Researchers have developed a mathematical technique that radically reduces the enormous computational costs of trying to model fluids that combine both liquid and gas phases, especially within rocket engines. Credit: Yokohama National University
Multiphase flow simulations are crucial in multiple industries, such as the oil and gas industry, as they allow researchers and engineers to predict the behavior of fluids that contain both liquid and gas. One of the challenges of modeling multiphase flow, especially when dealing with compressible flows, is the enormous computational costs of solving complex interactions between the different phases. Researchers at Yokohama National University (YNU) have developed a new mathematical technique that could reduce the computational burden of multiphase flow modeling and could be used to better simulate flows within rocket engines.
Computational modeling of multiphase flows is crucial, as vapor-filled cavities within liquid can collapse under high pressure, leading to shock waves that result in wear and tear to oil infrastructure, engines and other machinery. In rocket engines, simulating flow becomes even more complex due to instabilities such as resonance caused by fluctuations in the rate of heat release. Conventional methods for modeling compressible multiphase flow use a mathematical technique known as an exact Riemann solver, which is highly demanding to compute.
“An exact Riemann solver is a method of approximation in computational fluid dynamics to describe the flux across such discontinuities,” said first author Junya Aono, a computational fluid dynamicist with the Department of Mechanical Engineering and Material Science at YNU. “But it incurs high computation costs and also struggles with what’s called the carbuncle problem in which captured shock waves are distorted, potentially affecting heat transfer to the chamber containing the multiphase flow.”
To reduce the computational costs of compressible multiphase flow modeling, and overcome the carbuncle problem, the researchers sought a mathematical method that would remove the need for an exact Riemann solver. In their approach, the team adapted a technique known as the Simple Low-dissipation Advection Upstream Splitting Method 2 (SLAU2), which does not involve tunable parameters, is easy to code and is less susceptible to the carbuncle phenomenon. The authors wrote that numerical experiments conducted using the modified SLAU2 scheme showed that it could be used to compute a wide spectrum of multiphase flows without numerical instability or serious oscillations. This research was published in the Journal of Computational Physics.
“We concluded that SLAU2 with an appropriate amount of dissipation at the gas-liquid interface can obtain stable solutions even in the presence of a strong shock or a high-pressure ratio,” the authors wrote. “The modifications did not involve any iterative procedures, such as those required by the exact Riemann solver; thus, its computational cost is quite low.”
The researchers now plan to apply their new technique to practical 3D compressible multiphase flow simulations, particularly with respect to rocket engines.