Katsuhisa Noto

Dependence of heat island phenomena on stable stratification and heat quantity in a calm environment

Dependence of heat island atmosphere on stable stratification and the heat quantity is elucidated by (i) visualizing and measuring the thermal flow over a heated source in a calm and stratified conditions in a laboratory experiment, (ii) finding new type of flow patterns, (iii) determining flow states by the PSD gradients, (iv) comparing with the existing results, and (v) discussing physically to extend the laboratory experiment to a real urban atmosphere. The heat quantity transferred from urban areas makes flow patterns tall. The stable stratification suppresses the plume height, increases the swaying amplitude and turbulence, and produces a vortex pair near the plume top. With increasing the heat quantity and/or decreasing the stable stratification, the plume changes from the type of the steady fumigation with local circulations accumulating heat, which agrees well with Okes model, to the types of fumigation with the swaying motion, the mushroom, the maximum amplitude of the swaying motion, having a glasses-like vortex pair, and shedding vortices upwards, wherein the last two types of plumes the urban heat easily dissipates upwards. The results agree well with heat island phenomena which occur during night in winter and gigantic columns of clouds which occur during daytime in summer.

Spectra and Critical Grashof Numbers for Turbulent Transition in a Thermal Plume

Turbulent transition and turbulence characteristics of the thermal plume above a line heat source in unstratified air are elucidated by visualizing the plume, measuring the temperature, and analyzing the spectrum of the measured temperature. Large-scale vortices occur in the turbulent region, and they have the same frequency as the laminar swaying motion. Spectra S(s) can be approximated by 0.130f (Hz) -5/3 in the inertia-convective subrange and 0.275f (Hz) -3.0 in the inertia-diffusive subrange. The spectrum enables us to exactly determine the local state of flow, i.e., laminar, transitional, or turbulent. Grashof numbers for the beginning and end of a transition are Gr = 2.0 × 10 8 and Gr = 2.0 × 10 9 . The transitional region is divided into the initial and final stages at Gr b = 7.52 × 10 8

Formulation and Numerical Methodology for Three-Dimensional Wake of Heated Circular Cylinder

ABSTRACT A time-dependent three-dimensional wake of a heated circular cylinder is formulated. Its numerical methodology is presented, and computed results in an isothermal and a buoyant wakes are validated as follows. First, a wake with buoyancy from a heated circular cylinder with infinite spanwise length is formulated as a three-dimensional and time-dependent thermal flow with body force and varying density and properties. Second, a numerical methodology for the above formulations is obtained by employing grid generation using elliptic partial differential equations and by extending the highly simplified marker-and-cell (HSMAC) method to the flow with varying density and properties. At an isothermal condition, the present formulation and methodology become those for an isothermal fluid flow. Third, for the isothermal wake at Reynolds numbers of 100 and 300, the Strouhal numbers, time-averaged drag coefficients, and root-mean-squared (RMS) amplitudes of the lift coefficient, vorticity distribution, and streaklines are computed and presented. Fourth, in the air buoyant wake, the time-averaged mean Nusselt numbers at the Grashof numbers 0 and 490 and the Reynolds number 70 agree well with the previous results. Last, the buoyant wake at Reynolds number 300 and Richardson number 0.3 of air is computed and presented.

Generation of the Karman vortex street at low Reynolds number due to cooling a cylinder: Cause and fluid type effect by numerical computation

The aim is to clarify a main cause and a fluid-type effect of the generation of the Karman vortex street due to cooling a cylinder at a low Reynolds number where the isothermal wake is not a Karman vortex street but the wavy wake. The two-dimensional, laminar, time-dependent continuity equation; Navier–Stokes equations with the buoyancy term; and energy equation are solved numerically by finite difference methods in the wake from a cooled circular cylinder submerged in an upward freestream of mercury, air, or water. The main cause is clarified and is that one is the generation of the wake vorticity, which never occurs in any isothermal wake, and the other the stable arrangement with amplified asymmetry of the vorticity distribution in the wake. When the Prandtl number and / or the cylinder temperature are decreased, the Karman vortex street is generated easily and has a smaller wake frequency, smaller vortex speed, and larger vortex spiral than those in any isothermal wake. The characteristics of the Karman vortex street generated by cooling a cylinder therefore never occur in any isothermal wake.

Thermal plume turbulent enhancement, reverse transition, and relaminarization in stably stratified enclosure

For a thermally buoyant plume in stably stratified ambient air at the heating rate Q = 0.32-27.8 W/m, flow patterns are visualized experimentally, the time-dependent temperature is measured, and the power spectrum density (PSD) is obtained. The PSDs have gradients with -9/2 and -8.0 in the laminar state and -5 and -3.0 in the turbulent state. In addition, the frequency hand of turbulence is higher than that of the swaying motion, where stable stratification increases the swaying frequency by 37% at the stratification degree st = 0.3 K/cm. Flow regions of the laminar, transitional, and turbulent states at any location are determined. When the flow regions are plotted on visualization photographs, the turbulent transition, reverse transition, and relaminarization are specified and compared with unstratified results

Numerical Computation for Buoyancy Effect on Three-Dimensionality and Vortex Dislocation in Heated Wake with Vertical Mainstream

For a heated circular cylinder wake with a vertical mainstream of air at Reynolds number 300 and Richardson number 0.3, the time-dependent three-dimensionality leading to the vortex dislocation is analyzed by direct numerical simulation (DNS). Time-series images of 3-D streaklines are obtained. The computed results are compared with those in the isothermal wake. The three-dimensionality and vortex dislocation in the heated wake are discussed, and the positive buoyancy effects are revealed. Buoyancy effects are as follows: (1) an increase of the upward velocity u in the whole wake (Effect I); (2) activation of three-dimensionality in the nearwake (Effect II); (3) suppression of the Karman vortex street in the farwake (Effect III); (4) suppression of the three-dimensionality and vortex dislocation in the farwake (Effect IV). Effect IV is more dominant than Effect III. Because of buoyancy, the vortex dislocation is more suppressed than the Karman vortex street. Because of Effect II, the nearwake dominant frequency f p of spanwise velocity w is increased to 2f wake and 5f wake . Because of Effect IV, Λ d and Λ v in the farwake are increased to Λ d fallingdotseqΛ v = 3 (Mode-A*). Here f wake is the wake frequency, and Λ v and Λ d are the spanwise wavelengths of ω x , ω y , and vortex dislocation normalized by the cylinder diameter.

Direct Numerical Simulation of Turbulent Thermal Plume in Stably Stratified Ambient: Formulation, Numerical Methodology, Reverse Transition, Relaminarization, and Turbulent Enhancement

For the turbulent thermal plume of air developing in stably stratified air above a square heated plate on a horizontal solid surface with infinite area, the formulation and numerical methodology for direct numerical simulation (DNS) are developed, the DNS data at the Rayleigh number Ra = 1 × 107 are obtained by DNS computation, and the reverse transition, relaminarization, and turbulence enhancement are elucidated by the present DNS. Main conclusions are as follows. 1. The governing equation system for DNS of the turbulent plume in stratified ambient is 3-D and time-dependent with buoyancy and varying density and properties and without assumption of turbulent, transitional, or laminar state, and is applicable to any thermal conditions of heated plate and any stratification degree. 2. In the present DNS, the turbulent behavior, i.e., the high-frequency motion, the viscous dissipation, etc. can be reasonably considered, but the viscous dissipation heat is omitted because it is extremely small in the thermal plume. 3. The numerical method for DNS of the above governing equation system is developed. 4. The criterion determining the turbulent, transitional, and laminar states is obtained. The turbulent, transitional, and laminar regions in the plume are shown in the region map. 5. The grid size, the time step, and the frequency and resolution of space and time of the Kolmogorov microscale are validated for DNS by using the power spectrum density (PSD). 6. The variations and mechanisms of the distributions of temperature and velocity in the upward direction in the stable stratification are elucidated. 7. At the weakly stratified ambient, turbulence is enhanced near the plate center. 8. At any degree of stable stratification, the turbulence is suppressed. Whether turbulence exists or not near the plate center leads to different mechanisms of the turbulence suppression, i.e., the reverse transition and relaminarization.

Numerical Computation of a New Vortex (A Cooled Vortex Street) and its Generation Mechanism in a Cooled Circular Cylinder Wake at Low Reynolds Number

A strongly cooled, circular cylinder wake with an upward main stream of air at low Reynolds number Re, i.e., 15 ≦ Re ≦ 44, is analyzed numerically, and is elucidated as follows. (1) A new vortex street, i.e., a “cooled vortex street,” is discovered, develops in the range of computed Re, i.e., 15 ≦ Re ≦ 44, has strong asymmetry, and is extremely different from the Karman vortex. (2) The vortex street occurring in the cooled wake is either the Karman vortex street or the cooled vortex street. No vortex street except these vortex streets ever occurs in a wake. (3) The critical Reynolds number Rec, i.e., the minimum Re occurring in the Karman vortex street by cooling a cylinder, is nearly 24. When the isothermal wake is cooled weakly, the Karman vortex street certainly develops at Re > 24, but never occurs at any cooling rate at Re < 24. The generation mechanism of the cooled vortex street is elucidated by employing the computed vorticity and temperature distributions as follows. (1) With an extreme increase in the cooling rate, the wake vorticity is generated strongly by the temperature gradient, the absolute value of vorticity in shear layers becomes extremely large, and the shear layers are elongated remarkably. The angle between shear layers and the wake width increase remarkably. (2) As a result, shear layers roll up considerably, and their tips reach the midplane alternately. Extremely large-scale vorticity-concentrated tips are generated, and move to the downstream. Thus a stable wake, i.e., the cooled vortex street, is generated. That is, the stable rolling of shear layers is realized only in the Karman and the cooled vortex streets.

Formulations and Direct Numerical Simulation Methods for Effects of Coriolis Force, Latitude, and Stably Stratified Ambient on a Large-Scale Thermal Plume

A thermal plume with (1) the Coriolis force depending on the latitude of the earth, (2) turbulence, (3) varying density and properties, (4) hydrostatic pressure of air column weight placed above a heated square, and (5) stably stratified ambient is first elucidated. The earth model is employed as an analytical model, time-dependent three-dimensional governing equations are formulated, and a direct numerical simulation (DNS) methodology is obtained. Then, the plume without the Coriolis force is computed, the grid dependence is discussed, and the computed results are compared with previous results. As a result, the formulations, numerical methods, and computed results are validated. At the North Pole, a laminar plume with the Coriolis force rises spirally with the earths rotation in an anticlockwise direction. However, the turbulent plume with the Coriolis has a thin column rotating very quickly and spirally in the clockwise direction. The rotations and heights of laminar and turbulent plumes are suppressed by a stably stratified ambient and/or a decrease of latitude. With increasing Rayleigh number, the rotation direction in the plume is varied to clockwise in the turbulent state from anticlockwise in the laminar state. Whether the thermal flow is turbulent or not is determined by the slopes of power spectrum density (PSD) of time-series data of computed temperature, and a sufficient number of grids and time steps exist in the Kolmogorov microscale.

Temperature field with thermal cylinders in buoyant flow in stably stratified air

ABSTRACT The aim of this work is to clarify characteristics of time-dependent temperature behavior in a buoyant flow in stably stratified air in an enclosure. For this aim, the two-dimensional, laminar, time-dependent continuity equation, Navier-Stokes equations with the buoyancy term, and energy equation are solved numerically by finite-difference methods. The computed results at unstratified condition agree well with the previous results, and validate the numerical accuracy. The present computational methods and procedures are therefore valid, and have sufficient grid resolution. As a result, at an adiabatic ceiling of the enclosure or in stably stratified air in the enclosure, a thermal cylinder with high temperature is discovered to occur intermittently near the plume front, and moves upward. However, a thermal cylinder never occurs at unstratified condition. Furthermore, a thermal cylinder exists in both the instantaneous crossover (COI) region at adiabatic condition and the time-averaged crossover (COM) region at stratified condition. In other words, when a thermal cylinder exists, the region with a thermal cylinder is certainly either COM or COI.