Pressure-time Traces Research Articles

Model predictive control of mixing controlled compression ignition operation for low reactivity fuels

Using gasoline or other low reactivity fuels with a pilot injection or port fuel injection in a compression ignition engine has shown great potential in reducing NOx emissions while keeping high thermal efficiency compared to diesel. However, excessive combustion noise is caused by a high maximum pressure rise rate in the cylinder due to the higher fractions of premixed charge of the low-reactivity fuel. This noise can result in structural damage to engine components and as such, combustion noise limits the range of the operating parameters and makes the control of such engines challenging. In this study, a simulation environment was built up in MATLAB/Simulink leveraging a physics-based zero-dimension combustion model to capture the in-cylinder pressure time traces as well as metrics relevant to thermal efficiency and combustion noise. In order to also facilitate the control of emissions, machine learning models were investigated to capture NOx emissions. A kernel-based extreme learning machine (K-ELM) performed best and had a coefficient of correlation (R-squared) of 0.998. The combustion and NOx emission models are valid for not only conventional gasoline fuel but also oxygenated alternative fuel blends at three different pilot injection strategies. In order to track key combustion metrics while keeping noise and emissions within constraints, a model predictive control (MPC) was applied for a compression ignition engine operating with a range of potential fuels and fuel injection strategies. The MPC is validated under different scenarios, including a load step change, fuel type change, and injection strategy change, with proportional–integral (PI) control as the baseline. The simulation results show that MPC reduces about 26% of ringing intensity in the transient process and 17% at the steady state for E30. Generally, MPC can optimize the overall performance through modifying the main injection timing, pilot fuel mass, and exhaust gas recirculation (EGR) fraction.

Visualization of spontaneous ignition and flame behavior in tubes with and without obstacles during the high-pressure hydrogen release

This paper studies the effects of triangle obstacles inside the tube on the ignition mechanism and subsequent flame development in a semi-confined space when high-pressure hydrogen sudden release. Smooth tube and obstructed tube with optical glasses are constructed where controlled high-pressure hydrogen are released. High-speed direct photography is used to image the flame evolution while pressure transducers are used to obtain pressure-time traces both inside the tube and exhaust chamber. These cases that hydrogen with various burst pressure jets into the smooth and obstructed tubes are tested. It is found that spontaneous ignition occurs in the boundary layer of the tube in the smooth tube, a complete fire spanning the cross-section is reached as the flame propagates within the mixing region. The appearance of obstacles is found to have a significant effect on the ignition mechanism and flame structure. A two-way dissemination reflected shock wave forms and three possible ignition region emerges surrounding the obstacles. The flame propagation restricted between the leading shock wave and hydrogen jet. The flame experiences a split that the front flame in the vicinity of the obstacle gradually dies out and the rear flame continues propagating within the mixing region. The flame evolution and pressure variation in the exhaust chamber show that obstacles inside the tube do not aggravate the disaster in the semi-confined chamber.

Phase-averaged and cycle-to-cycle analysis of jet dynamics in a scaled up vocal-fold model.

Phase-averaged and cycle-to-cycle analysis of key contributors to sound production in phonation is examined in a scaled-up vocal-fold model. Simultaneous temporally and spatially resolved pressure and velocity measurements permitted examination of each term in the streamwise integral momentum equation. The relative sizes of these terms were used to address the issue of whether transglottal pressure is a surrogate for vocal-fold drag, a quantity directly related to sound production. Further, time traces of transglottal pressure and volume flow rate provided insight into the role of cycle-to-cycle variations in voiced sound production which affect voice quality. Experiments were conducted using a 10× scaled-up model in a free-surface water tunnel. Two-dimensional vocal-fold models with semi-circular ends inside a square duct were driven with constant opening and closing speeds. The time from opening to closed, To , was half the oscillation period. Time-resolved digital particle image velocimetry (DPIV) and pressure measurements along the duct centreline were made for 3650 ≤ Re ≤ 8100 and equivalent life frequencies from 52.5 to 97.5 Hz. Results showed that transglottal pressure does serve as a surrogate for the vocal-fold drag. However, smaller but non-negligible momentum flux and inertia terms, caused by the jet and vocal-fold motions, may also contribute to vocal-fold drag. Further, cycle-to-cycle variations including jet switching and modulation are inherent in flows of this type despite their high degrees of symmetry and repeatability. The origins of these variations and their potential role in sound production and voice quality are discussed.

An experimental and computational investigation of air-borne noise generation mechanisms in tires

The complex nature of the tire/road noise generation process makes it difficult to isolate and study each mechanism individually. This paper presents an experimental and numerical investigation of air-borne tire noise generation mechanisms for a realistic tire. Experimentally, a single slot is cut into the tire and the noise data are measured and studied. Air-borne noise is isolated by filling the slot with foam and comparing the resulting frequency spectra. Numerically, a previously developed computational fluid dynamics tire noise prediction model is employed to predict the air-borne noise for the same tire, under similar operating conditions. A direct comparison between the experimental and computational results is also presented in terms of pressure time traces and spectral characteristics. Comparisons indicate that the computational model is capable of predicting the noise generated by the air pockets in the tire. While providing a deeper understanding of the causes of air-borne noise, this paper also aims to demonstrate the use of a computational tool that can be used to obtain a reasonably accurate prediction of air-borne tire noise.

Rotary sloshing induced by impeller action in unbaffled stirred vessels

Unbaffled stirred tanks are characterized by a highly swirling fluid motion and, unless they are completely filled and closed with a lid, a central whirlpool takes place, whose depth depends on the impeller rotational speed. In some cases, periodic rotating waves appear, regardless of the axial symmetry of the system. These waves may result into undesirable periodic stresses for the structure, the vessel and the process connections.In this paper, a comprehensive experimental study on the onset and the characterization of periodic free-surface oscillations in unbaffled stirred vessels is carried out. Different wave shapes (or oscillation modes) may be observed, depending on the operating conditions. The oscillation mode of the free liquid surface is experimentally evaluated by both visual observation and measurements of the local dynamic pressure time traces. The oscillation frequency is identified from the time traces by means of simple Fast Fourier Transform.The natural frequency of each oscillation mode is in excellent agreement with predictions obtained by the theory of sloshing in case of still liquids in cylinders, but the effect of impeller is here analyzed in detail.Several experiments using different tank geometries, filling ratios and liquid viscosities were carried out. In all cases, the observed frequency was found to increase linearly with the impeller speed, with a slope that depends on the impeller geometry and on the oscillation mode under analysis. A simple predictive model is developed and validated by comparison with experimental data.

Lagrangian coherent structures during combustion instability in a premixed-flame backward-step combustor.

This paper quantitatively examines the occurrence of large-scale coherent structures in the flow field during combustion instability in comparison with the flow-combustion-acoustic system when it is stable. For this purpose, the features in the recirculation zone of the confined flow past a backward-facing step are studied in terms of Lagrangian coherent structures. The experiments are conducted at a Reynolds number of 18600 and an equivalence ratio of 0.9 of the premixed fuel-air mixture for two combustor lengths, the long duct corresponding to instability and the short one to the stable case. Simultaneous measurements of the velocity field using time-resolved particle image velocimetry and the CH^{*} chemiluminescence of the flame along with pressure time traces are obtained. The extracted ridges of the finite-time Lyapunov exponent (FTLE) fields delineate dynamically distinct regions of the flow field. The presence of large-scale vortical structures and their modulation over different time instants are well captured by the FTLE ridges for the long combustor where high-amplitude acoustic oscillations are self-excited. In contrast, small-scale vortices signifying Kelvin-Helmholtz instability are observed in the short duct case. Saddle-type flow features are found to separate the distinct flow structures for both combustor lengths. The FTLE ridges are found to align with the flame boundaries in the upstream regions, whereas farther downstream, the alignment is weaker due to dilatation of the flow by the flame's heat release. Specifically, the FTLE ridges encompass the flame curl-up for both the combustor lengths, and thus act as the surrogate flame boundaries. The flame is found to propagate upstream from an earlier vortex roll-up to a newer one along the backward-time FTLE ridge connecting the two structures.

Intermuscular pressure between synergistic muscles correlates with muscle force.

The purpose of the study was to examine the relationship between muscle force generated during isometric contractions (i.e. at a constant muscle-tendon unit length) and the intermuscular (between adjacent muscles) pressure in synergistic muscles. Therefore, the pressure at the contact area of the gastrocnemius and plantaris muscle was measured synchronously to the force of the whole calf musculature in the rabbit species Oryctolagus cuniculus Similar results were obtained when using a conductive pressure sensor, or a fibre-optic pressure transducer connected to a water-filled balloon. Both methods revealed a strong linear relationship between force and pressure in the ascending limb of the force-length relationship. The shape of the measured force-time and pressure-time traces was almost identical for each contraction (r=0.97). Intermuscular pressure ranged between 100 and 700 mbar (70,000 Pa) for forces up to 287 N. These pressures are similar to previous (intramuscular) recordings within skeletal muscles of different vertebrate species. Furthermore, our results suggest that the rise in intermuscular pressure during contraction may reduce the force production in muscle packages (compartments).

Multiple ignitions and the stability of rotating detonation waves

We perform a numerical study on rotating detonation engines (RDE). The simulations demonstrate the feasibility of creating multiple detonation waves and examine their stabilization process. The computations are based on the three-dimensional Euler equations with reactive sources. The Arrhenius chemistry model is used to calculate the reaction rate of the pre-mixed stoichiometric hydrogen-air mixture. The simulations show the oscillation phenomenon characterized by the pressure-time traces and the stabilization process. Also, the results indicate the existence of one-, two-, and eight-wave propagation modes in the fully-developed detonation flow. The initial detonation waves dominate the flow throughout the stabilization process in the one- and two-wave modes. On the other hand, the eight-wave mode is the result of the generation of new detonation waves during the intermediate stage. The simulations are compared with the experimental studies to confirm the existence of the multi-wave modes discussed herein. In addition, it is found that the velocity of detonation waves decreases with the increase of the number of detonation waves, which is also reported in some experiments.

Characterization of instabilities in a Rotating Detonation Combustor

Rotating Detonation Combustor (RDC) operation is investigated under different air and fuel flow rates, and varied geometries to reveal four fundamentally different instabilities. Select test points are chosen to study these instabilities using qualitative and quantitative tools. First, for RDC operation at lean limits, or with subsonic air injection, or with large fuel injection orifices, the detonation wave inside the combustor undergoes aperiodic chaotic propagation around the combustor annulus characterized by incoherent pressure-time traces. The high incoherence in recorded pressure, along with the considerable variation in subsequent pressure peaks suggests numerous failure and re-initiation of the detonation wave. Second, almost all operating points at the variety of conditions tested exhibit some degree of low frequency sinusoidal oscillations characterized by periodic waxing and waning of subsequent detonation peak pressures. It occurs between 200 Hz and 500 Hz for the operating maps studied. Third, the phenomenon of mode switching in the RDC is also defined as instability since the sudden change in the number of detonation waves existing in the combustor is temporally unpredictable, and often unpredictable for a given geometry. It is found that RDC operation is more stable when there are multiple detonation waves inside the chamber. With a back-pressurizing convergent nozzle, at certain operating points, the RDC exhibits axisymmetric pulsed operation like the Pulsed Detonation Combustor (PDC). There is significant evidence to suggest that these longitudinal pulsed detonations (LPD) are manifested due to shock-reflection from the RDC exit followed by a subsequent shock-initiation of the fresh reactants. The frequency of this instability is around 3.8 kHz for the test case investigated.

Optical Methods for Studies of Self-Excited Oscillations and the Effect of Dampers in a High Pressure Single Sector Combustor

Self-excited periodic instabilities in a staged lean burn injector could be forced by operating the combustor at off-design conditions. These pressure oscillations were studied in a high pressure single sector combustor with optical access. Two damper configurations were installed and tested with respect to their damping efficiency in relation to the configuration without dampers. For a variety of test conditions, derived from a part load case, time traces of pressure in the combustor were measured, and amplitudes were derived from their Fourier transformation. These measurements were performed for several combinations of the operating parameters, i.e., injector pressure drop, air/fuel ratio (AFR), pilot/main fuel split, and preheat temperature. These tests “ranked” the respective damper configurations and their individual efficiency with respect to the configuration without dampers. Although a general trend could be observed, the ranking was not strictly consistent for all operating conditions. For several test cases, preferably with pronounced self-excited pressure oscillations, phase-resolved planar optical measurement techniques were applied to investigate the change of spatial structures of fuel, reaction zones, and temperature distributions over a period of an oscillation. A pulsating motion was detected for both pilot and main flame, driven by a pulsating transport of the liquid fuel. This pulsation, in turn, is caused by a fluctuating air velocity, in connection with a prefilming airblast type atomizer. A phase shift between pilot and main injector heat release was observed, corresponding to a shift of fuel penetration. Local Rayleigh indices were calculated qualitatively, based on phase-resolved OH chemiluminescence used as marker for heat release, and corresponding pressure values. This identified regions, where a local amplification of pressure oscillations occurred. These regions were largely identical to the reaction regions of pilot and main injector, whereas the recirculation zone between the injector flows was found to exhibit a damping effect.

Turbulent premixed flames of CNG, LPG, and H2 propagating past repeated obstacles

This paper presents a comparative study of turbulent premixed flames of three different fuels propagating past repeated solid obstacles. Compressed natural gas (CNG), liquefied petroleum gas (LPG), and hydrogen are employed separately at two different equivalence ratios. All three fuels are tested at an equivalence ration of 0.8 giving a good comparison between the cases. Three baffle plates and two obstacles with different blockage ratios are used in a range of configurations. In all tests, the mixture is initially at rest when ignited from a single point near the base of the chamber. Pressure–time traces as well as high-speed images of laser induced fluorescence from OH (HS–LIF–OH) are measured. The overpressure, pressure gradients, time to reach the peak pressure, location and speed of the flame front as well images of OH are compared for the three fuels.It is true for all fuels that the peak pressure and its rate of change can be increased by increasing the blockage ratio. For the same equivalence ratio of 0.8, the peak pressure and rate of change for hydrogen flames were about an order of magnitude higher than for LPG or CNG flames. For a given configuration of obstacles, the structure of hydrogen flames shows less distortion and wrinkling than for the other two hydrocarbon fuels at the same equivalence ratio. A good correlation seems to exist between the peak pressure, its rate of change and the time to reach the peak. The data forms a good platform for validating models of turbulent premixed combustion.

Warpage Characterization of Thin and Centrally-Gated Injection Molded Part by Applying Cavity Pressure Measurement

Two types of injection molded parts including parts with thin shell feature and parts molded with radial flow pattern are highly susceptible to the warpage. In this research, the warpage performance of a thin and centrally-gated disk was experimentally investigated. The melt pressure-time traces of two different locations inside the mold cavity were monitored by employing piezoelectric transducers. The results indicated that the pressure difference magnitude of melt at two locations along the radial flow path is related to the extent of molded part deformation. Moreover, it was pointed out that the high magnitude of warpage is because of two conflicting actions in the molded part comprising expansion as a result of viscoelastic recovery in the central region, and thermal contraction in the edge region of the thin disk. The molding variables encompassing injection speed, holding pressure, back pressure, mold temperature and screw rotational speed affected the thin disks deformation in order of significance.

Water Slug Formation and Motion in Gas Flow Channels: The Effects of Geometry, Surface Wettability, And Gravity

Water emerging from ∼100 μm pores into millimeter-size gas flow channels forms drops that grow and become slugs which span the flow channel. Flowing gas causes the slugs to detach and move down the channel. The effect of channel geometry, surface wettability, and gravity on the formation and motion of water slugs has been analyzed using high-speed video images of the drops and differential pressure-time traces. Drops grow and appear, assuming a sequence of shapes that minimize the total interfacial energy of the gas-liquid and liquid-solid interfaces. The drops are initially spherical caps centered on the pore (the liquid contacts one wall). Above a certain size, the drops move to the corner, forming "corner drops" (the liquid contacts two walls). Corner drops grow across the channel, evolving into partial liquid bridges (drops confined by three walls), and finally the drops span the channel cross-section forming slugs (contacting all four walls). Smaller slugs are formed in channels with hydrophobic walls than in channels with hydrophilic walls. Smaller slugs are formed in channels with curved walls than in square or rectangular channels. Slugs move when the differential gas pressure overcomes the force to move the advancing and receding gas-liquid-solid contact lines of the slugs. Residual water left behind in corners by moving slugs reduces the barriers for drops to form slugs, causing the steady-state slug volumes to be smaller than those seen at start-up in dry channels.

Regarding the perturbed operating process of DB propellant rocket motor at extreme initial grain temperatures

Despite many decades of study, the combustion instability of several DB propellants is still of particular concern, especially at extreme grain temperature conditions of rocket motor operating. The purpose of the first part of the paper is to give an overview of our main experimental results on combustion instabilities and pressure oscillations in DB propellant segmented grain rocket motors (SPRM-01, large L/D ratio), working at extreme initial grain temperatures. Thus, we recorded some particular pressure-time traces with significant perturbed pressure signal that was FFT analysed. An updated mathematical model incorporating transient frequency-dependent combustion response, in conjunction with pressure-dependent burning, is applied to investigate and predict the DB propellant combustion instability phenomenon. The susceptibility of the tested motor SPRM-01 with DB propellant to get a perturbed working and to go unstable with pressure was evidenced and this risk has to be evaluated. In the last part of our paper we evaluated the influence of recorded perturbed thrust on the rocket behaviour on the trajectory. The study revealed that at firing-table initial conditions, this kind of perturbed motor operating may not lead to an unstable rocket flight, but the ballistic parameters would be influenced in an unacceptable manner.

Bifurcations of Self-Excited Ducted Laminar Premixed Flames

Bifurcation analysis is performed on experimental data obtained from a simple setup comprising ducted laminar premixed conical flames in order to investigate the features of nonlinear thermoacoustic oscillations. It is observed that as the bifurcation parameter is varied, the system undergoes a series of bifurcations leading to characteristically different nonlinear oscillations. Through the application of nonlinear time series analysis to pressure and flame (CH* chemiluminescence) intensity time traces, these oscillations are characterized as periodic, aperiodic, or chaotic oscillations, and subsequently the nature of the obtained bifurcations is explained based on dynamical systems theory. Nonlinear interaction between the flames and the acoustic modes of the duct is clearly reflected in the high speed flame images acquired simultaneously with pressure time series.

Droplet and slug formation in polymer electrolyte membrane fuel cell flow channels: The role of interfacial forces

A microfluidic device is employed to emulate water droplet emergence from a porous electrode and slug formation in the gas flow channel of a PEM fuel cell. Liquid water emerges from a 50 μm pore forming a droplet; the droplet grows to span the entire cross-section of a microchannel and transitions into a slug which detaches and is swept downstream. Droplet growth, slug formation, detachment, and motion are analyzed using high-speed video images and pressure–time traces. Slug volume is controlled primarily by channel geometry, interfacial forces, and gravity. As water slugs move downstream, they leave residual micro-droplets that act as nucleation sites for the next droplet-to-slug transition. Residual liquid in the form of micro-droplets results in a significant decrease in slug volume between the very first slug formed in an initially dry channel and the ultimate “steady-state” slug. A physics-based model is presented to predict slug volumes and pressure drops for slug detachment and motion.

A multi-mode shock tube for investigation of blast-induced traumatic brain injury.

Blast-induced mild traumatic brain injury (bTBI) has become increasingly common in recent military conflicts. The mechanisms by which non-impact blast exposure results in bTBI are incompletely understood. Current small animal bTBI models predominantly utilize compressed air-driven membrane rupture as their blast wave source, while large animal models use chemical explosives. The pressure-time signature of each blast mode is unique, making it difficult to evaluate the contributions of the different components of the blast wave to bTBI when using a single blast source. We utilized a multi-mode shock tube, the McMillan blast device, capable of utilizing compressed air- and compressed helium-driven membrane rupture, and the explosives oxyhydrogen and cyclotrimethylenetrinitramine (RDX, the primary component of C-4 plastic explosives) as the driving source. At similar maximal blast overpressures, the positive pressure phase of compressed air-driven blasts was longer, and the positive impulse was greater, than those observed for shockwaves produced by other driving sources. Helium-driven shockwaves more closely resembled RDX blasts, but by displacing air created a hypoxic environment within the shock tube. Pressure-time traces from oxyhydrogen-driven shockwaves were very similar those produced by RDX, although they resulted in elevated carbon monoxide levels due to combustion of the polyethylene bag used to contain the gases within the shock tube prior to detonation. Rats exposed to compressed air-driven blasts had more pronounced vascular damage than those exposed to oxyhydrogen-driven blasts of the same peak overpressure, indicating that differences in blast wave characteristics other than peak overpressure may influence the extent of bTBI. Use of this multi-mode shock tube in small animal models will enable comparison of the extent of brain injury with the pressure-time signature produced using each blast mode, facilitating evaluation of the blast wave components contributing to bTBI.

Measurements of Speed of Sound in Lean and Rich Natural Gas Mixtures at Pressures up to 37 MPa Using a Specialized Rupture Tube

Measurements of the speed of sound in 42 different compositions of lean, medium, and rich natural-gas mixtures using a specialized high-pressure rupture tube have been conducted. The rupture tube is made of stainless steel (internal diameter = 38.1 mm and length = 42 m), and is instrumented with 13 high-frequency-response dynamic pressure transducers (Endevco) mounted very close to the rupture end and along the length of the tube to capture the pressure-time traces of the decompression wave. Tests were conducted for initial pressures ranging from 10 MPa to 37 MPa and a temperature range from −25°C to+68°C. Gas mixture compositions were controlled by mixing conventional natural-gas mixtures from an adjacent gas pipeline with richer components of alkanes. Temperature control is achieved by a heat tracer along the tube with a set point at the desired gas temperature of the particular test. Uncertainty analysis indicated that the uncertainty in the experimentally determined speed of sound in the undisturbed gas mixture at the initial pressure and temperature is on the order of 0.306 %. The measured speeds of sound were compared to predictions by five equations of state, namely; the Benedict–Webb–Rubin–Starling (BWRS), AGA-8, Peng–Robinson (PR), Redlich–Kwong–Soave (RK–Soave), and Groupe Europeen de Recherches Gazieres (GERG-2004) equations.

Measurement of Decompression Wave Speed in Rich Gas Mixtures at High Pressures (370 bars) Using a Specialized Rupture Tube

Measurements of decompression wave speed in conventional and rich natural gas mixtures following rupture of a high-pressure pipe have been conducted. A high-pressure stainless steel rupture tube (internal diameter=38.1 mm and 42 m long) has been constructed and instrumented with 16 high frequency-response pressure transducers mounted very close to the rupture end and along the length of the tube to capture the pressure-time traces of the decompression wave. Tests were conducted for initial pressures of 33–37 MPa-a and a temperature range of 21–68°C. The experimentally determined decompression wave speeds were compared with both GASDECOM and PIPEDECOM predictions with and without nonequilibrium condensation delays at phase crossing. The interception points of the isentropes representing the decompression process with the corresponding phase envelope of each mixture were correlated with the respective plateaus observed in the decompression wave speed profiles. Additionally, speeds of sound in the undisturbed gas mixtures at the initial pressures and temperatures were compared with predictions by five equations of state, namely, BWRS, AGA-8, Peng–Robinson, Soave–Redlich–Kwong, and Groupe Européen de Recherches Gaziéres. The measured gas decompression curves were used to predict the fracture arrest toughness needed to assure fracture control in natural gas pipelines. The rupture tube test results have shown that the Charpy fracture arrest values predicted using GASEDCOM are within +7% (conservative) and −11% (nonconservative) of the rupture tube predicted values. Similarly, PIPEDECOM with no temperature delay provides fracture arrest values that are within +13% and −20% of the rupture tube predicted values, while PIPEDECOM with a 1°C temperature delay provides fracture arrest values that are within 0% and −20% of the rupture tube predicted values. Ideally, it would be better if the predicted values by the equations of state were above the rupture tube predicted values to make the predictions conservative but that was not always the case.

Effects of position and frequency of obstacles on turbulent premixed propagating flames

This paper studies the effects of the number and location of solid obstacles on the rate of propagation of turbulent premixed flames. A vented explosion chamber is constructed where controlled premixed flames are ignited from rest to propagate past grids or baffles plates as well as other solid obstacles strategically positioned in the chamber. Laser Induced Fluorescence (LIF) is used to image OH which is used as an indicator of the reaction zone while pressure transducers are used to obtain pressure–time traces. Single grids or baffle plates located at different distances from the ignition source are tested. Two as well as three baffle plates are also investigated in varying configurations. It is found that while the peak overpressure increases with increasing number of grids or baffle plates, a limit is reached where the pressure starts to decrease. The location of the obstacles is found to have a significant effect on the overpressure and the flame structure. Higher overpressures are obtained when the baffle plates and obstacles are stacked closer together hence not allowing turbulence to decay. LIF images for OH show that the reaction zones become more contorted with increasing number of baffle plates in the flame path.