Computational modeling of the body force−driven homogeneous atmospheric boundary layer

U posljednjih se tridesetak godina u vjetroinženjerstvu sve više koriste metode računalne dinamike fluida za modeliranje kompleksnih pojava u atmosferskom strujanju. Stoga je u sklopu doktorskog istraživanja razvijen novi računalni model neutralno temperaturno stratificiranog, stacionarnog, homogenog i ravninskog atmosferskog graničnog sloja (inženjerskog atmosferskog graničnog sloja) u kojem je strujanje uzrokovano dodatnom masenom silom promjenjivom po visini. Dodatna masena sila, koja fizikalno predstavlja dodatnu silu gradijenta tlaka promjenjivu po visini, uvrštena je u jednadžbu količine gibanja, pri čemu joj je početna vrijednost određena derivacijom poznate raspodjele naprezanja. Kako bi se generirale raspodjele naprezanja u skladu s dostupnim atmosferskim ili eksperimentalnim podatcima, vrijednosti dodatne masene sile su tijekom računalne simulacije (koristeći tehniku domene preteče) korigirane primjenom korekcijske procedure ugrađene u računalni algoritam za modeliranje strujanja fluida otvorenog koda OpenFOAM®. Strujanje inženjerskog atmosferskog graničnog sloja modelirano je tehnikom domene sljednika i tehnikom domene preteče u praznoj dvodimenzionalnoj računalnoj domeni, koristeći pet različitih modela turbulencije temeljenih na rješavanju vremenski osrednjenih Navier−Stokesovih jednadžbi: standardni k−ε, RNG k−ε, realizable k−ε, Wilcoxov k−ω i Menterov k−ω SST. Generirani profili osrednjene brzine, kinetičke energije turbulencije i disipacije ili specifične disipacije kinetičke energije turbulencije potom su korišteni kao ulazni profili za računalno modeliranje opterećenja zgrada uslijed vjetra, strujanje u atmosferskom graničnom sloju iznad brda jednostavne geometrije i proračun brzine strujanja vjetra na visinama koje odgovaraju visinama pješaka u okolini uzdignute zgrade. Dobiveni rezultati pokazuju da je novim modelom moguće ostvariti karakteristike strujanja u skladu s atmosferskim i eksperimentalnim podatcima, prethodnim računalnim simulacijama, te već postojećim modelima atmosferskog graničnog sloja.Proper characterization of atmospheric flow is one of the most important tasks in wind engineering. This is because the characteristics of atmospheric flow may affect a wide range of human activities, such as the wind loading of structures, pedestrian wind comfort in urban areas, building and bridge aerodynamics, traffic safety, the dispersion of exhaust gases produced by industrial combustion or vehicles, the natural ventilation of buildings, structural aeroacoustics, the siting of wind farms, the aerodynamics of wind turbine rotors, and wind-induced vibrations. A good understanding of atmospheric flow characteristics may also prevent serious structural damage caused by the effects of strong winds, and may reduce the risk of human casualties. The main research tools in wind engineering are atmospheric on-site measurements, measurements in wind tunnels, and the computational modelling of atmospheric flows by using computational fluid dynamics (CFD). Although atmospheric and laboratory measurements are still an essential tool to investigate atmospheric flow characteristics, CFD has been increasingly used in the last 30 years to model complex atmospheric flows. When compared to atmospheric and laboratory techniques, CFD is nowadays usually a less expensive and more efficient research tool. It is also less time consuming and allows for the computational modelling of the entire flow fields, which is usually not possible when flow characteristics are measured on site or in wind tunnels. Moreover, the computational modelling technique allows for effective control of the inflow characteristics, such as inflow wind speed or turbulence intensity. The atmospheric boundary layer (ABL) is the lowest layer of the Earth’s atmosphere, whose characteristics are mainly affected by the Earth’s surface. Theoretical models and atmospheric measurements have shown that in strong wind conditions, the ABL flow might be modelled as neutrally stratified, stationary, homogeneous and unidirectional. As strong wind conditions are often most interesting for wind engineers, the neutrally stratified, stationary, homogeneous and unidirectional ABL is also referred to as engineering ABL. Although large-eddy simulations have been increasingly used for the computational modelling of atmospheric turbulence, steady RANS (Reynolds-Averaged Navier-Stokes) is still a widespread tool for the modelling of atmospheric turbulence. This is because it is not so time consuming when compared to large-eddy simulations, and consequently it allows for the faster generation of computational results. The engineering ABL flow in an empty computational domain is computationally modelled by using the precursor domain technique or the successor domain technique. The former ensures flow homogeneity inside the computational domain as the Neumann boundary condition is applied at the inlet and the outlet boundaries of the domain for all modelled quantities (e.g. mean velocity, turbulence kinetic energy), or because the inlet and the outlet boundaries are treated as periodic boundaries. Unlike the precursor domain technique, the successor domain technique does not a priori ensure the homogeneity of the flow because the inflow profiles for the modelled quantities are defined at the inlet boundary, and the Neumann boundary condition is applied at the outlet boundary. Accordingly, the pressure gradient that could occur in the computational domain modifies the inflow profiles along the computational domain. When the successor domain technique is used, the inlet boundary conditions for the modelled quantities must be implemented in the employed CFD algorithm. This is not the case with the precursor domain technique. However, the force (or the forces) that drive the flow throughout the computational domain need to be explicitly modelled when the precursor domain technique is employed. Hypothesis and research methodologies A novel computational model for engineering ABL simulation was developed. The flow generated by the presented model is driven by the additional body force that varies with the increase in height. The body force was implemented in the momentum equation and its initial value was determined by deriving the known targeted stress distribution. This body force was derived by analysing the realistic neutrally stratified, stationary and homogeneous ABL, where the flow veers with the increase in height due to the effects of the Coriolis force. By analysing the forces that drive and retard such flow, it was shown that the flow in the neutrally stratified, stationary and homogeneous ABL is driven by the pressure gradient force that varies with the increase in height. This pressure gradient force is at its maximum close to the ground, while it declines as the height increases until it vanishes at geostrophic height. The performed analysis confirmed that the engineering ABL flow may be generated by applying the additional body force that varies with the increase in height, in the same manner as the flow in the neutrally stratified, stationary and homogeneous ABL is driven by the pressure gradient force that varies as the height increases. The initial body force values were corrected during the performed precursor domain technique computation by the correction procedure implemented in the open-source CFD algorithm OpenFOAM®. This was done to ensure that the computationally modelled stress distribution matches the experimental or theoretical stress distribution. The research hypothesis are as follows: a) The appropriate stress, mean velocity, and turbulence kinetic energy profiles that agree with the theoretical distributions or the atmospheric and laboratory measurements may be generated by the computational modelling of the engineering ABL flow driven by the additional body force implemented in the momentum equation. The implemented body force varies with the increase in height. b) The new model for the engineering ABL computation may be used to computationally model the problems related to the environmental and structural aerodynamics. The new computational model was tested by the computational analysis of the engineering ABL flow in an empty computational domain. The engineering ABL was computationally modelled by using both the precursor and the successor domain techniques, together with the five various steady RANS turbulence models, i.e. standard k−ε, RNG k−ε, realizable k−ε, Wilcox's k−ω, and Menter's k−ω SST turbulence model. The generated computational results were also compared to the computational results generated by using the shear stress-driven and the pressure-driven engineering ABL models. The profiles of the mean velocity, turbulence kinetic energy and dissipation rate or specific dissipation rate generated by the precursor domain technique using the presented engineering ABL model driven by the body force that varies with the increase in height were subsequently used as the inflow profiles at the inlet boundary of the computational domain when specific problems related to the wind engineering were studied. This was done to investigate the ability of the presented computational model to determine wind loads on structures (the pressure coefficient distribution on the building model surfaces and the drag force coefficient of the building model) and the characteristics of the engineering ABL flow above hilly terrain (mean velocity speed-up at the hill crest, the positions of the separation and the reattachment of the flow, turbulence kinetic energy distribution in the wake region behind the hill), and to estimate pedestrian wind comfort in the vicinity of a lift-up building (mean velocities at pedestrian-level heights). Computational results The computational results generated by using the new model of the engineering ABL in combination with the precursor domain technique confirm that the obtained flow is homogeneous due to the Neumann boundary condition applied at the inlet and the outlet boundaries of the computational domain. The obtained results also indicate that the pressure gradient generated in the computational domain does not influence the flow. Moreover, the computationally generated flow is mostly driven by the additional body force that varies with the increase in height, whereas the pressure gradient actually represents the error of the calibrated body force calculated by the correction procedure implemented in the CFD algorithm. Computational modelling of the engineering ABL flows in an empty computational domain showed that inactive turbulence modelling is the main prerequisite to achieve distributions of the turbulence kinetic energy in agreement with the atmospheric and laboratory measurements. It was also demonstrated that appropriate distributions of the turbulence kinetic energy cannot be achieved when the standard values of the turbulence model constants are used, as calculated turbulence kinetic energy values are significantly lower than the values predicted by the measurements. On the contrary, the computational modelling of the engineering ABL flow above the hill showed that modification of the turbulence model constants may seriously affect the mean wind speed-up values near the crest of the hill, the locations of the separation and the reattachment of the flow, and may also affect the turbulence kinetic energy distributions in the wake region behind the hill. When compared to the experimental measurements, the best results were obtained using the standard values of the turbulence model constants, i.e. without inactive turbulence modelling. Computational modelling of the engineering ABL flow in an empty computational domain by using the shear stress-driven, pressure-driven and body force-driven ABL models showed that experimental stress values can be reproduced only by a new computational model based on the additional body force that varies with the increase in height. The stress and the turbulence kinetic energy profiles obtained using the shear-stress-driven ABL model remain constant with the increase in height, while they decrease linearly with the increase in height when the pressure-driven ABL model is employed. All three ABL models generated similar mean velocity profiles. The obtained mean velocity, stress and turbulence kinetic energy profiles indicated that the choice of the steady RANS turbulence model affects only the mean velocity profile results. It was also confirmed that the precursor domain technique produces results that agree well with the results obtained using the successor domain technique. When the profiles generated by using the precursor domain technique and the presented computational model based on the body force that varies with the increase in height are set at the inlet boundary, the flow generated by using the successor domain technique without the additional body force can be considered homogeneous (in comparison with the results obtained by using the successor domain technique with the applied additional body force). Computational modelling of the engineering ABL flow over the cubic building model by using the shear stress-driven, pressure-driven and the body force-driven models showed that the additional body force implemented in the momentum equation does not affect the computational pressure coefficient distributions on the cubic building surfaces. The pressure coefficient distributions on these surfaces and the total drag force of the building are primarily affected by the choice of the steady RANS turbulence model, while the obtained results indicate that the employed ABL model does not influence the wind loads on buildings. The computational results also confirmed the appearance of the stagnation pressure anomaly caused by high values of the modelled turbulent viscosity, which is a drawback of the steady RANS turbulence models. When the profiles generated by using the precursor domain technique and the new computational model based on the body force that varies with the increase in height are set at the inlet boundary, the profiles generated by using the successor domain technique without the additional body force agree well with the results obtained by using the successor domain technique with the applied additional body force. These results indicate that the additional body force implemented in the momentum equation does not influence the pressure coefficient distributions on the cubic building surfaces and the calculated drag force coefficient. The mean wind speed-up values at the crest of the hill, the locations of the separation and the reattachment of the flow and the turbulence kinetic energy distributions in the wake region behind the hill generated by the computational modelling of the engineering ABL flow above the hill are mostly affected by the inactive turbulence modelling. When compared to the laboratory measurements, the best results were obtained using the standard values of the turbulence model constants. The obtained results also indicate that the mean wind speed-up values at the crest of the hill, the locations of the separation and the reattachment of the flow and the turbulence kinetic energy distributions in the wake region behind the hill are affected by the roughness of the hill surface and the slope of the hill. Computationally modelled mean velocity values at pedestrian-level heights in the vicinity of a lift-up building by using the shear stress-driven, pressure-driven and body force-driven ABL models together with the five various steady RANS turbulence models showed that the choice of the ABL model does not influence the computational results. On the contrary, the obtained results indicate that the computationally modelled mean velocity values are mostly affected by the employed steady RANS turbulence model. When the profiles generated by using the precursor domain technique and the presented computational model based on the body force that varies with the increase in height are set at the inlet boundary, the mean velocity values generated by using the successor domain technique without the additional body force agree well with the mean velocity values obtained by using the successor domain technique with the applied additional body force. These results indicate that the additional body force implemented in the momentum equation does not influence the mean velocity results at pedestrian-level heights in the vicinity of a lift-up building. Conclusion and scientific contribution The novel computational model was developed for the computational modelling of the engineering ABL flow that is driven by the additional body force that varies with the increase in height. This additional body force is implemented in the momentum equation along the constant pressure gradient force. The implemented body force represents the additional pressure gradient force that varies with the increase in height, in the same manner as the pressure gradient force varies in the neutrally stratified, stationary and homogeneous ABL where the flow varies with the height due to the Coriolis force. The initial body force value was determined by deriving the known targeted stress distribution and was corrected during the computational analysis by the correction procedure implemented in the CFD algorithm. The computational results obtained by modelling the engineering ABL flow in an empty computational domain using the developed engineering ABL model showed that the presented model is capable of reproducing mean velocity, turbulence kinetic energy and stress profiles in agreement with the theoretical distributions and atmospheric or laboratory measurements. The obtained results also indicate that appropriate stress profiles can be computationally reproduced only when the flow is modelled by using the precursor domain technique and the new engineering ABL model driven by the body force that is calibrated during the computation using the correction procedure implemented in the CFD algorithm. The performed computational investigation also showed that the shear stress-driven, pressure-driven and body force-driven engineering ABL flow can be properly modelled by using the precursor domain technique. The pressure-driven engineering ABL flow was modelled for the first time in combination with the RNG k−ε and realizable k−ε turbulence models using the precursor domain technique. Computational simulations of wind loads on a cubic building, the engineering ABL flow above hilly terrain, and mean velocity values at pedestrian-level heights in the vicinity of the lift-up building showed that the developed model can be adopted for modelling common problems in environmental and structural aerodynamics, as the obtained results agree well with the available laboratory measurements or previous computational simulations. The computational modelling of the engineering ABL flow above hilly terrain confirmed that inactive turbulence modelling generates mean wind speed-up at the crest of the hill that does not agree with laboratory measurements and previous computational simulations. Inactive turbulence modelling also produces a large wake behind the hill and high turbulence kinetic energy in the wake. The performed computations confirm that the standard values of the steady RANS turbulence model constants need to be used to computationally model problems in environmental and structural aerodynamics