Finite Volume Discretization Method Research Articles

A conservative implicit scheme for three-dimensional steady flows of diatomic gases in all flow regimes using unstructured meshes in the physical and velocity spaces

A conservative implicit scheme in the finite volume discrete velocity method framework is proposed for solving the three-dimensional steady flows of molecular gases in all flow regimes from continuum one to free-molecular one. This work is based on the Boltzmann–Rykov model equation, which is a nonlinear relaxation model and can describe the thermodynamic non-equilibrium of diatomic gas flows. The macroscopic equations are solved implicitly together with the Rykov model equation to find a predicted equilibrium distribution first at each iteration step. As a result, the collision term of the Rykov model equation can be discretized in a fully implicit way for fast convergence in all flow regimes. At the cell interface, an asymptotic preserving simplified multi-scale numerical flux is developed to relieve the limitation of grid size and time step in all flow regimes, which can keep the multi-scale property and achieve high computational efficiency. The integral error compensation technique is used to keep the scheme conservative and greatly reduce the number of unstructured discrete velocity space (DVS) meshes. Furthermore, an empirical criterion based on the numerical experiments of the Apollo 6 command module is suggested to guide the generation of three-dimensional unstructured DVS. The accuracy and efficiency of the present method are demonstrated by a number of three-dimensional classic cases, covering different flow regimes.

A reconstructed approach for online prediction of transient heat flux and interior temperature distribution in thermal protect system

Thermal protect system (TPS) is a crucial part of spacecraft to shield them from the aerodynamic heating during the atmospheric entry/re-entry. In this paper, the aerodynamic heating on the surface of a reusable launch vehicle is predicted to achieve rational design of the TPS. The conduction-radiation heat transfer in the TPS that was regard as a kind of index graded medium, was computed using finite volume method and discrete ordinate method. The extended Kalman filtering coupled with Rauch-Tung-Striebel smoother is introduced for calculating the inverse problem to obtain the time-variant heat flux and interior temperature fields in TPS. The impact of the structure parameters and future measurement temperature information on the lag and stability of retrieval results is investigated. The actual heat flux generated at NASA Langley Research Center for the Reusable Launch Vehicle is employed for examining the effectiveness and dependability of the proposed approach. The numerical results demonstrate the present approach can realize precise and on-line prediction of the time-variant heat flux and interior temperature fields in TPS.

Aerothermodynamic Analysis of Space Recovery Experiment Capsule at Mach 6

The main focus of this paper is to compute the flowfield and assess the aerodynamic drag of Space Recovery Experiment (SRE) modules at freestream Mach 6 at zero angle of incidence. Time-dependent Compressible axisymmetric Navier-Stokes equations are numerically simulated using a finite volume discretization method with a three-stage Runge-Kutta time-stepping scheme. The computed shock stand-off distance, pressure ratio across normal shock and stagnation point heat flux are showing satisfactory results with the analytical solutions.Available wind tunnel data such as Schlieren images, oil flow pictures and fore-body aerodynamic drag are compared with numerical results.Influence of various ramp angles of the SRE modules on surface pressure, flow separation, skin friction coefficient, wall heat flux and fore and base aerodynamic drag coefficients are investigated using present numerical data.

Numerical Analysis on Detonation Wave and Combustion Efficiency of Pulse Detonation Combustor With U-Shape Combustor

Abstract The research work is carried out for deflagration and detonation combustion processes at different equivalence ratios of hydrogen–air mixtures in a pulse detonation combustor (PDC). Furthermore, the U-shape channel curvature radius and thickness effect on detonation wave propagation are also investigated. This numerical simulation has been done using a SIMPLE algorithm with the finite volume discretization method and laminar finite rate chemistry for volumetric reaction in the Ansys Fluent platform. The numerical result shows that the U-bend radius of R = 3.5 cm can enhance the faster deflagration-to-detonation transition. So far, the fully developed detonation wave was found near the curvature area of the detonation tube having a width of W = 8 cm. This enhanced detonation wave velocity reaches 2775 m/s, which is higher than the C-J detonation velocity. Furthermore, the entropy generation has been analyzed in two modes of the combustion process. The entropy generation number of 0.76 and 0.7 is obtained from the deflagration and detonation combustion processes. However, the entropy production rate is less in the detonation combustion process, but thermal entropy generation is more in the deflagration combustion process with a magnitude of 3.5 kJ/kg K for an equivalence ratio of φ = 1.5. A combustion efficiency of 78% is found in the detonation combustion process, which is comparatively higher than the deflagration process.

Development and analysis of moments preserving finite volume schemes for multi-variate nonlinear breakage model

Modelling and simulation of collisional particle breakage mechanisms are crucial in several physical phenomena (asteroid belts, molecular clouds, raindrop distribution etc.) and process industries (chemical, pharmaceutical, material etc.). This paper deals with the development and analysis of schemes to numerically solve the multi-dimensional nonlinear collisional fragmentation model. Two numerical techniques are presented based on the finite volume discretization method. It is shown that the proposed schemes are consistent with the hypervolume conservation property. Moreover, the number preservation property law also holds for one of them. Detailed mathematical discussions are presented to establish the convergence analysis and consistency of the multi-dimensional schemes under predefined restrictions on the kernel and initial data. The proposed schemes are shown to be second-order convergent. Finally, several numerical computations (one-, two- and three-dimensional fragmentation) are performed to validate the numerical schemes.

Real-time estimation of thermal boundary conditions and internal temperature fields for thermal protection system of aerospace vehicle via temperature sequence

Aerospace vehicles go through extremely aerothermal heating upon entry into the atmospheric, which need to employ the reliable thermal protection system (TPS). The boundary heat flux and inner temperature information for aerospace vehicles are required to design the TPS. The direct measurement for temperature and heat fluxes is quite difficult mission. In this study, unscented Kalman filtering, is an indirect measurement method based on inner surface temperature information and is introduced to reconstruct the transient heat flux and inner temperature fields of TPS in real-time, which is regarded as a graded index medium. The finite volume method and discrete ordinate method are utilized to solve the energy equation and radiative transfer equation to obtain measurement temperature, respectively. Based on the measurement temperature signal, the unscented Kalman filtering technique is applied to reconstruct the surface heat flux and inner temperature field of the TPS. Simulation results indicate the time-dependent boundary heat flux and inner temperature fields can be estimated using proposed method. The effects of thickness, refractive index, measurement noise, and process noise on the reconstructed results are studied in detail. Retrieval results show the proposed technique is more precise and robust than Kalman filtering method in the nonlinear system.

150USRT Class R-513A Refrigerant Two-Stage Centrifugal Compressor Design Point and Separation Point Flow Field Simulation Analysis

This study used computational fluid dynamics for low greenhouse effect refrigerant (R-513A) simulation analysis in the two-stage 150 USRT class oil-free centrifugal refrigerant compressor using integrated part load value (IPLV) and internal flow field. The compressor rotor speed and mass flow rate for the IPLV working conditions with various loads were planned using Stage 1 and Stage 2 simulations, respectively. The performance and flow field numerical simulation analyses for the two-stage centrifugal compressor is discussed. This study used Ansys-CFX software for numerical simulation analysis and the conservation form of a 3D steady-state Navier–Stokes equation set with the finite volume discretization method for computation. The computing mode produced better computing efficiency and flexible mesh setting using the k-omega (k-ω) model, which has better computational performance in the near wall boundary layer and low Reynolds number flow field (used as the turbulence model) for simulation. The R-513A refrigerant property setting was calculated using the Soave–Redlich–Kwong gas equation. This study discusses the shaft work, pressure ratio, and isentropic efficiency and also describes the main research findings with the meridional pressure, isentropic efficiency contour maps, and flow field velocity vector diagrams. According to the numerical simulation results, in Stage 1 and Stage 2 simulations, the isentropic efficiency produced the highest numerical results in the 75% load case, which are 88.19% and 89.06%, respectively. The isentropic efficiency decreased to 75.93% and 82.26%, respectively, in the 25% load case. The flow field velocity vector diagram shows that in the 25% load case, there was back-flow field distribution near the impeller shroud. The compressor performance was also analyzed.

A multi-degree-of-freedom gas kinetic multi-prediction implicit scheme

A multi-scale implicit multi-degree-of-freedom (MDOF) kinetic model with molecular translational, rotational and vibrational effects is presented. The evolution and exchange of energy among translational, rotational and vibrational degrees of freedom are demonstrated by three coupled relaxation processes. An orthogonal polynomial system is used to involve heat-transfer and viscosity properties in construction of a sequence of objective distribution functions at various relaxation stages. Based on finite volume discrete velocity method framework, the asymptotic preserving discrete unified gas-kinetic scheme (DUGKS) flux is adopted to preserve particle motion information. A second-order prediction scheme based on the Navier-Stokes flux is constructed to predict macroscopic variables from macroscopic residuals for implicit DUGKS iteration, which contains a multiple prediction methodology. The current MDOF kinetic model provides a concrete insight into energy exchange between the rotational and vibrational degrees of freedom during molecular inelastic collisions. The accurate prediction procedure significantly accelerates convergence. Several numerical test cases, including rarefied gas flow in lid-driven cavity, variable specific heat ratio shock structure, hypersonic circular cylinder flows at different Knudsen and Mach numbers, and hypersonic flat plate flow, are performed to validate the accuracy and efficiency of present model. All numerical results of the present method agreed well with those of the reference data. A 2∼3 orders-of-magnitude improvements in computational efficiency of the multi-scale implicit method are achieved compared with the explicit method. It demonstrated that the present method is a promising scheme considering vibration-rotation-translation energy exchange of poly-atomic molecules for the fast simulation of multi-scale flows from low-speed incompressible flow to hypersonic flow, from continuum to rarefied regime.

Longwave modeling of thin film flow of a generalized second-grade fluid down a slanted plate

The free surface dynamics of a thin film of a generalized second-grade fluid flowing down a slanted plate subjected to the action of gravity have been studied. A nonlinear evolution equation for the dynamics of the thin liquid film is derived using the long-wavelength approximation. The model allows to investigate the impact of fluid rheology and geometrical parameters on the thin film’s height. The nonlinear dynamics equation is implicitly approximated on a uniform grid by applying the finite volume discretization method, which uses upwind discretization of the flux function and first-order discretization of the time differential term. The investigation reveals that the free surface deformation trends are similar for the Newtonian and non-Newtonian fluids but the non-Newtonian fluid properties substantially influenced the size and shape of the deformation. It is also found that the shear-thinning fluid moves faster down to the plate compared to the Newtonian and shear-thickening fluid.

Numerical Simulation of an Air-Bubble System for Ice Resistance Reduction

Ships sailing through cold regions frequently encounter floe ice fields. An air-bubble system that reduces friction between the hull and ice floes is thus considered useful for the reduction of ice-induced resistance. In this study, a numerical analysis procedure based on coupled finite volume method (FVM) and discrete element method (DEM) is proposed to simulate complicated hull-water-gas-ice interactions for ice-going ships installed with air-bubble systems. The simulations reveal that after turning on the air-bubble system ice floes in contact with the hull side wall are pushed away from the hull by the gas-water mixture, resulting in an ice-free zone close to the side hull. It is found that the drag reduction rate increases with the increase of ventilation, while the bow ventilation plays a deciding role in the overall ice-resistance reduction. The proposed procedure is expected to facilitate design of new generations of ice-going ships.

MATHEMATICAL MODELING AND 3D NUMERICAL SIMULATION OF A SOLAR POND EXPOSED TO TWO SOLAR REFLECTORS

The salinity gradient solar pond is simply a pool of water with different mass percentages of salt that collects and stores solar thermal energy. When solar radiation comes into contact with the water in the basin, it will become the site of two opposing actions, namely the effect of temperature which expands the liquid in its lower parts, thus reducing their density and favoring ascending currents coming from Archimedes' buoyancy and the effect of salinity which increases this density and prevents the liquid from rising. As a result, the converted thermal energy is trapped in the bottom of the basin. The more the temperature of the water increases, the more the fields of application in different uses of this thermal energy widen. As it is also important to indicate that the high temperature of the storage area allows ponds located in cold areas to save their operating temperatures during the winter period. In an attempt to increase the temperature of the bottom water, we have installed 2 solar reflectors on both sides of the pond which have the role of reflecting solar radiation and returning it to the surface of the pond. This has a positive influence on its thermal performance. The mathematical model governing the pond dynamics is based on the special 3-direction heat equation with an initial condition and 6 boundary conditions. The finite volume discretization method in 3D was used, the Camsol software was applied for finer steps. The numerical results showed that the pond with reflectors recorded a temperature exceeding $ 13\degree\text{C} $ compared to the pond without reflectors. Convergence, consistency and stability were discussed. %and stability were discussed.‏

Numerical Simulations of the Hydrodynamic Performance of the Propeller with Wake Equalizing Duct behind the Ship

The equalizing wake flow into the propeller behind the ship is important from the hydrodynamic performance viewpoint. In this study, numerical simulations of the DTMB4119 propeller with two symmetric and asymmetric duct types behind the KRISO container ship (KCS) are performed using computational fluid dynamics (CFD). In order to improve the wake equaling flow, a combined duct and stators configurations were installed before the propeller in the stern of the ship and its hydrodynamic performance was studied using CFD. A duct with the NACA4415 section and two types of stator configurations are selected. The STAR-CCM+ software that uses the finite volume discretization method was used to solve the governing equations of the fluid flow. In simulating the turbulence model, the standard k-ω model was used and the solution method was validated by comparing the available experimental data. Output parameters such as thrust coefficient and torque coefficient in the open-water condition and behind the ship have been presented and discussed. Improvements in the propeller performance after mounting the asymmetric and symmetric ducts are found at 4.8% and 6.57%, respectively. So, it is concluded that the symmetric duct is more affected by the propeller performance and, hence, reduced fuel consumption considerably.

Computational Fluid Dynamics Analysis and Design of Payload Shroud of Satellite Launch Vehicle

The main focus of the present paper is to computational fluid dynamics analysis and design of payload fairing of satellite launch vehicle at freestream Mach number range of 0.6 - 3.0. Initially, time-dependent compressible three-dimensional Euler equations are solved employing a finite volume discretization method with a multi-stage Runge-Kutta time-stepping scheme to compute surface pressure and aerodynamic coefficients at various payload fairing and at angle of attack up to 5o with an increment of 1o. Payload fairing dimensions are selected that satisfies permissible structure load on satellite launch vehicle. Detailed flowfield simulation is carried out on the selected payload fairing employing axisymmetric compressible Reynolds-average Navier-Stokes equations to assess unsteady flowfield characteristics. The numerical simulations are used to locate terminal shock on the payload fairing at transonic Mach number. Unsteady flow characteristics are used to compute acoustic load. Shock standoff distances at supersonic speeds are tabulated and compared with the analytical solution. Schlieren images and oil flow pictures are compared with experimental results and in good agreement. Aerodynamic shape optimization of satellite launch vehicle payload fairing shape has been performed to satisfy structural load at maximum drag and dynamic pressure.

Real-time reconstruction of thermal boundary condition of porous media via temperature sequence

Porous media are widely applied in numerous technological field due to its excellent thermal, mechanical and exchange properties. Because of involving multi-scale and multi-effect coupling, only a few studies are dedicated to heat flux estimation of porous media. In this study, on the basis of the finite volume method (FVM) and discrete ordinate method (DOM), a novel method is proposed to introduce the geometric analytical formulas of thermal properties into the multi-scale heat transfer problem of porous materials. Then, the temperature sequence in a short time are used as measurement information for inverse analysis. The time-varying heat flux of NiCrAl porous materials, copper and aluminum are reconstructed based on Kalman filter coupled with the recursive least square estimator (KF-RLSE). In addition, the sensitivity of the photothermal properties to temperature response information is analyzed. The effects of porosity, scattering albedo and specularity parameter on the accuracy and stability of the reconstructed heat flux are investigated. The numerical results with the noise level 0–0.3 show that the predicted boundary heat flux is less than 0.2 for NRMSE and more than 0.99 for the correlation coefficient, proving the validity of the proposed method.

Application of LES combined with a wave equation for the simulation of noise induced by a flow past a generic side mirror

The paper presents validation results of a hybrid simulation method for aeroacoustics in turbulent flows at low Mach numbers. The hybrid method implemented in the Ansys Fluent® CFD package applies a scale-resolving turbulence model to compute the noise sources in an incompressible flow, while the noise propagation is modeled by a wave equation formulated for the acoustic potential. The selected test case deals with a flow and a sound field around a generic side view mirror of a car. The SBES model by Menter, which belongs to the class of the RANS-LES models, is used for the flow simulation. It switches to the Large Eddy Simulation (LES) mode in separated mixing layers and recirculation zone behind the mirror as well as in the following wake, where flow develops intensive turbulence and dominating noise sources. The acoustics wave equation is formulated in the model form of Kaltenbacher et al. and is applied in the time domain. The overall calculation is performed as a transient co-simulation on the same mesh using the finite-volume discretization method for both the flow and the acoustics parts. The wave equation is advanced in time using the HHT-α method. Obtained distribution of the mean wall pressure over the mirror surface closely matches the experimental one. Rich content of the resolved turbulent vortices in the separation zone and good agreement of the calculated and measured wall pressure spectra at sensor locations downstream the mirror evidence a proper LES resolution quality of noise sources. Comparison of the computed noise spectra at the remote microphones with the experimental data demonstrates the sound propagation accuracy and validates the overall aeroacoustics simulation method.

Performance Simulation of a Modified Geothermal Grain Dryer Based at Menengai Well 3 in Kenya

Geothermal energy can be effectively utilized for grain drying to reduce carbon emissions and also cut operational costs associated with conventional methods. The main challenges encountered in the use of the geothermal grain dryer, such as in Menengai, Kenya, include uneven grain drying and long throughput times. Grains near the hot air inlet dry at a faster rate compared to those near the exhaust end. Therefore, the grains must be recirculated within the dryer to achieve uniform moisture distribution. Grain recirculation is energy-intensive as it utilizes electricity running the elevator motors in addition to the suction pump. A Computational Fluid Dynamics (CFD) model was developed to study the airflow pattern and its impact on drying of maize. The model was simulated in ANSYS 21 and validated using experimental data. Finite volume discretization method was employed for meshing. Pressure-based segregated solver was used in the Computational Fluid Dynamics (CFD) simulation. Also, K-Omega turbulent model was used for enhancing wall treatment. The findings indicate that non-uniform hot air distribution across the grain buffer section causes uneven drying. Introducing filleted flow-guides results in a relatively uniform velocity, temperature, and turbulence kinetic energy distribution across the dryer. The average velocity and temperature magnitudes in lower compartments increased by 153.3% and 0.25% respectively for the improved dryer. In the upper compartments, the velocity and temperature increase were 176.5% and 0.22% respectively.

Discrete phase model of blood flow in a roughness microchannel simulating the formation of pseudointima

Purpose: The goal of the present study was the development of discrete phase model to simulate the phenomenon of backfilling a morphologically complex surface by red blood cells (RBCs) in a flow microchannel and to anticipate the conditions of forming a pseudointima. The objective of the experimental studies that inspired the development of the simulation was to create a surface that stimulates the formation of the pseudointima layer. Methods: The finite volume method (FVM) and discrete particle method (DPM) were applied to develop the target model. In addition, a mixture model and a roughness model of bottom layer were tested in the present study to show their influence on simulation the phenomenon of backfilling a morphologically complex surface by RBCs in a flow microchannel. Results: Numerical models were developed including: a) FVM models to compare the effect of applying boundary conditions with/without roughness and cubes, as well as the analysis of their influence on blood velocity and shear stress; b) mixture models to compare the effect of applying different boundary conditions and cubes on computed results; c) DPM models to compare the effect of applying and not applying roughness as a boundary condition; d) DPM models with a morphologically complex surface and RBCs collisions to present RBCs concentration, velocity and time distributions during flow in a channel. Conclusions: The analysis carried out for the developed numerical models indicates that DPM model with cubes computes the best results. It also shows the backfilling of a morphologically complex surface of the bottom microchannel with RBCs.

Numerical investigation of laminar forced convection and entropy generation of Fe3O4/water nanofluids in different cross-sectioned channel geometries

In this study, forced convection of nanofluid flow in various channel geometries with a hydraulic diameter of 16 mm and length of 1.5 m under laminar flow condition has been investigated numerically. Constant heat flux of 6 kW/m2 has been applied on to the surfaces of the channels. Fe3O4/water nanofluid has been used in the analyses to enhance the convective heat transfer of the base fluid. Analyses have been performed for Reynolds numbers between 500≤Re≤2000, and for volume concentrations of nanoparticles between 1% and 5% in cylindrical, square, rectangle, and triangle cross-sectioned channel geometries. The finite volume discretization method has been used to solve the governing equations. The effects of some parameters; Reynolds number, nanoparticle volume fractions, channel geometries on the average Nusselt number, Darcy friction factor and entropy generation have been investigated in detail. The results indicate that nanofluid offers further convective heat transfer enhancement according to base fluid and cylindrical cross-sectioned channel gives the best heat transfer performance among other cross-sectioned channel geometries. Using water as a working fluid, cylindrical cross-sectioned channel geometry gives the highest heat transfer rate among other channel geometries, whereas triangle one gives the lowest. Cylindrical cross-sectioned channel geometry offers up to 77.6% enhancement compared to triangle cross-sectioned channel geometry for the same hydraulic diameter and same heat flux. However, triangle cross-sectioned channel geometry has highest convective heat transfer increment ratio (4.12%) for changing working fluid as water to nanofluid. Also, some new Nu correlations based on the channel geometries and nanoparticle volume fractions were proposed in the present study.

Benchmark Test Cases for Non-Gray Radiative Heat Transfer Calculation using FSK Look-Up Table

Three test cases in the categories of homogeneous non-isothermal, non-homogeneous isothermal and non-homogeneous non-isothermal have been developed to validate the two-dimensional interpolation technique for calculation of non-gray radiative heat flux on the walls of the system. The participating gases H 2 O and CO 2 of different mole fractions and temperatures are considered in different zones of the test cases. HITEMP-2010 database has been used to calculate the absorption coefficients of H 2 O and CO 2 at different mole fractions and temperatures. Further, the random variation of absorption coefficients with spectrum has been reordered in smooth monotonically increasing smooth function using full spectrum k-distribution method (FSK). A look-up table is developed for different mole fractions and temperatures of gases H 2 O and CO 2. The calculation of absorption coefficients at thermodynamic states other than look up table has been performed using two dimensional interpolation techniques. The geometry of test cases have been divided into three zones whose conditions on the first and last zones are same as available in look-up table while interpolation is used for the middle zone. The radiative transfer equation is solved numerically by finite volume discrete ordinate method (FVDOM). The results have been compared with FSK method and have been found that interpolation techniques are giving satisfactory results with extremely less computational resource and time.

Radiative heat transfer calculation for mixture of gases using full spectrum k-distribution method

The full spectrum k-distribution method is used to obtain radiative heat flux and divergence of radiative heat flux for two test cases, containing mixture of CO 2 and H 2 O at different concentration and temperature keeping pressure constant. The k-distribution for mixture of gases is obtained from individual gas k-distribution using three different mixing models, viz., superposition, multiplication and hybrid model. Further, the radiative transfer equation (RTE) is solved by the finite volume discrete ordinate method (FVDOM) to obtain the radiative flux and the radiation source term. The results obtained were compared with the FSK from spectral addition and LBL method. The multiplication mixing model provides better accuracy compared to other mixing models considered in the present study.