Session J24: Convection and Buoyancy-Driven Flows: General

Validation of Cryogenic Propellant Tank Self-Pressurization by Leveraging Reduced Order Modeling within Computational Fluid Dynamics Simulation

Validation of cryogenic propellant tank self-pressurization was performed using a hybrid Computational Fluid Dynamics (CFD) and reduced order modeling methodology. Data from a liquid hydrogen ground test conducted at the K-site facility at the National Aeronautics and Space Administration (NASA) Glenn Research Center was used for the validation effort. Liquid phase dynamics were explicitly resolved with a CFD tool. Vapor phase dynamics were modeled as a point mass that communicated heat from the tank wall to the liquid phase via a boundary condition used at the gas-liquid interface. The method proved to be more accurate, robust, and efficient than explicit resolution of the dynamics using a standard Volume of Fluid (VOF) methodology. The subject pressurization process was found to be heavily dependent upon both the relatively high liquid temperature gradient near the gas-liquid interface and the natural convection flow path. Modeling the gas-liquid interface as an immovable surface eliminated spurious velocities near the gas-liquid interface which are observed to destroy the interface temperature gradient in VOF simulations, and correspondingly enabled more rapid simulation since interface advection was not allowed. The single phase computational domain also facilitated the ability to demonstrate spatial resolution convergence of natural convection cells within the liquid which significantly impacted the tank pressurization rate. This work was used to demonstrate the critical physics for tank self-pressurization and numerical methodologies that may be used to best resolve those physics. The findings informed development and operation of production level CFD tools used in the Fluid Dynamics Branch at NASA Marshall Space Flight Center.   

A Galerkin-based reduced-order modeling strategy for unsteady plumes

Buoyant plumes exist in a variety of different contexts, including volcanic eruptions, thermal columns, smokestacks, and high temperature burners. At the base of the plume, large-scale vortices form as the flow rapidly accelerates upwards. These structures have an important effect on the entrainment and mixing properties of the flow, but they are not easily captured using standard models. In this talk, we will discuss reduced-order modeling strategies using a combination of Galerkin projection, proper orthogonal decomposition, and sparse regression to build a reduced-order model (ROM) that accurately capture these large vortical structures in a computationally efficient manner. The ROM construction will be based on direct numerical simulations (DNS) of axisymmetric helium plumes where adaptive mesh refinement was used to supply additional resolution to the local flow structures. We will first compare the ROM and the DNS using a variety of different statistics, including Reynolds and Favre averages, oscillation frequency, streamwise fluxes, and kinetic energy production mechanisms. Using the Navier-Stokes equations, we will then examine the most active terms that contribute to the coefficients in set of ordinary differential equations comprising the ROM.   

Linear stability analysis of boundary layer flows with thermal effects

The study of shear flows with thermal effects finds several applications in weather prediction, heat exchangers, chemical vapor deposition (CVD), among others. In some of these applications, for example in CVD, one needs to ensure a laminar flow to keep the quality of the process. To investigate the thermal influence in shear flows, a local linear stability approach is adopted in this work. This analysis allows the investigation of mixed convection flows including their response to infinitesimal disturbances. The incompressible form of the Navier-Stokes equations is employed together with the Oberbeck-Boussinesq approximation to model the present flows and, therefore, include buoyancy effects. The setup studied consists of the Blasius boundary layer heated from below. To assess the stability properties with respect to critical parameters (Reynolds and Grashof numbers, oblique wavenumbers), modal and non-modal analyses are employed.   

Special characteristics of a double-diffusive instability found in oceans

The evolution of horizontal double-diffusive layers (DDLs) is one of the outcomes of double-diffusive convection found in many natural and industrial transport processes e.g., DDLs in oceans, earth's mantle, solar ponds etc. A CFD based fluent model is developed for the investigation of different characteristics of the onset, sustenance, merging and disappearance of DDLs by imposing lateral thermal gradients in a stably stratified compositional field. A specially oriented large-scale convection roll was found inside each DDL and each roll was driven by the competing density change due to pre-existing compositional and imposed thermal field. Various combinations of solutal and thermal Rayleigh numbers were investigated to study different flow regimes and the effect on the number, width and time of sustenance of DDLs. A merging mechanism has been explained along with the special characteristics of sudden drop and rise of heat transfer coefficients on the sidewalls and average velocity in the whole domain. The present study is expected to be useful in correlating double-diffusive convection in many large-scale applications including oceanography, metallurgy, geology, etc. The model was also developed for 3-D geometry and the results were quite similar to that of 2-D simulations.   

Direct numerical simulation of forced thermal convection in asymmetrically heated channels

We carry out direct numerical simulation (DNS) of turbulent channel flows at different Prandtl numbers and up to friction Reynolds number Re_τ≈2000, considering flow cases with both symmetric and asymmetric heating[1-2]. The latter configuration has been studied considerably less, although it is certainly the most relevant for engineering applications, where heating is often concentrated on one wall. We show that one-sided heating modifies the temperature fluctuations in the outer layer, where we observe large-scale eddies extending well beyond the channel half height. We show that also in the case of one-sided heating the temperature profile exhibits a logarithmic layer and a wake region, which can be approximated using a parabolic profile. We use these universal features of turbulence to derive analytical approximations for the Stanton number, and to quantify the thermal efficiency of one-sided-heated channels compared the idealized symmetric cases. We find that the thermal efficiency is reduced by up to 30% at low Prandtl number, whereas the increasing relevance of turbulent convection tends to level off the differences at higher Prandtl number, with a heat transfer reduction of about 10% at Pr=4.

    

Thermal convection in a cylindrical layer heated from below and cooled at the top and side boundaries.

Motivated by nuclear safety issues, we study heat flux exchanges in a thin cylinder with an imposed flux at the bottom and top (not necessarily equal) and a fixed temperature on the side. We combine Direct Numerical Simulations and a theoretical approach to derive scaling laws for the temperature difference between top and bottom and for the mean temperature of the system. We find two scaling laws depending on the flux aspect ratio. The first one is controlled by heat exchanges on the side, for which we recover classical laws of the vertical convection (George & Capp 1978). The second one is driven by top-bottom heat transfers analogous to Rayleigh-Bénard convection (Grossmann & Lohse 2000). In addition to averaged quantities, we show that heat flux fluctuations at the side wall are large and highly intermittent, which might impact safety protocols.

    

Heat transfer enhancement over passive motion inducing surfaces

Biofouling significantly diminishes the performance of applications that rely on heat transfer. Coatings are often applied to reduce biofouling, but create additional losses in thermal performance due to their low thermal conductivity. Liquid Infused Surfaces (LIS) are an interesting alternative for these coatings. LIS create a mobile interface between an internal liquid and an external flow. The motion within the internal liquid has been shown to reduce drag in both laminar and turbulent flows, and has the capacity to enhance convection within the surface. Due to this, LIS have potential to decrease drag and yield anti-biofouling effects without loss in thermal performance. An experimental study is performed to measure drag reduction and heat transfer over LIS. Surface modifications are explored to enhance these features and to mimic the canonical surfaces used in a numerical study that indicates significant heat transfer enhancement over LIS. Drag reduction and heat transfer measurements are performed in microfluidic channels to study laminar external flows. Retention of the internal liquid is also studied.   

Machine learning assisted models for convective boundary heat transfer in turbulent fire simulations along wall/ceiling/floor

Accurate modeling of convective boundary heat flux is vital for the predictive modeling of turbulent fire along a solid surface like walls, floors and ceilings. High grid-resolution near the surface is required to produce accurate modeling of the heat flux on the surface. This requirement is not feasible in engineering modeling studies of fires along a surface. Wall models are thus needed to reconstruct boundary heat flux so that the grid requirement is not so restrictive. In this work, we examine the feasibility and potential of using machine learning to reconstruct the convective boundary heat flux in fire modeling. High-fidelity large-eddy simulations of several turbulent wall fire propagating along a vertical wall, a ceiling, and a floor are conducted to produce the training data for machine learning. A temperature gradient correction factor is introduced to compensate for the loss of accuracy of temperature gradient when discretized on a coarse grid. The machine learning model is used to train the model for the correction factor. The performance of the trained model is assessed for the different fire cases. Good performance is observed.   

Analog rain experiment: plumes of soluble particles

Rain plays a major role in the climate system. A key ingredient of the rain process is the coupling between flow and phase change. We have set up an analog experiment, where the air in the atmosphere is replaced by water in a tank, and the phase change between rain droplets and water vapor is replaced by salt particles dissolving in water.

To mimic the rain, a certain amount of salt is injected into the water tank. The sedimentation of the particles leads to the formation of a plume. The salt particles dissolved partly during falling. Non-dissolving particles, like sand or plastic beads, are also used as a reference. This non-dissolving plume is comparable to plumes obtained by the injection of a heavy liquid.

The particle concentration is measured by light absorption and velocity field by PIV. For both cases, the particle concentration profile shows a Gaussian shape, whose width increases linearly with height. The width of salt plume is more narrow and vertical compared to non-dissolving plume. The plume particle flux is measured by integration of the local concentration along the horizontal direction. It is roughly constant for non-dissolving plumes, but decreases linearly for salt plumes due to dissolution. The hydrodynamic behaviors of the plume are investigated and modeled.

    

Effect of thermal stratification on the transport and dispersion of polydispersed expiratory particles

The COVID-19 pandemic highlighted the importance of indoor air quality on the exposure to respiratory diseases. During an expiratory event, a multiphase turbulent buoyant cloud is released in which particles of various sizes are suspended and exhibit different physical behaviour based on their size. The fluid dynamics of this process are complex, and it is important that the spatiotemporal variations and turbulent mixing of these particles are captured well to reflect reality.

This work investigates the effect of indoor thermal stratification on the behaviour of the turbulent buoyant exhalation jet, and the subsequent particle dispersion pattern. Cases with increasing temperature gradient are compared to an isothermal base case, and the influence of stratification on the dynamics of different sized particles entrained in the jet is discussed. A finite-difference large-eddy simulation in-house code is used to solve the filtered Navier-Stokes and energy equations on a staggered grid for the continuous (air) phase, while the dispersed phase (liquid particles) is modelled by a Lagrangian Particle Tracking algorithm. Realistic particle size distribution and emission rate are used, and the particle volume fraction is computed to quantify the spatiotemporal evolution of infection risk.   

Finite-amplitude Instability Analysis of Non-isothermal Annular Parallel Flow through Porous Medium

Weakly nonlinear stability analysis of stably stratified non-isothermal parallel water flow in a tall vertical annulus filled with a highly permeable porous medium is investigated in the current work. The flow stability is described by the volume averaged Navier Stokes equations [1, 2]. The effect of the curvature parameter on the bifurcation and instability of the considered flow has been investigated via finite-amplitude analysis centered around cubic Landau equation. A wide range of Reynolds number (Re), four different values of curvature parameter (C), two values of form drag coefficient (c_F), two values of media permeability ( in terms of Darcy number, Da) and a fixed value of Prandtl number (Pr = 7) are considered. The finite-amplitude analysis predicts supercritical as well as subcritical bifurcation in the vicinity of instability boundary. In most of the parametric space, the bifurcation is supercritical, whereas for Da = 10^-2 and cF = 6x10^-4 subcritical bifurcation exists in a very small range of Re that too for two values of C only. However, the non-isothermal parallel water flow through a vertical channel exhibits only supercritical bifurcation[3]. In the supercritical (subcritical) regime, the equilibrium (threshold) amplitude is investigated as a function of different controlling parameters. As the gap between the cylinders increases, the threshold amplitude below which the flow remains nonlinearly stable grows. Moreover, the influence of nonlinear interaction of different harmonics on the Nusselt number (Nu) and friction coefficient (C_f) on both the walls of the annulus has been also investigated. Nu for the distorted state is always less than the Nusselt number for the basic state. C_f at the inner wall is always greater than the C_f at the outer wall. The skin friction at the outer wall is either constant or a decreasing function of Ra.   

Harnessing buoyancy-driven instability to enhance thermal membrane desalination

Membrane Distillation (MD) is an emerging method of desalinating complex wastewaters and hypersaline brines. MD faces two technological challenges. 1) temperature polarization, is the cooling of the feed in a thermal boundary layer that forms at the membrane due heat lost to evaporation. This reduces the local rate of permeate production. 2) concentration polarization, is the accumulation of solutes in a simultaneous concentration boundary layer on the membrane. This leads to precipitation of solutes.

Surprisingly, no prior work considers that temperature and concentration polarization increase the feed density near the membrane. We show that with gravity properly oriented, this can trigger a buoyancy-driven instability in which plumes of cool, solute-rich, feed sink away from the membrane. This brings warm, low-concentration, feed to the membrane, mitigating temperature and concentration polarization. We perform computational fluid dynamics simulations to explore the dependence of buoyancy-driven instability on the operating and feed conditions and show how to sustain the instability over long membrane surfaces.