Velocity and concentration measurements in a model diesel engine

Laser Doppler anemometry and Rayleigh scattering have been used to quantify the velocity and concentration fields after the start of injection in a model diesel engine motored at 200 rpm in the absence of compression. Fuel injection was simulated by a transient jet of vapour Freon-12 initiated at 40 degrees before top-dead-centre through a nozzle incorporated into the centre of a permanently open intake valve. Swirl was induced by means of 60 degree vanes located in the inlet, port. The piston configurations comprised a flat and a re-entrant piston-bowl.The results indicate that for the two nozzle geometries investigated the mass flux decays faster than momentum with nearly constant decay rates along the centreline. The nozzle with the larger exit diameter and wider jet angle gave rise to slower decay of both mass and momentum with associated lower velocity and concentration fluctuations.List of symbols D ₀ nozzle diameter - r radial coordinate - mean axial velocity - mean axial velocity at the centreline - ₀ mean axial velocity at the nozzle exit - rms of axial velocity fluctuations - mean concentration (mole fraction) - mean concentration at the nozzle exit - rms of concentration fluctuations - x axial coordinate A version of this paper was presented at the ASME Winter Annual Meeting of 1984 and printed in AMD, Vol. 66     

An Experimental Investigation of the Turbulence Structure of a Lifted H2/N2 Jet Flame in a Vitiated Co-Flow

Measurements of mean velocity components, turbulent intensity, and Reynolds shear stress are presented in a turbulent lifted H₂/N₂ jet flame as well as non-reacting air jet issuing into a vitiated co-flow by laser doppler velocimetry (LDV) technique. The objectives of this paper are to obtain a velocity data base missing in the previous experiment data of the Dibble burner and so provide initial and flow field data for evaluating the validity of various numerical codes describing the turbulent partially premixed flames on this burner. It is found that the potential core is shortened due to the high ratio of jet density to co-flow density in the non-reacting cases. However, the existence of flame suppressed turbulence in the upstream region of the jet dominates the length of potential core in the reacting cases. At the centreline, the normalized axial velocities in the reacting cases are higher than the non-reacting cases, and the relative turbulent intensities of the reacting flow are smaller than in the non-reacting flow, where a self-preserving behaviour for the relative turbulent intensities exists at the downstream region. The profiles of mean axial velocity in the lifted flame distribute between the non-reacting jet and non-premixed flame both in the axial and radial distributions. The radial distributions of turbulent kinetic energy in the lifted flames exhibit a change in distributions indicating the difference of stabilisation mechanisms of the two lifted flame. The experimental results presented will guide the development of an improved modelling for such flames.     

Jet flow field during screech

Measurements were made of the flow field structure and the near field parameters of a jet exhausting from a sonic nozzle with a 1.27 cm exit diameter. Compressed air was used for obtaining stagnation pressures up to 5 atmospheres. The jet exhausted vertically from a settling chamber into an acoustically insulated room and through an insulated duct out through the roof. Measurements were made with several different reflecting surfaces at the nozzle exit as well as an insulating surface. Schlieren pictures at 500,000 frames/s were taken. Overall sound pressure level, impact pressure level downstream, and sound frequency analyzer measurements were made.It was found that with a reflecting surface there was a radial oscillation of the jet which had the same frequency as the dominant sound (screech) frequency emitted by the jet. No axial motion of the inviscid part of the flow structure was detected. The insulated surface at the nozzle exit appeared to shift the dominant frequencies of the sound generated into the region above the audible (>16 KHz). A reflecting surface yielded pure tones (screech) with one or two harmonics. The dominant (screech) frequency decreased as the stagnation pressure increased. The screech frequency was found to be approximately inversely proportional to the length of the first shock cell.Nomenclature C ₀ speed of sound in ambient gas - D diameter of nozzle exit - f frequency of pure tone (screech frequency) - L ₁ length of first cell, distance between nozzle exit plane and intersection of shock with shear layer - M Mach number based on isentropic expansion to ambient pressure - P ₀ stagnation chamber pressure - P _a ambient pressure - P _i impact pressure - R _LB distance from nozzle centerline to left boundary of jet - R _RB distance from nozzle centerline to right boundary of jet - t time - period of screech, 1/f - X _E axial distance of eddy from nozzle exit plane - X _I axial distance of third cell shock intersection from nozzle exit plane - Y _I transverse distance of third cell shock intersection from nozzle centerline     

Very large‐scale computation of very small‐scale motions in a fully developed pipe flow

Local isotropy theory is examined using direct numerical simulation in a fully developed pipe flow at two Reynolds numbers Re_τ=1285.6 and 684.8. The approach to local isotropy is assessed with reference to the two Kolmogorov classical equations for longitudinal and transverse velocity structure functions. The results for the second‐order longitudinal structure functions in both the dissipative and inertial ranges indicate an improved agreement with the local isotropy hypothesis as the centreline is approached. However, the transverse structure functions satisfy isotropy neither in the dissipative range or in the inertial range. The distribution of the longitudinal and transverse structure functions also shows a substantial Reynolds number dependance in the logarithmic region of the flow and beyond. The results for the third‐order longitudinal structure function demonstrate an increased Reynolds number influence, and a deteriorating tendency to local isotropy for large separations. Contour images of axial velocity differences in the dissipative and inertial ranges have exhibited interesting patterns in relation to those of the instantaneous axial velocity. Finally, the results obtained in this investigation are in very good agreement with other published experimental and numerical data on channel and duct flows. Copyright © 2010 John Wiley & Sons, Ltd.     

Axisymmetric stagnation flow obliquely impinging on a moving circular cylinder with uniform transpiration

Laminar stagnation flow, axisymmetrically yet obliquely impinging on a moving circular cylinder, is formulated as an exact solution of the Navier–Stokes equations. Axial velocity is time‐dependent, whereas the surface transpiration is uniform and steady. The impinging free stream is steady with a strain rate k?. The governing parameters are the stagnation‐flow Reynolds number Re=k?a²/2ν, and the dimensionless transpiration S=U₀/k?a. An exact solution is obtained by reducing the Navier–Stokes equations to a system of differential equations governed by Reynolds number and the dimensionless wall transpiration rate, S. The system of Boundary Value Problems is then solved by the shooting method and by deploying a finite difference scheme as a semi‐similar solution. The results are presented for velocity similarity functions, axial shear stress and stream functions for a variety of cases. Shear stresses in all cases increase with the increase in Reynolds number and suction rate. The effect of different parameters on the deflection of viscous stagnation circle is also determined. Copyright © 2010 John Wiley & Sons, Ltd.     

Simplified Navier-Stokes Equations for Internal Mixed Flows and a Numerical Method of Solution

Simplified Navier-Stokes equations, of the elliptic and hyperbolic type in the subsonic and supersonic flow regions, respectively, are derived for viscous flows in channels and nozzles with curved walls whose local radii of longitudinal curvature are comparable with the transverse channel dimensions. A new numerical method is developed for the system of equations obtained. This method is of the evolution type along the longitudinal coordinate and includes global iterations of the streamline direction field and the longitudinal pressure gradient field. The effectiveness of the method is illustrated with reference to the solution of the direct Laval nozzle problem for an air flow at Reynolds numbers Re10⁴ and 10⁶ in conical nozzles with throat curvatures K _w=1.0 and 1.6 (K _w is the curvature divided by the inverse radius of the nozzle throat). Two iterations are sufficient to calculate the nozzle flow rate and power correct to 0.01%.     

Velocity measurements in a plane turbulent air jet at moderate Reynolds numbers

An experimental investigation of the moderate Reynolds number plane air jets was undertaken and the effect of the jet Reynolds number on the turbulent flow structure was determined. The Reynolds number, which was defined by the jet exit conditions, was varied between 1000 and 7000. Other initial conditions, such as the initial turbulence intensity, were kept constant throughout the experiments. Both hot-wire and laser Doppler anemometry were used for the velocity measurements. In the moderate Reynolds number regime, the turbulent flow structure is in transition. The average size and the number of the large scale of turbulence (per unit length of jet) was unaffected by the Reynolds number. A broadening of the turbulent spectra with increasing Reynolds number was observed. This indicated that there is a decrease in the strength of the large eddies resulting from a reduction of the relative energy available to them. This diminished the jet mixing with the ambient as the Reynolds number increased. Higher Reynolds numbers led to lower jet dilution and spread rates. On the other hand, at higher Reynolds numbers the dependence of jet mixing on Reynolds number became less significant as the turbulent flow structure developed into a self-preserving state.List of symbols b _u velocity half-width of the jet - C _u, C _u,0 constants defining the velocity decay rate - D nozzle width - E _u one dimensional power spectrum of velocity fluctuations - f frequency - K _u, K _u,0 constants defining the jet spread rate - k wavenumber (2f/U) - L longitudinal integral scale - R ₁₁ correlation function - r separation distance - Re jet Reynolds number (U ₀ D/v) - St Strouhal number (fD/U ₀) - t time - U axial component of the mean velocity - U _m mean velocity on the jet axis - U ₀ mean velocity at the jet exit - u the rms of u - u fluctuating component of the axial velocity - V lateral component of the mean velocity - fluctuating component of the lateral velocity - x axial distance from the nozzle exit - y lateral distance from the jet axis - z spanwise distance from the jet axis - v kinematic viscosity - time lag A version of this paper was presented as paper no. 86-0038 at the AIAA 24th Aerospace Sciences Meeting, Reno NV, USA, January 1986     

Prediction of stagnation point heat transfer for a slot jet impinging on a flat surface

The fluid flow and heat transfer for a slot jet impinging on a flat plate has been analysed for different nozzle-to-plate spacing. The available potential flow solution has been used to solve the boundary layer and energy equations by using the Blasius-Frossling series solution method. The friction factor and Nusselt number have been evaluated as a function of the dimensionless distance from the stagnation point. Correlation for the Stanton number at the Stagnation point, is obtained in terms of velocity gradient at the stagnation point and Reynolds number.

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Berechnung des Wärmeübergangs am Staupunkt für einen Strahl, der senkrecht auf eine ebene Fläche trifft

Zusammenfassung Für einen Fluidstrahl, der senkrecht auf eine ebene Platte trifft, wurden für verschiedene Anordnungen von Düse und Platte Strömung und Wärmeübertragung untersucht. Die beschreibende Potentialtheorie wurde verwendet, um die Grenzschicht und Energiegleichungen mit Hilfe der Blasius-Frossling-Reihenentwicklung zu lösen. Reibungsfaktor und Nusseltzahl sind als eine Funktion des dimensionslosen Abstandes vom Staupunkt dargestellt. Die Beziehung für die Stanton-Zahl am Staupunkt ist in den Ausdrücken des Geschwindigkeitsgradienten am Staupunkt und der Reynoldszahl enthalten.

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Nomenclature A ₁ dimensionless coefficient - a dimensionless parameter - b dimensionless parameter - C _f friction factor,C _f= ₀/(1/2w ² ) - C _p specific heat at constant pressure - F ₀ function ofPr and - G ₄ function ofPr and - f ₁ function of - h heat transfer coefficient - k thermal conductivity - l half-width of slot nozzle - Nu Nusselt number,Nu=hl/k - Pr Prandtl number,Pr=v/ - Re Reynolds number,Re=w l/v - St Stanton number,St=Nu/(Re · Pr) - t temperature - t _w wall temperature - t ambient temperature - U dimensionless velocity,U=u/w - U _f dimensionless free-stream velocity,U _f =u _f /w - U _s dimensionless mainstream velocity along the plate,U _s =u _s /w - u velocity component inx-direction - u _f free stream velocity - u _s mainstream velocity along the plate - w velocity component inz-direction - w velocity at the nozzle exit - x coordination along the plate - X dimensionless distance from the stagnation point along the plate,X=x/l - Y ratio ofU _s andU _f ,Y=U _s /U _f - z coordinate perpendicular to the plate - z _n height of the nozzle above the plate - Z dimensionless height of the nozzle above the plate,Z=z _n /l - thermal diffusivity,=k/( C _p) - dimensionless parameter - dimensionless coordinate perpendicular to the plate - viscosity - kinematic viscosity - ₀ shear stress at the wall - stream function     

Flame-Flow Interaction in Premixed Turbulent Flames During Transient Head-On Quenching

This paper reports on experimental investigations of turbulent flame-wall interaction (FWI) during transient head-on quenching (HOQ) of premixed flames. The entire process, including flame-wall approach and flame quenching, was analyzed using high repetition rate particle image velocimetry (PIV) and simultaneous flame front tracking based on laser-induced fluorescence (LIF) of the OH molecule. The influence of convection upon flame structures and flow fields was analyzed qualitatively and quantitatively for the fuels methane (CH₄) and ethylene (C₂H₄) at ? = 1. For this transient FWI, flames were initialized by laser spark ignition 5 mm above the burner nozzle. Subsequently, flames propagated against a steel wall, located 32 mm above the burner nozzle, where they were eventually quenched in the HOQ regime due to enthalpy losses. Twenty ignition events were recorded and analyzed for each fuel. Quenching distances were 179 μm for CH₄ and 159 μm for C₂H₄, which lead by nondimensionalization with flame thickness to Peclet numbers of 3.1 and 5.5, respectively. Flame wrinkling and fresh gas velocity fluctuations proved flame and flow laminarization during wall approach. Velocity fluctuations cause flame wrinkling, which is higher for CH₄ than C₂H₄ despite lower velocity fluctuations. Lewis number effects explained this phenomenon. Results from flame propagation showed that convection dominates propagation far from the wall and differences in flame propagation are related to the different laminar flame speeds of the fuels. Close to the wall flames of both fuels propagate similarly, but experimental results clearly indicate a decrease in intrinsic flame speed. In general, the experimental results are in good agreement with other experimental studies and several numerical studies, which are mainly based on direct numerical simulations.     

Rayleigh scattering temperature measurements in a plane turbulent air jet at moderate Reynolds numbers

Rayleigh scattering temperature measurements were made in a slightly heated plane jet at various Reynolds numbers and the effect of this parameter on the temperature field was determined. The axial and lateral distributions of the mean and rms temperature as well as the temperature spectra along the jet axis were determined. Results indicated that increasing Reynolds numbers led to lower levels of rms temperature and jet dilution in the moderate Reynolds number regime (between 700 and 2500). It was also found that slower spread rates of the thermal jet occured with larger Reynolds numbers in this regime.List of symbols b _T temperature half-width of the jet - C calibration constant for Rayleigh scattering optics - C _T, C _T,0 constants defining the temperature decay rate - D nozzle width - E _T power spectrum of temperature fluctuations - f frequency - I _L laser light intensity - I _R Rayleigh signal intensity - K _T, K _T,0 constants defining the jet spread rate - k wavenumber (2f/ U) - N total molecular number density - Re Reynolds number (U ₀D/) - T mean excess temperature - T _m mean excess temperature on the jet axis - T ₀ mean excess temperature at jet exit - T fluctuating temperature - U local mean velocity - U ₀ mean velocity at the jet exit - x axial distance from the nozzle exit - y lateral distance from the jet axis - z spanwise distance from the jet axis - Rayleigh scattering cross section - density - kinematic viscosity A version of this paper was presented as paper no 86-WA/ HT-98 at the 1986 ASME Winter Annual Meeting.     

Local heat transfer distribution between smooth flat surface and impinging air jet from a circular nozzle at low Reynolds numbers

An experimental investigation is performed to study the effect of jet to plate spacing and low Reynolds number on the local heat transfer distribution to normally impinging submerged circular air jet on a smooth and flat surface. A single jet from a straight circular nozzle of length-to-diameter ratio (l/d) of 83 is tested. Reynolds number based on nozzle exit condition is varied between 500 and 8,000 and jet-to-plate spacing between 0.5 and 8 nozzle diameters. The local heat transfer characteristics are obtained using thermal images from infrared thermal imaging technique. It was observed that at lower Reynolds numbers, the effect of jet to plate distances covered during the study on the stagnation point Nusselt numbers is minimal. At all jet to plate distances, the stagnation point Nusselt numbers decrease monotonically with the maximum occurring at a z/d of 0.5 as opposed to the stagnation point Nusselt numbers at high Reynolds numbers which occur around a z/d of 6.     

Stability of Periodic Clusters in Globally Coupled Maps

The phenomenon of partial synchronization, or clustering, in a system of globally coupled C ¹-smooth maps is analyzed. We prove the stability of equally populated K-clustered states with n-periodic temporal dynamics, referred to as P _n C _K-states. For this purpose, we first obtain formulas giving a relation between longitudinal and transverse multipliers of the in-cluster periodic orbits, and then, using these formulas, we find exact parameter intervals for transverse stability. We conclude that, typically, for symmetric P _n C _K-states, in-cluster stability implies transverse stability. Moreover, transverse stability can take place even if in-cluster dynamics are unstable.     

Hall effects on MHD flow in a rotating system with heat transfer characteristics

Closed-form solutions are derived for the steady magnetohydrodynamic (MHD) viscous flow in a parallel plate channel system with perfectly conducting walls in a rotating frame of reference, in the presence of Hall currents, heat transfer and a transverse uniform magnetic field. A mathematical analysis is described to evaluate the velocity, induced magnetic field and mass flow rate distributions, for a wide range of the governing parameters. Asymptotic behavior of the solution is analyzed for large M ² (Hartmann number squared) and K ² (rotation parameter). The heat transfer aspect is considered also with Joule and viscous heating effects present. Boundary layers arise close to the channel walls for large K ², i.e. strong rotation of the channel. For slowly rotating systems (small K ²), Hall current parameter (m) reduces primary mass flow rate (Q _x /R ρ v). Heat transfer rate at the upper plate (d θ/d η) _η=1 decreases, while at the lower plate (d θ/d η) _η=−1 increases, with increase in either K ² or m. For constant values of the rotation parameter, K ², heat transfer rate at both plates exhibits an oscillatory pattern with an increase in Hall current parameter, m. The response of the primary and secondary velocity components and also the primary and secondary induced magnetic field components to the control parameters is also studied graphically. Applications of the study arise in rotating MHD induction machine energy generators, planetary and solar plasma fluid dynamics systems, magnetic field control of materials processing systems, hybrid magnetic propulsion systems for space travel etc.     

Velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium

In this paper the velocity and temperature distributions on a semi-infinite flat plate embedded in a saturated porous medium are obtained for the governing equations (Kaviany [7]) following the technique adopted by Chandrashekara [2] which are concerned with the interesting situations of the existence of transverse, velocity and thermal boundary layers. Here the pressure gradient is just balanced by the first and second order solid matrix resistances for small permeability and observed that by increasing of the flow resistance the asymptotic value for the heat transfer rate increases. Further we concluded that the transverse boundary layers are thicker than that of axial boundary layers. Hence we evaluated the expressions for the boundary layer thickness, the shear stress at the semi-infinite plate and _T (the ratio of the thicknesses of the thermal boundary layer and momentum boundary layer). The variations of these quantities for different values of the porous parameterB and the flow resistanceF have been discussed in detail with the help of tables. The curves for velocity and temperature distributions have been plotted for different values ofB andF.Lastly we have evaluated the heat fluxq(x) and found that it depends entirely upon the Reynolds numberRe, Prandtl numberPr,B andF.     

Velocity and Strain-Rate Characteristics of Opposed Isothermal Flows

Velocity measurements in the isothermal flows created by an opposed nozzle configuration are reported with emphasis on the axis, stagnation plane and the distributions of mean and instantaneous strain rates. The instrumentation comprised particle image velocimetry (PIV) with silicon oil droplets added to the flows upstream of both nozzles with the laser sheet passing through the axis between the nozzles. The results identify the regions of high strain rates and quantify the development of the mean and turbulent components of the flow from the nozzle exits as a function of bulk velocities from 3 to 8.2 m/s and nozzle separations from 0.4 to 1.0 diameters. Results show, for example, the rise in the values of axial and radial normal stress towards the stagnation plane with values increasing by up to 300% and 160% respectively. The maximum mean strain rate occurred just over one nozzle radius from the axis at the smallest separation and with values that increased from 450 to 950 s⁻¹ with decreasing separation at a bulk velocity of 3.0 m/s. Probability density functions were near Gaussian and hence much larger instantaneous strain rates were observed. The PIV image size had the advantage that it allowed the entire flow field to be viewed in terms of velocity vectors and derived quantities include mean strain rates. Small asymmetry of the flow and the higher strain rates at finite distances from the nominal impingement plane were observed. The experimental results permitted the domain of applicability of different modelling approaches to be defined more accurately and calculations were performed with different turbulence models. The results showed that two-equation turbulence models did not represent turbulence intensities close to impingement and that Reynolds stress closures produce superior agreement. It was further shown that ad hoc modifications to the dissipation equation, such as those based on the ratio of the turbulent to mean strain time scale, can improve results at the expense of generality. It is also shown that mean flows are well reproduced by a Reynolds stress closure for all nozzle separations. Comments are included on the implications of the results for investigations of reacting flows and extinction.     

Three dimensional free convection flow and heat transfer along a porous vertical plate

The free convection flow along a vertical porous plate with transverse sinusoidal suction velocity distribution is investigated. Due to this type of suction velocity at the plate the flow becomes three dimensional one. For the asymptotic flow condition, the wall shear stress in the direction of main flow for different values of buoyancy parameter G is obtained. For G=0, the skin friction in the direction of free stream and the rate of heat transfer from the plate to the fluid are given. It is found that these results differ from those obtained by Gersten and Gross.     

Mixed Convection in Water Near the Density Extremum Along a Vertical Plate with Sinusoidal Surface Temperature Variation Embedded in a Porous Medium

A steady laminar boundary layer flowing along a vertical plate immersed in a Darcy–Brinkman porous medium saturated with water at 4°C is studied. The plate temperature varies sinusoidally along the plate between 0 and 8°C where the density of water varies parabolically and is almost symmetrical at about 4°C. Except for the existence of the buoyancy force, it is assumed that either the plate moves upwards or the ambient water moves upwards (moving stream). The results are obtained with the direct numerical solution of the boundary layer equations taking into account the temperature dependence of water thermophysical properties (ρ, μ and c _p). Results are presented for the wall temperature gradient and the wall shear stress along the plate for free convection and mixed convection. Temperature and velocity profiles are also presented.     

Fractal-Generated Turbulence in Opposed Jet Flows

The opposed jet configuration presents a canonical geometry suitable for the evaluation of calculation methods seeking to reproduce the impact of strain and re-distribution on turbulent transport in reacting and non-reacting flows. The geometry has the advantage of good optical access and, in principle, an absence of complex boundary conditions. Disadvantages include low frequency flow motion at high nozzle separations and comparatively low turbulence levels causing bulk strain to exceed the turbulent contribution at small nozzle separations. In the current work, fractal generated turbulence has been used to increase the turbulent strain and velocity measurements for isothermal flows are reported with an emphasis on the axis, stagnation plane and the distribution of mean and instantaneous strain rates. Energy spectra were also determined. The instrumentation comprised hot-wire anemometry and particle image velocimetry with the flows to both nozzles seeded with 1  $\upmu$ m silicon oil droplets providing a relaxation time of ? 3 $\upmu$ s. It is shown that fractal grids increase the turbulent Reynolds number range from 48–125 to 109–220 for bulk velocities from 4 to 8 m/s as compared to conventional perforated plate turbulence generators. Low frequency motion of the order 10 Hz could not be completely eliminated and probability density functions were determined for the location of the stagnation plane. Results show that the fluctuation in the position of the stagnation plane is of the order of the integral length scale, which was determined to be 3.1±0.1 mm at the nozzle exits through the use of hot-wire anemometry. Flow statistics close to the fractal plate located upstream of the nozzle exit were also determined using a transparent glass nozzle.     

Heat flux measurements in stagnation point methane/air flames with thermographic phosphors

Light-induced phosphorescence from thermographic phosphors was used to study the wall temperatures and heat fluxes from nearly one-dimensional flat premixed flames. The investigated flames were stoichiometric, lean and rich laminar methane/air flames with equivalence ratios of φ = 1, φ = 0.75 and φ = 1.25 at ambient pressure. The flames were burning in a stagnation point arrangement against a water-cooled plate. The central part of this plate was an alumina ceramic plate coated from both sides with chromium-doped alumina (ruby) and excited with a Nd:YAG laser or a green light-emitting diode (LED) array to measure the wall temperature from both sides and thus the heat flux rate from the flame. The outlet velocity of the gases was varied from 0.1 to 1.2 m/s. The burner to plate distance (H) ranged from 0.5 to 2 times the burner exit diameter (d = 30 mm). The measured heat flux rates indicate the change of the flame stabilization mechanism from a burner stabilized to a stagnation plate stabilized flame. The results were compared to modeling results of a one-dimensional stagnation point flow, with a detailed reaction mechanism. In order to prove the model, gas phase temperatures were measured by OH-LIF for a stoichiometric stagnation point flame. It turns out that the flame stabilization mechanism and with it the heat fluxes change from low to high mass fluxes. This geometry may be well suited for further studies of the elementary flame wall interaction.     

Numerical Investigation of a Bluff-Body Stabilised Nonpremixed Flame with Differential Reynolds-Stress Models

A numerical investigation of a bluff-body stabilised nonpremixedflame, and the corresponding nonreacting flow, has been performed withdifferential Reynolds-stress models (DRSMs). The equilibrium chemistry model is employed and an assumed-shape beta function PDFapproach is used to represent the interaction between turbulence andchemistry. The Reynolds flux of the mixture fraction is obtained from atransport equation, hence a full second moment closure is used. Toclarify the applicability of the existing DRSMs in this complex flame,several models, including LRR-IP model, JM model, SSG model as well as amodified LRR-IP model, have been applied and evaluated. The existingmodels, with default values of the coefficients, cannot provide overallsatisfactory predictions for this challenging test case. The standardLRR-IP model over predicts the centreline velocity decay rate, andtherefore does not perform satisfactory. The modified LRR-IP model, withmodel constant C _∈1 = 1.6 instead of the standard value1.44 (here named BM-M1), gives better results for the mean velocity.However in the nonreacting case this does not lead to improvement inpredicting rms fluctuating velocities especially downstream of therecirculation zone. Motivated by the need to improve the prediction, anew modification of the LRR-IP model is proposed (BM-M2), with modelconstant C ₂ = 0.7in the pressure strain correlation rather thanthe standard value 0.6. With the new modified model, a verysignificant improvement of the prediction of flow field is obtained inthe nonreacting case, whereas in the reacting case the prediction ofthe flow field is of the same overall quality as with BM-M1. This showsthat some DRSMs have different behaviour in the nonreacting case andthe reacting case. In the reacting case also the mean and variance ofmixture fraction are considered and it is found that the best resultsare obtained with the BM-M1 model, with SSG as second best. Combiningthe results for flow field and mixture fraction field it is concludedthat the BM-M1 model is recommended for further studies of thisbluff-body stabilised flame. Grid independence of the result isdemonstrated.