arXiv subjects

Vineeth Vijaya Kumar

Publications and source records attributed to Vineeth Vijaya Kumar.

4 recordsLinked to original sources

arXiv2025

Verification of Convergent-Divergent Nozzle Designs in Propulsion Aerospace Applications

The performance of convergent and divergent nozzles is critical in aerospace propulsion systems, where the efficient expansion of high-temperature, high-pressure gases directly impacts thrust generation. In this study, we investigate a series of nozzle geometries using numerical simulations in ANSYS Fluent, guided by classical compressible flow theory, initially developed by Ludwig Prandtl. The governing equations of conservation of mass, momentum, and energy are solved under steady-state conditions, with emphasis on shock formation, boundary-layer effects, and Mach number distributions across the nozzle throat and divergent section. Parametric analyses are conducted to evaluate the influence of nozzle contour, area ratio, and throat geometry on flow acceleration and thrust coefficient. The results demonstrate close agreement with theoretical predictions of isentropic compressible flow while also highlighting deviations due to viscous and three-dimensional effects. These findings provide design insights for optimizing nozzle performance across propulsion applications, from launch vehicles to high-speed air-breathing systems. We obtained absolute error differences of 2.05 percent, 6.03 percent, and 9.9 percent in the throat temperature measurements for the RL10B2, SSME-40k, and A-1 nozzles, respectively.

physics.flu-dyn↗

arXiv2025

Cross-Model Verification of Wall-Bounded Flows using Finite-JAX

Accurate prediction of wall-bounded flows remains central to advancing both theoretical understanding and computational methods in fluid mechanics. In this study, we perform a numerical simulation of channel flow using a complementary approach: a high-performance, differentiable finite-difference solver developed in JAX (Finite-JAX), and an analytical solution derived from the Navier-Stokes Equations, also known as the Hagen-Poiseuille equation. The solver is applied to the incompressible Navier-Stokes equations, along with appropriate boundary conditions, to capture canonical flow features, including velocity profiles and pressure gradients. Cross-model verification is conducted by systematically comparing numerical results between Finite-JAX and the analytical solution, with a focus on velocity distributions. In addition, numerical results are benchmarked against analytical solutions for the laminar regime, allowing direct quantification of the verification accuracy. Our findings demonstrate that cross-model verification not only strengthens confidence in simulation fidelity but also provides a pathway for integrating differentiable solvers with established computational fluid dynamics platforms, paving the way for future fluid flow research. The performance of Finite-JAX on Wall-Bounded Flows is 0.014765 in the L2 norm.

physics.flu-dyn↗

arXiv2025

Numerical and analytical modeling of heat equation in current-carrying conductors using the heat equation implemented using Finite-JAX

Current-carrying conductors inevitably experience resistive heating due to the material's finite electrical conductivity. The resulting temperature distribution within the wire has essential implications for structural integrity, efficiency, and long-term reliability of electronic and power systems. In this work, we model the steady-state heat distribution in a current-carrying wire using the classical heat conduction equation. In a two-dimensional formulation, heat transport is considered both along and across the conductor. The governing partial differential equation is discretized using finite-difference methods implemented in Finite-JAX, with appropriate initial and boundary conditions, including the Dirichlet condition relevant to practical scenarios. Time integration is performed using the Euler explicit scheme, and stability constraints are systematically examined. To assess the accuracy of the numerical approach, we compare the computed temperature fields with the exact analytical solution of the heat equation for canonical geometry. Results show that the numerical prediction converges toward the analytical solution, with error norms decreasing at the expected order of accuracy. This study demonstrates how the heat equation provides a rigorous mathematical foundation for modeling resistive heating in conductors. The errors between the numerical and analytical solutions are 1.981 K, 0.8975 K, and 0.7917 K, corresponding to the L-infinity, L1, and L2 norms. For tensor computations, TPUs deliver the highest performance, surpassing GPUs and CPUs.

math.NA↗

arXiv2025

Computational Aerothermal Framework and Analysis of Stetson Mach 6 Blunt Cone

Accurately predicting aerothermal behavior is paramount for the effective design of hypersonic vehicles, as aerodynamic heating plays a pivotal role in influencing performance metrics and structural integrity. This study introduces a computational aerothermal framework and analyzes a blunt cone subjected to Mach 6 conditions, drawing inspiration from Stetson foundational experimental work published in 1983. While the findings offer significant insights into the phenomena at play, the study highlights an urgent necessity for integrating chemical kinetics to comprehensively capture non-equilibrium effects, thereby enhancing the predictive accuracy of computational fluid dynamics (CFD) simulations. This research implements a one-way coupling method between CFD simulations and heat conduction analysis, facilitating a thorough investigation of surface heat transfer characteristics. The numerical results elucidate discrete roughness elements' impact on surface heating and fluid dynamics within high-speed airflow. Furthermore, the investigation underscores the critical importance of accounting for non-equilibrium thermochemical effects in aerothermal modeling to bolster the accuracy of high-enthalpy flow simulations. By refining predictive computational tools and deepening understanding of hypersonic aerothermal mechanisms, this research lays a robust groundwork for future experimental and computational endeavors, significantly contributing to advancing high-speed flight applications.

physics.flu-dyn↗