Inviscid Calculations Research Articles

Study on the influence of expansion waves on the reflection type of shock wave in double-wedge configurations

Abstract This paper investigates how variations in the relative positioning between the expansion fan emitted from the triple point in the shock/shock interference on double-wedge geometries in confined spaces and the incidence point of oblique shocks influence the transition of oblique shock reflection types, and understands the roles of expansion waves in inhibiting MR. Predictive analysis through the shock polar line provides critical values for the transition of oblique shock reflection types under the influence of expansion fan effects. The position where the shock/expansion fan undergoes post-oblique reflection on the opposite sidewall can be controlled by adjusting the model’s contraction ratio (H 1/H 2). This study uses the density-based solver blastFOAM in openFOAM to numerically solve the Euler equations, conducting inviscid calculations of shock/shock interactions induced by double wedges in confined spaces with ideal gases. This study compares pressure values in different regions obtained from numerical simulations and examines the reflection types of oblique shocks on opposite sidewalls, confirming the feasibility of shock polar analysis and the accuracy of theoretical predictions.

Centrifugal Compressors Gas-Dynamic Characteristics Influence on the Refrigerating Machines Efficiency

The article is devoted to the study R134a refrigerating machine efficiency and consisting of a centrifugal compressor, a condenser, a temperature-regulating valve and an evaporator. The main purpose of the work is to analyze the centrifugal compressor gas dynamic characteristics effect on the refrigeration machine vapor-compression cycle efficiency. This goal is achieved through the study by actual working process numerical experiment in the refrigeration machine centrifugal compressor with an idealized process for other elements. The object of the study are the refrigeration machine characteristics, expressed by the theoretical refrigeration coefficient COPRt. Single-stage centrifugal compressors with the design conditional flow coefficient in the range from 0.035 to 0.12 are considered. The design of centrifugal compressors was carried out according to a new calculation method to the flow part efficiency increase. The method comprehensively combines the inviscid and viscous flow calculations with the use of the single-criteria and multiparametric optimization. Previously, the method was tested and compared with experimental data. The most important result is the results of the refrigeration cycle efficiency evaluating through the centrifugal compressors highly efficient flow parts design methodology application. An increase in COPRt was obtained taking into account the centrifugal compressor actual process in the range from 2.6% to 7.2%. The significance of the results obtained lies in the possibility of using high-efficiency centrifugal compressors gas dynamic characteristics for the chillers refrigeration cycles analysis and calculation. The level of the compressors isentropic efficiency ranges from 0.80 to 0.85, depending on the design conditional flow coefficient.

Computational Fluid Dynamics Study of NACA 0012 Airfoil Performance with OpenFOAM®

Numerical methodologies have been implemented in most recent years in order to predict the lift and drag coefficients, the flow velocity, and the pressure distributions around the airfoil profiles in order to develop powerful computational tools based on the analysis of the main features, which describe the optimal wing or blade performance and predict a functional aerodynamic profile implemented to obtain the better energy efficiency generated, for different airplane designs. Computational Fluid Dynamics (CFD) analysis, computation, and prediction of inviscid and viscous two-dimensional flows are based on unsteady simulations of large systems with linear equations solved in a reasonable amount of computing resources. In this sense, Reynolds Averaged Navier Stokes (RANS) approach is generally applied for simulating the mean quantities of turbulent flows with high efficiency in the solving of differential equations of fluid flows into the control volume. However, Large Eddy Simulations are widely recognized to capture the main turbulent effects in a free stream influenced by the inertial forces of the airfoil displacement. Therefore, this research presents a CFD study of the NACA 0012 airfoil with the aim of checking the level of prediction and the numerical performance methodologies proposed by recent numerical reviews developed to study the description of turbulent flows analyzed with the Navier Stokes equations for incompressible flows with small temperature differences between the airfoil surface, and the air free stream. Numerical results have been analyzed in order to compare URANS and LES data used to predict physical variables and turbulent quantities that perform the airfoil profile in the virtual environment offered by OpenFOAM software.

Intermittent unsteady propulsion with a combined heaving and pitching foil

Inviscid computations are presented of a self-propelled virtual body connected to a combined heaving and pitching foil that uses continuous and intermittent motions. It is determined that intermittent swimming can improve efficiency when the dimensionless heave ratio is $h^* < 0.7$ while it degrades efficiency for $h^* \geq 0.7$. This is a consequence of the physical origins of the force production for pitch-dominated ($h^* < 0.5$) and heave-dominated ($h^* > 0.5$) motions. Based on insight derived from classic unsteady thin airfoil theory, it is discovered that pitch-dominated motions are driven by added-mass-based thrust production where self-propelled efficiency is maximized for high reduced frequencies, while heave-dominated motions are driven by circulatory-based thrust production where self-propelled efficiency is maximized by low reduced frequencies. Regardless of the dimensionless heave ratio the reduced frequency is high for small amplitude motions, high Lighthill numbers, and low duty cycles and vice versa. Moreover, during intermittent swimming, the stopping vortex that is shed at the junction of the bursting and coasting phases becomes negligibly weak for $h^* < 0.5$ and small amplitude motions of $A^* = 0.4$. This study provides insight into the mechanistic trade-offs that occur when biological or bio-inspired swimmers continuously or intermittently use combined heaving and pitching hydrofoils.

Performance of Two Types of High Speed, High Efficiency ‎Axisymmetric Intakes

Performance of two axisymmetric air intakes are compared at conditions suitable for Mach number range from 2 to 8. First is the Busemann intake and second is the reversed isentropic nozzle. The isentropic nozzle is built by the method of characteristics. The contour of this nozzle is taken as a compression surface for the incoming flow. Performances of these two intakes are compared by comparison of both viscous and inviscid CFD calculations at Mach 6. Viscous flow calculations show that the total pressure recovery in compression section is 0.8316 in the Busemann intake and 0.869 in the reversed isentropic nozzle intake.

Characterization of aerodynamic performance of ducted wind turbines: A numerical study

AbstractThe complex aerodynamic interactions between the rotor and the duct has to be accounted for the design of ducted wind turbines (DWTs). A numerical study to investigate the characteristics of flow around the DWT using a simplified duct–actuator disc (AD) model is carried out. Inviscid and viscous flow calculations are performed to understand the effects of the duct shape and variable AD loadings on the aerodynamic performance coefficients. The analysis shows that the overall aerodynamic performance of the DWT can be increased by increasing the duct cross‐sectional camber. Finally, flow fields using viscous calculations are examined to interpret the effects of inner duct wall flow separation on the overall DWT performance.

Multi-element ducts for ducted wind turbines: a numerical study

Abstract. Multi-element ducts are used to improve the aerodynamic performance of ducted wind turbines (DWTs). Steady-state, two-dimensional computational fluid dynamics (CFD) simulations are performed for a multi-element duct geometry consisting of a duct and a flap; the goal is to evaluate the effects on the aerodynamic performance of the radial gap length and the deflection angle of the flap. Solutions from inviscid and viscous flow calculations are compared. It is found that increasing the radial gap length results in an augmentation of the total thrust generated by the DWT, whereas a larger deflection angle has an opposite effect. Reasonable to good agreement is seen between the inviscid and viscous flow calculations, except for multi-element duct configurations characterized by large flap deflection angles. The viscous effects become stronger at large flap deflection angles, and the inviscid calculations are incapable of taking this phenomenon into account.

Centrifugal compressor impeller loading factor analysis

The loading factor performance modelling is an important part of centrifugal compressor performance calculation. The presented information on model stages’ test data confirms the fact that the loading factor versus flow coefficient at an impeller exit is a linear function independent of Mach number (subsonic flow). The test data and the design characteristics of the series of 10 model stages are compared with the calculation of an inviscid flow and with calculations done using the NUMECA software. Math models offered by the authors, and inviscid calculations solve the problem of a primary design. The CFD-calculation for final solution is non-satisfactory. If the loading factor is calculated by total temperature difference and flow coefficient is calculated by a continuity equation, the performance is not quite linear and lies much higher. For the considered stages CFD-calculation inaccuracy is + (0,06 … 0,12). CFD-calculated flow coefficient is inside 0,96 … 0,98 of the measured and of the calculated by the Math model.

High Angle-of-Attack Pitching Moment Characteristics of Slender-Bodied Reusable Rocket

The development of a fully reusable vertical-takeoff, vertical-landing rocket is indispensable for reducing space transportation costs. However, there are many technical issues associated with such vehicles, such as the safe execution of a turnover maneuver during return flight. It is known that a relatively desirable pitching moment characteristic for turnover can be accomplished by employing a slender-body configuration, but the reason for this is not well understood. In this study, a delayed detached-eddy simulation on the aerodynamic characteristics of such a slender-bodied reusable rocket is carried out for angles of attack between 0 and 180 deg using unstructured compressible computational fluid dynamics. Inviscid calculations are also conducted to distinguish the pitching moment contribution of the body configuration itself from the effects of viscosity and turbulence. It was found that two types of vortices were formed at 0–90 deg, and these vortices affected the pitching moment distribution. Three types of vortices generated at 90–180 deg were also observed. Combined with the results of the inviscid simulation, it is concluded that the pitching moment characteristic is greatly impacted by the behaviors of these vortices and bubbles.

Towards improving the aerodynamic performance of a ducted wind turbine: A numerical study

This paper aims to study the aerodynamic performance of ducted wind turbines (DWT) using inviscid and viscous flow calculations by accounting for the mutual interaction between the duct and the rotor. Two generalized duct cross section geometries are considered while the rotor is modelled as an actuator disc with constant thrust coefficient. The analysis shows the opportunity to significantly increase the overall aerodynamic performance of the DWT by a correct choice of the optimal rotor loading for a given duct geometry. Present results clearly indicate that the increased duct cross section camber leads to an improved performance for a DWT. Finally, some insights on the changes occurring to the performance coefficients are obtained through a detailed flow analysis.

Inviscid and RANS Simulation of the NASA-CRM Using the Cartesian Flow Solver UTCart

Inviscid and Reynolds-averaged Navier-Stokes (RANS) simulations of transonic flows around the NASA Common Research Model are conducted using the Cartesian flow solver UTCart. The immersed boundary method is used to represent the smooth geometry surfaces on the Cartesian grids. The wall function is combined with the immersed boundary method to reproduce the turbulent boundary layer on the geometry surface in the RANS simulations. In the inviscid calculations, the qualitative flow feature including the position on the shock-wave on the wing shows agreement with the reference result a body-fitted grid. In the RANS calculations, the trend of pitching moment and drag shows fair agreement with the reference result, while prediction of the flow separation at high angle of attack is still difficult. Compared with the reference result, the differences in the total drag coefficient at a moderate angle of attack on the medium grid (33 million cells) and the fine grid (99 million cells) are 31 drag counts (10%) and 20 drag counts (6.5%), respectively. Furthermore, each of the calculated aerodynamic coefficients shows a consistent trend of grid convergence toward the reference result.

The numerical study of the rake angle of impeller blade in centrifugal compressor

Investigated impellers have blade surfaces formed by straight generatrix. Blade profiles on shroud and disc surfaces are optimized by velocity diagram control (inviscid, quasi-three dimensional calculations). The blade profiles at hub and shroud blade-to-blade surfaces must be coordinated. A designer can choose the generatrix position at a trailing edge for it. The position is defined by the rake angle that is the angle between a trailing edge generatrix and a meridional plane. Two stages with 3D impellers, vaneless diffusers and return channels were investigated. Seven candidates of impellers of these stages with rake angles in range plus-minus 30 degrees were designed and investigated by quasi-three-dimensional inviscid calculation. CFD-calculations were made for the stages with these impellers. The optimal rake angle is minus 20 degrees for the high flow rate impeller due to lesser blade surface area and favorable meridian velocity field. Zero rake angle is optimal for the medium flow rate impeller where blade surface area is not so important. The combination of inviscid and viscid calculations is the informative instrument for further studies.

Secondary Flow Control in Low Aspect Ratio Vanes Using Splitters

Low aspect ratio vanes, often the result of overall engine architecture constraints, create strong secondary flows and high end-wall loss. In this paper, a splitter concept is demonstrated that reduces secondary flow strength and improves stage performance. An analytic conceptual study, corroborated by inviscid computations, shows that the total secondary kinetic energy (SKE) of the secondary flow vortices is reduced when the number of passages is increased and, for a given number of vanes, when the inlet end-wall boundary layer is evenly distributed between the passages. Viscous computations show that, for this to be achieved in a splitter configuration, the pressure-side leg of the low aspect ratio vane horseshoe vortex, must enter the adjacent passage (and not “jump” in front of the splitter leading edge). For a target turbine application, four vane designs were produced using a multi-objective optimization approach. These designs represent current practice for a low aspect ratio vane, a design exempt from thickness constraints, and two designs incorporating splitter vanes. Each geometry is tested experimentally, as a sector, within a low-speed turbine stage. The vane designs with splitter geometries were found to reduce the measured secondary kinetic energy, by up to 85%, to a value similar to the design exempt from thickness constraints. The resulting flow field was also more uniform in both the circumferential and radial directions. One splitter design was selected for a full annulus test where a mixed-out loss reduction, compared to the current practice design, of 15.3% was measured and the stage efficiency increased by 0.88%.

A study on the numerical dissipation of the Spectral Difference method for freely decaying and wall-bounded turbulence

Abstract This paper aims at understanding the numerical dissipation mechanisms related to the Spectral Difference (SD) method in the context of three-dimensional (3D) turbulence. The numerical dissipation stemming from the discretization of the convective terms is studied by performing inviscid computations of the transitional Taylor–Green vortex and isotropic turbulence configurations. The Taylor–Green vortex computations show that the increase in the order of accuracy restricts the numerical dissipation to smaller scales which, in turn, leads to a better representation of transitional mechanisms. However, isotropic turbulence computations using a fifth-order accuracy or above show obvious manifestations of under-resolution (such as the onset of oscillations and numerical noise), which suggests that the high-order numerical dissipation alone is unable to mimic the dissipation originating from sub-grid scales in the case freely decaying turbulence. Computations of the channel flow configuration at R e τ = 1000 at typical large-eddy simulation resolutions show that under-resolved SD discretizations using a high order of accuracy (fifth and sixth) lead to an excellent prediction of the wall-friction, the velocity profiles, the turbulent structures near the wall and the energy spectra, while lower order discretizations lead to an underestimation of the wall-friction and globally a poor representation of wall-bounded turbulence. The present study emphasizes the benefit of using high-order SD discretizations for an accurate representation of turbulent phenomena (namely, transitional and wall-bounded turbulence) but also the necessity of combining this approach with dynamic large-eddy simulation models or appropriate regularization techniques which would activate only where needed to recover physically consistent results, e.g. , in regions where fully developed turbulence is present.

Coupled analysis on the thickness-shear vibrations of a quartz plate resonator covered with micro-beams immersed in inviscid liquid and computation of the induced frequency-shift by the surface loadings

ABSTRACTThe dynamic equations of a quartz crystal resonator (QCR) vibrating in the thickness-shear modes (TSM) with the upper surface covered by an array of micro-beams, while the micro-beams are immersed in inviscid liquid, is established. A frequency-dependent effective mass ratio is put forward to simulate the effect of surface loadings (micro-beams immersed in liquid) on the dynamic characteristics of QCR. The seeping depth of vibration energy into liquid is analyzed and the added mass of liquid to micro-beams is examined. The induced frequency-shift of the compound QCR system consisting of QCR and the surface loadings is calculated in detail.

The numerical analysis of wind turbine airfoils at high angles of attack

Despite decades of research, the accurate numerical simulation of severely separated flows is still one of the major problems in computational fluid dynamics. In this paper, a viscous-coupled 3D panel method is proposed for the aerodynamic analysis of wind turbine airfoils at high angles of attack. The Hess–Smith panel method is adopted for inviscid calculations, and an empirically based boundary layer analysis is performed in order to determine the separation point. The separated thick wake is then modelled as an extension of the surface geometry along which a constant pressure distribution is assumed. The wake geometry is determined iteratively, and an outer iterative loop is run to update the location of the separation point. The validity of the current method’s results is assessed by comparison with experimental and numerical results for several high thickness wind turbine airfoils, namely NACA 63-430, FFA-W3-301, FFA-W3-241, and DU 91-W2-250. At low angles of attack, pressure data predicted by the current method show excellent agreement with the experimental data, as well as the referenced numerical data. At higher angles of attack, the current method shows reasonable agreement with the experimental data, while the referenced numerical data significantly overestimate the −C p distribution along the suction surface.

Effects of Numerical Diffusion on the Computation of Viscous Supersonic Flow Over a Flat Plate

The effects of numerical diffusion on the computation of supersonic viscous flow over a flat plate at zero incidences are numerically investigated. The inviscid flux terms in the Navier–Stokes equations are computed using three schemes, namely, van Leer’s Flux Vector Splitting, Liou and Steffen’s Advection Upstream Splitting Method (AUSM) and Jaisankar and Raghurama Rao’s Diffusion Regulated Local Lax Friedrichs (DRLLF) schemes. The results are correlated with the inherent numerical diffusion of these schemes. The study is also motivated by the necessity to examine whether reduced artificial viscosity can be used with the DRLLF scheme in computing viscous flows than was suggested in the original paper on inviscid computation. It is demonstrated that reduced artificial viscosity is not only possible, but it results in a scheme that is very efficient in the computation of the standard supersonic viscous flow over a flat plate, in that it is comparable in accuracy to the AUSM scheme in the boundary layer and better than it in shock resolution. Even with the reduced artificial viscosity suggested in this paper the DRLLF scheme shows good convergence behaviour comparable with the other two schemes.

21015 翼端間から発生する渦糸対と平板の干渉の可視化計測

In this study, we focus on substance transportation of counter-rotating vortex-pair in the uniform flow, and its interaction with a flat plate is visualized. A water tunnel and aluminum wings (NACA0012) are used to generate a wing-tip vortex pair. Visualization dyes used are fluorescein sodium salt and rhodamine B. The vortex-plate interactions with periodic entrainment are observed when the distance between a plate and vortex-pair are relatively close each other. Experiment and an inviscid vortex dynamics calculation with an Oseen vortex are different when vortex and plate are close, where the effect of a secondary vortex induced by viscosity is important.

Different Approximation Levels in Using CFD for the Design of Hypersonic Vehicles

In this paper the importance of using accurate CFD simulations in the design of hypersonic vehicles is stressed. The attention is focused on the one hand on the need to providing the vehicle designer with the estimated error bars together with the nominal values of the design parameters. On the other hand it is underlined how, in the different design phases, different levels of accuracy can be used, from simple inviscid computations to complex viscous non-equilibrium modellization, depending on the problem that must be solved. Then, the attention is focused on the kinetic models, from the classic macroscopic to the advanced models based on the state-to-state approach. Some examples of test cases that were used in the last years to validate CFD codes with respect to the kinetic modeling are presented, with the aim of emphasizing the potential advantages in using the state-to-state approach. Finally, preliminary results of the numerical rebuilding of wind tunnel test cases that are currently being performed in the framework of the Phys4Entry Project for code validation are shown.

Generation of steady longitudinal vortices in hypersonic boundary layer

AbstractIn this paper we study the three-dimensional perturbations produced in a hypersonic boundary layer by a small wall roughness. The flow analysis is performed under the assumption that the Reynolds number, $R{e}_{0} = {\rho }_{\infty } {V}_{\infty } L/ {\mu }_{0} $, and Mach number, ${M}_{\infty } = {V}_{\infty } / {a}_{\infty } $, are large, but the hypersonic interaction parameter, $\chi = { M}_{\infty }^{2} R{ e}_{0}^{- 1/ 2} $, is small. Here ${V}_{\infty } $, ${\rho }_{\infty } $ and ${a}_{\infty } $ are the flow velocity, gas density and speed of sound in the free stream, ${\mu }_{0} $ is the dynamic viscosity coefficient at the ‘stagnation temperature’, and $L$ is the characteristic distance the boundary layer develops along the body surface before encountering a roughness. We choose the longitudinal and spanwise dimensions of the roughness to be $O({\chi }^{3/ 4} )$ quantities. In this case the flow field around the roughness may be described in the framework of the hypersonic viscous–inviscid interaction theory, also known as the triple-deck model. Our main interest in this paper is the nonlinear behaviour of the perturbations. We study these by means of numerical solution of the triple-deck equations, for which purpose a modification of the ‘skewed shear’ technique suggested by Smith (United Technologies Research Center Tech. Rep. 83-46, 1983) has been used. The technique requires global iterations to adjust the viscous and inviscid parts of the flow. Convergence of such iterations is known to be a major problem in viscous–inviscid calculations. In order to achieve improved stability of the method, both the momentum equation for the viscous part of the flow, and the equations describing the interaction with the flow outside the boundary layer, are treated implicitly in this study. The calculations confirm the fact that in this sort of flow the perturbations are capable of propagating upstream in the boundary layer, resulting in a perturbation field which surrounds the roughness on all sides. We found that the perturbations decay rather fast with the distance from the roughness everywhere except in the wake behind the roughness. We found that if the height of the roughness is small, then the perturbations also decay in the wake, though much more slowly than outside the wake. However, if the roughness height exceeds some critical value, then two symmetric counter-rotating vortices form in the wake. They appear to support themselves and grow as the distance from the roughness increases.