Methods for Measuring and Computing the Reference Temperature in Newton’s Law of Cooling for External Flows

Newton’s law of cooling is a reduced-order model that characterizes convective heat transfer. It relates the heat flux between a fluid and a solid, q_s'', to the difference in temperature between solid’s surface, T_s, and a reference temperature in the flow, T_ref, via a heat transfer coefficient, h. For external flows, the adiabatic-wall temperature, T_aw, is often used as T_ref, which assumes if the T_s on a non-adiabatic surface equals T_awlocally, then q_s'' = 0 at that location. When using T_aw as T_ref, different local values of h are obtained for different T_sdistributions applied to the same convective problem. Therefore, Green’s function has been proposed as an improved reduced model for convection with the claim that it is independent of the T_sdistribution. However, determining the Green’s function influence coefficients is often significantly more expensive than determining T_awand h for use in Newton’s law of cooling.In this work, a film-cooling convective problem is studied where a non-adiabatic surface has locations where T_s= T_aw. However, it is demonstrated that q_s'' =/= 0 at these locations and h obtained via T_awis undefined and not meaningful or useful. Therefore, a new framework to interpret Newton’s law of cooling and obtain T_ref and h is developed, named the state-space method, which guarantees T_s - T_ref = 0 when/where q_s'' = 0 and a meaningful and useful h. Using the new state-space method, it is found that is h reasonably independent of the T_sdistribution for laminar flow over a flat plate if it is obtained using T_sdistributions with the same spatial temperature gradient. For these sets of T_s distributions, the spatial gradient of T_refis inversely related to the spatial T_sgradient. Using this insight, a model is developed to predict q_s'' for an arbitrary T_s distribution which is potentially cheaper to obtain for a given convection problem than the Green’s function influence coefficients. Furthermore, it is shown that the Green’s function influence coefficients can depend on the T_s distributions which are used to obtain them.

In this paper, the effects of adiabatic and isothermal conditions on the statistics in compressible turbulent channel flow are investigated using direct numerical simulation (DNS). DNS of two compressible turbulent channel flows (Cases 1 and 2) are performed using a mixed Fourier Galerkin and B-spline collocation method. Case 1 is compressible turbulent channel flow between isothermal walls, which corresponds to DNS performed by Coleman et al. (1995). Case 2 is the flow between adiabatic and isothermal walls. The flow of Case 2 can be a very useful framework for the present objective, since it is the simplest turbulent channel flow with an adiabatic wall and provides ideal information for modelling the compressible turbulent flow near the adiabatic wall. Note that compressible turbulent channel flow between adiabatic walls is not stationary if there is no sink of heat. In Cases 1 and 2, the Mach number based on the bulk velocity and sound speed at the isothermal wall is 1.5, and the Reynolds number based on the bulk density, bulk velocity, channel half-width, and viscosity at the isothermal wall is 3000. To compare compressible and incompressible turbulent flows, DNS of two incompressible turbulent channel flows with passive scalar transport (Cases A and B) are performed using a mixed Fourier Galerkin and Chebyshev tau method. The wall boundary conditions of Cases A and B correspond to those of Cases 1 and 2, respectively. Case A corresponds to the DNS of Kim & Moin (1989). In Cases A and B, the Reynolds number based on the friction velocity, the channel half-width, and the kinematic viscosity is 150. The mean velocity and temperature near adiabatic and isothermal walls for compressible turbulent channel flow can be explained using the non-dimensional heat flux and the friction Mach number. It is found that Morkovin's hypothesis is not applicable to the near-wall asymptotic behaviour of the wall-normal turbulence intensity even if the variable property effect is taken into account. The mechanism of the energy transfers among the internal energy, mean and turbulent kinetic energiesis investigated, and the difference between the energy transfers near isothermal and adiabatic walls is revealed. Morkovin's hypothesis is not applicable to the correlation coeffcient between velocity and temperature fluctuations near the adiabatic wall.

In order to help answer questions about the magnitude of heat flux to the liquid argon in a liquid argon calorimeter which could cause boiling (bubbles), calculations estimating the heat flux which can be removed by free convection were made in February, 1988. These calculations are intended to be an estimate of the heat flux above which boiling would occur. No formal writeup was made of these calculations, although the graph dated 3 Feb 88 and revised (adding low-velocity forced convection lines) 19 Feb 88 was presented in several meetings and widely distributed. With this description of the calculations, copies of the original graph and calculations are being added to the D0 Engineering Note files. The liquid argon surface is in equilibrium with argon vapor at a pressure of 1.3 bar, so the surface is at 89.70 K. The liquid is entirely at this surface temperature throughout the bulk of the volume, except locally where it is warmed by a solid surface at a higher temperature than the bulk liquid. This surface temperature is taken to be the boiling temperature of argon at the pressure corresponding to 1.3 bar plus the liquid head; hence it is a function of depth below the surface. The free and forced convection correlations used are 'from Kreith, 'Heat Transfer', for heated flat plates in a large (i.e., no other objects nearby enough to disturb the flow) uniform volume of fluid. Heat flux is a function of plate size, really length along the flow path (since a boundary layer increases in thickness starting from the leading edge of the plate), and orientation (i.e., vertical or horizontal). The maximum heat flux which can be carried away by free convection (i.e., the heat flux above which boiling occurs) is .001 W/sq.cm. at 4 inches below the surface and 0.1 to 0.2 W/sq.cm. 15 feet below the surface. Forced convection over a 1 cm plate with a fluid velocity of 1 cm/sec, or a 10 cm plate at 10 cm/sec, is about like free convection. The line for much higher heat flux is 10 cm/sec flow over a 1 cm plate.

Dynamic software testing and evaluation are important software engineering subjects and can be used to improve reliability. In this paper, we propose a dynamic software testing and evaluation model based on the state space method. In this model, the run time features of software are quantified into one state vector; the program scale, difficulties, structures, and development expenses are quantified into one input vector; the total software complexity is quantified into one output vector; and the software testing and evaluation process is regarded as a feedback control process. Dynamic software testing and evaluation with the state space method can adaptively regulate the critical factors that drastically affect software reliability. Experimental results show that the proposed method is useful for reducing costs, shortening developing time, and improving reliability.

When an autonomous robot is to learn its behavior, whether an appropriate state space is available or not is a critical issue for the flexibility and efficiency of the learning process. What is problematic is that it is usually very difficult to prepare such an ideal state space manually beforehand. We propose a new state space method. With this, behavior-based robots can autonomously rebuild their state spaces after they accumulate behavior experience using initial state spaces. This reconstruction approach is more advantageous than the conventional state space construction methods or incremental state partitioning methods in that it achieves both the efficiency in the learning process and the optimality of the resultant behavior performance.

Quantifying ecological thresholds from response surfaces

Deep reinforcement learning based planning method in state space for lunar rovers

A State Space Boundary Element Method with Analytical Formulas for Nearly Singular Integrals

The subject of study is the process of forming algorithms for controlling the angular and translational movements of a two-wheeled experimental sample (TWES). The aim is to develop approaches to the formation of control algorithms for the translational and angular movements of a non-stationary automatic control object. Tasks: to concretize the process of synthesis of a control algorithm by state according to the criterion of the minimum integral of the weighted error modulus for a linear mathematical description of an automatic control object in the state space. Form a block diagram of an automatic control system by the state. Improve the approach to the synthesis of output control algorithms for mathematical description in the frequency domain of short-period and long-period motions of TWES. Illustrate the peculiarity of the approach using a specific example of a TWES under control and disturbing influences. Develop a simulation scheme in the Simulink environment and investigate responses to external step influences. Develop an approach to the formation of control algorithms by the diagnosis of TWES as an object of automatic control. Describe the procedure and means of deep diagnostics of emergencies of TWES. Develop algorithms for restoring the operability of the automatic rational control system. Used methods are a method of state space, the method of relative functions, the method of transfer functions, the method of optimization by integral criterion, the method of synthesis by logarithmic asymptotic frequency characteristics, methods of diagnosing and restoring operability. The following Results: three approaches were formed to the formation of control algorithms of the angular and translational movements of the TWES using linear mathematical descriptions in the time and frequency domains. Conclusions. The scientific novelty lies in the formation of approaches to the combined control of angular and translational movements, considering the structural and parametric features of the mathematical descriptions of TWES.

The state space model provides an unifying framework for analyzing time series. For the classical Box–Jenkins analysis, state space methods are useful when estimating the autoregressive and moving average coefficients by exact maximum likelihood and when missing values are present. In the case of unobserved components time series models with interpretable components such as trend, seasonal, cycle and irregular, state space methods provide the tools for estimation, signal extraction and diagnostic checking. Indeed, all linear time series models can be cast into state space including dynamic regression models and cubic spline smoothing models.

The pulp and paper industry in Indonesia is the tenth largest producer in the world, with Acacia and Eucalyptus as the main genera used for production; however, limited publications exist related to Eucalyptus growth models in Indonesia compared with other regions. Time-based models have been developed in which height, stand density, and basal area are predicted based on initial conditions and age. In contrast, a state–space approach utilizes the rate of change of these three state variables. Previous direct comparisons of these two approaches are generally limited. Consequently, the objective of this study was to compare two stand-level growth modeling approaches for Eucalyptus hybrid species on Sumatera (Sumatra) Island using both time-based and state–space methods. Our results indicate that dynamic models using either time-based or state–space approaches are adequate for predicting stand parameters to rotation age. A modified Bazukis matrix indicated that the behavior of both methods produced reliable predictions that were biologically reasonable in terms of stand development; however, the time-based approach provided better performance than the state–space approach on a variety of equivalence tests and goodness-of-fit statistics. Overall, the analysis highlights the advantages and disadvantages of these two commonly used, yet highly contrasting, stand-level growth modeling approaches, which need further consideration and evaluation.

A Practitioner's Guide and MATLAB Toolbox for Mixed Frequency State Space Models

Time-series analysis of pressure fluctuations in gas–solid fluidized beds – A review

Various analytical techniques are available for modeling multivariate time series data. One such approach is the State Space Model, which can be employed to model this type of data. In this study, the data to be analyzed are data on the Indonesia Rupiah (IDR) exchange rate (ExR) against the US Dollar (USD), oil and gas exports (OGE), money supply (MS) and non-oil and gas exports (non-OGE) from January 2008 to December 2019. The aim of this study is to identify the most suitable state space model for the given data. In this research, the state space method will be applied to multivariate time series data, with the state space represented in the Vector Autoregressive (VAR) model to explore the interrelationships among groups of observed variables. The VAR model is a statistical technique used to analyze the relationships between variables in the dataset, employing the Granger Causality Test. The state space model is utilized to model and forecast multiple interconnected time series, where the variables exhibit dynamic interactions and to examine additional unobserved variables in the time series data. Based on the analysis results and the minimum value of the Akaike Information Criterion (AIC), the optimal VAR model identified is the VAR (6) model. The results of forecasting values using the state space model show that the predicted values and the real values for the state space model are very closed to each other.

State space calculations for discrete probability densities