Pre-shock Mach Number Research Articles

Effect of Unsteady Fan-Intake Interaction on Short Intake Design

Abstract The next generation of ultrahigh bypass ratio civil aero-engines promises notable engine cycle benefits. However, these benefits can be significantly eroded by a possible increase in nacelle weight and drag due to the typical larger fan diameters. More compact nacelles, with shorter intakes, may be required to enable a net reduction in aero-engine fuel burn. The aim of this paper is to assess the influence of the design style of short intakes on the unsteady interaction under crosswind conditions between fan and intake, with a focus on the separation onset and characteristics of the boundary layer within the intake. Three intake designs were assessed, and a hierarchical computational fluid dynamics (CFD) approach was used to determine and quantify primary aerodynamic interactions between the fan and the intake design. Similar to previous findings for a specific intake configuration, both intake flow unsteadiness and the unsteady upstream perturbations from the fan have a detrimental effect on the separation onset for the range of intake designs. The separation of the boundary layer within the intake was shock driven for the three different design styles. The simulations also quantified the unsteady intake flows with an emphasis on the spectral characteristics and engine-order signatures of the flow distortion. Overall, this work showed that is beneficial for the intake boundary layer to delay the diffusion closer to the fan and reduce the preshock Mach number to mitigate the adverse unsteady interaction between the fan and the shock.

Characteristics of Shock-Induced Boundary-Layer Separation on Nacelles Under Windmilling Diversion Conditions

The boundary layer on the external cowl of an aeroengine nacelle under windmilling diversion conditions is subjected to a notable adverse pressure gradient due to the interaction with a near-normal shock wave. Within the context of computational fluid dynamics (CFD) methods, the correct representation of the characteristics of the boundary layer is a major challenge in capturing the onset of the separation. This is important for the aerodynamic design of the nacelle, as it may assist in the characterization of candidate designs. This work uses experimental data obtained from a quasi-2D rig configuration to provide an assessment of the CFD methods typically used within an industrial context. A range of operating conditions are investigated to assess the sensitivity of the boundary layer to changes in inlet Mach number and mass flow through a notional windmilling engine. Fully turbulent and transitional boundary-layer computations are used to determine the characteristics of the boundary layer and the interaction with the shock on the nacelle cowl. The correlation between the onset of shock-induced boundary-layer separation and the preshock Mach number is assessed, and it was found that the CFD is able to discern the onset of boundary-layer separation.

Neural network-based multi-point, multi-objective optimisation for transonic applications

In the context of aircraft applications, the overall design process can be challenging due to the different aerodynamic requirements at several operating conditions and the total associated computational overhead. For this reason, the use of low order models for the optimisation of complex non-linear problems is sometimes used. This paper addresses the challenge of transonic aerodynamic design optimisation through the integration of a set of neural networks for the prediction of integral values, the classification of flow features and the estimation of flow field characteristics. The design method improves the computational efficiency relative to an expensive design process driven by Computational Fluid Dynamics (CFD) evaluations. The approach is used for the multi-point, multi-objective optimisation of a compact aero-engine nacelle in which the design outcomes are validated using a CFD in-the-loop optimisation strategy. It is demonstrated that the method based on the neural network capability identifies similar nacelle designs at a 75% reduction in the overall computational cost, a drag uncertainty prediction within 2.8%, and a predictive accuracy for the classification metric of 98%. For downselected configurations, the main flow characteristics in terms of peak Mach number, pre-shock Mach number and shock location are well predicted by the neural network models compared with the CFD-based evaluations.

Shock loss measurements in non-ideal supersonic flows of organic vapors

This paper presents the first ever direct measurements of total pressure losses across shocks in supersonic flows of organic vapors in non-ideal conditions, so in the thermodynamic region close to the liquid–vapor saturation curve and the critical point where the ideal gas law is not applicable. Experiments were carried out with fluid siloxane MM (hexamethyldisiloxane, C_6H_{18}OSi_2), commonly employed in medium-/high-temperature organic Rankine cycles (ORCs), in the Test Rig for Organic VApors (TROVA), a blowdown wind tunnel at the Laboratory of Compressible fluid dynamics for Renewable Energy Applications (CREA lab) of Politecnico di Milano. A total pressure probe was inserted in superheated MM vapor flow at Mach number sim 1.5 with total conditions in the range 215-230~^circ hbox {C} and 2-12~hbox {bar} at varying levels of non-ideality, with a compressibility factor evaluated at total conditions between Z_text {T}=0.68-0.98. These operating conditions are representative of the first-stage stator of ORC turbines. Measured shock losses were compared with those calculated from pre-shock quantities by solving conservation equations across a normal shock, with differences always below 2 % attesting a satisfactory reliability of the implemented experimental procedure. An in-depth analysis was then carried out, highlighting the direct effects of non-ideality on shock intensity. Even at the mildly non-ideal conditions with Z_text {T}gtrsim 0.70 considered here, non-ideality was responsible for a significantly stronger shock compared to the ideal gas limit at same pre-shock Mach number, with differences as large as 6%.Graphical abstract

Disc accretion shocks with alpha viscosity

ABSTRACT Shocks in rotating disc accretion flows under the vertically hydrostatic equilibrium are examined, taking into account the α viscosity. For the case that the stress tensor is proportional to the gas pressure, and neglects the effects of the mixture of gas and radiation pressure, we derive analytical expressions for jump conditions of disc accretion shocks with alpha viscosity; they would be useful for various disc accretion problems. As in the usual accretion disc, the alpha viscosity works as angular momentum transport and heat generation. When a steadily standing shock wave is generated in a disc, due to the viscous effect, the azimuthal velocity discontinuously decreases in the post-shock region inside the front. For sufficiently strong shocks, the post-shock azimuthal velocity vanishes; in other words, the rotating accretion flows turn to the radially accretion ones, after passing the shock front. This vanishing condition is roughly expressed as $\alpha {\cal M}_1/{\cal M}_{\varphi 1}$ 1, where α is the viscous alpha parameter, ${\cal M}_1$ the pre-shock radial Mach number, and ${\cal M}_{\varphi 1}$ the pre-shock azimuthal Mach number. Furthermore, due to the viscous heating, the disc height increases and the surface density decreases in the post-shock region, compared to the non-viscous case. This angular momentum transport via disc shocks would affect the accretion spin-up of the central objects and accretion problems in general.

Shock wave structure in non-ideal dilute gases under variable Prandtl number

This paper investigates the structure of normal shock waves for a planar steady flow of non-ideal dilute gases under variable viscosity and thermal conductivity using the Navier–Stokes–Fourier approach to the continuum model. The gas is assumed to follow the simplified van der Waals equation of state along with the power-law temperature-dependent coefficients of shear viscosity, bulk viscosity, and thermal conductivity. A closed system of nonlinear differential equations having a variable Prandtl number ( $$\Pr $$ ) is formulated. Exact analytical solutions of the shock wave structure in non-ideal gases are derived for $$\Pr \rightarrow \infty $$ and $$\Pr \rightarrow 0$$ limits, and the corresponding profiles for velocity and temperature are obtained. For $$\Pr \rightarrow 0$$ , an isothermal shock is encountered for high Mach numbers. It appears sooner in non-ideal gases. The solution profiles for $$\Pr =2/3$$ are obtained numerically and compared with the corresponding profiles for $$\Pr \rightarrow 0$$ , 3/4, and $$\infty $$ under the same initial conditions. Qualitative agreement is obtained with the theoretical and experimental results for the shock wave structure. The inverse shock thickness is computed for different values of $$\Pr $$ , and it is found that the inverse shock thickness increases with an increase in the Prandtl number. The bulk viscosity, the non-idealness parameter, the specific heat ratio, the power-law index, and the pre-shock Mach number have a significant effect on the shock wave structure.

Radiative shocks in spherical accretion

ABSTRACT In order to explore various aspects of radiative shocks, we examine standing radiative shock waves in spherical accretion flows onto a central gravitating body under the equilibrium diffusion approximation. In contrast to the usual one-dimensional shock, in radiative shocks a radiative precursor appears in the pre-shock region before the shock front, due to the radiative diffusion effect. Furthermore, in spherical flows around a central object the gravitational potential varies in this radiative precursor, and a curvature effect also exists. We first formulate such radiative shocks in spherical flows, derive the overall jump conditions, and solve the structure of the radiative precursor for both the gas and radiation pressure dominated cases. Since the jump conditions contain the coordinates of both ends of the radiative precursor, we must obtain both the solution and the endpoints of the precursor simultaneously. We find that the gravitational effect is not significant, although it cannot be ignored. The curvature effect exerts a strong influence on the structure and width of the precursor. The precursor starting point x1 normalized by the shock radius is roughly expressed by $x_1={\cal M}_1^{1/7}$ for a radiation pressure dominated shock, while $x_1=1.21^{({\cal M}_1-1)}$ for a gas pressure one, where ${\cal M}_1$ is the pre-shock Mach number.

Experimental observation of oblique shock waves in steady non-ideal flows

Steady oblique shock waves are observed for the first time in non-ideal supersonic flows of single-phase organic vapors. A diamond-shaped airfoil with semi-aperture 7.5^{circ } at the leading edge and 10^{circ } at the trailing edge is placed within a uniform supersonic stream (Mach number M = 1.5) of siloxane fluid MDM (octamethyltrisiloxane, hbox {C}_8hbox {H}_{24}hbox {O}_2hbox {Si}_3). Oblique shock waves are observed at varying stagnation conditions in the pre-shock state, for a set of flow deviation angles obtained by changing the attitude of the model with respect to the wind tunnel axis. Stagnation temperatures and pressures reduced by critical values range from 0.928 to 0.979 and from 0.200 to 0.615, respectively. Oblique shock waves are characterized through independent measurements of pressure, temperature and Mach number. Stagnation pressure and temperature are measured in the wind-tunnel settling chamber, while the pre-shock, post-shock and post-expansion static pressures are measured at selected locations close to the airfoil. Direct measurement of the flow Mach number is provided by schlieren visualizations. Experimental results agree with the shock wave theory for two-dimensional steady flows, complemented with state-of-the-art thermodynamic models, and deviate from their well-known, dilute-gas predictions. In particular, measurements show the non-ideal dependence of the pressure ratio across the shock on stagnation conditions in addition to the well-known dependence on the pre-shock Mach number, specific heat ratio and flow deviation angle typical of dilute gas conditions.Graphical abstract

Non-ideal oblique shock waves

From the analysis of the isentropic limit of weak compression shock waves, oblique shock waves in which the post-shock Mach number is larger than the pre-shock Mach number, named non-ideal oblique shocks, are admissible in substances characterized by moderate molecular complexity and in the close proximity to the liquid–vapour saturation curve. Non-ideal oblique shocks of finite amplitude are systematically analysed, clarifying the roles of the pre-shock thermodynamic state and Mach number. The necessary conditions for the occurrence of non-ideal oblique shocks of finite amplitude are singled out. In the parameter space of pre-shock thermodynamic states and Mach number, a new domain is defined which embeds the pre-shock states for which the Mach number increase can possibly take place. The present findings are confirmed by state-of-the-art thermodynamic models applied to selected commercially available fluids, including siloxanes and hydrocarbons currently used as working fluids in renewable energy systems.

Kriging-assisted design optimization of S-shape supersonic compressor cascades

In this paper, multi-objective design optimization of a supersonic compressor cascade was dealt with. The geometry considered was an S-shaped 2D cascade developed and tested at DLR (DLR-PAV-1.5), operating under unique incidence and inlet Mach number equal to 1.5 so as to develop approximately a static pressure ratio of 2. In such conditions, the cascade shows a strong lambda shock-boundary layer interaction. Methodology included the use of an in-house Kriging-assisted evolutionary algorithm driving an iterative loop which includes a parametric code for geometry representation and the ANSYS Fluent© solver for flow calculation. Cascade optimization was carried out by varying the shapes of both the suction and the pressure sides while maintaining the unique incidence condition using an iterative CFD-based procedure. The objectives were to minimize the cascade total pressure losses and to maximize the static pressure ratio using a Pareto ranking criterion. Results showed that loss coefficient could be reduced by 25% and the static pressure ratio could be improved by 6.5% as a results of a decrease in the pre-shock Mach number by virtue of an extended pre-compression mechanism that involves the entire suction surface upstream of the passage shock.

Shock train generated turbulence inside a nozzle with a small opening angle

The flow inside an over expanding rectangular nozzle with a small opening angle of 1.6° is investigated by means of high-speed schlieren and shadowgraph photography, pressure probes and hot-wire anemometry on the nozzle centre line in order to measure the turbulent fluctuations generated by the occurring shock wave/boundary layer interaction. Additionally, an optical shock capturing tool is deployed to measure the amplitude and frequency of the shock train oscillation. Varying the back pressure, the pre-shock Mach number is changed between Ma1 = 1.1 and 2.1. Two different modes of turbulence generation and distribution are detected. For a single normal shock and a normal shock train, the normal Reynolds stress \( \overline{{u^{\prime 2} }} \) on the channel axis is only slightly increased compared to the free stream value, whereas for the cases of a lambda foot shock train and an x-type shock train, a strong intensification by forming a turbulent mixing zone can be observed.

Turbulent Transonic Flow Over Smooth and Rough Circular Arc Bumps in a Freestream

Turbulent transonic freestream flow over a plane smooth surface embedded with smooth and rough circular arc bumps is computed and analyzed using the k – ω turbulence model to determine the global effect of surface roughness on the shock/boundary layer interaction. Computations are done for various freestream Mach numbers, equivalent sand grain surface roughness heights of the bump, and radius of the bump. The influence of the increase in surface roughness height transcends over onto the shock boundary layer zone and the observations are discussed. It is observed that the surface roughness causes upstream movement of the shock, increases the skin friction coefficient, extends the separation length, reduces the pre-shock Mach number, and enhances the shock/boundary layer interaction zone.

3‐D Modeling of Shock‐induced Precursor Decomposition and Nano‐Particle Growth

AbstractIn the ongoing joint project “Gasdynamically induced nano–particles” (PAK 75/1) a novel method of gas–phase synthesis of nano–particles is being developed [1]. This project is supported by the Deutsche Forschungsgemeinschaft (DFG), the pilotfacility is erected in collaboration with Evonik Degussa, Hanau, Germany. The key features of the new method are the static temperature increase across a stationary shock to provide ignition conditions of the precursor and the subsequent gasdynamic quenching of the particle growth when the desired particle diameter of 10−8m is reached. In this work the decomposition of the precursor, the reactive heat release and the particle growth are coupled with the 3–D transonic flow inside the particle reactor. The simulation results show the effect of shock/boundary layer interactions on the decomposition reaction as well as the effects of the reactive heat release on the shock location and the resulting particle size distribution. The Reynolds number at the shock location is Rex=9·106, the boundary layer thickness is δ=2.2 mm and the pre–shock Mach number is M=1.58. The complex transonic reactive flow within the particle reactor requires a high mesh resolution to resolve the local details of the internal flow problem. In addition, an efficient particle model is required. The formation and growth of the particles are modeled by three separate reactions. The primary reaction is the decomposition of the precursor and the production of monomers. It is modeled by a one step reaction described by an Arrhenius equation. The secondary reaction, the formation of critical nuclei is in our case negligible, because of the high supersaturation ratio of the order of 103 instantly after the primary reaction, where the monomers are already critical nuclei. The tertiary reaction is the particle growth by surface condensation, coagulation and single–aggregation. To simulate the particle growth we apply a local monodisperse bimodal formulation. Thereby, the monodisperse model of Kruis et al. [2] is extended by an additional discrete monodisperse mode for the critical nuclei. This method describes the local particle size due to turbulent mixing, coagulation and coalescence. The coagulation starts in the Knudsen regime Kn ≫ 1 and reaches the continuum regime with particle diameters of the order of 10−8m and a mean free path of the same order of magnitude. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Transonic radial compressor inlet design

The design of radial compressor inlets for transonic flow is examined. A theoretical model [1] quantifies the losses in the tip sections caused by the choke margin (incidence) and the blockage of the blades. It identifies clear design rules for the tip sections: to achieve the highest efficiency, these require minimum blockage (low blade thickness and splitter vanes) and low choke margin (close to the unique-incidence condition). Simulations of the NASA rotor 37 transonic axial compressor (with CFX-TASCflow) are used to validate the use of three-dimensional viscous computational fluid dynamics (CFD) for transonic compressor inlets and to demonstrate that the key performance features suggested by the simple model are also modelled in three-dimensional viscous flow simulations. The simple model together with CFD simulations has been used for the design of tip sections at the inlet of a transonic radial compressor. CFD simulations were used to select the position of the shock to give a low choke margin, to reduce the preshock Mach number and also to optimize the shape and position of the leading edge of the splitter vanes.

Numerical analysis of sweep effects in shrouded propfan rotors

To study blade sweep effects on loss production and energy transfer a numerical analysis has been undertaken on three 10-bladed fan rotors with low-pressure ratio and different sweep. Pressure ratio and sweep are in the typical range of propfans. The results of two rotors with 30-deg forwardand backward-swept blades are compared to those of an unswept propfan rotor. The geometry of the profiles of the swept rotors on each cylindrical position is identical with that of the unswept rotor. The numerical analysis shows that the total pressure ratio of the swept rotors is lower than that of the unswept rotor over the whole span. Only in the vicinity of the hub is the pressure ratio higher in the case of the forward-swept rotor. The decrease of the total pressure ratio at midspan, by sweeping the rotor, is due to an oblique shock with lower preshock Mach number and an increase of the boundary layer at the suction side. Sweeping the rotor has the effect to induce strong radial pressure gradients at the leading edge. The deflection of the flow towards and off the end-walls due to this pressure gradient has the effect of a changed diffusion and expansion of the flow in the vicinity of the endwalls. The emphasis of this article is not to directly provide rotors with better pressure ratios and efficiencies, but to explain the basic effects by sweeping fan-rotors as references for improving the rotor-aerodynamic.

An Investigation of a Strong Shock-Wave Turbulent Boundary Layer Interaction in a Supersonic Compressor Cascade

Experiments have been performed in a supersonic cascade facility to elucidate the fluid dynamic phenomena and loss mechanism of a strong shock-wave turbulent boundary layer interaction in a compressor cascade. The cascade geometry is typical for a transonic fan tip section that operates with a relative inlet Mach number of 1.5, a flow turning of about 3 deg, and a static pressure ratio of 2.15. The strong oblique and partly normal blade passage shock-wave with a preshock Mach number level of 1.42 to 1.52 induces a turbulent boundary layer separation on the blade suction surface. The free-stream Reynolds number based on chord length was about 2.7 × 106. Cascade overall performance, blade surface pressure distributions, Schlieren photographs, and surface visualizations are presented. Detailed Mach number and flow direction profiles of the interaction region (lambda shock) and the corresponding boundary layer have been determined using a Laser-2-Focus anemometer. The obtained results indicated that the axial blade passage stream sheet contraction (axial velocity density ratio) has a significant influence on the mechanism of strong interaction and the resulting total pressure losses.