Numerical simulation of compression corner flows at Mach number 9

At hypersonic speeds, the external wall temperatures of an aerospace vehicle vary significantly. As a result, there is a considerable heat transfer variation between the boundary layer and the wall of the hypersonic vehicle. In this article, numerical computations are performed to investigate the effect of wall temperature on the separation bubble length in laminar hypersonic shock-wave/boundary-layer interaction flows over double-cone configuration at the Mach number of 12.2. The flow field is described in detail in terms of different shocks, expansion fans, shear layer and separation bubble. The variation of the Prandtl number has a negligible effect on the flow field and wall data. A specific heat ratio of less than 1.4 results in the better prediction of wall pressure and heat flux in the shock/boundary-layer interaction region. It is observed that as the wall temperature is increased, the separation bubble size and hence the separation shock length increases. The high firmness of the laminar boundary-layer at a high Mach number shows that the wall temperature in the shock/boundary-layer interaction region has little effect. The peak wall pressure and heat flux decrease with an increase in wall temperature. An estimation is developed between separation bubble length and wall temperature based on the computed results.

Laminar-to-turbulent transition phenomena are ubiquitous in natural and industrial flows. As to the Reynolds-averaged Navier–Stokes (RANS) simulation method, the workhorse for accurate prediction of such flow regime boils down to the consideration of the transition effect in turbulence modeling. In this paper, an industrial–practical transition–turbulence model with excellent accuracy, robustness, and efficiency is established by the fully connected artificial neural network (ANN), which maps the relation between the RANS mean flow variables and an intermittency factor. A one-equation local correlation-based transition model coupled with Menter's shear stress transport (SST) model is taken as the benchmark. The present two-way coupling ANN model is trained with two National Advisory Committee for Aeronautics (NACA) airfoils, that is, NACA0012 and NACA2418, at various angles of attack and Mach numbers, while tested with the A-airfoil, NACA0015, and RAE 2822 supercritical airfoils in different flow states. The a posteriori test results manifest that the mean pressure coefficient, skin friction coefficient, size of laminar separation bubble, mean streamwise velocity, Reynolds shear stress, and lift/drag/moment coefficient predicted by the ANN model are all in good agreement with those given by the benchmark transition-based SST model. Furthermore, the ANN model exhibits higher calculation efficiency and convergence speed than the traditional transition-predictive SST model. The present work may pave a new way for machine learning methods to be used in integrated transition–turbulence modeling toward industrial applications.

In the combustor inlet diffuser section of gas turbine engine, high-velocity air from compressor flows into the diffuser, where a considerable portion of the inlet velocity head PT3 − PS3 is converted to static pressure (PS) before the airflow enters the combustor. Modern high through-flow turbine engine compressors are highly loaded and usually have high inlet Mach numbers. With high compressor exit Mach numbers, the velocity head at the compressor exit station may be as high as 10% of the total pressure. The function of the diffuser is to recover a large proportion of this energy. Otherwise, the resulting higher total pressure loss would result in a significantly higher level of engine specific fuel consumption. The diffuser performance must also be sensitive to inlet velocity profiles and geometrical variations of the combustor relative to the location of the pre-diffuser exit flow path. Low diffuser pressure losses with high Mach numbers are more rapidly achieved with increasing length. However, diffuser length must be short to minimize engine length and weight. A good diffuser design should have a well considered balance between the confliction requirements for low pressure losses and short engine lengths. The present paper describes the effect of divergence angle on diffuser performance for gas turbine combustion chamber using Computational Fluid Dynamic Approach. The flow through the diffuser is numerically solved for divergence angles ranging from 5 to 25°. The flow separation and formation of wake regions are studied.

An existing three dimensional Navier-Stokes flow solver with an explicit Runge-Kutta algorithm and a low Reynolds number k-ε turbulence model has been modified in order to simulate turbomachinery flows in a more efficient manner. The solver has been made to converge more rapidly through use of the mutligrid technique. Stability problems associated with use of multigrid in conjunction with two equation turbulence models are addressed and techniques to alleviate instability are investigated. Validation for the new code was performed with a transonic turbine cascade tested by Perdichizzi. In the fully three dimensional turbulent cascade, real convergence (i.e. CPU time) was improved nearly two times the original code. Robustness was enhanced with the full multigrid initialization procedure. The same test case was then used to perform a series of simulations that investigated the effect of different exit Mach numbers on secondary flow features. This permitted an in depth study into the mechanisms of secondary flow formation and secondary losses at high Mach numbers. In this cascade, it was found that secondary losses and secondary flow deviation, which are fairly constant in incompressible flows with similar geometries, underwent a large reduction in the compressible flow range. The structure of the trailing edge shock system and the reduced endwall boundary layer at supersonic exit conditions were shown to be very significant in reducing the amount of secondary flow and losses.

Despite a steady decrease in the overall usage of wind tunnels due to the increasing reliability and speed of computational fluid dynamics (CFD), ground testing remains a fundamental part of the development of an air vehicle. In this context, one of the new trends is represented by data assimilation (DA), whereby experimental and numerical measurements are combined together in an attempt to extract more complete and accurate information from the available data. This work presents an assessment of a variational data assimilation framework for the problem of wind tunnel wall interference corrections. The methodology minimizes the discrepancy between experimental measurements and the corresponding values from a Reynolds-averaged Navier-Stokes (RANS) simulation by optimally tuning the free-stream angle of attack and Mach number, as well as a corrective field for the turbulence model. The framework is first validated on synthetic data, and then tested on two cases at high Mach number and low angle of attack using pressure coefficients on the model’s surface as the reference measurements. The assimilated pressure coefficients match the reference ones better than those obtained from a linear correction technique. Furthermore, assimilating also a corrective term in the turbulence model improves the quality of the results with respect to assimilating only the angle of attack and Mach number.

The effect of Mach number on the evolution of instabilities in the compressible mixing layer is investigated. The full time-dependent compressible Navier–Stokes equations are solved numerically for a temporally evolving mixing layer using a mixed spectral and high-order finite difference method. The convective Mach number Mc (the ratio of the velocity difference to the sum of the free-stream sound speeds) is used as the compressibility parameter. Simulations with random initial conditions confirm the prediction of linear stability theory that at high Mach numbers (Mc > 0.6) oblique waves grow more rapidly than two-dimensional waves. Simulations are then presented of the nonlinear temporal evolution of the most rapidly amplified linear instability waves. A change in the developed large-scale structure is observed as the Mach number is increased, with vortical regions oriented in a more oblique manner at the higher Mach numbers. At convective Mach numbers above unity the two-dimensional instability is found to have little effect on the flow development, which is dominated by the oblique instability waves. The nonlinear structure which develops from a pair of equal and opposite oblique instability waves is found to resemble a pair of inclined A-vortices which are staggered in the streamwise direction. A fully nonlinear computation with a random initial condition shows the development of large-scale structure similar to the simulations with forcing. It is concluded that there are strong compressibility effects on the structure of the mixing layer and that highly three-dimensional structures develop from the primary inflexional instability of the flow at high Mach numbers.

The use of a monorail ro (; kE::t sled system is detailed and recomme nded as a method of obtaining aerodyna mic data in a regime of high Mach and Reynolds numbers .The aerodyna mic and mechanical design of the Sandia rocket sleds is described , and the data c ollection system discussed in detail.The system has been successfu lly used by Sandia Laborato ry t o a cquire pressure data on conecylinders .These data are compared with data from free-fligh t r ockP.ts, wind-tunn el tests, anrl computer calcula tions.A principal advantage of the sled testing method is the high degree of accuracy possible in determini ng actual test condition s, which include Mach number, static pressure , and static temperat ure .Explorato ry tests indicate that sleds may be used to collect other types of experiment al data such as heat-tran sfer and boundary -layer transition .The high-spee d sled testing technique appears to be the most promis ing method of simulatin g flight condition s at low altitudes at Mach numbers up to M = 8.To date, excellent data have been obtained at a velocity of 7430 ft/sec (M = 6.53) which to our knowledg e is the highest velocity ever attained by a ro cket sled.At this speed, and the Holloman Air Force Base track altitude, the Reynolds number was 42 x 106 per ft, and the -dynamic pressure, 55,000 lbs/ft2. I. Introduct ionDuring wind tunnel and f:;:-ee-fiigh t rocket tests of slightly blunted, slender ( 5 to 2 5 degree half-angle ) cone-cyli nder bodies, it was noted that at Mach numbers greater than 4, the surface pressure ratio, Pm/P cn (measure d surface pressure divided by free-stre am static pressure) , in the region just aft of the cone-cyli nder junction was a strong function of free-stre am Reynolds number.Attempts to gather wind tunnel data at Reynolds numbers over 107 per ft and Mach numbers over M = 4. 5 were thwarted by inadequat e high-pressure facilities and/ or inadequat e pressure measurin g capabiliti es to meet the accuracy requirem e nt of 2 percent of the pressure ratio .

Transonic limit cycle oscillation behavior of an aeroelastic airfoil with free-play

The present paper discusses the base pressure and heat transfer of various blunt bodies at hypersonic speeds. It is shown that the base to stagnation pressure ratio of a blunt body is relatively independent of the Mach and Reynolds numbers in hypersonic flow. The base to stagnation heat transfer, however, shows a dependency on the latter, as it is found to increase with Reynolds numnber. Experimental results of surface heat transfer rate around a cylinder model are presented. These data were obtained in a free piston shock tunnel with total enthalpy of 3.98 MJ/kg. The free-stream unit Reynolds number per metre and Mach number were 1.47 × 106 and 10.9 respectively. The fore-body heat transfer results show good agreement with the theories of Lees and Kemp et al. The base region heat transfer data showed a local minimum at around 130° from the stagnation point followed by a gradual recovery towards the rear stagnation region. The magnitudes of heat transfer ratio in the base region were representative of those in the base region of planetary entry type configurations.

The objective of this paper is to analyze the 3D buffet phenomenon which appears on a swept wing at a high Mach number and/or high angle of attack. This aerodynamic instability induces strong wall pressure fluctuations and as such limits aircraft envelope. Consequently, it is interesting to understand this phenomenon in order to not only improve aircraft performance but also to provide more flexibility during the design phase. Results from two wind tunnel tests on a 3D half wing-body configuration are presented for several freestream Mach numbers (0.78–0.86) and Reynolds numbers (2.83 × 106–8.49 × 106, based on the aerodynamic mean chord). The buffet phenomenon is characterized using steady and unsteady wall pressure measurements. By opposition to the 2D buffet which exhibits rather a well marked peak in the pressure spectra, the 3D buffet is characterized by a broadband bump at a much higher Strouhal number (between 4 and 7 times higher). It is also observed that two different instabilities coexist on the suction side of the wing: the 3D buffet phenomenon (with Strouhal numbers ranging between 0.2 and 0.6) and the Kelvin-Helmholtz instability (with Strouhal numbers ranging between 1 and 4). Each phenomenon has a different Strouhal number but also different convection velocities and propagation directions.

Corresponding to Oswatitsch’s Mach number independence principle the Mach number of hypersonic inviscid flows, , does not affect components of various non-dimensional formulations such as velocity and density, pressure coefficients and Mach number behind a strong shock. On this account, the principle is significant in the development process for hypersonic vehicles. Oswatitsch deduced a system of partial differential equations which describes hypersonic flow. These equations are the basic gasdynamic equations as well as Crocco’s theorem which are reduced for the case of very high Mach numbers, . Their numerical solution can not only result in simplified algorithms prospectively utilized to describe the flow around bodies flying mainly in the lower stratosphere with very high Mach numbers. It also offers a deeper understanding of similarity effects for hypersonic flows. In this paper, a solution method for Oswatisch’s equations for perfect gas, based on a 4-step Runge-Kutta-algorithm, is presented including a fast shock-fitting procedure. An analysis of numerical stability is followed by a detailed comparison of results for different Mach numbers and ratios of the specific heats.

Many electrically and heat conducting fluid flows cannot be described within the framework of incompressible medium or by compressible magnetohydrodynamic equations on the assumption of polytropic (or adiabatic) process. Therefore, we consider a heat conducting compressible fluid with the use of an energy equation. Application of large eddy simulation approach to heat conducting compressible magnetohydrodynamics is considered. The system of the filtered magnetohydrodynamic equations with the total energy equation using the mass-weighted filtering procedure has been obtained. It is shown that novel subgrid-scale terms arise in the Favre-filtered equations due to the presence of a magnetic field in the total energy equation. Parametrizations of these extra terms are developed. In order to derive these subgrid-scale terms, we use an approach based on generalized central moments. Computations at various Mach numbers are made for decaying compressible magnetohydrodynamic turbulence. The obtained numerical large eddy simulation results are analyzed on the basis of comparison with results of numerical experiments performed by direct numerical simulation. Validity of large eddy simulation method is thus demonstrated. It is shown that consideration of the subgrid-scale terms in the total energy equation scarcely affects the kinetic and the magnetic energy for low and even high Mach number, while for the temperature the presence of subgrid-scale models in the energy equation is an important condition for improvement in calculation accuracy of thermodynamic quantities. The technique with the mass-weighted filtering and with the use of various types of subgrid-scale models provides good calculation accuracy for different problems for compressible fluid in the absence of discontinuities, associated with the appearance of shocks, in other words, when the value of the Mach number is low or moderate (that is, the flow is subsonic). For supersonic magnetohydrodynamic flows, it is necessary to use special numerical methods.

This paper presents an investigation of Reynolds-averaged Navier-Stokes (RANS) turbulence models used in computational fluid dynamics (CFD) simulations of boundary layer flow and heat transfer in high Mach number flows. This study evaluates an industry standard RANS turbulence model (k-ω SST [1]) and a recently proposed modification to that model [2], for prediction of the mean velocity field in selected test cases. The test cases were previously documented by Duan et al. [3], who used direct numerical simulation (DNS) to calculate boundary layer flow of an ideal gas over a flat plate at freestream Mach numbers ranging from 2.5 to 14 and wall to recovery temperature ratios of 0.18 to 1. Boundary layer profiles were evaluated at two streamwise locations, one where the boundary layer height matched the DNS data and the second where the wall shear stress matched DNS data. Results show that the accuracy of RANS models degrades for high-speed regimes compared to incompressible or subsonic flow but that the compressibility correction factor [2] improves the results for some of the test cases.

Introduction T purpose of the present note is to indicate some general correlations of the available wake-transition data for spheres, cones, wedges, cylinders, and sphere-cones ; the parameters used are the freestream Reynolds number (based on the transition length measured from the base of the body) and the freestream Mach number Additionally, it is found that, by multiplying the Reynolds number by a suitable Mach number function, the effects of body shape are scaled out (within the inherent scatter), and the data for all body shapes correlate This Mach number function is the square of the ratio of freestream Mach number to local inviscid Mach number in the wake region

Tests of a 40% scale model of the inlet to a rocket-based combined-cycle (RBCC) engine were conducted in the NASA Lewis Research Center's 1-Foot by 1-Foot Supersonic Wind Tunnel at Mach numbers from 4 to 6. The full-scale RBCC engine is currently being tested at the NASA Lewis Plum Brook Station Hypersonic Tunnel Facility (HTF). The RBCC engine flowpath is divided into three rectangular channels by two struts. Each strut in the full-scale engine contains three small rocket chambers which exhaust out of the trailing edge. The leading edges of the struts begin ahead of the cowl lip to provide transverse compression surfaces within the inlet. Two non-compressi ve outer sidewalls represent planes of symmetry. Objectives of the sub-scale inlet tests included determining the starting and performance characteristics of a baseline leading edge strut configuration, and an alternate configuration. The effects of precompression plate boundary layer ingestion and freestream Reynolds number were also investigated. Detailed pilotpressure surveys at the strut trailing edge station were used to establish the inlet performance and also guide the design of ramjet fuel injectors for the full-scale engine. These measurements, surface static pressures, and oil flow visualization were used to validate an inlet CFD analysis. A remotely-actuated plug was used to simulate combustion back-pressure during the tests. Pilot-pressure surveys were obtained by traversing a remotely-actuated, 12-tube rake across the flowpath. Inlet performance for Mach 4 through 6 is summarized for all configurations tested. Results indicate that the untapered strut configuration generally sustained higher back-pressure, and had lower distortion than the tapered strut configuration. In addition, the untapered strut configuration self-started at all Mach numbers tested. The untapered strut configuration was subsequently chosen for the full-scale engine. Pilot-pressure surveys, and surface static pressure distributions have been published previously for the untapered strut configuration at the HTF test Mach numbers of 5 and 6. This report presents summary performance data for all the strut configurations at Mach numbers 4, 5, and 6.