Fractal analysis of turbulent premixed flame surface

The fractal-like character of the laminar flamelet surface in turbulent premixed combustion of lean methane/air mixtures was studied by using the laser tomography technique to visualize the instantaneous flame surface in the two-dimensional section cut by the laser sheet. The fractal analysis of the surface revealed that the surface actually exhibits a self-similarity behavior in a narrow range of scale, and the value of fractal dimension can be defined. The inner cutoff scale was the laminar flame thickness, while the outer cutoff scale was the flame size. The fractal dimension was found to depend on the orientation of the section, and to increase towards downstream. It is suggested that the observed fractal-like character is not directly connected to approach flow turbulence, but should represent certain aspects of the flamelet itself.     

Experimental criteria for the determination of fractal parameters of premixed turbulent flames

The influence of spatial resolution, digitization noise, the number of records used for averaging, and the method of analysis on the determination of the fractal parameters of a high Damköhler number, methane/air, premixed, turbulent stagnation-point flame are investigated in this paper. The flow exit velocity was 5 m/s and the turbulent Reynolds number was 70 based on a integral scale of 3 mm and a turbulent intensity of 7%. The light source was a copper vapor laser which delivered 20 nsecs, 5 mJ pulses at 4 kHz and the tomographic cross-sections of the flame were recorded by a high speed movie camera. The spatial resolution of the images is 155 × 121 m/pixel with a field of view of 50 × 65 mm. The stepping caliper technique for obtaining the fractal parameters is found to give the clearest indication of the cutoffs and the effects of noise. It is necessary to ensemble average the results from more than 25 statistically independent images to reduce sufficiently the scatter in the fractal parameters. The effects of reduced spatial resolution on fractal plots are estimated by artificial degradation of the resolution of the digitized flame boundaries. The effect of pixel resolution, an apparent increase in flame length below the inner scale rolloff, appears in the fractal plots when the measurent scale is less than approximately twice the pixel resolution. Although a clearer determination of fractal parameters is obtained by local averaging of the flame boundaries which removes digitization noise, at low spatial resolution this technique can reduce the fractal dimension. The degree of fractal isotropy of the flame surface can have a significant effect on the estimation of the flame surface area and hence burning rate from two-dimensional images. To estimate this isotropy a determination of the outer cutoff is required and three-dimensional measurements are probably also necessary.     

Topology of turbulent premixed flame fronts resolved by simultaneous planar imaging of LIPF of OH radical and rayleigh scattering

 Planar images of Rayleigh scattering and laser-induced predissociative OH-fluorescence (OH-LIPF) have been obtained simultaneously in turbulent premixed jet flames on a single-shot basis. The geometric structure of temperature and OH isocontours were extracted for fractal analysis. A power-law fractal behavior can be identified in the ensemble-averaged flame length measure. It was found that the inner and outer cut-off scales of OH contours are larger than those of the iso-temperature contours; while the OH images show comparatively smaller fractal dimensions. The joint-pdf ’s between flame temperature and OH LIPF signals at different heights are also derived to evaluate the flame stretch effect on local flame structure. Comparison of image pairs near the extinction limit suggests that Rayleigh thermometry is more adequate to characterize the fine-scale flame front wrinkling in highly stretched turbulent premixed flames. Received: 12 September 1997/Accepted: 19 May 1998     

Liquid film break-up in a model of a prefilming airblast nozzle

 The paper describes the atomisation process of a liquid in an axissymmetric shear layer formed through the interaction of turbulent coaxial jets (respectively, inner and outer jets), with and without swirl, in a model airblast prefilming atomiser. The atomisation process and spray quality was studied using different visualisation techniques, namely laser shadowgraphy and digital image acquisition. The experiments were conducted for different liquid flow rates, Reynolds numbers ranging from 6600 to 66000 and 27300 to 92900 for the inner and outer air flows, respectively, for different outer flow swirl levels, and two liquid film thicknesses −0.2 and 0.7 mm. All the tests were carried out at atmospheric pressure and using water. The results include the analysis of the film structure at break-up and of the break-up length, and suggest that the deterioration of the liquid film close to the atomising edge exhibits a periodic behaviour and is mainly dependent on the inner air velocity. Film thickness strongly affects the time and length scales of the break-up process for the lower range of air velocities. For higher inner air velocities, the break-up length and time become less dependent on liquid flow rate and initial film thickness. Received: 14 March 1997/Accepted: 27 October 1997     

Velocity statistics along the stagnation line of an axi- symmetric stagnating turbulent flow

 Velocity statistics along the stagnation line of an axi-symmetric wall stagnating turbulent flow are studied experimentally. A low turbulence, uniform air flow from a nozzle type air supply with an exit diameter of 50 mm stagnates at a wall located 50 mm downstream. A flow velocity is set to 3 m/s, 10 mm downstream from the exit of the air supply. Instantaneous values of streamwise and radial velocities are measured by laser-Doppler velocimetry. The turbulence level in the air flow is changed by use of turbulence generator. When the turbulence generator is not installed in the air supply, the mean velocity profile in the streamwise direction fits well with that of a laminar viscous flow with the rms value of velocity fluctuations low near the wall. With the turbulence generator installed, a significant turbulence structure appears near the wall. When the wall is approached, the rms value of velocity fluctuations in the streamwise direction decreases monotonically while the profile of the rms value in the radial direction reaches a maximum near the wall. The increase in the rms value of velocity fluctuations in the radial direction near the wall is attributed to the bi-modal histogram of the fluctuating velocity in the radial direction. Near the wall, the instantaneous stagnation streamline fluctuates and the probability of the mean location of the stagnation point reaches a maximum not at the stagnation line but on a circle around the stagnation line, resulting in the bi-modal histogram. Turbulence statistics, the rms value of velocity fluctuation and the turbulent kinetic energy, can be normalized successfully by similarity parameters based on the strain rate and the reference turbulent kinetic energy introduced by Champion and Libby. Received: 7 April 1995/Accepted: 27 September 1996     

A pulse-expansion wave tube for nucleation studies at high pressures

 The design and performance of a new pulse-expansion wave tube for nucleation studies at high pressures are described. The pulse-expansion wave tube is a special shock tube in which a nucleation pulse is formed at the endwall of the high pressure section. The nucleation pulse is due to reflections of the initial shock wave at a local widening situated in the low pressure section at a short distance from the diaphragm. The nucleation pulse has a duration of the order of 200 μs, while nucleation pressures that can be achieved range from 1 to 50 bar total pressure. Droplet size and droplet number density can accurately be determined by a 90°-Mie light scattering method and a light extinction method. The range of nucleation rates that can be measured is 10⁸ cm^-3 s^-1<J<10¹¹ cm^-3 s^-1. We will illustrate the functioning and possibilities of the new pulse-expansion wave tube by nucleation rate measurements in the gas-vapour mixture nitrogen/water in the temperature range 200–260 K, and in the mixture methane/n-nonane as a function of supersaturation S at various total pressures up to 40 bar and temperatures around 240 K. Received: 5 June 1996/Accepted: 9 December 1996     

A ballistic compressor-based experiment for the visualization of liquid propellant jet combustion above 100 MPa

 This paper describes the components and operation of an experimental setup for the visualization of liquid propellant (LP) jet combustion at pressures above 100 MPa. The apparatus consists of an in-line ballistic compressor and LP injector. The ballistic compressor, based on a modified 76 mm gun, provides high-pressure (ca. 55 MPa) clear hot gas for the jet ignition. A piston (projectile) is fired toward a test chamber beyond the barrel’s end, and its rebound is arrested in a transition section that seals the test chamber to the barrel. The LP jet is injected once the piston is restrained, and combustion of the jet further elevates the pressure. At a preset pressure, a disc in the piston ruptures and the combustion gas vents sonically into the barrel. If a monopropellant is used, the jet injection-combustion process then resembles liquid rocket combustion but at very high pressures (ca. 140 MPa). This paper discusses the ballistics of the compression and compares experimental results to those predicted by a numerical model of the apparatus. Experimentally, a pressure of 70 MPa was achieved upon a 12.5 volumetric compression factor by firing a 10 kg piston into 1.04 MPa argon using a charge of 75 g of small-grain M1 propellant. Received: 16 December 1996/Accepted: 15 July 1997     

Experimental investigation on turbulent flow in a square-sectioned 90-degree bend

The development of steady, turbulent flow in a 90° section of a curved square duct was studied at a Reynolds number of 4 × 10⁴ by hot-wire anemometer. The curved duct has a cross-section measuring 80 × 80 mm and a curvature radius ratio of 4 and is connected with a long, straight duct at its both ends. The longitudinal and lateral components of mean and fluctuating velocities, and the Reynolds stresses were measured by the method of rotating a probe with an inclined hot-wire. The velocity fields of the primary and secondary flows, and the Reynolds stress distributions in the cross-section were illustrated in the form of contour map. The development of the primary flow was found to be connected with a strong pressure gradient near the outer and inner wall and a secondary flow induced in the cross-section of the bend by a pressure difference between the outer and inner wall and a centrifugal force acting on the fluid; the fluid is accelerated near the inner wall and decelerated near the outer wall between the bend angle ϕ ≅ 0° and ϕ ≅ 30°, but an increase and decrease of the fluid velocity are reversed between ϕ ≅ 30° and ϕ ≅ 90°. The fluctuating velocity correlations, i.e. the Reynolds stresses follow a complicated progress according to the complex development of the primary flow. The results obtained can be available to verify various types of turbulence models and to develop new models. Received: 10 May 1999/Accepted: 15 March 2000     

LES of Low to High Turbulent Combustion in an Elevated Pressure Environment

A subgrid scale flame surface density combustion model for the Large Eddy Simulation (LES) of premixed combustion is derived and validated. The model is based on fractal characteristics of the flame surface, assuming a self similar wrinkling of the flame between smallest and largest wrinkling length scales. Experimental and direct numerical simulation databases as well as theoretical models are used to derive a model for the fractal parameters, namely the cut-off lengths and the fractal dimension suitable in the LES context. The combustion model is designed with the intent to simulate low as well as high Reynolds number premixed turbulent flame propagation and with a focus on correct scaling with pressure. The combustion model is validated by simulations of turbulent Bunsen flames with methane and propane fuel at pressure levels between 0.1 MPa and 2 MPa and at turbulence levels of $0 < u^{\prime }/s_{L}^{0} < 11$ , conditions typical for spark ignition engines. The predicted turbulent flame speed is in a very good agreement with the experimental data and a smooth transition from resolved flame wrinkling to fully modelled, nearly subgrid-only wrinkling is realized. Evaluating the influence of mesh resolution shows a predicted mean flame surface and turbulent flame speed independent of mesh resolution for cases with 9–86 % resolved flame surface. Additional simulations of a highly turbulent jet flame at 0.1 MPa and 0.5 MPa and the comparison with experimental data in terms of flame shape, velocity field and turbulent fluctuations validates the model also at conditions typical for gas turbines.     

Fractal analysis of atomizing liquid flows

The work reported in this paper questions the relevance of using fractal concept to study liquid primary atomization process by characterizing the shape of the continuous liquid flow from the nozzle exit to the end of the atomization process. First, three fractal methods were tested on synthetic images in order to define the best adapted protocol to the objective of the study. It appeared that the Euclidean distance mapping was the best appropriate method. Second, this technique was applied to analyze series of images of atomizing liquid flows obtained for several working conditions. This application demonstrates that atomizing liquid flows are fractal objects and that primary atomization can be reasonably seen as fractal processes. The appropriateness of fractal concept was also demonstrated by the fact that fractal characteristics such as textural or structural fractal dimension and inner cutoff scale are physically representative of the process investigated here.     

Local mixture injection to extend the lean limit of spark-ignition engines

 The effect of charge stratification by direct, in-cylinder injection of a small quantity of propane-air mixture in a single-cylinder, propane-fuelled, spart-ignition engine, has been determined in terms of in-cylinder pressure, flame visualisation and exhaust emissions. The operating conditions ranged from low load to wide open throttle at 1000 and 1500 rpm, and with quiescent and swirling in-cylinder flows. The effects of injection-driven flow and turbulence on combustion have been considered independently of mixture strength by assessing the consequences of injecting a local mixture of an equivalence ratio equal to that of the port-induced charge. The results provide further evidence to support the concept of direct in-cylinder mixture injection. At 1000 rpm and low load, faster development of the flame kernel and subsequent enflamed area were observed, together with a 60% increase in peak cylinder combustion pressure at an overall equivalence ratio of 0.7 (A/F of 22.5). The relative effect of local-charge stratification increased with reduction in equivalence ratio at this engine speed and without increase in emissions; at 1500 rpm, stable combustion was achieved even at an equivalence ratio of 0.61 (A/F of 25.8), which was below the flammability limit of the homogeneous port-only propane/ air mixture. Unthrottled engine operation produced similar results so that at an equivalence ratio of 0.55 (A/F of 28.5), for example, the Coefficient of variation of the indicated mean effective pressure was reduced from 0.4 to less than 0.1 by mixture local injection. With a shrouded inlet valve generating mean gas velocities of 6 m/s at the time of ignition in the vicinity of the spark plug, control of rich mixture injection both with and against the bulk in-cylinder flow, resulted in stable combustion with Coefficient of variation of the indicated mean effective pressure of less than 0.1 at an equivalence ratio of 0.55 (A/F of 28.5). Received: 28 October 1997/Accepted: 23 March 1998     

Experimental investigation on turbulent flow through a circular-sectioned 180° bend

The steady, developing turbulent flow in a circular-sectioned 180° bend has been investigated. The bend had a radius of 104 mm and a curvature radius ratio of 4.0 with long, straight upstream and downstream pipes. Measurements of the longitudinal, radial and circumferential components of mean velocity, and corresponding components of the Reynolds stress were obtained with a hot wire anemometer at a Reynolds number of 6×10⁴ and at various longitudinal stations. The velocity fields of the primary and secondary flows and the Reynolds stresses were illustrated in the form of contour map or vector diagram. Moreover, the mean quantities characterizing the bend flow, i.e., the deflection of the primary flow in the cross section, the intensity of the secondary flow and the turbulence energy, were shown in a graphic form against the longitudinal distances. In the section upstream from a bend angle of about 60°, both the flows through the 180° and the 90° bend are closely similar in their behavior. In the section from the bend angle of 90°, the high-velocity regions, however, occur near the upper and lower walls as a result of strong secondary flow and the turbulence with high level emerges in the central region of the bend. Just behind the bend exit, an additional pair of vortices appears in the outer part of the cross section owing to the transverse pressure difference. In the downstream tangent, the flow returns slowly to the proper flow in a straight pipe, but it needs a longer distance for recovery than in the 90° bend. Received: 23 April 1998/Accepted: 24 April 1999     

Development and characterization of a variable turbulence generation system

Experimental turbulent combustion studies require systems that can simulate the turbulence intensities [u′/U ₀ ~ 20–30% (Koutmos and McGuirk in Exp Fluids 7(5):344–354, 1989)] and operating conditions of real systems. Furthermore, it is important to have systems where turbulence intensity can be varied independently of mean flow velocity, as quantities such as turbulent flame speed and turbulent flame brush thickness exhibit complex and not yet fully understood dependencies upon both U ₀ and u′. Finally, high pressure operation in a highly pre-heated environment requires systems that can be sealed, withstand high gas temperatures, and have remotely variable turbulence intensity that does not require system shut down and disassembly. This paper describes the development and characterization of a variable turbulence generation system for turbulent combustion studies. The system is capable of a wide range of turbulence intensities (10–30%) and turbulent Reynolds numbers (140–2,200) over a range of flow velocities. An important aspect of this system is the ability to vary the turbulence intensity remotely, without changing the mean flow velocity. This system is similar to the turbulence generators described by Videto and Santavicca (Combust Sci Technol 76(1):159–164, 1991) and Coppola and Gomez (Exp Therm Fluid Sci 33(7):1037–1048, 2009), where variable blockage ratio slots are located upstream of a contoured nozzle. Vortical structures from the slots impinge on the walls of the contoured nozzle to produce fine-scale turbulence. The flow field was characterized for two nozzle diameters using three-component Laser Doppler velocimetry (LDV) and hotwire anemometry for mean flow velocities from 4 to 50 m/s. This paper describes the key design features of the system, as well as the variation of mean and RMS velocity, integral length scales, and spectra with nozzle diameter, flow velocity, and turbulence generator blockage ratio.     

Generating arbitrarily sized interrogation windows for correlation-based analysis of particle image velocimetry recordings

 We describe a technique that allows an arbitrary size of the interrogation window when using the traditional FFT algorithm in analysing PIV recordings by either cross- or auto-correlation methods. The length and width of the effective interrogation window are no longer required to be composed of a number of pixels making a power of 2 (16, 32, 64 etc). This gives a higher flexibility in selecting the appropriate window size. Received: 28 January 1997/Accepted: 11 August 1997     

High speed optical tomography system for quantitative measurement and visualization of dynamic features in a round jet

An optical tomography system that is capable of operating at frame rates of up to 5 kHz has been used to obtain spatially resolved cross-sectional temperature images of a heated round jet. These tomographic images show dynamic details in the evolving vortical flow structures found in the near field of the jet that are consistent with previous studies of low speed jet flow. Reconstructions produced by the system are quantitative temperature distributions of a planar cross section of the jet measuring temperature differences with a spatial resolution of 1.4 mm. Received: 31 July 1997/Accepted: 18 December 1997     

PIV measurements of a microchannel flow

 A particle image velocimetry (PIV) system has been developed to measure velocity fields with order 1-μm spatial resolution. The technique uses 200 nm diameter flow-tracing particles, a pulsed Nd:YAG laser, an inverted epi-fluorescent microscope, and a cooled interline-transfer CCD camera to record high-resolution particle-image fields. The spatial resolution of the PIV technique is limited primarily by the diffraction-limited resolution of the recording optics. The accuracy of the PIV system was demonstrated by measuring the known flow field in a 30 μm×300 μm (nominal dimension) microchannel. The resulting velocity fields have a spatial resolution, defined by the size of the first window of the interrogation spot and out of plane resolution of 13.6 μm× 0.9 μm×1.8 μm, in the streamwise, wall-normal, and out of plane directions, respectively. By overlapping the interrogation spots by 50% to satisfy the Nyquist sampling criterion, a velocity-vector spacing of 450 nm in the wall-normal direction is achieved. These measurements are accurate to within 2% full-scale resolution, and are the highest spatially resolved PIV measurements published to date. Received: 29 October 1998/Accepted: 10 March 1999     

An analysis of subgrid-resolved scale interactions with use of results from direct numerical simulations

Subgrid nonlinear interaction and energy transfer are analyzed using direct numerical simulations of isotropic turbulence. Influences of cutoff wave number at different ranges of scale on the energetics and dynamics have been investigated. It is observed that subgrid-subgrid interaction dominates the turbulent dynamics when cut-off wave number locates in the energy-containing range while resolved-subgrid interaction dominates if it is in the dissipation range. By decomposing the subgrid energy transfer and nonlinear interaction into ‘forward’ and ‘backward’ groups according to the sign of triadic interaction, we find that individually each group has very large contribution, but the net of them is much smaller, implying that tremendous cancellation happens between these two groups.     

Simultaneous velocity and scalar measurements in premixed recirculating flames

 The use of a laser-Doppler velocimeter has been extended to the analysis of turbulent heat transfer in a strongly sheared disc-stabilised propane-air flame through its combination with either laser Rayleigh scattering or digitally-compensated fine-wire thermocouples. The laser velocimeter was based on a conventional forward scattering system from the green light of a 5W Argon-Ion laser, while the Rayleigh signals used the blue line of the same laser. The procedure for the numeric compensation of the thermocouple signals included analysis of the effect of velocity and temperature on the time constant of the thermocouple and was optimised to allow combined velocity–temperature samples acquired by a purpose-built digital interference with a frequency up to 2000 Hz, without deterioration of the thermocouple by particle accretion. The maximum effective data rate for the combined Rayleigh/LDV system is shown to be around 130 Hz, which corresponds to a data rate of valid Doppler signals around 400 Hz and statistics based on more than 15 000 measurements is made possible. The results obtained with the two systems agree qualitatively, although the use of thermocouples attenuates the measured velocity-temperature correlations. The results are used to assess the extent to which turbulent mixing in flames is altered by the accompanying heat release and quantify the processes of non-gradient diffusion in a strongly recirculating premixed flame. Received: 15 November 1996/Accepted: 2 September 1997     

Turbulence structure in an annuli with strongly heated inner cylinder

This structure of turbulent flow in an annulus with strong inner cylinder wall heating has been studied in terms of velocity and temperature with wall temperatures up to 707 °C and a Reynolds number of 48,000. With increase in wall heating, the turbulence very close to the wall was suppressed due to an increase in the kinematic viscosity. In the inner region, the intermittent mixing became intensive and the turbulent intensity increased whereas, in the outer region, the turbulence was suppressed since intermittent mixing was no longer effective. The results show that the thermal structure can be considered in terms of a passive scalar for wall temperatures less then around 200 °C, except in the leading region of the heated area. Received: 2 March 1998/Accepted: 2 November 1998