Numerical modeling of pin–fin micro heat exchangers

A micro heat exchanger (MHE) can effectively control the temperature of surfaces in high heat flux applications. In this study, several turbulence models are analyzed using a 3D finite element model of a MHE. The MHE consists of a narrow planar flow passage between flat parallel plates with small cylindrical pin fins spanning these walls. The pin fin array geometry investigated is staggered, with pin diameters of 0.5, 5.1 and 8.5 mm, height to diameter ratio of 1.0 and streamwise (longitudinal) and spanwise (transverse) to diameter ratios of 1.5 and 2.5, respectively. Pressure loss and heat transfer simulated results for 4,000 ≤ Re ≤ 50,000 are reported and compared with previously published numerical and experimental results. It was found that the flat micro pin fin overall thermal performance always exceeds that of the parallel plate counterpart (smooth channel) by a factor of as much as 2.2 for the 8.5 mm diameter pins, and by 4 for the 0.5 mm diameter pins in the investigated Reynolds number range. Further, among the six turbulence models investigated, the RNG model tends to be the best model to predict both the Nusselt number and the friction factor and capture the main feature of the flow field in MHE.     

Experimental study on the heat transfer and pressure drop of a cross-flow heat exchanger with different pin–fin arrays

In this study, convective heat transfer and pressure drop in a cross-flow heat exchanger with hexagonal, square and circular (HSC) pin–fin arrays were studied experimentally. The pin–fins were arranged in an in-line manner. For the applied conditions, the optimal spacing of the pin–fin in the span-wise and stream-wise directions has been determined. The variable parameters are the relative longitudinal pitch (S _L /D = 2, 2.8, 3.5), and the relative transverse pitch was kept constant at S _T /D = 2. The performances of all pin–fins were compared with each other. The experimental results showed that the use of hexagonal pin–fins, compared to the square and circular pin–fins, can lead to an advantage in terms of heat transfer enhancement. The optimal inter-fin pitches are provided based on the largest Nusselt number under the same pumping power, while the optimal inter-fin pitches of hexagonal pin–fins are S _T /D = 2 and S _L /D = 2.8. Empirical equations are derived to correlate the mean Nusselt number and friction coefficient as a function of the Reynolds number, pin–fin frontal surface area, total surface area, and total number. Consequently, the general empirical formula is given in the present form.

Numerical simulation of a compressible vortex–wall interaction

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number \(M = 1.36\)) and shock-embedded \((M = 1.57)\) compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for \(M = 1.36\) and it reaches up to 60 % for \(M = 1.57\). The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.     

Hybrid liquid metal–water cooling system for heat dissipation of high power density microdevices

The recent decades have witnessed a remarkable advancement of very large scale integrated circuits (VLSI) and electronic equipments in micro-electronic industry. Meanwhile, the ever increasing power density of microdevices leads to the tough issue that thermal management becomes rather hard to solve. Conventional water cooling is widely used, but the convective coefficient is not high enough. Liquid metal owns much higher convective coefficient and has been identified as an effective coolant recently, but the high cost greatly precludes its large scale utilization. In this paper, a hybrid liquid metal–water cooling system which combines the advantages of both water and liquid metal cooling was proposed and demonstrated. By utilizing a liquid metal “heat spreader” in front of the water cooling module, this system not only owns more excellent cooling capability than that based on water alone, but also has much lower initial cost compared with absolute liquid metal cooling system. A series of experiments under different operation conditions have been performed to evaluate the cooling performance of this hybrid system. The compared results with absolute water cooling and liquid metal cooling system showed that the cooling capability of the new system is competitive with absolute liquid metal cooling, but the initial cost could be much lower. The theoretical thermal resistance model and economic feasibility also have been analyzed and discussed, which shows that the hybrid liquid metal–water cooling system is quite feasible and useful.     

Numerical simulation and stability analysis of a novel reaction–diffusion COVID-19 model

Nonlinear Dynamics - In this study, a novel reaction–diffusion model for the spread of the new coronavirus (COVID-19) is investigated. The model is a spatial extension of the recent COVID-19...     

Numerical simulation of shock–vortex interaction in Schardin’s problem

Shock diffraction over a two-dimensional wedge and subsequent shock–vortex interaction have been numerically simulated using the AUSM $+$ + scheme. After the passage of the incident shock over the wedge, the generated tip vortex interacts with a reflected shock. The resulting shock pattern has been captured well. It matches the existing experimental and numerical results reported in the literature. We solve the Navier–Stokes equations using high accuracy schemes and extend the existing results by focussing on the Kelvin–Helmholtz instability generated vortices which follow a spiral path to the vortex core and on their way interact with shock waves embedded within the vortex. Vortex detection algorithms have been used to visualize the spiral structure of the initial vortex and its final breakdown into a turbulent state. Plotting the dilatation field we notice a new source of diverging acoustic waves and a lambda shock at the wedge tip.     

A rheological equation for anisotropic–anelastic media and simulation of field seismograms

In many cases, geological formations are composed of layers of dissimilar properties whose thicknesses are small compared to the wavelength of the seismic signal, as for instance, a sandstone formation that has intra-reservoir thin mudstone layers. A proper model is represented by an anisotropic (transversely isotropic) and viscoelastic stress–strain relation. In this work, we consider a sandstone reservoir, such as the Utsira formation, saturated with CO₂ and use White’s mesoscopic model to describe the energy loss of the seismic waves. The mudstone layers are assumed to be isotropic, poroelastic and lossless. Then, Backus averaging provides the complex and frequency-dependent stiffnesses of the transversely isotropic (TI) long-wavelength equivalent medium. We obtain the associated wave velocities and quality factors as a function of frequency and propagation direction, while the synthetic seismograms are computed with a finite-element (FE) method in the space-frequency domain. In this way, the frequency-dependent properties of the medium are modeled exactly, without the need of approximations with viscoelastic mechanical models. Numerical simulations of synthetic seismograms show results in agreement with the predictions of the theories and significant differences due to attenuation and anisotropic effects compared to the ideal isotropic and lossless rheology.     

Numerical study of turbulent flow and heat transfer of Al2O3–water mixture in a square duct with uniform heat flux

Turbulent flow and convective heat transfer of a nanofluid made of Al₂O₃ (1–4 vol.%) and water through a square duct is numerically studied. Single-phase model, volumetric concentration, temperature-dependent physical properties, uniform wall heat flux boundary condition and Renormalization Group Theory k-ε turbulent model are used in the computational analysis. A comparison of the results with the previous experimental and numerical data revealed 8.3 and 10.2 % mean deviations, respectively. Numerical results illustrated that Nu number is directly proportional with Re number and volumetric concentration. For a given Re number, increasing the volumetric concentration of nanoparticles does not have significant effect on the dimensionless velocity contours. At a constant dimensionless temperature, increasing the particle volume concentration increases the size of the temperature profile. Maximum value of dimensionless temperature increases with increasing x/D_h value for a given Re number and volumetric concentration.     

Dynamic problems for and stress–strain state of inhomogeneous shell structures under stationary and nonstationary loads

This paper reviews studies and analyzes results on the effect of discrete ribs on the dynamic characteristics of rectangular plates and cylindrical shells. Use is made of the vibration equations derived from the classical theories of beams, plates, and shells. The effect of Pasternak’s elastic foundation on the critical velocities of a structurally orthotropic model of a ribbed cylindrical shell is determined. Nonstationary problems are solved for perforated and ribbed shells of revolution filled with a fluid or resting on an elastic foundation and subjected to moving or impulsive loads. Results from studies of the behavior of sandwich shell structures under impulsive loads of various types are presented     

Numerical investigation of fluid–particle interactions for embolic stroke

Roughly one-third of all strokes are caused by an embolus traveling to a cerebral artery and blocking blood flow in the brain. The objective of this study is to gain a detailed understanding of the dynamics of embolic particles within arteries. Patient computed tomography image is used to construct a three-dimensional model of the carotid bifurcation. An idealized carotid bifurcation model of same vessel diameters was also constructed for comparison. Blood flow velocities and embolic particle trajectories are resolved using a coupled Euler–Lagrange approach. Blood is modeled as a Newtonian fluid, discretized using the finite volume method, with physiologically appropriate inflow and outflow boundary conditions. The embolus trajectory is modeled using Lagrangian particle equations accounting for embolus interaction with blood as well as vessel wall. Both one- and two-way fluid–particle coupling are considered, the latter being implemented using momentum sources augmented to the discretized flow equations. It was observed that for small-to-moderate particle sizes (relative to vessel diameters), the estimated particle distribution ratio—with and without the inclusion of two-way fluid–particle momentum exchange—were found to be similar. The maximum observed differences in distribution ratio with and without the coupling were found to be higher for the idealized bifurcation model. Additionally, the distribution was found to be reasonably matching the volumetric flow distribution for the idealized model, while a notable deviation from volumetric flow was observed in the anatomical model. It was also observed from an analysis of particle path lines that particle interaction with helical flow, characteristic of anatomical vasculature models, could play a prominent role in transport of embolic particle. The results indicate therefore that flow helicity could be an important hemodynamic indicator for analysis of embolus particle transport. Additionally, in the presence of helical flow, and vessel curvature, inclusion of two-way momentum exchange was found to have a secondary effect for transporting small to moderate embolus particles—and one-way coupling could be used as a reasonable approximation, thereby causing substantial savings in computational resources.     

Numerical simulation with a TVD–FVM method for circular cylinder wake control by a fairing

A water drop-shaped fairing is applied to control the wake behind a circular cylinder and to suppress the formation of Karman vortex street in this paper. The results are evaluated using high resolution CFD technique. A finite-volume total variation diminishing (TVD) approach based upon the recently proposed elemental velocity vector transformation (EVVT) method, which aims at solving the incompressible turbulent flow for irregular boundary conditions with renormalization group (RNG) turbulence model, is used to simulate the flow field around circular cylinder systems. The calculations are carried out with cylinder systems with and without fairings, while the fairings have different top shape angles within the range of $30°~90°$. The Reynolds number ranges from 1000 to 50 000. It is shown that the simulation results of present numerical method reaches good agreement with the available experimental and numerical simulation data of typical circular cylinder flow and a fixed fairing cylinder system flow. Compared with bare cylinder, the faired bluff structures can obviously reduce the lift and drag forces and alter the vortex shedding frequency. Overall, the mean drag coefficient can be reduced up to about (10–31)% and the RMS lift coefficient can be reduced up to (30–99)% for all faired systems at given Reynolds numbers. The influence of Reynolds number and attack angles on the flow field characters of bare cylinder and faired cylinders is also discussed. The faired structures with shape angles within $30°~45°$under zero-attack-angle-inflow case are considered as the optimal structures, with which the mean drag coefficient and the RMS lift coefficient can be reduced up to (26–31)% and (98–99)%, respectively. Considering the influence of attack angles on lift and drag coefficients reduction, 75° shaped faired structure may be taken as a proper option.     

A model establishment and numerical simulation of dynamic coupled hydraulic–mechanical–electric–structural system for hydropower station

Nonlinear Dynamics - A nonlinear dynamic coupled model for hydropower station system, which contains the model of water-carriage system, water turbine system, speed governor system,...     

Fluid–structure coupling modelling and parameter optimization of a direct-acting relief valve for underwater application

Nonlinear Dynamics - Direct-acting relief valve is widely applied in pumps for control of pump pressure; when it is applied by underwater equipment, its dynamic stability is challenged by the...     

Numerical simulation of counter-current flow field in the downcomer of a liquid–solid circulating fluidized bed

A comprehensive study on the hydrodynamics in the downcomer of a liquid–solid circulating fluidized bed (LSCFB) is crucial in the control and optimization of the extraction process using an ion exchange LSCFB. A computational fluid dynamics model is proposed in this study to simulate the counter-current two-phase flow in the downcomer of the LSCFB. The model is based on the Eulerian–Eulerian approach incorporating the kinetic theory of granular flow. The predicted results agree well with our earlier experimental data. Furthermore, it is shown that the bed expansion of the particles in the downcomer is directly affected by the superficial liquid velocity in downcomer and solids circulation rate. The model also predicts the residence time of solid particles in the downcomer using a pulse technique. It is demonstrated that the increase in the superficial liquid velocity decreases the solids dispersion in the downcomer of the LSCFB.     

Numerical simulation of gas–solid flow with two fluid model in a spouted-fluid bed

The flow characteristics in a spouted-fluid bed differ from those in spouted or fluidized beds because of the injection of the spouting gas and the introduction of a fluidizing gas. The flow behavior of gas–solid phases was predicted using the Eulerian–Eulerian two-fluid model (TFM) approach with kinetic theory for granular flow to obtain the flow patterns in spouted-fluid beds. The gas flux and gas incident angle have a significant influence on the porosity and particle concentration in gas–solid spouted-fluid beds. The fluidizing gas flux affects the flow behavior of particles in the fountain. In the spouted-fluid bed, the solids volume fraction is low in the spout and high in the annulus. However, the solids volume fraction is reduced near the wall.     

Numerical simulation of hydrogen–air reacting flows in rectangular channels with catalytic surface reactions

In this work a prediction was numerically modeled for a catalytically stabilized thermal combustion of a lean homogeneous mixture of air and hydrogen. The mixture flows in a narrow rectangular channel lined with a thin coating of platinum catalyst. The solution using an in-house code is based on the steady state partial differential continuity, momentum and energy conservation equations for the mixture and species involved in the reactions. A marching technique is used along the streamwise direction to solve the 2-D plane-symmetric laminar flow of the gas. Two chemical kinetic reaction mechanisms were included; one for the gas phase reactions consisting of 17 elementary reactions; of which 7 are forward–backward reactions while the other mechanism is for the surface reactions—which are the prime mover of the combustion under a lean mixture condition—consisting of 16 elementary reactions. The results were compared with a former congruent experimental work where temperature was measured using thermocouples, while using PLIF laser for measuring water and hydrogen mole fractions. The comparison showed good agreement. More results for the velocities, mole fractions of other species were carried out across the transverse and along the streamwise directions providing a complete picture of overall mechanism—gas and surface—and on the production, consumptions and travel of the different species. The variations of the average OH mole fraction with the streamwise direction showed a sudden increase in the region where the ignition occurred. Also the rate of reactions of the entire surface species were calculated along the streamwise direction and a surface water production flux equation was derived by calculating the law of mass action’s constants from the concentrations of hydrogen, oxygen and the rate of formation of water near the surface.     

Green’s function solution for transient heat conduction in annular fin during solidification of phase change material

The Green’s function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.     

Numerical and Experimental Study of Rayleigh–Bénard–Kelvin Convection

We performed experimental and numerical studies of combined effects of thermal buoyancy and magnetization force applied on a cubical enclosure of a paramagnetic fluid heated from below and cooled from top. The temperature difference between the hot and cold wall was kept constant. After considering neutral situation (i.e. a pure natural convection case), magnetic fields of different intensity were imposed. The magnetization force produced significant changes in flow (transition from laminar to turbulent regimes), wall-heat transfer (enhancement) and turbulence (turbulence structures reorganization). The strong magnetic field and its gradients were generated by a superconducting magnet which can generate magnetic field up to 10 T and where gradients of the magnetic induction can reach up to 900 T²/m. A good agreement between experiments and numerical simulations was obtained in predicting the integral wall heat transfer over entire range of considered working parameters. Numerical simulations provided a detailed insights into changes of the local wall-heat transfer and long-term time averaged first and second moments for different strengths of the imposed magnetic induction.     

Numerical simulation of terrain-induced severe slugging coupled by hydrodynamic slugs in a pipeline–riser system

A numerical study based on a one-dimensional two-fluid model is carried out to describe the transient hydrodynamic slugging and terrain-induced severe slugging in a pipeline–riser system. The system of equations is rendered well-posed by interfacial pressure model for the riser. The selected flow conditions are restricted in the well-posed region for the horizontal and the downward inclined pipes to ensure the hydrodynamic slug characteristics are predicted correctly. The validity of the model is examined by water faucet problem and horizontal slug flow experiments. Simulations with and without slug capturing are conducted to address the effect of hydrodynamic slugs on severe slugging. It has been found that more accurate predictions are obtained by taking hydrodynamic slugs into account. At low superficial gas velocity, the simulation without slug capturing tends to overestimate the severe slugging period. When hydrodynamic slugs are captured, the upstream gas expansion is suppressed by the hydrodynamic slugs. At relatively high superficial gas velocity, the simulation without slug capturing tends to underestimate the severe slugging period. When hydrodynamic slugs are captured, the upstream compressible volume is greatly enlarged by the blowout of the hydrodynamic slugs. In both situations, the influences of the hydrodynamic slugs can reduce the errors of the predicted severe slugging characteristics.