ABSTRACT. After a brief introduction I shall discusss Large Eddy Simulations andsolutions of Reynolds equations (RANS) for mean fields with a focus on reliability.  For LES, the examples are drawn from our studies ofcanonical flows, especially round jets, compressor cascade flows, andcombustion.  For RANS an example is of transverse injection into asupersonic stream.  This will lead into some thoughts on studies for the near future.

ABSTRACT. This work shows the direct numerical simulation (DNS) of flow over an experimental small turbofan engine (STFE) using the in-house developed unstructured grid compressible Navier-Stokes solver named ANUROOP. Simulations have been performed for the inlet Reynolds number of 152,000 (based on inlet velocity and chord length of blade) with zero and 10% inlet free-stream turbulence intensity (FSTI). The task of establishing optimal mesh size to ensure well-resolved, physically accurate DNS results at this high Reynolds number is accomplished using a zonal grid refinement approach. For this, five levels of grid refinements successively along the streamwise and spanwise direction of the blade are made and DNS results at 94, 129,258, 329 and 512 million grid cells are compared. The DNS results at 129 million and higher mesh resolution suggests the presence of flow separation near the trailing edge of suction side of the blade. Further, the enforcement of 10% free stream suggests almost 1/3rd contraction in flow separation bubble. This indicates the complex dynamics and presence of bypass flow transitions to turbulence across the free shear layer

ABSTRACT. The stator hub corner separation is an inherent phenomenon that causes severe aerodynamic blockage and total pressure losses eventually leading to blade stall. The present study deals with the unsteady three-dimensional flow separation and its evolution over time in the stator passage using unsteady numerical simulation at the near stall condition. The results show that the hub corner separation started before the peak efficiency point. The tip corner separation began at the near stall condition and is induced by the vortices coming from the upstream rotor passage. Overall blockage of 48% was created by the corner separation at the hub and tip. The fast furrier transform of the unsteady pressure signals showed the dominant frequencies 0.06×BPF (Blade passing frequency), 0.12×BPF, and 0.44×BPF. Apparently, the first two frequencies are related to the rotor tip leakage flow instabilities and the third one is related to the vortex shading in the stator hub separation zone.

ABSTRACT. Low-pressure turbine blades are vulnerable to flow separation at higher altitudes, thus precautionary steps must be taken to suppress flow separation and increase turbine efficiency. There are various active and passive flow control techniques for the suppression of boundary layer separation - the latter techniques are easy to implement and do not require additional power or add extra weight. Therefore, in this study, a passive control strategy in the form of a single depression (dimple) on the suction side of the blade is used to investigate the benefits in terms of separation control and wake losses. Particularly, a dimple is engraved at 65% chord on a highly curved Pak-B blade and unsteady numerical studies were performed at low Reynolds number conditions at Re = 50,000 and 100, 000. In both cases, the presence of dimples effectively energizes flows which leads to a significant reduction in the size of separation bubbles. Consequently, the wake losses also get reduced in the control cases. More benefits are observed for the lower Re flow, where the unmodified case exhibits a large separation bubble.

ABSTRACT. The development of supersonic aircraft requires the accurate prediction of shock waves and interference caused by shock waves generated by sharp-edged objects. It is also necessary to accurately predict the heat flux on the wall surface to deal with aerodynamic heating. In this study, computations were performed by using a Building-Cube Method implemented with the Ghost Cell Immersed Boundary Method to predict the surface heat flux on a wedge under supersonic flow. From the computed results, the pressure and temperature distributions and heat fluxes were evaluated and the influence of mesh resolution and boundary conditions on the results was shown. Based on the results of this study, attempts will be made to improve the accuracy of the estimation of surface heat flux over sharp objects.

ABSTRACT. A Turbine Based Combined Cycle (TBCC) with a dual mode scramjet is a key candidate for future end-to-end hypersonic flight. The design of scramjet inlets is critical for the overall performance of the engine. With a variable supersonic inlet, the throat area decreases to reduce flow loss, but excessive contraction seen in terms of Internal Contraction Ratio (ICR) will increase the risk of unstart. Two-dimensional unsteady numerical simulations are conducted to reveal the flow features and physical mechanisms of the start, unstart, and restart states. The results show that a flow response hysteresis phenomenon appears, and restart is only realized when the throat area is increased. It is found that separation ahead of the inlet held in place by the separation shock affects the hysteresis and ability to return to its original operating condition. The option of utilizing bleed to delay unstart and bring stability to the flow is also explored.

ABSTRACT. Pylon-cavity based flame stabilizers for scramjet are gaining interest due to increase in the perpetration and mixing of fuel. Researchers have noted that positioning a pylon before the cavity improves the efficiency of mixing. However, the impact of the pylon on the downstream region of the cavity remains unexplored. To address this gap, the current study investigates the consequences of fuel injection when a pylon is placed downstream of the cavity, exploring injection ahead of the cavity to understand the impact of the pylon placed downstream of the cavity. Numerical simulation is employed, utilizing a hybrid RANS/LES simulation with an enhanced delayed detached eddy simulation (IDDES) turbulence model. To gain a deeper understanding of the mixing dynamics, additional investigation using dynamic mode decomposition (DMD) has been performed.

ABSTRACT. Swirled jets are technologically important flows that have wide ranging applications in gas turbine propulsion and power generation systems. Combustors in these devices use nozzles that impart swirl to the flow as it passes through. Sufficiently high values of swirl intensity cause the axial vortex in the flow to break down and create an axi-symmetric recirculation zone in the flow - commonly referred to as the ‘vortex breakdown bubble’ (VBB). The precessing vortex core (PVC) is a self-excited instability that occurs in this flow due to the precession of the VBB around the flow axis. The presence of PVCs is known to critically influence combustor performance with regard to pollutant emissions and thermoacoustic instability. This talk focuses on how the PVC arises and how its occurrence can be controlled by passive nozzle geometry changes.

First, I will summarize results from a theoretical and experimental of a swirled axi-symmetric jet at a Reynolds number, – the subject of several studies in Jacqueline O’Connor’s group at Penn. State. The experiments show the onset of vortex breakdown at a critical swirl number, accompanied by a simultaneous emergence of a stable limit cycle PVC oscillation. I will show that this is a self-excited instability caused by vortex breakdown which then grows into a stable limit cycle flow oscillation. The limit cycle is driven by internal feedback at the upstream end of the breakdown bubble.

Next, I will show results from experiments and LES studies performed on a swirl nozzle with cylindrical co-axial centrebodies of various diameters. These results show that the PVC can be controlled by varying the cross-sectional diameter of the centrebody. Results from stability analysis show that the centrebody disrupts the flow in the region responsible for sustaining self-excited oscillaitons, thereby, suppressing the PVC.

Finally, I will show results from another study on PVC oscillations in the PRECCINSTA model GT combustor that was the subject of a recent experimental campaign at DLR Stuttgart. In this case, flame attachment onto the centrebody due to H2 enrichment of the fuel disrupts internal feedback and causes PVC suppression.

These results therefore suggest a broad guideline for PVC management by design in swirl nozzles. The computational methods described can provide quantitatively accurate predictions that can guide nozzle design optimization to achieve this goal.

ABSTRACT. Viscous fingering is a critical phenomenon observed in various natural and technological processes, including flows in porous media [1], enhanced oil recovery [2], and microfluidics [3]. It occurs when a less viscous fluid displaces a more viscous fluid in a porous medium or within the confined environment of a Hele-Shaw cell [1,4]. Recent studies have highlighted the positive influence of intense fingering on fluid mixing in confined systems like microfluidic devices [5-6]. Since these confined fluid systems typically operate at low Reynolds numbers, where inertial effects are negligible and turbulence does not occur, achieving enhanced fluid mixing becomes challenging. Furthermore, the application of an alternating injection protocol has been shown to further improve fluid mixing in both rectangular and radial Hele-Shaw cells [6-7]. We present a theoretical investigation of the enhanced mixing in a porous medium induced by viscous fingering (VF) and alternate injection during radial displacement. It is found that the alternating injection leads to the formation of distinct fluid layers, effectively increasing the interfacial contact area between the fluids and promoting mixing. These results align with previous numerical studies, thus validating the novel linear stability analysis technique employed in this study. References: [1] C. T. Tan and G. M. Homsy, Physics of Fluids, 30(5):1239–1245, 1987. [2] L. W Lake, Enhanced oil recovery, 1989. [3] Y. K. Suh and S. Kang, Micromachines, 1(3):82–111, 2010. [4] R. Govindarajan and K. C. Sahu, Annual review of fluid mechanics, 46:331–353, 2014. [5] Jha, et al., Physical review letters, 106(19):194502, 2011. [6] Jha, et al., Physical review letters, 111(14):144501, 2013. [7] Chen et al., Physical Review E, 92(4):043008, 2015.

ABSTRACT. Direct numerical simulations of laminar viscous layers for supersonic flows are used to study the evolution of naturally occurring as well as externally imposed disturbances under supersonic flow conditions. Receptivity analysis of such flows reveals that artificially produced disturbances (such as wall suction and blowing) have a broad spectrum of wavelength and spectral characteristics. The predictions from linear stability theory reveal that instabilities within the compressible boundary layer are associated with small amplitude disturbances. These in turn, tend to excite the normal modes of the boundary layer, described as T-S type disturbances [1]. The compressibility effects contrast with incompressible studies in the sense that former is associated with (slow/fast) acoustic as well as entropic modes, that arise out of viscous interaction [2].

Such problems find applications in design and testing of supersonic/hypersonic aircrafts, where the fluid structure interaction and flow properties heavily depend on understanding of transition phenomena. Transition; resulting to turbulence has an impact on drag, skin-friction and consequently performance. The receptivity and fluctuation growth/decay are highly sensitive to Mach number, Reynolds number, flow geometry and boundary conditions.

At this stage, it is important to consider some numerical methods developed for linear stability analysis. The system of equations is stiff, with terms of different orders, the compound matrix method (CMM) developed by Somvanshi et. al. [3] has been considered. The approach is to create auxiliary variables from the primitive, and use them to create a new set of compound equations for propagation. The neutral curve for M = 4 is generated using [3] and helps in making intelligent estimates of Reynolds number based on displacement thickness, Reδ ∗ against frequency ω.

This article sets up the compressible Navier-Stokes equations, over an adiabatic flat plate in a parallel free-stream. Fluctuations are introduced through the wall blowing and suction mechanism, and propagate downstream under the influence of supersonic (M = 4) flow. Equations are written in flux vector form, with no-slip and free-stream boundary conditions at the wall and top surface of the simulation domain. As a reference point, we use the neutral curve published in [3]

ABSTRACT. We conducted a study on density-driven flow using numerical simulation. The sinking fluid was set as a fluid with a higher density than the environmental fluid, which was set as a non-Newtonian fluid of power-law type with flow behavior index ranging from 0.7 to 1.4 (the fluid is Newtonian when the index equals 1.0). During the simulation process, we fixed the concentration on the upper boundary to the saturation concentration and set all boundaries to be impermeable. During the simulation process, the dissolution flux undergoes a series of changes, from the initially diffusion-dominated regime to convection-dominated regime due to the appearance of finger structures, and then to the transition of finger structures merging into larger plumes. Finally, it enters the shut-down regime as the plumes start to reach the impermeable bottom boundary. In the process of plume sinking in the simulation, different flow behavior indexes have an impact on the downward velocity, shape of plumes, and the dissolution flux of the flow field. Our research motivation is to analyze CO2-enhanced oil recovery (CO2-EOR) in Carbon Capture and Storage (CCS). As some of the oil belongs to non-Newtonian fluid, when the density difference generated by the CO2 dissolution in oil starts to flow downward, it creates a density-driven flow field under non-Newtonian fluid, this is the reason why we studied this topic.

ABSTRACT. The location of the aerodynamic center plays a significant role in determining the static stability of an aerial vehicle. Experiments at a very high Reynolds number have shown that the aerodynamic center of a thin symmetrical airfoil is at the quarter chord point. In this study, we explore the aerodynamic center of a finite wing for various semi-aspect ratios in the context of low Reynolds number flows.

ABSTRACT. Laminar separation bubbles are often found on airfoil surface at low Reynolds number. The laminar separation bubble is classified as short or long bubble and there is poor understanding about the same. Drag polar shows drag rise at moderate Cl for flow at Reynolds number less than 105 and the flow mechanism is not well understood. Numerical flow simulations have been carried out over Eppler 387 airfoil using two transition models. The computations have been performed using Fluent software at two Reynolds numbers of 0.6x105 and 1.0x105 and three turbulence intensities of 0.03 %, 0.1 % and 0.5 % are used to compute the flow. Based on the studies, a new definition of short and long bubble has been postulated and the reason for drag rise at moderate lift coefficient for Reynolds number less than 105, is attributed to occurrence of long bubble on the airfoil surface, has been clearly demonstrated.

ABSTRACT. When an aircraft flies through icing clouds, supercooled water droplets collide with the aircraft’s surface and form ice in freezing conditions. This accumulated ice alters the wing’s shape, negatively impacting its aerodynamic properties by posing a threat to flight safety. In this study, we used computational simulation to analyze how icing affects the aerodynamic performance of medium-sized transport aircraft. We observed that the height of ice accumulated on the leading edge of the main and tail wings reached up to 5.3 cm. The degradation in aerodynamic performance was notably significant under glaze ice conditions due to the complex ice geometry. In this study, the effect of icing on the lift and drag coefficient was investigated. The lift coefficient was found to decrease substantially, while the drag coefficient increased significantly. Ice accretion can in turn affect the cruising range and endurance performance of medium-sized transport aircraft.

ABSTRACT. The Implicit Gradient Reconstruction (IGR) essentially involves introducing a ᵩ parameter in an upwind flux formula operating on cell averaged state available from a finite volume state update procedure. This seamlessly merges three steps in the computation of explicit residual, namely, (linear) solution reconstruction, limiting and flux computation. The accuracy of this procedure is established through a number of standard test cases. Apart from considerably simplifying the computation of explicit residual, the proposed methodology obviates memory intensive storage of solution gradients. The smaller memory foot print will result in better cache utilization and therefore better parallel performance, on large scale parallel computing platforms. In addition, the simplicity of the procedure, allows higher order implementation of turbulence model equations, resulting in better wake capturing.

ABSTRACT. The Implicit Gradient Reconstruction (IGR) procedure uses first order flux formulation along with φ parameter to achieve second order of accuracy. In the present work three non-linear variants of φ formulation are presented for non-linear vector conservation laws. The IGR procedure allows dissipation control wave by wave and this aspect is demonstrated on the subsonic flow past OMAR5 multi-element airfoil.

ABSTRACT. This study presents a critical assessment of a pressure-based solver (PBS) in resolving complex interactions of shocks, turbulent structures etc.. The canonical problem chosen to be resolved in this study is of mode staging in axisymmetric supersonic jet screech. The screech phenomenon exhibits staging behavior characterized by frequency and azimuthal structure changes at specific frequencies. The PBS simulations in the popular ANSYS Fluent software-suite were validated against numerical work and experimental measurements, and results were analyzed. Simulations are performed on supersonic jets which emits dual high frequency screech tones at particular Mach numbers. At lower end of these supersonic Mach numbers, the flow can involve vanishingly weak shock strengths which is routinely captured in experiments and by density based solvers in literature. The limitations of the pressure-based solver in resolving complex shock flow phenomena and predicting mode staging are highlighted at vanishingly weak Mach numbers, emphasizing the need for further investigation given the recent popularity of such solvers for all Mach numbers including in high-speed flow.

ABSTRACT. Application of fertilizers and pesticides using drones for agricultural purposes has gained importance in recent years. Typically, copter configurations are used rather than fixed wing drones for better control. Sprayers are usually mounted under the drone and well within the propeller wash which requires one to understand the spray dynamics. In this study, we make use of a Panel method to compute the propeller wash characteristics and further add a spray model to compute distribution of fertilizer. The velocity behind the propeller was computed and compared with more accurate but computationally expensive RANS simulations and also experimental measurements. We show that the panel method can be deployed usefully for the purpose.

ABSTRACT. Pump as turbine (PAT) is a proven green technology for energy recovery and microhydro power applications. Improving the PAT performance by geometric means is an ongoing process. In the present research, the computational fluid dynamics (CFD) tool is utilized to investigate the impact of impeller diameter and number of blades on the internal hydraulics and performance of PAT, revealing a 2.6 % decrease in efficiency when reducing impeller diameter from 260 mm to 230 mm due to increased secondary flow and wake, similarly with increasing the number of blades led to decreased in efficiency primarily due to increased secondary flow, wake, and frictional losses. The proposal put forth by other researchers suggests that decreasing the impeller diameter in a PAT could potentially enhance its efficiency during part load conditions. However, it is imperative to conduct a comprehensive and rigorous investigation to thoroughly examine this assertion.

ABSTRACT. Micro Gas Turbine Engines used in UAV propulsion require higher pressure ratio and higher efficiency. They use centrifugal compressors as they give higher compression in a single stage, generally 4:1, and occupy smaller area when compared with axial compressors. Pressure rise in the compressor occurs in both the impeller and diffuser. Diffuser causes the static pressure rise by reducing the velocity of the flow entering the combustion chamber for efficient combustion. A KJ66 MGT centrifugal compressor is considered in this study. A numerical simulation of this compressor with diffuser configurations such as vaneless, wedge, wedge and axial de-swirl vanes, and cross vane diffusers are carried out. The diffuser diameter is constrained by the engine diameter so the diffusers are designed within these limits. The cross vane diffuser with twelve number of blades performed much better among the twelve, fourteen, and sixteen number of blades cross vane diffuser. In comparison with the vaneless diffuser this cross vane diffuser showed that its stall margin increased by 19%. There is a 4.8 % increase in the maximum total pressure ratio and 8.21 % increase in maximum efficiency achieved by this cross vane diffuser.

ABSTRACT. A coupled 3D aero-thermo-elastic analysis is performed on an inclined flat plate exposed to Mach 7 hypersonic flow at an altitude of 25 km, representing the scramjet forebody ramp. A multi-physics coupling framework involving computational fluid dynamics and computational thermo-structural dynamics modules is established and validated. The disparity between fluid, thermal, and structural domain time scales leads to a conservative approach in modeling by treating the fluid domain as static and the thermo-structural domain as dynamic. The response of the inclined flat plate in terms of static (1-way) and dynamic (2-way) behavior under aero-thermal, aero-elastic, thermo-elastic, and aero-thermo-elastic coupling is discussed.

ABSTRACT. The paper’s focus pivots around studying the significant flow features and predicting the heat transfer and skin friction distribution over the HIFiRE-1 flight research vehicle. Towards this end, inviscid and viscous flow analyses are performed for the axisymmetric model using the Stanford University Unstructured (SU2) solver for supersonic and hypersonic flow conditions. The study commences with the verification of the present simulations using the RANS equations coupled with the SST turbulence model, by comparing the results with experimental and post-flight simulation data obtained from the literature. The domain is discretized using a high-resolution structured grid with approximately 0.6 million grid points. The results from the simulations are compared to the experimental pressure and heat transfer data, and the performance of the turbulence model in the separated boundary layer is studied in detail. Large heat transfer rates and strong shock wave/boundary layer interactions (SBLI) are observed as expected. Consequently, the results obtained from simulation agrees well with the experimental data.

ABSTRACT. In the current study, an attempt has been made to ascertain the extent of plasma attenuation levels and communication blackout zone of the Gaganyaan Crew Module during its reentry hypersonic descent. The paper utilizes CFD based electron number density computation, followed by signal attenuation level determination using theoretical relations. This methodology is validated against flight and literature reported data of a similar reentry flight capsule, ARD, where good match between the two datasets is obtained. With this confidence, signal attenuation prediction for the flight conditions of Gaganyaan Crew Module is carried out for altitudes between 90km and 40km. Significant plasma attenuation occurs between 75km to 55km altitude, which is the zone of communication blackout for Crew Module aft mounted antenna.

ABSTRACT. This paper demonstrates the use of adjoint based shape sensitivities to make incremental changes in stability derivatives. For this purpose, the primal, tangent linear and adjoint meshfree least squares kinetic upwind method (LSKUM) based solvers for 2D inviscid compressible flows are employed. The tangent linear and adjoint LSKUM solvers are constructed using algorithmic differentiation techniques. Here, the tangent solver computes the stability derivative and the adjoint solver yields the shape sensitivites of stability derivative. Numerical results are shown for the MS0313 airfoil to make incremental changes in the stability derivatives through shape perturbations.

ABSTRACT. In the automotive industry, multi-element wings have been used to improve the aerodynamics of race cars. Multi-element wings can enhance a vehicle's handling and stability by reducing drag and increasing downforce, allowing it to corner more effectively and achieve higher speeds. Performance gains by utilizing the ground effect are highly sensitive to the wing setup. This study focuses on identifying the optimum design parameters for the airfoil to achieve the desired downforce and drag performance. The design parameters chosen are ride height, flap overlap, flap angle, and the gap between the main element and the flap. These parameters are optimized for three different use cases: high downforce, low drag, and a setup with the highest airfoil efficiency. The force coefficient and flow field data were gathered using two-dimensional (2D) Reynolds Averaged Navier Stokes (RANS) simulations, with the turbulent flow modeled using the k-ω Shear Stress Transport (SST) turbulence model. The Improved Harris Hawks Optimization (HHO) algorithm was used to obtain the optimal configuration of the double-element and the resulting designs showed a significant improvement in downforce and drag performance compared to the baseline designs. Improved HHO was further compared with other state-of-the-art algorithms for assessing the algorithm's performance for a problem with highly non-linear behavior, where it was able to demonstrate its ability to obtain the optimal solutions more efficiently.

ABSTRACT. Takeoff and landing are always the most challenging phases for any aircraft. The situation gets more complicated for an unmanned autonomous aircraft where there is no human in the loop to control the aircraft. An autonomous aircraft flies solely based on onboard control system which controls the aircraft based on sensor data. In the case of a tailless autonomous flying wing class of aircraft which don’t have the inherent stability, the takeoff and landing becomes a highly challenging and complex problem. The success of autonomous takeoff and landing of such tailless aircrafts depends heavily on the accurate prediction of aerodynamic characteristics of the aircraft in the vicinity of the ground. Unlike conventional aircrafts, the tailless aircrafts don’t have high lift devices like flaps for takeoff and landing. Longitudinal control during takeoff and landing of these aircrafts are carried out using elevons which are deflected upwards as against the typical downward deflection resulting in the modification of aerodynamics near the ground due to the change in airfoil camber. There is no comprehensive work reported in literature which brings out the effect of ground on the aerodynamics of a tailless aircraft. CFD studies are carried out using HiFUN software using overset mesh approach for different ground heights for a typical tailless aircraft configuration and the results are brought out in the abstract. Studies are also proposed to be carried out to characterize the effect of elevon deflections on the aerodynamic characteristics of this configuration near the vicinity of the ground and the results will be presented in the full length paper.

ABSTRACT. This study presents the results of the computational exercise performed to analyse the flow over a transport aircraft using an open-source Computational Fluid Dynamics (CFD) solver. From the simulations, we estimate the values of local angles of attack at the measuring vane mounted on the aircraft. With the aid of various visualisation techniques, we identify the regions of separation which form under certain flight conditions. We find that the separation pockets appear at a combination of high angles of sideslip but low angles of attack. This is an unexpected result, and we attempt to explain the reason and also its significance. These simulations help us understand the fluid flow around the aircraft and optimise the location of the angle of attack vane.

ABSTRACT. Simulation of flow over a typical twin-propeller multi-role light transport aircraft in all the possible combinations of sense of rotation of propeller is attempted in this study with RANS-BEM solver. Flow over wing is highly influenced by the propeller slip-stream and hence simulation becomes compute intensive even with moderate fidelity propeller model (BEM) in combination with industry standard turbulent simulation approach (RANS). Upon comparing the performance of all the possible ways of propeller rotation, it is found that, in-board up rotation turns out to be the best way from aerodynamic point of view, which is well in agreement with literature. The reason behind this behaviour is explained with the help of span-wise distributions of aerodynamic forces and flow visualisations.

Many aircrafts are designed with co-rotating propellers like the present configuration under study similar to C-130H/J aircraft. which results into production of net yawing moment. Hence, the penalties which need to be paid with co-rotating propellers compared to the optimum sense of rotation (both in-board up) are also given. All these effects are found at different Mach & Reynolds number combinations and zero degree angle of attack as it is close to level flight.

ABSTRACT. This study investigates the effectiveness of Compact Adaptive Filtering (CAF) proposed by Visbal and Gaitonde (2005) \cite{visbal2005shock} in solving the Compressible Navier-Stokes equations under the Flux-Reconstruction framework for both smooth and shock-containing flows. The transfer function of the standard pade-type filter is studied on Gauss-Legendre, Gauss-Lobotto, and uniform node arrangements. The filter transfer function is modified to account for the non-uniform nodal arrangement. Three categories of test cases will be employed for the final presentation, covering low subsonic ($M<0.3$), high subsonic ($0.3<M<0.8$), and supersonic flows ($M>1$). The results corresponding to Kelvin-Helmholtz instability and Inviscid Taylor-Greene vortex test cases performed under the first category, showed that without filtering, oscillations increased progressively, resulting in solution divergence. Conversely, filtering produced robust and physically accurate results. The shock capturing attempted in the present study employing CAF includes a shock aware spatially adaptive filter designed to prevent Gibbs oscillations near the discontinuities. Alongside filtering, local finite difference discretization (sub-cell FD) is utilized to enhance stability in the regions with shocks. Positive outcomes were observed in the Sod, Shu-Osher, and 2D-Riemann problem test cases, with minor oscillations in the 2D-Riemann problem. Overall, the study indicates that CAF is highly effective in low subsonic and high-subsonic flows. Nonetheless, in shock-containing flows, the use of local sub-cell finite differencing is necessary to produce stable and oscillation-free results.

ABSTRACT. Compressible Navier-Stokes solvers currently used in the industry rely on first and second-order spatial discretization by use of Finite Difference or Finite Volume methods. While these approaches are robust and reliable, they tend to be highly dissipative, due to which simulating and capturing complex turbulent flows becomes a challenge. As such, there is a growing interest in the development of higher-order schemes to accurately model such flows. Direct Flux Reconstruction is one such novel higher-order scheme based on the Discontinuous Finite Element family. Using the in-house developed DFR-based solver; we solve problems that involve simulating shock boundary layer interactions.

ABSTRACT. Simulations of flow problems, often considered benchmarks for high-order CFD codes, have been performed in the present study using the Direct Flux Reconstruction approach. These problems contain strong discontinuities (such as shocks), for modelling of which, a modal filter for shock capturing and a positivity-preservation scheme have been used to provide robustness to the flow solver. While dissipating the spurious oscillations that arise in the vicinity of discontinuities, such as shocks, is necessary to attain stability, over-dissipation at other discontinuities, such as contact discontinuity, would not capture essential flow structures. Thus, in the present study, we use an adaptive filter to provide robustness to the flow solver while preserving other flow features. A positivity-preservation scheme further adds to the robustness offered by shock capturing by preventing the undershoots of the physical quantities to negative values, when high-order approximations are involved or in the vicinity of low pressures and densities.