scholarly journals Shock-less Hypersonic Intakes

2021 ◽  
Author(s):  
Seyed Hossein Miri
Keyword(s):  
Exact Solution ◽  
Mach Number ◽  
Finite Volume Method ◽  
Conical Flow ◽  
Low Mach Number ◽  
Simulation Based ◽  
Line Singularity ◽  
Air Intake ◽  
Volume Method ◽  
Intake Flow

The accuracy of CFD for simulating hypersonic air intake flow is verified by calculating the flow inside a Busemann type intake. The CFD results are then compared against the “exact” solution for the Busemann intake as calculated from the Taylor-McColl equations for conical flow. The method proposed by G. Emanuel (the Lens Analogy) for generating an intake shape that transforms parallel and uniform hypersonic (freestream) flow isentropically to another parallel and uniform, less hypersonic, flow has been verified by CFD (SOLVER II) simulation, based on Finite Volume Method (FVM). The shock-less (isentropic) nature of the Lens Analogy (LA) flow shapes has been explored at both on and off-design Mach numbers. The Lens Analogy (LA) method exhibits a limit line (singularity) for low Mach number flows, where the streamlines perform an unrealistic reversal in direction. CFD calculations show no corresponding anomalies.

scholarly journals Shock-less Hypersonic Intakes

2021 ◽  
Author(s):  
Seyed Hossein Miri
Keyword(s):  
Exact Solution ◽  
Mach Number ◽  
Finite Volume Method ◽  
Conical Flow ◽  
Low Mach Number ◽  
Simulation Based ◽  
Line Singularity ◽  
Air Intake ◽  
Volume Method ◽  
Intake Flow

The accuracy of CFD for simulating hypersonic air intake flow is verified by calculating the flow inside a Busemann type intake. The CFD results are then compared against the “exact” solution for the Busemann intake as calculated from the Taylor-McColl equations for conical flow. The method proposed by G. Emanuel (the Lens Analogy) for generating an intake shape that transforms parallel and uniform hypersonic (freestream) flow isentropically to another parallel and uniform, less hypersonic, flow has been verified by CFD (SOLVER II) simulation, based on Finite Volume Method (FVM). The shock-less (isentropic) nature of the Lens Analogy (LA) flow shapes has been explored at both on and off-design Mach numbers. The Lens Analogy (LA) method exhibits a limit line (singularity) for low Mach number flows, where the streamlines perform an unrealistic reversal in direction. CFD calculations show no corresponding anomalies.

scholarly journals Exact solution and the multidimensional Godunov scheme for the acoustic equations

2022 ◽  
Author(s):  
Wasilij Barsukow ◽  
Christian Klingenberg
Keyword(s):  
Exact Solution ◽  
Mach Number ◽  
Euler Equations ◽  
Two Dimensions ◽  
Finite Volume Scheme ◽  
Godunov Scheme ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Acoustic Equations ◽  
Spatial Dimensions

The acoustic equations derived as a linearization of the Euler equations are a valuable system for studies of multi-dimensional solutions. Additionally they possess a low Mach number limit analogous to that of the Euler equations. Aiming at understanding the behaviour of the multi-dimensional Godunov scheme in this limit, first the exact solution of the corresponding Cauchy problem in three spatial dimensions is derived. The appearance of logarithmic singularities in the exact solution of the 4-quadrant Riemann Problem in two dimensions is discussed. The solution formulae are then used to obtain the multidimensional Godunov finite volume scheme in two dimensions. It is shown to be superior to the dimensionally split upwind/Roe scheme concerning its domain of stability and ability to resolve multi-dimensional Riemann problems. It is shown experimentally and theoretically that despite taking into account multi-dimensional information it is, however, not able to resolve the low Mach number limit.

scholarly journals Semiconservative reduced speed of sound technique for low Mach number flows with large density variations

2019 ◽  
Vol 622 ◽  
pp. A157 ◽  
Author(s):  
H. Iijima ◽  
H. Hotta ◽  
S. Imada
Keyword(s):  
Mach Number ◽  
Speed Of Sound ◽  
Mass Density ◽  
Low Mach Number ◽  
Efficient Simulation ◽  
Large Density ◽  
Background Density ◽  
Density Perturbations ◽  
Volume Method ◽  
Numerical Domain

Context. The reduced speed of sound technique (RSST) has been used for efficient simulation of low Mach number flows in solar and stellar convection zones. The basic RSST equations are hyperbolic and are suitable for parallel computation by domain decomposition. The application of RSST is limited to cases in which density perturbations are much smaller than the background density. In addition, nonconservative variables are required to be evolved using this method, which is not suitable in cases where discontinuities such as shock waves coexist in a single numerical domain. Aims. In this study, we suggest a new semiconservative formulation of the RSST that can be applied to low Mach number flows with large density variations. Methods. We derive the wave speed of the original and newly suggested methods to clarify that these methods can reduce the speed of sound without affecting the entropy wave. The equations are implemented using the finite volume method. Several numerical tests are carried out to verify the suggested methods. Results. The analysis and numerical results show that the original RSST is not applicable when mass density variations are large. In contrast, the newly suggested methods are found to be efficient in such cases. We also suggest variants of the RSST that conserve momentum in the machine precision. The newly suggested variants are formulated as semiconservative equations, which reduce to the conservative form of the Euler equations when the speed of sound is not reduced. This property is advantageous when both high and low Mach number regions are included in the numerical domain. Conclusions. The newly suggested forms of RSST can be applied to a wider range of low Mach number flows.

scholarly journals Convergence Analysis of a Discontinuous Finite Volume Method for the Signorini Problem

2020 ◽  
Vol 12 (4) ◽  
pp. 49
Author(s):  
Yuping Zeng ◽  
Fen Liang
Keyword(s):  
Exact Solution ◽  
Error Estimate ◽  
Convergence Analysis ◽  
Finite Volume Method ◽  
Finite Volume ◽  
A Priori ◽  
Energy Norm ◽  
Signorini Problem ◽  
A Priori Error Estimate ◽  
Volume Method

We introduce and analyze a discontinuous finite volume method for the Signorini problem. Under suitable regularity assumptions on the exact solution, we derive an optimal a priori error estimate in the energy norm.

The Implementation of Cell-Centred Finite Volume Method over Five Nozzle Models

2013 ◽  
Vol 393 ◽  
pp. 305-310
Author(s):  
Abobaker Mohammed Alakashi ◽  
Hamidon Bin Salleh ◽  
Bambang Basuno
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Mach Number ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Finite Volume Methods ◽  
Partial Differential ◽  
One Dimensional ◽  
Flow Domain ◽  
Volume Method

The continued research and development of high-order methods in Computational Fluid Dynamics (CFD) is primarily motivated by their potential to significantly reduce the computational cost and memory usage required to obtain a solution to a desired level of accuracy. The present work presents the developed computer code based on Finite Volume Methods (FVM) Cell-centred Finite Volume Method applied for the case of Quasi One dimensional Inviscid Compressible flow, namely the flow pass through a convergent divergent nozzle. In absence of the viscosity, the governing equation of fluid motion is well known as Euler equation. This equation can behave as Elliptic or as Hyperbolic partial differential equation depended on the local value of its flow Mach number. As result, along the flow domain, governed by two types of partial differential equation, in the region in which the local mach number is less than one, the governing equation is elliptic while the other part is hyperbolic due to the local Mach number is a higher than one. Such a mixed type of equation is difficult to be solved since the boundary between those two flow domains is not clear. However by treating as time dependent flow problems, in respect to time, the Euler equation becomes a hyperbolic partial differential equation over the whole flow domain. There are various Finite Volume Methods can be used for solving hyperbolic type of equation, such as Cell-centered scheme, Cusp Scheme Roe Upwind Scheme and TVD Scheme. The present work will concentrate on the case of one dimensional flow problem through five nozzle models. The results of implementation of Cell Centred Finite Volume method to these five flow nozzle problems are very encouraging. This approach able to capture the presence of shock wave with very good results.

Sign in / Sign up

Export Citation Format

Share Document