Convective Heating Rates Research Articles

Downscaling, parameterization, decomposition, compression: a perspective from the multiresolution analysis

Abstract. Geophysical models in general, and atmospheric models more specifically, are always limited in spatial resolutions. Due to this limitation, we face with two different needs. The first is a need for knowing (or "downscaling") more spatial details (e.g., precipitation distribution) than having model simulations for practical applications, such as hydrological modelling. The second is a need for "parameterizing" the subgrid-scale physical processes in order to represent the feedbacks of these processes on to the resolved scales (e.g., the convective heating rate). The present article begins by remarking that it is essential to consider the downscaling and parametrization as an "inverse" of each other: downscaling seeks a detail of the subgrid-scale processes, then the parameterization seeks an integrated effect of the former into the resolved scales. A consideration on why those two closely-related operations are traditionally treated separately, gives insights of the fundamental limitations of the current downscalings and parameterizations. The multiresolution analysis (such as those based on wavelet) provides an important conceptual framework for developing a unified formulation for the downscaling and parameterization. In the vocabulary of multiresolution analysis, these two operations may be considered as types of decompression and compression. A new type of a subgrid-scale representation scheme, NAM-SCA (nonhydrostatic anelastic model with segmentally-constant approximation), is introduced under this framework.

Numerical Methods to Determine Convective Heating Rates on Aerodynamic Surfaces

The approach for the present work is to develop a one-dimensional heat conduction model to infer the surface heating rates from the temperature data. The temperature history is obtained from a nickel thin film sensor mounted on a quartz substrate during a supersonic flight test. Polynomial curve fitting with regression analysis and cubic spline methods are used to fit the temperature data. One-dimensional numerical schemes are developed to infer surface heating rates by using Duhamel's superposition integral. Since the temperature data are acquired for 10 s, the one-dimensional behavior of heat penetration might not be applicable for entire time scale. In order to include the lateral conduction of heat along the depth of substrate, finite-element analysis of a more realistic gauge-substrate system is carried out with commercial package ANSYS 11. With the inputs of surface heating rates predicted from Duhamel's superposition integral, the temperature history are then recovered at various depths of the subs...

Application of axisymmetric analog to unstructured grid for aeroheating prediction of hypersonic vehicles

PurposeThe purpose of this paper is to present an engineering inviscid‐boundary layer method for the calculation of convective heating rates on three‐dimensional non‐axisymmetric geometries at angle of attack.Design/methodology/approachBased on the axisymmetric analog, convective heating rates are calculated along the surface streamlines which are determined using the inviscid properties calculated on an unstructured grid.FindingsSince the method is capable of using inviscid properties calculated on an unstructured grid, it is applicable to a variety of configurations and it requires much less computational effort than a Navier‐Stokes code. The results of the present method are evaluated on different wing body configurations in laminar and turbulent hypersonic equilibrium flows. In comparison to experimental data, the present results are found to be fairly accurate in the windward and leeward regions.Practical implicationsWith this approach, heating rates can be predicted on general three‐dimensional configurations at hypersonic speeds in an accurate and fast scheme.Originality/valueIn order to calculate the heating rates at any specific point on the surface, a technique is developed to calculate the inviscid surface streamlines in a backward manner using the inviscid velocity components. The metric coefficients are also calculated using a new simple technique.

Convective heat-transfer rate distributions over a missile shaped body flying at hypersonic speeds

Experiments are carried out with air as the test gas to obtain the surface convective heating rate on a missile shaped body flying at hypersonic speeds. The effect of fins on the surface heating rates of missile frustum is also investigated. The tests are performed in a hypersonic shock tunnel at stagnation enthalpy of 2 MJ/kg and zero degree angle of attack. The experiments are conducted at flow Mach number of 5.75 and 8 with an effective test time of 1 ms. The measured stagnation-point heat-transfer data compares well with the theoretical value estimated using Fay and Riddell expression. The measured heat-transfer rate with fin configuration is slightly higher than that of model without fin. The normalized values of experimentally measured heat transfer rate and Stanton number compare well with the numerically estimated results.

Sensitivity of Numerical Simulations of the Early Rapid Intensification of Hurricane Emily to Cumulus Parameterization Schemes in Different Model Horizontal Resolutions

A series of numerical experiments are conducted to examine the sensitivity of the numerical simulation of Hurricane Emily’s (2005) early rapid intensification to the cumulus parameterization schemes in the advanced research version of Weather Research and Forecasting (WRF) model at different horizontal resolutions. Results indicate that the numerical simulations are very sensitive to the choices of cumulus schemes at 9 km grid spacings. Specifically, with different cumulus schemes, the simulated minimum central sea level pressure (SLP) varies by 41 hPa during the 54 h forecast period. In contrast, only about 10 hPa difference is produced in minimum central SLP by varying planetary boundary layer (PBL) parameterization schemes in the same simulation period. Physical and dynamic mechanisms associated with this sensitivity are investigated. It is found that the intensity of the simulated storm depends highly on the magnitude and structure of surface latent heat flux and convective heating rate over the storm eyewall. The use of cumulus schemes is helpful for the model to reproduce those favorable conditions that cause the storm deepening. However, at 3 km resolution, the cumulus schemes do not result in any notable difference in the storm intensity and track forecasts. Only a slight difference is found in the simulated storm precipitation structure. Compared with cumulus schemes, the PBL schemes have significant impacts on Emily’s intensity forecast at 3 km resolution; the minimum central SLP varies by 37 hPa with the use of a different PBL scheme in the WRF model.

Latitudinal Variations of the Convective Source and Propagation Condition of Inertio-Gravity Waves in the Tropics

Abstract Latitudinal variations of the convective source and vertical propagation condition of inertio-gravity waves (IGWs) in the tropical region (30°S–30°N) are examined using high-resolution Global Cloud Imagery (GCI) and 6-hourly NCEP–NCAR reanalysis data, respectively, for 1 yr (March 1985–February 1986). The convective source is estimated by calculating the deep convective heating (DCH) rate using the brightness temperature of the GCI data. The latitudinal variation of DCH is found to be significant throughout the year. The ratio of the maximum to minimum values of DCH in the annual mean is 3.2 and it is much larger in the June–August (JJA) and December–February (DJF) means. Spectral analyses show that DCH has a dominant period of 1 day, a zonal wavelength of about 1600 km, and a Gaussian-type phase-speed spectrum with a peak at the zero phase speed. The vertical propagation condition of IGWs is determined, in the zonal wavenumber and frequency domain, by two factors: (i) latitude, which determines the Coriolis parameter, and (ii) the basic-state wind structure in the target height range of wave propagation. It was found that the basic-state wind significantly influences the wave propagation condition in the lower stratosphere between 150 and 30 hPa, and accordingly a large portion of the source spectrum is filtered out. This is prominent not only in the latitudes higher than 15° where strong negative shear exists, but also near the equator where strong positive shear associated with the westerly phase of the quasi-biennial oscillation (QBO) filters out large portions of the low-frequency components of the convective source. There is no simple relationship between the ground-based frequency and latitude; lower latitudes are not always favorable for low-frequency IGWs to be observed in the stratosphere. The basic-state wind in the Tropics, which has seasonal, annual, and interannual variations, plays a major role not only in determining the wave propagation condition in the stratosphere but also in producing convective sources in the troposphere.

Calculation of Stagnation-Point Heating Rates Associated with Stardust Vehicle

Stagnation-point heating rate is calculated for the Stardust entry vehicle and for its heat-shieldmodels tested in an arcjetwind tunnel. The calculations aremade for the convective component for both the laminar and turbulent cases, the radiative component produced by the gas flow, and the radiative component produced by solid particles. A onedimensional viscous shock layer method is used with an up-to-date thermochemical, gas–surface interaction, radiation, turbulence, and particulate models. For the flight cases, radiation absorption in the boundary layer is found to increase the convective heating rate by a factor of up to two. The calculated sums of all heating rates for the flight cases are nearly the same as those obtained by Olynick et al., and are substantially larger than those by Gupta. The calculated sums of all heating rates for the arcjet test cases are smaller than those calculated by the formula of Fay and Riddell, and are nearly the same as those experimentally determined using copper calorimeters.

AGN‐driven Convection in Galaxy‐Cluster Plasmas

This paper describes how active galactic nuclei can heat galaxy-cluster plasmas by driving convection in the intracluster medium. A model is proposed in which a central supermassive black hole accretes intracluster plasma at the Bondi rate Bondi and powers a radio source. The central radio source produces cosmic rays, which mix into the thermal plasma. The cosmic-ray luminosity Lcr is ∝Bondic2. The cosmic-ray pressure gradient drives convection, which causes plasma heating. It is assumed that plasma heating balances radiative cooling. The plasma heating rate is self-regulating because Bondi is a decreasing function of the specific entropy near the cluster center s0; if heating exceeds cooling, then s0 increases, Bondi and Lcr decrease, and the convective heating rate is reduced. This paper focuses on the role of intracluster magnetic fields, which affect convection by causing heat and cosmic rays to diffuse primarily along magnetic field lines. A new stability criterion is derived for convection in a thermal-plasma/cosmic-ray fluid, and equations for the average fluid properties in a convective cluster are obtained with the use of a nonlocal two-fluid mixing-length theory. Numerical solutions of the model equations compare reasonably well with observations without requiring fine-tuning of the model parameters.

Implementation of a gravity wave source spectrum parameterization dependent on the properties of convection in the Whole Atmosphere Community Climate Model (WACCM)

This article describes the implementation of a new source spectrum parameterization for convectively generated gravity waves in the Whole Atmosphere Community Climate Model, version 2 (WACCM2). This parameterization is active in the tropics and is interactive with the underlying convection. The gravity wave spectrum at each model grid point and time step is determined based on the convective heating depth, tropospheric wind, and the convective heating rate. This parameterization introduces more realistic spatial and temporal distributions of gravity wave activity and yields gravity wave characteristics related to the underlying wave source. We present the estimated gravity wave momentum flux phase speed spectra at 100 hPa as well as the gravity wave drag in the middle and upper atmosphere using the new source spectrum representation. We also show the effects of this more physically based parameterization on the structure of the stratospheric and mesospheric semi‐annual oscillations of the zonal wind compared to a simulation with uniform gravity wave distribution. We conclude that the interaction of the gravity wave parameterization with tropospheric characteristics is a positive step toward a more physical representation of the middle and upper atmosphere.

Film cooling effectiveness on a large angle blunt cone flying at hypersonic speed

Effectiveness of film cooling technique to reduce convective heating rates for a large angle blunt cone flying at hypersonic Mach number and its effect on the aerodynamic characteristics is investigated experimentally by measuring surface heat-transfer rates and aerodynamic drag coefficient simultaneously. The test model is a 60° apex-angle blunt cone with an internally mounted accelerometer balance system for measuring aerodynamic drag and an array of surface mounted platinum thin film gauges for measuring heat-transfer rates. The coolant gas (air, carbon dioxide, and/or helium) is injected into the hypersonic flow at the nose of the test model. The experiments are performed at a flow free stream Mach number of 5.75 and 0° angle of attack for stagnation enthalpies of 1.16MJ∕kg and 1.6MJ∕kg with and without gas injection. About 30%–45% overall reduction in heat-transfer rates is observed with helium as coolant gas except at stagnation regions. With all other coolants, the reduction in surface heat-transfer rate is between 10%–25%. The aerodynamic drag coefficient is found to increase by 12% with helium injection whereas with other gases this increase is about 27%.

Response of Heatshield Material at Stagnation Point of Pioneer-Venus Probes

The ablation, pyrolysis gas formation and removal, and heat conduction phenomena at the stagnation point of theheatshieldforthefourPioneer-Venusprobevehiclesarecalculated.Themotionofthepyrolysisgasiscalculated by solvingthemassand momentum equationsforthegas,accountingforfrictionandinertial forces. Thedeveloped computer code gives satisfactory results when applied to two ground-based cases and one e ight-test case. For the calculation of the Pioneer-Venus e ight cases, recently calculated values of convective and radiative heating rates are used. Good agreement is seen in thermocouple temperature for the day probe and north probe for which the entry angle and e ight trajectory are known. For the night probe and large probe, for which entry angle and e ight trajectory are unknown, agreement is poor.

Stagnation-Point Heat Transfer Rates for Pioneer-Venus Probes

Summary The convective and radiative heat transfer rates are calculated for the stagnation region of the Pioneer- Venus Probe vehicles during their entry flights into the planet Venus. The nonequilibrium thermochemical state of the flow is calculated using a viscous shock layer method accounting for oxidation of heatshield surface by atomic oxygen and for pyrolysis-gas injection. Radiative transport along the stagnation streamline is calculated using a lineby-line technique and tangent-slab approximation. For both radiative and convective heating rates, the present results are substantially smaller than the earlier values obtained assuming equilibrium.

Effects of the Mean Walker Circulations on the Zonal Variability of Tropical CISK Waves

Abstract An idealized zonally asymmetric mean state in the Tropics is used to investigate the effects of atmospheric mean Walker circulations and sea surface temperatures on the zonal variability of tropical waves with positive- only wave–CISK heating. First, the effects of the zonally symmetric vertical and meridional shears of the mean zonal flow are investigated with different vertical profiles of convective heating and temperature lapse rate. With the observed vertical profile of temperature lapse rate in the Tropics, the effect of the vertical shear of the mean zonal flow on the fast waves (period about 2 weeks) associated with a maximum heating in the upper troposphere is found to be opposite to that on the slow waves (period about 4 weeks) with a maximum heating in the middle troposphere, while the vertical shear effects with an idealized constant lapse rate are quite similar. The meridional shear of the mean zonal flow acts only to reduce the effects of the vertical shear of the mean zonal flow. S...

Biosphere feedback on regional climate in tropical north Africa

The impact of land-surface degradation over the Sahel area on seasonal variations of atmospheric and hydrological components over tropical north Africa are investigated in a general-circulation model numerical experiment, together with the mechanisms involved. The model was integrated for four years with and without vegetation change over the Sahel region with different initial atmospheric conditions. The results demonstrate that the degradation of the land surface can have a significant impact on the Sahelian regional climate. It increases the surface air temperature and reduces the precipitation, runoff and soil moisture over the Sahel region during the July-August-September (JAS) season. The impact is not only limited to the specified desertification area and the JAS season but is found also to the south of this area and extends into the October-November-December season. The changes in the annual rainfall cycle and the JAS mean surface temperature over the Sahel area are consistent with the observed climate anomalies of the past 40 years. The changes in rainfall to the south of the Sahel including eastern Africa are also in line with the observed anomalies. The reduction in total diabatic heating rate and relative increase in subsidence motion in the upper troposphere are consistnet with the rainfall anomalies. The variations in convective heating rate, which were caused by changes in latent-heat flux from the land surface and moisture flux convergence in the atmosphere, are the dominating factors in this process. The radiative cooling is a secondary effect. The influence of the initial conditions on the simulation of the soil water balance is also analysed.

Biosphere feedback on regional climate in tropical North Africa

AbstractThe impact of land‐surface degradation over the Sahel area on seasonal variations of atmospheric and hydrological components over tropical north Africa are investigated in a general‐circulation model numerical experiment, together with the mechanisms involved. The model was integrated for four years with and without vegetation change over the Sahel region with different initial atmospheric conditions. The results demonstrate that the degradation of the land surface can have a significant impact on the Sahelian regional climate. It increases the surface air temperature and reduces the precipitation, runoff and soil moisture over the Sahel region during the July‐August‐September (JAS) season. The impact is not only limited to the specified desertification area and the JAS season but is found also to the south of this area and extends into the October‐November‐December season. The changes in the annual rainfall cycle and the JAS mean surface temperature over the Sahel area are consistent with the observed climate anomalies of the past 40 years. The changes in rainfall to the south of the Sahel including eastern Africa are also in line with the observed anomalies.The reduction in total diabatic heating rate and relative increase in subsidence motion in the upper troposphere are consistnet with the rainfall anomalies. The variations in convective heating rate, which were caused by changes in latent‐heat flux from the land surface and moisture flux convergence in the atmosphere, are the dominating factors in this process. The radiative cooling is a secondary effect. The influence of the initial conditions on the simulation of the soil water balance is also analysed.

Monsoon rainfall simulations with the Kuo and Betts-Miller schemes

Two numerical experiments are performed using a nested grid regional model to study the performance of the Kuo and the Betts-Miller cumulus parameterization schemes in simulating the rainfall during an active monsoon period. Results indicate that the monsoon circulation features, such as the Somali jet and monsoon depression are better simulated with the Kuo scheme. With the Kuo scheme, predicted intensity and associated rainfall of the monsoon depression are in good agreement with the observations. Uncertainty in the adjustment parameters in the Betts-Miller scheme appears to have lead to the poor prediction of rainfall. Also, the Betts-Miller scheme showed considerable sensitivity to the convergence in the lower troposphere in the initial conditions over the Arabian Sea, leading to a prediction of a spurious intense tropical cyclone. This cyclone replaced the normal heat-low over the desert region. Rainfall distribution and its maximum along the west coast of India were predicted better with the Kuo scheme. Area-averaged convective heating rates indicated that the cumulus convection is deeper and more intense with the Kuo scheme. Also, area averaged evaporation rates far exceeded the rainfall rates with the Betts-Miller scheme while with the Kuo scheme these rates are in balance after the spinup period. Forecast erros in the zonally averaged specific humidities indicate that the model atmosphere is more humid with the Betts-Miller scheme.

Flat surface heat-transfer correlations for Martian entry

Analytic expressions have been derived for estimating the nonablating laminar and turbulent boundary-layer convective heating rates on inclined flat surfaces for the Martian atmosphere in thermochemical equilibrium. The equations are valid in the speed and altitude regime where aerobraking would occur at Mars. Comparisons with limited experimental measurements and calculations for CO2 (the Martian atmosphere is 95.6 percent CO2) yielded reasonably good agreement, especially for the ratios of heating rates in CO2 to those in air at the same conditions. In the aerobraking speed regime, the laminar flat surface boundary layer heating rates are 15-25 percent greater at Mars than in air. The differences between the turbulent heating rates are even more pronounced. The turbulent heating rates can be over 50 percent greater at Mars than in air at the same flight conditions.

Potential Vorticity Modeling of the ITCZ and the Hadley Circulation

A simple zonally symmetric balanced model of the Hadley circulation is presented. The model is based on potential vorticity arguments and consists of a predictive equation for the potential pseudodensity and an invertibility principle to diagnose the associated balanced wind and mass fields. When the theory is formulated in the potential latitude coordinate, the meridional advection is implicit in the coordinate transformation, which makes the prediction equation for potential pseudodensity analytically solvable. For convective heating patterns that simulate the ITCZ, the model produces upper and lower tropospheric potential vorticity anomalies of opposite sign. The associated winds are easterly at low levels and westerly aloft, except between the equator and the ITCZ, where there are low-level westerlies and upper-level easterlies. Since the potential vorticity anomalies develop within a background state that has potential vorticity increasing to the north, reversed poleward gradients of potential vorticity are produced, just as has been observed in the west African region. For typical convective heating rates, significant potential vorticity gradient reversals occur quickly—on the order of a couple of days. According to the Charney–Stern theorem, such zonal flows are expected to be unstable. In this sense the ITCZ is self-destructive and should not be viewed as a strictly steady state feature of the tropical circulation. In addition, according to this scenario, the potential vorticity dynamics of the west African region are not unique, and we should expect a similar ITCZ formation–breakdown cycle to occur in other tropical regions such as the tropical east Pacific and northern Australia.

Monte Carlo simulation of re-entry flows using a bimodal vibration model

The role of vibration-dis sociation coupling in flows representative of aeroassisted transfer vehicles with afterbodies is considered. The physical model employed is motivated by the recent work of Sharma et al.4 In this model, a bimodal representation, determined by the vibrational levels, is assumed for each diatomic molecule. Only molecules in the upper states are allowed to dissociate. The model is incorporated into the direct simulation Monte Carlo method of Bird and used to calculate steady flows past two geometries: a 5-deg blunt wedge and the project Fire configuration. Five chemical species are considered. It is shown that the new model results in reduced dissociation. Moreover, the convective heating rate increases for a finite catalytic wall and is essentially the same for a fully catalytic wall. Finally, for the conditions studied, the effect of the afterbody on the pressure distribution, heat transfer, and skin friction is minimal.

Numerical Solution of Minimax Optimal Control Problems by Multiple Shooting

This paper presents a numerical method for the solution of optimal control problems of the Čebšev - type : Minimize the functional I [ x,u ] = max 0 ≤ t ≤ t f C ( x ( t ) ) + ∫ 0 t f L ( x, u ) dt subject to the constraints x ˙ = f x, u , 0 ≤ t ≤ t f , x t ɛ R n r x 0 , x t f = 0 ɛ R k u t ɛ U C R 1 The genera] way to attack optimal control problems by indirect methods is to derive necessary conditions in order to build up a boundary value problem with respect to the state variables and the aajoints. For this purpose a standard - transformation due to Warga has been used. This technique converts the minimax problem into an equivalent optimal control problem with a state — variable inequality constraint. Using this way the highly developed theory on the necessary conditions for state — restricted problems can be applied advantageously. In addition the results concerning the order of the constraint are transfered to minimax problems. The cases of regular and singular Hamiltonian are to be distinguished. In the regular case the necessary conditions mainly coincide with the conditions earlier derived by Powers. In addition, however, one obtains a sign — condition for the Lagrange multiplier corresponding to the state constraint. More complicated is the singular case, i.e. the problem depends linearly on the control variable. This is due to the more complicated switching structure of these problems. The junction conditions for state restricted problems developed by Maurer are transfered to the minimax case. These conditions are most important in order to predict whether the maximum of the Čebyšev — function C(x(t)) is unique or flat. In particular, it is shown that a singular problem of the order one may have a unique maximum. Evidently, this is impossible in the regular case. Assuming that the switching structure of the solution trajectory can be estimated, a boundary value problem for the state and adjoint variables is derived. This boundary value problem contains certain boundary conditions which are to be satisfied at (unknown) switching points. Such problems can be treated numerically by the earlier developed multiple shooting code BOUNDSCO. This routine is briefly described. It is a modification of the well known multiple shooting code BOUNDSOL for two—point boundary value problems due to Bulirsch. The method is applied to two real-life problems. The first example is the well-known reentry problem. The pay-off is changed in order to minimize a combination of the total stagnation point convective heating rate and the maximal heating rate : I = c 1 max 0 ≤ t ≤ t f q ˙ t + C 2 ∫ 0 t f q ˙ t dt where q ˙ = 10 v 3 ζ v: velocity, ζ: atmospheric density. This regular minimax problem is of the order one. Therefore the optimal heating rate q ˙ (t) has a flat maximum. Numerical solutions of this problem are obtained by a homotopy method with respect to the weights C 1 and C 2 . The second example is a realistic model for optimal heating and cooling of a house by solar energy. The aim is to determine control histories for heating and cooling such that the inside temperature has a minimal deviation from a desired value T D : I = c 1 max 0 ≤ t ≤ t f T I − T D + C 2 ∫ 0 24 T I − T D 2 dt. The resulting minimax problem is singular and of the order one. For various values of C 1 and C 2 numerical solutions of this problem are presented.