improvement of the process efficiency. This work proposes the evaluation of an aqueous solution of carboxymethylcellulose (CMC) analyzing two azimuthal planes, AZ 0° and 45°, and four blade positions, AR 0°, 22.5°,45° and 67.5°, by ensemble-averaged and angle-resolved PIV measurements, respectively, in a stirred tank equipped with a pitched-turbine impeller. Results are shown in terms of time-averaged velocity, shear rate, apparent viscosity and Reynolds number fields. Differences between both PIV measurements approaches were significant in terms of velocity magnitude and characteristics of trailing vortices. The results demonstrate that the shear rate is strongly influenced by spatial resolution. The highest shear rates were obtained in the impeller region. The presence of a vortex above the blade resulted in high values of local Reynolds number, reflecting the presence of turbulence in that region.

Experimental Study and Conjugate Heat Transfer Simulation of Pulsating Flow in Straight and 90° Curved Square Pipes

The turbulent pulsating flow and heat transfer in straight and 90° curved square pipes are investigated in this study. Both experimental temperature field measurements at the cross-sections of the pipes and conjugate heat transfer (CHT) simulation were performed. The steady turbulent flow was investigated and compared to the pulsating flow under the same time-averaged Reynolds number. The time-averaged Reynolds number of the pulsating flow, as well as the steady flow, was approximately 60,000. The Womersley number of the pulsating flow was 43.1, corresponding to a 30 Hz pulsating frequency. Meanwhile, the Dean number in the curved pipe was approximately 31,000. The results showed that the local heat flux of the pulsating flow was greater than that of the steady flow when the location was closer to the upstream pulsation generator. However, the total heat flux of the pulsating flow was less than that of the steady flow. Moreover, the instantaneous velocity and temperature fields of the simulation were used to demonstrate the heat transfer mechanism of the pulsating flow. The behaviors, such as the obvious separation between the air and pipe wall, the low-temperature core impingement, and the reverse flow, suppress the heat transfer.

A COMMENT ON UNSTEADY–PERIODIC FLOW FRICTION FACTOR: AN ANALYSIS ON EXPERIMENTAL DATA GATHERED IN PULSATILE PIPE FLOWS

In 1940’s, Schultz- Grunow proposed that time-average value of friction factor, λ_u,ta was similar to its corresponding steady state value, λ for the presence of gradual and slow oscillations in pulsatile flows. A recent approach was available for low frequency pulsatile flows through narrow channels in transitional and turbulent regimes by Zhuang et al, in 2016 and 2017. In this analysis; extensive experimental data of λ_u,ta in fully laminar and turbulent sinusoidal flow are processed in the measured time-average Reynolds number range of 1390 ≤ Re_ta ≤ 60000 disregarding the transitional regime. The ranges of dimensionless frequency-Womersley number, √(ω') and oscillation amplitude, A_1 are 2.72 ≤ √(ω') ≤ 28 and 0.05 ≤ A_1≤ 0.96 respectively. A multiplication element is defined as Mel = Re_ta×√(ω^'). A modified friction multiplier, λ_(Mel ) which is similar to the conceptual parameter of Zhuang et al’s friction factor ratio C ( λ_Mel = λ_(u,ta)/λ ) is also referred. The correlation of λ_Mel = λ_Mel (Mel) is dependent on flow regime and the magnitude of Re_ta for the range of √(ω^') > 1.32. The proposal of Schultz-Grunow is verified irrespective of the oscillations in turbulent regime since the magnitude of λ_Mel = 1 is observed for turbulent flow cases with Re_(ta ) ≥ 35000. In laminar regime the magnitude of Re_(ta ) is governing the fact. The magnitude of λ_Mel varies in 0.589 ≤ λ_Mel ≤ 28.125 for Re_(ta ) ≤ 5000 while λ_Mel = 1 is obtained for Re_(ta ) > 5000. The graphical representation of λ_Mel = λ_Mel (Mel) can be considered as a counterpart of Moody Diagram in pulsatile fields for a significant practice.

Experimental study of transient friction characteristics and velocity distribution of pulsatile flow in rod bundles

Rod bundles are widely used in various devices and energy engineering including heat exchangers, nuclear fuel assembly and so on. The transient fluctuation of flow rate in the thermal devices is a common phenomenon under accident scenarios or ocean condition, the study of pulsatile flows has significant practical relevance for the design and safety of thermal devices. In order to determine the flow characteristics of pulsatile flows in rod bundles, the experimental investigations for transient friction loss and evolution of flow field of pulsatile flows of a 5 × 5 rod bundle (P/D = 1.326) are performed. The experiments were conducted under the ranges of time-averaged Reynolds number Reta = 2000–7000, pulsatile amplitude Au = 0.2–0.6 and pulsatile period T = 10 s–100 s. A comparison of friction factors under steady flows and pulsatile flows is performed to determine the influence of pulsatile flows on frictional characteristics. The results show that the transient friction factors versus flow rate under pulsatile flow presents an “oval” shape, and the “oval” shape has a variation with pulsatile parameters changing. To further reveal the details of pulsatile flow fields, the evolution of flow pattern in the pulsatile flow of Reta = 5200, Au = 0.6, T = 10 s is visualized in rod bundles by Particle Image Velocimetry (PIV). The velocity distribution in different stages of pulsatile flows are displayed and discussed. The influence of velocity gradient and turbulent shear stress in the whole pulsatile period for frictional loss is analyzed, and the variation of transient friction factors under different pulsatile parameters is revealed. The results describe transient behaviors to contribute a better understanding for transient flows in fuel assemblies.

Experimental study of velocity components of low-RE pulsatile flow through bare rod bundle

The possibility of unsteady flow through rod bundles is currently gaining attention from researchers.Velocity components of pulsatile flow (time-averaged Reynolds number = 0.7–4.0 × 103) through 5 × 5 square array bare rod bundles (P/D = 1.326 and W/D = 1.268) has been investigated experimentally. The responses of axial and lateral velocities to the sinusoidal imposed pulsation were different. The axial velocity responded directly to the imposed pulsation while the lateral velocity diminished. Also, the response in the subchannels and gaps was different. The axial velocity in the gaps followed the imposed trend, while at the subchannel, the acceleration was steep but the deceleration steady. Lateral velocity in the gaps and subchannels differs by an average of 40%. Turbulence was higher on the rod surfaces compare to other points. The dissimilarity in the acceleration and deceleration half-cycles suggests that there is a difference in the instantaneous parameters during acceleration and deceleration. Further in situ measurements of the pressure field is a potential follow-up study.

Periodically driven Taylor–Couette turbulence

We study periodically driven Taylor–Couette turbulence, i.e. the flow confined between two concentric, independently rotating cylinders. Here, the inner cylinder is driven sinusoidally while the outer cylinder is kept at rest (time-averaged Reynolds number is $Re_{i}=5\times 10^{5}$). Using particle image velocimetry, we measure the velocity over a wide range of modulation periods, corresponding to a change in Womersley number in the range $15\leqslant Wo\leqslant 114$. To understand how the flow responds to a given modulation, we calculate the phase delay and amplitude response of the azimuthal velocity. In agreement with earlier theoretical and numerical work, we find that for large modulation periods the system follows the given modulation of the driving, i.e. the behaviour of the system is quasi-stationary. For smaller modulation periods, the flow cannot follow the modulation, and the flow velocity responds with a phase delay and a smaller amplitude response to the given modulation. If we compare our results with numerical and theoretical results for the laminar case, we find that the scalings of the phase delay and the amplitude response are similar. However, the local response in the bulk of the flow is independent of the distance to the modulated boundary. Apparently, the turbulent mixing is strong enough to prevent the flow from having radius-dependent responses to the given modulation.

Characteristics of the wall shear stress in pulsating wall-bounded turbulent flows

A pulsating turbulent pipe flow has been investigated experimentally using hot-film anemometry and particle image velocimetry. Particularly, a ‘paradoxical phenomenon’ that is known to occur for a range of forcing frequencies and time-averaged Reynolds numbers has been investigated in detail. The paradoxical phenomenon is that the oscillating component of the wall shear stress exhibits a smaller amplitude in a turbulent flow compared to in a laminar flow exposed to the same oscillation in the pressure gradient. In here, the phenomenon is explained by splitting the response of the wall shear stress into one contribution resulting from the imposed pressure gradient τ∼p, and a second contribution resulting from the oscillating Reynolds shear stress, τ∼t. At the conditions of maximum reduction of the wall shear stress amplitude, τ∼p and τ∼t are nearly 136° out of phase. The contributions are thus interfering destructively, this being the ultimate reason for the reduced amplitude. It is also shown that the level of reduction is dependent on the imposed forcing amplitude, this in turn residing from a dependence of the time-development of the oscillating Reynolds shear stress on the forcing amplitude.

Heat transfer characteristics of oscillating flow in a narrow channel under rolling motion

In order to investigate the effect of ocean conditions on heat transfer characteristics of oscillating flow in a narrow channel, a series of experimental researches were performed. The results demonstrate that the mass flux fluctuates with the rolling motion, and the fluctuation intensity of the mass flux is enhanced with the increase of rolling amplitude and rolling frequency due to the effect of additional pressure drop on the fluid. The relative pulsating amplitude of mass flux, Reynolds number and Nusselt number increases with the increase of rolling amplitude, however it decreases with the increase of rolling period, Prandtl number and time average Reynolds number. The time average Nusselt number under rolling motion is equal to that under steady state, and can be predicted by the Sieder-Tate correlation in the laminar flow region and the Gnielinski correlation in the turbulent flow region. Base on the relationship between the relative pulsating amplitude of Reynolds number and Nusselt number a new correlation was developed to predict the instantaneous heat transfer characteristic of oscillating flow under rolling motion condition.

The friction characteristics of low-frequency transitional pulsatile flows in narrow channel

Narrow or mini-channels are widely used in various devices of process and energy engineering including research-reactors, compact heat exchangers and fuel cells. Friction characteristics in laminar–turbulent transition range of low-frequency pulsatile flows in a narrow rectangular duct have been studied. The experiments were conducted under the conditions of time-averaged Reynolds number 575<Reta<5583, pulsatile amplitude 0.056<Au<0.988, and dimensionless frequency 0.52⩽ω′⩽2.34. The results indicate that: (1) the impact of flow fluctuation on friction characteristics is most significant in the transitional range. The pulsatile amplitude and dimensionless frequency have comprehensive impact on time-averaged friction characteristics. The ratio C (C=λta/λst) of time-averaged friction factor to steady-state friction factor, increases with the increasing pulsatile amplitude Au and dimensionless frequency ω′. A dimensionless acceleration was proposed to analyze the influence form and degree of pulsatile parameters. (2) The increasing of ω′ and Au cause a decrease in the pulsatile critical Reynolds number Reta,cr. In addition, a correlation is proposed to predict the pulsatile critical Reynolds number. Transitional pulsatile flow may undergo cross regime process, i.e., laminar, transition, turbulence and re-laminarization. The decrease of pulsatile critical Reynolds number caused by the increasing ω′ and Au, and the cross regime process was inferred to be responsible for the increase of time-averaged friction factor.

Heat transfer enhancement by velocity field excitation for an impinging round jet

ABSTRACTIn this paper the effect of inlet velocity field excitation on heat transfer by an impinging round jet has been investigated using Large Eddy Simulations (LESs). The time-averaged bulk Reynolds number (Re) of the jet for all cases is 23,000 and the dimensionless jet’s outlet-to-target wall distance (H) is two diameters. The Strouhal number (St) corresponding to the preferred mode of the unexcited jet is estimated through LES. The jet is then excited at different frequencies. The amplitude of excitation is kept at 50% of the bulk inlet velocity. It has been found that the excitation of the jet velocity field causes only large-scale excitation. Heat transfer enhancement is found to be possible with inlet velocity field excitation.

AN OVERVIEW ON PULSATILE FLOW DYNAMICS

Pulsatile flow dynamics in reference to the relevant experimental research on the manner between the time periods of 1997- 2015 is presented in this paper. The flow field under discussion is generated through a rigid circular cross-sectional pipe as an axial slightly- compressible and sinusoidal one in a controlled range of the oscillation parameters. Laminar and turbulent flow regimes are considered with a particular emphasis devoted to the transitional characteristics of laminar pulsatile flow into turbulence. The definitions of the flow characteristics, the methodology of the experimental studies and the results on the physical nature of the field are described. The departure of pulsatile flow from a steady one is presented in reference to the velocity field and frictional field analyse sunder the influence of oscillation frequency and amplitude. In this context, the critical magnitudes of Womersley number, time-averaged Reynolds number and oscillation amplitude to estimate the ranges of pulsatile flow field are proposed

Local experimental heat transfer of single-phase pulsating laminar flow in a square mini-channel

Disturbing a single-phase laminar internal convective flow with a particular pulsating flow frequency alters the thermal and hydrodynamic boundary layer, thus affecting the inter-particle momentum and energy exchange. Due to this externally imposed flow disturbance, augmentation in the heat transfer may be expected. Obviously, parameters like pulsating flow frequency vis-à-vis viscous time scales and the imposed pulsating amplitude will play an important role. Conclusions from reported literature on this and related problems are rather incoherent. Lack of experimental data, especially in micro-/mini internal convective flow situations, with imposed flow pulsations, motivates this study. Non-intrusive infra-red thermography has been utilized to scrutinize heat transfer augmentation during single-phase laminar pulsating flow in a square mini-channel of cross-section 3 mm × 3 mm, electrically heated from one side by a thin SS strip heater (70 μm, negligible thermal inertia); all the other three sides of the channel are insulated. The study is done at different pulsating flow frequencies of 0.05 Hz, 1.00 Hz and 3.00 Hz (Wo = 0.8, 3.4 and 5.9, respectively). These values are chosen because pulsatile velocity profiles exhibit different characteristics for Wo > 1 (annular effect, i.e., peak velocity near the channel walls) and Wo < 1 (conventional parabolic profile). Local streamwise heat transfer coefficient has been determined using the time averaged spatial IR thermograms of the heater surface and the local fluid temperature, linearly interpolated from measured value of inlet and outlet bulk mean mixing temperature. It is observed that for measured frequency range, the overall enhancement in the heat transfer is not attractive for laminar pulsating flow in comparison to steady flow with same time-averaged flow Reynolds number. The change is either marginal or highly limited, primarily occurring in the developing length of the channel. Thus, the results suggest that heat transfer enhancement due to periodic pulsating flow is questionable, and at best, rather limited.

Thermal Management Using Pulsating Jet Cooling Technology

The existing methods of heat removal from compact electronic devises are known to be deficient as the evolving technology demands more power density and accordingly better cooling techniques. Impinging jets can be used as a satisfactory method for thermal management of electronic devices with limited space and volume. Pulsating flows can produce an additional enhancement in heat transfer rate compared to steady flows. This article is part of a comprehensive experimental and numerical study performed on pulsating jet cooling technology. The experimental approach explores heat transfer performance of a pulsating air jet impinging onto a flat surface for nozzle-to-surface distances 1 ≤ H/D ≤ 6, Reynolds numbers 1,300 ≤ Re ≤ 2,800 pulsation frequency 2Hz ≤ f ≤ 65Hz, and Strouhal number 0.0012 ≤ Sr = fD/Um ≤ 0.084. The time-resolved velocity at the nozzle exit is measured to quantify the turbulence intensity profile. The numerical methodology is firstly validated using the experimental local Nusselt number distribution for the steady jet with the same geometry and boundary conditions. For a time-averaged Reynolds number of 6,000, the heat transfer enhancement using the pulsating jet for 9Hz ≤ f ≤ 55Hz and 0.017 ≤ Sr ≤ 0.102 and 1 ≤ H/D ≤ 6 are calculated. For the same range of Sr number, the numerical and experimental methods show consistent results.

Hydrodynamics of piston-driven laminar pulsating flow: Part 2. Fully developed flow

Piston-driven pulsating flow is a specific type of pressure-driven pulsating flows. In this study, piston-driven laminar pulsating flow in a pipe is studied. This study mainly exists of two parts: developing flow and fully developed flow. In this part, hydrodynamically fully developed flow is examined analytically, numerically and experimentally. A constant value of the time-averaged Reynolds number is considered, Re=1000. In the theoretical studies, both analytical and numerical, an inlet velocity profile representing the experimental case, i.e., the piston driven flow, is assumed. In the experiments, in the hydrodynamically fully developed region, radial velocity distribution and pressure drop are obtained using hot-wire anemometer and pressure transmitter, respectively. The effect pulsation frequency on the friction coefficient as well as velocity profiles are obtained. A good agreement is observed among analytical, numerical and experimental results.

Hydrodynamics of piston-driven laminar pulsating flow: Part 1. Developing flow

Piston-driven pulsating flow is a specific type of pressure-driven pulsating flows. In this study, piston-driven laminar pulsating flow in a pipe is studied. This study mainly consists of two parts: developing flow and fully developed flow. In this part, hydrodynamically developing flow is examined numerically. A commercially available CFD package, FLUENT, is used in the simulations. A constant value of the time-averaged Reynolds number is considered, Re=1000. The piston velocity is incorporated into the inlet velocity profile at the inlet. Effect of the pulsation frequency on the friction coefficient as well as axial velocity field is obtained.