C. L. Merkle

C. L. Merkle
Purdue University West Lafayette | Purdue · School of Aeronautics and Astronautics

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323
Publications
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Publications

Publications (323)
Article
Full-text available
Large-scale engineering systems, such as propulsive engines, ship structures, and wind farms, feature complex, multi-scale interactions between multiple physical phenomena. Characterizing the operation and performance of such systems requires detailed computational models. Even with advances in modern computational capabilities, however, high-fidel...
Article
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the structure of the governing equations. Least-squares-based minimization is leveraged to guarantee symmetrization and d...
Preprint
Full-text available
A projection-based formulation is presented for non-linear model reduction of problems with extreme scale disparity. The approach allows for the selection of an arbitrary, but complete, set of solution variables while preserving the conservative form of the governing equations. Least-squares-based minimization is leveraged to guarantee symmetrizati...
Article
Full-text available
The impact of chemical reactions on the robustness and accuracy of projection-based reduced-order models (ROMs) of fluid flows is investigated. Both Galerkin and least squares Petrov–Galerkin ROMs are shown to be less robust in reacting flows as compared with nonreacting flows. In particular, reacting flow ROMs show a strong sensitivity to resoluti...
Preprint
Full-text available
The impact of chemical reactions on the robustness and accuracy of projection-based Reduced-Order Models (ROMs) of fluid flows is investigated. Both Galerkin and Least-Squares Petrov Galerkin ROMs are shown to be less robust in reacting flows as compared to non-reacting flows. In particular, reacting flow ROMs show a strong sensitivity to \st{the}...
Article
Full-text available
A multifidelity framework oriented toward efficient modeling of combustion dynamics that integrates a reducedorder model (ROM) for the combustion response into the Euler equations is proposed. The ROM is developed from computational fluid dynamics (CFD) simulations of a combusting flow that is periodically forced at the boundaries of a reduced doma...
Article
The current study investigates the use of solution filtering and artificial dissipation as stabilization methods for time-accurate computations, notably focusing on how the decoupling of dissipation from integration impacts simulation error. Rewriting solution filtering in an effective artificial-dissipation form explicitly reveals the issue of tem...
Article
A method for obtaining combustion response functions from experiments or detailed computational fluid dynamic (CFD) analyses is described and used in a quasi one dimensional approach for the study of longitudinal combustion instability. The goal is to reproduce the behavior of several geometrical configurations of a single element combustor, once a...
Article
Combustion instability phenomenon arises from the coupling between heat release and acoustics. Several studies have been carried out in the past years with very different tools, from analytical studies to high fidelity simulations, like large eddy simulations (LES) or hybrid RANS-LES simulations. Despite the promising results, the computational eff...
Article
Full-text available
The unsteady gas dynamic field in a closed combustor is determined by the nonlinear interactions between chamber acoustics, hydrodynamics, and turbulent combustion that can energize these modes. These interactions are studied in detail using hybrid RANS/large eddy simulations (RANS = Reynolds Averaged Navier-Stokes) of a non-premixed, high-pressure...
Conference Paper
This study makes a comparison between artificial dissipation and filtering schemes as stabilization techniques for time-accurate fluid dynamics simulations. Specifically, we use von Neumann stability analysis to assess these alternatives in terms of their concurrent ability to maintain solution quality through proper preservation of low frequency c...
Article
Full-text available
A solution procedure for the fully coupled Navier–Stokes and Maxwell equations is described. The approach implements a conservative fluid formulation in which the Lorentz body force and Ohmic heating terms are recast as convective terms. This removes explicit sources from the fluid equations, which have previously introduced severe stiffness and de...
Conference Paper
The paper provides a fundamental overview of turbulence and turbulent combustion models for large eddy simulations of reacting flowfields. The focus is on examining model assumptions in the context of aerospace propulsion applications, which typically involve high-speed flows, high pressures, compressible phenomena such as shocks, ignition dynamics...
Article
The coupled system of the Navier–Stokes and Maxwell equations are recast into a strong conservative form, which allows the fluid coupling to the Maxwell system to be written in terms of flux divergence rather than explicit source terms. This effectively removes source terms from the Navier–Stokes equations, although retaining an exact coupling to t...
Conference Paper
Full-text available
This paper details the development a unified hyperbolic model for fluid dynamics coupled to electromagnetics. The advantage to the model presented is that it includes the accurate physical behavior for several plasmas of aerospace interest; it can effectively capture both magnetohydrodynamic and electrohydrodynamic limits of the plasma, in addition...
Article
Galerkin's method is applied to reduce a high-order PDE system to a lower-order ODE system using POD eigen-basis to develop a reduced order model (ROM) describing the combustion response to acoustic excitations. A one-dimensional reaction-advection scalar equation is used as a representative equation to investigate the overall approach. Both linear...
Conference Paper
An investigation of the instability mechanism present in a laboratory rocket combustor is performed using computational fluid dynamics (CFD) simulations. Three cases are considered which show different levels of instability experimentally. Computations reveal three main aspects to the instability mechanism, the timing of the pressure pulses, increa...
Conference Paper
Full-text available
The AUSM family of schemes has been successful in simulating fluid dynamic and magnetohydrodynamic flows. In this paper, we extend the AUSM method to solve the Navier-Stokes equations coupled to the full Maxwell equations. This approach permits the inclusion of electromagnetic wave propagation, displacement current and charge separation effects. Va...
Article
Three-dimensional simulations of combustion instability can provide extremely valuable insight into the problem physics, but they represent an enormous investment in time and, thus, may preclude parametric studies that are practical with two-dimensional simulations. Three numerical simulations of an unstable laboratory rocket combustor were perform...
Article
The interface area increase produced by large-amplitude wave refraction through an interface that separates fluids with different densities can have important physiochemical consequences, such as a fuel consumption rate increase in the case of a shock-flame interaction. Using the results of numerical simulations along with a scaling analysis, a uni...
Conference Paper
Full-text available
The effects of electromagnetic wave propagation, charge separation and higher-frequency effects can play a significant role in a plasma. Although the magnetohydrodynamic (MHD) model is the incumbent approach for describing plasmas of engineering interest, this model is incapable of resolving these features. In this paper, we introduce a split-flux...
Article
Unsteady Navier-Stokes simulations are used to study the static and dynamic discharge characteristics of shear-thinning fluids passing through plain-orifice atomizers fed by a crossflow. The crossflow velocity is varied to assess implications of feeding fluid in a multi-element injector fed from a common manifold. Large and distinct horseshoe vorti...
Article
Measured and computed mean and fluctuating radiation intensities are reported for a subsonic exhaust plume and used to characterize the influence of turbulent fluctuations on mean radiation properties. Narrowband radiation intensity measurements were acquired using an infrared camera fitted with a narrowband filter (4.34 +/- 0.1 mu m). Unsteady thr...
Conference Paper
Combustion behavior of gas phase hypergolic propellant Mono-methyl Hydrazine (MMH) with Red Fuming Nitric Acid (RFNA) as an oxidizer is studied numerically. Simulations are carried out to characterize the involved fundamental processes as well as to study an experimental arrangement of impinging element injectors. The operating pressure is varied r...
Conference Paper
Combustion instability arises from the coupling between unsteady combustion and acoustic modes in a combustion chamber. A study comprising concurrent experiment and LES simulation of a single element rocket combustor was conducted. The goal was to evaluate the a priori predictive ability of the computational model with regards to self-excited combu...
Conference Paper
Full-text available
A solution procedure for the Navier-Stokes equations coupled with the full Maxwell equations is described. The approach implements a strongly conservative fluid formulation in which the Lorentz force and Ohmic heating terms are recast as convective terms. This removes explicit sources from the Navier-Stokes equations, which have previously introduc...
Article
The effects of chamber diameter and wall cooling on the flow characteristics of unielement combustors are studied computationally by means of unsteady simulations. The combustor of interest burns a combination of oxygen and hydrogen in a confined chamber at high pressures. The reactants are injected through coaxial channels of diameter considerably...
Article
Computational analyses of the effects of oxidiser injector length on combustion instability in a choked high pressure combustor are described. The configuration is based on companion experiments using gaseous methane and decomposed hydrogen peroxide as reactants. The generic behaviour of one injector length is first investigated in detail to invest...
Article
Improved understanding of radiation emissions from exhaust plumes are needed for safety applications. Relevant literature has focused on characterizing mean radiation properties of exhaust plumes. Turbulent radiation properties reported for flames have been used to provide insight into scalar distribution within the flows, improve understanding of...
Article
Major obstacles in overcoming combustion instability include the absence of a mechanistic and a priori prediction capability, and the difficulty in studying instability in the laboratory due to the perceived need for testing at the full-scale pressure and geometry to ensure that important processes are maintained. A hierarchal approach toward combu...
Article
A series of axisymmetric Navier-Stokes simulations were performed to study the mean and unsteady characteristics of gel propellant orifice flows at conditions representative of rocket injectors. The rheology of the gel was simulated assuming a shear-thinning fluid behaving in accordance with the Carreau-Yasuda model. The effects of Reynolds number...
Conference Paper
Numerical simulations of gaseous methane and decomposed hydrogen peroxide in a laboratory rocket combustor were performed in order to determine how to best calculate the Rayleigh index. Calculations using four levels of spatial refinement show the level of refinement necessary to identify the regions of ampliflcation and damping is significantly co...
Conference Paper
The cap-shock pattern from both experiments and simulations are presented. By axisymmetrical calculations, the cap-shock pattern at a nozzle pressure ratio = 20 is simulated as exhibited by an experimental visualization using hydroxyl tagging velocimetry. It is con- firmed that the steady shock structures are driven by an Mach reflection with an in...
Conference Paper
Detailed computational simulations are used to model the stability characteristics in a high pressure combustor. The configuration is based on companion experiment in which an axisymmetric dump combustor was fed by separate fuel and oxidizer streams. In the present paper, the effects of different modeling parameters on the predictions of instabilit...
Conference Paper
Computational and experimental efforts to investigate the injector flow characteristics for gel propellants are presented. Two different types of injectors are considered: a tapered tube and plain-orifice type. Paran/Thixatrol and Water/HPC Gels are used as working fluids and are modeled as a shear-thinning fluid. Flows are characterized by a time-...
Article
The main contributing effects leading to premixed laminar flame fuel consumption rate changes following variable strength shock or expansion wave passage were studied analytically and numerically. The effects were separated into two groups: gas compression, or one-dimensional effects, and flame front distortion, or two-dimensional effects. The firs...
Article
Cavitating flow simulation is of practical importance for many engineering systems, such as marine propellers, pump impellers, nozzles, injectors, torpedoes, etc. The present work is to test a new cavitation model. The governing equation is the Navier-Stokes equation based on an homogeneous mixture model. The solver employs an implicit precondition...
Article
Full-text available
Time-averaged predictions from unsteady solutions of the two-dimensional Navier–Stokes equations are contrasted with Reynolds-averaged results for a reacting flow problem in a high pressure combustor. The goal is to determine whether the two-dimensional unsteady approximation can be useful as an engineering analysis in problems for which time-avera...
Article
A numerical procedure that applies to both the magnetic diffusion and wave propagation regimes of a general plasma/electromagnetic system is presented. The method solves the full Maxwell equations, with or without displacement current, in combination with the Navier Stokes equations. The combined system is placed in a fully coupled conservation for...
Conference Paper
A method for enhancing the robustness of implicit computational algorithms without adversely impacting their efficiency is investigated. The method requires control over two key issues: obtaining a reliable estimate of the magnitude of the solution change and defining a realistic limit for its allowable variation. The magnitude of the solution chan...
Conference Paper
An efficient reconstruction procedure on adaptive Cartesian mesh for evaluating the constitutive properties of a complex fluid from general or specialized thermodynamic databases is presented. Reconstruction is accomplished on a triangular subdivision of the 2D Cartesian mesh covering thermodynamic plane of interest that ensures function continuity...
Article
Source terms often appear in various fluid dynamic problems. These source terms not only have an important impact on the physics of the flow but they can also impact the reliability of CFD algorithms. A general recommendation is to treat negative values (sinks) implicitly, while positive values (sources) should be evaluated explicitly. Although thi...
Article
Vortex sheet production by shocks and expansion waves refracting at a density discontinuity was examined and compared using an analytical solution and numerical simulations. The analytical solution showed that with a small exception, vortex sheet strength is generally stronger in fast/slow shock refractions. In contrast, expansion waves generated a...
Article
Detailed computational simulations are used to compare the effect of backstep height on the stability characteristics of an axisymmetric dump combustor fed by separate fuel mid oxidizer streams. Companion experiments demonstrate a dramatic increase in the amplitude of pressure oscillations for the smaller backstep due to combustion instability. The...
Article
The initial transient leading to stationary conditions in unsteady combustion simulations is investigated by considering flow establishment in model combustors. Quiescent initial conditions with the chamber initially filled with an inert, hot gas are used to provide physically realistic starting conditions and robust, reliable combustion initiation...
Conference Paper
The flow around an isolated fan blade is analyzed. Three speed lines were computed from choke to stall and beyond with both a clean inlet and with radial distortion. An in-house implicit second-order solver with upwind discretization of fluxes and dual-time stepping for unsteady calculations was used. The turbulent viscosity was computed using a κ-...
Conference Paper
Previous unsteady computational studies have demonstrated combustion instability for a single-element rocket engine, matching experimental instability trends. The current paper seeks to better understand the mechanisms of combustion instability by demonstrating and evaluating possible diagnostics using computational data. Specifically, the followin...
Conference Paper
Numerical simulations of a transient flow of helium injected into an established background flow of nitrogen were carried out to identify the dominant features of the transient mixing process between these two dissimilar gases. The geometry of interest is composed of two helium slots on either side of a central nitrogen channel feeding into a ‘two-...
Conference Paper
The flow analysis around blades of a transonic fan is presented for both clean and radially distorted inlets. Computations are shown for four-blade passages that are accomplished with a second order accurate code using a k-ω turbulence model. The mass flow rate along a speed line is controlled by varying a choked nozzle downstream of the fan. The r...
Article
The knowledge of the flow behavior inside asymmetrically heated channels is of great importance to improve design and performance of regeneratively cooled rocket engines. The modeling of the coolant flow is a challenging task because of its particular features, such as the high wall temperature gradient, the high Reynolds number, the three-dimensio...
Conference Paper
A series of axisymmetric parametric investigations are conducted to assess the overall flowfield and discharge coefficient of power-law gelled fluids flowing within plain orifice atomizers. Steady calculations have been employed to assess discharge characteristics for various length-to-diameter ratios, inlet lip roundness and chamfer depths/sizes....
Conference Paper
The static tests of Purdue experimental shrouded plug nozzle which is a sub-scale model of the Gulfstream concept without the bypass exhaust stream is the focus of current computational and experimental effort. The static tests brought to light unsteady characteristics related shock/shock and shock/boundary layer interactions. Through a series of s...
Article
A method for enhancing the reliability of implicit computational algorithms and decreasing their sensitivity to initial conditions without adversely impacting their efficiency is investigated. Efficient convergence is maintained by specifying a large global Courant (CFL) number while reliability is improved by limiting the local CFL number such tha...
Conference Paper
Unsteady simulations of the mixing and combustion of oxygen and hydrogen in a confined chamber at high pressures are presented. The reactants are injected through coaxial channels of diameter considerably smaller than the chamber resulting in a large recirculation region between the injector face and the outer wall. The chamber is terminated by a c...
Chapter
Full-text available
Preconditioned time-marching CFD methods have become established as an accurate and efficient framework for all Mach numbers [1]. However, unsteady solution efficiency and accuracy suffer when the combination of low Mach numbers and high Strouhal numbers is encountered, especially in the context of high-fidelity turbulent and/or acoustics problems...
Conference Paper
The initial transient leading to stationary conditions in unsteady combustion simulations is investigated by considering flow establishment in model combustors. Quiescent initial conditions with the chamber initially filled with an inert, hot gas are used to provide physically realistic starting conditions and robust, reliable combustion initiation...
Conference Paper
The aerodynamic instability known as rotating stall of an isolated fan is considered. Steady and unsteady 3-D simulations were carried out for flows around a high-speed transonic aero-engine fan. Several speed characteristic lines of the performance map were analyzed ranging from almost subsonic to transonic flow conditions with strong shocks. Unst...
Article
The development of a velocity-based mechanistic combustion response model and its application to liquid rocket engines is described. A time lag model is applied to capture the periodic process of vortex shedding that is hypothesized to be the primary mechanism of combustion instability in the studied combustor configuration. A linearized Euler equa...
Article
A computational fluid dynamics analysis of acoustic modes and instabilities in an experimental longitudinal test chamber is presented. The experimental configuration is a uni-element recessed injector post combined with a variable-length combustion chamber. The computations employ the nonlinear Euler equations with mass and heat addition in the inj...
Article
Full-text available
Computational fluid dynamics (CFD) has the potential to improve the historical rocket injector design process by evaluating the sensitivity of performance and injector-driven thermal environments to the details of the injector geometry and key operational parameters. Methodical verification and validation efforts on a range of coaxial injector elem...
Conference Paper
Numerical simulations of a start-up helium flow injected into an established background flow of nitrogen are carried out to identify the dominant features of the transient mixing process between these two dissimilar gases. Simulations were accomplished on both two- and three-dimensional grids and are compared with companion experiments of mixing in...
Conference Paper
Detailed computational simulations are used to compare the stability characteristics of a single-element longitudinal rocket combustor for two different combustor configurations. Companion experiments demonstrate that a slight decrease in the combustor diameter causes a dramatic increase in the amplitude of combustor oscillations. The present simul...
Article
The transient injection and mixing between nitrogen and helium in a confined chamber at atmospheric pressure is studied experimentally. The 2D injector and mixing chamber contained a middle injection slot for nitrogen flanked by a pair of outer slots for helium. Experiments were conducted by introducing the helium streams into a previously establis...
Article
Internal wave reverberation processes in multiple-tube, pulsed detonation engines are considered. The study is based on a two-dimensional analysis of dual- and triple-detonation tubes exhausting through a common nozzle. Computations are first performed for a series of dual-tube configurations in which the intertube geometry is varied parametrically...
Conference Paper
A general numerical method is developed with the capability to predict the transient thermal boundary layer response under various flow and thermal conditions. The transient thermal boundary layer variation due to a moving compressible turbulent fluid of varying temperature was numerically studied on a 2-D semi-infinite flat plate. The Reynolds-ave...
Conference Paper
The pulsed inductive thruster has shown promise as a high power, high specific impulse electric propulsion engine. As ingenious as the existing pulsed inductive thruster designs are they still contain drawbacks, most notably the complicated drive coil geometry and propellant injection system. Through computational methods, it is the goal of this re...
Conference Paper
A Wave Rotor Combustion Rig (WRCR) is under development by a team including Purdue University, Rolls-Royce (Liberty Works©) and Indiana University-Purdue University. Theoretically, the wave rotor configuration provides improved efficiency for gas turbine machines via a nearly constant volume combustion process that permits a significant pressure ri...
Conference Paper
The effect of channel rotation and hot jet igniter placement on the overall combustion rate has been investigated for a wave rotor combustor under experimental low-pressure test conditions using two-dimensional numerical simulations of combustion and gas dynamics. The ignition was provided by a jet of hot gas. Unlike with quiescent hot-wall ignitio...
Conference Paper
A numerical procedure that applies to both the magnetic diffusion (MHD) and wave propagation regimes of a general plasma/electromagnetic system is presented. The method solves the full Maxwell equations, with or without displacement current, in combination with the Navier-Stokes equations. The combined system is placed in fully coupled conservation...