Injection Reynolds Number Research Articles

Effect of an inclined magnetic field on dispersion of solute in a pulsatile flow through a channel of absorptive porous walls

The present investigation gives an insight to comprehend the complex mechanism of species transport through porous walls, which has applications for crude oil refining, oil reservoir engineering, and separation of metal from fluids. The paper analyzes the impact of an inclined magnetic field on mass transport phenomena of solute through an unsteady, viscous, incompressible, and electrically conducting fluid flowing between two parallel plates. Both plates are permeable, and the flow is driven by a periodic pressure gradient. At both channel walls, the first order boundary reaction is applied. The governing time depending advection and diffusion equation is solved numerically based on Aris's method of moments. To determine the axial mean concentration distribution of solute, the first four central moments are used in a Hermite polynomial representation. It is significant to note that the dispersion of tracer is more significant for the low frequencies rather than the high frequencies. The behavior of the dispersion process of the tracer is studied for various flow parameters such as the angle of inclination of the magnetic field (α), Hartmann number (M), absorption parameter (β), suction Reynolds number (R), injection Reynolds number (R′), Womersley number (ω), and dispersion time (t) for both purely oscillatory and combined flows. It is significant to note that with the increment of R, α, and M, the amplitude of the dispersion coefficient of the solute reduces. On the other hand, an opposite phenomenon is observed for R′. It is seen that the transport coefficient moves cyclically with a double frequency period for all values of R and R′. Also, it is found that the peak of the mean concentration distribution enhances with the increment of α and M because the flow velocity decreases.

Transient energy growth analysis of flat-plate boundary layer with an oblique and non-uniform wall suction and injection

This paper presents a non-modal bi-global linear stability analysis of an incompressible flat-plate boundary layer under the effects of oblique and non-uniform wall suction and injection. The base flow velocity profile is two-dimensional and fully non-parallel. The flow is laminar at the inflow boundary, and no reverse flow occurs in the flow domain. The Chebyshev spectral collocation method has been used for the discretization of the governing stability equations. The discretized stability equations along with appropriate boundary conditions form an initial value problem (IVP). The transient energy growth (G(t)) and associated optimal perturbations are computed for different oblique angles (θ=30°,60°,90°,120°, and 150°), suction and injection intensities (I=0.5%, 1.5%, and 2.5% of U∞), Reynolds numbers (Re=195,284, and 411), and different spanwise wavenumbers (β=0−2) for uniform and non-uniform profiles of wall suction and injection. The behaviour of the boundary layer is found to be approximately similar but opposite in nature for θ=90° to 180° and θ=0° to 90° due to lower transpiration intensity. The G(t) decreases with the increase in θ from 0° to 90° for wall suction due to the damping of T–S modes. However, an opposite trend has been observed for injection due to the amplification of T–S modes. The uniform profile is found to be more effective than the non-uniform profiles of suction and injection in terms of their impact on the stability of the boundary layer. The 2D spatial structures of the optimal perturbations are damped and flow becomes modally stable as the spanwise wavenumber (β) is increased.

Analyzing the effects of suction and injection Reynolds number on the transport process in a hydromagnetic flow through a channel of reactive porous walls

The present paper analyzes the effects of suction and injection Reynolds number on the dispersion process of solute in an incompressible magneto-hydrodynamics flow through a channel. The walls of the channel are permeable and a first order heterogeneous reaction is applied on it. Also, an inclined magnetic field is employed at both walls of the channel. The unsteady convection-diffusion equation is solved semi-analytically to find out the coefficient of dispersion, skewness and kurtosis of the solute distribution for all time period. Using Hermite polynomial representation, the distribution of mean concentration is obtained. The effects of various parameters such as suction Reynolds number (R), injection Reynolds number (R′), boundary absorption parameter (β), inclination angle of the magnetic field (α), Hartmann number (M) and dispersion time (t) on dispersion process of the solute are examined. It is shown that with the increment of suction Reynolds number, the peak of the mean concentration of solute enhances prominently. But, when injection Reynolds number increases, the amplitude of the mean concentration decreases. The current research gives an insight to understand the complex behavior of transport process of the solute in a hydro-magnetic channel flow with reactive porous walls.

Numerical investigation of an inertization system for a radiative coil coating oven

In this work the inertization of a radiative curing oven for coil coating is numerically investigated. Inertization chambers (IC) — comprised by a confined impinging slot jet and an exhaust slot — are applied at the curing oven openings to prevent external air from entering and toxic solvents from exiting the oven, avoiding simultaneously the contamination of the external surroundings and the development of explosive conditions within the oven. The influence of the main IC operating parameters — extracted-to-injected mass flow rate ratio (Ψ), coil plate-to-jet velocity ratio, injection Reynolds number, and oven pressure — on the safety of the sealing process is investigated considering the validated k-kl-ω transition RANS model. To guarantee safety conditions regarding the IC placed at the metal strip entrance, the corresponding range for Ψ was found to be between 0.8 and 1.6 considering oven pressures ranging from −20 to 20Pa. For the IC placed at the metal strip exit and considering high coil velocities, safety conditions can only be observed with negative oven pressures. Overall, this procedure found a Ψ range between 0.8 and 1.2 that complies with the restrictive safety criteria for a realistic oven operation with typical coil velocities and oven pressures ranging from −20 to 10Pa.

A numerical study on breakup of a liquid jet in an axial electric field

A liquid jet injected from a nozzle stretches in the direction of the applied electric field and subsequently emits multiple droplets on pinch-off. It is hypothesized that the size and frequency of the drops can be manipulated by varying the electric field strength and flow rate, which is essential in electrohydrodynamic jet printing. Numerical simulations of the electrified jet breakup are performed using an in-house code based on the Dual Grid Level Set Method. To comprehend the impact of the electric and hydrodynamic forces, three dimensionless parameters are introduced: injection velocity (0.01≤Vinj≤0.15), Reynolds number (10≤Re≤100) and electric Bond number (0≤Boe≤30).Our results indicate the transition from dripping to micro-dripping and micro-jetting (at high Vinj) with increasing Boe. The critical Boe, at which this transition occurs, is found to escalate with an increase in Re. The stability of the micro-dripping mode is characterized by the balancing of the electrical and viscous shear stresses. Although the influence of the electric Bond number on the jet breakup length is marginal, it has a significant effect on the droplet diameter and formation frequency. A re-formulated scaling law suggests that the jet breakup length is mainly affected by injection velocity and Reynolds number.

Analysis of the re-entrant jet to twin vortex flow regimes transition in ventilated cavitation

The combination of ventilated cavitation (injection of a non-condensable gas in a liquid flow) and natural cavitation (flow vaporization due to a local pressure drop) is studied with a numerical model based on a homogeneous multiphase flow approach, using two transport equations for vapor and air. Ventilated cavitation behind an axisymmetric body is simulated and the results compare well with previous experimental data for both the reentrant jet and the twin vortex flow patterns. The transition between the two regimes is found to be primarily related to a critical shift of the vortices generated behind the body, due to air injection. It is also shown that the critical value of σc⋅Fr (product of ventilated cavitation number with the Froude number) at the transition depends strongly on the shape of the body. The influence of the baseline flow without air injection (Reynolds number and natural cavitation) on the transition is also analyzed. When natural cavitation is negligible, only the twin vortex regime is obtained for a Reynolds number Re < 8 104, while for a higher Re, the ventilation air flow coefficient at transition CQt varies almost linearly with Ln (Re). In presence of additional natural cavitation, (σ < 1), a decrease of CQt is observed. This phenomenon is amplified when natural cavitation increases. This drop of CQt can be directly related to the amount of vapor generated in the flow field, as it is shown that it corresponds to the maximum positive flux of vapor behind the body.

Theoretical analysis of unsteady squeezing nanofluid flow with physical properties.

Theoretical analysis of physical characteristics of unsteady, squeezing nanofluid flow is studied. The flow of nanofluid between two plates that placed parallel in a rotating system by keeping the variable physical properties: viscosity and thermal conductivity. It is analyzed by using Navier Stokes Equation, Energy Equation and Concentration equation. The prominent equations are transformed by virtue of suitable similarity transformation. Nanofluid model includes the important effects of Thermophoresis and Brownian motion. For analysis graphical results are drawn for verity parameters of our interest i.e., Injection parameter, Squeezing number, Prandtle number and Schmidt number are investigated for the Velocity field, Temperature variation and Concentration profile numerically. The findings underline that the parameter of skin friction increases when the Squeezing Reynolds number, Injection parameter and Prandtle number increases. However, it shows inverse relationship with Schmidt number and Rotation parameter. Furthermore, direct relationship of Nusselt number with injection parameter and Reynolds number is observed while its relation with Schmidt number, Rotation parameter, Brownian parameter and Thermophoretic parameter shows an opposite trend. The results are thus obtained through Parametric Continuation Method (PCM) which is further validated through BVP4c. Moreover, the results are tabulated and set forth for comparison of findings through PCM and BVP4c which shows that the obtained results correspond to each other.

Heat transfer and flow velocity study of a row of jets emerging from a perforated pipe at a low Reynolds number

Aerodynamic and thermal experimental investigations were carried out on a row of circular low Reynolds jets emerging from a perforated pipe. Particle Image Velocimetry and Infrared Thermography were performed to determine flow velocity fields and local Nusselt number variations along the impinged plate. Jet Reynolds number (1500<Rej<5000), upstream crossflow in the pipe (1.5<VR<9.7), injection-to-plate distance (3<H/d<7) as well as center-to-center jet spacing (2.25<p/d<5.8) were all taken into account. Measurements were compared to those of a fully developed circular jet issuing from a long tube under the same conditions (3000<Rej<5000 and 3<H/d<7). Experimental results showed that jets tend to emerge with an effective cross-sectional area reduced to a crescent shape unlike that of axisymmetric fully developed jets; their specific structure was attributed to flow deflection from the pipe to the holes and resulted in heat transfer specificities differing from those of a fully developed jet. Heat transfer rates were found to be primarily dependent on injection Reynolds number, injection-to-plate distance and center-to-center spacing, and they were found to be relatively low compared to a fully developed jet.

Similarity solutions of the Navier-Stokes equations for an injection-driven flow between two orthogonally moving porous discs

An incompressible fluid is in motion after injection in the space between two parallel porous discs that can move away or come closer along the same axis passing perpendicular to the midpoints of their respective surfaces. The desire of well describing the incompressible fluid flow patterns and the fact that the velocity field of the axisymmetric flow has two components lead to introduce the stream function in the governing equations. A similarity method is applied to transform the vorticity equation satisfied by the stream function into a nonlinear ordinary differential equation. Thus, the analysis is restricted to solving a two-point boundary-value problem containing two control parameters, notably the Reynolds number and a nondimensional parameter representing the measure of the increase or the decrease in volume of the flow domain. Among the main results, it is found that, the high expansion in volume of the flow domain causes flow reversal for low values of the injection Reynolds number, while the contraction in volume of the flow domain creates a linear behavior of the axial velocity for a small injection Reynolds number and a flattening of the radial velocity profile for all the Reynolds numbers.

Investigation of theoretical scaling laws using large eddy simulations for airborne spreading of viral contagion from sneezing and coughing.

Using a set of large eddy point-particle simulations, we explore the fluid dynamics of an ejected puff resulting from a cough/sneeze. The ejection contains over 61 000 potentially virus-laden droplets at an injection Reynolds number of about 46 000, comparable to an actual cough/sneeze. We observe that global puff properties, such as centroid, puff volume, momentum, and buoyancy vary little across realizations. Other properties, such as maximum extent, shape, and edge velocity of the puff, may exhibit substantial variation. In many realizations, a portion of the puff splits off and advances along a random direction, while keeping airborne droplet nuclei afloat. This peeled-off portion provides a mechanism for virus-laden droplets to travel over large distances in a short amount of time. We also observe that the vast majority of droplets remain suspended within the puff after all liquid has evaporated. The main objectives of the study are to (i) evaluate assumptions of Balachandar's et al. theory [Int. J. Multiphase Flow 132, 103439 (2020)], which include buoyancy effects, shape of the puff, and droplet evaporation rate, (ii) obtain values of closure parameters, which include location and time of the virtual origin, and puff entrainment and drag coefficients, and (iii) evaluate the accuracy of the theory in predicting the shape, size, and location of the puff, as well as droplet number density long after ejection. The theory adequately predicts global puff properties including size, velocity, and distance traveled, the largest size of droplets that exit the puff due to settling, and the droplet size distribution within the puff long after ejection.

KELLER-BOX SOLUTION OF THE STAGNATION POINT MICROPOLAR FLUID FLOW BETWEEN POROUS PLATES WITH INJECTION

The present study deals with the steady axisymmetric flow of micropolar fluid between two parallel porous plates when the fluid is injected through both walls at the same rate. The influence of velocity slip at the porous surface is analyzed. A detailed finite-difference solution is developed for the resulting non-linear coupled differential equations representing velocities and microrotation. The numerical computations are obtained for radial, axial velocities, and microrotation for varying injection Reynolds number, micropolar parameter, and slip coefficient. Further, a comparison of the results is given with those obtained in the literature with different methods as special cases.

Computational analysis of entropy generation in radiative viscous fluid flow

Main focus of present article is to discuss viscous fluid flow over a stretchable plate. The fluid saturates porous medium. Further, the magnetic field, thermal radiation, Joule heating and viscous dissipation impacts are accounted. Entropy generation is evaluated. Obtained PDE’s system of the considered problem is converted to non-dimensional form by suitable variables. PDE’s system (dimensionless) is tackled by a numerical scheme known as finite difference technique. The outcomes of entropy, velocity, skin friction, temperature and Bejan and Nusselt numbers through variation of influential variables are analyzed. The obtained output shows that velocity enhances with injection parameter and Reynolds number; however, it decreases with porosity and Hartmann number. Temperature increases through Eckert, Reynolds and Hartmann numbers. Entropy boosts with Reynolds, Hartmann and Prandtl numbers.

Defect-mediated turbulence in bubbly Taylor-Couette flow

We investigate experimentally the defect-mediated turbulence (DMT) which is induced by bubbles injection in a Taylor-Couette flow when the inner cylinder is rotating while the outer cylinder is fixed. Bubbles of 1.2 mm in diameter are injected at the bottom of a Taylor-Couette device of radii ratio equal to 0.91. The tangential Reynolds number range is [2 200, 19 300] and the air injection rate varies up to 800 ml/min. For these conditions of the experiments, bubbles are trapped in the gap by the Taylor vortices and arranged as patterns (toroidal, wavy toroidal, spirals, and wavy spirals). Visualizations of the bubble patterns were carried out. When decreasing the Reynolds number or increasing the air injection rate, spiral and toroidal patterns can coexist in a composite flow. Defects occur in the bubble’s patterns (merging or splitting of the Taylor vortex pairs). By analyzing the space-time diagram of bubbles patterns and their complex demodulation, we highlight different regimes and transitions in the DMT of the bubbly Taylor-Couette flow. The control parameter of the transitions is the air volumetric fraction, which evolves as the ratio between the axial injection Reynolds number and the tangential Reynolds number. By increasing the air volumetric fraction, the defects in the DMT flows are classified as three flow regimes: (i) structured composite flow where the defects are periodic in space and time, (ii) intermittency defects chaos where the defects zones alternate randomly with the patterns in time and space, and (iii) developed defects chaos with a large defects density. The statistical properties of these three regimes of the DMT are analyzed in the framework of the complex Ginzburg-Landau equation.

Flow and heat transfer of a compressible impinging jet

The influence of injection Mach number over the flow and heat transfer of an impinging air jet is investigated. For a given injection Reynolds number, jets with different injection diameters have been studied, decoupling the effects of injection Reynolds and Mach numbers. Three injection diameters were used, varying injection Mach number from 0.3 to 0.8. The effects of injection-to-plate distance were also studied. Flow was studied using Particle Image Velocimetry and infrared thermography was used to investigate both Nusselt number and adiabatic wall temperature (also called recuperation temperature) variations along the plate. The main effect of Mach number rise on the flow is a decrease in the number of Kelvin-Helmholtz vortices, reducing the amplitude of the secondary maximum of Nusselt number, particularly for low injection to plate spacing. Moreover, for Mach number low values, the adiabatic wall temperature is nearly constant whereas for higher values variations occur depending on injection-to-plate distance. For low distances, the mean radial velocity close to the wall, which presents relatively high values, reduces the temperature above the jet injection total temperature. For higher injection-to-plate distances, ambient air, with higher static temperature, is brought into the jet, increasing the static temperature of the jet and leading to adiabatic wall temperature superior to jet injection total temperature.

Rheological behaviour of various metal-based nano-fluids between rotating discs: a new insight

Abstract In this study, nanofluid flow and heat transfer between two contracting and rotating disks are investigated. Brownian motion is considered to simulate viscosity of nanofluid and Patel model is used to predict the behavior of thermal conductivity of nanofluid. The governing equations are solved via the fourthorder Runge–Kutta method. Different kinds of nanoparticles are examined. Effects of active parameters such as nanoparticle volume fraction, rotational Reynolds number, injection Reynolds number, and expansion ratio are considered. Results indicate that Nusselt number is a decreasing function of expansion ratio while it is increasing function of other parameters such as nanoparticle volume fraction, rotational Reynolds number, and injection Reynolds number. Also, it can be found that maximum value of heat transfer enhancement is obtained by selecting the silver (Ag) as nanoparticle.

Stabilization Mechanisms of Swirling Premixed Flames With an Axial-Plus-Tangential Swirler

The stabilization of premixed flames within a swirling flow produced by an axial-plus-tangential swirler is investigated in an atmospheric test rig. In this system, flames are stabilized aerodynamically away from the solid components of the combustor without the help of any solid anchoring device. Experiments are reported for lean CH4/air mixtures, eventually also diluted with N2, with injection Reynolds numbers varying from 8500 to 25,000. Changes of the flame shape are examined with OH* chemiluminescence and OH laser-induced fluorescence measurements as a function of the operating conditions. Particle image velocimetry (PIV) measurements are used to reveal the structure of the velocity field in nonreacting and reacting conditions. It is shown that the axial-plus-tangential swirler allows to easily control the flame shape and the position of the flame leading edge with respect to the injector outlet. The ratio of the bulk injection velocity over the laminar burning velocity Ub/SL, the adiabatic flame temperature Tad, and the swirl number S0 are shown to control the flame shape and its position inside the combustion chamber. It is then shown that the axial velocity field produced by the axial-plus-tangential swirler is different from those produced by purely axial or radial devices. It takes here a W-shape profile with three local maxima and two minima. The mean turbulent flame front also takes this W-shape in an axial plane, with two lower positions located slightly off-axis and corresponding to the positions where the axial flow velocity is the lowest. It is finally shown that these positions can be inferred from axial flow velocity profiles under nonreacting conditions.

On the viscous core boundary layer of the injection and suction driven channel flows with expanding or contracting walls

AbstractThis work extends a sequence of studies devoted to the analysis of the laminar flow in porous channels with retracting walls. This problem was originally used to model slab propellant grain regression. After identifying a subtle endpoint singularity that affects the former solution in its third derivative, a stretched variable is introduced to capture the rapid variations in the channel's core. The core refers to the midsection plane where the shear layer is displaced due to hard blowing at the walls. Then using matched‐asymptotic expansions with logarithmic corrections, a composite solution is developed following successive integrations that start with the fourth derivative. In the process, the inner correction is retrieved from the fourth‐order equation governing the symmetric injection‐driven flow near the core. The resulting approximation is expressed in terms of generalized hypergeometric functions and is confirmed using numerics and limiting process verifications. The composite solution is shown to outperform the former, outer solution, as the core is approached or as the injection Reynolds number is increased. Without undermining the practicality of the former solution outside the thin core region, the development of a matched‐asymptotic approximation enables us to suppress the often overlooked singular terms, thus ensuring a uniformly valid outcome down to the third and fourth derivatives, which affect the pressure distribution and its normal gradients.

Central recirculation zones and instability waves in internal swirling flows with an annular entry

The characteristics of the central recirculation zone and the induced instability waves of a swirling flow in a cylindrical chamber with a slip head end have been numerically investigated using the Galerkin finite element method. The effects of Reynolds number as well as swirl level adjusted by the injection angle were examined systematically. The results indicate that at a high swirl level the flow is characterized by an axisymmetric central recirculation zone (CRZ). The fluid in the CRZ takes on a solid-body rotation driven by the outer main flow through a free shear layer. Both the solid-body rotating central flow and the free shear layer provide the potential for the development of instability waves. When the injection angle increases beyond a critical value, the basic axisymmetric flow loses stability, and instability waves develop. In the range of Reynolds numbers considered in this study, three kinds of instability were identified: inertial waves in the central flow, and azimuthal and longitudinal Kelvin-Helmholtz waves in the free shear layer. These three types of waves interact with each other and mix together. The mode selection of the azimuthal waves depends strongly on the injection angle, through the perimeter of the free shear layer. Compared with the injection angle, the Reynolds number plays a minor role in mode selection. The flow topologies and characteristics of different flow states are analyzed in detail, and the dependence of flow states on the injection angle and Reynolds number is summarized. Finally, a linear analysis of azimuthal instabilities is carried out; it confirms the mode selection mechanisms demonstrated by the numerical simulation.

Flow and heat transfer of hot impinging jets issuing from lobed nozzles

This article studies the aerodynamic and thermal characteristics of impinging jets issued from lobed injections. They are compared to “traditional” jets issuing from tube. All nozzles have the same free area Ao, and the equivalent diameter for a tube is D = 14 mm. Experiments have been conducted for injection Reynolds numbers from 23,000 to 45,000, for orifice-to-plate distances from H/D = 1–5 and for an injection jet temperature: T∞ ≤ Tj ≤ 50 °C. Flow measurement has shown very specific tridimensional flows particularly for small injection-to-plate spacing (H/D = 1 or 2) and resulting heat transfer rates are very different from those of a jet issuing from a tube. For higher impinging distances, flows and heat transfer become more axisymmetric and more similar to those due to tubular injection.

Viscous Mean Flow Approximations for Porous Tubes with Radially Regressing Walls

The mean gaseous motion in solid rocket motors has been traditionally described using an inviscid solution in a porous tube of fixed radius and uniform wall injection. This model, usually referred to as the Taylor–Culick profile, consists of a rotational solution that captures the bulk gaseous motion in a frictionless rocket chamber. In practice, however, the port radius increases as the propellant burns, thus leading to time-dependent effects on the mean flow. This work considers the related problem in the context of viscous motion in a porous tube and allows the radius to be time dependent. By implementing a similarity transformation in space and time, the incompressible Navier–Stokes equations are first reduced to a nonlinear fourth-order ordinary differential equation with four boundary conditions. This equation is then solved both numerically and asymptotically, using the injection Reynolds number and the dimensionless wall regression ratio as primary and secondary perturbation parameters. In this manner, closed-form analytical solutions are obtained for both large and small Reynolds number with small-to-moderate . The resulting approximations are then compared with the numerical solution obtained for an equivalent third-order ordinary differential equation in which both shooting and the irregular limit that affects the fourth-order formulation are circumvented. This code is found to be capable of producing the stable solutions for this problem over a wide range of Reynolds numbers and wall regression ratios.