Turbulence Modeling Validation, Testing, and Development

The primary objective of this work is to provide accurate numerical solutions for selected flow fields and to compare and evaluate the performance of selected turbulence models with experimental results. Four popular turbulence models have been tested and validated against experimental data often turbulent flows. The models are: (1) the two-equation k-epsilon model of Wilcox, (2) the two-equation k-epsilon model of Launder and Sharma, (3) the two-equation k-omega/k-epsilon SST model of Menter, and (4) the one-equation model of Spalart and Allmaras. The flows investigated are five free shear flows consisting of a mixing layer, a round jet, a plane jet, a plane wake, and a compressible mixing layer; and five boundary layer flows consisting of an incompressible flat plate, a Mach 5 adiabatic flat plate, a separated boundary layer, an axisymmetric shock-wave/boundary layer interaction, and an RAE 2822 transonic airfoil. The experimental data for these flows are well established and have been extensively used in model developments. The results are shown in the following four sections: Part A describes the equations of motion and boundary conditions; Part B describes the model equations, constants, parameters, boundary conditions, and numerical implementation; and Parts C and D describe the experimental data and the performance of the models in the free-shear flows and the boundary layer flows, respectively

Synthetic Turbulence, Fractal Interpolation and Large-Eddy Simulation

Fractal Interpolation has been proposed in the literature as an efficient way to construct closure models for the numerical solution of coarse-grained Navier-Stokes equations. It is based on synthetically generating a scale-invariant subgrid-scale field and analytically evaluating its effects on large resolved scales. In this paper, we propose an extension of previous work by developing a multiaffine fractal interpolation scheme and demonstrate that it preserves not only the fractal dimension but also the higher-order structure functions and the non-Gaussian probability density function of the velocity increments. Extensive a-priori analyses of atmospheric boundary layer measurements further reveal that this Multiaffine closure model has the potential for satisfactory performance in large-eddy simulations. The pertinence of this newly proposed methodology in the case of passive scalars is also discussed

The Lag Model Applied to High Speed Flows

The Lag model has shown great promise in prediction of low speed and transonic separations. The predictions of the model, along with other models (Spalart-Allmaras and Menter SST) are assessed for various high speed flowfields. In addition to skin friction and separation predictions, the prediction of heat transfer are compared among these models, and some fundamental building block flowfields, are investigated

Turbulence compressibility corrections

The basic objective of this research was to identify, develop and recommend turbulence models which could be incorporated into CFD codes used in the design of the National AeroSpace Plane vehicles. To accomplish this goal, a combined effort consisting of experimental and theoretical phases was undertaken. The experimental phase consisted of a literature survey to collect and assess a database of well documented experimental flows, with emphasis on high speed or hypersonic flows, which could be used to validate turbulence models. Since it was anticipated that this database would be incomplete and would need supplementing, additional experiments in the NASA Ames 3.5-Foot Hypersonic Wind Tunnel (HWT) were also undertaken. The theoretical phase consisted of identifying promising turbulence models through applications to simple flows, and then investigating more promising models in applications to complex flows. The complex flows were selected from the database developed in the first phase of the study. For these flows it was anticipated that model performance would not be entirely satisfactory, so that model improvements or corrections would be required. The primary goals of the investigation were essentially achieved. A large database of flows was collected and assessed, a number of additional hypersonic experiments were conducted in the Ames HWT, and two turbulence models (kappa-epsilon and kappa-omega models with corrections) were determined which gave superior performance for most of the flows studied and are now recommended for NASP applications

Convergence to SPDEs in Stratonovich form

We consider the perturbation of parabolic operators of the form $\partial_t+P(x,D)$ by large-amplitude highly oscillatory spatially dependent potentials modeled as Gaussian random fields. The amplitude of the potential is chosen so that the solution to the random equation is affected by the randomness at the leading order. We show that, when the dimension is smaller than the order of the elliptic pseudo-differential operator $P(x,D)$, the perturbed parabolic equation admits a solution given by a Duhamel expansion. Moreover, as the correlation length of the potential vanishes, we show that the latter solution converges in distribution to the solution of a stochastic parabolic equation with a multiplicative term that should be interpreted in the Stratonovich sense. The theory of mild solutions for such stochastic partial differential equations is developed. The behavior described above should be contrasted to the case of dimensions that are larger than or equal to the order of the elliptic pseudo-differential operator $P(x,D)$. In the latter case, the solution to the random equation converges strongly to the solution of a homogenized (deterministic) parabolic equation as is shown in the companion paper [2]. The stochastic model is therefore valid only for sufficiently small space dimensions in this class of parabolic problems.Comment: 21 page

Тромботическая окклюзия у пациентов с острым ишемическим инсультом

Currently, reperfusion therapy is the main method of treating patients with ischemic stroke (IS). The safety and efficacy of systemic thrombolytic therapy with a recombinant tissue plasminogen activator in patients with IS within 3 hours, and then 4.5 hours after the onset of symptoms of the disease was demonstrated in the NINDS (1995) and ECASS III (2008) studies. In 2018, based on the results of five studies, clear indications were formulated for performing thrombectomy (TE) in patients with IS, which involve the detection of thrombosis of a large stroke-associated artery. Given the continuous growth in the number of the adult population, which constitutes the bulk of patients with IS, information on the prevalence of patients with thrombotic occlusion of cerebral arteries, who are potential candidates for TE, may be important for regional vascular centers.Aim of study. To describe IS patients admitted within the 6-hour “therapeutic window”.Materials and methods. The study included 145 patients with cerebral IS who were admitted within the first 6 hours after the onset of symptoms of the disease. All patients underwent computed tomographic (CT) angiography in order to verify the occlusion of the cerebral artery.Results. In our study, a correlation was established between the NIHSS severity of IS and the likelihood of verification of stroke-related artery thrombosis by CT angiography, but in 32.6% of patients with severe stroke (NIHSS at least score 14), no thrombotic occlusion was detected, and in 13% of patients with a clinic of mild acute cerebrovascular accident (NIHSS no more than 6), on the contrary, thrombotic occlusion was detected. Mortality in patients with verified thrombotic occlusion of the cerebral artery was higher than in patients without it (38% versus 10.5%, p<0.001). Such a significant difference in the mortality rate was due to the initially more severe stroke (NIHSS at admission 17 [10; 23] versus 5 [2; 10], p><0.001) in patients with thrombotic occlusion of a stroke-related artery, as well as a higher incidence of severe swallowing disorders (30% versus 9.5%, p ><0.002), which are a risk factor for pneumonia, as well as a higher frequency of such a comorbid background as chronic kidney disease and atrial fibrillation (30% versus 13.7%, p=0.018% and 58% versus 29.5%, p=0.001, respectively). CONCLUSION 1. Thrombosis of the cerebral stroke-associated artery was detected in 34.5% of patients with ischemic stroke who were admitted within the first 6 hours from the onset of the disease. 2. The main reason for the failure to perform thrombectomy in patients with ischemic stroke admitted within the 6-hour therapeutic window is the lack of verification of stroke-related artery thrombosis using computed tomographic angiography. Due to thrombosis at a different location (other than thrombosis of the internal carotid artery and / or M1 segment of the middle cerebral artery), 10% of patients with verified thrombosis did not meet the currently existing selection criteria for thrombectomy. Keywords: ischemic stroke, reperfusion therapy, cerebral artery thrombosis, cryptogenic stroke>˂0.001). Such a significant difference in the mortality rate was due to the initially more severe stroke (NIHSS at admission 17 [10; 23] versus 5 [2; 10], p˂0.001) in patients with thrombotic occlusion of a stroke-related artery, as well as a higher incidence of severe swallowing disorders (30% versus 9.5%, p˂0.002), which are a risk factor for pneumonia, as well as a higher frequency of such a comorbid background as chronic kidney disease and atrial fibrillation (30% versus 13.7%, p=0.018% and 58% versus 29.5%, p=0.001, respectively).Conclusion. 1. Thrombosis of the cerebral stroke-associated artery was detected in 34.5% of patients with ischemic stroke who were admitted within the first 6 hours from the onset of the disease. 2. The main reason for the failure to perform thrombectomy in patients with ischemic stroke admitted within the 6-hour therapeutic window is the lack of verification of stroke-related artery thrombosis using computed tomographic angiography. Due to thrombosis at a different location (other than thrombosis of the internal carotid artery and / or M1 segment of the middle cerebral artery), 10% of patients with verified thrombosis did not meet the currently existing selection criteria for thrombectomy. В настоящее время реперфузионная терапия является основным методом лечения пациентов с ишемическим инсультом (ИИ). Безопасность и эффективность системной тромболитической терапии при помощи рекомбинантного тканевого активатора плазминогена у пациентов с ИИ в пределах 3 часов, а в последующем 4,5 часа от начала симптомов заболевания была продемонстрирована в исследованиях NINDS (1995) и ECASS III (2008). В 2018 году, основываясь на результатах пяти исследований, были сформулированы четкие показания для выполнения тромбэктомии (ТЭ) у пациентов с ИИ, которые подразумевают выявление тромбоза крупной инсульт-связанной артерии. В условиях непрерывного роста числа взрослого населения, составляющего основную массу пациентов с ИИ, информация о распространенности больных с тромботической окклюзией церебральных артерий, являющихся потенциальными претендентами для выполнения ТЭ, может быть важной для региональных сосудистых центров.Цель исследования. Охарактеризовать пациентов с ИИ, поступающих в 6-часовом «терапевтическом окне».Материал и методы. В исследование включены 145 пациентов с церебральным ИИ, поступивших в первые 6 часов от начала развития симптомов заболевания. Всем пациентам с целью верификации окклюзии церебральной артерии выполняли компьютерную томографическую (КТ) ангиографию.Результаты. В нашем исследовании была установлена корреляция между тяжестью ИИ по шкале NIHSS и вероятностью верификации при помощи КТ-ангиографии тромбоза инсульт-связанной артерии, но у 32,6% пациентов с клиникой тяжелого инсульта (NIHSS не менее 14 баллов) не было выявлено тромботической окклюзии, а у 13% пациентов с клиникой легко протекающего острого нарушения мозгового кровообращения (NIHSS не более 6 баллов), напротив, тромботическая окклюзия была выявлена. Летальность у пациентов с верифицированной тромботической окклюзией церебральной артерии была статистически значимо выше, чем у пациентов без таковой (38% против 10,5%, р<0,001). Столь значительная разница между показателями летальности была обусловлена исходно более тяжелым инсультом (оценка по NIHSS при поступлении 17 [10; 23] против 5 [2; 10], p><0,001, статистически значимо) у больных с тромботической окклюзией инсульт-связанной артерии, а также большей частотой статистически значимых грубых расстройств глотания (30% против 9,5%, p><0,002, статистически значимо), являющихся фактором риска развития пневмонии и такого коморбидного фона, как хроническая болезнь почек и фибрилляция предсердий (30% против 13,7%, р=0,018 и 58% против 29,5%, р=0,001 соответственно). Выводы 1. Тромбоз церебральной инсульт-связанной артерии выявлен у 34,5% пациентов с ишемическим инсультом, поступающих в первые 6 часов от начала заболевания. 2. Основной причиной невыполнения тромбэктомии у пациентов с ишемическим инсультом, поступивших в 6-часовом «терапевтическом окне», является отсутствие верификации тромбоза инсульт-связанной артерии при помощи компьютерной томографической ангиографии. По причине тромбоза другой локализации (отличной от тромбоза внутренней сонной артерии и/или М1 сегмента средней мозговой артерии) 10% пациентов с верифицированным тромбозом не соответствовали существующим в настоящее время критериям отбора для выполнения тромбэктомии. Ключевые слова: ишемический инсульт, реперфузионная терапия, тромбоз мозговой артерии, криптогенный инсульт>˂ 0,001). Столь значительная разница между показателями летальности была обусловлена исходно более тяжелым инсультом (оценка по NIHSS при поступлении 17 [10; 23] против 5 [2; 10], p˂ 0,001, статистически значимо) у больных с тромботической окклюзией инсульт-связанной артерии, а также большей частотой статистически значимых грубых расстройств глотания (30% против 9,5%, p˂ 0,002, статистически значимо), являющихся фактором риска развития пневмонии и такого коморбидного фона, как хроническая болезнь почек и фибрилляция предсердий (30% против 13,7%, р=0,018 и 58% против 29,5%, р=0,001 соответственно).Выводы. 1. Тромбоз церебральной инсульт-связанной артерии выявлен у 34,5% пациентов с ишемическим инсультом, поступающих в первые 6 часов от начала заболевания. 2. Основной причиной невыполнения тромбэктомии у пациентов с ишемическим инсультом, поступивших в 6-часовом «терапевтическом окне», является отсутствие верификации тромбоза инсульт-связанной артерии при помощи компьютерной томографической ангиографии. По причине тромбоза другой локализации (отличной от тромбоза внутренней сонной артерии и/или М1 сегмента средней мозговой артерии) 10% пациентов с верифицированным тромбозом не соответствовали существующим в настоящее время критериям отбора для выполнения тромбэктомии.