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A high-order-accurate finite-difference approach to direct simulations of transition and turbulence in compressible flows is described. Attention is given to the high-free-stream disturbance case in which transition to turbulence occurs close to the leading edge. In effect, computation requirements are reduced. A method for numerically generating free-stream disturbances is presented.
Abstract. The wind turbine design process requires performing thousands of simulations for a wide range of inflow and control conditions, which necessitates computationally efficient yet time-accurate models, especially when considering wind farm settings. To this end, FAST.Farm is a dynamic-wake-meandering-based mid-fidelity engineering tool developed by the National Renewable Energy Laboratory targeted at accurately and efficiently predicting wind turbine power production and structural loading in wind farm settings, including wake interactions between turbines. This work is an extension of a study that addressed constructing a diurnal cycle evolution based on experimental data (Quon, 2024). Here, this inflow is used to validate the turbine structural and wake-meandering response between experimental data, FAST.Farm simulation results, and high-fidelity large-eddy simulation results from the coupled Simulator fOr Wind Farm Applications (SOWFA)–OpenFAST tool. The validation occurs within the nocturnal stable boundary layer when corresponding meteorological and turbine data are available. To this end, we compared the load results from FAST.Farm and SOWFA–OpenFAST to multi-turbine measurements from a subset of a full-scale wind farm. Computational predictions of blade-root and tower-base bending loads are compared to 10 min statistics of strain gauge measurements during 3.5 h of the evolving stable boundary layer, generally with good agreement. This time period coincided with an active wake-steering campaign of an upstream turbine, resulting in time-varying yaw positions of all turbines. Wake meandering was also compared between the computational solutions, generally with excellent agreement. Simulations were based on a high-fidelity precursor constructed from inflow measurements and using state-of-the-art mesoscale-to-microscale coupling.
Wind fields were measured with the ground-based NASA/MSFC lidar are compared with the in situ NASA RB-57 aircraft measurements. The mean wind fields, the turbulence intensities, and the turbulence spectra determined from measurements by both systems are in very good agreement. Turbulence intensities and spectra were calculated from the fluctuations with time in the radial wind speed component. The second moment or Doppler frequency spectral width of the lidar measurements was also compared with turbulence intensities measured by the aircraft. These second moments could only be resolved at the very low altitudes (in three range bins). Turbulence intensities estimated from the spectral width data were an order of magnitude higher than those measured by the aircraft. An interesting boundary layer evolved during the progress of the experiment. The breakup of a stable boundary layer resulted in winds blowing in one direction above 600 m msl and in the opposite direction below that level. Both the aircraft and the lidar systems clearly identified this unusual boundary layer flow and showed the identical trends.
A numerical model has been developed for investigating boundary layer transition control for a flat plate boundary layer. Active control of a periodically forced boundary layer in an incompressible fluid is studied using surface heating techniques. The spatially evolving boundary layer is simulated. The Navier-Stokes and energy equations are integrated using a fully implicit finite difference/spectral method. Temperature perturbations are introduced locally along finite heater strips to directly attenuate the instability waves in the flow. A feedback control loop is employed in which a downstream sensor is used to monitor wall shear stress fluctuations. Active control of small amplitude two-dimensional and three-dimensional disturbances is numerically simulated. With proper phase control, in-phase reinforcement and out-of-phase attenuation are demonstrated. A receptivity study of the localized temperature perturbations is made. It is shown that narrow heater strips are more receptive in that they maximize the amplitude level of the disturbances in the flow. Active control of the early stages of the fundamental breakdown process is also numerically simulated. Control is achieved with either two-dimensional or three-dimensional control inputs.
This report documents the development, validation, and application of a spectrally accurate boundary-layer code, WINGBL2, which has been designed specifically for use in stability analyses of swept-wing configurations. Currently, we consider only the quasi-three-dimensional case of an infinitely long wing of constant cross section. The effects of streamwise curvature, streamwise pressure gradient, and wall suction and/or blowing are taken into account in the governing equations and boundary conditions. The boundary-layer equations are formulated both for the attachment-line flow and for the evolving boundary layer. The boundary-layer equations are solved by marching in the direction perpendicular to the leading edge, for which high-order (up to fifth) backward differencing techniques are used. In the wall-normal direction, a spectral collocation method, based upon Chebyshev polynomial approximations, is exploited. The accuracy, efficiency, and user-friendliness of WINGBL2 make it well suited for applications to linear stability theory, parabolized stability equation methodology, direct numerical simulation, and large-eddy simulation. The method is validated against existing schemes for three test cases, including incompressible swept Hiemenz flow and Mach 2.4 flow over an airfoil swept at 70 deg to the free stream.
The results from direct numerical simulations of a spatially evolving, supersonic, flat-plate turbulent boundary-layer flow, with free-stream Mach number of 2.25 are presented. The simulated flow field extends from a transition region, initiated by wall suction and blowing near the inflow boundary, into the fully turbulent regime. Distributions of mean and turbulent flow quantities are obtained and an analysis of these quantities is performed at a downstream station corresponding to Re(sub x)= 5.548 x10(exp 6) based on distance from the leading edge.
Surface heating techniques to control the three-dimensional laminar-turbulent transition process are numerically investigated for a water boundary layer. The Navier-Stokes and energy equations are solved using a fully implicit finite difference/spectral method. The spatially evolving boundary layer is simulated. Results of both passive and active methods of control are shown for small amplitude two-dimensional and three-dimensional disturbance waves. Control is also applied to the early stages of the secondary instability process using passive or active control techniques.
Recently Hall and Seddougui (1989) considered the secondary instability of large amplitude Goertler vortices in a growing boundary layer evolving into a three-dimensional flow with wavy vortex boundaries. They obtained a pair of coupled, linear ordinary differential equations for this instability which constituted an eigenproblem for the wavelength and frequency of this wavy mode. Investigations into the nonlinear version of this problem by Seddougui and Bassom have revealed several omissions in the numerical work of Hall and Seddougui. These issues are addressed in this note. In particular, it is found that many neutrally stable modes are possible. The properties of such modes are derived in a high wavenumber limit and it is shown that the combination of the results of Hall and Seddougui and the modifications made here lead to conclusions which are consistent with the available experimental observations.
Turbulent flows that exhibit inhomogeneities in the streamwise direction pose a particular challenge to numerical simulation approaches due to the need to prescribe time-dependent turbulent inflow conditions. In most cases the flow downstream is more or less 'driven' by the conditions at the inlet, making it necessary to specify realistic turbulent fluctuations that are in equilibrium with the assumed mean flow. This requirement often dictates that the inflow data should satisfy the Navier-Stokes equations, which in turn implies that an independent simulation be used to generate them. Detailed simulations for the purpose of creating inflow conditions can be costly and thus certain levels of approximation are desirable. In this paper we shall focus on an approximate yet accurate method for generating inflow conditions for spatially-developing boundary layer simulations. The proposed method is essentially a simplification of the method of Spalart and Leonard (1985), who devised an ingenious transformation that allows for the calculation of spatially evolving boundary layers in conjunction with periodic boundary conditions applied in the streamwise direction. While this method is elegant and highly accurate, it is more complicated than is necessary for the purpose of generating inflow data. A few key approximations are used in this work to arrive at a 'modified Spalart method' that is very easy to implement and efficient to use. The new method is shown to yield results that compare well with the computations of Spalart (1988). When used as a means of generating inflow data, the modified Spalart method is shown to be superior to existing approaches.
Turbulent spots evolving in a laminar boundary layer on a nominally zero pressure gradient flat plate are investigated. The plate is towed through an 18 m water channel, using a carriage that rides on a continuously replenished oil film giving a vibrationless tow. Turbulent spots are initiated using a solenoid valve that ejects a small amount of fluid through a minute hole on the working surface. A novel visualization technique that utilizes fluorescent dye excited by a sheet of laser light is employed. Some new aspects of the growth and entrainment of turbulent spots, especially with regard to lateral growth, are inferred from the present experiments. To supplement the information on lateral spreading, a turbulent wedge created by placing a roughness element in the laminar boundary layer is also studied both visually and with probe measurements. The present results show that, in addition to entrainment, another mechanism is needed to explain the lateral growth characteristics of a turbulent region in a laminar boundary layer. This mechanism, termed growth by destabilization, appears to be a result of the turbulence destabilizing the unstable laminar boundary layer in its vicinity. To further understand the growth mechanisms, the turbulence in the spot is modulated using drag-reducing additives and salinity stratification.
In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows associated with geometrically complex configurations. However, success in terms of accuracy and reliability has been limited to cases where the effects of turbulence and transition could be modeled in a straightforward manner. Even in simple flows, the accurate computation of skin friction and heat transfer using existing turbulence models has proved to be a difficult task, one that has required extensive fine-tuning of the turbulence models used. In more complex flows (for example, in turbomachinery flows in which vortices and wakes impinge on airfoil surfaces causing periodic transitions from laminar to turbulent flow) the development of a model that accounts for all scales of turbulence and predicts the onset of transition is an extremely difficult task. Fortunately, current trends in computing suggest that it may be possible to perform direct simulations of turbulence and transition at moderate Reynolds numbers in some complex cases in the near future. This presentation will focus on direct simulations of transition and turbulence using high-order accurate finite-difference methods. The advantage of the finite-difference approach over spectral methods is that complex geometries can be treated in a straightforward manner. Additionally, finite-difference techniques are the prevailing methods in existing application codes. An application of accurate finite-difference methods to direct simulations of transition and turbulence in a spatially evolving boundary layer subjected to high levels of freestream turbulence will be presented.
In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows associated with geometrically complex configurations. However, success in terms of accuracy and reliability has been limited to cases where the effects of turbulence and transition could be modeled in a straightforward manner. Even in simple flows, the accurate computation of skin friction and heat transfer using existing turbulence models has proved to be a difficult task, one that has required extensive fine-tuning of the turbulence models used. In more complex flows (for example, in turbomachinery flows in which vortices and wakes impinge on airfoil surfaces causing periodic transitions from laminar to turbulent flow) the development of a model that accounts for all scales of turbulence and predicts the onset of transition is an extremely difficult task. Fortunately, current trends in computing suggest that it may be possible to perform direct simulations of turbulence and transition at moderate Reynolds numbers in some complex cases in the near future. This presentation will focus on direct simulations of transition and turbulence using high-order accurate finite-difference methods. The advantage of the finite-difference approach over spectral methods is that complex geometries can be treated in a straightforward manner. Additionally, finite-difference techniques are the prevailing methods in existing application codes. An application of high-order-accurate finite-difference methods to direct simulations of transition and turbulence in a spatially evolving boundary layer subjected to high levels of freestream turbulence will be presented.
This report deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux, were shown to compare well with experiment. The results indicate that the essential features of the transition process have been captured. The numerical method used here can be applied to complex geometries in a straightforward manner.
The work in this report was conducted at NASA Ames Research Center during the period from August 1993 to January 1995 deals with the direct numerical simulation of transitional and turbulent flow at low Mach numbers using high-order-accurate finite-difference techniques. A computation of transition to turbulence of the spatially-evolving boundary layer on a heated flat plate in the presence of relatively high freestream turbulence was performed. The geometry and flow conditions were chosen to match earlier experiments. The development of the momentum and thermal boundary layers was documented. Velocity and temperature profiles, as well as distributions of skin friction, surface heat transfer rate, Reynolds shear stress, and turbulent heat flux were shown to compare well with experiment. The numerical method used here can be applied to complex geometries in a straightforward manner.
Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.
The linear and the nonlinear stability of disturbances that propagate along the attachment line of a three-dimensional boundary layer is considered. The spatially evolving disturbances in the boundary layer are computed by direct numerical simulation (DNS) of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced either by forcing at the in ow or by applying suction and blowing at the wall. Quasi-parallel linear stability theory and a nonparallel theory yield notably different stability characteristics for disturbances near the critical Reynolds number; the DNS results con rm the latter theory. Previously, a weakly nonlinear theory and computations revealed a high wave-number region of subcritical disturbance growth. More recent computations have failed to achieve this subcritical growth. The present computational results indicate the presence of subcritically growing disturbances; the results support the weakly nonlinear theory. Furthermore, an explanation is provided for the previous theoretical and computational discrepancy. In addition, the present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line.
Abstract Methane (CH 4 ) contributes significantly to global warming. However, accurate identification of CH 4 sources for reducing CH 4 emissions is often hampered by inadequate accuracy and spatiotemporal coverage of CH 4 detection, and lack of accurate CH 4 forward modeling used in top‐down inversion systems. In this study, a field experiment was conducted in Pampa, Texas using two CH 4 sensors (LI‐COR and OGI camera) to detect CH 4 releases. We investigated whether high‐resolution simulations using the Weather Research and Forecasting (WRF) model with greenhouse gases (WRF‐GHG) could accurately simulate the CH 4 plumes in the presence of evolving atmospheric boundary layer from sunrise to noon. CH 4 plumes showed substantial variation in time. At a release rate of ∼17.5 kg hr −1 , the maximum enhancement of CH 4 measured by LI‐COR was 2.6 ppm at sunrise (7:36 a.m.), 250 m from the release location. Within half an hour after sunrise, this enhancement decreased to 0.3–0.4 ppm. The enhancement was 0.2 ppm by 10:00 a.m. and further dropped to less than 0.1 ppm after 11:30 a.m. Due to the low temperature at sunrise, the OGI camera failed to detect the CH 4 plume. The WRF‐GHG large‐eddy simulation (LES) with 32 m grid spacing successfully reproduced these CH 4 enhancements. In situ measurements together with numerical simulations illustrate the impact of the transition from a stable boundary layer in the early morning to a convective boundary layer at noon on the dispersion of CH 4 plumes. Additionally, CH 4 plumes from a cattle farm in Oklahoma are briefly examined using the same modeling approach.
The objective of this project was to evaluate and develop subgrid-scale (SGS) turbulence models for large eddy simulations (LES) of compressible flows. During the first phase of the project results from LES using the dynamic SGS model were compared to those of direct numerical simulations (DNS) of compressible homogeneous turbulence. The second phase of the project involved implementing the dynamic SGS model in a NASA code for simulating supersonic flow over a flat-plate. The model has been successfully coded and a series of simulations has been completed. One of the major findings of the work is that numerical errors associated with the finite differencing scheme used in the code can overwhelm the SGS model and adversely affect the LES results. Attached to this overview are three submitted papers: 'Evaluation of the Dynamic Model for Simulations of Compressible Decaying Isotropic Turbulence'; 'The effect of the formulation of nonlinear terms on aliasing errors in spectral methods'; and 'Large-Eddy Simulation of a Spatially Evolving Compressible Boundary Layer Flow'.