Navier-Stokes Code Research Articles

A high-order characteristics upwind FV method for incompressible flow and heat transfer simulation on unstructured grids

This paper presents a new unstructured-grid upwind finite-volume algorithm for accurate numerical simulation of incompressible flows and convection heat transfer on unstructured grids. It is an upwind method at both the differential equation level and discretized equation level, based on the method of characteristics. This is made possible with the introduction of Chorin's (J. Comput. Phys. 2 (1967) 12–26), artificial compressibility formulation to the incompressible flow equations. Flow variables are calculated along characteristics and their initial values are interpolated based on the signs of the corresponding characteristic speed. In addition, an upwind-biased interpolation method of third-order accuracy is used for interpolating flow variables on unstructured grids. With these inherent upwinding techniques for evaluating convection fluxes at control volume surfaces, no artificial viscosity is required. And the method is accurate and less sensitive to the grid orientation, thus suitable for unstructured grid application. The use of the finite-volume method combined with unstructured grids makes the scheme very flexible in dealing with very complex boundary geometries, while remaining to be fully conservative at the cell as well as global level. The discretized equations are solved by an explicit multistage Runge–Kutta time stepping scheme which is found to be efficient in terms of CPU and memory overheads. A computer code has been developed which uses the numerical methods presented, and a highly efficient edge-based data structure for flux calculation and data storage. A number of well-documented test cases, including 2D laminar flow in a channel with a backward-facing step, forced and natural convection flows, have been calculated in order to validate the code and evaluate the performance of the numerical algorithm. Good agreement between the computed and measured results have been obtained for all the cases. To demonstrate the accuracy of the third-order scheme, flow in another channel with a backward-facing step studied by Gartling (Int. J. Numer. Meth. Fluids (1990) 11) is simulated with both the third-order and first-order schemes. It is shown that the third-order scheme can produce a velocity profile across the channel that has perfect agreement with that of Gartling (local citation), whilst the first-order scheme cannot even predict the separation near the upper wall. The proposed numerical methods are also used to calculate 3D incompressible inviscid flows, and results show that the method is accurate and robust for general 3D simulation. The 3D Navier–Stokes code is later used to study a lid-driven cavity flow at a Reynolds number of 400. The unstructured grid used has 97,336 nodes and 455,625 tetrahedral elements with strong grid clustering near the walls. The convergence rate is found to be satisfactory, which shows that the method is also robust for 3D Navier–Stokes simulation. The results obtained agree well with those reported by Jiang et al. (Comput. Meth. Appl. Mech. Eng. 114 (109) (1994)). Results obtained using the second-order central scheme with artificial viscosity are also presented for comparison. It is observed that the third-order characteristics scheme is more accurate than the latter, thus confirming its third-order accuracy.

COMPUTATIONAL SIMULATION OF DYNAMIC STALL ON THE NLR 7301 AIRFOIL

The dynamic stall behavior of the supercritical NLR 7301 airfoil is analyzed with a 2-D thin-layer Navier–Stokes code. The code solves the compressible Reynolds-averaged Navier-Stokes equations with an upwind biased numerical scheme in combination with the Baldwin–Lomax or the Baldwin–Barth turbulence models. The effect of boundary layer transition is incorporated using the transition length model of Gostelow et al. The transition onset location is determined with Michel's formula or it can be specified as an input parameter. The two turbulence models yield significantly different steady-state lift coefficients at incidences greater than 8°. The use of the one-equation Baldwin–Barth model together with the Gostelow transition model is found to give substantially better agreement with the experimental data of McCroskeyet al. than the Baldwin–Lomax model. Also, the unsteady computations are strongly affected by the choice of the turbulence model. The Baldwin–Barth model predicts the lift hysteresis loops consistently better than the algebraic turbulence model. However, the one-equation model improves the prediction of the moment hysteresis loops only for one test case.

Study of Icing Effects on Performance and Controllability of an Accident Aircraft

The activities at NASA John H. Glenn Research Center at Lewis Field in support of a National Transportation Safety Board accident investigation are described. An icing research tunnel (IRT) test was conducted in January 1998. Most conditions for the test were based on raw and derived data from the flight data recorder recovered from the accident and on the current understanding of the meteorological conditions near the accident. Using a two-dimensional Navier-Stokes code, the flowfield and resultant lift and drag were calculated for the wing section with various ice shapes accreted in the IRT test. Before the final calculations could be performed extensive examinations of geometry smoothing and turbulence modeling were conducted

Passive control of shock wave–boundary-layer interactions

AbstractThe passive control of a shock wave-boundary-layer interaction involves placing a porous surface beneath the interaction, allowing high pressure air from the flow downstream of the shock wave to recirculate through a plenum chamber into the low pressure flow upstream of the wave.The simple case of a normal shock wave at a Mach number of 1·4 interacting with the turbulent boundary layer on a flat wall is investigated both experimentally and numerically. The experimental investigation made use of holographic interferometry, while the computational section of the investigation made use of a Navier-Stokes code to derive pressure gradients, boundary-layer properties and total pressure losses in the interaction region. It is found that the structure of shock wave-boundary-layer interactions with passive control consists of a leading, oblique shock wave followed by a lambda foot. The oblique wave originates from the upstream end of the porous region, and its strength is determined by the magnitude of the local blowing velocities. The shape of the lambda foot depends on the position of the main shock relative to the control region, resembling an uncontrolled foot when the main shock wave is towards the downstream end of the porosity, but becoming increasingly large as the shock moves upstream and eventually merging with the leading, oblique shock to form a single, large, lambda structure.Improved forms of passive control are suggested based on the findings of this investigation, including the use of passive control systems which incorporate streamwise variations in the level of porosity.

Heat transfer on a film-cooled rotating blade

Abstract A multi-block, three-dimensional Navier–Stokes code has been used to compute heat transfer coefficient on the blade, hub and shroud for a rotating high-pressure turbine blade with 172 film-cooling holes in eight rows. Film-cooling effectiveness is also computed on the adiabatic blade. Wilcox's k – ω model is used for modeling the turbulence. Of the eight rows of holes, three are staggered on the shower-head with compound-angled holes. The multi-block grid consists of 4818 elementary blocks which were merged into 280 super blocks. The viscous grid has nearly two million cells. Each hole-exit, in its true oval shape, has 80 cells within it so that coolant velocity, temperature, k and ω distributions can be specified at these hole-exits. For the given parameters, heat transfer coefficient on the cooled, isothermal blade is found to be high in the tip region, and in the leading edge region between the hub and blade mid-span. The effectiveness over the cooled, adiabatic blade is the lowest in these regions. Results for an uncooled blade are also shown, providing a direct comparison with those for the cooled blade. The heat transfer coefficient is much higher on the blade tip and shroud as compared to that on the hub for both the cooled and the uncooled cases. Effect of gridding the tip clearance gap vs. use of a tip clearance model, as well as the effect of different orientation of coolant ejection from shower-head holes is found to be small as far as the heat transfer coefficient or the adiabatic effectiveness on the blade surface is concerned.

The Impact of Viscous Effects on the Aerodynamic Damping of Vibrating Transonic Compressor Blades—A Numerical Study

A parametric study which investigates the influence of viscous effects on the damping behavior of vibrating compressor cascades is presented here. To demonstrate the dependence of unsteady aerodynamic forces on the flow viscosity, a computational study was performed for a transonic compressor cascade of which the blades underwent tuned pitching oscillations while the flow conditions extended from fully subsonic to highly transonic flow. Additionally, the reduced frequency and Reynolds number were varied. In order to check the linear behavior of the aerodynamic forces, all calculations were carried out for three different oscillation amplitudes. Comparisons with inviscid Euler results helped identify the influence of viscous effects. The computations were performed with a Navier-Stokes code, the basic features of which are the use of an AUSM upwind scheme, an implicit time integration, and the implementation of the Baldwin-Lomax turbulence model. In order to demonstrate the possibility of this code to correctly predict the unsteady behavior of strong shock-boundary layer interactions, the experiment of Yamamoto and Tanida on a self-induced shock oscillation due to shock-boundary layer interaction was calculated. A significant improvement in the prediction of the shock amplitude was achieved by a slight modification of the Baldwin Lomax turbulence model. An important result of the presented compressor cascade investigations is that viscous effects may cause a significant change in the aerodynamic damping. This behavior is demonstrated by two cases in which an Euler calculation predicts a damped oscillation whereas a Navier-Stokes computation leads to an excited vibration. It was found that the reason for these contrary results are shock-boundary-layer interactions which dramatically change the aerodynamic damping.

A Navier–Stokes Analysis of the Stall Flutter Characteristics of the Buffum Cascade

Numerical stall flutter prediction methods are much needed, as modern jet engines require blade designs close to the stability boundaries of the performance map. A Quasi-3D Navier–Stokes code is used to analyze the flow over the oscillating cascade designed and manufactured by Pratt & Whitney, and studied at the NASA Glenn Research Center by Buffum et al. The numerical method solves for the governing equations with a fully implicit time-marching technique in a single passage by making use of a direct-store, periodic boundary condition. For turbulence modeling, the Baldwin–Lomax model is used. To account for transition, the criterion to predict the onset location suggested by Baldwin and Lomax is incorporated. Buffum et al. investigated two incidence cases for three different Mach numbers. The low-incidence case at a Mach number of 0.5 exhibited the formation of small separation bubbles at reduced oscillation frequencies of 0.8 and 1.2. For this case the present approach yielded good agreement with the steady and oscillatory measurements. At high incidence at the same Mach number of 0.5 the measured steady-state pressure distribution and the separation bubble on the upper surface was also found in good agreement with the experiment. But computations for oscillations at high incidence failed to predict the negative damping contribution caused by the leading edge separation. [S0889-504X(00)01304-0]

CFD-simulation of the flow through a fluidic element

The outflow channel of the fluidic jet reaction control element (FLE) and hence the direction of the thrust vector may be controlled by the injection of a secondary jet through one of the slits downstream of the inlet nozzle in the side walls. The main medium used is gaseous nitrogen, which is supplied from a reservoir chamber. Depending on the pressure there, three different operating modes can be distinguished. In order to reduce development time, the DLR Euler and Navier–Stokes code FLOWer has been extended for the numerical simulation of the flow through a fluidic element. In the present paper the code is verified and validated for this application. The influence of grid density, turbulence model, boundary conditions and the geometry of the external walls is investigated. The code is validated by comparing numerically obtained results with experimental data, including wall pressure and thrust measurements as well as differential interferometry photos. Numerical solutions are obtained for chamber pressures ranging from 60 to 100 bar, considering each case with and without injection of a secondary mass flow.

Recasting the Fay-Riddell formulae for computing the stagnation point heat flux

The Fay-Riddell formulae, used to compute the heat flux at the stagnation point of spherical bodies in very high speed, laminar flow and dissociating air, have been revived and recast. As these formulae were obtained by fitting a number of results of the original Fay-Riddell computing procedure, which suffered from inaccuracies concerning operative parameters, it is to be expected that these inaccuracies also influence the correctness of the formulae. A sensitivity analysis has been made in order to identify the most critical parameter. Recast formulae have been calibrated using the results of the improved version of the Fay-Riddell computing procedure and then validated both by numerical results of a Navier-Stokes code and by experimental data. For this purpose two sets of heat flux measurements have been made in HEBDAF (high enthalpy blown-down arc facility) at the University of Naples, matching the operating conditions of the formula for a frozen boundary layer and non-catalytic wall. Recast formulae are valid in the range of free-stream total enthalpy between 3 and 37 MJ/kg.

Multiobjective genetic algorithm applied to aerodynamic design of cascade airfoils

A multiobjective genetic algorithm (GA) based on Fonseca-Fleming's Pareto-based ranking and fitness-sharing techniques has been applied to aerodynamic shape optimization of cascade airfoil design. Airfoil performance is evaluated by a Navier-Stokes code. Evaluation of GA population is parallelized on the Numerical Wind Tunnel, a parallel vector machine. The present multiobjective design seeks high pressure rise, high flow turning angle, and low total pressure loss at a low Mach number. Pareto solutions that perform better than existing control diffusion airfoils were obtained.

Control of Pseudo-Shock by the Slot-Injection.

It is well known that the boundary layer separation, which is induced by the adverse pressure gradient of pseudo-shock, affects the dynamical feature of the pseudo-shock such as the shape of the first shock, the pressure recovery rate and the self-induced oscillation. So, it is considered that the suppression of the separation is effective on the shock wave/boundary layer interaction. In this research, the boundary layer control with the slot injection is studied experimentally and numerically. The expriments were carried out in a blow-down supersonic wind tunnel at a free stream Mach number of 2.0. Numerical simulations were made with the 2-D compressible Navier-Stokes code. In sloving the equations, 2nd-order accurate Harten-Yee's upwind TVD scheme and κ-ε turbulence model modifed for compressibility effects were used. The result shows that the separtion is appreciably suppressed and the first shock changes in its shape, so that the wall pressure fluctuation is greatly suppressed. In addition, the small slot high results in the lower total pressure loss.

Mach Number Effects on Turbine Blade Transition Length Prediction

The effect of a Mach number correction on a model for predicting the length of transition was investigated. The transition length decreases as the turbulent spot production rate increases. Many of the data for predicting the spot production rate come from low-speed flow experiments. Recent data and analysis showed that the spot production rate is affected by Mach number. The degree of agreement between analysis and data for turbine blade heat transfer without film cooling is strongly dependent on accurately predicting the length of transition. Consequently, turbine blade heat transfer data sets were used to validate a transition length turbulence model. A method for modifying models for the length of transition to account for Mach number effects is presented. The modification was made to two transition length models. The modified models were incorporated into the two-dimensional Navier–Stokes code, RVCQ3D. Comparisons were made between predicted and measured midspan surface heat transfer for stator and rotor turbine blades. The results showed that accounting for Mach number effects significantly improved the agreement with the experimental data.

A review of European code-validation studies in high-enthalpy flow

The paper focuses on the experiments performed in the European high–enthalpy facilities during the crewed space flight hypersonic ground testing technology programme. Emphasis is placed on simple configuration testing enabling validation of the physical modelling within non–equilibrium Navier–Stokes codes. The high–enthalpy facilities used are the ONERA hot shot F4 and the DLR Stalker tube HEG. The simple configurations are the Nozzle, the Electre blunt code, the hyperboloid flare, and the 70 degree blunt cone. In addition to these axisymmetric configurations, the Halis/Orbiter configuration was extensively tested and numerically computed to validate the ground to flight extrapolation methodology. Real gas effects on aerodynamic forces and in particular on pitching moment for the Halis have been reproduced in the F4 and compared with flight. The paper concludes with a series of recommendations for additional improvements in nozzle calibrations using non–intrusive methods and for an increased use of CFD for the design of experiments, the definition of the test environment, the interpretation of the results and finally the extrapolation to flight.

Numerical Simulation of the Shock-Tip Leakage Vortex Interaction in a HPC Front Stage

For a single-stage transonic compressor rig at the TU Darmstadt, three-dimensional viscous simulations are compared to L2F measurements and data from the EGV leading edge instrumentation to demonstrate the predictive capability of the Navier–Stokes code TRACE_S. In a second step the separated regions at the blade tip are investigated in detail to gain insight into the mechanisms of tip leakage vortex-shock interaction at operating points close to stall, peak efficiency, and choke. At the casing the simulations reveal a region with axially reversed flow, leading to a rotationally asymmetric displacement of the outermost stream surface and a localized additional pitch-averaged blockage of approximately 2 percent. Loss mechanisms and streamline patterns deduced from the simulation are also discussed. Although the flow is essentially three-dimensional, a simple model for local blockage from tip leakage is demonstrated to significantly improve two-dimensional simulations on S1-surfaces.

Development of an Implicit Method for Multi-fluid Flow Simulations

A fully coupled implicit method has been developed for solving the viscous full multi-fluid equations, which incorporate transport and generation of mass and momentum for each component present in a system. This work presents stability analysis and representative computational results of this algorithm. The stability analyses demonstrate the performance of several iterative schemes applied to the solution of the linearized block system which arises in the fully implicit formulation. These include block Jacobi and symmetric block Gauss–Siedel schemes using two forms of relaxation. A hierarchy of increasing physical complexity is pursued, starting with one-dimensional, two-fluid systems with minimum inter-field dynamic coupling and no mass transfer. These analyses are then extended to systems employing physically important inter-field forces (drag, dispersion, virtual mass). The effects of mass transfer, multiple fields (i.e., more than 2), and multiple dimensions are considered. A two-fluid Navier–Stokes code has been developed, guided by the stability analyses. One-dimensional and two-dimensional results generated with this code are presented, which verify the validity of the stability analyses presented for the coupled scheme, and the effectiveness of the method for flows of engineering relevance.

Computation of shock/boundary-layer interactions in bump channels with transport-type turbulence models

In this paper, an explicit time-marching finite-volume scheme has been used together with a number of convergence acceleration techniques such as the multigrid strategy. Two types of turbulence models, a Johnson—King (J—K) model and a two-layer k-ε/k-l model, have been incorporated and modified to model internal compressible flows with multiple walls. Some modifications have been made of the inner layer viscosity formulations of the J—K model in order to improve its predictive capability for flow separation. Partially implicit treatment of the transport-type equations of turbulence in the models is adopted, because the source terms in these equations can cause numerical stiffness when there are flow separation, sharp gradients and high cell-aspect ratio near the solid wall. A two-dimensional arc-bump flow investigated experimentally by Liu and Squire [X. Liu and L.C. Squire, Interaction on curved surface at transonic speed, in: Turbulent Shear/Shock Wave Interactions, IUTAM Symposium Palaiseau 1985 (Springer, Berlin Heidelberg 1985) 93–104.] was calculated using the J—K model with satisfactory agreement with the corresponding measurement. Although efficient and accurate, it is found that the J—K model lacks the theoretical generality to be extended to model three-dimensional (3D) complex internal flows with multiple walls. Therefore, a two-layer k-ε model is employed for 3D flow computation. Various measures are adopted to ensure stable and convergent numerical solution. A three-dimensional transonic channel flow with multiple shock/boundary layer interactions was studied with the aforementioned two-layer model and numerical methods. The results are compared with experimental measurements [J. Cahen, V. Couaillier, J. Delery and T. Pot, Validation of Navier—Stokes code using a k-ε turbulence model applied to a three-dimensional transonic tunnel, AIAA paper AIAA-93-0293, AIAA 1993] and numerical results obtained by using a Low-Reynolds-Number (LRN) k-ε model [VUB/FFA, Turbulence Models in EURANUS and the 3D Delery bump, Technical Report SNWP3.3/01, VUB, Pleinlaan 2, 1050 Brussels, Belgium and FFA, P.O. Box 11021, S-161 11 Bromma, Sweden 1993]. Compared with other (LRN) two-equation models, the two-layer model implemented is promising in modeling very complex 3D internal flows in terms of efficiency, robustness and accuracy. The two-layer model permits uniform distribution of flow properties to be specified as initial condition which makes the simulation easier to be carried out.

Observations on three-dimensional nonlinear transonic wall-interference assessment and correction using semispan wing data

The current interest in semispan wing testing generally places a greater demand on understanding wall-interference effects than is required in conventional sting-mounted model testing. As part of NASA Langley Research Center's development and evaluation of transonic wind-tunnel wall-interference assessment and correction (WIAC) ideas and methods, a nonlinear, three-dimensional, transonic WIAC code has been applied to four sets of transonic semispan wing data. These data were acquired nearly 20 years ago for the specific purpose of evaluating three-dimensional transonic computational fluid dynamics methodologies and included the measured wall (or near wall) pressure data that are required by the WIAC procedure. Previous papers have focused on the evaluation of nonlinear WIAC and other correction-method results by monitoring the correlations of corrected data and by using a Navier–Stokes code as an independent “free air” check. In the present paper, synoptic observations are made in regard to the transonic WIAC results and the factors that affect these results.

Parallelization of a multiblock flow code: an engineering implementation

Current trends in computer hardware are dictating a gradual shift toward the use of clusters of relatively inexpensive but powerful workstations, or massively parallel processing (MPP) machines, for scientific computing. However, most computational fluid dynamics (CFD) codes in use today were developed for large, shared-memory machines and are not readily portable to the distributed computing environment. One major hurdle in porting CFD codes to distributed computing platforms is the difficulty encountered in partitioning the problem so that the computation-to-communication ratio for each compute node (process) is maximized and the idle time during which one node waits for other nodes to transfer data is minimized. In the present work, pertinent issues involved in the parallelization of a widely used multiblock Navier–Stokes code TLNS3D are discussed. An engineering approach is used here to parallelize this code so that minimal deviation from the original (nonparallel) code is incurred. A natural partitioning along grid blocks is adopted in which one or more blocks are distributed to each of the available nodes. An automatic, static load-balancing strategy is employed for equitable distribution of computational work to specified nodes. Both parallel virtual machine (PVM) and message passing interface (MPI) protocols are incorporated for data communication to allow maximum portability to a wide range of computer configurations. Results are presented that are comparable with a priori estimates of performance for distributed computing and that are competitive in terms of central processing unit (CPU) time and wall time usage with large, shared-memory supercomputers.

Heat transfer on a film-cooled rotating blade using different turbulence models

A three-dimensional Navier–Stokes code has been used to compute the heat transfer coefficient on a film-cooled, rotating turbine blade. The blade chosen is the ACE rotor with five rows containing 93 film cooling holes covering the entire span. This is the only film-cooled rotating blade over which experimental data is available for comparison. Over 2.278 million grid points are used to compute the flow over the blade including the tip clearance region, using Wilcoxs k– ω model, Coakleys q– ω model, and the zero-equation Baldwin–Lomax (B–L) model. A reasonably good comparison with the experimental data is obtained on the suction surface for all the turbulence models. At the leading edge, the B–L model yields a better comparison than the two-equation models. On the pressure surface, however, the comparison between the experimental data and the prediction from the k– ω model is much better than from the other two models. Overall, the k– ω model provides the best comparison with the experimental data. However, the two-equation models require at least 40% more computational resources than the B–L model.

Flutter Computation of Turbomachinery Cascades Using a Parallel Unsteady Navier-Stokes Code

A quasi-three-dimensional multigrid Navier-Stokes solver on single- and multiple-passage domains is presented for solving unsteady flows around oscillating turbine and compressor blades. The conventional direct store method is used for applying the phase-shifted periodic boundary condition over a single blade passage. A parallel version of the solver using the message passing interface standard is developed for multiple-passage computations. In parallel multiple-passage computations, the phase-shifted periodic boundary condition is converted to a simple in-phase periodic condition. Euler and Navier-Stokes solutions are obtained for unsteady flows through an oscillating turbine cascade blade row with both the sequential and the parallel codes. It is found that the parallel code offers almost linear speedup with a slope close to 1 on multiple CPUs. In addition, significant improvement is achieved in convergence of the computation to a periodic unsteady state in the parallel multiple-passage computations due to the use of the in-phase periodic boundary conditions compared with that in the single-passage computations with phase-shifted periodic boundary conditions via the direct store method. The parallel Navier-Stokes code is also used to calculate the flow through an oscillating compressor cascade. Results are compared with experimental data and computations by other authors.