Bernard Parent

Numerical Investigation of Transverse Hydrogen Jet into Supersonic Crossflow Using Detached-Eddy Simulation

A three-dimensional unsteady reacting flowfield that is generated by transverse hydrogen injection into a supersonic mainstream is numerically investigated using detached-eddy simulation and a finite-rate chemistry model. Grid refinement with the grid-convergence-index concept is applied to the instantaneous flowfield for assessing the grid resolution and solution convergence.Validation is performed for the jet penetration height, and the predicted result is in good agreement with experimental trends. The results indicate that jet vortical structures are generated as the interacting counter-rotating vortices become alternately detached in the upstream recirculation region. Although the numerical OH distribution reproduces the experimental OH–planar-laser-induced fluorescence well, there are some disparities in the ignition delay times due to the restricted availability of experimental and numerical data. The effects of the turbulence model on combustion are identified by a comparative analysis of the Reynolds-averaged Navier–Stokes and detached-eddy simulation approaches. Their effects are quantified by the production ofH2O, which is the primary species of hydrogen combustion.

Effect of geometrical parameters on the mixing performance of cantilevered ramp injectors

A cantilevered ramp fuel-injection strategy is considered as a means to deliver rapid mixing for use in scramjets and shock-induced combustion ramjets (shcramjets). The primary objective is to perform parametric studies of the injector array spacing, injection angle, and sweeping angle at a convective Mach number of 1.5. Analysis of the three-dimensional steady-state hypersonic e owe elds is accomplished through the WARP code, using the Yee‐Roe e ux-limiting scheme and theWilcox k-! turbulencemodel, along with the Wilcox dilatational dissipation correction. A closer array spacing is shown to increase signie cantly the mixing efe ciency in the near e eld, and a direct relationship between initial fuel/air contact surface and mixing efe ciency growth is apparent. A change in the injector angle from 4 to 16 deg induces a 9% augmentation in the mixing efe ciency but more than a twofold increase in the thrust potential losses. A sweeping angle of i3.5 deg is observed to result into signie cantly better fuel penetration, translating into a 28% increase in the mixing efe ciency for a sweep angle decreased from 3.5 to i3.5 deg. It is observed that an air cushion between the wall and the hydrogen is sufe ciently thick to prevent fuel penetrating the boundary layer when 1 ) the fuel is injected at an angle of »10 deg or more, 2 ) an array spacing of at least the height of the injector is used, and 3 ) a swept ramp cone guration is avoided.

Validation of the Wilcox k-omega Model for Flows Characteristic to Hypersonic Airbreathing Propulsion

Numerical results obtained with the WARP code solving the 1988 Wilcox k‐ω two-equation model are compared with experimental data of flowfields characteristic of hypersonic airbreathing propulsion. The problems chosen for the comparison include a shock/boundary-layer interaction case, a reacting and inert planar mixing case, and two ramp injector mixing cases. In addition, a comparison is performed with empirical correlations on the basis of skin friction for flow over a flat plate and shear layer growth for a free shear layer. The agreement between the numerical and experimental results varies between being reasonable and excellent, with a discrepancy generally not exceeding 20%. It is found that the grid-induced error can be reduced to an acceptable level for most problems with a reasonable mesh size. However, the free shear layer and the shock/boundary-layer interaction cases require a considerably finer mesh. The Wilcox dilatational dissipation correction is seen to be beneficial in predicting the growth of a free shear layer at a high convective Mach number, but its use is considered either questionable or detrimental for the other cases. A proper choice of the turbulent Schmidt number is observed to be crucial in predicting the injectant mole fraction contours for one of the ramp injector cases, with the best agreement obtained with Schmidt number Sct fixed to 0.25. For the inert planar mixing case, overall better agreement is obtained when setting both the turbulent Prandtl and Schmidt number to 0.5.

Suppression of Premature Ignition in the Premixed Inlet Flow of a Shcramjet

This paper addresses the problem of premature ignition in a shock induced combustion ramjet (shcramjet) inlet. Previous studies have developed fuel injectors and inlet configurations that maximize the mixing efficiency in a shcramjet inlet while maintaining inlet losses at a minimum. A chemically reacting study of previously recommended shcramjet inlets finds premature ignition to occur primarily in the boundary layer in the last 15% of the inlet, spreading into the core flow prior to the inlet exit. Both gaseous nitrogen and additional hydrogen are then injected into the inlet flowfield in an attempt to suppress the flame. Various inflow conditions are considered, and injected using various geometries. Premature ignition is suppressed most feasibly by the injection of additional hydrogen through a backward facing step (slot injector) located just before the second inlet shock, such that the global equivalence ratio of the premixed flow exiting the inlet is one. The performance of the original inlet remains unaltered and the frictional force on the inlet wall is reduced by 10% due to the hydrogen slot injection. All turbulent, chemically reacting, three dimensional, mixing flowfields are solved using the WARP code which solves the FANS equations closed by the Wilcox kω turbulence model and the Wilcox dilatational dissipation correction. Chemical kinetics are modeled by a 9 species, 20 reaction model by Jachimowski.

Numerical Investigation of the Turbulent Mixing Performance of a Cantilevered Ramp Injector

An injector geometry is considered for fuel delivery in a high-enthalpy, high-Mach-number airflow typical of that found in hypersonic propulsion systems such as the scramjet and shock-induced combustion ramjet or shcramjet. It is thought to embody the characteristics of both conventional ramp and low-angle wall injection techniques. The objective is to investigate the turbulent hypervelocity fuel/air mixing characteristics of the considered injector geometry, with particular emphasis on the effect of the convective Mach number and global equivalence ratio on its mixing efficiency. The analysis of the three-dimensional hypervelocity mixing flow is based on the Favre-averaged Navier-Stokes equations closed by the Wilcox kω turbulence model for a multispecies gas. A Roe scheme turned second-order accurate through a symmetric total-variation-diminishing limiter is used for the spatial discretization while approximate factorization is used to iterate in pseudotime

Hypervelocity Fuel/Air Mixing in Mixed-Compression Inlets of Shcramjets

This paper investigates the mixing of hydrogen fuel with air in the mixing duct of a mixed-compression shock-induced combustion ramjet (shcramjet) inlet. Mixing augmentation through the use of cantilevered ramp injector arrays on opposite shcramjet inlet walls is studied and the influence of relative array locations is quantified. Studies were undertaken numerically using the WARP code that solves the Favre-averaged Navier-Stokes equations closed by the Wilcox k-w turbulence model. Air-based mixing efficiencies of up to 0.58-0.68 were achieved with thrust potential losses less than that gained from high-speed fuel injection. Shocks created from the fuel injector structures play a major role in the mixing behavior of the fuel jets on the opposing side of the mixing duct. Chemically reacting studies verified for the correct selection of spanwise displacement of the fuel injectors, an air buffer created between the fuel and walls suppresses premature ignition while still allowing for a mixing efficiency of up to 0.46-0.54.

Formation and Stability of Near Chapman-Jouguet Standing Oblique Detonation Waves

A numerical investigation of the behavior of standing oblique detonation waves (ODWs) near the Chapman-Jouguet (minimum entropy) point is the main purpose of this investigation. The laminar, two-dimensional Navier-Stokes equations coupled with a nonequilibrium hydrogen-air combustion model based on chemical kinetics are used to represent the physical system. The equations are solved with the window allocatable resolver for propulsion computational fluid dynamics code. A time-accurate simulation of the formation of a standing ODW near the Chapman-Jouguet condition yields a nonoscillatory, stable structure. The stability of the ODW to inhomogeneities in the oncoming fuel-air mixture is assessed through other time-accurate simulations by artificially introducing small disturbances consisting of pure air just upstream of the ODW structure.

Hypervelocity Fuel/Air Mixing in a Shcramjet Inlet

The mixing of fuel with air in the inlet of a shock-induced combustion ramjet (shcramjet) is presented. The study is limited to nonreacting hydrogen/air mixing in an external-compression inlet at a flight Mach number of 11 and at a dynamic pressure of 1400 psf (67,032 Pa), with use of an array of cantilevered ramp injectors. Results are obtained using the WARP code solving the Favre-averaged Navier‐Stokes equations closed by the Wilcox kω turbulence model and the Wilcox dilatational dissipation correction, discretized by the Yee‐Roe flux-limited scheme. Because of the fuel being injected at a very high speed, fuel injection in the inlet is found to increase the thrust potential considerably, with a gain exceeding the losses by 40‐120%. Losses due to skin friction are seen to play a significant role in the inlet, because they are estimated to make up as much as 50‐70% of the thrust potential losses. The use of a turbulence model that can predict the wall shear stress accurately is, hence, crucial in assessing the losses accurately in a shcramjet inlet. Substituting the second inlet shock by a Prandtl‐Meyer compression fan is encouraged because it decreases the thrust potential losses and reduces the risk of premature ignition by reducing the static temperature, while decreasing the mixing efficiency by a mere 6%. One approach that is observed to be successful at increasing the mixing efficiency in the inlet is alternating the injection angle along the injector array. The use of two injection angles of 9 and 16 deg is seen to result in a 32% increase in the mixing efficiency at the expense of a 14% increase in the losses when compared to a single injection angle of 10 deg. When alternating injection angles are used, the mixing efficiency reaches as much as 0.47 at the inlet exit.

Positivity-preserving high-resolution schemes for systems of conservation laws

A new class of flux-limited schemes for systems of conservation laws is presented that is both high-resolution and positivity-preserving. The schemes are obtained by extending the Steger-Warming method to second-order accuracy through the use of component-wise TVD flux limiters while ensuring that the coefficients of the discretization equation are positive. A coefficient is considered positive if it has all-positive eigenvalues and has the same eigenvectors as those of the convective flux Jacobian evaluated at the corresponding node. For certain systems of conservation laws, such as the Euler equations for instance, this condition is sufficient to guarantee positivity-preservation. The method proposed is advantaged over previous positivity-preserving flux-limited schemes by being capable to capture with high resolution all wave types (including contact discontinuities, shocks, and expansion fans). Several test cases are considered in which the Euler equations in generalized curvilinear coordinates are solved in 1D, 2D, and 3D. The test cases confirm that the proposed schemes are positivity-preserving while not being significantly more dissipative than the conventional TVD methods. The schemes are written in general matrix form and can be used to solve other systems of conservation laws, as long as they are homogeneous of degree one.

Hypersonic Mixing Enhancement by Compression at a High Convective Mach Number

The effect of an oblique shock and of a Prandtl‐Meyer compression fan on the characteristics of the turbulent mixing of a square-cross-section hydrogen jet in hypervelocity air is presented. The air properties before the compression process are set to those found after the first shock of a two-shock external compression shcramjet inlet at a flight Mach number of 11 and an altitude of 34.5 km. The hydrogen properties are such that the convective Mach number is 1.2, the global equivalence ratio is 0.68, and the pressure of the hydrogen matches the pressure of the air at injection. Also presented is an algebraic expression approximating increase in mixing efficiency growth through compression. The algebraic expression is based on available empirical correlations for the turbulent mixing layer and is simplified for the special case of a high-convective-Mach-number mixing layer in which the Mach numbers of both streams are high. The numerical results are obtained by using the WARP code to solve the Favre-averaged Navier‐Stokes equations closed by the Wilcox kω turbulence model and the Wilcox dilatational dissipation correction, discretized by the Yee‐Roe flux-limited scheme. Results obtained indicate increase in the mixing efficiency growth by 5.7 and 6.3 times through the oblique shock and the compression fan, respectively. Despite generating weaker axial vortices, the compression fan results into a greater increase mixing efficiency growth because of a higher density increase.