Mixing Measurements in a Supersonic Expansion-Ramp Combustor

This paper reports results on molecular mixing for injection via an expansion-ramp into a supersonic freestream with M ₁ = 1.5. This geometry produces a compressible turbulent shear layer between an upper, high-speed “air” stream and a lower, low-speed “fuel” stream, injected through an expansion-ramp at α = 30° to the high-speed freestream. Mass injection is chosen to force the shear layer to attach to the lower guide wall. This results in part of the flow being directed upstream, forming a recirculation zone. Employing the hypergolic hydrogen-fluorine chemical reaction and pairs of “flip” experiments, molecular mixing is quantified by measuring the resulting temperature rise. Initial experiments established the fast-chemistry limit for this flow in terms of a Damköhler number (Da). For Da ≥ 1.4, molecularly mixed fluid effectively reacts to completion. Parameters varied in these experiments were the measurement station location, the injection velocity of the (lower) “fuel” stream, the stoichiometry for the flip experiments, and the density ratio of the fuel and air streams. As expected, mixing increases with increasing distance from the injection surface. The mixed fluid fraction increases by 12% when changing the fuel-to-air stream density ratio from 1 to 0.2. Comparisons with measurements at subsonic (high-speed) “air” stream velocities show that the trend of decreasing mixing with increasing speed documented in free-shear layer flows is also encountered in these flows. The current geometry produces higher mixing levels than do free shear layers.     

Combined forced and natural convection in laminar film flow

A mathematical model for the flow and heat transfer in a gravity-driven liquid film is presented, in which the strict Boussinesq approximation is adopted to account for buoyancy. A similarity transformation reduces the governing equations to a coupled set of ordinary differential equations. The resulting two-parameter problem is solved numerically for Prandtl numbers ranging from 1 to 1000. Favourable buoyancy arises when the temperatureT _w of the isothermal surface is lower than the temperatureT ₀ of the incoming fluid, and the principal effects of the aiding buoyancy are to increase the wall shear and heat transfer rate. For unfavourable buoyancy (T _w>T ₀), the buoyancy force and gravity act in opposite directions and the flow in the film boundary layer decelerates, whereas the friction and heat transfer are reduced. The observed effects of buoyancy diminish appreciably for higher Prandtl numbers.     

Investigation on rough rice drying kinetics at various thin layers of a deep bed

Moisture content gradients along the bed column are commonly neglected during simulation of deep-bed grain drying. In this study, rough rice drying kinetics at various thin layers of a deep bed was investigated. The experiments were conducted under different drying conditions and the data were compared with the values predicted by a previously developed non-equilibrium model for numerical simulation of grain drying. The moisture content gradients related to the rough rice column indicated that the higher the drying layer, the more was the moisture content at each drying time. The constant drying rate period was observed neither for any thin layers nor for the entire drying column. The drying rate of the lower layers continuously decreased with drying time, whereas that of the upper layers firstly increased and then decreased. The implemented model predicted drying process with a high accuracy at various layers. However, the values of maximum relative error (RE _max ) and mean relative error (MRE) increased as the air temperature increased, and reversely decreased with the air velocity. The higher values of MRE and RE _max were related to the layer 1 (0–5 cm bed height) at temperature of 60 °C and air velocity of 0.4 m s^?1, and the lower values belonged to the layer 4 (15–20 cm bed height) at temperature of 40 °C and air velocity of 0.9 m s^?1.     

Mixed convection adjacent to inclined flat surfaces embedded in a porous medium

An analysis is performed to study the flow and heat transfer characteristics of laminar mixed convection boundary layer flows from inclined (including horizontal and vertical) surfaces embedded in a saturated porous medium with constant aiding external flows and uniform surface temperature. Both the streamwise and normal components of the buoyancy forces are retained in the momentum equations. Nondimensionalization of the boundary layer equations results in the following three governing parameter: (1)Gr/Re, the ratio of the Grashof number to the Reynolds number; (2)Pe _x =Re _x Pr, the Peclet number; (3) φ, the angle of inclination from the horizontal. The resulting nonsimilar equations are solved by an efficient implicit finite-difference scheme. Numerical results are presented for flows with different values ofGr/Re in the range of 0 to 50, over a wide range of the Peclet numbersPe _x, and various values of φ ranging from 0 to 90 degrees. It is found that the local surface heat transfer rate increases with increasing the local Peclet number. In addition, as the plate is tilted from the horizontal to the vertical orientation, the local Nusselt number increases for a given Peclet number and the effect of the buoyancy force on the surface heat transfer rate increases.     

Multicomponent Reynolds-averaged Navier–Stokes simulations of reshocked Richtmyer–Meshkov instability-induced mixing

A third-order weighted essentially nonoscillatory (WENO) finite-difference implementation of a two-equation K–ε multicomponent Reynolds-averaged Navier–Stokes (RANS) model is used to simulate reshocked Richtmyer–Meshkov turbulent mixing of air and sulfur hexafluoride at incident shock Mach numbers Ma_s = 1.24, 1.50, 1.98 with Atwood number At = 0.67 and Ma_s = 1.45 with At = ?0.67. The predicted mixing layer width evolutions are compared with experimental measurements of the width before and after reshock [M. Vetter, B. Sturtevant, Shock Waves 4 (1995) 247; F. Poggi, M.H. Thorembey, G. Rodriguez, Phys. Fluids 10 (1998) 2698] and with the analytical self-similar power-law solution of the simplified model equations before reshock. A new procedure is introduced for the specification of the initial turbulent kinetic energy and its dissipation rate, in which these quantities are related by the linear instability growth rate. The predicted mixing layer widths before reshock are shown to be sensitive to changes in the initial turbulent kinetic energy and its dissipation rate, while the widths after reshock are sensitive to changes in the model coefficients C_ε0 and σ_ρ appearing in the buoyancy (shock) production terms in the turbulent kinetic energy and dissipation rate equations. A set of model coefficients and initial conditions is shown to predict mixing layer widths in generally good agreement with the pre-reshock experimental data, and very good agreement with the post-reshock data for all cases. Budgets of the turbulent kinetic energy equation just before and after reshock for the Ma_s = 1.24 case are used to identify the principal physical mechanisms generating turbulence in reshocked Richtmyer–Meshkov instability: buoyancy production (pressure work) and shear production. Numerical convergence of the mixing layer widths under spatial grid refinement is also demonstrated for each of the Mach numbers considered.     

Using Micro-Raman Spectroscopy to Assess MEMS Si/SiO2 Membranes Exhibiting Negative Spring Constant Behavior

We introduce a novel micro-mechanical structure that exhibits two regions of stable linear positive and negative stiffness. Springs, cantilevers, beams and any other geometry that display an increasing return force that is proportional to the displacement can be considered to have a “Hookean” positive spring constant, or stiffness. Less well known is the opposite characteristic of a reducing return force for a given deflection, or negative stiffness. Unfortunately many simple negative stiffness structures exhibit unstable buckling and require additional moving components during deflection to avoid deforming out of its useful shape. In Micro-Electro-Mechanical Systems (MEMS) devices, buckling caused by stress at the interface of silicon and thermally grown SiO₂ causes tensile and compressive forces that will warp structures if the silicon layer is thin enough. The 1 mm² membrane structures presented here utilizes this effect but overcome this limitation and empirically demonstrates linearity in both regions. The Si/SiO₂ membranes presented deflect ~17 μm from their pre-released position. The load deflection curves produced exhibit positive linear stiffness with an inflection point holding nearly constant with a slight negative stiffness. Depositing a 0.05 μm titanium and 0.3 μm layer of gold on top of the Si/SiO₂ membrane reduces the initial deflection to ~13.5 μm. However, the load deflection curve produced illustrates both a linear positive and negative spring constant with a fairly sharp inflection point. These results are potentially useful to selectively tune the spring constant of mechanical structures used in MEMS. The structures presented are manufactured using typical micromachining techniques and can be fabricated in-situ with other MEMS devices.     

Global nonlinear stability for a triply diffusive convection in a porous layer

A triply convective-diffusive fluid mixture saturating a porous horizontal layer in the Darcy–Oberbeck–Boussinesq scheme is studied. The nonlinear stability analysis of the conduction solution is performed when the layer is heated from below and salted from above by one salt and below by another salt. Denoting by P _i , (i = 1, 2), the salts Prandtl numbers, it is shown that in the cases {P ₁ = 1; P ₂ = 1; P ₁ = P ₂} do not exist subcritical instabilities and the thermal Rayleigh critical number of global stability in a simple closed form is given. The methodology used and the results obtained appear to be new in the existing literature and useful for the applications.     

Forced Convection Heat Transfer from a Heated Cylinder in an Axial Background Flow in a Porous Medium: Three Exactly Solvable Cases

Assuming a background flow of velocity U = U(x) in the axial direction x of a circular cylinder with surface temperature distribution T _w = T _w (x) in a saturated porous medium, for the temperature boundary layer occurring on the cylinder three exactly solvable cases are identified. The functions {U(x), T _w (x)} associated with these cases are given explicitly, and the corresponding exact solutions are expressed in terms of the modified Bessel function K ₀ (z), the incomplete Gamma function Γ (a, z) and the confluent hypergeometric function U(a, b, z), respectively. The correlation between the Nusselt number and the Péclet number as well as the curvature effects on the heat transfer are discussed in all these cases in detail. Some “universal” features of the exponential surface temperature distribution are also pointed out.     

Instabilities in two-liquid layers subject to a horizontal temperature gradient

We study theoretically the stability of two superposed fluid layers heated laterally. The fluids are supposed to be immiscible, the interface undeformable and of infinite horizontal extension. Combined thermocapillary and buoyancy forces give rise to a basic flow when a temperature difference is applied. The calculations are performed for a melt of GaAs under a layer of molten B₂O₃, a configuration of considerable technological importance. Four different flow patterns and five temperature configurations are found for the basic state in this system. A linear stability analysis shows that the basic state may be destabilized by oscillatory motions leading to the so-called hydrothermal waves. Depending on the relative height of the two layers these hydrothermal waves propagate parallel or perpendicular to the temperature gradient. This analysis reveals that these perturbations can alter significantly the liquid flow in the liquid-encapsulated crystal growth techniques. PACS 47.20.Dz, 47.20.Bp, 47.54.+r, 47.27.Te, 44.25.+f, 47.20.Ma     

Natural Convection as an Asymmetrical Factor of the Transport Through Porous Membrane

For nonionic substances, which density of solution depends on its concentration, concentration polarization of the membrane in horizontal plane depends not only on diffusion but on the hydrodynamic instabilities at the membrane surfaces also. Such instabilities are the cause of asymmetry of membrane transport in gravitational field. On the basis of results of glucose transport through the Nephrophan membrane in horizontal plane we can state that this asymmetry was observed for the cases with concentration Rayleigh number greater than critical value (R _C )_crit = 1709.3. The mathematical model based on Kedem–Katchalsky equations and Rayleigh number was presented. On the basis of this model and the dependence of volume flux through the Nephrophan membrane as a function of glucose concentration in the upper (configuration B) and lower (configuration A) chamber of the membrane system, the dependencies of thickness of concentration boundary layer, Rayleigh number, and introduced coefficient of asymmetry as a function of glucose concentration were presented for both configurations. These dependencies show that asymmetry of the membrane transport is observed for glucose concentration higher than 0.015 mol l^?1.     

Comparison of magnetic resonance concentration measurements in water to temperature measurements in compressible air flows

Magnetic resonance imaging (MRI) measurements in liquid flows provide highly detailed 3D mean velocity and concentration data in complex turbulent mixing flow applications. The scalar transport analogy is applied to infer the mean temperature distribution in high speed gas flows directly from the MRI concentration measurements in liquid. Compressibility effects on turbulent mixing are known to be weak for simple flows at high subsonic Mach number, and it was not known if this would hold in more complex flows characteristic of practical applications. Furthermore, the MRI measurements are often done at lower Reynolds number than the compressible application, although both are generally done in fully turbulent flows. The hypothesis is that the conclusions from MRI measurements performed in water are transferable to high subsonic Mach number applications. The present experiment is designed to compare stagnation temperature measurements in high speed airflow (M = 0.7) to concentration measurements in an identical water flow apparatus. The flow configuration was a low aspect ratio wall jet with a thick splitter plate producing a 3D complex downstream flow mixing the wall-jet fluid with the mainstream flow. The three-dimensional velocity field is documented using magnetic resonance velocimetry in the water experiment, and the mixing is quantified by measuring the mean concentration distribution of wall-jet fluid marked with dissolved copper sulfate. The airflow experiments are operated with a temperature difference between the main stream and the wall jet. Profiles of the stagnation temperature are measured with a shielded thermocouple probe. The results show excellent agreement between normalized temperature and concentration profiles after correction of the temperature measurements for the effects of energy separation. The agreement is within 1 % near the edges of the mixing layer, which suggests that the mixing characteristics of the large scale turbulence structures are the same in the two flows.     

Unsteady near wake of a flat disk normal to a wall

The unsteady wake of a flat disk (diameter D) located at a distance of H from a flat plate has been experimentally investigated at a Reynolds number Re _D  = 1.3 × 10⁵. Tests have been performed for a range of gap ratio (H/D), spanning from 0.3 to 1.75. The leading edge of the flat plate is either streamlined (elliptical) or blunt (square). These configurations have been studied with PIV, high speed PIV and multi-arrayed off-set fluctuating pressure measurements. The results show a progressive increase of the complexity of the flow and of the interaction as the gap ratio decreases. For large values of H/D (1.75), the interaction is weak and the power spectral densities (PSD) exhibit a strong peak associated with the vortex shedding events (St = 0.131) – St = fD/U _∞ is the Strouhal number. For lower values of H/D (0.75), the magnitude of the wall fluctuating pressure increases significantly. A large band contribution is associated with the unsteady wake structure and turbulence. A slight increase of the shedding frequency (St = 0.145) is observed. A critical value of the gap ratio (about 0.35) has been determined. Below this critical value, a three-dimensional separated region is observed and the natural vortex shedding process is very strongly altered. These changes induce a great modification of the fluctuating pressure at the wall. Each interaction reacts in a different way to perturbed upstream conditions. In particular, the disk is an overwhelming perturbation for the lowest H/D value studied here and the relative influence of the upstream turbulence on the wall fluctuating pressure below the near wake region is moderate.     

Enhanced heat transfer performances of molten salt mixed convection in a vertical annular duct

The mixed convection heat transfer of upward molten salt flow in a vertical annular duct is experimentally and numerically studied. The heat transfer performances of mixed convection are measured under Reynolds number 2,500–12,000 and inlet temperature 300–400 °C, and Nusselt number of molten salt flow with cooled inner wall monotonically increases with buoyancy number. The mixed convection is further simulated by low-Reynolds number k-ε model and variable properties, and the heat transfer tendency from numerical results agrees with that from experiments. At low Reynolds number, the natural convection plays more important role in the mixed convection. As the buoyancy number rises, the thickness of flow boundary layer near the inner wall increases, while the effective thermal conductivity remarkably rises, so the enhanced heat transfer of mixed convection is mainly affected by the effective thermal conductivity due to turbulent diffusion.     

On hot-wire diagnostics in Rayleigh–Taylor mixing layers

Two hot-wire flow diagnostics have been developed to measure a variety of turbulence statistics in the buoyancy driven, air-helium Rayleigh–Taylor mixing layer. The first diagnostic uses a multi-position, multi-overheat (MPMO) single wire technique that is based on evaluating the wire response function to variations in density, velocity and orientation, and gives time-averaged statistics inside the mixing layer. The second diagnostic utilizes the concept of temperature as a fluid marker, and employs a simultaneous three-wire/cold-wire anemometry technique (S3WCA) to measure instantaneous statistics. Both of these diagnostics have been validated in a low Atwood number (A _t  ≤ 0.04), small density difference regime, that allowed validation of the diagnostics with similar experiments done in a hot-water/cold-water water channel facility. Good agreement is found for the measured growth parameters for the mixing layer, velocity fluctuation anisotropy, velocity fluctuation p.d.f behavior, and measurements of molecular mixing. We describe in detail the MPMO and S3WCA diagnostics, and the validation measurements in the low Atwood number regime (A _t  ≤ 0.04). We also outline the advantages of each technique for measurement of turbulence statistics in fluid mixtures with large density differences.     

Effets des forces de Coriolis sur le seuil convectif stationnaire d'une couche liquide confinée en cellule de Hele–Shaw annulaire en rotationEffects of the Coriolis forces on the stationary convectif threshold of a liquid layer confined in an annular Hele–Shaw Cell in rotation

The convective instability of a horizontal liquid layer confined in an annular Hele–Shaw cell subject to a constant rotation and submitted to a centrifugal gradient of temperature is investigated. Using a linear stability analysis, we study the effects of both Coriolis forces and curvature aspect on the stationary convective threshold when the Prandtl number is of the order of unity or larger than unity. We show that the Coriolis forces have a stabilizing effect, and the wave number is independent of these forces. However, a multicellular regime in the radial direction is observed for small Ekman numbers. The results related to the influence of the curvature are also shown. To cite this article: S. Ramezani et al., C. R. Mecanique 330 (2002) 633–640.     

Experimental study of a hypersonic shock layer stability on a circular surface of compressionL'étude expérimentale de la stabilité d'une couche de choc hypersonique sur une surface circulaire de compression

The method of electron-beam fluorescence is applied to study the evolution of natural and artificial periodic disturbances on a developed streaky structure in the shock layer on a circular compression surface model. The model is exposed to a hypersonic nitrogen flow with a Mach number M_∞=21 and unit Reynolds number Re_1∞=6×10⁵ m^?1. Data on the effect of surface curvature and temperature on disturbance characteristics are obtained. To cite this article: S.G. Mironov, V.M. Aniskin, C. R. Mecanique 332 (2004).     

Theoretical solution of simultaneous heat and mass transfer by free convection about a vertical flat plate

In this paper we present a numerical solution for stationary simultaneous heat and mass transfer in the laminar boundary layer on a vertical flat plate. The theory is based on a simple physical model that treats the two buoyancy effects (originating from temperature and concentration differences) as mutually independant and additional forces. Results are given for the case of Pr=0.71, Sc=0.63 and equally directed body forces. Our experimental data for the same conditions show close agreement and these seems to be no need for a more complicated theory.     

Mixed convection heat transfer from three heated square cylinders in cross-flow at low Reynolds numbers

This paper presents the effects of cross buoyancy and Prandtl number on the flow and heat transfer characteristics around three equal isothermal square cylinders arranged in a staggered configuration within an unconfined medium. Transient two-dimensional numerical simulations are performed with a finite volume code based on the SIMPLEC algorithm in a collocated grid system. The pertinent dimensionless parameters, such as Reynolds, Prandtl and Richardson numbers are considered in the range of 1 ≤ Re ≤ 30, 0.7 ≤ Pr ≤ 100 and 0 ≤ Ri ≤ 1. The representative streamlines, vortex structures and isotherm patterns are presented and discussed. In addition, the overall drag and lift coefficients and average Nusselt numbers are determined to elucidate the effects of Reynolds, Prandtl and Richardson numbers on flow and heat transfer. The flow is observed to be steady for all the ranges of parameters considered. The drag coefficient is found to decrease with Re (for Ri = 0) and Ri at low Pr, whereas it increases with Pr at higher Ri. The lift coefficient decreases with Ri at low Pr and increases with Pr at higher Ri. The time and surface average cylinder Nusselt number is found to increase monotonically with Re as well as Pr while it remains almost insensitive to Ri at low Pr.     

Passive and reactive scalar measurements in a transient high-Schmidt-number Rayleigh–Taylor mixing layer

An experimental study of mixing induced by Rayleigh?CTaylor (RT) instability at an Atwood number (A _t ) ~7.5?×?10^?4 and Schmidt number (Sc) ~1,000 has been performed. A new transient experimental facility developed on the working principles of the draw-tank facility at Cambridge (Dalziel et al. in J Fluid Mech, 399:1?C48, 1999) has been established and enhanced to observe a higher (2×) Reynolds number regime. Water and brine were used to produce the RT density stratification. The evolution of the instability was studied using passive and reactive scalar techniques and quantified using optical diagnostic methods. The data were combined to estimate local and global mixing metrics representative of the mixing mechanism across the mixing layer. In comparison with parameters reported from analogous experiments, the mixing phenomenon at a high Sc shows a strong dependency on the initial conditions prevailing at the onset of the instability and the evidence of a delay in the mixing transition. Values of global and integral mixing parameters did not reach late-time asymptotic values that have been reported previously from steady-state experiments (Texas A&M Water Channel) and may be attributed to the effect of the barrier pull and the overturning mechanism that is thought to hinder the progress of the mixing layer.     

Combined heat and mass transfer by laminar natural convection from a vertical plate

Simultaneous heat and mass transfer in buoyancy-induced laminar boundary-layer flow along a vertical plate is studied for any ratio of the solutal buoyancy force to the thermal buoyancy force by using a new similarity transformation. The effects of the buoyancy ratio and Lewis number on the rates of heat and mass transfer are presented explicitly for most practical gaseous solutions (Pr=0.7, 0.21≤Sc≤2.1) and aqueous solutions (Pr=7, 140≤Sc≤1400). Very accurate correlations of the mass transfer and heat transfer rates are developed for the cases of single and combined buoyancy forces.