A Morphing Continuum Approach to Supersonic Flow Over a Compression Ramp

Cheikh, Mohamad Ibrahim; Chen, James M.

doi:10.2514/6.2017-3460

Cited by 4 publications

(7 citation statements)

References 32 publications

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“…Since these particles mimic the behavior of eddies, this expression can be used to approximate turbulent kinetic energy. In the simulations of turbulence before and after a shock, this term will carry the information about eddy energy transfer [16,22].…”

Section: Fig 1 Evolution Of General Structure With Associated Sub-scmentioning

confidence: 99%

Morphing Continuum Simulation of Transonic Flow over Axisymmetric Hill

2018

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Finite volume simulations of turbulent boundary layer flow over an axisymmetric hill are performed for Re H = 6500 using Morphing Continuum Theory (MCT), and compared with DNS data from Castagna et. al. and experimental data obtained by Simpson. The inlet profile was specified by inputting values from the profile specified by Castagna et. al. Rootmean-square velocity fluctuations are inputted using the new variable of gyration from MCT. Additional terms introduced by MCT lead to a new formulation of the Q-criterion, which allows for the visualization of three-dimensional turbulent structures including a hairpin vortices. Streamline plots of the separation bubble show a more confined bubble than Castagna et. al., but agree well on the separation and reconnection points. The surface pressure coefficient matches Simpson much more closely than Castagna et. al. MCT data was obtained on a 6.72 × 10 6 cell mesh containing a smaller number of cells by an order of magnitude than that of the DNS mesh of 5.4 × 10 7 by Castagna et. al. The effects of the particle on the larger structures are inferred from the variation in the new variable of gyration.

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Section: Fig 1 Evolution Of General Structure With Associated Sub-scmentioning

confidence: 99%

Morphing Continuum Simulation of Transonic Flow over Axisymmetric Hill

2018

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“…III. NUMERICAL METHODS Equations 21 -24 can be directly discretized and solved with the classical finite difference method [42]; however, in order to adopt modern numerical schemes, such as finite volume method [48,61], spectral difference method [43,62,63], spectral volume method [64,65] and others [66], the governing equations should be cast into the conservation forms. Chen et.…”

Section: B Constitutive Equationsmentioning

confidence: 99%

“…Several researchers have started focusing on numerical methods for MCT [42][43][44][45]67]. More specifically, three different numerical schemes are introduced in the past few years: (1) finite difference method with second order temporal and spatial accuracy for incompressible flows [42]; (2) finite volume method with second order shock preserving scheme for compressible flows [48]; and (3) high order spectral difference method for compressible flows [43]. In this study, the finite volume method with second order shock preserving scheme is used and summarized as follows.…”

Section: B Constitutive Equationsmentioning

confidence: 99%

“…This second order generalized Lax-Friedrich flux was implemented in the NS framework. Cheikh and Chen further demonstrated that this approach also provides a second order accuracy in space for MCT [48]. If the discretized equations are solved in a explicit manner, the unsteady term can be marched with Runge-Kutta method of any order in temporal accuracy.…”

Section: B Constitutive Equationsmentioning

confidence: 99%

“…With the rapid developments on the numerical solvers, a series of studies were published on incompressible and compressible turbulence and their statistical characteristics [46][47][48][49]. Cheikh and Chen validated that MCT is capable of predicting the velocity profile over a compression ramp in a supersonic turbulence [48]. However, MCT is still relatively new to turbulence community.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Morphing continuum theory for turbulence: Theory, computation, and visualization

Chen

2017

Phys. Rev. E

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A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance laws are deduced and presented from the ColemanNoll procedure and Onsager's reciprocal relations. The governing equations are then arranged in conservation form and solved through the finite volume method with a second order Lax-Friedrichs scheme for shock preservation. A numerical example of transonic flow over a three-dimensional bump is presented using MCT and the finite volume method. The comparison shows that MCTbased DNS provides a better prediction than NS-based DNS with less than 10% of the mesh number when compared with experiments. A MCT-based and frame-indifferent Q-criterion is also derived to show the coherent eddy structure of the downstream turbulence in the numerical example. It should be emphasized that unlike the NS-based G-criterion, the MCT-based Q-criterion is objective without the limitation of Galilean-invariance.

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First-order approximation to the Boltzmann–Curtiss equation for flows with local spin

Wonnell

Chen

2019

J Eng Math

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The first-order approximation to the solution of the Boltzmann-Curtiss transport equation is derived. The resulting distribution function treats the rotation or gyration of spherical particles as an independent classical variable, deviating from the quantum mechanical treatment of molecular rotation found in the Wang Chang-Uhlenbeck equation. The Boltzmann-Curtiss equation, therefore, does not treat different rotational motions as separate molecular species. The first-order distribution function yields momentum equations for the translational velocity and gyration that match the form of the governing equations of morphing continuum theory (MCT), a theory derived from the approach of rational continuum thermomechanics. The contribution of the local rotation to the Cauchy stress and the viscous diffusion are found to be proportional to an identical expression based off the relaxation time, number density, and equilibrium temperature of the fluid. When gyration is equated to the macroscopic angular velocity, the kinetic description reduces to the first-order approximation for a classical monatomic gas, and the governing equations match the form of the Navier-Stokes equations. The relaxation time used for this approximation is shown to be more complex due to the additional variable of local rotation. The approach of De Groot and Mazur is invoked to give an initial approximation for the relaxation of the gyration. The incorporation of this relaxation time, and other physical parameters, into the coefficients of the governing equations provides a more in-depth physical treatment of the new terms in the MCT equations, allowing experimenters to

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A Morphing Continuum Approach to Supersonic Flow Over a Compression Ramp

Cited by 4 publications

References 32 publications

Morphing Continuum Simulation of Transonic Flow over Axisymmetric Hill

Morphing Continuum Simulation of Transonic Flow over Axisymmetric Hill

Morphing continuum theory for turbulence: Theory, computation, and visualization

First-order approximation to the Boltzmann–Curtiss equation for flows with local spin

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