Inviscid Flow Research Articles

Computational Studies of the Aerophysical Characteristics on the Head Part of the Supersonic Body of Rotation During Flight Along Trajectories

The use of modern computer systems for calculating the aerophysical characteristics of supersonic bodies of revolution together with the calculation of the flight trajectory under conditions of continuously changing Mach and Reynolds numbers of the oncoming flow, the presence of transient regimes and non-isothermality in near-wall flows is often not possible due to the complexity of the organisation of the computational process. By using a number of integral methods for calculating inviscid flows and viscous compressible near-wall flows, taking into account the non isothermality and intermittency of the boundary layer, a method has been developed for calculating the friction and heating of supersonic bodies of revolution on the flight trajectory. On the basis of well-known flight experiments, the correlation dependences of the Reynolds numbers of the beginning of the transition on sharp cones were obtained and the method of corrections for spherical blunting of the head part was implemented. By calculating the intermittency function, the changeability of flow regimes in the boundary layer is established for a number of trajectories of the supersonic uncontrolled rocket projectile. Calculated dependences for aerodynamic friction, heat fluxes and projectile wall temperature on the flight time are obtained. The concept of combined calculation of aerophysical characteristics on the flight trajectory using numerical and integral methods is proposed.

Numerical and experimental study on the addition of surface roughness to micro-propellers

Micro aerial vehicles are making a large impact in applications such as search-and-rescue, package delivery, and recreation. Unfortunately, these diminutive drones are currently constrained to carrying small payloads, in large part because they use propellers optimized for larger aircraft and inviscid flow regimes. Fully realizing the potential of emerging microflyers requires next-generation propellers that are specifically designed for low Reynolds number conditions and that include new features advantageous in highly viscous flows. One aspect that has received limited attention in the literature is the addition of roughness to propeller blades as a method of reducing drag and increasing thrust. To investigate this possibility, we used direct numerical simulation to conduct a numerical investigation of smooth and rough propellers. Our results indicate that roughness produces a 2% increase in thrust and a 5% decrease in power relative to a baseline smooth propeller operating at the same Reynolds number of Rec = 6500, held constant by rotational speed. We complement our numerical findings using thrust-stand-based experiments of 3D-printed propellers identical to those of the numerical simulations. Our study indicates that surface roughness is an additional parameter within the design space for micro-propellers, which may offer improved drone efficiencies and payloads.

Smooth symmetric transonic isothermal flows with nonzero angular velocity

In this paper, the steady inviscid flows with radial symmetry for the isothermal Euler system are studied in an annulus. We present a complete classification of transonic radially symmetric flow patterns in term of physical boundary conditions at the inner and outer circle. By solving the one side boundary problem, we obtain that there exist accelerating or decelerating smooth transonic flows in an annulus. Moreover, the structural stability of these smooth symmetric transonic flows with nonzero angular velocity are further investigated. Furthermore, we examine the transonic solutions with shocks as well via prescribing suitable boundary conditions on the inner and outer circle.

FEM-BEM modeling dynamic responses of saturated soil around a fluid-filled lined tunnel subjected to water hammer

Dynamic stress responses of saturated soil around a fluid-filled lined tunnel caused by a water hammer are investigated by a frequency-domain FEM-BEM coupled model. The fluid is modeled as an inviscid and compressible fluid, the lining is modeled by elastic medium and conceptualized as a hollow cylinder of finite length, and the saturated poroelastic medium is adopted to model the soil. Initially, governing equations of fluid and those of lining are solved by FEM in the frequency domain, while those of soil are solved by BEM in the same domain. In the following, fluid, lining, and soil are coupled based on the conditions of deformation compatibility and force balance on their interfaces. Water pressure (inside the tunnel), the distribution of lining displacement and dynamic stress responses of saturated soil generated by the water hammer are presented. It is concluded that the dynamic stresses and the pore pressure change periodically in saturated soil under a water hammer. Modeling soil as an elastic medium inaccurately evaluates the distribution of lining displacement. The soil permeability has a significant influence on the normal stresses of soil and pore pressure but has a slight effect on the shear stresses of soil.

Transformation of a fully nonlinear breather-like package of internal waves over a bottom step in a layered fluid

In this paper, we study the process of transformation of a localized wave packet over a bottom step in a three-layer fluid, in which the height of the step is equal to or exceeds the thickness of the lower layer; therefore, density stratification becomes two-layer in the shallow water zone. In numerical experiments, both the height of the step and the width of the step were varied. The problem is solved in the framework of a fully nonlinear model of hydrodynamics of an inviscid incompressible stratified fluid. The primary analysis consisted in estimating the values of dimensionless parameters used, as a rule, in runup problems: the Froude and Iribarren numbers, the ratio of the characteristic wavelength to the characteristic slope width, the ratio of the topographic slope to the characteristic wave beam angle. Since the “cutoff” line for the lower pycnocline is partially or completely located on a step, one could expect the effects of run-up, breaking or reflection of waves propagating along the lower pycnocline, but this doesn’t happen. It is shown that the reflection of the wave packet from the step is minimal in all cases considered, a strong steepening of the wave is observed, but no breaking occurs in this case — the wave then just quickly decays on the lower pycnocline. An analysis of the spectral amplitudes and energy fields allows us to conclude that there is a transfer of energy from the lower pycnocline to the upper one. The breather in a two-layer fluid cannot exist, but the wave packet formed in the upper pycnocline after its destruction has much higher energy than it has before the step.

On the spurious effects in Lamb-vector-based force decomposition methods

Recent methods based on Lamb vector integration allow for a far-field formulation and decomposition of the whole aerodynamic force, with identification of local flow structures associated with the force generation. Different exact Lamb-vector-based force formulations were proposed in the past and the decomposition of total drag into lift-induced and parasite contributions was subject of very recent studies. However, inconsistencies were also reported, raising questions on the physical role of a non-zero induced drag found in two-dimensional flows. Moreover, the effect of the arbitrary pole (appearing in Lamb-vector-based formulas) on the numerical accuracy of such methods was never investigated. Additionally, the separation of parasite drag into viscous and wave drag contributions by Lamb vector field analysis is still questioned. In this paper, the accuracy of different force formulas and of the drag decomposition in lift-induced and parasite contributions is first analyzed, for steady flows. Two-dimensional numerical solutions around RAE2822 and NACA0012 airfoils are considered, the latter in both inviscid and viscous flows (at low and high Reynolds number), to analyze consistency between lift-induced/parasite drag definitions and the drag generated in isentropic flow conditions (reversible drag) or due to entropy production (irreversible drag). A spurious induced drag contribution (related to the streamwise momentum perturbation) is identified, resulting in negative induced drag values in two-dimensional flows. The effect of a shift in the pole location is also analysed, with reference to its impact on the total force and on drag decomposition accuracy, then a new approach to parasite drag breakdown into physical constituents (viscous and wave contributions) is proposed and results are compared against predictions obtained using consolidated thermodynamic-based methods and against available results from recent literature.

Velocity and energy of periodic travelling interfacial waves between two bounded fluids

For a periodic travelling irrotational wave propagating at the interface between two homogeneous, incompressible and inviscid fluids bounded by horizontal planes, we generalise the Stokes definitions for the velocity of the wave propagation. Under certain conditions imposed on the horizontal velocity of the motion at the interface and supposing that the horizontal components of the velocity in each layer never reach the wave speed, we prove that the mean horizontal velocity of propagation of the wave is greater than the generalised mean horizontal velocity of the mass of the fluid. We show that, for interfacial waves of small amplitude, the excess kinetic and potential energy of the fluid have the same magnitude, but different signs, and for the nonlinear setting, we prove that the excess kinetic energy is negative.

Dispersion of axisymmetric longitudinal waves propagating in an inhomogeneous prestressed hollow cylinder immersed in an inviscid compressible fluid

The paper investigates the dispersion of axisymmetric waves in a cylinder with inhomogeneous initial stresses caused by the hydrostatic pressure of the compressible inviscid fluid in which this cylinder is immersed. In the context of this study, the motion of the cylinder is described by the three-dimensional linearized equations for elastic waves in bodies with initial stresses, but the flow of the fluid is described by the linearized Navier-Stokes equations for compressible (barotropic) inviscid fluids. The initial stresses in the cylinder, due to the action of hydrostatic pressure on the outer surface of the cylinder, are determined according to the well-known Lame formulas of classical linear elasticity theory. The corresponding eigenvalue problem for the dispersion of axisymmetric waves propagating in the hydro-elastic system under consideration is solved using the discrete-analytic method. The dispersion equation is obtained and solved numerically. Concrete numerical investigations are carried out for three pairs of materials: Soft Rubber + Glycerin, Lucite + Water and Steel + Water. The dispersion curves obtained for these pairs of materials are presented and discussed for different values of the intensity of the external pressure. In particular, it is found that the inhomogeneous initial stresses in the cylinder cause zero group velocity (ZGV) points to appear on the dispersion curves of the lowest modes. However, the ZGV points (or modes) appear on the dispersion curves of the higher modes as a result of the contact of the hollow cylinder with the fluid.

Analysis of radiative absorption of acoustic Lamb waves in plates loaded with an inviscid non-conducting fluid.

The dependence of radiation losses into a liquid on the value of the displacement component U_3 normal to the plate on the surface of a piezoelectric plate was experimentally studied for Lamb waves of various orders. Waves whose phase velocity V_n in the plate are considered greater than the velocity of the longitudinal volumetric acoustic wave in the liquid V_l. It is shown that at small values of U3 there is no radiation into the liquid and the magnitude of radiation losses is close to zero even at V_n V_l; at large values of U_3, the magnitude of radiation losses is large and for Lamb waves in the YZ-LiNbO3 plate with a thickness normalized to the wavelength of 1.75 and frequency 16.97 MHz it reaches a value of 4 dB/mm, comparable to the radiative losses of surface acoustic waves in the same material.

Mapping Mean Velocity Field over Bed Forms Using Simplified Empirical-Moment Concept Approach

The log-wake law was successful in mapping velocity fields for uniform flow over flat surfaces, even in cases of wake effects (velocity dips, wall effects, and secondary currents). However, natural riverbeds with undulations and bedforms challenge these models. This study introduces a moment-based empirical method for rough estimation of the velocity fields over stationary 2D bedforms. It proposes three polynomial velocity profile templates (first, fifth, and eighth orders) with coefficients deduced analytically while taking into account an array of flow conditions and assumptions, including slip velocity at the bed, mass and moment of momentum conservations, imposing inviscid potential flow near the water surface, and incorporation of near-bed shear stress utilizing a moment-based Chezy formula. Remarkably, the coefficients of these polynomials are primarily reliant on two crucial velocity scales, the depth-averaged velocity (uo) and the moment-derived integral velocity (u1), along with the dimensionless reattachment coefficient (Kr). Validation of the proposed approach comes from ten lab experiments, spanning Froude numbers from 0.1 to 0.32, offering empirical data to validate the obtained velocity profiles and to establish the relationship of the spatial variation in the normalized u1 velocity along bedforms. This study reveals that the assumption of a slip boundary condition at the bed generally enhances the accuracy of predicted velocity profiles. The eighth-order polynomial profile excels within the eddy zone and close to reattachment points, while the fifth-order profile performs better downstream, approaching the crest. Importantly, the efficacy of this approach extends beyond water flow to encompass airflow scenarios, such as airflow over a negative step. The research findings highlight that linear velocity, as employed in Vertically Averaged and Moment models (VAM), exhibits approximately 70% less velocity mismatch compared to constant Vertically Averaged (VA) models. Moreover, the utilization of the fifth-order and eighth-order velocity profiles results in substantial improvements, reducing velocity mismatch by approximately 86% and 90%, respectively, in comparison to VA models. The insights gained from this study hold significant implications for advancing vertically averaged and moment-based models, enabling the generation of approximate yet more realistic velocity fields in scenarios involving flow over bedforms. These findings directly impact applications related to sediment transport and mixing phenomena.

On the global-in-time inviscid limit of the 3D degenerate compressible Navier-Stokes equations

In this paper, the global-in-time inviscid limit of the three-dimensional (3D) isentropic compressible Navier-Stokes equations is considered. First, when viscosity coefficients are given as a constant multiple of density's power ((ρϵ)δ with δ>1), for regular solutions to the corresponding Cauchy problem, via introducing one “quasi-symmetric hyperbolic”–“degenerate elliptic” coupled structure to control the behavior of the velocity near the vacuum, we establish the uniform energy estimates for the local sound speed in H3 and (ρϵ)δ−12 in H2 with respect to the viscosity coefficients for arbitrarily large time under some smallness assumption on the initial density. Second, by making full use of this structure's quasi-symmetric property and the weak smooth effect on solutions, we prove the strong convergence of the regular solutions of the degenerate viscous flow to that of the inviscid flow with vacuum in H2 for arbitrarily large time. It is worth pointing out that the result obtained here seems to be the first one on the global-in-time inviscid limit of solutions with large velocities and vacuum for compressible flow in 3D space without any symmetric assumption.

Adjoint and Direct Characteristic Equations for Two-Dimensional Compressible Euler Flows

The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D steady-state Euler equations and the first goal of this paper is to present a linear algebra analysis that greatly simplifies the discussion of the number of independent characteristic equations satisfied along a family of characteristic curves. This method may be applied for both the direct and the adjoint problem. Our second goal is to directly derive in conservative variables the characteristic equations of 2D compressible inviscid flows. Finally, the theoretical results are assessed for a nozzle flow with a classical scheme and its dual consistent discrete adjoint.

The Influence of the Material Properties of an Inhomogeneous Pre-Stressed Hollow Cylinder Containing an Inviscid Fluid on the Dispersion of Quasi-Scholte Waves

The Influence of the Material Properties of an Inhomogeneous Pre-Stressed Hollow Cylinder Containing an Inviscid Fluid on the Dispersion of Quasi-Scholte Waves

A two-phase fluid model for epidemic flow.

We propose a new mathematical and computational modeling framework that incorporates fluid dynamics to study the spatial spread of infectious diseases. We model the susceptible and infected populations as two inviscid fluids which interact with each other. Their motion at the macroscopic level characterizes the progression and spread of the epidemic. To implement the two-phase flow model, we employ high-order numerical methods from computational fluid dynamics. We apply this model to simulate the COVID-19 outbreaks in the city of Wuhan in China and the state of Tennessee in the US. Our modeling and simulation framework allows us to conduct a detailed investigation into the complex spatiotemporal dynamics related to the transmission and spread of COVID-19.

Fundamental solutions to ship-motion problems with viscous effects

The fundamental solution of the ship-motion problem, known as the ship-motion Green function associated with a pulsating and translating source, is formulated and analyzed based on the weakly damped free-surface flows. The inclusion of viscous effects modifies the dispersion relation, resulting in the existence of three wavenumbers instead of two, as observed in inviscid fluids. The Green function with viscous effects is examined in relation to these three complex wavenumbers, and novel formulations of Havelock's type are developed. Special attention is paid to the analysis of several numerical issues and the treatment to resolve them. The wavenumber integral function involved is analyzed using contour integration in the complex plane, leading to a classical formulation that includes the exponential integral function and a constant function representing the contributions of residues. Additionally, new series and Taylor expansions are developed to facilitate the integration of the ship-motion Green function on ship hull and the free surface. Furthermore, derivatives and antiderivatives of the wavenumber integral function have been obtained for all three formulations. Numerical examples are included to illustrate the soundness of the formulations and their efficiency in numerical evaluations. At the critical frequency, in particular, the Green function with viscous effects is shown to be finite and its magnitude decreases along the horizontal distance from the source. Finally, benefits of introducing viscous effects in the fundamental solution are examined and emphasized in the discussion and conclusions.

High temperature non-equilibrium flow characteristics of impinging shock/flat-plate turbulent boundary layer interaction at Mach 8.42

There are fewer reports on the impinging shock/boundary layer interaction in the high Mach number and high-temperature flow than that in the supersonic flow. High-temperature flow characteristics of the impinging shock/flat-plate turbulent boundary layer interaction (IS/FTBLI) at Mach 8.42 are numerically investigated by solving two-dimensional Reynolds averaged Navier–Stokes equations coupling with the thermal–chemical non-equilibrium model. An impinging shock is formed by the wedge with a 10° deflection angle. The inviscid flow parameters ahead of the cowl of a Mach 12 inlet are selected as the free-stream condition of this study. The primary emphasis of this study lies in understanding the thermal–chemical non-equilibrium effects in the IS/FTBLI. Moreover, the chemical non-equilibrium effects similar to previous reports from others are utilized for the comparative analysis. Our findings reveal that the vibrational or thermal non-equilibrium effects exhibit maximum prominence subsequent to the intersection of the impinging shock with separation shock, as well as in the convergence area of compression waves during the flow reattachment. On the other hand, the chemical non-equilibrium effects predominantly result from oxygen dissociation and atomic nitrogen production within the boundary layer; the chemical reactions are most intense within the separation zone. By comparing with a thermally perfect gas, a reduction in the flow separation is observed in the chemical non-equilibrium effects, but the flow separation is enhanced in the thermal–chemical non-equilibrium effects. The insights gained from our research are expected to contribute to the development of flow control technology in hypersonic IS/FTBLI scenarios and aid in configuring wave structures in the inner compression section of high Mach number scramjet inlets.

A free-streamline boundary-layer model for small-amplitude oscillation regime of square cylinder under vortex-induced rotation

Numerical studies about vortex-induced rotation (VIR) have shown that six regimes exist for the dynamics of square cylinder under VIR at small Reynolds numbers; however, theoretical explanations are still rare. Aiming at stepping a little further, we select one of these regimes, that is, small-amplitude oscillation regime, to develop an analytical model. In the present model, we expand the symmetric free streamline theory to an inviscid flow pasting an inclined plate and introduce the Blasius boundary layer theory in the calculation of viscous torque on a square cylinder. This model is supported by comparing with numerical results using the immersed boundary method. Results explain the mechanism of small-amplitude oscillation regime: the main sources of the out-of-phase torque come from the imbalanced distribution of pressure on the windward face and the asymmetric distribution of pressure and viscous force on the top/bottom face. An alternative way to determine the local flow parameters by global dynamic quantities is also proposed based on this model.

A discrete adjoint framework coupled with adaptive PCE for robust aerodynamic optimization of turbomachinery under flow uncertainty

Flow uncertainty is commonly encountered in turbomachinery. To mitigate the negative effects caused by the flow uncertainty, a framework coupled with adaptive polynomial chaos expansion (PCE) and discrete adjoint method for robust aerodynamic design optimization (RADO) of turbomachinery blades is developed. The optimization framework relies on gradient algorithms, which effectively avoids “dimensional curse” problem. Adaptive PCE method improves the efficiency of uncertainty quantification and only once PCE model need to be constructed in per optimization step, making the framework highly efficient. The PCE matrix and chain rule are employed to determine the gradient of the RADO objective function. This framework is employed for optimizing turbine blade, considering both inviscid and viscous flow. Monte Carlo simulation and finite difference PCE are used to validate the reliability of uncertainty quantification and gradient propagation methods. A comparative analysis of the optimization results obtained by both RADO and deterministic aerodynamic design optimization (DADO) is demonstrated. The higher robustness brought by RADO indicates the practicality of this framework in robust optimization of turbomachinery blades.

Wave Resistance Caused by a Point Load Steadily Moving on the Surface of a Floating Viscoelastic Plate

The wave resistance caused by a point load steadily moving on an infinitely extended viscoelastic plate floating on an inviscid fluid is analytically studied, which can be used to describe the response due to the motion of amphibious air-cushion vehicles on the continuous ice sheet on the ocean. The action of concentrated and distributed point loads are both considered. Under the assumptions that the fluid is incompressible and homogeneous and the motion of the fluid is irrotational, the Laplace equation is taken as the governing equation. For the floating plate, the Kelvin–Voigt viscoelastic model is employed. At the plate–fluid interface, linearized boundary conditions are used when the wave amplitude generated is less than its wavelength. The Fourier integral transform is performed to achieve the formal solution. The residue theorem is applied to derive the response of flexural–gravity wave resistance. It is indicated that for a point load with a uniform rectilinear motion, the wave resistance shows a sharp decrease with the increase in the moving speed when the load velocity is greater than the minimum phase velocity. There is no steady wave resistance when the load velocity is smaller than the minimum phase velocity. The effects of different parameters are obtained. Wave resistance decreases with the increasing plate thickness, viscoelastic parameter, and Poisson’s ratio, especially for a small value of viscoelastic parameter.

Similarity Analysis for Two-Dimensional Hypersonic Inlets Restart

The restart ability of inlets is significant to the robustness of hypersonic airbreathing vehicles. Classic starting theories based on the one-dimensional and inviscid flow assumption cannot predict the restart boundary accurately. To overcome the classic theories, the restart characteristics of two-dimensional contraction ducts in viscous flow are numerically studied. The restart boundaries for different configurations and flow conditions are determined, and the restart similarity laws are discovered. With the proposed dimensionless quantities (the dimensionless cowl length and the effective throat-entrance area ratio), the influences of multiple factors on restart are described simultaneously in a concise self-similar formulation. The restart characteristics can be described with any two variables in cowl angle, dimensionless cowl length, and effective area ratio. The restarts of two-dimensional inlets are classified into three types of the short-cowl, transitional, and long-cowl restarts according to the features of restart boundary lines and the flow structure. The three restart types are dominated by the competition between the cowl shock system and cowl tail expansion waves, the cowl shock system alone, and the complementation between the cowl shock system and throat choke, respectively. The wall pressure criteria for restart are correlated with the dimensionless cowl length and the characteristic separation scale at the restart critical state. It is observed that Kantrowitz limit is not generalizable for restart boundaries.