Jet Space Research Articles

Effects of jet diameter and spacing in a micromixer-like burner for clean oxy-fuel combustion in gas turbines

The effects of jet diameter and spacing on flame structure and stability are examined in an oxy-methane micromixer-like burner for potential implementation in zero-emission gas turbines. Three burner headend geometries (HE1, HE2, and HE3) are compared at fixed flame-base velocity of 5.2 m/s and over ranges of equivalence ratio and oxygen fraction (O2 vol% in the O2/CO2 oxidizer). HE1 has 61 jets of 3.175-mm diameter, arranged on a hexagonal matrix with a uniform jet spacing of 5.5 mm. HE2 has 37 jets of 3.970-mm diameter (25% increase), also arranged hexagonally with a spacing of 5.5 mm. HE2 has fewer jets to maintain almost the same combustor power. HE3 is similar to HE2, but with a jet spacing of 7.0 mm (27% increase). The three blowout limits were found to be only ∼45 K apart, despite the considerable differences in jet diameter and spacing, which demonstrates the remarkable geometry flexibility of micromixers. HE1 outperformed HE2 and HE3. Increasing the jet diameter adversely affects flame stability, because the burner deviates from the stable lean-direct-injection concept. Increasing jet spacing is also unfavorable. The adiabatic flame temperature is the primary parameter controlling the structure and stability of premixed methane flames for different burner geometries.

Flow and heat transfer characteristics of a swirling impinging jet issuing from a threaded nozzle

A new swirler to excite the swirling jet is proposed to achieve the uniform and efficient impingement cooling, that is, the inner wall of a circular hole is provided with four spiral grooves similar to the conventional circular hole with internal threads. An experimental system is established to study the heat transfer and flow characteristics of the impingement surface. Experiments using smoke flow visualization technology are carried out at Reynolds number (Re) of 6000 in free space with/without impingement target respectively to investigate the complex flow field of swirling impinging jets (SIJ), and the effects of jet airflow diffusion and swirl angle on the airflow diffusion are analyzed. Heat transfer experiments are carried out for the swirl angle varying from 0° to 45° at Re varying from 6000 to 30000 for the jet spacing to the nozzle hydraulic diameter (H/dj) varying from 1 to 8. The impingement heat transfer rate of the target surface is found to increase slightly with the increase of the swirl angle. Compared with the conventional round hole and the non-swirling impinging jet (the nozzle with the angle of 0°), the swirling jet impingement with a certain swirl angle can effectively improve the overall heat transfer rate of the target surface. At H/dj =2 and H/dj =4, the local Nusselt number (Nu) at the stagnation point of the SIJ with the swirl angle of 45° is 7.4% and 11.4% higher than those of conventional round hole jet, respectively. Local Nu on the target surface has a nonlinear proportional relationship with Re, and the maximum Nu is obtained at the location of r/dj=0.7 at a higher Re. With the increase of H/dj, the effect of the swirling flow on impingement heat transfer weakens, and even disappears. An averaged Nusselt number correlation is presented over 6000≤Re≤30000，0°≤θ≤45°, and 1≤H/dj≤8, which matches the experimental results very well.

Control of Shock-Induced Separation of a Turbulent Boundary Layer Using Air-Jet Vortex Generators

An experimental analysis was carried out to study the control effectiveness and turbulence behavior of an array of steady air-jet vortex generators on a shock-induced boundary-layer separation. Control was applied to a 24° compression-ramp interaction at Mach 2.52 and . A parametric study varying the jet spacing revealed that an adequate interaction between the vortices is essential for effective control, and the most favorable control effect was achieved with a jet spacing of . This case was analyzed in more detail using particle image velocimetry. The results reveal a strong corrugation of the separation zone due to the injection of the jets with a substantial reduction in its area along the entire spanwise extent of the air-jet array, compared with the uncontrolled case. Measurements of velocity fluctuations along the interaction region also show that the jet injection results in a reduction in turbulent intensity after reattachment, contributing to an overall reduction in amplification factor across the interaction region. The expected increase in turbulent mixing, which is essentially responsible for the control effect, was confirmed in the region in-between jet injection and separation shock. Farther away from the surface, the flow is not affected, which reduces potential drag penalties.

Numerical Optimization of Heat Transfer from Multiple Jets Impinging on a Moving Curved Surface for Industrial Drying Machines

Jet impingements enhance the heat and mass transfer rate in industrial drying machines. The designer should optimize the design parameters of industrial drying equipment to achieve maximum heat transfer rate. The heat transfer between multiple jets and a moving curved surface is more difficult to study due to the changing boundaries and the effect of surface curvature but is also very relevant in industrial drying applications. SST k-ω turbulence model is used to simulate a real geometry for industrial drying applications. The SST k-ω turbulence model succeeded with reasonable accuracy in reproducing the experimental results. The jet to surface distance, jet to jet spacing, jet inlet velocity, jet angle, and surface velocity are chosen as the design parameters. For the optimization of the impinging round jet, the average Nu number on the moving curved surface is set as the objective functions to be maximized. The SHERPA search algorithm is used to search for the optimal point from the weighted sum of all objectives method. One correlation is developed and validated for the average Nu number. It is found that the maximum average Nu number correlates with high values of jet inlet velocity (Vj), jet angle (θ) and jet to jet spacing (S/d) and low values of the jet to surface distance (H/d) and relative surface velocity (VR). The agreement in the prediction of the average Nu number between the numerical simulation and correlation is found to be reasonable and all the data points deviate from the correlation by less than 4%.

Intermittent modal coupling in screeching underexpanded circular twin jets

Abstract

Complex structures on jet spaces and bosonic Fock space dynamics for causal variational principles

Based on conservation laws for surface layer integrals for critical points of causal variational principles, it is shown how jet spaces can be endowed with an almost-complex structure. We analyze under which conditions the almost-complex structure can be integrated to a canonical complex structure. Combined with the scalar product expressed by a surface layer integral, we obtain a complex Hilbert space $\mathfrak{h}$. The Euler-Lagrange equations of the causal variational principle describe a nonlinear time evolution on $\mathfrak{h}$. Rewriting multilinear operators on $\mathfrak{h}$ as linear operators on corresponding tensor products and using a conservation law for a nonlinear surface layer integral, we obtain a linear norm-preserving time evolution on bosonic Fock spaces. The so-called holomorphic approximation is introduced, in which the dynamics is described by a unitary time evolution on the bosonic Fock space. The error of this approximation is quantified. Our constructions explain why and under which assumptions critical points of causal variational principles give rise to a second-quantized, unitary dynamics on Fock spaces.

Numerical analysis of inclined jet impingement heat transfer in microchannel

Abstract The current study focuses on investigating of the performance of inclined microjet array to reduce the temperature of electronic devices. The capacity of the inclined jet arrays has been investigated through a computational fluid dynamics analysis for incompressible laminar flow to find out surface temperature, pressure drop, and flow chaos for the change in jet spacing and diameter, which is related to the number of jets under the constrained heat sink volume. Five different jet arrays consisting of 4, 5, 9, 13, and 16 jets were investigated for different jet diameters. The jet inclination kept constant at 45° to the impingement surface. The results show that the average exit liquid temperature increases with increasing the number of jets. The effects also manifest as the number of jets increases the pressure drop reduces monotonously for all jet diameters under constant mass flow rate in the module. Inclined microjet impingement heat sink having 13 jets showed better potential than the other microjet array configurations.

Functorial LCH for immersed Lagrangian cobordisms

For $1$-dimensional Legendrian submanifolds of $1$-jet spaces, we extend the functorality of the Legendrian contact homology DG-algebra (DGA) from embedded exact Lagrangian cobordisms, as in \cite{EHK}, to a class of immersed exact Lagrangian cobordisms by considering their Legendrian lifts as conical Legendrian cobordisms. To a conical Legendrian cobordism $\Sigma$ from $\Lambda_-$ to $\Lambda_+$, we associate an immersed DGA map, which is a diagram $$\alg(\Lambda_+) \stackrel{f}{\rightarrow} \alg(\Sigma) \stackrel{i}{\hookleftarrow} \alg(\Lambda_-), $$ where $f$ is a DGA map and $i$ is an inclusion map. This construction gives a functor between suitably defined categories of Legendrians with immersed Lagrangian cobordisms and DGAs with immersed DGA maps. In an algebraic preliminary, we consider an analog of the mapping cylinder construction in the setting of DG-algebras and establish several of its properties. As an application we give examples of augmentations of Legendrian twist knots that can be induced by an immersed filling with a single double point but cannot be induced by any orientable embedded filling.

Effect of downstream sinusoidal wall on mixing performance of hydrogen multi-jets at supersonic flow: Numerical study

Fuel mixing and penetration are known as substantial factor for advance of current scramjet engine. In this article, mixing and distribution of multi hydrogen jets are investigated under the impacts of downstream sinusoidal wall. This research tries to estimate the fuel jet interactions through the deflection of flow by downstream wavy wall. To perform our investigations, computational fluid dynamic with SST turbulence model is employed to simulate sonic multi hydrogen cross jets at supersonic air stream (M=4). The influences of fuel jet gaps and downstream wavy profile are comprehensively studied to disclose the importance of downstream on the fuel distribution and mixing region. Our results indicate that the fuel distribution in the downstream is substantially limited by increasing the frequency of downstream wavy wall. It is also noticed that the fuel concentration is decreased by increasing the jet space on the symmetry plane.

Quantitative Singularity Theory for Random Polynomials

Abstract Motivated by Hilbert’s 16th problem we discuss the probabilities of topological features of a system of random homogeneous polynomials. The distribution for the polynomials is the Kostlan distribution. The topological features we consider are type-$W$ singular loci. This is a term that we introduce and that is defined by a list of equalities and inequalities on the derivatives of the polynomials. In technical terms a type-$W$ singular locus is the set of points where the jet of the Kostlan polynomials belongs to a semialgebraic subset $W$ of the jet space, which we require to be invariant under orthogonal change of variables. For instance, the zero set of polynomial functions or the set of critical points fall under this definition. We will show that, with overwhelming probability, the type-$W$ singular locus of a Kostlan polynomial is ambient isotopic to that of a polynomial of lower degree. As a crucial result, this implies that complicated topological configurations are rare. Our results extend earlier results from Diatta and Lerario who considered the special case of the zero set of a single polynomial. Furthermore, for a given polynomial function $p$ we provide a deterministic bound for the radius of the ball in the space of differentiable functions with center $p$, in which the $W$-singularity structure is constant.

From PDEs to Pfaffian fibrations

We explain how to encode the essential data of a PDE on jet bundle into a more intrinsic object called Pfaffian fibration. We provide motivations to study this new notion and show how prolongations, integrability and linearisations of PDEs generalise to this setting.

Singularity confinement in delay-differential Painlevé equations

We study singularity confinement phenomena in examples of delay-differential Painlevé equations, which involve shifts and derivatives with respect to a single independent variable. We propose a geometric interpretation of our results in terms of mappings between jet spaces, defining certain singularities analogous to those of interest in the singularity analysis of discrete systems, and what it means for them to be confined. For three previously studied examples of delay-differential Painlevé equations, we describe all such singularities and show they are confined in the sense of our geometric description.

Numerical Simulation of Flow through a Sudden Contraction Split into Four Parallel Round Jets

Parallel jets are of profound importance in design of nuclear reactor components as well as other industrial applications. Vertical flow through a sudden contraction split into four round jets was numerically investigated using computational fluid dynamics (CFD). Results showed that jet spacing and jet size are the main parameters influencing the resulting flow field. In the upstream, both radial and streamwise velocity profiles drastically changed on approaching the contraction plane. Downstream, the flow field remained symmetric about the main axis. Velocity decay rate was found to be influenced by jet spacing, size and mixing characteristics. The results provide useful insights into mixing of multiple confined jets.

Secondary fuel jet strategies on mixing enhancement performance of rocket-based combined cycle engine

The mixed augmentation performance between secondary fuel jet and uneven supersonic inflow is a significant evaluation index of the rocket-based combined cycle engine. In this study, the effects of the secondary fuel jet on the flow field structure and mixing enhancement performance are discussed by changing both the secondary fuel jet angle and spacing of multiple rows of jet holes. The three-dimensional coupled implicit Reynolds averaged Navier-Stokes equations, SST k-ω turbulence model, and eddy dissipation concept (EDC) reaction model were adopted to evaluate the flow field structure with a sonic hydrogen jet. It is indicated that the 135° fuel jet has the largest penetration depth value, followed by the 90° fuel jet, whereas the 45° fuel jet has the smallest penetration depth value. However, the 45° fuel jet possesses the best mixing performance, it easily induces a pair of downstream counter-rotating vortex, and the oblique torque is further generated to aggravate the tearing ability to the jet. The three jet holes induce a stronger shock wave and form a larger barrier under the 90° jet. Additionally, when the spacing between the multiple rows of jet holes reduces, penetration depth is easily created. Further, when the spacing of the three rows of jet holes is larger, the fluctuation of the mixing coefficient increases.

Effect of free stream angle on mixing performance of hydrogen multi-jets in supersonic combustion chamber

The fuel mixing process within the combustion chamber is a critical procedure for advance of scramjet engine. In current study, the influence of free stream angle on the fuel mixing process of multi jets was thoroughly investigated. This research attempts to applied computational technique to disclose the structure of multi-fuel jets when the supersonic air stream is not normal to the jet direction. The effect of both positive and negative supersonic free stream on the diffusion and penetration of multi-hydrogen jets is fully described. The attention of this research is the flow structure of the multi jets and their interaction in the presence of different free stream angle. Our results indicate that the positive free stream angle expands the mixing zone in the downstream while the negative angle of free stream limited jet distribution inside the combustor. Our results show that mixing efficiency increase approximately 50% when the angle of free stream augments from +20° to −20°. According to our findings, mixing efficiency surges up to 17% when the jet spaces are increased from 4Dj to 10 Dj.

Orbifold hyperbolicity

AbstractWe define and study jet bundles in the geometric orbifold category. We show that the usual arguments from the compact and the logarithmic settings do not all extend to this more general framework. This is illustrated by simple examples of orbifold pairs of general type that do not admit any global jet differential, even if some of these examples satisfy the Green–Griffiths–Lang conjecture. This contrasts with an important result of Demailly (Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture, Pure Appl. Math. Q.7(2011), 1165–1207) proving that compact varieties of general type always admit jet differentials. We illustrate the usefulness of the study of orbifold jets by establishing the hyperbolicity of some orbifold surfaces, that cannot be derived from the current techniques in Nevanlinna theory. We also conjecture that Demailly's theorem should hold for orbifold pairs with smooth boundary divisors under a certain natural multiplicity condition, and provide some evidence towards it.

Minimal log discrepancies of determinantal varieties via jet schemes

We compute the minimal log discrepancies of determinantal varieties of square matrices, and more generally of pairs (Dk,∑αiDki) consisting of a determinantal variety (of square matrices) and an R-linear sum of determinantal subvarieties. Our result implies the semicontinuity conjecture for minimal log discrepancies of such pairs. For these computations, we use the description of minimal log discrepancies via codimensions of cylinders in the space of jets; this necessitates the computations of an explicit generator for the canonical differential forms and the Nash ideal of determinantal varieties, which may be of independent interest.

Estimates on the Markov convexity of Carnot groups and quantitative nonembeddability

We show that every graded nilpotent Lie group G of step r, equipped with a left invariant metric homogeneous with respect to the dilations induced by the grading, (this includes all Carnot groups with Carnot-Caratheodory metric) is Markov p-convex for all p∈[2r,∞). We also show that this is sharp whenever G is a Carnot group with r≤3, a free Carnot group, or a jet space group; such groups are not Markov p-convex for any p∈(0,2r). This continues a line of research started by Li who proved this sharp result when G is the Heisenberg group. As corollaries, we obtain new estimates on the non-biLipschitz embeddability of some finitely generated nilpotent groups into nilpotent Lie groups of lower step. Sharp estimates of this type are known when the domain is the Heisenberg group and the target is a uniformly convex Banach space or L1, but not when the target is a nonabelian nilpotent group.

Influence of upstream strut on hydrogen fuel distribution inside the supersonic combustion chamber

The efficient fuel mixing in the combustion tank enhances the overall performance of scramjet. Current attempt examines the existence of the strut on the fuel mixing of the multi hydrogen jets at supersonic flow. The numerical approach was employed to visualize the 3D flow behind the strut with multi fuel-jets. The free-stream Mach is 2.2, and four multi jets released hydrogen inside the combustor with the sonic condition. The impact of jet arrangements and the total pressure ratio on the mixing effect of the strut is fully described. Our results indicate that fuel mixing and penetration improved due to the formation of the large subsonic region behind the strut. According to achieved results, the increasing jet space from 1Dj to 5Dj raises the overall mixing to 15% in our proposed model.

Effects of Frequency and Jet to Surface Spacing on Synthetic Jet Impingement Heat Transfer

Synthetic jet is a new technique for electronic chip cooling, which combines stagnant air to form a jet resulting from periodic diaphragm oscillations in a cavity. In this work, the heat transfer characteristics of a synthetic jet are investigated experimentally and numerically. A Piston-cylinder arrangement powers the synthetic jet through a circular orifice for the impingement of jet on the heated surface. Air is considered as the cooling medium. The major parameters identified to describe the impinging jet heat transfer are Reynolds number, frequency, ratio of jet spacing to diameter(Z/D) and nozzle geometry. Numerical studies have been carried out using the finite volume based commercial software ANSYS Fluent. The turbulent model used is k-ω model. The dimensionless distance between the nozzle and plate surface is in the range 2 to 16. Numerical results are in fair agreement with experimental results. As the frequency increases the average Nusselt number increases. High frequency synthetic jets were found to remove more heat than low frequency jets for small Z/D ratio, while low frequency jets are more effective at larger Z/D ratio. Nusselt number is maximum at the stagnation point and there occurs a secondary peak at lower Z/D ratios. Synthetic jet with rectangular orifice is more effective as compared to circular and square geometries.