Sharif Digital Repository

A shock control bump (SCB) is a flow control method which uses local small deformations in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, we have used a multi-point adjoint optimization scheme to optimize shape and location of the SCB. Practically, this introduces transonic airfoils equipped with the SCB which are simultaneously optimized for different off-design transonic flight conditions. Here, we use this optimization algorithm to enhance and optimize the performance of SCBs in two benchmark airfoils, i.e., RAE-2822 and... 

A shock control bump (SCB) is a flow control method which uses a local small deformation in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, both equally and variably weighted multi-point optimization and a robust adjoint optimization scheme are used to optimize the SCB. The numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm are used to find the optimum location and shape of the SCB for two benchmark aerofoils. A multi-point optimization method under a constant-lift-coefficient constraint is... 

A shock control bump (SCB) is a flow control method that uses local small deformations in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, we have used a multi-point adjoint optimization scheme to optimize shape and location of the SCB. Practically, this introduces transonic airfoils equipped with the SCB that are simultaneously optimized for different off-design transonic flight conditions. Here, we use this optimization algorithm to enhance and optimize the performance of SCBs in two benchmark airfoils, i.e., RAE-2822 and... 

Both shock control bump (SCB) and suction and blowing are flow control methods used to control the shock wave/boundary layer interaction (SWBLI) in order to reduce the resulting wave drag in transonic flows. A SCB uses a small local surface deformation to reduce the shock-wave strength, while suction decreases the boundary-layer thickness and blowing delays the flow separation. Here a multi-point optimization method under a constant-lift-coefficient constraint is used to find the optimum design of SCB and suction and blowing. These flow control methods are used separately or together on a RAE-2822 supercritical airfoil for a wide range of off-design transonic Mach numbers. The RANS flow... 

Shock Control Bump (SCB) reduces the wave drag in transonic ight. To control the boundary layer separation and to reduce the wave drag for two transonic airfoils, RAE-2822 and NACA-64A010, we investigate the application of two flow control methods, i.e. suction and blowing, to add them to the SCB. An adjoint gradient-based optimization algorithm is used to find the optimum shape and location of SCB. The performance of both Hybrid Suction/SCB (HSS) and Hybrid Blowing/SCB (HBS) is a function of the sucked or injected mass flow rate and their position. A parametric study is performed to find the near optimum values of the aerodynamic coefficients and efficiency. A RANS solver is validated and... 

Neutron noise induced by propagating disturbances in VVER-type reactor core is addressed in this paper. The spatial discretization of the governing equations is based on the box-scheme finite difference method for triangular-z geometry. Using the derived equations, a 3-D 2-group neutron noise simulator (called TRIDYN-3) is developed for hexagonal-structured reactor core, by which the discrete form of both the forward and adjoint reactor dynamic transfer functions (in the frequency domain) can be calculated. In addition, both types of noise sources, namely point-like and traveling perturbations, can be modeled by TRIDYN-3. The results are then benchmarked in different cases. Considering the... 

In this paper, localization of a noise source from limited neutron detectors sparsely distributed throughout the core of a typical VVER-1000 reactor is investigated. For this purpose, developing a 2-D neutron noise simulator for hexagonal geometries based on the 2-group diffusion approximation, the reactor dynamic transfer function is calculated. The boxscheme finite difference method is first developed for hexagonal geometries, to be used for spatial discretisation of both 2-D 2-group static and noise diffusion equations. The dynamic state is assumed in the frequency domain which leads to discarding of the time disrcetisation. The developed 2-D 2- group neutron noise simulator calculates... 

In this paper, the development of a neutron noise simulator for hexagonal-structured reactor cores using both the forward and the adjoint methods is reported. The spatial discretisation of both 2-D 2-group static and dynamic equations is based on a developed box-scheme finite difference method for hexagonal mesh boxes. Using the power iteration method for the static calculations, the 2-group neutron flux and its adjoint with the corresponding eigenvalues are obtained by the developed static simulator. The results are then benchmarked against the well-known CITATION computer code. The dynamic calculations are performed in the frequency domain which leads to discarding of the time... 

In this paper, we establish the existence and uniqueness of the mild solution for stochastic Volterra equation with a non-self-adjoint operator. The specific Volterra equation that we consider is a generalization of the fractional differential equation. To obtain the mild solution for the case of multiplicative problem, the resolvent property of the linear perturbation of a sectorial operator will be considered. © 2023 World Scientific Publishing Company  

The exact calculation of point kinetic parameters is very important in nuclear reactor safety assessment, and most sophisticated safety codes such as RELAP5, PARCS, DYN3D, and PARET are using these parameters in their dynamic models. These parameters include effective delayed neutron fractions as well as mean generation time. These parameters are adjoint-weighted, and adjoint flux is employed as a weighting function in their evaluation. Adjoint flux calculation is an easy task for most of deterministic codes, but its evaluation is cumbersome for Monte Carlo codes. However, in recent years, some sophisticated techniques have been proposed for Monte Carlo-based point kinetic parameters... 

Classic identifiability analysis of flow barriers in incompressible single-phase flow reveals that it is not possible to identify the location and permeability of low-permeability barriers from production data (wellbore pressures and rates), and that only averaged reservoir properties in between wells can be identified. We extend the classic analysis by including compressibility effects. We use two approaches: a twin experiment with synthetic production data for use with a time-domain parameter-estimation technique, and a transfer-function formalism in the form of bilaterally coupled four-ports allowing for an analysis in the frequency domain. We investigate the identifiability, from noisy... 

Various methods for solving the forward/adjoint equation in hexagonal and rectangular geometries are known in the literatures. In this paper, the solution of multigroup forward/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of equations is based on Galerkin FEM (GFEM) using unstructured triangle elements. Calculations are performed for both linear and quadratic approximations of the shape function; based on which results are compared. Using power iteration method for the forward and adjoint calculations, the forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then... 

In the present study, the neutron noise, i.e. The stationary fluctuation of the neutron flux around its mean value, is calculated in 2-group forward and adjoint diffusion theory for both hexagonal and rectangular reactor cores. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of equations is based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured triangle elements. Using power iteration method, forward and adjoint fluxes with the corresponding eigenvalues are obtained. The results are then benchmarked against the valid results for BIBLIS-2D and IAEA-2D benchmark problems and DONJON computer code. The... 

Abstract In this paper, the solution of multi-group neutron/adjoint equation using Finite Element Method (FEM) for hexagonal and rectangular reactor cores is reported. The spatial discretization of the neutron diffusion equation is performed based on two different Finite Element Methods (FEMs) using unstructured triangular elements generated by Gambit software. Calculations are performed using Galerkin and Generalized Least Squares FEMs; based on which results are compared. Using the power iteration method for the neutron and adjoint calculations, the neutron and adjoint flux distributions with the corresponding eigenvalues are obtained. The results are then validated against the valid... 

In the present study, the neutron noise, i.e. the stationary fluctuation of the neutron flux around its mean value is calculated based on the 2G, 3D neutron diffusion theory. To this end, the static neutron calculation is performed at the first stage. The spatial discretization of the neutron diffusion equation is performed based on linear approximation of Galerkin Finite Element Method (GFEM) using unstructured tetrahedron elements. Using power iteration method, neutron flux and corresponding eigen-value are obtained. The results are then benchmarked against the valid results for VVER-1000 (3D) benchmark problem. In the second stage, the neutron noise equation is solved using GFEM and... 

In the present paper, development of the three-dimensional (3D) computational code based on Galerkin finite element method (GFEM) for solving the multigroup forward/adjoint diffusion equation in both rectangular and hexagonal geometries is reported. Linear approximation of shape functions in the GFEM with unstructured tetrahedron elements is used in the calculation. Both criticality and fixed source calculations may be performed using the developed GFEM-3D computational code. An acceptable level of accuracy at a low computational cost is the main advantage of applying the unstructured tetrahedron elements. The unstructured tetrahedron elements generated with Gambit software are used in the... 

The purpose of the present study is to develop the neutron diffusion solver and neutron noise simulator based on the Boundary Element Method (BEM). The 2-D, 2-G neutron/adjoint diffusion equation and corresponding neutron/adjoint noise equation were solved using the mentioned method. The developed neutron static and noise simulator based on the finite element method gives accurate results when the more number of the elements is used. The motivation of the present research is to use the boundary element method to reduce the computational cost. The boundary element method attempts to use the given boundary conditions to fit boundary values into the integral equation, rather than values... 

In the present study, the development of a neutron noise simulator, DYN-ACNEM, using the Average Current Nodal Expansion Method (ACNEM) in 2-G, 2-D hexagonal geometries is reported. In first stage, the static neutron calculation is performed. The neutron/adjoint flux distribution and corresponding eigen-values are calculated using the algorithm developed based on power iteration method by considering the coarse meshes. The results of the static calculation are validated against the well-known IAEA-2D benchmark problem. In the second stage, the dynamic calculation is performed in the frequency domain in which the dimension of the variable space of the noise equations is lower than the time... 

Accurate calculation of kinetic parameters is of utmost importance in the safety analysis of a nuclear reactor. In the current paper, two approaches are investigated to evaluate these parameters in energy phase space. In the first approach, these parameters are derived from an energy-continuous form of the forward and adjoint transport equations and then integrals with respect to the energy variable are replaced by weighted summations over the energy groups, while in the second approach these parameters are extracted from the multi-group forward equation and its associate adjoint equation in which their multigroup constants are weighted by forward spectrum. The difference of weighting... 

To quantify the core barrel motion (CBM) in a pressurized water reactor, a scaling factor can be calculated to convert the Root Mean Square (RMS) value of the ex-core signals (%) to the core barrel motion amplitude (mil) (Thompson et al., 1980). In the current paper, a scaling factor is calculated using the direct and adjoint methods for a typical VVER-1000 reactor. The scaling factor is calculated using the perturbed parameters that result from CBM. The results show that the calculated scaling factors are not the same in one and two-dimensional modeling, and strongly depend on the ex-core detector location. The linearity assumption of relative detector response versus the small displacement...