Development of an AMR Octree DSMC approach for shock dominated flows

Key strategies used in the development of a scalable, three-dimensional direct simulation Monte Carlo (DSMC) program are described. The code employs an Octree based adaptive mesh refinement (AMR) that gives flexibility in capturing multi-scale physics. It is coupled with a robust cut-cell algorithm to incorporate complex triangulated geometries. With the use of distributed memory systems and Message-Passing-Interface (MPI) for communication, the code is potentially scalable. However, to simulate continuum-like conditions involving multi-scale physics, better scalability that has yet been achieved is desirable. The thesis identifies two main performance bottlenecks in simulating at continuum-like conditions, first, improving the scalability of the code for more than 128 processors by reducing the communication and evenly balancing the computational load, and second, improve the algorithmic performance of the code by eliminating the expensive recursive tree traversal inherent in Octree based mesh structure. In order to resolve the first issue sophisticated graph-partitioners have been used, however, without success. The thesis also explains the special considerations required for embedded geometries in a parallel computational environment. An efficient algorithm is discussed that allows for the checking of particle-surface interaction only if they are close enough to the geometry. The code calculates various surface coefficients and employs the Borgnakke-Larsen continuous relaxation model to simulate inelastic collisions of diatomic molecules. Finally, these strategies and models are validated by simulating hypersonic flows of argon and nitrogen over a hemisphere and double-wedge configuration and the solutions are compared with the results obtained from an older DSMC code known as SMILE

A kinetic approach to studying low-frequency molecular fluctuations in a one-dimensional shock

Low-frequency molecular fluctuations in the translational nonequilibrium zone of one-dimensional strong shock waves are characterised for the first time in a kinetic collisional framework in the Mach number range $2\le M\le 10$. Our analysis draws upon the well-known bimodal nature of the probability density function (PDF) of gas particles in the shock, as opposed to their Maxwellian distribution in the freestream, the latter exhibiting an order of magnitude higher dominant frequencies than the former. Inside the (finite-thickness) shock region, the strong correlation between perturbations in the bimodal PDF and fluctuations in the normal stress suggests introducing a novel two-bin model to describe the reduced-order dynamics of a large number of collision interactions of gas particles. Our model correctly predicts the order-of-magnitude difference in fluctuation frequencies in the shock versus those in the freestream and is consistent with the small-amplitude fluctuations obtained from the highly resolved Direct Simulation Monte Carlo (DSMC) computations of the same configuration. The variation of low-frequency fluctuations with changes in the conditions upstream of the shock revealed that these fluctuations can be described by a Strouhal number, based on the bulk velocity upstream of the shock and the shock-thickness based on the maximum density-gradient inside the shock, that remains practically independent of Mach number in the range examined. Our results are expected to have far-reaching implications for boundary conditions employed in the vicinity of shocks in the framework of flow instability and laminar-turbulent transition studies of flows containing both unsteady and nominally stationary shocks.Comment: 31 pages, 14 figures, and 2 supplementary movie

Analytical prediction of low-frequency fluctuations inside a one-dimensional shock

Linear instability of high-speed boundary layers is routinely examined assuming quiescent edge conditions, without reference to the internal structure of shocks or to instabilities potentially generated in them. Our recent work has shown that the kinetically modeled internal nonequilibrium zone of straight shocks away from solid boundaries exhibits low-frequency molecular fluctuations. The presence of the dominant low frequencies observed using the Direct Simulation Monte Carlo (DSMC) method has been explained as a consequence of the well-known bimodal probability density function (PDF) of the energy of particles inside a shock. Here, PDFs of particle energies are derived in the upstream and downstream equilibrium regions, as well as inside shocks, and it is shown for the first time that they have the form of the non-central chi-squared (NCCS) distributions. A linear correlation is proposed to relate the change in the shape of the analytical PDFs as a function of Mach number, within the range $3 \le M \le 10$, with the DSMC-derived average characteristic low-frequency of shocks, as computed in our earlier work. At a given Mach number $M=7.2$, varying the input translational temperature in the range $89 \le T_{tr,1}/(K) \le 1420$, it is shown that the variation in DSMC-derived low-frequencies is correlated with the change in most-probable-speed inside shocks at the location of maximum bulk velocity gradient. Using the proposed linear functions, average low-frequencies are estimated within the examined ranges of Mach number and input temperature and a semi-empirical relationship is derived to predict low-frequency oscillations in shocks. Our model can be used to provide realistic physics-based boundary conditions in receptivity and linear stability analysis studies of laminar-turbulent transition in high-speed flows.Comment: 22 pages, 6 figure

Linear Instability of Shock-Dominated Laminar Hypersonic Separated Flows

The self-excited spanwise homogeneous perturbations arising in shock-wave/boundary-layer interaction (SWBLI) system formed in a hypersonic flow of molecular nitrogen over a double wedge are investigated using the kinetic Direct Simulation Monte Carlo (DSMC) method. The flow has transitional Knudsen and unit Reynolds numbers of 3.4 x 10$^{-3}$ and 5.2 x 10$^4$ m$^{-1}$, respectively. Strong thermal nonequilibrium exists downstream of the Mach 7 detached (bow) shock generated due to the upper wedge surface. A linear instability mechanism is expected to make the pre-computed 2-D base flow potentially unstable under spanwise perturbations. The specific intent is to assess the growth rates of unstable modes, the wavelength, location, and origin of spanwise periodic flow structures, and the characteristic frequencies present in this interaction.Comment: 10 pages, 6 figures. To appear in the proceedings of the IUTAM Transition 201

Linear stability analysis of hypersonic boundary layers computed by a kinetic approach: a semi-infinite flat plate at 4.5 <= M-infinity <= 9

Linear stability analysis is performed using a combination of two-dimensional Direct Simulation Monte Carlo (DSMC) method for the computation of the basic state and solution of the pertinent eigenvalue problem, as applied to the canonical boundary layer on a semi-infinite flat plate. Three different gases are monitored, namely nitrogen, argon and air, the latter as a mixture of 79\% Nitrogen and 21\% Oxygen at a range of free-stream Mach numbers corresponding to flight at an altitude of 55km. A neural network has been utilised to predict and smooth the raw DSMC data; the steady laminar profiles obtained are in very good agreement with those computed by (self-similar) boundary layer theory, under isothermal or adiabatic wall conditions, subject to the appropriate slip corrections computed in the DSMC method. The leading eigenmode results pertaining to the unsmoothed DSMC profiles are compared against those of the classic boundary layer theory. Small quantitative, but no significant qualitative differences between the results of the two classes of steady base flows have been found at all parameters examined. The frequencies of the leading eigenmodes at all conditions examined are practically identical, while perturbations corresponding to the DSMC profiles are found to be systematically more damped than their counterparts arising in the boundary layer at the conditions examined, when the correct velocity slip and temperature jump boundary conditions are imposed in the base flow profiles; by contrast, when the classic no-slip boundary conditions are used, less damped/more unstable profiles are obtained, which would lead the flow to earlier transition. On the other hand, the DSMC profiles smoothed by the neural network are marginally more stable than their unsmoothed counterparts

On the synchronisation of three-dimensional shock layer and laminar separation bubble instabilities in hypersonic flow over a double wedge

Linear global instability of the three-dimensional (3-D), spanwise-homogeneous laminar separation bubble (LSB) induced by shock-wave/boundary-layer interaction (SBLI) in a Mach 7 flow of nitrogen over a $30^{\circ}-55^{\circ}$ double wedge is studied. At these conditions corresponding to a freestream unit Reynolds number, $Re_1=5.2\times 10^{4}$ m$^{-1}$, the flow exhibits rarefaction effects and comparable shock-thicknesses to the size of the boundary-layer at separation. This, in turn, requires the use of the high-fidelity Direct Simulation Monte Carlo (DSMC) method to accurately resolve unsteady flow features. We show for the first time that the LSB sustains self-excited, small-amplitude, 3-D perturbations that lead to spanwise-periodic flow structures not only in and downstream of the separated region, as seen in a multitude of experiments and numerical simulations, but also in the internal structure of the separation and detached shock layers. The spanwise-periodicity length and growth rate of the structures in the two zones are found to be identical. It is shown that the linear global instability leads to low-frequency unsteadiness of the triple point formed by the intersection of separation and detached shocks, corresponding to a Strouhal number of $St\sim0.02$. Linear superposition of the spanwise-homogeneous base flow and the leading 3-D flow eigenmode provides further evidence of the strong coupling between linear instability in the LSB and the shock layer

Proceedings of National Conference on Relevance of Engineering and Science for Environment and Society

This conference proceedings contains articles on the various research ideas of the academic community and practitioners presented at the National Conference on Relevance of Engineering and Science for Environment and Society (R{ES}2 2021). R{ES}2 2021 was organized by Shri Pandurang Pratishthan’s, Karmayogi Engineering College, Shelve, Pandharpur, India on July 25th, 2021. Conference Title: National Conference on Relevance of Engineering and Science for Environment and SocietyConference Acronym: R{ES}2 2021Conference Date: 25 July 2021Conference Location: Online (Virtual Mode)Conference Organizers: Shri Pandurang Pratishthan’s, Karmayogi Engineering College, Shelve, Pandharpur, India