• Nuclear Engineering and Technology
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• 제55권1호
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• pp.131-143
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• 2023

Constitutive equations in a nuclear reactor safety analysis code are mostly empirical correlations developed from experiments, which always accompany uncertainties. The accuracy of the code can be improved by modifying the constitutive equations fitting wider range of data with less uncertainty. Thus, the sensitivity of the code with respect to the constitutive equations is evaluated quantitatively in the paper to understand the room for improvement of the code. A new methodology is proposed which first starts by dividing the thermal hydraulic conditions into multiple sub-regimes using self-organizing map (SOM) clustering method. The sensitivity analysis is then conducted by multiplying an arbitrary set of coefficients to the constitutive equations for each sub-divided thermal-hydraulic regime with SOM to observe how the code accuracy varies. The randomly chosen multiplier coefficient represents the uncertainty of the constitutive equations. Furthermore, the set with the smallest error with the selected experimental data can be obtained and can provide insight which direction should the constitutive equations be modified to improve the code accuracy. The newly proposed method is applied to a steady-state experiment and a transient experiment to illustrate how the method can provide insight to the code developer.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.161-171
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• 1999

Aerodynamic sensitivity analysis codes are developed via the hand-differentiation using a direct differentiation method and an adjoint method respectively from discrete two-dimensional compressible Navier-Stokes equations. Unlike previous other researches, Baldwin-Lomax algebraic turbulence model is also differentiated by hand to obtain design sensitivities with respect to design variables of interest in turbulent flows. Discrete direct sensitivity equations and adjoint equations are efficiently solved by the same time integration scheme adopted in the flow solver routine. The required memory for the adjoint sensitivity code is greatly reduced at the cost of the computational time by allowing the large banded flux jacobian matrix unassembled. Direct sensitivity code results are found to be exactly coincident with sensitivity derivatives obtained by the finite difference. Adjoint code results of a turbulent flow case show slight deviations from the exact results due to the limitation of the algebraic turbulence model in implementing the adjoint formulation. However, current adjoint sensitivity code yields much more accurate sensitivity derivatives than the adjoint code with the turbulence eddy viscosity being kept constant, which is a usual assumption for the prior researches.

• 콘크리트학회논문집
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• 제11권4호
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• pp.73-81
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• 1999

The present study is to examine the ACI code equations for computing the unbonded tendon stress at flexural failure of prestressed beams. The equations examined for their validity are Eq. 18-4 and Eq. 18-5 of the ACI 318-95. Since the possibility of overestimation was expected with the equations, a numerical study, first, was carried out with influential variables included. From this study, it was found that amount of reinforcements, effective prestress, location of tendons, and loading type may affect the overestimation of the unbonded tendon stress. Then, an experimental study was carried out with those variables. A total of 8 specimens was tested to prove the theoretical findings as well as the effect of those variables. As a result. it was proven that the ACI Code equations can overestimate significantly the unbonded tendon stress for certain cases.

• 콘크리트학회논문집
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• 제11권3호
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• pp.113-122
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• 1999

The present study is to investigate the possibility of overestimation or underestimation when the ACI Code equations are used to evaluate the unbonded tendon stress. An experimental program was planned with 6 beams which divided into two groups. Each group consisted of 3 beams to check the possibility of overestimation or underestimation of unbonded tendon stress. The experimental results were also compared with various design equations including the one proposed by Moon and Lim. It was proven that the ACI Code equations may overestimate or underestimate the unbonded tendon stress in certain cases.

• 천문학회지
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• 제34권4호
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• pp.209-213
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• 2001

This paper describes the numerical solution to the hyperbolic system of magnetohydrodynamic (MHD) equations. First, by pointing out the approximations involved, the deal MHD equations are presented. Next, the MHD waves as well as the associated shocks and discontinuities, are presented. Then, based on the hyperbolicity of the ideal MHD equations, the application of upwind schemes, which have been developed for hydrodynamics, is discussed to solve the equations numerically. As an definite example, one and multi-dimensional codes based on the Total Variation Diminishing scheme are presented. The treatment in the multi-dimensional code, which maintains ${\nabla}{\cdot}$B = 0, is described. Through tests, the robustness of the upwind schemes for MHDs is demonstrated.

• Computers and Concrete
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• 제2권1호
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• pp.55-77
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• 2005

The closed form solution of the equilibrium equations in the ultimate design of reinforced concrete sections under biaxial bending is presented. The stresses in the materials are described by the Model Code 1990 equations. Computation of the integral equations is performed generally in terms of all variables. The deformed shape of the section in the ultimate conditions is defined by Heaviside functions. The procedure is convenient for the use of mathematical manipulation programs and the results are easily included into nonlinear analysis codes. The equations developed for rectangular sections can be applied for other sections, such as T, L, I for instance, by decomposition into rectangles. Numerical examples of the developed model for rectangular sections and composed sections are included.

• Structural Engineering and Mechanics
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• 제89권4호
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• pp.363-374
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• 2024

Significant changes have been made to estimate the punching shear capacity for edge column-slab joints in the latest editions of most current codes. The revised equations account for axial forces as well as moments conveyed to columns from slabs, which have a substantial impact on the punching resistance of such joints. Many key design parameters, such as reinforcement-ratio, concrete strength, size-effect, and critical-section perimeter, were treated differently or even ignored in various code provisions. Consequently, wide ranges of predicted punching shear strength were detected by applying different code formulas. Therefore, it is essential to assess the various current Codes' design-equations. Because of the similarity in estimated outcomes, only the ACI, EC, and SNiP are used in this study to cover a wide range of estimation ranges from highly conservative to unconservative. This paper is devoted to analyzing the techniques in these code provisions, comparing the estimated punching resistance with available experimental data, and finally developing efficient models predicting the punching capacity of edge column-slab connections. 63 samples from past investigations were chosen for validation. To appropriately predict the punching shear, newly updated equations for ACI and SNiP are provided based on nonlinear regression analysis. The proposed equations'results match the experimental data quite well.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2000년도 춘계 학술대회논문집
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• pp.66-72
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• 2000

Aerodynamic sensitivity analysis is performed for the Navier-Stokes equations coupled with two-equation turbulence models using a discrete adjoint method and a direct differentiation method respectively. Like the mean flow equations, the turbulence model equations are also hand-differentiated to accurately calculate the sensitivity derivatives of flow quantities with respect to design variables in turbulent viscous flows. Both the direct differentiation code and the adjoint variable code adopt the same time integration scheme with the flow solver to efficiently solve the differentiated equations. The sensitivity codes are then compared with the flow solver in terms of solution accuracy, computing time and computer memory requirements. The sensitivity derivatives obtained from the sensitivity codes with different turbulence models are compared with each other. Using two-equation turbulence models, it is observed that a usual assumption of constant turbulent eddy viscosity in adjoint methods may lead to seriously inaccurate results in highly turbulent flows.

• 한국전산유체공학회지
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• 제14권3호
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• pp.86-94
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• 2009

The non-conservative form of momentum equations is often used for some two-phase flow codes instead of a conservative form because of numerical convenience. Another non-conservative form, so called, a semi-conservative form can improve the numerical solution of these codes maintaining the numerical convenience. It is close to the conservative form but still maintains the feature of the non-conservative form. A semi-conservative form of the momentum equations and a non-conservative form of the momentum equations are implemented in CUPID[1] code. The numerical results of the semi-conservative and the non-conservative forms are compared against analytical solutions and the solutions of the FLUENT code that uses the conservative form. The results clearly showed that the semi-conservative form of the momentum equations provides better solutions than the non-conservative form, especially for heterogeneous two-phase flows.

• Wind and Structures
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• 제23권5호
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• pp.421-447
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• 2016

Wind-induced and earthquake-induced excitations on tall structures can be effectively controlled by Tuned Liquid Damper (TLD). This work presents a numerical simulation procedure to study the performance of tuned liquid tank- structure system through ${\sigma}$-transformation based fluid-structure coupled solver. For this, a 'C' based computational code is developed. Structural equations are coupled with fluid equations in order to achieve the transfer of sloshing forces to structure for damping. Structural equations are solved by fourth order Runge-Kutta method while fluid equations are solved using finite difference based sigma transformed algorithm. Code is validated with previously published results. The minimum displacement of structure is observed when the resonance condition of the coupled system is satisfied through proper tuning of TLD. Since real-time excitations are random in nature, the performance study of TLD under random excitation is also carried out in which the Bretschneider spectrum is used to generate the random input wave.