Mach Number Increases Research Articles

Effect of Compressibility on Velocity Profile and Friction Factor of Gaseous Laminar Flows in a Microtube

Abstract Laminar flow of nitrogen gas in a microtube was simulated numerically to obtain velocity profile and Fanning friction factor in a quasi-fully developed region. The numerical procedure based on Arbitrary-Lagrangian-Eulerian method solved two-dimensional compressible momentum and energy equations. The computations were performed for a wide range of Reynolds number in laminar flow regime with adiabatic wall condition. It was found that the velocity profile deviates from the parabola as Mach number increases, and the product of Fanning friction factor and Reynolds number is not a constant but a function of only Mach number. To explain the compressibility effect, a new theoretical flow model which gives the velocity profile of gaseous laminar flows in a microtube was proposed under the assumption of purely axial flow. The theoretical velocity profile is taking radial-direction density change into account, and coincides with the numerically obtained velocity profile. The proposed flow model also shows that the Fanning friction factor of a compressible flow in a microtube is expressed by a quadratic function of Mach number. The coefficient of the Mach squared term is 40% of the numerically obtained correlation. The compressibility effect on friction factor of gaseous laminar flows in a microtube partly results from velocity profile change which must occur to keep the mass velocity profile when density changes in radial direction. The remainder of the compressibility effect can be considered to result from actual mass transfer in the radial direction whose existence was demonstrated by the numerical results.

A numerical study on flow structure and combustion mechanism of supersonic mixed inflow with transverse jet

The flow mixing mechanism between sonic fuel jet and supersonic mixed inflow is one of the key technologies in rocket-based combined cycle engines. In this study, the flow mechanism of different supersonic airflow conditions on the flow field is discussed. The variable parameters are the Mach number and total pressure of the airflow. The three-dimensional Reynolds-averaged Navier-Stokes equations, two equations of the shear stress transport k-ω turbulence model, and the Eddy-dissipation concept reaction model are adopted to evaluate the flow field structure. The results reveal that the shear layer between the airflow and the rocket gases gradually slopes downward with the increase of Mach number. The bow shock induced by the jet develops to the upper wall and cuts off the shear layer vortex. Additionally, as the Mach number of the airflow decreases, the mixing and combustion efficiencies gradually increase. The Mach number has a slight influence on the penetration depth. Furthermore, when the total pressure of the airflow increases, the penetration depth and mixing efficiency sharply increase.

Supersonic Several Bells Design of Minimum Length Nozzle Contours for More Altitudes Level Adaptations

This wok focuses to develop a numerical computation program allowing to design new contours of a supersonic nozzle having several bells, adapted to several levels of different altitudes, going from sea level and progressively with the altitude up to space, giving a supersonic uniform and parallel flow to the exit section and a maximum possible thrust without loss, aiming to reduce considerably the side loads caused in the conventional and the dual bell nozzles when the ambient pressure decrease with the altitude. The first bell has a sonic, uniform and parallel inlet to the throat, and a sea level adaptation with a reduced supersonic Mach number, while the other bell have a supersonic, parallel and uniform inlet and an adaptation to a given altitude with a progressed increase of supersonic Mach number. The transition from one level of adaptation to another adjacent is done without mechanical activation. The purpose of this type of nozzle is to have the possibility of flying in several supersonic regimes adapted to several different altitudes with a reduced side loads. This type of nozzle is named by Several Bell Nozzle and has inflection points between bell and adjacent other. The design is done in the context of a calorically and thermally perfect gas. The problem is to design a typical bell having a uniform and parallel supersonic inlet and exit with two given Mach numbers. The design is made by the use of the Method of Characteristics. The resolution of the equations is done numerically by the finite difference corrector predictor algorithm. The validation of the results is controlled by the convergence of the ratio of the critical sections, calculated numerically, to that given by the theory. In this case, all the design parameters converge automatically to the desired solution. The application is made for axisymmetric MLN having 3, 4, 5 and 10 bells.

Numerical Simulation of Supersonic Carman Curve Bodies with Aerospike

Drag reduction is one of the important problems for the supersonic vehicles. As one of the drag reduction methods, aerospike has been used in some equipment because of its good drag reduction effect. In this paper, the numerical simulations of Carman curve bodies with different lengths of the aerospike and different radius of the flat cylindrical aerodisk in supersonic flow freestream are investigated. Based on the numerical simulations, the mechanism of drag reduction of the aerospike is discussed. The drag reduction effect influence of the parameters of the aerodisk radius and the aerospike length on the Carman curve body is analyzed. The aerodisk radius within a certain range is helpful for the drag reduction. The change of length of the aerospike has little effect on the drag of Carmen curve bodies. The drag reduction effect of the same aerospike becomes worse with the increase of the incoming Mach number.

Spark ignition and stability limits of spray kerosene flames under subatmospheric pressure conditions

Flame stability limits and ignition delay time of the flameholder are experimentally studied in this work at the pressure of 0.03 – 0.06 MPa, Mach number of 0.1 – 0.3, and temperature of 320 K – 800 K. The results indicate that the reduction in equivalence ratios of lean ignition and blowout can be achieved by the increase in pressure or Mach number. Temperature rise will first increase and then decrease the lean ignition equivalence ratio. While increasing lean blowout equivalence ratio was observed with increasing temperature. The envelope of the stable combustion between the pressure and Mach number is measured, and the lowest temperature of successful ignition is 300 K, acquired at Mach 0.1 and 0.06 MPa. Besides, the correlation between the equivalence ratios of flame stability and inlet parameters, such as pressure, Mach number, temperature, is developed. The ignition process of the flameholder is imaged, and the ignition delay time decreases with increased pressure or temperature. The ignition delay time is shown first to decrease and then increase with the increase in Mach number.

Effect of Mach number and plate thickness on the flow field and heat transfer characteristics of supersonic turbulent flow over a flat plate at different thermal boundary conditions

Conjugate heat transfer analysis of supersonic turbulent flow over a finite thickness flat plate is studied numerically. The flow field is modeled by employing the Favre averaged Navier–Stokes (FANS) equations. Turbulence is modeled with the Menter’s shear-stress-transport (SST) k−ω model. The comparison of NCHT (non-conjugate heat transfer) and CHT (conjugate heat transfer) analysis shows that the interface temperature and fluid temperature variation for the CHT analysis are lower compared to the NCHT analysis. The results indicate that the interface temperature is significantly increased for the low thermal conductivity plate material, due to the reduced rate of heat transfer. The effect of plate thickness on the flow field temperature variation is negligible. However, it is observed that the maximum interface temperature Ti,max increases with the increase in plate thickness. The values of maximum interface temperature difference between the 5 mm and 2 mm thick Steel-1006 plates at Mach numbers 2, 4, and 5 in non-dimensional (non-dimensionalized with free-stream temperature) form are 0.05594, 0.129, and 0.1816 respectively for the isothermal boundary condition. Results indicate that for Mach 2, the heated wall thermal boundary conditions acts like heat source, leading to the higher interface temperature, whereas for Mach 4, and 5 the heated wall thermal boundary conditions acts like heat sink, thus lowering the interface temperature. The results show that for NCHT analysis the leading edge shock strength, and mean pressure along the wall increases with an increase in Mach number. The non-conjugate results (flow and heat transfer characteristics) of the present numerical study is validated with the direct numerical simulation (DNS) results available in the literature.

Evaluation of exit pattern factors of an annular aero gas turbine combustor at altitude off-design conditions

Abstract This paper presents the experimental results of an annular combustor. A full scale full annular combustion chamber is tested at ground test stand simulating altitude off-design operating conditions. Traversing thermocouple rakes are used to measure temperatures over the entire annulus at combustor exit. The radial temperature profile is found to be a strong function of operating parameters while the circumferential pattern factor is within the design goal. Increase in reference Mach number at these off-design conditions has caused the redial temperature profiles to deviate and increase from the intended profile. These results will be used for benchmarking the computational model. The computational model will be used for detail study of the temperature non-uniformity over the entire flight envelope and also for modification of combustor liner for performance improvement.

Evaluation of exit pattern factors of an annular aero gas turbine combustor at altitude off-design conditions

Abstract This paper presents the experimental results of an annular combustor. A full scale full annular combustion chamber is tested at ground test stand simulating altitude off-design operating conditions. Traversing thermocouple rakes are used to measure temperatures over the entire annulus at combustor exit. The radial temperature profile is found to be a strong function of operating parameters while the circumferential pattern factor is within the design goal. Increase in reference Mach number at these off-design conditions has caused the redial temperature profiles to deviate and increase from the intended profile. These results will be used for benchmarking the computational model. The computational model will be used for detail study of the temperature non-uniformity over the entire flight envelope and also for modification of combustor liner for performance improvement.

Research on the Adjustable Guide Vane in a Compressor Sector Cascade

In order to simulate the inlet flow angle and Mach number of the tested blade, a row of guide vanes is set before the tested blade during the sector cascade experiment. In this paper, a kind of adjustable guide vane (AGV) is designed, which can rotate continuously and change the inlet flow angle of the tested blade conveniently and quickly. The variation rule of the clearance between the AGV and the end wall is introduced. The influence of the clearance on the flow field structure under different Mach number and incidence angle is studied by numerical and experimental methods. It is found that the clearance of the leading edge is small at the top and the root, and the leakage vortex is mixed with the passage vortex. The interaction between the leakage vortex and the passage vortex in the trailing edge results in the decrease of Mach number and the increase of flow angle at the AGV outlet. The clearance has little effect on the span of 20% - 80%. At the same incidence angle condition, with the increase of Mach number, the influence range of leakage vortex is expanded, and the variation magnitude of flow angle and Mach number at the top and root position is increased; At the same Mach number condition, with the decrease of the AGV rotation angle from positive to negative, the top clearance is increased gradually, and the root clearance is decreased gradually. The separation range at the top is expanded gradually, which results in the variation magnitude of flow angle and Mach number is increased, but the effect is opposite at the root of the AGV.

Investigation of Mach number effects on flow over a flat plate at Reynolds number of 1.0 × 104 by schlieren visualization

Flow over a flat plate with a 5% thickness ratio is investigated by schlieren visualization in compressible low-Reynolds-number conditions. The results show that flow separates at the leading-edge and laminar separation-bubble forms. The position of the maximum root mean square of the schlieren image which is related to the position of the vortex shedding moves downstream as a Mach number increases. Furthermore, the two-dimensional structure of generated vortices is maintained up to the trailing edge at the Mach number of 0.66. The frequency analysis of the time-series intensity value of the schlieren images also shows that the flow is stabilized with increasing the Mach number. The position of the end of the pressure plateau region matches the position where the root-mean-square value of the intensity image becomes a maximum due to vortex shedding.

Fuzzy Shannon wavelet finite element methodology of coupled heat transfer analysis for clearance leakage flow of single screw compressor

The Shannon wavelet function and its scale function are used as interpolating functions to establish the Shannon wavelet finite element. The temperature and velocity of every leakage path are calculated based on fuzzy Shannon wavelet finite element method, fuzzy Daubechies wavelet finite element model, fuzzy finite element method and experiment, and comparisons between numerical analysis results and experimental results show that fuzzy Shannon-cosine wavelet finite element method can get highest computing precision and accuracy. The coupling relationships between the flow and heat transfer of clearance leakage flow are analyzed based on fuzzy Shannon-cosine finite element method, and numerical results show that the Nusselt number of every leakage path decreases with increase of Mach number, the flow has great influence on heat transfer of clearance leakage flow of single screw compressor.

The performance of a scramjet combustor with cavity for Mach numbers 2.25, 2.52 and 2.75 with hydrogen as a fuel

The development of the scramjet engine is one of the most promising technologies of the 21st century. Researchers around the globe are making constant efforts to understand the physics and combustion characteristics of the supersonic flow in the combustor. In this paper, a computational approach has been implemented to investigate the flame characteristics of a cavity-based hydrogen-fuelled supersonic combustor for Mach numbers such as 2.25, 2.52 and 2.75 by using Ansys 14-FLUENT code. Two-equation standard K-ε turbulence model and the two dimensional compressible Reynolds Averaged Navier Stokes (RANS) have been used to carry out the simulations for the cavity based supersonic combustor. Concurrently, the validation for the present work is performed in accordance with an available experimental study already done in the literature. The results are in good agreement with the experimental results. This study attempts to understand the combustion characteristics by variation of Mach number and pressure. The results for the present study show an optimal Mach number range for which there is efficient combustion in the considered combustor. Besides, the results indicate that as the Mach number increases, there is a change in the oblique shock waves downstream of the fuel injection. For the considered Mach number range there was an enhancement in combustion which in turn enhances the performance of the scramjet combustor.

Effect of wavy wall strut fuel injector on shock wave development and mixing enhancement of fuel and air for a scramjet combustor

Abstract The shear mixing and streamline vortices are the notable parameters to influence the air–fuel mixing in hypersonic flows. The shock wave development and Mach number significantly influence the shear mixing phenomenon. Hence, this research introduced an unconventional strut and tested its performance for the generation of shock waves at different flow conditions (M = 2,4,6). The Reynolds-averaged Navier–Stokes equations are solved to evaluate the performance of the new strut. Both the DLR scramjet strut injector and wavy wall strut injector are assessed for the shear mixing development. Turbulence for the association of shock waves, mixing layer, and the boundary layer has been modeled with the SST k-ω model. The variation in shock development and its interactions are investigated further with an increase in Mach number. The scramjet flow structure differentiation found the increased number of oblique shock waves with the wavy wall strut fuel injector. It increases the turbulence level with increased streamline vortices, turbulent intensity, and turbulent kinetic energy. The shock wave generation analysis at different Mach numbers (M = 2,4,6) found fewer interactions between the shock wave and shear layer with increased Mach number. From the examination of shock wave generation and its interaction with the shear layer and analysis of turbulent parameters, it is found that the wavy wall strut has an appreciable effect on shock-induced blend augmentation of fuel and air.

Infrared signature of NEPE, HTPB rocket plume under varying flight conditions and motor size

In this study, radiation signatures of rocket plumes based on HTPB and NEPE propellants are simulated under varying altitudes, flight Mach numbers, and motor size. The flow field of plume is calculated by computational fluid dynamics, and the infrared signature is predicted using a Ludwig model. To verify the numerical method, experiments were conducted using small rocket motors and radiometric FTIR. The acceptable agreement between numerical calculation and the experiment was obtained in 2–5 μm wavelength region. The total radiance decreases with increasing altitude whether afterburning exists or not. A decreasing rate in the radiance of the plume with strong afterburning is larger than that of the plume with weak afterburning. The change in total intensity according to altitude depends on the afterburning and is directly affected by the radiating area. As the flight Mach number increases, total radiance, total intensity, and radiating area decrease. The motor size makes radiation intensity increase exponentially; exponent value is from 2.6 to 2.7. As the motor size increases, the effect of altitude increases, while the effect of flight Mach number decreases.

Criteria for hypersonic airbreathing propulsion and its experimental verification

Hypersonic airbreathing propulsion is one of the top techniques for future aerospace flight, but there are still no practical engines after seventy years' development. Two critical issues are identified to be the barriers for the ramjet-based engine that has been taken as the most potential concept of the hypersonic propulsion for decades. One issue is the upstream-traveling shock wave that develops from spontaneous waves resulting from continuous heat releases in combustors and can induce unsteady combustion that may lead to engine surging during scramjet engine operation. The other is the scramjet combustion mode that cannot satisfy thrust needs of hypersonic vehicles since its thermos-efficiency decreases as the flight Mach number increases. The two criteria are proposed for the ramjet-based hypersonic propulsion to identify combustion modes and avoid thermal choking. A standing oblique detonation ramjet (Sodramjet) engine concept is proposed based on the criteria by replacing diffusive combustion with an oblique detonation that is a unique pressure-gain phenomenon in nature. The Sodramjet engine model is developed with several flow control techniques, and tested successfully with the hypersonic flight-duplicated shock tunnel. The experimental data show that the Sodramjet engine model works steadily, and an oblique detonation can be made stationary in the engine combustor and is controllable. This research demonstrates the Sodramjet engine is a promising concept and can be operated stably with high thermal efficiency at hypersonic flow conditions.

Nonlinear transport of rarefied Couette flows from low speed to high speed

The nonlinear transport properties and macroscopic flow features of rarefied plane Couette flows from low speed to high speed for a monatomic gas are investigated in detail using the direct simulation Monte Carlo (DSMC) method. The effective viscosity and thermal conductivity are directly computed from the DSMC results according to the linear constitutive relations. The detailed structure of the Knudsen layer (KL) and the functional dependence of the effective transport coefficients on local Knudsen numbers in the whole system are presented and compared with existing theoretical models. The results show that the effective viscosity and thermal conductivity distributions in the KL for different Mach number flows can be recast into the same profile (i.e., isothermal scaling function) in terms of a scaled wall distance η=∫0y1/λ(y)dy, though the local flow is nonisothermal. For all cases, the shear-stress Knudsen number distributions across the channel show a well opposite trend to the effective transport coefficient profiles. The functional dependence between them in the bulk region always coincides with the normal solution that is derived from the Boltzmann model equations for unbounded shear flows, while that in the KL for low-speed cases shows a large difference with the normal solution. As the Mach number increases, the DSMC data in the KL can also agree approximately with the normal solution at a large shear-stress Knudsen number. These results can be very useful for developing phenomenological models to describe a wall-bounded rarefied shear flow, showing a good prospect in both microflow and high-altitude applications.

Study on the Hybrid Cooling of the Flame Tube in a Small Triple-Swirler Combustor

An experimental and numerical investigation is conducted to study the influence of different cooling schemes on the wall temperature of the flame tube in a small triple-swirler combustor in this paper. Two different cooling structures are adopted: the impingement-film and inclined multi-hole cooling structure (Scheme B, C), and the inclined multi-hole control group (Scheme A). The impact of parameters including inlet temperature (373–423 K), inlet Mach number (Ma) (0.12–0.18), and fuel–air ratio (FAR) (0.02–0.03) are discussed. The results show that the wall temperature of the flame tube rises with the increase in inlet temperature; as the inlet Mach number increases, the wall temperature (Scheme B, C) of the primary zone goes up and is distributed more uniformly; as FAR rises, the wall temperature in Scheme C is nearly unchanged, while it is increased in Scheme A and B. For the range of parameters considered in this study, the lowest wall temperature and the best cooling effect are observed in Scheme C. The experiment conducted on the impingement-film and inclined multi-hole structure shows a better cooling effect than that conducted on the traditional inclined multi-hole structure. Compared with the row number of multi-inclined holes, the diameter of jet hole has a more significant influence on the cooling effect.

Direct numerical simulation of subsonic, transonic and supersonic flow over an isolated sphere up to a Reynolds number of 1000

In the present study, compressible low-Reynolds-number flow past a stationary isolated sphere was investigated by direct numerical simulations of the Navier–Stokes equations using a body-fitted grid with high-order schemes. The Reynolds number based on free-stream quantities and the diameter of the sphere was set to be between 250 and 1000, and the free-stream Mach number was set to be between 0.3 and 2.0. As a result, it was clarified that the wake of the sphere is significantly stabilized as the Mach number increases, particularly at the Mach number greater than or equal to 0.95, but turbulent kinetic energy at the higher Mach numbers conditions is higher than that at the lower Mach numbers conditions of similar flow regimes. A rapid extension of the length of the recirculation region was observed under the transitional condition between the steady and unsteady flows. The drag coefficient increases as the Mach number increases mainly in the transonic regime and its increment is almost due to the increment in the pressure component. In addition, the increment in the drag coefficient is approximately a function of the Mach number and independent of the Reynolds number in the continuum regime. Moreover, the effect of the Mach and Reynolds numbers on the flow properties such as the drag coefficient and flow regime can approximately be characterized by the position of the separation point.

An Assessment of the Drag Models in the Case of a Shock Interacting With a Fixed Bed of Point Particles

Abstract In this work, three-dimensional Euler–Lagrange (EL) point-particle simulations of a shock wave interacting with a fixed bed of particles are carried out. The results from the particle-resolved (PR) simulations are used to assess the performance of the point-particle drag models during short time scales. We demonstrate that in a one-way coupled regime, the point-particle simulations recover the dominant gas dynamic features of the flow and are in a good agreement with the exact Riemann solution of a shock traveling through a sudden area contraction. Although the PR simulations are inviscid, we show that a dissipative drag is necessary to predict the mean behavior of the gas. As a model for the inviscid shock-induced (SI) drag two different models are presented in lieu of the quasi-steady drag. Finally, two-way coupled simulations are performed at four different particle volume fractions {0.10, 0.15, 0.20, 0.25} and three different incident shock Mach numbers {1.22, 1.66, 3.0} and compared against the data from PR inviscid simulations. At a lower Mach number (1.22), averaged flow quantities from the two-way coupled simulations agree well with the PR simulations. As the Mach number increases, we observe that the discrepancies between the point-particle and the PR simulations grow. A sensitivity analysis of the drag models involved reveals a strong influence of the inviscid-unsteady force on the gas quantities especially in the case of a strong shock interacting with a dense bed of particles. The use of Mach correlation beyond the subcritical regime coupled with the model for volume fraction correction is identified as a probable cause for the additional drag.

Investigation of wakes generated by fractal plates in the compressible flow regime using large-eddy simulations

We investigate flows interacting with square and fractal shape multi-scale structures in the compressible regime for Mach numbers under subsonic and supersonic upstream conditions using large-eddy simulations. We also aim at identifying similarities and differences that these interactions have with the corresponding interactions in the canonical incompressible flow problem. To account for the geometrical complexity associated with the fractal structures, we apply an immersed boundary method to model the no-slip boundary condition at the solid surfaces, with adequate mesh resolution in the vicinity of the small fractal features. We validate the numerical results through extensive comparisons with experimental wind tunnel measurements at a low Mach number. Similar to the incompressible flow case results, we find a breakup of the flow structures by the fractal plate and an increase in turbulent mixing in the downstream direction. As the Mach number increases, we observe noticeable wake meandering and higher spread rate of the wake in the lateral direction perpendicular to the streamwise–spanwise plane. Although not significant, we quantify the difference between the square and the fractal plates using two-point velocity correlations across the Mach number range. The wakes generated by the fractal plate in the compressible regime showed lower turbulent kinetic energy and energy spectra levels compared to those of the square case. Moreover, results in terms of the near-field pressure spectra seem to indicate that the fractal plate has the potential to reduce the aerodynamic noise.