_{1}

^{*}

We investigate the Taylor-Couette flow of a rotating ferrofluid under the influence of symmetry breaking transverse magnetic field in counter-rotating small-aspect-ratio setup. We find only changing the magnetic field strength can drive the dynamics from time-periodic limit-cycle solution to time-independent steady fixed-point solution and vice versa. Thereby both solutions exist in symmetry related offering mode - two symmetry with left-or right-winding characteristics due to finite transverse magnetic field. Furthermore the time-periodic limit-cycle solutions offer alternately stroboscoping both helical left-and right-winding contributions of mode-two symmetry. The Navier-Stokes equations are solved with a second order time splitting method combined with spatial discretization of hybrid finite difference and Galerkin method.

A diffusion flame is a very common practical system, such as a match flame or a candle flame, and is fundamental to many more complex systems. However, in a diffusion flame there is a relatively long time scale, allowing sufficient recombination reactions to take place such that it involves complex interaction of flow, transport and chemistry. There is more chemical and physical interaction in diffusion flames than in a premixed flame. The first systematic analysis of a confined, jet diffusion flame dates back to 1928 by Burke and Schumann (published in 1948) [_{x} emission in combustion processed and its formation mechanism have always been of interest. Being of particular interest is source of nitric oxide, which is a major pollutant to the atmosphere. It has been postulated that there are two major mechanisms Zeldovich thermal and Fennimore prompt NO in the production of total NO. Barlow and Carter (1993) [

Dong et al. [_{2} and (20% CO, 80% H_{2}), (40% CO, 60% H_{2}), (20% CO, 20% CO_{2}, 60% H_{2}) the results of their study show that the flames develop vertical structures in the primary jet associated with the buoyancy and shear layer instability, and the wall jet progresses parallel to the impinging plate forming large scale vortex rings at different locations and strengths as a consequence of the fuel compositions.

Choe McDaid et al. [

Zhen et al. [_{x} from swirling and non-swirling of an impinging inverse diffusion flames and they found that the parameters of air jet Reynolds numbers, overall equivalence ration and Nozzle to plate distance have significant influence on the overall pollutants emission. To reduce the NO_{x} production a new down fired combustion technology based on multiple injection and multiple staging was developed by Min Kuang et al. [

(LPG-H_{2}-air) and (CH_{4}-H_{2}-air) comparison shows a more significant change in the laminar burning speed, temperature and CO/NO_{x} emissions in the CH_{4} flames. Gurpreet et al. [

Nadjib et al. [

In the current study, we investigated an impinging diffusion flame with three fuels, Methane, Propane and Butane with fixed fuel jet velocity. We also reported on the temperature response to the increase of the CH atom mole fraction, on the other hand we studied the relation between NO fraction production and heating high temperature for a non-premixed turbulent hydrocarbons jet flame situation.

In the present study, Fluent [

The general form of transport equations for two dimensional stationary turbulent reactive flows can be written as:

where denotes 1, and diffusion coefficient

is 0, and respectively. is a source term. Fluent uses a control-volume-based technique to convert the governing equations to algebraic equations that can be solved numerically.

In order to resolve the turbulent flow problem we are used K-Epsilon turbulent RNG based model.

where and

The model constants appearing in the above equations are

and.

The effects of the mean strain rate and mean rotation on turbulent diffusion have been affected by using the renormalized RNG k- model Yakhot et al., 1992 [

with

where

Though the modification of the above constants of the model, it is intended to simulate and control the modelling of the energy dissipation. The RNG k- model is a modification version of the standard k- turbulent model. It adopts a non-equilibrium strain parameter, Where S is the strain rate modulus and the ratio is the turbulence time scale.

In non-premixed combustion, fuel and oxidizer enter the reaction zone in distinct streams. This is in contrast to premixed systems, in which reactants are mixed at the molecular level before burning. Examples of non-premixed combustion include methane combustion, pulverized coal furnaces, and diesel (compression) internalcombustion engines.

In order to resolve the turbulent chemistry interaction we are focused to use Pre PDF model based on the resolution of mean transport species equation and its variance

[

The species fractions considered in this investigation are

In order to model nitric oxide formation in a flame, the chemical reactions involving nitrogen compounds must be taken into account. The reactions

are the principle mechanisms in forming Zeldovich “thermal” NO; the reactions are the major paths in forming Fenimore “prompt” NO. In the numerical work, both Zeldovich thermal and Fenimore prompt formation of NO were included.

Using a 2D model, the impingement surface is parallel to the fuel jet; and the jet was spreading vertically on the impinging plate. The diameter of the fuel jet is 10 mm ^{−3} for all variables, while a residual of 10^{−6} was used for the energy equation. The second convergence criterion is ensuring that the value of a sensitive property (e.g., concentration of a radical species) at a critical spatial location has stabilized and is no longer changing with iterations.

In this simulation the temperature and concentration of major species C_{4}H_{10}, C_{3}H_{8}, CH_{4}, H_{2}, H_{2}O, CO_{2}, N_{2}, and O_{2} and minor species NO, CO, and OH was performed using Fluent software code. CH_{4}, C_{3}H_{8}, C_{4}H_{10}, was used as the fuel in the impinging jet.

Velocity magnitude, flame temperature and the structure of the turbulent flame region were compared with different fuel jet flames.

Figures 2-6 show contours plots for temperature and mass fractions of OH and CO_{2} and OH and NO and production rate plotted versus mixture fraction for flames C_{4}H_{10}, C_{3}H_{8}, and CH_{4} at the same axial location.

The effect of N_{2} dilution level, in the fuel stream, on the flame temperature is quite substantial with a drop from 1700 K in the case propane flame, to 1400 K in case of butane flame. The temperature at the centerline is 420 K and is the same for all cases. The mean temperature in the jet vicinity of the flow is 1200 K and is also consistent between all flames _{2} is maximal for the butane jet flame. The same results are obtained in

Figures 7 and 9 show how the calculated NO and CO_{2} concentrations vary with the three jet fuels for the same simulation conditions.

Figures 7-10 show radial profiles of temperature and mass fractions of OH and CO and NO and turbulent intensity for turbulent flames C_{4}H_{10}, C_{3}H_{8}, and CH_{4} at an axial position of 100 mm above the jet exit.

_{4}H_{10} is different