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The objective of the study is realizing the effect of fuel mass flow rate and flight speed on combustion in scramjet engine. DLR conical strut based scramjet combustor configuration was chosen and simulated the chemical reaction between the air and hydrogen fuel. A slot of size 40 mm × 0.295 mm provided at the center of the strut to injected hydrogen fuel from the rare side in to the downstream flow. ICEM CFD software is used for the generation of structured elements in computational domain for three dimensional flow analyses. Standard k-epsilon turbulence model and species transport equation is used in ANSYS fluent solver. The predicted temperature, velocity distribution along the axial length was compared with the experimental results and validated. The temperature distribution at different Mach numbers and mass flow rate reveals that the peak temperature increased with the flight speed and inlet fuel mass flow rate. The peak temperature noticed at the center of the combustor is around 3500 K at a flight speed of Mach 4. The predicted variation of temperature, pressure, velocity in the combustor and the flow structure for reacting flow facilitate good understanding of the combustion process in scramjet combustor. [ABSTRACT FROM AUTHOR]

Featured Application: Design of linear cascades for high-speed bladed machinery. This paper presents the development of high-specific-speed mixed flow/centrifugal compressor vaned diffusers. Specifically, the design of a test rig that will make the visualization of shock waves on diffuser vanes manageable is addressed in the current study. In this particular case, linearization of an existing state-of-the-art compressor stage was used. For the computational modeling, a series of RANS analyses were conducted to examine the flow characteristics of the two cases explored: a complete transonic cascade and an idealized periodic passage. The distinct behavior exhibited by each vane passage within the entire cascade offers the opportunity to analyze the shockwave structures across a mass flow range of ±9% around the design point. Overall, the pressure coefficient distributions and flow field patterns appear to align with the single-passage conditions, although there are some minor lateral wall influences, particularly in the first passage close to the suction lateral wall. However, because of the nature of the flow, which is characterized by high velocity and density differences near the vanes, the equivalent mass flow per individual passage was difficult to estimate. This may also be attributed to the small endwall axial vortices; nonetheless, for the purposes of this paper, this was of little consequence. [ABSTRACT FROM AUTHOR]

In this article, a numerical study of compressible and weak compressible Newtonian flows is achieved for a time marching, Galerkin algorithm. A comparison between two numerical techniques for such flows, namely the artificial compressibility method (AC–method) and the fully artificial compressibility method (FAC–method) is performed. In the first artificial compressibility parameter (C²) is added to the continuity equation, while this parameter is added to both continuity and momentum equations in the second technique. This strategy is implemented to treat the governing equations of Newtonian flow in cylindrical coordinates (axisymmetric). Particularly, this study concerns with the effect of the artificial compressibility parameters on the convergence level of solutions components. To confirm the analysis of these approaches, Poiseuille flow along a circular channel under an isothermal state is used as a simple test problem. The results show that when the AC-method is used there is a significant reduction in the level of time convergence of pressure and axial velocity compared to that with FAC-method. Here, for compressible flow the Tail model of state is employed to relate the pressure to density. In this context, the effect of Tail parameters and Reynolds number on the time convergence of solution components is also investigated in the present study. The results indicate a significant reduction in the time-stepping convergence as increasing in the {B,m}-value. In contrast, more difficulties are faced in the convergence when the level of the Reynolds number is increasing. [ABSTRACT FROM AUTHOR]

This paper presents the development of high-specific-speed mixed flow/centrifugal compressor vaned diffusers. Specifically, the design of a test rig that will make the visualization of shock waves on diffuser vanes manageable is addressed in the current study. In this particular case, linearization of an existing state-of-the-art compressor stage was used. For the computational modeling, a series of RANS analyses were conducted to examine the flow characteristics of the two cases explored: a complete transonic cascade and an idealized periodic passage. The distinct behavior exhibited by each vane passage within the entire cascade offers the opportunity to analyze the shockwave structures across a mass flow range of ±9% around the design point. Overall, the pressure coefficient distributions and flow field patterns appear to align with the single-passage conditions, although there are some minor lateral wall influences, particularly in the first passage close to the suction lateral wall. However, because of the nature of the flow, which is characterized by high velocity and density differences near the vanes, the equivalent mass flow per individual passage was difficult to estimate. This may also be attributed to the small endwall axial vortices; nonetheless, for the purposes of this paper, this was of little consequence.

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We show that the compressible Euler system for isentropic gas flow admits unbounded solutions. The examples are radial flows of similarity type and describe a spherically symmetric and continuous wave moving toward the origin. At time of focusing, both the density and the velocity become unbounded at the origin. This is followed by an expanding shock wave which slows down as it interacts with the incoming flow. While unbounded radial Euler flows have been known since the work of Guderley [Luftfahrtforschung, 19 (1942), pp. 302--311], those are at the borderline of the regime covered by the Euler model: The upstream pressure field vanishes identically (either because of vanishing temperature or vanishing density there). In contrast, the solutions we build exhibit an everywhere strictly positive pressure field, demonstrating that the geometric effect of wave focusing is strong enough on its own to drive the primary flow variables to infinity. [ABSTRACT FROM AUTHOR]

• The original completed Richardson extrapolation suffers from order limitation when used repeatedly. • A completed repeated Richardson extrapolation procedure for a more generic type of grid is presented. • The completed repeated Richardson extrapolation works with compressible fluid flow problems. • The achieved accuracy of first-order smooth solutions can be greatly improved. • The error magnitude of first-order solutions can be greatly reduced, even in solutions with shocks, except for the shock region. Richardson extrapolation is a powerful approach for reducing spatial discretization errors and increasing, in this way, the accuracy of the computed solution obtained by use of many numerical methods for solving different scientific and engineering problems. This approach has been used in a variety of computational fluid dynamics problems to reduce numerical errors, but its use has been restricted mainly to the computation of incompressible fluid flows and on grids with coincident nodes. In this work we present a completed repeated Richardson extrapolation (CRRE) procedure for a more generic type of grid not necessarily with coincident nodes, and test it on compressible fluid flows. Three tests are performed for one-dimensional and quasi-one-dimensional Euler equations: (i) Rayleigh flow, (ii) isentropic flow, and (iii) adiabatic flow through a nozzle. The last test involves a normal shock wave. To build a simple solver, these problems are solved by a first-order upwind-type finite difference method as the base scheme. The normal shock wave problem is also solved with a high-order weighted essentially nonoscillatory (WENO) scheme to compare it with the CRRE procedure. The procedure we propose can increase the achieved accuracy and significantly decrease the magnitude of the spatial error in all three tests. Its performance is best demonstrated in the Rayleigh flow test, where the spatial discretization error is reduced by seven orders of magnitude and the achieved accuracy is increased from 0.998 to 6.62 on a grid with 10,240 nodes. Similar performance is observed for isentropic flow, for which the spatial discretization error is reduced by nine orders of magnitude and the achieved accuracy is increased from 0.996 to 6.73 on a grid with 10,240 nodes. Finally, in adiabatic flow with a normal shock wave, the procedure can reduce the spatial discretization error both upstream and downstream of the shock. However, the more expensive high-order WENO scheme results in errors of lower magnitude upstream of the shock and a sharper shock transition for this shocked test case. [ABSTRACT FROM AUTHOR]

The phenomena of concentration and cavitation and the formation of delta shock waves and vacuum states in vanishing pressure limits of solutions to the generalized Chaplygin Euler equations of compressible fluid flow are analyzed. It is proved that, as the pressure vanishes, any two-shock-wave Riemann solution of the generalized Chaplygin Euler equations of compressible fluid flow tends to a delta-shock solution to the transport equations, and the intermediate density between them tends to a weighted δ -measure that forms a delta shock wave; any two-rarefaction-wave solution is shown to tend to two contact discontinuities connecting the constant states and vacuum states, which form a vacuum solution of the transport equations. Moreover, some numerical simulations completely coinciding with the theoretical analysis are presented. [ABSTRACT FROM AUTHOR]

• Compressible multicomponent flow simulations of high-speed LDI are conducted for various impact Mach numbers. • A self-similar structure for the pressure field is observed. • A data-driven approach for realistic and quick simulations of high-speed LDI is presented. Accurate prediction of the force exerted on a droplet during high-speed liquid droplet impingement (LDI) is challenging yet important for the safety management of nuclear/fossil power plants. This paper describes compressible multicomponent flow simulations and data-driven modeling of high-speed LDI. The compressible multicomponent flow simulations are conducted for various impact Mach numbers ranging from Ma = 0.045 to 0.077. Whereas the peak force associated with the water hammer shock exhibits dependency on the impact Mach number, a self-similar structure for the pressure field within the small region about the impact plane is observed during high-speed LDI. An important observation is that the nondimensional mass-averaged droplet velocity does not vary with the impact Mach number. Finally, a data-driven LPP approach is presented to obtain fast and highly realistic simulations of high-speed LDI. [ABSTRACT FROM AUTHOR]

We concern with the Riemann problem the compressible fluid flow with the generalized Chaplygin gas. With the analysis on the phase plane, we rigorously confirm the occurrence of delta shock wave with Dirac delta function in density. Then the formation mechanism, generalized Rankine–Hugoniot relation and entropy condition for the delta shock wave are clarified. Based on these preparations, five kinds of exact solutions are obtained. Finally, the corresponding numerical results are also presented to illustrate our analysis. [ABSTRACT FROM AUTHOR]

The evolution of surface profiles during erosion caused by the continuous impact of a liquid jet was studied using a water-jet apparatus. In this study, we focused on the erosion transition from the incubation stage to the accumulation stage during liquid impingement erosion, which is important for water-jet cleaning and aging management for nuclear power plants. By computing the local erosion rate distribution and surface roughness parameters, the formations of isolated pits and asperities were investigated. The structure of erosion caused by liquid impingement was extracted by using a dynamic mode decomposition technique. The surface profile changes were primarily caused by the formation of isolated pits and asperities during the incubation stage. The roughness parameters remained unchanged during the incubation stage, with barely measurable erosion depth, whereas the skewness of the surface profile began to increase during this stage. The initial erosion with a small-scale roughness gradually evolved into a large-scale crater. Dynamic mode decomposition analysis showed the presence of a short-wavelength (mode A) surface depression during the incubation stage, followed by a long-wavelength (mode B) erosion crater caused by the merging of mode A surface depressions during the accumulation stage. • Erosion stage transition in liquid impingement erosion was experimentally studied. • Dynamic mode decomposition method was employed to analyze the erosion stage transition. • Erosion stage transitions were highly correlated with the roughness parameters and modes. [ABSTRACT FROM AUTHOR]

Tubes are commonly used in pneumatic systems for transferring energy and control signals. Using the control volume method, a mathematical tube model has been developed, which takes into account the effect of resistance, capacitance and inertance on the dynamic properties of control and supply circuits of pneumatic systems. The adequacy of the computer model developed in Matlab/Simulink was verified by comparing the results of simulation studies with the results of experimental tests of airflow through tubes of varying diameter and length. The advantage of the computer model is the capability to model pneumatic systems under varying conditions of heat exchange with the environment by changing the coefficient of the polytropic process coefficient. [ABSTRACT FROM PUBLISHER]

This paper introduces a virtual boundary method for compressible viscous fluid flow that is capable of accurately representing moving bodies in flow and aeroacoustic simulations. The method is the compressible extension of the boundary data immersion method (BDIM, Maertens & Weymouth (2015), [18] ). The BDIM equations for the compressible Navier–Stokes equations are derived and the accuracy of the method for the hydrodynamic representation of solid bodies is demonstrated with challenging test cases, including a fully turbulent boundary layer flow and a supersonic instability wave. In addition we show that the compressible BDIM is able to accurately represent noise radiation from moving bodies and flow induced noise generation without any penalty in allowable time step. [ABSTRACT FROM AUTHOR]

• Numerical simulations of the high-speed droplet impact on a wet wall were carried out. • Mechanism of force generation in droplet and liquid film were investigated. • Force exerted on droplet decreases with increasing liquid film thickness. • Force exerted on liquid film increases with increasing liquid film thickness. Recent research (Fujisawa, 2022a) has shown that the time-dependent force exerted on a droplet during high-speed [ O (100 m/s)] impact on a planar rigid wall is quite different from that of low-speed [ O (1 m/s)] impact case owing to the compressibility of the droplet. Here, we consider a more general case of a high-speed liquid droplet impacting a wall where a liquid film is present on the wall surface. Three-component Euler simulations were performed to determine the characteristics of the time-dependent force exerted on the droplet during high-speed liquid droplet impact on a planar rigid wet wall. Several initial liquid film thicknesses were considered. The strength of the force exerted on the droplet decreases in magnitude as the liquid film thickness increases, whereas the total force increases with increasing liquid film thickness owing to the presence of a water hammer shock that is reflected inside the liquid film. [ABSTRACT FROM AUTHOR]

We describe an added-mass partitioned (AMP) algorithm for solving fluid–structure interaction (FSI) problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements. The computational approach is a mixed Eulerian–Lagrangian scheme that makes use of deforming composite grids (DCG) to treat large changes in the geometry in an accurate, flexible, and robust manner. The current work extends the AMP algorithm developed in Banks et al. [1] for linearly elasticity to the case of nonlinear solids. To ensure stability for the case of light solids, the new AMP algorithm embeds an approximate solution of a nonlinear fluid–solid Riemann (FSR) problem into the interface treatment. The solution to the FSR problem is derived and shown to be of a similar form to that derived for linear solids: the state on the interface being fundamentally an impedance-weighted average of the fluid and solid states. Numerical simulations demonstrate that the AMP algorithm is stable even for light solids when added-mass effects are large. The accuracy and stability of the AMP scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi-analytical solution that is obtained for a rotating solid disk immersed in a fluid. The scheme is applied to the simulation of a planar shock impacting a light elliptical-shaped solid, and comparisons are made between solutions of the FSI problem for a neo-Hookean solid, a linearly elastic solid, and a rigid solid. The ability of the approach to handle large deformations is demonstrated for a problem of a high-speed flow past a light, thin, and flexible solid beam. [ABSTRACT FROM AUTHOR]

The major purpose of this article is to extend the field synergy principle from incompressible fluid flow to compressible fluid flow. Theoretical analysis and numerical simulation are both conducted. Theoretical analysis indicates that for compressible boundary-layer flow, dot production of static pressure gradient and velocity, and viscous dissipation could be involved in energy equation, which are absent in the incompressible boundary-layer energy equation. Therefore, the heat transfer of the compressible flow is determined by the synergy between total enthalpy gradient and velocity, instead by the synergy between static temperature gradient and velocity, thereby extending the FSP from incompressible fluid flow to compressible flow. Detailed numerical analysis is conducted for the compressible boundary-layer flow to numerically verify the above findings. [ABSTRACT FROM AUTHOR]

In most of the papers published on compressible fluid using pseudo the bond graph approach, momentum and kinetic energy effects have been neglected due to low speed. However, in convergent–divergent nozzles that the flow is supersonic, these models will lose their validation. For the purpose of considering kinetic energy in compressible fluid flow, this paper introduces a new field (KE-field) to pseudo bond graph. This field can also be used to extract the momentum equation on the gaseous models. Furthermore, Karnopp’s suggested relation for an isentropic nozzle is developed to a convergent–divergent nozzle. The simulation results show that the thrust force obtained from the simulations has a very good agreement to analytical relationships. Therefore, it suggests that the KE-field can be used for modelling the thrust force. As bond graph method has been implemented in many software applications such as MS1, SYMBOLS2000 and 20SIM®, the new field can also be used in these software. [ABSTRACT FROM PUBLISHER]

In this study, modelling, frequency analysis, and optimization of control processes are considered for the fluid flow in pipeline systems. A mathematical model of controlled pipeline elements with distributed parameters is proposed to describe the dynamical behaviour of compressible fluid which is transported in a long rigid tube. By exploiting specific functions representing cross-sectional forces and effective displacements as well as linear approximations of fluidic resistances, the original problem with non-uniform parameters is reduced to a partial differential equation (PDE) system with constant coefficients and homogeneous initial and boundary conditions. Three numerical approaches are applied to an efficient analysis of natural vibrations and reliable control-oriented modelling of pipeline elements. The conventional Galerkin method is compared with the method of integrodifferential relations based on a weak formulation of the constitutive laws. In the latter approach, the original initial-boundary value problem is reduced to the minimization of an error functional which provides explicit energy estimates of the solution quality. A novel projection approach is implemented on the basis of the Petrov–Galerkin method combined with the method of integrodifferential relations. This technique benefits from the advantages of the above-mentioned projection and variational approaches, namely sufficient numerical stability, a lower differential order, and an explicit quality estimation. Numerical optimization procedures, making use of a modified finite element technique, are proposed to obtain a feedforward control strategy for changing the pressure and mass flow inside the pipeline system to a desired operating state. At this given finite point of time, residual elastic oscillations inside the pipeline are minimized. Numerical results, obtained for ideal as well as viscous fluid models, are analysed and discussed. [ABSTRACT FROM PUBLISHER]

Abstract: In this article we describe a stable partitioned algorithm that overcomes the added mass instability arising in fluid–structure interactions of light rigid bodies and inviscid compressible flow. The new algorithm is stable even for bodies with zero mass and zero moments of inertia. The approach is based on a local characteristic projection of the force on the rigid body and is a natural extension of the recently developed algorithm for coupling compressible flow and deformable bodies [1–3]. The new algorithm advances the solution in the fluid domain with a standard upwind scheme and explicit time-stepping. The Newton–Euler system of ordinary differential equations governing the motion of the rigid body is augmented by added mass correction terms. This system, which is very stiff for light bodies, is solved with an A-stable diagonally implicit Runge–Kutta scheme. The implicit system (there is one independent system for each body) consists of only scalar unknowns in or space dimensions and is fast to solve. The overall cost of the scheme is thus dominated by the cost of the explicit fluid solver. Normal mode analysis is used to prove the stability of the approximation for a one-dimensional model problem and numerical computations confirm these results. In multiple space dimensions the approach naturally reveals the form of the added mass tensors in the equations governing the motion of the rigid body. These tensors, which depend on certain surface integrals of the fluid impedance, couple the translational and angular velocities of the body. Numerical results in two space dimensions, based on the use of moving overlapping grids and adaptive mesh refinement, demonstrate the behavior and efficacy of the new scheme. These results include the simulation of the difficult problems of shock impingement on an ellipse and a more complex body with appendages, both with zero mass. [Copyright &y& Elsevier]

Abstract: This paper presents an effective second-order three-dimensional unstructured multi-material arbitrary Lagrangian–Eulerian (MMALE) method for compressible fluid dynamics. This is an integration work. The MMALE method utilizes Moment of Fluid (MOF) capability with interface reconstruction for multi-material modeling of immiscible fluids. It is of the explicit time-marching Lagrange plus remap type. In the Lagrangian phase, the staggered compatible discretization for Lagrangian gas dynamics is used also with Tipton’s pressure relaxation model for the closure of mixed cells. For the remapping phase, an improved second-order cell-intersection-based method for three-dimensional unstructured mesh is presented. It is conservative for remapping cell-centered variables such as density and internal energy. It is suitable for remapping between two meshes with different topology. By using this remapping method, the new material centroid position in the rezoned cells can be geometrically computed. This enables it to be combined with the MOF algorithm for constructing a second-order MMALE method. The MMALE method can be implemented on three-dimensional unstructured hexahedral meshes. Numerical results have proved the accuracy and robustness of the MMALE method. [Copyright &y& Elsevier]

Three commonly used thermal equations of state for carbon dioxide, as well as the ideal gas law, have been compared against a large number of measurement data taken from the literature. Complex equations of state reach a higher accuracy than simple ones. The inaccuracy of the density function can cause large errors in fluid property correlations, such as heat capacity or viscosity. The influence of this inaccuracy on the results of numerical simulations have been evaluated by two examples: The first one assumes isothermal gas expansion from a volume, while the second one considers heat transport along a fracture. For both examples, different equations of state have been utilized. The simulations have been performed on the scientific software platform OpenGeoSys. The difference among the particular simulation results is significant. Apparently small errors in the density function can cause considerably different results of otherwise identical simulation setups. [ABSTRACT FROM AUTHOR]

We propose a mixed finite-element method for the motion of a strongly viscous, ideal and isentropic gas. At the boundary we impose a Navier slip condition such that the velocity equation can be posed in mixed form with the vorticity as an auxiliary variable. In this formulation we design a finite-element method, where the velocity and vorticity are approximated with the div- and curl-conforming Nédélec elements, respectively, of the first order and first kind. The mixed scheme is coupled to a standard piecewise constant upwind discontinuous Galerkin discretization of the continuity equation. For the time discretization implicit Euler time stepping is used. Our main result is that the numerical solution converges to a weak solution as the discretization parameters go to zero. The convergence analysis is inspired by the continuous analysis of Feireisl and Lions for the compressible Navier–Stokes equations. Tools used in the analysis include an equation for the effective viscous flux and various renormalizations of the density scheme. [ABSTRACT FROM PUBLISHER]

We propose and analyze a finite element method for a semi-stationary Stokes system modeling compressible fluid flow subject to a Navierslip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element method using the lowest order Nédélec spaces of the first kind, while the continuity equation is approximated by a piecewise constant upwind discontinuous Galerkin method. Our main result states that the numerical method converges to a weak solution. The convergence proof consists of two main steps: (i) To establish strong spatial compactness of the velocity field, which is intricate since the element spaces are only div or curl conforming. (ii) To prove the strong convergence of the discontinuous Galerkin approximations, which is required in view of a nonlinear pressure function. Some tools involved in the analysis include a higher space-time integrability estimate for the discontinuous Galerkin approximations, an equation for the effective viscous flux, various renormalized formulations of the discontinuous Galerkin method, and weak convergence arguments. [ABSTRACT FROM AUTHOR]

• High-speed liquid droplet impact on a planar rigid wall was numerically studied. • Time-dependent force and droplet pressures were computed and analyzed. • Oscillatory behavior of the time-dependent force was caused the reverberation inside the droplet. • Increased time-dependent force was observed with increasing droplet impact velocity. In this study, the effect of the impact velocity of a droplet on the time-dependent force exerted on the droplet and droplet pressure during high-speed [ O (100 m/s)] liquid droplet impingement (LDI) on a planar rigid wall is numerically investigated. The force exerted on the droplet and droplet pressures are computed as a function of time, and its frequency spectrum is analyzed to explain the physical mechanisms that occur during high-speed LDI. The results show that high-speed LDI involves the formation of a water hammer shock and its reflection on the free surface of the droplet and wall, resulting in sustained reverberation inside the droplet. Therefore, the force curve shows oscillatory behavior and is quite different from that of the low-speed [ O (1 m/s)] impact case. Finally, the force and the droplet pressure are computed for various impact velocities of the droplet. [ABSTRACT FROM AUTHOR]