Injection Reynolds Number Research Articles

Effects of film cooling hole shape on heat transfer

AbstractThe effects of hole shapes, secondary injection Reynolds numbers, and blowing ratios on the heat transfer downstream of film cooling holes have been investigated by using a large‐scale low‐speed loop wind tunnel. The test model consists of five film cooling holes. Experiments on dustpan‐shaped holes, fan‐shaped holes, and round holes have been conducted with injection Reynolds number ranging from 10,000 to 25,000 and blowing ratio ranging from 0.3 to 2.0. Measurements are taken under 26 conditions. Results show that the critical blowing ratio is 1.3 for the dustpan‐ and fan‐shaped holes, 0.7 for the round holes. The turbulence generated by air injection through round holes is stronger than those through dustpan‐ and fan‐shaped holes. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(2): 73–80, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20005

Higher Mean-Flow Approximation for Solid Rocket Motors with Radially Regressing Walls

The bulk gas motion in a circular-port rocket motor is described using a rotational, incompressible, and viscous flow model that incorporates the effect of wall regression. The mathematical idealization developed is also applicable to semi-open porous tubes with expanding walls. Based on mass conservation, a linear variation in the mean axial velocity is ascertained. This relationship suggests investigating a spatial transformation of the Proudman-Johnson form. With the use of similar arguments, a temporal transformation is also introduced. When these transformations are applied in both space and time, the Navier-Stokes equations are reduced to a single, nonlinear, fourth-order differential equation. Following this exact Navier-Stokes reduction, the resulting problem is solved using variation of parameters and small-parameter perturbations. The asymptotic solutions for the velocity, pressure, vorticity, and shear are obtained as function of the injection Reynolds number Re and the dimensionless regression ratio a. By way of verification, it is shown that, as α/Re → 0, Yuan and Finkelstein's solutions can be restored from ours. Similarly, as α/Re → 0, Culick's inviscid profile is recovered. It is demonstrated that, for a range of small α/Re, inviscid solutions are practical. However, for fast burning propellants under development, the inviscid assumption deteriorates. Because it is applicable over a broader range of operating parameters, the current analysis leads to a closed-form mean-flow solution that can be used, instead of the inviscid profile, to 1) prescribe an adjusted aeroacoustic field, 2) describe the so-called acoustic boundary layer, 3) evaluate the viscous and rotational contributions to the acoustic stability growth rate factor, 4) track the evolution of hydrodynamic instability, and 5) accurately simulate the internal gasdynamics in rapidly regressing motors and cold-flow experiments with medium-to-high levels of injection.

Effects of Coflow on Turbulent Flame Puffs

Pulsed, turbulent jet diffusion flames in an air coflow of variable strength were examined experimentally. In all cases, the flames were fully modulated, that is, the fuel flow was completely shut off between pulses. Isolated puffs of unheated ethylene fuel were injected using a 2-mm-diam-nozzle into a combustor with an air coflow at 1-atm pressure. For short injection times (τ<50 ms), compact, pufflike structures were generated. The mean flame length of these puffs was at least 51% less than that of a steady-state, that is, nonpulsed, flame for the same injection Reynolds number. More elongated flame structures, with a flame length closer to that of steady-state flames, occurred for longer injection times of up to 300 ms. The addition of coflow generally causes an increase in the mean flame length. For short injection times (r < 50 ms), this resulted in an increase in flame length of up to 27% for a coflow strength of U cof /U jet = 0.02. The fractional increase in the flame length due to coflow of pulsed flames with longer injection times, as well as steady flames, was significantly less. The mean flame length for the flame with the coflow duct generally exceeded that of the corresponding free flame, even for the case of zero coflow. The amount of coflow required to achieve a given increase in mean flame length is quantitatively consistent with a scaling argument developed as part of this investigation.

Heat transfer to a row of impinging jets in consideration of optimization

In the current study the heated-thin-foil technique is used jointly with infrared thermography to evaluate accurately the heat transfer characteristics of one row of jets impinging on a flat plate. The impingement is confined by the test section and spent air is constrained to exit in only one direction. The configuration and parameters variation range are similar to those encountered in turbine internal cooling systems. The results are analysed in terms of local and averaged Nusselt number keeping in mind the design engineer preoccupation of minimizing the amount of cooling air taken from the compressor. The influence of the impingement distance Z/ d, injection Reynolds number Re and spanwise spacing p/ d between two holes of the row is presented. An optimum impingement distance is pointed out and some qualitative design rules for the two other parameters are underlined.

Unsteady Flow Evolution in Porous Chamber with Surface Mass Injection, Part 1: Free Oscillation

Unsteadye owevolutioninaporouschamberwithsurfacemassinjectionsimulatinganozzlelessrocketmotorhas been investigated numerically. The analysis is based on a large-eddy-simulation technique in which the spatially e ltered and Favre averaged conservation equations for large, energy-carrying turbulent structures are solved explicitly. The effect of the unresolved scales is modeled semi-empirically by considering adequate dissipation rates for the energy present in the resolved scale motions. The e owe eld is basically governed by the balance between the inertia force and pressure gradient, as opposed to viscouseffects and pressuregradient corresponding to channel e ows without transpiration. It accelerates from zero at the head end and becomes supersonic in the divergent section of the nozzle. Three successive regimes of development, laminar, transitional, and fully turbulent e ow, are observed. Transition to turbulence occurs away from the porous wall in the midsection of the motor, and the peak in the turbulence intensity moves closer to the wall farther downstream as the local Reynolds number increases. Increase in pseudoturbulence level at the injection surface causes early transition to turbulence. As the e ow develops farther downstream, the velocity proe le transits into the shape of a fully developed turbulent pipe e ow with surface transpiration. The compressibility effect also plays an important role, causing transition of the mean velocity proe les from their incompressible e ow counterparts as the local Mach number increases. The e ow evolution is characterized primarily by three nondimensional numbers: injection Reynolds number, centerline Reynolds number, and momentum e ux coefe cient.

Fingering Instability and Maximum Radius at High Rotational Bond Number

The spin-coating in the modern microfabrication practice takes place at a high rotational Bond number, Bo. An experimental study of fingering instability and maximum attainable radius at high Bo for both the injected liquid and released drop is presented. Compared to the released drop procedure, the effect of liquid injection tends to decrease the critical radius and the number of fingers at high Bo, although this effect is negligible for low Bo. The characteristics of apparent contact angles of the liquid front and the critical capillary number for high Bo are quite different from those for low Bo. This difference mainly comes from the competition between the speed of liquid spreading pushed by the centrifugal force and the speed of molecular wetting. For the number of fingers, are constant and independent of Bo. For high increases rapidly with Bo. The maximum attainable radius is almost independent of the fluid’s viscosity μ and injection Reynolds number but is only a function of Bo for the fluids of high viscosity considered in this work. © 2001 The Electrochemical Society. All rights reserved.

Gravity effects on stability and flickering motion of diffusion flames

Effects of gravity level on the flame stability and flickering motion were experimentally investigated for the propane jet diffusion flames. A spin tester was used to form the high gravity fields. Flames were observed under the various conditions of injection Reynolds number of the fuel jet and gravity level which were controlled independently. Regions of stable flame, flickering flame, and lifting flame were mapped with the gravity level and injection Reynolds number. Then, it could be pointed out that the onset of flame lifting was strongly affected by the gravity compared with the onset of flickering. Flickering frequency increased with an increase of gravity level. Gravity effect on the wavelength and wave velocity were also investigated to clarify the reason for the change of frequency. It was found that the increase of flickering frequency with the rise of gravity level was caused by the increase of wave velocity and the decrease of wavelength. Flickering frequencies obtained here could be summarized using Strouhal number and Froude number, and in a relation of St ∝ Fr -0.57. This result showed a good agreement with the previous results of Hamins obtained from normal gravity experiments.

Vapor and liquid flow in an asymmetrical flat plate heat pipe: a three-dimensional analytical and numerical investigation

In this work, an analytical and numerical study was carried out for the steady incompressible vapor and liquid flow in an asymmetrical flat plate heat pipe. The pseudo-three-dimensional analytical model employs the boundary layer approximation to describe the vapor flow under conditions including strong flow reversal and the method of matched asymptotic expansions to incorporate the non-Darcian effects for the liquid flow through the porous wicks. The coupling of the liquid flow in the top, bottom and vertical wicks is also included in the model. In the numerical study, a finite element scheme based on the Galerkin method of weighted residuals was used to solve the full set of nonlinear differential elliptical equations of motion and the continuity equation for the three-dimensional vapor flow. The analytical and numerical results for various injection Reynolds numbers are presented. The three-dimensional effects are discussed and the results show that a three-dimensional analysis is necessary if the vapor channel width-to-height ratio is less than 2.5. Very good agreement was found between the analytical and the numerical results. While showing, qualitatively and quantitatively, the pertinence and the effects of various physical parameters, the analytical results are quite useful for practical engineering purposes by providing an effective and rapid prediction method for the flat plate heat pipe operation.

Effects of uniform injection at the wall on the stability of Couette-like flows

A linear stability analysis of a family of nearly parallel wall-bounded flows with injection at the lower wall and suction at the upper one is presented. The mean pressure gradient is such that the streamwise velocity profile remains linear in spite of injection. An asymptotic analysis shows that, for weak injection, the expansion rate of linear perturbations is a linear function of the injection Reynolds number (based on the width of the domain and the injection velocity). This point is confirmed by a numerical solver that also shows that, due to the injection process, the eigenmodes are drastically reorganized in the complex plane. In particular, the eigenvalue distribution is no longer symmetric. Moreover, the imaginary part of the phase velocity tends to increase so that some modes may become linearly unstable. However, the base flow remains stable as long as the injection Reynolds number is lower than a critical value close to 48. It is also found that higher injection rates (injection Reynolds numbers greater than 80) stabilize the flow, as already observed for channel or rotating flows.

Numerical and analytical investigation of vapor flow in a disk-shaped heat pipe incorporating secondary flow

This paper presents a three-dimensional numerical analysis and a pseudo-three-dimensional analytical modeling of the steady incompressible vapor flow in an asymmetrical disk-shaped heat pipe heated from the top center area. The nonlinear differential elliptical equations of motion and the continuity equation were solved numerically over the entire vapor flow domain. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. The analytical model involves the use of the boundary layer approximation and the bifurcation of the flow field on the plane to describe the velocity profile under conditions including strong flow reversal. For both numerical and analytical studies, backflow was observed at the top entrance of the condensation zone for injection Reynolds number of 50 and higher. The three-dimensional effects and the effects of the secondary flow formation are discussed in this work. The numerical and analytical results establish that the pressure variations in the angular and transverse directions for a typical disk-shaped heat pipe are small and can be neglected. A very good agreement was found between the numerical results and the analytical results. The analytical model saves tremendous computer time compared with the numerical simulation, which requires CPU times five orders of magnitude larger than those for the analytical model.

The generation and regeneration of single hairpin vortices

The generation and growth of single hairpin vortices created by controlled surface fluid injection were examined experimentally within a laminar boundary layer over a range of Reynolds numbers. Flow visualization, using both dye and hydrogen bubbles, was employed in conjunction with hot-film anemometry to investigate the growth characteristics and evolution of these single hairpin vortices. Hydrogen-bubble visualization results reveal that the passage of a hairpin vortex can give rise to a low-speed streak pattern adjacent to the surface, and a turbulent pocket-like pattern farther removed from the surface. When the displacement and injection Reynolds numbers exceed critical levels, regeneration processes occur, which result in the development of new hairpin-like vortices by both (i) lateral deformation of the vortex lines comprising the initial hairpin vortex and (ii) a process of vortex-surface interaction, which causes the ejection of surface fluid and subsequent hairpin formation by viscous-inviscid interactions. The combination of these processes results in both lateral and streamwise growth of the initial hairpin-vortex structure, yielding a symmetric turbulent-spot type of behaviour.

A numerical study of the transition of jet diffusion flames

A numerical study on the transition from laminar to turbulent of two-dimensional fuel jet flames developed in a co-flowing air stream was made by adopting the flame surface model of infinite chemical reaction rate and unit Lewis number. The time dependent compressible Navier–Stokes equation was solved numerically with the equation for coupling function by using a finite difference method. The temperature-dependence of viscosity and diffusion coefficient were taken into account so as to study effects of increases of these coefficients on the transition. The numerical calculation was done for the case when methane is injected into a co-flowing air stream with variable injection Reynolds number up to 2500. When the Reynolds number was smaller than 1000 the flame, as well as the flow, remained laminar in the calculated domain. As the Reynolds number was increased above this value, a transition point appeared along the flame, downstream of which the flame and flow began to fluctuate. Two kinds of fluctuations were observed, a small scale fluctuation near the jet axis and a large scale fluctuation outside the flame surface, both of the same origin, due to the Kelvin–Helmholtz instability. The radial distributions of density and transport coefficients were found to play dominant roles in this instability, and hence in the transition mechanism. The decreased density in the flame accelerated the instability, while the increase in viscosity had a stabilizing effect. However, the most important effect was the increase in diffusion coefficient. The increase shifted the flame surface, where the large density decrease occurs, outside the shear layer of the jet and produced a thick viscous layer surrounding the jet which effectively suppressed the instability.

Internal flow field studies in a simulated cylindrical port rocket chamber

The objective of these studies is to experimentally characterize the mean and fluctuating flow field that develops along the length of a simulated cylindrical port rocket chamber. Flow simulation was accomplished by injecting ambient temperature nitrogen uniformly along the walls of 10.2-cm (4-in.) diam, porous-tube chambers connected to a choked sonic nozzle. Experiments were conducted with chamber L/D ratios of 9.5 and 14.3, at injection Mach numbers and Reynolds numbers typical of rocket motor values. Maximum Reynolds numbers based on injection and centerline velocities were, respectively, 1.8 x 10 and 1.6 x 10. Mean and fluctuating speed and turbulent shear stresses were measured in the principle coordinate directions using three-element hot-wire anemometers. The data show that noticeable velocity fluctuations in the head-end region generally decrease in intensity, relative to centerline speed, over the first five port diameters. At this point, regular velocity oscillations appear near the wall, just prior to the transition to turbulent flow. The oscillation frequency characteristics suggest the occurrence of vortical disturbances which exhibit pairing as they move away from the wall. The downstream turbulence development is characterized by a slow spreading toward the centerline: peak values of turbulence intensity and shear stress occur a few tenths of a port radius from the wall and remain relatively constant. Mean velocity profiles prior to transition show fair agreement with those derived for a rotational inviscid flow injected normal to the surface. A slow transition from these profiles occurs downstream in the turbulent region. Two surprising features of the flow were the occurrence of both buoyant flow influences and flow spinning in forward regions of the chamber.

Effects of bottom injection on heat transfer and fluid flow in rectangular cavities

A numerical study is performed for investigating the effects of bottom injection on the heat transfer in a cavity. The Reynolds number (based on the cavity height and bulk mean velocity over the cavity) ranges in value from 100 to 1000. The cavity aspect ratios W/D investigated are 1, 6, and 10. The injection flow rate varies between 2-20% of the bulk flow rate. With the injectant temperature maintained the same as the cavity wall temperature, the effects of injection-reduced cavity heat transfer are strongly dependent on all the parameters aforementioned. For given injection rate and Reynolds number, the degree of heat-transfer reduction increases with a decrease of cavity aspect ratio. In addition, the current results suggest that the heat-transfer correlations presented in previous studies for cavities with aspect ratio of unity overestimate the extent of heat-transfer reduction for wider cavities.

Overall Mass Transfer Between a Solid Surface and Submerged or Unsubmerged Liquid Multijets

Mass‐transfer coefficients between solid surfaces and submerged or unsubmerged liquid multijets are measured electrochemically. Various types of distributors are used; the open area ranging from less than 5 to more than 97%. Unsubmerged and submerged multijets perform differently at high values of when the injection Reynolds number is smaller than approximately 2000; the unsubmerged multijets interact with each other, thus forming a particular single jet which performs better than the corresponding submerged multijets.

Heat-transfer characteristics in annuli with blowing or suction at the walls

Numerical solutions were obtained for thermally and hydrodynamically developing laminar flow in annular passages with blowing and suction at the walls. Two separate thermal boundary conditions at the walls were studied: arbitrarily prescribed constant temperatures and constant heat fluxes at each wall. Cases involving blowing, suction, and impermeable walls were considered. Assuming that the properties of the fluid are constant and the injection or extraction velocities at the walls are uniform, the results were obtained in the form of pressure drops and Nusselt numbers. The results are presented for several inner-to-outer tube radius ratios, Prandtl numbers, and injection and extraction Reynolds numbers at the walls. ci,k Cp Dh dj,k = Ej,k — h K k Nu = P+ = P Pr

Viscous liquid flow in the initial portion of a permeable channel with transverse slot

The problem of flow in the initial segment of a permeable channel with transverse impermeable slot is solved. Behavior of the solution with change in geometric parameters and characteristic injection Reynolds number is analyzed.

On the Existence of Solutions of an Equation Arising in the Theory of Laminar Flow in a Uniformly Porous Channel with Injection

The existence of concave solutions of Berman's equation which describes the laminar flow in channels with injection through porous walls is established. It was found that the (unique) concave solutions exist for all injection Reynolds numbers R less than 0.

Fluctuating Flow of a Viscoelastic Fluid in a Porous Channel

The problem of flow of a viscoelastic fluid characterized by the well-known Rivlin-Ericksen constitutive equations is discussed, when such a fluid is driven by an unsteady pressure gradient in the region between two parallel porous plates. It is assumed that on one plate the fluid is injected with certain constant velocity and that it is sucked off at the other with the same velocity. The governing differential equations, which do not involve the cross-viscosity parameter, are solved using a pertubation scheme treating the viscoelastic parameter to be small. The behavior of instantaneous velocity profiles, and magnitude and the phase lag of mass flux, which depend on the injection Reynolds number, the frequency parameter, and the viscoelastic parameter are discussed for various values of these parameters. Some very interesting departures of these from the corresponding flow of classical viscous fluids are reported when one or both of the injection Reynolds number and frequency parameter are small or large.

Laminar flow of vapor between parallel disks with intense uniform asymmetric sublimation

The method of matching outer and inner asymptotic expansions is applied to the singular problem of laminar flow between sublimating disks at large injection Reynolds numbers.