Injection Reynolds Number Research Articles

Investigation of the small-scale statistics of turbulence in the Modane S1MA wind tunnel

This article describes the planning, set-up, turbulence characterization and analysis of measurements of a passive grid turbulence experiment that was carried out in the S1MA wind-tunnel from ONERA in Modane, in the context of the ESWIRP European project. This experiment aims at a detailed investigation of the statistical properties of turbulent flows at large Reynolds numbers. The primary goal is to take advantage of the unequaled large-scale dimensions of the ONERA S1MA wind-tunnel facility, to make available to the broad turbulence community high-quality experimental turbulence data with unprecendented resolution (both spatial and temporal) and accuracy (in terms of statistical convergence). With this goal, we designed the largest grid-generated turbulence experiment planned and performed to date. Grid turbulence is a canonical flow known to produce almost perfectly homogeneous and isotropic turbulence (HIT) which remains a unique framework to investigate fundamental physics of turbulent flows. Here, we present a brief description of the measurements, in particular those based on hot-wire diagnosis. By comparing results from classical hot-wires and from a nano-fabricated wire (developed at Princeton University), we show that our goal of resolving down to the smallest dissipative scales of the flow has been achieved. We also present the full characterization of the turbulence here, in terms of turbulent energy dissipation rate, injection and dissipation scales (both spatial and temporal) and Reynolds number.

A comparison between the stabilization of premixed swirling CO2-diluted methane oxy-flames and methane/air flames

Revamp of air powered industrial boilers to oxy-combustion operation raises several issues. In this study, the stabilization of CO2-diluted premixed swirling CH4/O2 flames is compared to operation with CH4/air flames by a set of experiments in a generic labscale combustor equipped with an axial-plus-tangential swirler. The investigated flames are stabilized aerodynamically within the swirling flow without help of any solid anchoring device. The structure of the turbulent swirling flames is examined by recording their OH∗ chemiluminescence. Laser induced OH fluorescence measurements are carried out to delineate the location of the flame front and burnt gases and infer the shape taken by the flame. Particle imaging velocimetry measurements reveal the corresponding velocity field. The temperature is also recorded with thermocouples in the internal and the external recirculation zones of the flow and inside the combustion chamber walls. These diagnostics reveal similarities between the topology of CH4/air and CH4/O2/CO2 flames near their stabilization point. For a fixed swirl number, it is found that N2- and CO2-diluted CH4/O2 flames at the same equivalence ratio feature very similar shapes provided the adiabatic flame temperature and the ratio of bulk velocity to laminar burning velocity are kept the same although the absolute value of bulk velocity and the general velocity level inside the combustor are different. This result was found for injection Reynolds numbers varying from Re=8500–28000 and for swirl numbers ranging from S0=0.5 to 1.2. The operability range of well stabilized CO2-diluted flames is however reduced. It is also found that the temperature of the burnt gases in the outer recirculation zone differs between the CO2- and N2 diluted combustible mixtures sharing the same adiabatic temperature, but this does not affect the stabilization of the flames near the burner outlet, the temperature in the burnt gases and inside the combustor sidewalls. The flame leading edge is stabilized on average off-axis due to the structure of the W axial velocity profile produced by the axial-plus-tangential swirler at the burner outlet. This study indicates that CO2-diluted CH4/O2 premixed swirling flames can be stabilized with similar shapes as CH4/air flames without design modification provided the suggested similarity is obeyed.

Heat transfer and flow structure of an impinging jet with upstream flow

In the present study, Particle Image Velocimetry and infrared thermography are used to investigate a jet issuing from a perforation with a crossflow on both sides of the perforated plate. This type of injection is typical of industrial applications such as combustion chamber or turbine blade cooling. The influence of five different parameters (Reu, e/D, Rej, Rec, H/D) has been considered. Due to the upstream flow influence, the injection flow is not axisymmetric: the highest mean velocity values are present in the lower part of the injection and on its sides forming a crescent shape jet with high velocity fluctuations in the jet core. The jet has global upward movement and its velocity rapidly decreases. Heat transfer rates resulting from its impingement are relatively low, compared to those of an academic jet issuing from a long tube. Moreover, Nusselt number distribution is not axisymmetric for low injection-to-plate spacing H/D. The injection Reynolds number and the injection-to-plate distance are the parameters with the greatest influence on heat transfer rates. Finally, correlations are deduced from heat transfer measurements.

Conjugate Jet Impingement Heat Transfer Investigation via Transient Thermography Method

Investigating the conduction–convection coupling, the present study is focused upon measurement of conjugate heat transfer ensuing jet impingement on a 15-mm-thick metallic plate. Based on a rapid change in jet temperature and using time-accurate infrared thermography, a transient measurement methodology is developed toward acquisition of heat transfer coefficients. The new technique is shown to have comparable levels of Nusselt number and effectiveness accuracy, all while significantly reducing the number of consecutive measurements and their duration. To highlight the significance of the conjugate effect, different plate materials (copper, steel, and Inconel) are employed to differ the solid thermal conductivities, resulting in Biot-number variations. The plate surface heat transfer is studied at two injection Reynolds numbers (34,000 and 37,000) and for two nozzle-to-plate distances (two and five jet diameters). The changes in slab material conductivity reveal small but quantifiable differences in heat transfer coefficients (up to locally and 9% globally). Furthermore, constituting an upper bound and lower bound, respectively, it is observed that all conjugate Nusselt number distributions lay within the two limits of isoheat flux and isothermal boundary condition cases.

Investigation of heat transfer for cooling turbine disks with a non-Newtonian fluid flow using DRA

A non-Newtonian viscoelastic fluid flow passes through the porous wall of an axisymmetric channel on a turbine disc for cooling application. The present article solves the couple equations (momentum and heat transfer) of a non-Newtonian fluid flow in an axisymmetric channel with a porous wall for turbine cooling applications by using the Duan–Rach Approach (DRA). The precious achievement of the present work is introducing a new and efficient approximate analytical technique that this method allows us to find a solution without using numerical methods to evaluate the undetermined coefficients. The approximate analytical investigation is carried out for different values of the embedding parameters namely: Reynolds number, Prandtl number, injection Reynolds number and power law index. The DRA results indicate that Nusselt number has direct relationship with Reynolds number, Prandtl number and power law index. Also the results were compared with numerical solution in order to verify the accuracy of the proposed method. It is seen that the current results in comparison with the numerical ones are in excellent agreement.

Heat transfer and flow structure of a multichannel impinging jet

High speed particle image velocimetry and infrared thermography were used to investigate the behavior of hot jets with specific injections. A jet exiting from a round nozzle, a jet resulting from a nozzle with a straight-lined structure (Sw = 0) and a jet resulting from a nozzle with a curved structure (Sw = 0.26) have been studied for nozzle-to-plate distances from one injection diameter to 6 and for three mass flow rates (corresponding to injection Reynolds number from 23,000 to 33,000). For small nozzle-to-plate distances, the presence of a structure (straight-lined or curved in the injection tube) modifies the flow and increases the Nusselt number values in comparison with classical round jet flows. These modifications tend to disappear with increasing nozzle-to-plate distance. Moreover, the swirling effect principally affects ambient air entrainment into the jet and consequently effectiveness.

The transition to turbulence of buoyant near-critical water jets

Observations of near-critical water jets are reported in the injection Reynolds number range of approximately 300–3000 to characterize their transition to turbulence. Three types of cases are described: (i) subcritical jet injected into subcritical water, (ii) supercritical jet injected into supercritical water, and (iii) supercritical jet injected into subcritical water. In each case, the working pressure was kept above the critical value to eliminate two-phase effects. For cases (i) and (ii), the transition behavior follows well known characteristics with transition to turbulence initially occurring near the tip of the jet with the transition location moving upstream nearer to the nozzle exit with an increase in injection Reynolds number. However, the transition behavior for case (iii) is quite different with significant buoyant effects leading to turbulent behavior at lower Reynolds numbers. Consideration of the pseudocritical region with strongly varying fluid properties, which is established in the mixing region between the jet and the cell fluid, yields an effective Froude number that is useful to elucidate this difference. The effective Froude number incorporates the Prandtl number of the mixing region to account for the large disparity between viscous and thermal length scales.

RETRACTED: Laminar flow and heat transfer of nanofluid between contracting and rotating disks by least square method

In this study, asymmetric laminar flow and heat transfer of nanofluid between contracting rotating disks are investigated. The fluids in the channel are water containing different nanoparticles Cu, Ag and Al2O3. The effective thermal conductivity and viscosity of nanofluid are calculated by the Chon and Brinkman models, respectively. The governing equations are solved via the fourth-order Runge–Kutta–Fehlberg method (NUM) and least square method (LSM). The effects of the nanoparticle volume fraction, rotational Reynolds number, injection Reynolds number, expansion ratio and s on flow and heat transfer are considered. The results show that as s increases temperature profile increases and the point of maximum radial velocity is shifted towards the middle of the two disks. Also the results indicated that temperature profile becomes more flat near the middle of two disks with the increase of injection but opposite trend is observed with increase of expansion ratio.

Investigation of the heat transfer of a non-Newtonian fluid flow in an axisymmetric channel with porous wall using Parameterized Perturbation Method (PPM)

In the present article Parameterized Perturbation Method (PPM) is used to obtain the solutions of momentum and heat transfer equations of non-Newtonian fluid flow in an axisymmetric channel with porous wall for turbine cooling applications. The validity of the results of PPM solution were verified by comparison with numerical results obtained using a fourth order Runge–Kutta method. These comparisons reveal that Parameterized Perturbation Method is a powerful approach for solving this problem. The analytical investigation is carried out for different governing parameters namely, Reynolds number, injection Reynolds number, Prandtl number and power law index. The results show that skin friction coefficient increases with increase of Reynolds number, especially at high Reynolds numbers. Also it can be found that Nusselt number has direct relationship with Reynolds number, Prandtl number and power law index.

Effects of suction/injection on unsteady reactive variable viscosity non-Newtonian fluid flow in a channel filled with porous medium and convective boundary conditions

Abstract A study on thermal effects of the suction/injection Reynolds number, in conjunction with other flow parameters, on an unsteady reactive temperature dependent viscosity third grade fluid in a porous channel filled with saturated porous medium is presented. It is assumed that the channel walls are subjected to asymmetric convective heat exchange with the surrounding medium and that exothermic chemical reactions take place within the flow system. The heat exchange with the ambient at the surfaces is assumed to obey Newton's law of cooling. The equations governing the flow system are expressed in non-dimensional form and a semi-implicit finite difference scheme is utilised to obtain the velocity and temperature profiles. The effects of the flow parameters on the temperature and velocity fields, the skin friction and the wall heat transfer rate are simulated and discussed. The suction/injection Reynolds number is observed to retard the velocity field. It is also observed that the suction/injection Reynolds number, the porous medium parameter, the Prandtl number and the Biot number have a retarding effect on the temperature field. The variable viscosity parameter and the suction injection Reynolds number increases the skin friction while the porous medium parameter and the Prandtl number diminish it. It is also revealed that the suction injection Reynolds number, the porous medium parameter and the Prandtl number have a diminishing effect on the rate of heat transfer at the channel walls.

A numerical study of fluid injection and mixing under near-critical conditions

Nitrogen injection under conditions close vicinity of the liquid-gas critical point is studied numerically. The fluid thermodynamic and transport properties vary drastically and exhibit anomalies in the near-critical regime. These anomalies can cause distinctive effects on heat-transfer and fluid-flow characteristics. To focus on the influence of thermodynamics on the flow field, a relatively low injection Reynolds number of 1 750 is adopted. For comparisons, a reference case with the same configuration and Reynolds number is simulated in the ideal gas regime. The model accommodates full conservation laws, real-fluid thermodynamic and transport phenomena. Results reveal that the flow features of the near-critical fluid jet are significantly different from their counterpart. The near-critical fluid jet spreads faster andmixes more efficiently with the ambient fluid along with a more rapidly development of the vortex pairing process. Detailed analysis at different streamwise locations including both the flat shear-layer region and fully developed vortex region reveals the important effect of volume dilatation and baroclinic torque in the near-critical fluid case. The former disturbs the shear layer and makes it more unstable. The volume dilatation and baroclinic effects strengthen the vorticity and stimulate the vortex rolling up and pairing process.

Control of the Separation Flow in a Sudden Enlargement

In the present paper, an experimental and numerical investigation of fluid flow and heat transfer in the case of wall injection besides main flow through a circular sudden enlargement are studied. The injected flow is achieved through an annular slot placed around the inner side wall of the step. The static pressure variation along the sudden enlargement length is measured and calculated at different values of injection ratio ( Q ) and injection flow angles. The average heat transfer with Reynolds number (ReJ) of injected flow at different values of the inlet flow angle is obtained. The velocity, turbulent kinetic energy and temperature contours are presented in this study. Reynolds number of injected flow is varied between 320 and 840, Reynolds number of main flow is between 5895 and 8450 and the injection flow angles are 0 o , 15 o , 30 o , 45 o and 60 o . In the injection case, the results indicate that, the pressure recovery coefficient increases by decreasing the injection ratio and increasing the flow angle. The average heat transfer coefficient increases as both injection Reynolds number and the injection flow angle increase. The numerical results showed that two recirculation zones generate behind the step between the injection flow and the main flow. The size of these recirculation zones decreases by increasing the injection flow rate. The turbulent kinetic energy increases within region between the recirculation zones and main zone also, it decays by injecting flow in the recirculation zone. The length for higher value of flow temperature decreases by injecting flow in the recirculation zone, and that length increases as the injection flow rate increases. The comparison between the experimental results and the numerical results gives good agreement using the k-e model with Leschziner and Rodi correction.

A NUMERICAL STUDY OF FLUID INJECTION AND MIXING UNDER NEAR-CRITICAL CONDITIONS

Nitrogen injection under conditions in close vicinity of liquid-gas critical point is studied through numerical simulation. The thermodynamic and transport properties of fluid exhibit anomalies in the near-critical fluid regime. These anomalies can cause distinctive effects on heat transfer and hydrodynamics. To focus on the influence of the highly variable properties and avoid the difficulties encountered in modeling high Reynolds number flows, a relatively low injection Reynolds number is adopted. A reference case with the same configuration and Reynolds number is also simulated in the ideal gas regime. Full conservation laws, real-fluid thermodynamic and transport phenomena are accommodated in the model. The obtained results reveal that the flow features of the near-critical fluid jet are significantly different from the ideal gas case. The near-critical fluid jet spreads faster and mixes better with the ambient fluid compared to the ideal gas jet. It is also identified that vortex pairing process develops faster in the near-critical case than in the ideal gas case. Detailed analysis of data at different streamwise positions including both flat shear layer region and fully developed vortex region reveals the effect of volume dilatation and baroclinic torque plays an important role in the near-critical fluid case. The volume dilatation effect disturbs the shear layer and makes it more unstable. The volume dilatation and baroclinic effects strengthen the vorticity and stimulate the vortex rolling up and pairing process.

Pressure Measurements in Jet Diffusion Using a Developed Hot-Wire Static Pressure Sensor

The aim of this experimental study is to investigate the diffusion of jets, with particular attention focused on the relationship between the static pressure and the stream wise mean velocity on the development of a two-dimensional air jet. A jet with three injection Reynolds numbers (Re=1.0×104, 2.0×104, 3.0×104) was generated in a two-dimensional wind tunnel. The velocity distributions were measured by an X-type hot-wire anemometer. The static pressure distributions were measured by a static pressure probe developed in our laboratory, which incorporates a hot-wire anemometer. There are two important characteristics for the hot-wire static pressure probe. The one is that mean static pressure and the static pressure fluctuation can be measured at the same time. The other is that the probe is not affected by the flow and the changes of physical properties (thermal conductivity) of gases, because the sensing hot-wire is always in the air bias flow. The sensitivity of the fstatic pressure probe is 92.3 mV/Pa. The frequency response is flat from 16 Hz to 2.5 kHz. As a result of the experiment, it was found that negative static pressure exists in the turbulent shear layer. It is considered that the entrainment processes from the negative static pressure by the vortex structure motion of the turbulent shear layer.

Rotational and Quasiviscous Cold Flow Models for Axisymmetric Hybrid Propellant Chambers

In this work, we present two simple mean flow solutions that mimic the bulk gas motion inside a full-length, cylindrical hybrid rocket engine. Two distinct methods are used. The first is based on steady, axisymmetric, rotational, and incompressible flow conditions. It leads to an Eulerian solution that observes the normal sidewall mass injection condition while assuming a sinusoidal injection profile at the head end wall. The second approach constitutes a slight improvement over the first in its inclusion of viscous effects. At the outset, a first order viscous approximation is constructed using regular perturbations in the reciprocal of the wall injection Reynolds number. The asymptotic approximation is derived from a general similarity reduced Navier–Stokes equation for a viscous tube with regressing porous walls. It is then compared and shown to agree remarkably well with two existing solutions. The resulting formulations enable us to model the streamtubes observed in conventional hybrid engines in which the parallel motion of gaseous oxidizer is coupled with the cross-streamwise (i.e., sidewall) addition of solid fuel. Furthermore, estimates for pressure, velocity, and vorticity distributions in the simulated engine are provided in closed form. Our idealized hybrid engine is modeled as a porous circular-port chamber with head end injection. The mathematical treatment is based on a standard similarity approach that is tailored to permit sinusoidal injection at the head end.

Transpiration cooling of a nose cone by various foreign gases

The transpiration cooling mechanisms used for thermal protection of a nose cone was investigated experimentally and numerically for various cooling gases. The effects of injection rates, model geometry, inlet temperature and Reynolds number of the main stream were studied for air, nitrogen, argon, carbon dioxide and helium. The experiments used a hot gas wind tunnel with T ∞ = 375 K and 425 K and Re ∞ = 4630–10,000. The experimental results indicated that even a small amount of coolant injection drastically reduced the heat transfer from the hot gases with the cooling effectiveness increasing with increasing injection rate, although the increases became smaller as the gas injection rate was further increased. The temperature and cooling effectiveness distribution along the transpiration surface of the nose cone model exhibited similar tendencies for all the coolants employed in present experimental research. The temperature decreased from the stagnation point towards the downstream region, then increased because of the non-uniform mass flow distribution of the coolant and thermal conduction from the metal backplane, whereas the cooling effectiveness variation was the reverse. The local cooling effectivenesses and thermal capacities were found to depend on the coolant thermophysical properties. Two-dimensional numerical simulations using the RNG κ−ε turbulence model for the main stream flow and the Darcy–Brinkman–Forchheimer momentum equations and thermal equilibrium model for the porous zone compared well with the general features in the experiments.

The structure of the velocity field in a confined flow driven by an array of opposed jets

We investigate the confined flow in a new turbulence box configuration. Fluid is injected through two sets of 16 vertically opposed jets and outflows through two top/bottom porous planes. The resulting flow is generated by pairs of opposed round jets with backflow and their subsequent interactions. The research issue being addressed here is that of the dependence of the velocity field structure on two parameters: the injection Reynolds number based on jet diameter Reinj, which is varied between 6000 and 28000, and the flow geometry. The latter issue is addressed by investigating two kinds of flow geometries: (i) recirculating opposed jets (ROJ), for which the distance among two consecutive jet nozzles is 2.4 diameters and the nozzle-to-nozzle distance among each two opposed jets is 6 diameters, and (ii) simple opposed jets (SOJ), for which the distance among two consecutive jet nozzles is 4 diameters and the nozzle-to-nozzle distance among each two opposed jets is 10 diameters. The instantaneous aspect of the flow field is dominated by vortical structures and it is strongly dependent on the flow geometry. For both flow geometries, no coherence between each two consecutive pairs of jets is observed. All the statistics (dimensionless profiles of mean velocities and kinetic energy, derived quantities, and inner scales) do not depend on the Reynolds number and they are only the result of the flow geometry. The ROJ geometry leads to a flow which is characterized by strong interactions between opposed and neighboring jets which lead to both top-bottom and left-right instabilities in the central region. This leads to a strong energy and enstrophy injection, which imposes its signature on the two-dimensional kinetic energy spectra regime, characterized by a kxy−3 scaling, associated to the vortical structures present in the flow. The classical kxy−5/3 regime is very poorly represented, most likely because it is supposed to be present at scales smaller than the particle image velocimetry cut-off. Only a small volume of the chamber is characterized by local homogeneity and isotropy. The SOJ geometry is associated to flow which exhibits large regions that are locally homogeneous and isotropic. However, the top-bottom instabilities remain present. The mean pressure increase in the center of the chamber is of maximum 20% of the dynamic pressure at the inlet and decreases with increasing Reynolds number. The two-dimensional kinetic energy spectra clearly exhibit the classical kxy−5/3 scaling range; this is the signature of pure turbulence that finds enough space to develop. A fine-scale analysis is performed for both flow geometries in a particular point where the return flow is locally homogeneous, isotropic, and Gaussian. After an estimation of the mean energy dissipation rate according to various methods, we find that the Reynolds number based on the Taylor microscale scales as Reinj1/2, as in classical flows, and attains a maximum value of 350.

Direct numerical simulation of turbulence in injection-driven plane channel flows

Compressible turbulent flow in a periodic plane channel with mass injecting walls is studied as a simplified model for core flow in a solid-propellant rocket motor with homogeneous propellant and other injection-driven internal flows. In this model problem, the streamwise direction was asymptotically homogenized by assuming that at large distances from the closed end, both the mean and rms of turbulent fluctuations evolve slowly in the streamwise direction when compared to the turbulent fluctuations themselves. The Navier–Stokes equations were then modified to account for this slow growth. A direct numerical simulation of the homogenized compressible injection-driven turbulent flow was then conducted for conditions occurring at a streamwise location situated 40 channel half-widths from the closed off end and at an injection Reynolds number of approximately 190. The turbulence in this model flow was found to be only weakly compressible, although significant compressibility existed in the mean flow. As in nontranspired channels, turbulence resulted in increased near-wall shear for the mean streamwise velocity. When normalized by the average rate of turbulence production, the magnitudes of near-wall velocity fluctuations were similar to those in the log region of nontranspired wall-bounded turbulence. However, the sharp peak in streamwise velocity fluctuations observed in nontranspired channels was absent. While streaks and inclined vortices were observed in the near-wall region, their structure was very similar to those observed in the log region of nontranspired channels. These differences are attributed to the absence of a viscous sublayer in the transpired case which in turn is the result of the fact that the no-slip condition for the transpired case is an inviscid boundary condition. That is, unlike nontranspired walls, with transpiration, zero tangential velocity boundary conditions can be imposed at the wall for the Euler (inviscid) equations. The results of this study have important implications on the ability of turbulence models to predict this flow.

Flow Induced in a Porous Medium due to a three dimensional couette flow Adjacent to it

The flow of a viscous fluid induced in a porous medium due to a uniform motion of a plate parallel to its surface has been discussed when there is a transverse sinusoidal injection of the fluid at the moving plate. The fluid fills the space between the plate and the porous medium which is fully saturated with the fluid. Due to this type of the injection velocity the flow in the clear fluid becomes three dimensional. It is assumed that the flow in the clear fluid region governed by Navier-Stokes equation and that in the porous medium by the Brinkman equation near the interface and by Darcy law far away from interface. It is found that with increase of the permeability of the porous medium the magnitude of the velocity component increase in both regions. In the porous region the velocity component parallel to motion of the plate is maximum at the interface and then decreases exponentially forming a boundary layer at the interface. Also the velocity component parallel to the motion of the plate decreases with the increase of injection Reynolds number Re and the magnitude of other velocity components increases with the increase of Re.

Unsteady Stokes Flow of Viscous Fluid between Two Parallel Porous Plates

Berman(1953) was the first researcher who studied the problem of steady flow of an incompressible viscous fluid through a porous channel with rectangular crosssection, when the Reynolds number is low. He obtained a perturbation solution assuming normal wall velocities to be equal. Then Sellars(1955) extended the problem studied by Berman when the Reynolds number is very high. Afterwards Yuan(1956) and Terill(1964) studied the problem for various values of suction and injection Reynolds numbers. Terill and Shrestha(1965) have analysed the same problem, assuming different normal velocities at the walls.