Jet Space Research Articles

Usage of extruded diamond multi-injectors for improvement of fuel mixing inside the supersonic combustion chamber

The main attention of this work is to investigate the usage of diamond multi extruded injectors on the fuel distribution in combustor of scramjet. This study applied the computational technique to simulate the transverse fuel jets released from extruded nozzles. The main focus is to evaluate the role of induced shock waves on the penetration and distribution of fuel jets. The effects of jet space and usage of annular nozzle for the fuel injection system are revealed. Results of this work shows that the gap of jet would be more efficient for mixing when the inner air jet is also used. Also, injection of the air from the core of annular nozzle significantly increase the fuel mixing.

Lagrangian Reduction by Stages in Field Theory

We propose a category of bundles in order to perform Lagrangian reduction by stages in covariant Field Theory. This category plays an analogous role to Lagrange–Poincaré bundles in Lagrangian reduction by stages in Mechanics and includes both jet bundles and reduced covariant configuration spaces. Furthermore, we analyze the resulting reconstruction condition and formulate the Noether theorem in this context. Finally, a model of a molecular strand with rotors is seen as an application of this theoretical frame.

Heat Transfer and Pressure Loss Correlations for Leading Edge, Jet Impingement Using Racetrack-Shaped Jets With Filleted Edges

Abstract This paper presents an experimental investigation of heat transfer and pressure loss for leading-edge jet impingement using racetrack-shaped jets. The majority of literature for gas turbine cooling applications considers jet impingement using square or sharp-edged orifices. However, the edge of the jet orifices generally has some degree of filleting (or rounding) along the edges, due to casting the airfoils or material wear due to long-term operation. Engineers need data under realistic engine configurations to improve the utilization of coolant while adequately protecting the airfoil. The current experimental study is a parametric investigation of heat transfer and pressure loss for leading-edge jet impingement, where the effects of jet Reynolds number (Re = 10,000–100,000), jet–to–jet spacing (s/d = 2–8), jet–to–target surface spacing (z/d = 2–4), surface curvature (D/d = 2.67–5.33), and jet fillet–to–jet plate thickness (r/l = 0.16–0.5) are each considered. The edge rounding at both the inlet and outlet of the jet plate yields reduced heat transfer compared to the square-edged jets. However, the fillets significantly improve the discharge coefficients associated with the racetrack-shaped orifices. With the extensive testing completed in this study, design correlations have been developed to predict the surface Nusselt number and discharge coefficients, with 10% and 19% deviation from experimental results, respectively. Engine designers can predict the level of heat transfer and pressure loss for leading-edge jet impingement using these correlations.

Effects of Variable Pressure Outlets for Array Jet Impingement Cooling With a Bidirectional Exit Air Scheme

Abstract Array jet impingement in conjunction with other cooling methods such as effusion cooling is used in gas turbine combustion zones to provide optimized cooling in the form of double wall cooling around a combustion chamber. Utilizing a transient liquid crystal (TLC) technique an experimental investigation into the effects of pressure gradients and single versus multiple exits for array jet impingement crossflow is evaluated in the form of a detailed heat transfer analysis. In this study, four pressure gradients to bias mass flow ratios as (1:1), (2:1), (3:1), and (1:0), two jet array configurations either inline or staggered with jet to jet spacings (x/D = y/D) of 1.4, 1.9, and 2.2, three jet to target distances (z/D) ranging from 2 to 4, and three Reynolds number from 5000 to 15,000 are considered. In total, a test matrix of 72 different performance conditions was evaluated. Results are presented as local and area averaged Nusselt number plots along with local heat transfer coefficient contours. Overall, Nusselt number decreases with increased (z/D) and increased pressure gradient bias toward a single exit from (1:1) to (1:0). There is also slightly better performance from inline jet array configurations compared to staggered configurations.

Gelfand duality for manifolds, and vector and other bundles

In general terms, Gelfand duality refers to a correspondence between a geometric, topological, or analytical category, and an algebraic category. For example, in smooth differential geometry, Gelfand duality refers to the topological embedding of a smooth manifold in the topological dual of its algebra of smooth functions. This is generalised here in two directions. First, the topological embeddings for manifolds are generalised to the cases of real analytic and Stein manifolds, using a unified cohomological argument. Second, this type of duality is extended to vector bundles, affine bundles, and jet bundles by using suitable classes of functions, the topological duals in which the embeddings take their values.

Enhancing ionic conductivity in polymer melts results in smaller diameter electrospun fibers

Chemically compatible additives were utilized to increase the ionic conductivity of polyethylene melts. When subjected to unconfined electrospinning, a predictable and significant decrease in the resultant fiber diameter with enhanced melt conductivity was observed. This generalized approach was confirmed for viscous melts, varying in conductivity over five orders of magnitude and viscosity 5×, from multiple commercial polyethylene formulations with various additives. These experimental results are connected to theory for the relevant length scales of capillary length, jet spacing, and jet radius. In particular, jet radius scales as conductivity to the −1/4 power. Fitting experimental fiber radius vs ionic conductivity data results in a similar power law exponent (−0.29). This trend, occurring at orders of magnitude higher viscosity and six orders of magnitude lower conductivity, is similar to results from needle-based, solution phase electrospinning, suggesting the generality of the effect. The connection between larger length scales, such as the distance between jets and the thickness of the film at the plate edge, and fluid properties (surface tension, viscosity, and conductivity) is also discussed.

Existence of a variational principle for PDEs with symmetries and current conservation

It is well-known from Noether's theorem that symmetries of a variational functional lead to conservation laws of the corresponding Euler-Lagrange equation. We reverse this statement and prove that a differential equation, which satisfies sufficiently many symmetries and corresponding conservation laws, leads to a variational functional, whose Euler-Lagrange equation is the given differential equation. Sufficiently many symmetries means that the set of symmetry vector fields satisfy span{Vp:V∈Sym}=TpE, that is, they span the tangent space TpE at each point p of a fiber bundle E, which describes the dependent- and independent coordinates. Higher order coordinates are described by the jet bundle JkE and we require no span-assumptions on TJkE. Our main theorem states that Noether's theorem can be reversed in this sense for second order differential equations, or more precisely, for so-called second order source forms on J2E, which are required to write the differential equation as a weak formulation (every Euler-Lagrange equation is derived from a first variation, that is, from a weak formulation). Counter examples show that our theorem is sharp.

Influence of extruded injector nozzle on fuel mixing and mass diffusion of multi fuel jets in the supersonic cross flow: computational study

The efficient injection system has a great role on the overall enactment of air breathing propulsion systems at supersonic flow. In this work, the usage of extruded multi-injectors in the fuel distribution and mixing through the combustor is fully investigated. The usage of the extruded nozzles considerably intensifies the formation of the vortices nearby the injectors and this research has tried to visualize the role of these vortices on the diffusion of the fuel jet through the combustor of the scramjet. The influences of the jet space on the strength of produced circulations are fully discussed. The simulation of the high-speed air stream moving the combustion chamber with extruded nozzles is done via Computational Fluid dynamics. Based on our computational data, the use of extruded multi-jets enhances the penetration and diffusion of the hydrogen cross jet in supersonic airflow. Increasing the gap between injectors improves fuel mixing performance by up to 27% downstream of the jets, primarily by enhancing the lateral penetration of the fuel jet.

Jet spaces over Carnot groups

Jet spaces over \mathbb{R}^n have been shown to have a canonical structure of stratified Lie groups (also known as Carnot groups). We construct jet spaces over stratified Lie groups adapted to horizontal differentiation and show that these jet spaces are themselves stratified Lie groups. Furthermore, we show that these jet spaces support a prolongation theory for contact maps, and in particular, a Bäcklund type theorem holds. A byproduct of these results is an embedding theorem that shows that every stratified Lie group of step s + 1 can be embedded in a jet space over a stratified Lie group of step s .

Spanwise-Inclined Jets in Supersonic Crossflow: Effects of Injection Pressure and Separation-Control Effectiveness

Motivated by the advantageous performance of air-jet vortex generators (AJVGs) in controlling shock-induced flow separation, we aim at understanding the effects of relevant injection parameters on the physical mechanisms involved, as well as on the control effectiveness. We performed implicit large-eddy simulations to examine the influence of injection pressure on a spanwise-inclined jet in supersonic crossflow at Mach 2.5 and with momentum-thickness Reynolds number 7000. Four injection pressures were considered. The jet and jet/crossflow interactions strengthen with injection pressure, which is reflected in an enhanced obliqueness and asymmetry of the flow topology, strengthening the induced major counter-rotating vortex pair (CVP). This strengthening of the major CVP stagnates at a certain threshold, above which the flow blockage and momentum influx caused by the jets become so strong that they counter the positive influence on the CVP. Subsequently, we installed these jets in an AJVG control setup for a 24 deg compression-ramp interaction with separation to analyze the control effectiveness and interplay of the injection pressure and jet spacing. The strongest effects on control effectiveness are not related to the injection pressure itself, but to interactions between the jet-induced shocks and vortical structures. Therefore, there is a strong link between jet spacing and injection pressure regarding the control effectiveness. Based on these observations, we provide recommendations for designing efficient AJVG control setups.

Experimental and Numerical Investigation of Flow Structure and Heat Transfer Behavior of Multiple Jet Impingement Using MgO-Water Nanofluids.

Nanofluids have attracted significant attention from researchers due to their ability to significantly enhance heat transfer, especially in jet impingement flows, which can improve their cooling performance. However, there is a lack of research on the use of nanofluids in multiple jet impingements, both in terms of experimental and numerical studies. Therefore, further investigation is necessary to fully understand the potential benefits and limitations of using nanofluids in this type of cooling system. Thus, an experimental and numerical investigation was performed to study the flow structure and heat transfer behavior of multiple jet impingement using MgO-water nanofluids with a 3 × 3 inline jet array at a nozzle-to-plate distance of 3 mm. The jet spacing was set to 3, 4.5, and 6 mm; the Reynolds number varies from 1000 to 10,000; and the particle volume fraction ranges from 0% to 0.15%. A 3D numerical analysis using ANSYS Fluent with SST k-ω turbulent model was presented. The single-phase model is adopted to predict the thermal physical nanofluid. The flow field and temperature distribution were investigated. Experimental results show that a nanofluid can provide a heat transfer enhancement at a small jet-to-jet spacing using a high particle volume fraction under a low Reynolds number; otherwise, an adverse effect on heat transfer may occur. The numerical results show that the single-phase model can predict the heat transfer trend of multiple jet impingement using nanofluids correctly but with significant deviation from experimental results because it cannot capture the effect of nanoparticles.

Experimental investigation of effect of iron oxide nanofluids with different morphology on heat transfer of multiple impinging jets

ABSTRACT This research aims to experimentally investigate the thermal performance of iron oxide nanofluids having different particle shapes for multiple impinging jet flow. The heat transfer performance of nanofluids with spherical like, faced nanocube and nanowires shapes prepared by hydrothermal synthesis was investigated experimentally. The weight percentage of the nanofluids examined in this study is 0.2 wt%, and different jet-to-jet spacing (B) and jet-to-plate distance (H) values were tested for each nanofluid. The experiments were carried out for laminar flow conditions, the temperature distribution was obtained through thermocouples, and the Nu number was calculated for each case. In experiments using nanowires, it was observed that the highest Nu numbers were obtained for jet-target/diameter ratio 2 for all cases (jet spaces and Reynolds numbers). Maximum Nu number enhancement was approximately 27.3% compared to pure water for the specified conditions. This value is quite significant since it was obtained with a relatively low concentration of nanofluids. It was observed that the particle size and morphology shape significantly impact nanofluids’ performance in heat transfer.

Local heat transfer characteristics of circular multiple air jet impinging on a semicircular concave surface

ABSTRACT The local heat transfer characteristics of circular multiple air jet impingement on semicircular concave surface were studied experimentally. For constant Reynolds number (Re = 9,000), the effect of jet to concave surface spacing (z/d = 1, 4.2, 6), ratio of curvature (D/d = 4.28, 6, 8.6), jet-to-jet spacing (s/d = 2.4, 4, 5.6), and number of jets were considered. The local heat transfer characteristics were determined by using infrared thermal camera and thin foil method. Lower curvature value ratio (D/d = 4.28) resulted higher average heat transfer coefficient due to broader spread of heat transfer distribution, whereas higher curvature ratio (D/d = 8.6) resulted in lower average heat transfer coefficient due to steeper heat transfer distribution in the stagnation area. At lower D/d, z/d, and s/d with seven jet configuration, the heat transfer coefficients were found effective as compared to other configurations due to broad heat transfer distribution and less interaction between the jets. At given D/d and s/d configuration, the stagnation Nu at θ = 0° do not coincide with jet hole center axis and this shift is more pronounced at higher z/d value. This could be due to additional push before jet impinging on concave surface. The secondary peaks were observed between two neighboring stagnation regions in Nu distribution along the center longitudinal line for lower z/d and higher s/d values. This resulted due to upwash that was obtained from jet interactions related to collisions with the wall jets. The correlations of stagnation line average Nu and overall average Nu were obtained. The coefficient of variance of local heat transfer coefficient for each configuration was determined, and correlation was proposed to analyze the degree of non-uniformity.

The catalytic effect of near-inertial waves on -plane zonal jets

Zonal jets and inertia–gravity waves are ubiquitous on planets such as Earth, Jupiter and Saturn. Motivated by the modification of energy flux of balanced flow by inertia–gravity waves, this paper studies the impact of near-inertial waves (NIWs) on zonal jets on a $\beta$ -plane. Using a two-dimensional quasi-geostrophic and NIW coupled system on a $\beta$ -plane (Xie & Vanneste, J. Fluid Mech., vol. 774, 2015, pp. 143–169), we find NIWs catalytically impact several features of zonal jets. The NIWs inhibit jet formation due to the waves’ catalytic induction of downscale mean energy flux. As the strength of NIWs increases, a critical point exists beyond which zonal jets are annihilated. The jet spacing is captured by the Rhines scale $L\sim \sqrt {U/\beta }$ with $U$ estimated from the upscale energy flux induced by the mean flow alone, which again shows that the NIWs’ impact is catalytic. Also, the temporal asymmetry of NIWs leads to the spatial asymmetry of jet dynamics. The jet profiles are asymmetric with a stronger shear on the left flank. And similar to the left turning of vortex dipole under the impact of NIWs, the NIW-modified jets migrate poleward. The NIWs also show a catalytic role in jet migration: the net momentum flux directly induced by NIWs is of secondary importance in the zonal mean momentum dynamics and impedes jet migration, while the advective effect of NIW-modified mean flow dominates the jet migration velocity.

Parameterisation of small-scale random forcing in β-plane turbulence

Zonal jet formation in $\beta$ -plane turbulence is investigated with the focus on whether an accurate closure can be developed for the eddy momentum fluxes due to small-scale random forcing. The approach of Srinivasan and Young (J. Atmos. Sci., vol. 71, 2014, pp. 2169–2185) is developed to give a relatively simple expression for the local Reynolds stress, due to a white-in-time random forcing with characteristic length scale much less than the jet spacing. In typical jet flows, however, it is demonstrated that the Srinivasan–Young flux is not the full story because momentum fluxes due to jet-scale waves, present as a result of distinct barotropic instabilities of the eastward and westward jets, respectively, also play a key role in the momentum balance. Numerical simulations that explicitly include the random forcing are then compared with those in which the Srinivasan–Young closure is applied. For typical jet flows, good agreement of the equilibrium zonal flow is found provided that the closure simulation is not truncated to be purely zonal, i.e. jet-scale secondary barotropic instabilities are allowed to develop. Flows in which the geometry or external forcing acts to suppress the development of secondary instabilities are also simulated, and for these flows the Srinivasan–Young closure is shown to be successful as a purely zonal closure. It is argued that vortex condensates in isotropic forced-dissipative 2D turbulence are an example of this latter situation.

Canonical Witt formal scheme extensions and p-torsion groups

We study the nth arithmetic jet space of the p-torsion subgroup attached to a smooth commutative formal group scheme. We show that the nth jet space above fits in the middle of a canonical short exact sequence between a power of the formal scheme of Witt vectors of length n and the p-torsion subgroup we started with. This result generalizes a result of Buium on roots of unity.

Geometric tool kit for higher-spin gravity (Part I): An introduction to the geometry of differential operators

This paper provides an introduction to the algebra and geometry of differential operators and jet bundles. Its point of view is guided by the leitmotiv that higher-spin gravity theories call for higher-order generalizations of Lie derivatives and diffeomorphisms. Nevertheless, the material covered here may be of general interest to anyone working on topics where geometrical (coordinate-free, global, generic) and mathematically rigorous definitions of differential operators are required.

Experimental Study on Flow and Heat Transfer Characteristics of Jet Array Impingement Combined with Kagome Truss Structures with/without Cross-flow

Jet array impingement providing high heat transfer are widely used in heat exchangers. However, the target plate is easily damaged impinged by high-speed air flow constantly. To solve this issue, Kagome truss structure is combined with jet array impingement to improve cooling performance in this paper. The flow and heat transfer characteristics of this composite structure in a heat exchanger unit with/without cross-flow were experimentally studied. Additionally, Kagome truss structures of circular and water-drop-shaped rods were used respectively in jet space and the results showed that the latter was beyond 7% higher than the former for the comprehensive thermal performance. When cross-flow was not added, the comprehensive thermal performance factor of the latter reached to a maximum of 1.656 at the Reynolds number of 5000. When cross-flow was added, the comprehensive thermal performance got worse at the cross-flow-to-jet velocity ratio of 1.0, while the best comprehensive thermal performances were found at the cross-flow-to-jet velocity ratio of 0.6 and at the mass flow rate proportion of cross-flow of 0.5, respectively. These results can provide a basic experimental data as a reference for designing new structures in advanced heat exchanger.

Arithmetic jet spaces

One of the primary objectives of this paper is to establish compatibility between two different jet space functors in the most general context. We first show an adjunction between the jet and the Witt functor on algebras. Following Borger's approach, we then construct the algebraic jet space functor in the general setting where the base is an arbitrary prolongation sequence. We then show that this functor is representable in the category of schemes and that Buium's jet space can be recovered by the π-adic completion of this representable scheme. As an application, this allows us to strengthen a result of Buium on the relation between Greenberg's transform and the special fiber of jet spaces, including the ramified case.

Perfectoid spaces arising from arithmetic jet spaces

Using arithmetic jet spaces, we attach perfectoid spaces to smooth schemes and to $\delta$-morphisms of smooth schemes. We also study perfectoid spaces attached to arithmetic differential equations defined by some of the remarkable $\delta$-morphisms appearing in the theory such as the $\delta$-characters of elliptic curves and the $\delta$-period map on modular curves.