Influence of Particle on Gas Detonation by Shock

There exist evidence, that the gaseous detonation passing through a cloud of solid particles could be attenuated or even suppressed. Contrary to these known works, in the present article, we have found that just one single 160-micron particle can serve as a trigger for the detonation onset. By numerical simulation, we have obtained that there are the concentration ratio limits, in which single particle is enough to initiate gaseous detonation, although without particle the detonation is not ignited in the same conditions in a tube of restricted size. In other words, the presence of a solid particle in the combustible mixture could decrease significantly the ignition delay time. Using of temperature pattern visualization, we have demonstrated that the ignition arises in the subsonic region located between the particle and the bow shock front. The approximations of the used model are discussed. It is shown that used assumptions are valid within investigated time intervals. The work performed with use of the supercomputer resources Interdepartmental Supercomputer Center Russian Academy of Sciences (ISC RAS)

An analytical model for asymmetric Mach reflection configuration in steady flows

An analytical model is presented for the configuration of Mach reflection (MR) due to the interaction of two-dimensional steady supersonic flow over asymmetric wedges. The present asymmetric MR model is an extension of an earlier model for the symmetric MR configuration. The overall Mach reflection (oMR) in the asymmetric wedge configuration is analysed as a combination of upper and lower half-domains of symmetric reflection configurations. Suitable assumptions are made to close the combined set of equations. The subsonic pocket downstream of the Mach stem is taken to be oriented along an average inclination, based on the streamline deflections by the Mach stem at the triple points. This assumption is found to give satisfactory results for all types of oMR configurations. The oMR configuration is predicted for all types of reflections such as direct Mach reflection (DiMR), stationary Mach reflection (StMR) and inverse Mach reflection (InMR). The reflection configuration and Mach stem shape given by the model for various sets of wedge angles, especially those giving rise to InMR, have been predicted and validated with the available numerical and experimental data. The von Neumann criterion for oMR is accurately predicted by this model. The asymmetric Mach stem profile is well captured. The variation of Mach stem height with wedge angle is also analysed and it is found that simplification of an asymmetric MR to a symmetric MR leads to over-prediction of the Mach stem height and hence the extent of the subsonic region.

Cooling Injection Effect on a Transonic Squealer Tip—Part II: Analysis of Aerothermal Interaction Physics

A basic attribute for turbine blade film cooling is that coolant injected should be largely passively convected by the local base flow. However, the effective working of the conventional wisdom may be compromised when the cooling injection strongly interacts with the base flow. Rotor blade tip of a transonic high-pressure (HP) turbine is one of such challenging regions for which basic understanding of the relevant aerothermal behavior as a basis for effective heat transfer/cooling design is lacking. The need to increase our understanding and predictability for high-speed transonic blade tip has been underlined by some recent findings that tip heat transfer characteristics in a transonic flow are qualitatively different from those at a low speed. Although there have been extensive studies previously on squealer blade tip cooling, there have been no published experimental studies under a transonic flow condition. The present study investigates the effect of cooling injection on a transonic squealer tip through a closely combined experimental and computational fluid dynamics (CFD) effort. The experimental and computational results as presented in Part I have consistently revealed some distinctive aerothermal signatures of the strong coolant-base flow interactions. In this paper, as Part II, detailed analyses using the validated CFD solutions are conducted to identify, analyze, and understand the causal links between the aerothermal signatures and the driving flow structures and physical mechanisms. It is shown that the interactions between the coolant injection and the base over-tip leakage (OTL) flow in the squealer tip region are much stronger in the frontal subsonic region than the rear transonic region. The dominant vortical flow structure is a counter-rotating vortex pair (CRVP) associated with each discrete cooling injection. High HTC stripes on the cavity floor are directly linked to the impingement heat transfer augmentation associated with one leg of the CRVP, which is considerably enhanced by the near-floor fluid movement driven by the overall pressure gradient along the camber line (CAM). The strength of the coolant-base flow interaction as signified by the augmented values of the HTC stripes is seen to correlate to the interplay and balance between the OTL flow and the CRVP structure. As such, for the frontal subsonic part of the cavity, there is a prevailing spanwise inward flow initiated by the CRVP, which has profoundly changed the local base flow, leading to high HTC stripes on the cavity floor. On the other hand, for the rear high speed part, the high inertia of the OTL flow dominates; thus, the vortical flow disturbances associated with the CRVP are largely passively convected, leaving clear signatures on the top surface of the suction surface rim. A further interesting side effect of the strong interaction in the frontal subsonic region is that there is considerable net heat flux reduction (NHFR) in an area seemingly unreachable by the injected coolant. The present results have confirmed that this is due to the large reduction in the local HTC as a consequence of the upstream propagated impact of the strong coolant-base flow interactions.

Cooling Injection Effect on a Transonic Squealer Tip: Part 2 — Analysis of Aerothermal Interaction Physics

A basic attribute for turbine blade film cooling is that coolant injected should be largely passively convected by the local base flow. However the effective working of the conventional wisdom may be compromised when the cooling injection strongly interacts with the base flow. Rotor blade tip of a transonic high-pressure (HP) turbine is one of such challenging regions for which basic understanding of the relevant aerothermal behavior as a basis for effective heat transfer/cooling design is lacking. The need to increase our understanding and predictability for high speed transonic blade tip has been underlined by some recent findings that tip heat transfer characteristics in a transonic flow are qualitatively different from those at a low speed. Although there have been extensive studies previously on squealer blade tip cooling, there have been no published experimental studies under a transonic flow condition. The present study investigates the effect of cooling injection on a transonic squealer tip through a closely combined experimental and CFD effort. The experimental and computational results as presented in Part 1 have consistently revealed some distinctive aerothermal signatures of the strong coolant-base flow interactions. In this paper as Part 2, detailed analyses using the validated CFD solutions are conducted to identify, analyze and understand the causal links between the aerothermal signatures and the driving flow structures and physical mechanisms. It is shown that the interactions between the coolant injection and the base Over-Tip Leakage (OTL) flow in the squealer tip region are much stronger in the frontal subsonic region than the rear transonic region. The dominant vortical flow structure is a counter-rotating vortex pair (CRVP) associated with each discrete cooling injection. High HTC stripes on the cavity floor are directly linked to the impingement heat transfer augmentation associated with one leg of the CRVP, which is considerably enhanced by the near-floor fluid movement driven by the overall pressure gradient along the camber line. The strength of the coolant-base flow interaction as signified by the augmented values of the HTC stripes is seen to correlate to the interplay and balance between the OTL flow and the CRVP structure. As such, for the frontal subsonic part of the cavity, there is a prevailing spanwise inward flow initiated by the CRVP, which has profoundly changed the local base flow, leading to high HTC stripes on the cavity floor. On the other hand, for the rear high speed part, the high inertia of the OTL flow dominates, thus the vortical flow disturbances associated with the CRVP are largely passively convected, leaving clear signatures on the top surface of the suction surface rim. A further interesting side-effect of the strong interaction in the frontal subsonic region is that there is considerable net heat flux reduction in an area seemingly unreachable by the injected coolant. The present results have confirmed that this is due to the large reduction in the local HTC as a consequence of the upstream propagated impact of the strong coolant-base flow interactions.

A new concept of transonic galactic outflows and its application to the Sombrero galaxy

We study fundamental properties of transonic galactic outflows in the gravitational potential of a cold dark matter halo (DMH) with a central super-massive black hole (SMBH) assuming a polytropic, steady and spherically symmetric state. We have classified the transonic solutions with respect to their topology in the phase space. As a result, we have found two types of transonic solutions characterized by a magnitude relationship between the gravity of DMH and that of SMBH. These two types of solutions have different loci of the transonic points; one transonic point is formed at a central region (< 0.01kpc) and another is at a distant region (> 100kpc). Also, mass fluxes and outflow velocities are different between the two solutions. These two transonic solutions may play different roles on the star formation history of galaxies and the metal contamination of intergalactic space. Furthermore, we have applied our model to the Sombrero galaxy. In this galaxy, the wide-spread hot gas is detected as an apparent trace of galactic outflows while the star-formation rate is disproportionately low, and the observed gas density distribution is quite similar to the hydrostatic state (Li et al. 2011). To solve this discrepancy, we propose a slowly accelerating outflow in which the transonic point forms in a distant region (~ 120 kpc) and the subsonic region spreads across the stellar distribution. In the subsonic region, the gas density distribution is similar to that of the hydrostatic state. Our model predicts the possibility of the slowly accelerating outflow in the Sombrero galaxy. Igarashi et al. 2014 used the isothermal model and well reproduced the observed gas density distribution, but the estimated mass flux (1.8M⊙/yr) is lager than the mass of the gas supplied by stars (0.3-0.4M⊙/yr). Then, we expect that the polytropic model may reproduce the observational mass of the supplied gas (Igarashi et al. 2015). Such slowly accelerating outflows should be distinguished from the conventional supersonic outflows frequently argued in star-forming galaxies.

Oscillations in cylinder wakes at Mach 4

The wake behind a circular cylinder in Mach 4 flow is examined experimentally in the Reynolds number range $2\times 10^{4}$ to $5\times 10^{5}$. Periodic oscillations of the sliplines in the wake are observed. The Strouhal number of the oscillations based on the diameter of the cylinder is found to increase monotonically from 0.30 to 0.50 with increasing Reynolds number. If the Strouhal number is formed using the length of the sliplines, however, it has a constant value of approximately 0.48 for all Reynolds numbers studied. This scaling indicates that the oscillations in supersonic flow are likely driven by acoustic signals propagating back and forth through the subsonic region between the separation points on the cylinder and the neck where the sliplines converge, unlike in subsonic flow where oscillations are caused by vortices shed from the cylinder surface.

Shock Wave Instability in a Channel with an Expansion Corner

2D and 3D transonic flows in a channel of variable cross-section are studied numerically using a solver based on the Reynolds-averaged Navier–Stokes equations. The flow velocity is supersonic at the inlet and outlet of the channel. Between the supersonic regions, there is a local subsonic region whose upstream boundary is a shock wave, whereas the downstream boundary is a sonic surface. The sonic surface gives rise to an instability of the shock wave position in the channel. Computations reveal a hysteresis in the shock position versus the inflow Mach number. A dependence of the hysteresis on the velocity profile given at the inlet is examined.

Coupling constants and the generalized Riemann problem for isothermal junction flow

We consider gas flow in pipe networks governed by the isothermal Euler equations. A set of coupling conditions is required to completely specify the Riemann problem at the junction. The momentum-related condition has no obvious expression and different approaches have been used in previous work. For the condition of equal momentum flux, Colombo and Garavello [A well posed Riemann problem for the p-system at a junction, Netw. Heterog. Media 1 (2006) 495–511] proved existence and uniqueness of solutions globally in time and locally in the subsonic region of the state space. If the entropy constraint is not considered, we are able to prove existence and uniqueness globally in the subsonic region for any momentum-related coupling constant satisfying a monotonicity requirement. The previously suggested conditions of equal pressure and equal momentum flux satisfy this requirement, but in general they both fail to fulfill the entropy constraint. The classical Bernoulli invariant is a natural scalar formulation of momentum conservation under ideal flow conditions. Our analysis shows that this invariant is monotone and unconditionally leads to solutions satisfying the entropy constraint. Of the coupling constants considered, this is therefore the only choice that guarantees the unique existence of entropy solutions to the N-junction Riemann problem for all initial data in the subsonic region.

Squealer Tip Leakage Flow Characteristics in Transonic Condition

The over-tip-leakage (OTL) flow characteristics for a typical squealer tip of a high-pressure turbine blade, which consists of subsonic and transonic flow, have been numerically investigated in the present study, in comparison with the corresponding flat tip results. For the squealer tip employed, flow choking behavior still exists above the tip surface, even though the Mach number is lower and the transonic region is smaller than that for the flat tip. Detailed flow structure analysis shows that most of the fluid entering the squealer cavity is from the frontal leading edge region. The fluid migrates along the cavity and is ejected at various locations near the suction side rim. These fluids form a large subsonic flow zone under the supersonic flow passing over the tip gap which reduces the OTL flow flux. The squealer design works even in the presence of choked OTL flow. Comparisons between results from three different cavity depths with and without relative casing motion suggest that the over-tip-leakage flow flux has much dependence upon the cavity depth for the subsonic region, but is less sensitive to the depth for the transonic tip flow region. Such behavior has been confirmed with and without the existence of relative casing motion.