Mach Number Contours Research Articles

Numerical evaluation of effects of the isolator height and the leading-edge bluntness on a scramjet inlet

Air-breathing hypersonic vehicles can be powered by scramjet (supersonic combustion ramjet) engines, whose inlet requires blunt leading edges in order to overcome the high heat fluxes that are inherent of hypersonic flights. Thus, this work has the purpose of evaluating, through detailed two-dimensional computational fluid dynamics analysis, the influence of the leading-edge bluntness and isolator height on the airflow of a scramjet intake. Three radii have been analyzed for the forebody and cowl leading edges: sharp, 0.5 and 1.0 mm. Moreover, two different isolator heights were varied: 15 and 20 mm. Fixed temperatures of 300 K and 1300 K were considered along the hypersonic vehicle wall. The static temperature, pressure, and Mach number contour are part of the analysis, as well as the Stanton number and the adiabatic kinetic efficiency of the scramjet. It was evidenced that both leading-edge bluntness and isolator height performed great influence on the intake airflow structure. Results showed that the isolator height had a major effect on the flow separation at the isolator entrance yielding a recirculation zone that increases with the isolator height. Furthermore, higher Stanton numbers and temperature along the isolator were found for the shorter isolator height due to stronger shock waves and higher frequency of shock-wave train. The leading-edge bluntness, in this analysis, was taken as a parameter to reduce the heat flux at the stagnation point of leading edges. However, a decrease in the adiabatic kinetic efficiency was observed when the leading-edge radius is increased. Moreover, blunt leading edges promoted a decrease in Stanton number along the scramjet intake walls and also a decrease in average temperatures throughout the isolator.

Effects of the Helmholtz Resonator on the Hartmann Whistle Operating at a High Nozzle Pressure Ratio

A numerical simulation is carried out to investigate the effect of the Helmholtz resonator capacity on the Hartmann whistle operating at high values of the nozzle pressure ratio using the turbulence model. The results of the present numerical simulations are compared to experimental data. The simulation results show that the frequency and amplitude of the Hartmann whistle with the Helmholtz resonator are obviously lower as compared to the conventional Hartmann whistle. Moreover, the Mach number contours and streamlines indicate that the Helmholtz resonator does not affect the shock-cell structure between the nozzle and the cavity, and the Hartmann whistle with the Helmholtz resonator has a. jet regurgitant mode that is different from the Hartmann whistle with a. straight resonator. The diameter of the Helmholtz resonator is an important factor affecting the fundamental frequency.

Numerical analysis of the effect of sweep-back angle on the stability derivatives of the grid fin

Because of high hinge moment of planar fin in supersonic flow, designers have become more attentive to the grid fin configuration in recent years. One of the disadvantages of the grid fin is its high drag force. Fortunately, this problem could be handled by implementing sweep-back angle. Few studies have been carried out to investigate the effects of the sweep-back angle on dynamic coefficients. In this paper, computational fluid dynamics is used to investigate the effect of grid fin’s sweep-back angle on the rolling and pitching dynamic coefficients in supersonic flow regime. The first step is dedicated to simulating two experimental geometries and detecting optimal mesh number and appropriate turbulence model. Unsteady dynamic coefficients along with moving mesh have been extracted by simulations. These coefficients are reported for different Mach numbers. In order to scrutinize the results, the static stability derivatives have been discussed, too. According to the simulations, each sweep-back angle has a unique trend of changing dynamic and static coefficients in terms of the Mach number. This trend is justified by studying Mach number contours for few states. Afterward, dynamic coefficients of the planar fin are presented and compared with the grid fin.

Aerodynamic design of the high pressure and low pressure axial turbines for the improved coal-fired recompression SCO2 reheated Brayton cycle

A new type of improved coal-fired recompression SCO2 Brayton cycle with a second split flow to the boiler was introduced. The design parameters of the high and low pressure turbines of the above SCO2 Brayton cycle were determined based on a consideration of the economics of the SCO2 system and the realization of the equipment. The self-compiled mean-line design program for two-stage SCO2 axial turbines was used to design the high and low pressure turbines for the 5 MW SCO2 Brayton cycle, with the important design data of the two turbines being given. RANS equations and the SST Turbulence Model were chosen for numerical simulation of the aerodynamic performance of two turbines in the design point and variable operating conditions that used ANSYS CFX and the real physical property data file of SCO2 from NIST software. Numerical results indicated that the isentropic efficiency of the SCO2 high pressure turbine and low pressure turbine with a good variable operating performance are 82.88% and 82.26% in the design point, respectively. The output power of the high pressure turbine and low pressure turbine are 3,251 kW and 6,156 kW, respectively, in the design point, which can meet the design requirements. The Cps curves, limited streamline spectrums, and the Mach number contours of the root, middle and top flow field of the turbine blades is reasonable.

Control of Aerodynamic Drag and Heating of Nose Cones Through Taper Spikes

The present work numerically and experimentally investigates Mach 5.8 flow past passively modified nose cone configurations such as taper/stepped taper spiked, spherically blunted, and parabolic nose cones at a fineness ratio of 3.6 and zero angle of attack in order to determine the best passively modified geometry that provides the control of both the aerodynamic drag coefficient and surface heat flux. The velocity vectors show the flow directions/recirculation zones and so on at the root of the taper as well as stepped taper spikes, whereas the Mach number contours show the features of shock in front of the taper/stepped taper spikes as well as the nose tip of the taper/stepped taper spiked blunted and parabolic nose cones. The present study reveals that the “stepped taper spiked parabolic nose cone” configuration provides lowest aerodynamic drag coefficient and surface heat flux as compared with all the other nose cone configurations investigated. The modifications in the flow/shock features such as the conversion of strong curved shock into weaker oblique shock waves, flow deceleration, and so on, at the root of the spike due to backward-facing steps in “stepped taper spiked parabolic nose cone” may be the reason for achieving lower aerodynamic drag/heating.

Hypersonic flow past a spherically blunted nose cone: A computational study

The present study investigates the aerodynamic characteristics of spherically blunted nose cone at a hypersonic Mach number of 5.8, numerically. The studies are conducted for different combinations of bluntness ratios and semi-cone angles, at zero angle of attack, in order to ascertain the nose cone parameters which provide minimum aerodynamic drag coefficient. The velocity vector shows the flow deceleration near the nose, re-acceleration through the sides as well the formation of recirculation zones. The structure of bow shock formed ahead of the nose as well as shock detachment distance is depicted by the Mach number contours. It is observed that the shock detachment distance follows linearly increasing behaviour with increase in bluntness ratios for all semi-cone angles studied. An empirical expression is developed for the shock detachment distance using the regression analysis, which reveals that it is mainly a function of bluntness ratio. It is observed that the aerodynamics drag coefficient attains a minimum value for smaller, bluntness ratios and semi-angle. Further, the aerodynamic drag coefficient is observed to be a strong function of bluntness ratios for smaller semi-cone angles.

Numerical Studies On Effect Of Changing Mach Number On Aero Disk Model On Flow Contours And Drag Force

A supersonic aircraft needs to travel in the atmosphere at different Mach numbers. In this paper the effect of Mach number on a body in hypersonic flow is studied. Also the effect of scaling on the flow behaviour is studied. As the original geometry taking more computational time, scaled model is used for further research. The geometry is modelled, meshed and solved in Ansys tool. Results are compared with available literature and further parametric study is done. There was no appreciable change found in the results obtained by scaled model compared with actual model. Hence Actual body[1] was scaled to 1/10th of its original scale body and simulated at different Mach numbers. The spike of the cone is fitted with an aero disk. Results shows that the angle of the bow shock inclined to body is found to be decreasing as the Mach number is increasing. Two separate shockwaves from disc and cone were found merged at higher Mach numbers. At starting Mach numbers the separation region was unaltered but after Mach number 3, Mach number contours show that flow deflected from aero disk has greater role in deciding the separation region ahead of cone. Further surface pressure graphs are plotted and effect on drag force were discussed.

Propagation of a strong shock over a random bed of spherical particles

Propagation of a strong incident shock through a bed of particles results in complex wave dynamics such as a reflected shock, a transmitted shock, and highly unsteady flow inside the particle bed. In this paper we present three-dimensional numerical simulations of shock propagation in air over a random bed of particles. We assume the flow is inviscid and governed by the Euler equations of gas dynamics. Simulations are carried out by varying the volume fraction of the particle bed at a fixed shock Mach number. We compute the unsteady inviscid streamwise and transverse drag coefficients as a function of time for each particle in the random bed for different volume fractions. We show that (i) there are significant variations in the peak drag for the particles in the bed, (ii) the mean peak drag as a function of streamwise distance through the bed decreases with a slope that increases as the volume fraction increases, and (iii) the deviation from the mean peak drag does not correlate with local volume fraction. We also present the local Mach number and pressure contours for the different volume fractions to explain the various observed complex physical mechanisms occurring during the shock–particle interactions. Since the shock interaction with the random bed of particles leads to transmitted and reflected waves, we compute the average flow properties to characterize the strength of the transmitted and reflected shock waves and quantify the energy dissipation inside the particle bed. Finally, to better understand the complex wave dynamics in a random bed, we consider a simpler approximation of a planar shock propagating in a duct with a sudden area change. We obtain Riemann solutions to this problem, which are used to compare with fully resolved numerical simulations.

Numerical simulation of a sonic-underexpanded jet impinging on a partially covered cylindrical Hartmann whistle

The present study numerically investigates the effect of a partially covered cylindrical shield on the flow/shock oscillation characteristics of a Hartmann whistle when the pulsating jet exits through the two small openings, (a) close to the cavity inlet, and (b) away from the cavity inlet, of the cylindrical shield. The relevant parameters that modify the flow/shock oscillations of the Hartmann whistle are the stand-off distance, nozzle pressure ratio, cavity length, cavity shield, jet diameter, etc. The pulsating nature of flow in a partially shielded Hartmann whistle is investigated for various stand-off distances to understand its effect in achieving effective flow control. The velocity vectors indicate that the partly shielded Hartmann whistle operates in the jet regurgitant mode with different regurgitant phases. It also shows that some amount of the jet near the cavity inlet gets diverted towards the shield and gets attached to it, whereas some exits out through the two shield openings which can be injected into the flow to be controlled. The Mach number contours indicate the flow deceleration/reacceleration zones, shock-cell structures as well as fluid column oscillations in shock-cells/cavity regions. The present study reveals that the stand-off distance and the jet diameter are the crucial parameters, which control the oscillation mechanisms in a partially covered Hartmann whistle for achieving effective flow control. Thus, this paper sufficiently demonstrates the role of stand-off distances, openings in the shield as well as jet diameter in modifying the flow/shock oscillation characteristics of a partially shielded Hartmann whistle in achieving the finest flow control.

Computational fluid dynamics of steam flow in a turbine control valve with a bell-shaped spindle

The steam flow in a bell-shaped control valve, located before an intermediate pressure cylinder of an ultra-supercritical steam turbine unit, was numerically investigated. Toward this end, the Reynolds-averaged Navier–Stokes (RANS) simulation approach using a shear stress transport (SST) turbulence model was first validated against wall pressure measurements in tests using a scaled valve model. The dependency of the full-scale valve’s steam flow patterns on its open ratio and pressure ratio was then established. The annular attachment flow and central detachment flow were classified and analyzed in terms of flow quantities including velocity vectors, Mach number contour, pressure distribution and turbulent kinetic energy contour. The numerical results demonstrate that the attachment flow was produced mainly by the annular wall-attached jet and the central reverse flow, whereas the detachment flow was mainly produced by the central detached-jet expansion and the ambient reverse flow. Further analysis of the flow field indicates that the transition from attachment flow to detachment flow could be satisfactorily explained in terms of the Coandă effect and was influenced mainly by the ratio of the valve seat’s radius to the valve’s lift displacement. In addition, when decreasing the valve’s pressure ratio to the critical detachment pressure ratio, two phenomena were observed: discrete elliptical regions with jet’s expansion-and-recompression in the Mach number contour and a spatial variation at the pressure profile along with reducing magnitude, which was induced by the interaction between the expansion wave and the compression wave in a Prandtl–Mayer expansion process. These findings are of great practical significance for the valve’s operation and design optimization.

Large-Eddy Simulation of Flow over a Wall-Mounted Hump with Separation and Reattachment

Wall-resolved large-eddy simulation of a model turbulent flow involving favorable and adverse pressure gradients, imposed by surface curvature of a wall-mounted hump, is performed for a spanwise-periodic computational domain. The flow acceleration over the front portion of the hump is strong enough to exceed the relaminarization criterion of Narasimha and Sreenivasan (“Relaminarization in Highly Accelerated Turbulent Boundary Layers,” Journal of Fluid Mechanics, Vol. 61, No. 3, 1973, pp. 417–447) but only over a relatively short streamwise extent. Although the flow does not relaminarize, turbulent skin-friction variation exhibits a plateau, also observed in the experiment of Greenblatt et al. (“A Separation Control CFD Validation Test Case, Part 1: Baseline and Steady Suction,” AIAA Journal, Vol. 44, No. 12, 2006, pp. 2820–2830), before it again continues to rise. The subsequent adverse pressure gradient is strong enough to cause flow separation. The location and extent of flow separation, including skin-friction distributions, compare reasonably well with experimental data. Computed velocity and Reynolds stress profiles are also compared with the experimental results. A systematic study of the effect of computational domain span, subgrid-scale model, tunnel backpressure, incoming boundary layer, grid refinement, Mach number, and top tunnel wall contour (which models the blockage effect of the experimental setup) is carried out, and sensitivity of the results to these parameters is discussed.

Meshfree simulation of flow around airfoil using different turbulent models

The moving least square meshfree method is used to solve the Reynolds-averaged Navier-Stokes equations with two different turbulence models: the renormalisation group (RNG) k-ε model and the Wilcox k-ω model. The moving least square approach with clouds-of-points reconstruction, which can provide results from highly anisotropic clouds of points, is adopted to approximate the spatial derivatives. Both the subsonic and transonic viscous flows around RAE2822 airfoil are simulated. The pressure coefficients of the airfoil surface are calculated, the Mach number contours of the flow fields are presented, and the mean velocity profiles of the boundary layer at different locations are investigated. Some unsteady viscous flow simulation results are also presented. The simulation results show a good agreement with the experiment results and other numerical simulation results. Overall, the simulation results demonstrate that the proposed meshfree numerical algorithm is accurate and capable of modelling turbulence flows around airfoils.

Meshfree Simulation of Flow around Airfoil using Different Turbulent Models

The moving least square meshfree method is used to solve the Reynolds-averaged Navier-Stokes equations with two different turbulence models: the renormalisation group (RNG) k-e model and the Wilcox k-ω model. The moving least square approach with clouds-of-points reconstruction, which can provide results from highly anisotropic clouds of points, is adopted to approximate the spatial derivatives. Both the subsonic and transonic viscous flows around RAE2822 airfoil are simulated. The pressure coefficients of the airfoil surface are calculated, the Mach number contours of the flow fields are presented, and the mean velocity profiles of the boundary layer at different locations are investigated. Some unsteady viscous flow simulation results are also presented. The simulation results show a good agreement with the experiment results and other numerical simulation results. Overall, the simulation results demonstrate that the proposed meshfree numerical algorithm is accurate and capable of modelling turbulence flows around airfoils.

Evaluation of scale-adaptive simulation for transonic cavity flows

Scale-adaptive simulations of transonic cavities with and without doors are presented in this paper. Results were compared with detached-eddy simulations for cavities with length-to-depth ratios of 5 and 7. The Mach and Reynolds numbers (based on the cavity length) were 0.85 and 6.5 × 106, respectively, and the grid sizes were 5.0 million for the clean cavity with doors-off and 5.5 million for the clean cavity with doors-on. Instantaneous Mach number contours showed that the shear layer broke down for both the doors on and doors off cases and that the flows had a high level of unsteadiness inside them. The two L/D ratios of cavities were seen to have similar acoustic signatures reaching maximum sound levels of 170 dB. Spectral analyses for the cavities without doors revealed that by changing the length-to-depth ratio from five to seven, the dominant acoustic modes at the front and rear of the cavities were shifted from the second and third modes to the first and second modes respectively. Proper orthogonal decomposition was used to reduce the data storage using modes constructed from flowfield snapshots taken at regular intervals.

Numerical simulation of jet flow impinging on a shielded Hartmann whistle

The present study numerically investigates the effect of shield on the flow characteristics of Hartmann whistle. The flow characteristics of un-shielded Hartmann whistle are compared with whistles of different shield heights 15 mm, 17 mm, 20 mm, 25 mm and 30 mm. The comparison of Mach number contours and transient velocity vectors of shielded Hartmann whistles with un-shielded ones for the same conditions reveal that the presence of shield causes the exiting jet to stick to the wall of the shield without causing spill-over around the cavity inlet, thus sustaining the shock oscillation as seen in the unshielded Hartmann whistle, which has intense flow/shock oscillation and spill-over around the cavity mouth. The velocity vectors indicate jet regurgitance in shielded whistles showing inflow and outflow phases like un-shielded ones with different regurgitant phases. The sinusoidal variation of mass flow rate at the cavity inlet in un-shielded Hartmann whistle indicates jet regurgitance as the primary operating mode with large flow diversion around the cavity mouth whereas the non-sinusoidal behavior in shielded ones represent that the jet regurgitance is not the dominant operating mode. Thus, this paper sufficiently demonstrates the effect of shield in modifying the flow/shock oscillations in the vicinity of the cavity mouth.

Effects of Circumferential Casing Grooves on the Performance of a Transonic Axial Compressor

AbstractThe casing groove is a highly effective method for improving the stall margin with the least detrimental effect on the peak efficiency in an axial compressor. In this work, a single casing groove with different heights and positions was numerically tested to evaluate effects of each geometric parameter on the stall margin in a transonic compressor. Validation between the simulation and experiment was conducted with a smooth casing as a reference case, and the computed and experimental results were compared in terms of performance curves, downstream flow properties and Mach number contours. Subsequently, the performance curves for each test case with a single casing groove were obtained from the numerical results and compared with each other to determine the appropriate position and height of the groove for increasing the stall margin. A casing groove installed near the leading edge was found to be effective for expanding the stable operating range in a transonic compressor, giving about 3% point improvement in the stall margin at the cost of a small drop in efficiency at the design point. An attempt was also made to understand the underlying mechanism of the casing groove based on the analysis of the numerical flow data.

Numerical simulation of fluidic thrust vectoring in an axisymmetric supersonic nozzle

Transverse secondary gas injection into an axisymmetric supersonic nozzle under standard atmosphere pressure is investigated to get the performance of thrust vectoring control. An analytical model was established based on the transverse injection flow. Three-dimensional CFD methods were performed with different transverse secondary injection models. To validate the ability of the numerical model, numerical results were compared with the analytical and experimental results. Overall pressure distributions show quite good match with the analytical and experimental results. The Mach number contours in different injection positions were obtained. Reflection of the bow shock occurred for xj/L = 0.6, not for xj/L = 0.9. Nozzle pressure ratio is also the key factor for shock vector control. Based on this data, thrust vectoring efficiency and system thrust ratio have been considered. Finally, the pressure distributions in different momentum flux ratios were studied in CFD and analytical models. The separating point of boundary layer is moving upstream with the increasing of momentum flux ratio. The result will provide the reference to the further development of shock vector control.

CFD simulation on the effect of primary nozzle geometries for a steam ejector in refrigeration cycle

In this study, the CFD technique was employed to investigate the effect of the primary nozzle geometries on the performance of an ejector used in the steam jet refrigeration cycle. In all cases, only one fixed-geometry mixing chamber together with eight different primary nozzles was investigated numerically using the commercial CFD package, FLUENT 6.3. The effects on the primary fluid pressure, mass flow rate and Mach number were observed and analyzed. The Mach number contour lines were used to explain the mixing process occurring inside the ejector. It was found that shock's position of the mixed fluid and the expansion angle of the primary fluid jet stream within the mixing chamber played a very important role in the ejector performance.

NUMERICAL SIMULATION OF MACH NUMBER AND ANGLE OF ATTACK INFLUENCE ON REGIMES OF TRANSONIC TURBULENT FLOWS OVER AIRFOILS

Reynolds-averaged Navier−Stokes equations along with the Spalart−Allmaras one-parameter differential turbulence model are applied to investigate the unsteady flow over airfoils. The pressure and friction coefficient distributions on the airfoil surface, Mach number contour lines, numerical schlieren photographs, as well as the values of the aerodynamic coefficients are presented. The influence of the flow structure on the aerodynamic characteristics is analyzed. A map of the transonic turbulent flow regimes around the NACA 0012 airfoil on the plane free-stream Mach number angle of attack is composed.

Computational fluid dynamics analysis of multi-element, high-lift aerofoil sections at transonic manoeuvre conditions

The application of a previously developed computational method to the prediction of high-lift performance for multi-element aerofoil sections operating at transonic flow conditions is described. The flows are computed by solving the Reynolds-averaged Navier–Stokes equations, using a full differential Reynolds-stress turbulence model to evaluate the various Reynolds-stress components appearing in the governing mean-flow equations. Algebraic wall functions are used to bridge the molecular viscosity-dominated region immediately adjacent to the aerofoil surfaces. An unstructured grid-based computational fluid dynamics (CFD) methodology is used to deal with the geometric complexity of the multi-element aerofoil configurations. Initial results are presented for the viscous, transonic flow development around the SKF 1.1 supercritical aerofoil section, equipped with either a trailing-edge flap or a leading-edge slat. Predicted surface pressure distributions generally compare well with experimental data for the two high-lift aerofoil geometries considered, at a free-stream Mach number of 0.6 and over a range of incidence angles. There are some discrepancies in the regions immediately downstream of shock wave/boundary layer interactions, possibly resulting from the use of wall-function boundary conditions in the computations. Predicted Mach number contours indicate the complexity of the transonic flow fields for high-lift configurations, with the slat wake passing through an extensive supersonic-flow region, terminated by a normal shock wave, on the main aerofoil upper surface, for example.