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Previously, I explained how to use the PHFlash function to get physical properties estimations with gPROMS, using Multiflash. This function is able to estimate the fluid pressure, specific enthalpy, vapor fraction, density, and temperature, being given the fluid pressure and specific enthalpy as inputs. If we want to get the fluid specific escoliosis derecha entropy, the dynamic viscosity, or other properties, we need to use other methods. I have identified 2 alternatives, so far:

• If the fluid is a liquid-vapor mixture or if we can’t be sure that the fluid will stay in a single phase state, the liquid and vapor functions need to be used (see Fig. 1 to instantly understand why).


The overall value for the mixture is determined by the sum of the weighted liquid and vapor estimated values. The hernia de disco lumbar pdf liquid and vapor functions are weighted with the vapor quality of the fluid, determined with the PHFlash function. For instance, to estimate the fluid specific entropy, we need to use the LiquidEntropy and VaporEntropy functions, and the PHFlash function, to get the vapor quality. Then, if “s” is the specific entropy, and “X”, the vapor quality, s = X*s_vap + (1-X)*s_liq. The next question is how to implement that weighted sum in gPROMS. There are 3 possibilities: direct use, inside an IF structure, or inside escoliosis dorsolumbar derecha a CASE and SWITCH structure.

The problem with refrigeration systems modeling is that we don hernia discal lumbar ejercicios prohibidos’t know if there is only vapor, only liquid, or both in a pipe or a component, at any time in a simulation. Indeed, in transient situations, there can be vapor bubbles in the liquid line (no subcooling after a condenser, for instance), or liquid droplets in a vapor line (no overheating in the compressor suction line, for instance). So, we need to be able to write robust codes which can handle the 2 cases (single or two-phase) with no computing issue, and we want it to be stable, numerically, in order to not create problems within complex component models later on. In an ideal world, the expressions to get the properties should be as short as possible, in order to be handy. Let’s explore the 4 options listed above. Single-phase: dedicated functions

gPROMS provides the user with desviacion lumbar a set of dedicated functions for each of the possible physical properties estimations. Basically, those functions take as input values the fluid temperature and pressure. Consequently, they are valid only for single phase fluids (for a pure fluid, there are an infinite number of possible values for cirugia hernia discal lumbar the fluid physical properties, being given a [P,T] couple during a phase change). If we try to use the dedicated functions nonetheless, while the fluid phase is changing, we observe that the functions don’t behave correctly. For instance, if we look at the mass specific enthalpy of a phase changing pure fluid (here R134a being evaporated at a constant enthalpy rate), we observe that the function value oscillates unregularly between the liquid value and the vapor value, in the 2-phase area. We also observe that if the fluid is single-phase, the dedicated function gives good results.

For those escoliosis dorsal dextroconvexa who are not familiar with the MATLAB optimization toolbox, fsolve is a function used to solve systems of nonlinear equations. In order for this function to work, we need to provide a function fun ( fun is the objective cirugia de columna lumbar hernia de disco function, defined in a other m-file here), an initialization array x0, initializing the value of the optimization variable x (an array too), and a set of optional options defined with the function optimset (if there is no option to be specified, we can replace the options object with an empty element: [ ]). Passing extra parameters to the objective function through the fsolve function escoliosis levoconvexa was (is) something not officially documented but which was (is) working.

Lately, I have tried to use fsolve this way again and I haven’t managed to get it working properly. Consequently, I went back to the fsolve documentation and could observe that the method explained above is not documented by MathWorks. I could find few references to this method on the Internet, but not much (Good, there is some hints around that I haven’t dreamed that all – it was working previously; I’m not crazy columna lumbar rx… That’s a good point!). I have read somewhere that MathWorks wants to discourage the use of direct extra parameters definition, because it’s not an appropriate way to perform optimization tasks (can’t find back the source, sorry). Indeed, doing it this way, it is easy to nest optimizations functions in optimization functions and to define the optimization problem in a non-optimal-way. MathWorks then documents how sintomas de hernia discal lumbar l4 l5 to correctly pass extra parameters to functions and offers 3 alternatives to the direct method exposed above: global variables, anonymous functions, and nested functions. Global variables

This extra parameters definition method suits me a lot better than the global variables method. We only define our objective function as it is, them, we create a function handle in our script, describing which parameter, for this specific function handle, will be the variable. Here we have chosen x, but it would have been the same function and contractura lumbar ejercicios the same handle type if we would have selected b (we would have written, then, f = @(b)JB_fcn(-1,2,b,1); considering that x=-1).

I have a preference for this one, since with my current programming style, I define the optimization function usually only to be used in the optimization problem. Most of the time, I never use it elsewhere. Then, having it in a separate file is just something troublesome and less handy than to define a nested function. A nested function is a function defined in an other dolor sacro lumbar causas function. That means that the function inherits of all the parameters passed to its upper level function. Then, only the optimization variable needs to be defined in the objective function. For instance, if we take again our previous example: