Laminar Mixing Layer Research Articles

Physics-informed neural networks coupled with flamelet/progress variable model for solving combustion physics considering detailed reaction mechanism

In recent years, physics-informed neural networks (PINNs) have shown potential as a method for solving combustion physics. However, current efforts using PINNs for the direct predictions of multi-dimensional flames only use global reaction mechanisms. Considering detailed chemistry is crucial for understanding detailed combustion physics, and how to accurately and efficiently consider detailed mechanisms under the framework of PINNs has not been explored yet and is still an open question. To this end, this paper proposes a PINN/flamelet/progress variable (FPV) approach to accurately and efficiently solve combustion physics, considering detailed chemistry. Specifically, the combustion thermophysical properties are tabulated using several control variables, with the FPV model considering detailed chemistry. Then, PINNs are used to solve the governing equations of continuity, momentum, and control variables with the thermophysical properties extracted from the FPV library. The performance of the proposed PINN/FPV approach is assessed for diffusion flames in a two-dimensional laminar mixing layer by comparing it with the computational fluid dynamics (CFD) results. It has been found that the PINN/FPV model can accurately reproduce the flow and combustion fields, regardless of the presence or absence of observation points. The quantitative statistics demonstrated that the mean relative error was less than 10%, and R2 values were all higher than 0.94. The applicability and stability of this model were further verified on other unseen cases with variable parameters. This study provides an efficient and accurate method to consider detailed reaction mechanisms in solving combustion physics using PINNs.

Opposed jet burner and Tsuji burner for representative laminar flamelet with differential molecular diffusion for non-premixed combustion modeling

Modeling differential molecular diffusion in turbulent non-premixed combustion remains challenging for flamelet models. Laminar flamelet is a key building block of flamelet models for turbulent combustion. One significant challenge that has not been adequately addressed is the representativity of laminar flamelet for the characteristics of differential molecular diffusion in turbulent combustion. Laminar flamelet is typically generated based on two conceptual burner configurations, the opposed jet burner and the Tsuji burner. The two burners are commonly viewed to be equivalent for the description of laminar flamelet structures. In this work, a major difference between them is revealed for the first time when they are used to represent differential molecular diffusion. The traditional opposed jet burner yields almost fixed equal diffusion locations defined as the points with equal values of mixture fractions based on different elements in the mixture fraction space. The Tsuji burner, with a slight extension, can produce a continuous variation of the equal diffusion locations in the mixture fraction space. This variation of the equal diffusion locations is shown to be an important feature of non-premixed combustion, as demonstrated in a laminar jet mixing layer, a turbulent jet mixing layer, and a turbulent jet non-premixed flame. Theoretical analysis is conducted based on an idealized opposed jet mixing layer to identify the major cause of the difference between the two burners. It is found that the inlet diffusion caused the major difference in differential molecular diffusion in the two burners. The curvature difference, another main difference between the two burners, however, is not found to cause any major difference in differential molecular diffusion in the two burners. Based on the finding, a modified opposed jet burner with disabled inlet diffusion is introduced and is shown to be able to reproduce the feature of differential molecular diffusion observed in the Tsuji burner. Both burners, after properly generalized with suitable boundary conditions and additional parameters (like the velocity ratio of fuel and oxidizer), are expected to be suitable and equivalent choices for the generation of representative laminar flamelets that can be used eventually in flamelet modeling of differential molecular diffusion in turbulent non-premixed combustion.Novelty and significance statement: (1) A significant difference between the opposed jet burner and the Tsuji burner is revealed for generating representative laminar flamelet with differential molecular diffusion (under specific conditions); (2) The flamelet generated from the Tsuji burner is shown to be representative of differential molecular diffusion found in practically relevant mixing and combustion problems; (3) The treatment of inlet diffusion is identified to be the major cause of the difference observed between the two burners; (4) Modifications are introduced to the opposed jet burner to reconcile the two different burners for producing representative flamelet that can be used in the modeling of differential molecular diffusion in turbulent non-premixed combustion.

LES of a turbulent lifted methanol spray flame using a novel spray flamelet/progress variable model

Turbulent spray flames are complex combustion configurations and are difficult to be accurately simulated. In this paper, we focus on further development and validation of the two-phase spray flamelet/progress variable (TSFPV) model, which is first proposed in our previous work and shows sound performance because it is able to consider the effect of droplet evaporation on the flamelet structure. A spray evaporation source term (SEST) model is improved in the present work to model the evaporation sources and is applied to the calculation of one-dimensional laminar counterflow flames to generate the spray flamelet library. The SEST model is validated on the configuration of two-dimensional counterflow spray flames, and the a priori and a posteriori results show good agreement with the solutions using the Lagrangian particle tracking (LPT) method. The effect of pre-vaporized fuel vapor is further considered in the spray flamelet library, in which both the spray and gaseous flame regimes are covered. The TSFPV model is well validated on the configuration of the laminar mixing layer by comparing the a priori and a posteriori results with detailed chemistry (DC) solutions. Large Eddy Simulation (LES) of the Sydney turbulent lifted methanol spray flame Mt2A is conducted using the TSFPV model. The flame lift-off is correctly captured and the final predicted lift-off height is very close to the experimental value. The predicted mean droplet velocities show good agreement with experimental measurements, and the rms velocities agree well with the experimental data at downstream locations with a late jet breakup. The droplet size increases along the downstream direction and this trend is well reproduced in the current simulation, though the local peak value of droplet size near the upstream shear layer is not well captured. The central jet temperature at upstream locations is also well predicted by the TSFPV model. Overall, the results show good agreement with the experimental measurements, which illustrates the potential of the TSFPV model for spray combustion modeling.

Direct numerical simulations of auto-igniting mixing layers in ammonia and ammonia-hydrogen combustion under engine-relevant conditions

This study investigated auto-ignition characteristics of ammonia-air and ammonia-hydrogen-air laminar and turbulent mixing layers by means of direct numerical simulations (DNS) under elevated pressure conditions. The results show that elevated pressure and hydrogen addition accelerate the auto-ignition process, reducing the auto-ignition delay time. Analysis of the heat release rate revealed that the first peak of the heat release rate corresponds to the increment of appearance in temperature (induction stage) and the second peak of the heat release rate corresponds to the steady maximum temperature regime (thermal runaway stage). The results found that both induction and thermal runaway stages are affected by turbulence for pure ammonia-air mixing layers, while only the thermal runaway stage is affected by turbulence for ammonia-hydrogen-air mixing layers. The auto-ignition occurs along the most reactive mixture fraction with lower scalar dissipation rate, being further reduced by elevated pressure and hydrogen addition. Three radicals (NH2, OH, HNO) distinguish the entire auto-ignition process very well for all cases.

Two-phase developing laminar mixing layer at supercritical pressures

Numerical analysis of a shear layer between a cool liquid n-decane hydrocarbon and a hot oxygen gas at supercritical pressures shows that a well-defined phase equilibrium can be established. Variable properties are considered with the product ρμ in the gas phase showing a nearly constant result within the laminar flow region with no instabilities. Sufficiently thick diffusion layers form around the liquid-gas interface to support the case of continuum theory and phase equilibrium. While molecules are exchanged for both species at all pressures, net mass flux across the interface shifts as pressure is increased. Net vaporization occurs for low pressures while net condensation occurs at higher pressures. For a mixture of n-decane and oxygen, the transition occurs around 50 bar. The equilibrium values at the interface quickly reach their downstream asymptotes. For all cases, profiles of diffusing-advecting quantities collapse to a similar solution (i.e., function of one independent variable). Validity of the boundary layer approximation and similarity are shown in both phases for Reynolds numbers greater than 239 at 150 bar. Results for other pressures are also taken at high Reynolds numbers. Thereby, the validity of the boundary layer approximation and similarity are expected. However, at very high pressures, the similar one-dimensional profiles vary for different problem constraints.

Cluster-based network model

Abstract

Self-similar solution of a supercritical two-phase laminar mixing layer

Previous works for a liquid suddenly contacting a gas at a supercritical pressure show the coexistence of both phases and the generation of diffusion layers on both sides of the liquid-gas interface due to local thermodynamic phase equilibrium. A related numerical study of a laminar mixing layer between the liquid and gas streams in the near field of the splitter plate suggests that mass, momentum and thermal diffusion layers evolve in a self-similar manner at very high pressures. In this paper, the high-pressure, two-phase, laminar mixing-layer equations are recast in terms of a similarity variable. A liquid hydrocarbon and gaseous oxygen are considered. Freestream conditions and proper matching conditions at the liquid-gas interface are applied. To solve the system of equations, a real-fluid thermodynamic model based on the Soave-Redlich-Kwong equation of state is selected. A comparison with results obtained by directly solving the laminar mixing-layer equations shows the validity of the similarity approach applied to non-ideal two-phase flows. Even when the gas is hotter than the liquid, net condensation can occur at high pressures while heat conducts into the liquid. Finally, a generalized correlation is proposed to represent the evolution of the mixing layer thickness for different problem configurations.

Nonlinear evolution and acoustic radiation of coherent structures in subsonic turbulent free shear layers

Large-scale coherent structures are present in compressible free shear flows, where they are known to be a main source of aerodynamic noise. Previous studies showed that these structures may be treated as instability waves or wavepackets supported by the underlying turbulent mean flow. By adopting this viewpoint in the framework of triple decomposition of the instantaneous flow into the mean field, coherent motion and small-scale turbulence, a strongly nonlinear dynamical model was constructed to describe the formation and development of coherent structures in incompressible turbulent free shear layers (Wu & Zhuang, J. Fluid Mech., vol. 787, 2016, pp. 396–439). That model is now extended to compressible flows, for which the coherent structures are extracted through a density-weighted (Favre) phase average. The nonlinear non-equilibrium critical-layer theory for instability waves in a laminar compressible mixing layer is adapted to analyse coherent structures in its turbulent counterpart. The strong non-parallelism associated with the fast spreading of the turbulent mean flow is taken into account and found to be significant. The model also accounts for the effect of fine-scale turbulence on coherent structures via a gradient type of closure model which now allows for a phase lag between the phase-averaged small-scale Reynolds stresses and the strain rates of coherent structures. The analysis results in an evolution system comprising of an amplitude equation, the critical-layer temperature and vorticity equations along with the appropriate initial and boundary conditions. The physical processes of acoustic radiation from the coherent structures are described by examining the far-field asymptote of the hydrodynamic fluctuations. We demonstrate that the nonlinearly generated slowly breathing mean-flow distortion radiates low-frequency sound waves. The true physical sources are identified. Equivalent sources in a Lighthill type of acoustic analogy context also arise, but they cannot be fully determined before the acoustic field is calculated, in which sense the radiated sound waves act back on the source. The numerical solutions to the evolution system show that coherent structures attenuate nonlinearly and their vorticity field rolls up to form the characteristic rollers. A study is also made of coherent structures represented by modulated wavetrains consisting of sideband modes, in which case nonlinear interactions generate components with frequencies that are combinations of those of the dominant modes. These components, especially the difference-frequency one, acquire significant amplitudes. Finally, the directivity and spectrum of the emitted acoustic field are calculated for both cases where the coherent structures consist of discrete, and a continuum of, sideband modes.

Vorticity-production mechanisms in shock/mixing-layer interaction problems

In this study, we investigate analytically the importance of different vorticity-production mechanisms contributing to the shock-induced vorticity caused by the interaction of a steady oblique shock wave with a steady, planar, supersonic, laminar mixing layer. The inviscid analysis is performed under the condition of a supersonic post-shock flow, which guarantees that the shock refraction remains regular. Special attention is paid to the vorticity production induced by a change in shock strength along the shock. Our analysis subdivides the total vorticity production into its contributions due to bulk or volumetric compression, pre-shock density gradients and variable shock strength. The latter is the only contribution dependent on the shock-wave curvature. The magnitudes of these contributions are analysed for two limiting cases, i.e., the interaction of an oblique shock wave with a constant-density shear layer and the interaction with a constant-velocity mixing layer with density gradients only. Possible implications for shock/mixing-layer interactions occurring in scramjet combustors are briefly discussed.

On streamwise vortices in Large Eddy Simulations of initially laminar plane mixing layers

This paper details the influence of the nature of imposed inflow fluctuations on Large Eddy Simulations of a spatially developing turbulent mixing layer originating from laminar boundary layers. A simulation with imposed white-noise random fluctuations, commonly used in numerical simulations, produces mean-flow statistics that agree well with reference experimental data. Whilst flow visualisation images show evidence for streamwise vorticity in this simulation, quantitative statistics do not reveal the presence of statistically stationary streamwise vortices. A further simulation that uses physically-correlated inflow fluctuations also produces good mean-flow statistical agreement with reference data. From secondary shear stress contours it can be inferred that this simulation does, however, predict the presence of statistically stationary streamwise vortices. The properties of the streamwise vortices are in good agreement with experimental data. The data presented here indicate that, even for initially laminar conditions, plane mixing layer simulations require accurate physically correlated inflow conditions in order to reproduce the flow features found experimentally.

Weak-Shock Interactions with Transonic Laminar Mixing Layers of Fuels for High-Speed Propulsion

This paper extends to transonic mixing layers an analysis of Lighthill (“Reflection at a Laminar Boundary Layer of a Weak Steady Disturbance to a Supersonic Stream, Neglecting Viscosity and Heat Conduction,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 54, No. 3, 1950, pp. 303–325.) on the interaction between weak shocks and laminar boundary layers. As in that work, the analysis is carried out under linear-inviscid assumptions for the perturbation field, with streamwise changes of the base flow neglected, as is appropriate given the slenderness of the mixing-layer flow. The steady-disturbance profile is determined by taking a Fourier transform along the longitudinal coordinate. Closed-form analytical functions for the pressure field are derived in the small- and large-wave-number limits, and vorticity disturbances are obtained as functions of the pressure perturbations. The analysis is particularized to ethylene–air and hydrogen–air mixing layers, for which the dynamics are of current interest for hypersonic propulsion. The results provide, in particular, the effective distance of upstream influence of the pressure perturbation in the subsonic stream. The resulting value, which scales with the thickness of the subsonic layer, is much smaller than the upstream influence distances encountered in boundary layers. This study may serve as a basis to understand shock-induced autoignition and flameholding phenomena in simplified versions of non-premixed supersonic-combustion problems.

A priori evaluation of subgrid-scale combustion models for diesel engine applications

Abstract Large Eddy Simulation (LES) is being increasingly used for turbulent reacting flows in diesel engines. The accuracy of LES depends strongly on the accuracy of the subgrid-scale models, which are employed. In this study, two-dimensional DNS of autoigniting turbulent mixing layers are performed at temperature and pressure conditions similar to those observed in diesel engines. The DNS results are used to evaluate the performance of two common subgrid-scale combustion models that are employed in diesel combustion modeling – the perfectly stirred reactor (PSR) model and the unsteady flamelet progress variable (UFPV) model. It is shown that the effect of turbulence on the reaction zone is not felt during the early ignition stage, and in this stage, the PSR model performance is superior to that of the UFPV model. For a laminar mixing layer, which evolves under the influence of turbulence into a turbulent mixing layer, the PSR model performance deteriorates drastically with increasing time, and the UFPV model is shown to be a more suitable subgrid-scale model. The choice of the subgrid-scale combustion model is also shown to strongly depend on the filter size, i.e. the LES grid size. For filter sizes smaller than the mixing layer thickness, the PSR model performs reasonably well whereas the UFPV model outperforms the PSR model for larger filter sizes.

Dynamics of thermal ignition of spray flames in mixing layers

AbstractConditions are identified under which analyses of laminar mixing layers can shed light on aspects of turbulent spray combustion. With this in mind, laminar spray-combustion models are formulated for both non-premixed and partially premixed systems. The laminar mixing layer separating a hot-air stream from a monodisperse spray carried by either an inert gas or air is investigated numerically and analytically in an effort to increase understanding of the ignition process leading to stabilization of high-speed spray combustion. The problem is formulated in an Eulerian framework, with the conservation equations written in the boundary-layer approximation and with a one-step Arrhenius model adopted for the chemistry description. The numerical integrations unveil two different types of ignition behaviour depending on the fuel availability in the reaction kernel, which in turn depends on the rates of droplet vaporization and fuel-vapour diffusion. When sufficient fuel is available near the hot boundary, as occurs when the thermochemical properties of heptane are employed for the fuel in the integrations, combustion is established through a precipitous temperature increase at a well-defined thermal-runaway location, a phenomenon that is amenable to a theoretical analysis based on activation-energy asymptotics, presented here, following earlier ideas developed in describing unsteady gaseous ignition in mixing layers. By way of contrast, when the amount of fuel vapour reaching the hot boundary is small, as is observed in the computations employing the thermochemical properties of methanol, the incipient chemical reaction gives rise to a slowly developing lean deflagration that consumes the available fuel as it propagates across the mixing layer towards the spray. The flame structure that develops downstream from the ignition point depends on the fuel considered and also on the spray carrier gas, with fuel sprays carried by air displaying either a lean deflagration bounding a region of distributed reaction or a distinct double-flame structure with a rich premixed flame on the spray side and a diffusion flame on the air side. Results are calculated for the distributions of mixture fraction and scalar dissipation rate across the mixing layer that reveal complexities that serve to identify differences between spray-flamelet and gaseous-flamelet problems.

Relaminarization in supersonic microjets at low Reynolds numbers

Results of measuring the length of the supersonic portion of the air jets that flow out of axisymmetric sonic nozzles 10.4 μm-1 mm in diameter are presented. The measurements are carried out in a range of degree of jet noncalculation of 1–30 and in a wide Reynolds number range, including the laminar and turbulent flow modes. It is shown that the Reynolds number calculated from the nozzle diameter and the outlet parameters of gas is the parameter that governs jet flow. It is found that, for a laminar jet mixing layer, the length of the supersonic portion sharply increases. When the jet mixing layer becomes turbulent, the length of the supersonic portion decreases. The effect of increasing the length of the supersonic portion after its decrease due to the turbulization of flow in a jet and a growth in the Reynolds number is first discovered.

A canonical model for stratified flow in estuaries and rivers

We present both fully resolved direct numerical simulation and large eddy simulation results for turbulent stratified flow in an open channel with periodic boundaries in the stream-wise direction and no-slip vertical sidewalls in the span-wise direction. A uniform heat source term is applied in the top 20% of the domain, approximating the solar heat flux into a river system. After each time step the total scalar flux input into the domain is uniformly removed allowing a fully developed flow field to be evolved and statistics collected. This approach allows fully developed stratified flow to be simulated with a density profile which includes a lower non-stratified region, steep thermocline and an upper laminar mixed layer region. The Reynolds number for the flows is in the range 5400-7300 and the bulk Richardson number in the range 0-0.4. References R. P. Garg, J. H. Ferziger, S. G. Monismith, and J. R. Koseff. Stably stratified turbulent channel flows. I. Stratification regimes and turbulence suppression mechanism. Phys. Fluids , 12(10):2569--2594, 2000. doi:10.1063/1.1288608 . S. Komori, H. Ueda, F. Ogino, and T. Mizushina. Turbulence structure in stably stratified open-channel flow. J. Fluid Mech. , 130:13--26, 1983. doi:10.1017/S0022112083000944 . Lei Wang and Xi-Yun Lu. Large eddy simulation of stably stratified turbulent open channel flows with low- to high-Prandtl number. Int. J. Heat and Mass Transfer , 48(10):1883 -- 1897, 2005. doi:10.1016/j.ijheatmasstransfer.2004.12.017 . J. R. Taylor, S. Sarkar, and V. Armenio. Large eddy simulation of stably stratified open channel flow. Phys. Fluids , 17(11):116602, 2005. doi:10.1063/1.2130747 . J. S. Turner. A note on wind mixing at the seasonal thermocline. Deep-Sea Res. , 16(Suppl.):297--300, 1969. P. E. Holloway. A criterion for thermal stratification in a wind-mixed System. J. Phys. Oceanogr. , 10:861--869, 1980. 2.0.CO;2>doi:10.1175/1520-0485(1980)010 2.0.CO;2 J. H. Simpson and J. R. Hunter. Fronts in the Irish sea. Nature , 250:404--406, 1974. doi:10.1038/250404a0 . M. Bormans and I. T. Webster. A mixing criterion for turbid rivers. Environmental Modelling and Software with Environment Data News , 12(4):329--333, 1997. doi:10.1016/S1364-8152(97)00032-7 . M. Germano, U. Piomelli, P. Moin, and W. H. Cabot. A dynamic subgrid-scale stress model. Phys. Fluids A , 3(7):1760--1765, 1991. doi:10.1063/1.857955 . S. B. Pope. Turbulent Flows . Cambridge University Press, 2000. S. W. Armfield and R. Street. Fractional step methods for the Navier--Stokes equations on non-staggered grids. ANZIAM Journal , 42:C134--C156, 2000. http://journal.austms.org.au/ojs/index.php/ANZIAMJ/article/view/593 . S. W. Armfield, S. E. Norris, P. Morgan, and R. Street. A parallel non-staggered Navier--Stokes solver implemented on a workstation cluster. In S. Armfield, P. Morgan, and K. Srinvas, editors, Proceedings of the Second International Conference on Computational Fluid Dynamics , pages 30--45, Sydney, July 15-19 2002. J. H. Ferziger and M. Peric. Computational Methods for Fluid Dynamics . Springer, third edition, 2002.

Direct numerical simulation of autoigniting mixing layers in MILD combustion

MILD combustion is a new combustion technology which promises an enhanced efficiency and reduced emission of pollutants. It is characterized by a high degree of preheating and dilution of the reactants. Since the temperature of the reactants is higher than that of autoignition, a complex interplay between turbulent mixing, molecular transport and chemical kinetics occurs. In order to reveal the fundamental reaction structures of MILD combustion, the process of a cold methane–hydrogen fuel jet issuing in a hot diluted coflow and the subsequent ignition process is modeled by direct numerical simulation of autoigniting mixing layers using detailed chemistry and transport models. Detailed analysis of one-dimensional laminar mixing layers shows that the ignition process is dominated by hydrogen chemistry and that non-unity Lewis number effects are of the utmost importance for modeling of autoignition. High scalar dissipation rates in mixing layers delay the autoignition time, but have a negligible effect on the chemical pathway followed during ignition. This supports the idea of using homogeneous reactor simulations for the construction of chemistry look-up tables. Simulations of two-dimensional turbulent mixing layers confirm the effect of scalar dissipation rate on autoignition time. The turbulence–chemistry interaction is limited under the investigated conditions, because the reaction layer lies at the edge of the mixing layer due to the very small value of the stoichiometric mixture fraction. When the oxidizer stream is more diluted, the autoignition time is delayed, allowing the developing turbulence to interact more with the ignition chemistry. The results of these direct numerical simulations employing a detailed reaction mechanism are expected to be used for the development of tabulated chemistry models and sub-grid scale models for large-eddy simulations of MILD combustion.

Homotopy simulation of axisymmetric laminar mixed convection nanofluid boundary layer flow over a vertical cylinder

In this paper, the semi-analytical/numerical technique known as the homotopy analysis method (HAM) is employed to derive solutions for the laminar axisymmetric mixed convection boundary-layer nanofluid flow past a vertical cylinder. The similarity solutions are employed to transform the parabolic partial differential conservation equations into system of nonlinear, coupled ordinary differential equations, subject to appropriate boundary conditions. A comparison has been done to verify the obtained results with the purely numerical results of Grosan and Pop (2011) with excellent correlation achieved. The effects of nanoparticle volume fraction, curvature parameter and mixed convection or buoyancy parameter on the dimensionless velocity and temperature distributions, skin friction and wall temperature gradients are illustrated graphically. HAM is found to demonstrate excellent potential for simulating nanofluid dynamics problems. Applications of the study include materials processing and also thermal enhancement of energy systems.

Linear and nonlinear instability waves in spatially developing two-phase mixing layers

Two-phase laminar mixing layers are susceptible to shear-flow and interfacial instabilities, which originate from infinitesimal disturbances. Linear stability theory has successfully described the early stages of instability. In particular, parallel-flow linear analyses have demonstrated the presence of mode competition, where the dominant unstable mode can vary between internal and interfacial modes, depending on the flow parameters. However, the dynamics of two-phase mixing layers can be sensitive to additional factors, such as the spreading of the mean flow. In addition, beyond the early linear stage, the amplitude of the instability waves becomes finite and nonlinear effects become appreciable. As a result, an accurate description of the evolution of the mixing layer must account for nonlinear interactions including the generation of higher harmonics of the instability waves and the modification of the mean flow. These effects are investigated herein using the framework of the nonlinear parabolized stability equations. The formulation includes nonparallel effects, nonlinear modal interactions, a coupled mean flow correction, and finite amplitude deformation of the interface. Mode competition between liquid and interfacial modes is investigated. We demonstrate that nonparallelism and streamwise evolution of the flow can significantly alter the predictions of locally parallel, linear stability analyses. This is followed by a discussion on nonlinear interactions of two- and three-dimensional instability waves. It is shown that nonlinear effects can serve dual purposes. On one hand, they can be a limiting mechanism for the growth of instability waves. On the other hand, they can destabilize high frequency, linearly stable modes, and thus lead to the generation of smaller scale features in the flow.

MHD free convection and mass transfer flow over an infinite vertical porous plate with viscous dissipation

An unsteady, two-dimensional, hydromagnetic, laminar mixed convective boundary layer flow of an incompressible and electrically-conducting fluid along an infinite vertical plate embedded in the porous medium with heat and mass transfer is analyzed, by taking into account the effect of viscous dissipation. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and graphical results for velocity, temperature and concentration profiles within the boundary layer are discussed. The results show that increased cooling (Gr > 0) of the plate and the Eckert number leads to a rise in the velocity profile. Also, an increase in Eckert number leads to an increase in the temperature. Effects of Sc on velocity and concentration are discussed and shown graphically.

The dynamics of nonlinear instability waves in laminar heated and unheated compressible mixing layers

Previous studies have shown that when using instability wave theories to model compressible laminar mixing layers, explicitly accounting for nonlinear processes such as the mean flow correction and modal interactions is necessary in order to properly capture vortex roll-up and pairing phenomena. In this study, we examine the effects of heating when using the nonlinear instability wave formulation on two-dimensional compressible mixing layers. We compare the results of both heated and unheated, supersonic and subsonic laminar mixing layer calculations using both the nonlinear parabolized stability equations (PSE) and Navier–Stokes equations. For all supersonic mixing layers, we find that the nonlinear stability method adequately captures the roll-up process and agrees well with direct calculations. While the same is true for the unheated subsonic mixing layer, in the heated subsonic mixing layer, we find that baroclinic vorticity generation, in addition to nonlinear interactions, plays a significant role in governing the vorticity dynamics. We observe that in the presence of large density stratifications in subsonic flows, approximations made in the streamwise pressure gradient of the PSE formulation can lead to discrepancies in the vortex dynamics. Error estimates for the approximations to the baroclinic term show that discrepancies are directly proportional to the temperature difference and inversely proportional to the Reynolds number.