Large Eddy Simulation Results Research Articles

Improved scale-resolved predictions of flow and heat transfer past a bluff body using partially averaged Navier–Stokes and a high-order eddy viscosity closure

The partially averaged Navier–Stokes (PANS) methodology has emerged as a viable bridging method of turbulence computations. Partially averaged Navier–Stokes methodology allows the user to implicitly choose the filter cut-off seamlessly in the inertial sub-range of motion. In past, most PANS simulations have been performed using the linear eddy viscosity closure for the unclosed turbulent stresses. Recently, evaluation of the advantages of higher order eddy viscosity closures with the PANS methodology has also been initiated. With our motivation to make further progress in this direction, this study presents an evaluation of PANS methodology wherein the turbulent stresses are modelled involving closures up to the cubic products of the resolved strain-rate and the rotation-rate tensors. After appropriately adapting a popular Reynolds-averaged Navier Stokes cubic closure for the PANS paradigm, an extensive evaluation of the method is performed in the flow past a heated sphere at a Reynolds number of 10,000. Time-averaged PANS predictions of surface-related as well as wake-related quantities are compared against available experimental, direct numerical simulation as well as large eddy simulation results. Indeed, very significant improvements are demonstrated by the PANS methodology in conjunction with the cubic eddy viscosity closure when compared to the corresponding predictions of the PANS methodology using a linear or even a quadratic eddy viscosity closure. This study demonstrates the promising augmentative ability of the higher eddy-viscosity to the PANS framework in performing improved simulations of the separated flows.

Characterization of the density-driven counter-flow through a doorway using Large Eddy Simulation

The density-driven bidirectional flow through an open doorway is of prime importance for ventilation and heat distribution between rooms in buildings. Although this flow has been extensively studied in the past, some important flow characteristics, such as unsteady flow phenomena, have not been documented in detail. Therefore, a high-resolution Large Eddy Simulation (LES) of the bulk flow through a doorway is performed. This LES can also serve as a reference solution to compare the accuracy of simpler evaluation methods, from the standard theoretical model calibrated using a discharge coefficient (Cd) to CFD solving the Reynolds-Averaged Navier-Stokes (RANS) equations. Based on LES results, the bidirectional flow can generate turbulent mixing in the middle of the doorway. However, the effects remain limited to the close vicinity of the neutral plane. The bidirectional airstream in the doorway further develops into two non-isothermal jets that entrain a fraction of the airflow. Furthermore, the two jets create large unsteady flow structures when they expand in the adjoining rooms. The results show that unsteady RANS is a good alternative to the resource-intensive LES if the analysis of turbulent jets is not of interest. The standard theoretical model demonstrates that two-dimensional contraction is the dominant effect driving the Cd value, while the viscous effects have a minor influence. Unlike previous studies, LES results show that viscous effects tend to increase the Cd as they moderate the contraction effect. This paper also provides guidelines for the laboratory measurement of Cd and its use in building performance simulation tools.

Modelling Study of Cycle-To-Cycle Variations (CCV) in Spark Ignition (SI)-Controlled Auto-Ignition (CAI) Hybrid Combustion Engine by Using Reynolds-Averaged Navier–Stokes (RANS) and Large Eddy Simulation (LES)

The spark ignition (SI)-controlled auto-ignition (CAI) hybrid combustion is characterized by early flame propagation combustion and subsequent auto-ignition combustion. The application of combined SI–CAI hybrid combustion can be used to effectively extend the operating range of CAI combustion and achieve smooth transitions between SI and CAI combustion modes. However, SI–CAI hybrid combustion can produce significant cycle-to-cycle variations (CCV). In order to better understand the sources of CCV and minimize its occurrence, the large eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) approaches were employed in this study to model and understand the cyclic phenomenon of SI–CAI hybrid combustion. Both the multi-cycle LES and RANS simulations were analyzed against the experimental measurements in a single cylinder engine at 1500 rpm and a 5.43 bar average indicated the mean effective pressure (IMEP). The detailed analysis of the in-cylinder pressure traces, IMEP, in-cylinder peak pressure (PP), peak pressure rise rate (PPRR) and the crank angles with fuel mass burned fraction at 10%, 50%, 90% and mode transition was performed. The results indicate that overall, the adopted LES simulations could effectively predict the cyclic variations in the hybrid combustion observed in the experiments, while the RANS simulations failed to reproduce the cyclic characteristics at the chosen engine operating conditions. Based on the LES results, the correlation and visualization studies indicate that the cyclic variations in the local velocity around the spark plug lead to the variations in the early flame propagation, which in turn produce temperature fluctuations among the cycles and result in greater variations in the subsequent auto-ignition combustion events.

Evaluation and Improvement of a TKE-Based Eddy-Diffusivity Mass-Flux (EDMF) Planetary Boundary Layer Scheme in Hurricane Conditions

Abstract Accurately representing boundary layer turbulent processes in numerical models is critical to improve tropical cyclone forecasts. A new turbulence kinetic energy (TKE)-based moist eddy-diffusivity mass-flux (EDMF-TKE) planetary boundary layer scheme has been implemented in NOAA’s Hurricane Analysis and Forecast System (HAFS). This study evaluates EDMF-TKE in hurricane conditions based on a recently developed framework using large-eddy simulation (LES). Single-column modeling tests indicate that EDMF-TKE produces much greater TKE values below 500-m height than LES benchmark runs in different high-wind conditions. To improve these results, two parameters in the TKE scheme were modified to ensure a match between the PBL and surface-layer parameterizations. Additional improvements were made by reducing the maximum allowable mixing length to 40 m based on LES and observations, by adopting a different definition of boundary layer height, and by reducing nonlocal mass fluxes in high-wind conditions. With these modifications, the profiles of TKE, eddy viscosity, and winds compare much better with LES results. Three-dimensional idealized simulations and an ensemble of HAFS forecasts of Hurricane Michael (2018) consistently show that the modified EDMF-TKE tends to produce a stronger vortex with a smaller radius of maximum wind than the original EDMF-TKE, while the radius of gale-force wind is unaffected. The modified EDMF-TKE code produces smaller eddy viscosity within the boundary layer compared to the original code, which contributes to stronger inflow, especially within the annulus of 1–3 times the radius of maximum wind. The modified EDMF-TKE shows promise to improve forecast skill of rapid intensification in sheared environments.

Turbulence Effects on the Formation of Cold Fog Over Complex Terrain With Large‐Eddy Simulation

AbstractA large eddy simulation (LES) embedded in the mesoscale community Weather Research and Forecasting model is used to examine the effects of turbulence on cold fog formation over Heber Valley in northern Utah in the U.S. The LES results indicate that large‐scale turbulent eddies prevail and dominate the mixing effects in the planetary boundary layer (PBL). The combination of turbulence mixing effects, mountain‐valley flow, and ultra‐cold valley temperature lead to fog formation in the LES simulation. The omission of the turbulent eddies in the PBL parameterization results in a weak mixing effect in the PBL and weakens the near‐surface air cooling, thus failing to reproduce the fog in the simulation. This study indicates the essential role of turbulence in fog formation over complex terrain. Turbulent eddies exist over complex terrain and can enhance mixing effects, and thus the conditions for fog formation.

Pollutant dispersion by tall buildings: laboratory experiments and Large-Eddy Simulation

Pollutant dispersion by a tall-building cluster within a low-rise neighbourhood of Beijing is investigated using both full-scale Large-Eddy Simulation and water flume experiments at 1:2400 model-to-full scale with Particle Image Velocimetry and Planar Laser-Induced Fluorescence. The Large-Eddy Simulation and flume results of this realistic test case agree remarkably well despite differences in the inflow conditions and scale. Tall buildings have strong influence on the local flow and the development of the rooftop shear layer which dominates vertical momentum and scalar fluxes. Additional measurements using tall-buildings-only models at both 1:2400 and 1:4800 scales indicates the rooftop shear layer is insensitive to the scale. The relatively thicker incoming boundary layer affects the Reynolds stresses, the relative size of the pollutant source affects the concentration statistics and the relative laser-sheet thickness affects the spatially averaged results of the measured flow field. Low-rise buildings around the tall building cluster cause minor but non-negligible offsets in the peak magnitude and vertical location, and have a similar influence on the velocity and concentration statistics as the scale choice. These observations are generally applicable to pollutant dispersion of realistic tall building clusters in cities. The consistency between simulations and water tunnel experiments indicates the suitability of both methodologies.Graphical abstract

Correlations Between Wake Phenomena and Fatigue Loads Within Large Wind Farms: A Large-Eddy Simulation Study

This work proposes a methodology aiming at simulating the whole wind farm behavior, from the wake phenomena to the wind turbine fatigue loads, in a both accurate and efficient way and for a large range of operating conditions. This approach is based on Large Eddy Simulation (LES), coupled to an Actuator Disk (AD) approach. In order to recover pertinent fatigue loads with that wind turbine model, the blade trajectories are replicated through the disk and the AD aerodynamic forces are interpolated onto these “virtual blades” at each time step. The wake centerline is also tracked in the whole wind farm, in order to highlight the correlations between the wake phenomena and the wind turbine fatigue damage. The described methodology is deployed in simulations of the Horns Rev wind farm for several wind directions. The time-averaged power production is first compared to measurements and other LES results, with a very good agreement for large wind sectors. We then investigate the fatigue loads for several machines inside the wind farm and wind directions. We clearly show the link between the upstream wake movement and the resulting high and low frequency oscillations of the root bending moments and of the yaw and tilt moments, and therefore on the resulting fatigue equivalent loads. This study demonstrates the capacity of the numerical tool to accurately capture the wind farm flow and the rotor behaviors, as well as the correlations between the wake phenomena and the resulting fatigue loads.

Tuning of an engineering wind farm model using measurements from Large Eddy Simulations

In this work, we develop a model tuning framework to calibrate analytical wind farm models by using virtual measurements from Large Eddy Simulations (LES). A Gaussian wake deficit model coupled with a recursive wake merging methodology is utilized to simulate different inflow conditions through a virtual wind farm, which has been previously used in a suite of LES to providing a reference wind farm database. Using velocity and power measurements from the reference database, a ridge regression based calibration is conducted for the wake model parameters. Without calibration, large errors up to 20% initially persisted between the analytical model and LES for the same inflow conditions, which were subsequently observed to reduce below 6% after model tuning. The tuned models were then used to analyze farm performance for cases with optimal wake steering set points, and it was observed that the predicted gains were in better accordance with LES results.

Large eddy simulation of fuel sensitivity in a realistic spray combustor I. Near blowout analysis

Understanding combustion and flame stabilization of alternate fuels is necessary to establish their use in mainstream aviation. An Eulerian-Lagrangian (EL) large eddy simulation (LES) study is conducted using a fully compressible solver for a Referee Rig combustor, developed within the National Jet Fuel Combustion Program, (NJFCP). The Referee Rig contains multiple swirlers, dilution jets, and effusion holes, mimicking the complex flow-field in a real gas turbine combustor. Conditions as in the experiments for near blowout (NBO) operation are simulated for two fuels identified by NJFCP: a baseline fuel (A2) and an alternate fuel (C1). Time-averaged LES results are shown to provide a reasonable match against the experimental droplet statistics and OH* chemiluminescence data for both the fuels. Several post-processing tools, such as, conditional averaging, flame index, chemically explosive mode analysis (CEMA) are used to understand flame stabilization mechanism and burning behavior under NBO condition. Flame anchor point is shown to be premixed, but most heat release results from fuel pockets burning in the shear layer in a non-premixed manner. Pressure signatures at various locations and other time-varying properties show fuel-sensitive effects, even though the time-averaged behavior is similar between A2 and C1. When compared to A2, C1 shows a higher premixed burning and it is shown to be dependent on the slower burning behavior of C1 at NBO.

The influence of non-conformal grid interfaces on the results of large eddy simulation of centrifugal blood pumps.

Computational fluid dynamics has been widely used to assist the design and evaluation of blood pumps. Discretization errors associated with computational grid may influence the credibility of numerical simulations. Non-conformal grid interfaces commonly exist in rotary machines, including rotary blood pumps. Should grid size across the interface differ greatly, large errors may occur. This study explored the effects of non-conformal grid interface on the prediction of the flow field and hemolysis in blood pumps using large eddy simulation (LES). Two benchmarks, a nozzle model and a centrifugal blood pump were chosen as test cases. This study found that non-conformal grid interfaces with considerable change of grid sizes led to discontinuities of flow variables and brought errors to metrics such as pressure head (7%) and hemolysis (up to 14%). The results on the full unstructured grid are more accurate with negligible changes of flow variables across the non-conformal grid interface. A full unstructured grid should be employed for centrifugal blood pumps to minimize the influence of non-conformal grid interfaces for LES simulations.

Turbulent transport and reactions of plant-emitted hydrocarbons in an Amazonian rain forest

The processes governing the temporal and spatial patterns of isoprene and monoterpenes emitted by a rainforest in the central Amazon region of Brazil is investigated using a combination of field experiments and numerical simulations. Specifically, Large Eddy Simulations (LES) were used to resolve emissions of isoprene and monoterpenes, turbulent transport, and air chemistry. The coupled chemistry-transport LES included the effects of isoprene and monoterpenes reactivity due to reactions with hydroxyl radical and ozone. The LES results are used to compute vertically resolved budgets of isoprene and monoterpenes in the rainforest canopy in response to emissions, turbulent transport, surface deposition, and air chemistry. Results indicated that emission and dispersion dominated the isoprene budget as the gases were transported out of the canopy space. In a region limited by nitrogen oxides (with prevailing nitric oxide levels of < 0.5 parts per billion), the in-canopy chemical destruction removed approximately 10% of locally emitted monoterpenes. Hydroxyl radical production rates from the ozonolysis of monoterpenes amounted to ≈2×106radicalscm−3s−1 and had similar magnitude to the light-dependent hydroxyl radical formation. One key conclusion was that the Amazonia rainforest abundantly emitted monoterpenes whose in-canopy ozonolysis yielded hydroxyl radicals in amounts similar to the magnitude of light-dependent formation. Reactions of monoterpenes and isoprene with hydroxyl radical and ozone were necessary for the maintenance of the Amazon rainforest canopy as a photochemically active environment suitable to generate oxidants and secondary organic aerosols.

On the application and grid-size sensitivity of the urban dispersion model CAIRDIO v2.0 under real city weather conditions

Abstract. There is a gap between the need for city-wide air-quality simulations considering the intra-urban variability and mircoscale dispersion features and the computational capacities that conventional urban microscale models require. This gap can be bridged by targeting model applications on the gray zone situated between the mesoscale and large-eddy scale. The urban dispersion model CAIRDIO is a new contribution to the class of computational-fluid dynamics models operating in this scale range. It uses a diffuse-obstacle boundary method to represent buildings as physical obstacles at gray-zone resolutions in the order of tens of meters. The main objective of this approach is to find an acceptable compromise between computationally inexpensive grid sizes for spatially comprehensive applications and the required accuracy in the description of building and boundary-layer effects. In this paper, CAIRDIO is applied on the simulation of black carbon and particulate matter dispersion for an entire mid-size city using a uniform horizontal grid spacing of 40 m. For model evaluation, measurements from five operational air monitoring stations representative for the urban background and high-traffic roads are used. The comparison also includes the mesoscale host simulation, which provides the boundary conditions. The measurements show a dominant influence of the mixing layer evolution at background sites, and therefore both the mesoscale and large-eddy simulation (LES) results are in good agreement with the observed air pollution levels. In contrast, at the high-traffic sites the proximity to emissions and the interactions with the building environment lead to a significantly amplified diurnal variability in pollutant concentrations. These urban road conditions can only be reasonably well represented by CAIRDIO while the meosocale simulation indiscriminately reproduces a typical urban-background profile, resulting in a large positive model bias. Remaining model discrepancies are further addressed by a grid-spacing sensitivity study using offline-nested refined domains. The results show that modeled peak concentrations within street canyons can be further improved by decreasing the horizontal grid spacing down to 10 m, but not beyond. Obviously, the default grid spacing of 40 m is too coarse to represent the specific environment within narrow street canyons. The accuracy gains from the grid refinements are still only modest compared to the remaining model error, which to a large extent can be attributed to uncertainties in the emissions. Finally, the study shows that the proposed gray-scale modeling is a promising downscaling approach for urban air-quality applications. The results, however, also show that aspects other than the actual resolution of flow patterns and numerical effects can determine the simulations at the urban microscale.

Effects of Bulk Flow Pulsation on Film Cooling Involving Compound Angle

The main flow could be unsteady in flow fields of film cooling for several reasons such as flow interactions between the rotor and the stator in the turbine. Understanding the characteristics of the film-cooling flow with an unsteady flow is important in the design of gas turbines. The effects of 36-Hz pulsations in the main flow on the streamwise velocity distributions, turbulence statistics, and temperature fluctuations in the film-cooling flow from a cylindrical hole with an orientation angle are investigated by numerical methods. Large-eddy simulation (LES) results match the experimental data with an acceptable accuracy, whereas the Reynolds-averaged Navier–Stokes simulation (RANS) results show large deviations with the experimental data and the LES results. Under 36-Hz pulsations, the URANS results predict a weaker streamwise velocity of the coolant jet that blocks the main flow compared with the LES. With 36-Hz pulsations at the time-averaged blowing ratio of 0.5, urms, the root mean squared fluctuating velocity in the streamwise direction around the coolant core increased due to intensive mixing, and vrms, the root mean squared fluctuating velocity in the wall-normal direction, increased along the trajectory of the injected coolant. Moreover, wrms, the root mean squared fluctuating velocity in the spanwise direction, increased around the wall compared to those at a steady state. The dimensionless temperature fluctuations increased in the region of the core of the coolant compared with those at a steady state. When the orientation angle was 30°, the distribution of the results moved in the z-direction; however, the overall trend was similar to that of a simple angle.

Comparative study of transonic shock–boundary layer interactions due to surface heating and cooling on an airfoil

Implicit large eddy simulation results are compared to investigate the effects of wall-heating and wall-cooling on shock–boundary layer interaction over an airfoil. Heat flux is provided on the suction surface of the airfoil from x/c=0.40 to x/c=0.50 for a Mach number of 0.72 and a Reynolds number based on chord of Re=16.2×106. Flow quantities are compared for the effects of heating and cooling. Numerical Schlieren snapshots reveal an oscillation of the shock wave and its interaction with upstream propagating Kutta waves generated from the trailing edge of the airfoil. Quantitative data obtained from these Schlieren snapshots and the mean aerodynamic load values indicate a reduction in frequency of oscillation of shock wave and a decrease in shock strength for the case of heating. Flow control by heating shows higher fluctuations in flow features evident from instantaneous quantities. Both imposed excitations lead to a marginal increase in aerodynamic efficiency (lift/drag). We also compare the integral aerodynamic parameters, such as lift and drag coefficients, and their ratio, Cl, Cd,and Cl/Cd. The simulations reported here follow the techniques used in Sengupta et al. [“Thermal control of transonic shock–boundary layer interaction over a natural laminar flow airfoil,” Phys. Fluids 33(12), 126110 (2021)].

Numerical Prediction and Suppression of Thermoacoustic Longitudinal Mode in Annular Combustor

Many industrial applications, such as gas turbines or aeroengines, are subject to thermoacoustic instability, especially in the lean combustion regime. In this paper, the linearized Navier–Stokes equations (LNSEs) framework is applied to predict the acoustic liner damping effects with real geometry and different bias flow velocities. The results show that the LNSEs can capture the tilt angle effect of the orifice or grazing and bias flow coupling phenomenon. The forced large-eddy simulation results of premixed methane flame present the same trend in gain and phase of the flame transfer function with the equation. Then, the flame response model is coupled into the Helmholtz and LNSE solvers. The mean flow from Reynolds-averaged Navier–Stokes calculation is used in the LNSEs, and no assumption of liner geometry is made. The linear stability analysis reveals that the velocity fluctuation in the combustion is also damped when a stable acoustic mode is achieved with the acoustic liner. The flame dynamic, the hydrodynamic, and the acoustic phenomena can all be considered when using the LNSEs. This indicates that the LNSEs may allow us to consider a more complex mechanism that can affect the thermoacoustic inability in the combustor system and help us to design better dampers to control.

Reynolds and dispersive shear stress in free-surface turbulent channel flow over square bars.

Reynolds and dispersive shear stresses in turbulent flow over spanwise-aligned square bars in an open channel flow are examined. Results of large-eddy simulation of flow over two different bar spacings corresponding to transitional and k-type (reattaching flow) roughness are analyzed. The Reynolds shear stress contribution to the momentum loss (or the friction factor, respectively) is greater than the dispersive shear stress contribution. By increasing the bars spacing, however, the contribution of the dispersive shear stress increases while the Reynolds shear stress contribution decreases, which is due to a standing wave at the water surface in the flow over k-type roughness which results in significant spatial variations in the time-averaged velocities. Strong sweep events take place and contribute to the friction coefficient. Investigating the dynamics of the flow reveals that there is momentum source below the crest of the bars and momentum sink above them, leading to acceleration or deceleration of flow, respectively. The contribution of dispersive shear stress is significant only in the deceleration of the flow near the crest of the bars and in the acceleration of the flow under the water surface. Quantification of the three components of total kinetic energy, i.e. mean, turbulent, and wake kinetic energy, reveals that the largest contribution is that of the mean flow in both geometries. By increasing the bar spacing, the contributions of turbulent and wake kinetic energy, which are localized at the bar height, increase, while the kinetic energy of the mean flow decreases.

A Library of Large‐Eddy Simulations Forced by Global Climate Models

AbstractAdvances in high‐performance computing have enabled large‐eddy simulations (LES) of turbulence, convection, and clouds. However, their potential to improve parameterizations in global climate models (GCMs) is only beginning to be harnessed, with relatively few canonical LES available so far. The purpose of this paper is to begin creating a public LES library that expands the training data available for calibrating and evaluating GCM parameterizations. To do so, we use an experimental setup in which LES are driven by large‐scale forcings from GCMs, which in principle can be used at any location, any time of year, and in any climate state. We use this setup to create a library of LES of clouds across the tropics and subtropics, in the present and in a warmer climate, with a focus on the transition from stratocumulus to shallow cumulus over the East Pacific. The LES results are relatively insensitive to the choice of host GCM driving the LES. Driven with large‐scale forcing under global warming, the LES simulate a positive but weak shortwave cloud feedback, adding to the accumulating evidence that low clouds amplify global warming.

How do water and CO2 impact the stability and emissions of the combustion in a micro gas turbine? — A Large Eddy Simulations comparison

Micro Gas Turbines have to become more operational and fuel flexible, and carbon clean. Applying cycle humidification and Exhaust Gas Recirculation (EGR) in combination with Carbon Capture offers a solution. However, current advanced mGT cycle development is limited by the combustor. To improve the cycle performance further, stable and complete combustion has to be achieved under unconventional diluted conditions. Accurate data predicting the stability and performance of specific mGT combustors under these diluted conditions are still missing. A comparison between classic natural gas combustion in an mGT and three diluted cases with water and/or CO2 using Large Eddy Simulations (LES) is presented in this paper. Results show that complete and stable combustion was reached for all cases. Although the flow dynamics are identical, diluted operating conditions lead to a wider reaction zone. An outlet temperature reduction could be observed in the water diluted cases due to the higher specific heat of the humidified combustion air. Regarding CO emissions, the humidified case presents slightly lower concentrations (25 ppm) compared to the reference case (32 ppm), while the dry EGR case shows the highest values (50 ppm). Based on high fidelity LES results, the feasibility of mGT combustor operating under diluted conditions has been proven.

Modeling of Cube Array Roughness: RANS, Large Eddy Simulation, and Direct Numerical Simulation

AbstractFlow over arrays of cubes is an extensively studied model problem for rough wall turbulent boundary layers. While considerable research has been performed in computationally investigating these topologies using direct numerical simulation (DNS) and large eddy simulation (LES), the ability of sublayer-resolved Reynolds-averaged Navier–Stokes (RANS) to predict the bulk flow phenomena of these systems is relatively unexplored, especially at low and high packing densities. Here, RANS simulations are conducted on six different packing densities of cubes in aligned and staggered configurations. The packing densities investigated span from what would classically be defined as isolated, up to those in the d-type roughness regime, filling in the gap in the present literature. Three different sublayer-resolved turbulence closure models were tested for each case: a low Reynolds number k–ϵ model, the Menter k–ω SST model, and a full Reynolds stress model. Comparisons of the velocity fields, secondary flow features, and drag coefficients are made between the RANS results and existing LES and DNS results. There is a significant degree of variability in the performance of the various RANS models across all comparison metrics. However, the Reynolds stress model demonstrated the best accuracy in terms of the mean velocity profile as well as drag partition across the range of packing densities.

Low-Grid-Resolution-RANS-Based Data Assimilation of Time-Averaged Separated Flow Obtained by LES

ABSTRACT The objective of this study is to obtain accurate flow field analysis results in a short computational time by using data assimilation, which increases the accuracy of Reynolds averaged Navier-Stokes (RANS) simulations with low grid resolution. The large-eddy simulation (LES) results are assimilated into RANS simulations. In those simulations, the turbulence-model parameters are optimised by an ensemble Kalman filter with a proposed method for adaptive hyperparameter optimisation. The target of calculations is the flow field around a square cylinder of the Reynolds number of approximately . Only the surface pressure of the square cylinder is used as an observation variable. For this shape, the assimilated RANS flow field is similar to that given by the LES analysis, and the drag coefficient reproducibility is improved by . The turbulence-model parameters are also used in the analyses of different cross-sectional shape and are found to improve the reproducibility of the flow field.