COMPUTER-IMPLEMENTED METHOD FOR THE NUMERICAL SIMULATION OF A HEAT EXCHANGER

Abstract

A computer-implemented method for the numerical simulation of a heat exchanger with a numerical model comprising a plurality of elemental volumes such that they all correspond to the same configuration such that the joint of all the elemental volumes reproduces the volume in which heat transfer occurs between a hot fluid and a cold fluid. The simulation method establishes an iterative method on the set of elemental volumes in such a way that the relevant variables of each volume are updated using the data provided by the interpolation module without the need to run a classical simulation on the flow. The result is the assessment of the variables of interest in the entire volume of the heat exchanger for predetermined operating conditions.

Claims

1. A method for simulation of a heat exchanger, wherein the heat exchanger is configured to exchange heat between a first fluid (f.sub.h) and a second fluid (f.sub.c), the first fluid (f.sub.h) being a hot fluid and the second fluid (f.sub.c) being a cold fluid; the heat exchanger comprising a first input port and a first output port for the first fluid (f.sub.h) and, a second input port and a second output port for the second fluid (f.sub.c), the heat exchanger comprising an heat exchange volume comprising a heat exchanging wall separating the first fluid (f.sub.h) and the second fluid (f.sub.c) and for exchanging heat between the two fluids (f.sub.h, f.sub.c), and wherein the method comprises the following steps: generating a numerical model according to the following steps: discretizing the heat exchange volume in elemental volumes (EV), wherein each elemental volume (EV) comprises: a first inlet boundary region (EVIh) and a first outlet boundary region (EVOh) for the first fluid (f.sub.h); a second inlet boundary region (EVIc) and a second outlet boundary region (EVOc) for the second fluid (f.sub.c); at least a portion of the heat exchanging wall separating the first fluid (f.sub.h) and the second fluid (f.sub.c); wherein the portion of the heat exchanging wall and the inlet and outlet boundary regions (EVIh, EVOh, EVIc, EVOc) of all elemental volumes (EV) have the same configuration and shape; wherein a discretization is such that a union of the elemental volumes (EV) is the heat exchange volume and a union of portions of the heat exchanging wall is the heat exchanging wall of the heat exchanger; allocating a data structure for storing fluid parameters and thermal properties of the heat exchanging wall, for storing at least, at each elemental volume (EV), fluid values for the first fluid (f.sub.h) and for the second fluid (f.sub.c); populating fluid values corresponding to boundary conditions of the heat exchanger at the inlet and outlet boundary regions; instantiating an estimation module for providing the fluid values at the outlet regions (EVOh, EVOc) of an elemental volume (EV) when inputting fluid values at the inlet regions (EVIh, EVIc) by estimating results of a numerical simulation of the reference elemental volume (EV); iterating over all the elemental volumes (EV) having available values at the inlet regions, at each iteration updating the values at the outlet regions by using the estimation module, iterating until a predetermined norm evaluated over the increments of updated values is below a predetermined threshold value; returning at least one fluid value of the allocated data structure storing the elemental volumes as the result of the previous iterative step.

2. The method according to claim 1, wherein generating a numerical model comprises generating: a first reference volume model (rf1), the first reference volume model (rf1) comprising boundary regions of the first fluid (f.sub.h) and a portion of a heat exchanging wall for separating a first fluid (f.sub.h) and a second fluid (f.sub.c), and a second reference volume model (rf2), the second reference volume model (rf2) comprising boundary regions of the second fluid (f.sub.c) and the same portion of a heat exchanging wall for separating a first fluid (f.sub.h) and a second fluid (f.sub.c), wherein the boundary regions of the first reference volume model (rf1) and the portion of the heat exchanging wall of the first reference volume model (rf1) have the shape of the volume housing the first fluid (f.sub.h) and the portion of the heat exchanging wall of any of the elemental volumes (EV) and, the boundary regions of the second reference volume model (rf2) and the portion of the heat exchanging wall of the second reference volume model (rf2) have the shape of the volume housing the second fluid (f.sub.c) and the portion of the heat exchanging wall of any of the elemental volumes (EV); sampling a predetermined first multidimensional-domain for fluid variables for the first fluid (f.sub.h) at the inlet boundary regions of the first reference volume model (rf1) and for heat exchanging wall temperature (T.sub.w) and, sampling a predetermined second multidimensional-domain for fluid variables for the second fluid (f.sub.c) at the inlet boundary regions of a second reference volume model (rf2) and for heat exchanging wall temperature (T.sub.w); for each sampled point of the first multidimensional-domain carrying out a numerical fluid simulation of the first reference volume model (rf1) determining the values of the fluid variables of the first fluid (f.sub.h) at the outlet boundary regions (EVOh) responsive to the inlet fluid values at the inlet boundary regions (EVIh); and, for each sampled point of the second multidimensional-domain carrying out a numerical fluid simulation of the second reference volume model (rf2) determining the values of the fluid variables of the second fluid (f.sub.c) at the outlet boundary regions (EVOc) responsive to the inlet fluid values at the inlet boundary regions (EVIc); instantiating a first interpolation module (IM1) for providing the fluid values at the outlet region (EVOh) when inputting fluid values at the inlet region (EVIh) of the first reference volume model (rf1) by interpolating results of the simulations of the first reference elemental volume model (rf1); and, instantiating a second interpolation module (IM2) for providing the fluid values at the outlet region (EVOc) when inputting fluid values at the inlet region (EVIc) of the second reference volume model (rf2) by interpolating results of the simulations of the second reference elemental volume model (rf2).

3. The method according to claim 2, wherein iterating on an elemental volume (EV), each iteration comprises the following steps: predetermining an initial value of the temperature (T.sub.w) of the portion of the heat exchanging wall of the elemental volume (EV), said value preferably selected between the temperature at the inlet region of the first fluid (f.sub.h) and the temperature at the inlet region of the second fluid (f.sub.c); determining Q.sub.h, the heat transferred from the first fluid (f.sub.h) to the portion of the heat exchanging wall; determining Q.sub.c, the heat transferred from the portion of the heat exchanging wall to the second fluid (f.sub.c); updating the value of the temperature (T.sub.w) of the portion of the heat exchanging wall responsive to a difference Q.sub.hQ.sub.c.

4. The method according to claim 3, wherein the initial value of the temperature (T.sub.w) of the portion of the heat exchanging wall of the elemental volume (EV) is (T.sub.in.sup.h+T.sub.in.sup.c), wherein T n is the temperature of the first fluid (f.sub.h) at the inlet boundary region (EVIh) and T.sub.in.sup.c is the temperature of the second fluid (f.sub.c) at the inlet boundary region (EVIc).

5. The method according to claim 3, wherein
Q.sub.h={dot over (m)}.sub.hC.sub.p.sup.h(Ttot.sub.in.sup.hTtot.sub.out.sup.h) and Q.sub.c={dot over (m)}.sub.cC.sub.p.sup.c(Ttot.sub.out.sup.cTtot.sub.in.sup.c), being {dot over (m)}.sub.h and {dot over (m)}.sub.c a mass flow of the first fluid (f.sub.h) and the second fluid (f.sub.c) respectively; C.sub.p.sup.h and C.sub.p.sup.c a heat capacity at constant pressure of the first fluid (f.sub.h) and the second fluid (f.sub.c) respectively; and, Ttot denotes a total temperature of the fluid wherein h, c indexes denotes the first fluid (f.sub.h) and the second fluid (f.sub.c) respectively and in, out denotes at the inlet boundary region and the outlet boundary region respectively.

6. The method according to claim 3, wherein when Q.sub.h>Q.sub.c a value of the temperature (T.sub.w) of the portion of the heat exchanging wall is updated incrementing a value e and, if Q.sub.h<Q.sub.c a value of the temperature (T.sub.w) of the portion of the heat exchanging wall is updated decrementing said value e, wherein e is a ratio between the heat transfer according to the values of the current iteration and, the maximum heat transfer; said ratio being preferably estimated as: $e=\stackrel{.}{m_h}{C}_p^h\left({\mathrm{Ttot}}_{\mathrm{in}}^h-{\mathrm{Ttot}}_{\mathrm{out}}^h\right)/C_{\min }\left({\mathrm{Ttot}}_{\mathrm{in}}^h-{\mathrm{Ttot}}_{\mathrm{out}}^c\right)$ wherein C.sub.min=min({dot over (m)}.sub.hC.sub.p.sup.h,{dot over (m)}.sub.cC.sub.p.sup.c).

7. The method according to claim 1, wherein one or more inlet conditions at the inlet port at least for the first fluid (f.sub.h) are homogeneous wherein the iteration over the elemental volumes (EV) are extended over a layer of elemental volumes (EV) and, the fluid and thermal properties propagated to the rest of the heat exchange volume.

8. The method according to claim 1, wherein a set of elemental volumes (EV) are shifted in such a way that: the portion of the heat exchanging wall of each shifted elemental volume (EV) is the former boundary of two adjacent elemental volumes (EV); a region of the shifted elemental volume (EV) housing the first fluid (f.sub.h) and a region of the shifted elemental volume (EV) housing the second fluid (f.sub.c) are those regions being adjacent and housed in the two adjacent non-shifted elemental volumes (EV).

9. The method according to claim 1, wherein the iterative method is also executed over the shifted elemental volumes (EV).

10. A non-transitory computer readable media storing a computer program product comprising instructions which, when the computer program is executed by a computer, cause the computer to carry out the steps of the method according to claim 1.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0106] These and other features and advantages of the invention will be seen more clearly from the following detailed description of a preferred embodiment provided only by way of illustrative and non-limiting example in reference to the attached drawings.

[0107] FIG. 1 shows a heat exchanger and schematically an elemental volume used during the simulation. This figure shows the real scale of the elemental volume compared to the size of the heat exchanger.

[0108] FIG. 2 shows schematically the heat exchanging volume and, over it, an elemental volume that is split into two reference models used for determining the fluid and thermal properties at the outlet of the elemental element.

[0109] FIG. 3 shows a table of cells wherein each cell represents an elemental volume of a specific layer observed according to a plan view.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0110] As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product.

[0111] FIG. 1 shows a heat exchanger (1), in particular, a bleed heat exchanger (1) which is part of a bleed system in an aircraft. Hot bleed air is coming from compressor high pressure stage and is regulated to required pressure and temperature using valves and the heat exchanger (1) respectively.

[0112] The hot air entering the heat exchanger (1) is cooled down to around 200 C. using fan air which is typically in the range of 5 C. to 10 C. The regulated bleed air is then sent to cabin Packs (used for cabin pressurization and cooling) and other consumers.

[0113] Thus, two fluids are distinguished, a first fluid (f.sub.h) and a second fluid (f.sub.c). The first fluid (f.sub.h) is the hot fluid and the second fluid (f.sub.c) is the cold fluid. The hot fluid (f.sub.h) transfers part of its heat to the cold fluid (f.sub.c) through the multiple heat exchange walls (1.6) arranged in the interior of the heat exchanger (1), in particular in the heat exchanging volume (1.5).

[0114] This same FIG. 1 shows an inlet port, identified as first input (1.1) for the first fluid (f.sub.h) located on the left side of the figure and an outlet port, identified as first outlet port (1.2) located at the opposite end. The second fluid (f.sub.c) enters into a second inlet port (1.3) located on one side and exits through a second outlet port (1.4) on the opposite side giving rise to two cross flows.

[0115] The inner structure of the heat exchanger (1), according to this example embodiment, is by stacked layers. Each layer allows the passage of one fluid and another alternately so that between layers there is a heat exchanging wall (1.6). Additionally, to increase heat transfer, within each layer there are fins perpendicular to the heat exchanging walls (1.6) favoring convection exchange.

[0116] This layered structure is according to this embodiment example although it is possible to use more complex structures such as generating two sets of conduits, one for the first fluid (f.sub.h) and one for the second fluid (f.sub.c), where the two sets of conduits are formed by generating a partition wall by means of a gyroid verifying periodicity conditions in the three main directions of space. This partition wall is the heat exchanging wall (1.6) for this other example.

[0117] Continuing with the example shown in FIG. 1, the heat exchanging volume (1.5) formed by the previously described layers is in the shape of a prism with a rectangular base as shown schematically in FIG. 2. In this schematic representation the heat exchanging walls (1.6) are arranged horizontally according to the orientation of the figure separating layers through which the first fluid (f.sub.h) and the second fluid (f.sub.c) flow alternately can be seen in an enlarged form. Also highlighted with thicker lines are the fins that have a cross section with a square wave configuration.

[0118] In this heat exchanger (1), a simulation method will be carried out to determine the overall behavior of the heat exchanger (1) and in particular to determine the flow and thermodynamic conditions at the outlet as a function of the known inlet conditions.

[0119] In a first stage, a discretization of the heat exchanging volume (1.5) into a plurality of elemental volumes (EV) is carried out. In FIG. 2 only one elemental volume (EV) has been shown, however the entire heat exchanging volume (1.5) has been discretized.

[0120] Each of the elemental volumes (EV) has been appropriately chosen wherein each elemental volume (EV) comprises: [0121] a first inlet boundary region (EVIh) and a first outlet boundary region (EVOh) for the first fluid (f.sub.h); [0122] a second inlet boundary region (EVIc) and a second outlet boundary region (EVOc) for the second fluid (f.sub.c); [0123] at least a portion (1.6.1) of the heat exchanging wall (1.6) separating the first fluid (f.sub.h) and the second fluid (f.sub.c); [0124] wherein the portion (1.6.1) of the heat exchanging wall (1.6) and the inlet and outlet boundary regions (EVIh, EVOh, EVIc, EVOc) of all elemental volumes (EV) have the same configuration and shape; [0125] wherein the discretization is such that the union of elemental volumes (EV) is the heat exchange volume (1.5) and the union of portions (1.6.1) of the heat exchanging wall (1.6) is the heat exchanging wall (1.6) of the heat exchanger (1).

[0126] Even if a heat exchanging wall (1.6) is identified, such heat exchanging wall (1.6) in this case comprises all the plates in the stratified structure.

[0127] The central part of FIG. 2 shows enlarged and schematically (i.e. it shows more heat exchanging fins than the cube represented in dashed lines identifying the way of discretizing the heat exchanging volume) the elemental volume (EV).

[0128] In this embodiment the elemental volume (EV) has in the lower part a space divided by fins and through which flows the second fluid and, in the upper part a space also divided by fins and through which flows the first fluid. Both spaces are separated by a portion of the heat exchanging wall (1.6.1).

[0129] In this specific case, inlet conditions allows to solve only a single layer of elemental volumes (EV) and propagating the result to the rest of elemental volumes (EV) by copying the results layer by layer. The single layer of elemental volumes (EV) has a hot layer and a cold layer separated by a heat exchanging wall (1.6).

[0130] The elemental volume (EV) is decoupled into a hot and a cold side separately as shown in FIG. 2, each side generates a reference volume model, a first reference volume model (rf1) for the hot layer comprising the hot layer and the heat exchanging wall (1.6) and, a second reference volume model (rf2) for the cold layer comprising the cold layer and the same heat exchanging wall (1.6).

[0131] The first reference volume model (rf1) has the inlet boundary region (EVIh) and the outlet boundary region (EVOh) of the first fluid (f.sub.h). The second reference volume model (rf2) has the inlet boundary region (EVIc) and the outlet boundary region (EVOc) of the second fluid (f.sub.c).

[0132] In both reference volume models (rf1, rf2), inlet conditions are: [0133] flow rate ({dot over (m)}.sub.h, {dot over (m)}.sub.c); [0134] total pressure (totP.sub.in.sup.h, totP.sub.in.sup.c); [0135] static temperature (T.sub.in.sup.h, T.sub.in.sup.c); [0136] wall temperature (T.sub.w).

[0137] From these fluid and thermal variables, a CFD simulation provides the output variables: [0138] static temperature (T.sub.out.sup.h, T.sub.out.sup.c); [0139] static pressure drop (dP.sub.h, dP.sub.c); [0140] outlet velocity (v.sub.out.sup.h, v.sub.out.sup.c).

[0141] In this case, four scalars are the input variables generating a four-dimensional domain for the first reference volume model (rf1) and a four-dimensional domain for the second reference volume model (rf2).

[0142] Both domains as sampled, for instance generating a partition for each inlet variable. Other sampling methods may be chosen but this case generates a multidimensional grid that may be stored using look-up tables.

[0143] For each sample, a CFD simulations provides the output variables at the sampled points of the multidimensional domain. From these set of simulations, it is instantiated: [0144] a first interpolation module (IM1) for providing the fluid values at the outlet region (EVOh) when inputting fluid values at the inlet region (EVIh) of the first reference volume model (rf1) by interpolating the results of the simulations of the first reference elemental volume model (rf1); and, [0145] a second interpolation module (IM2) for providing the fluid values at the outlet region (EVOc) when inputting fluid values at the inlet region (EVIc) of the second reference volume model (rf2) by interpolating the results of the simulations of the second reference elemental volume model (rf2).

[0146] The first and the second interpolation module (IM1, IM2) will be used for determining the fluid values at the outlet region (EVOh. EVOc) with no need of simulating any further volume.

[0147] In particular, in this specific example, the first and the second interpolation module (IM1, IM2) are implemented using regressions analysis and provides at the outlet: [0148] static temperature (T.sub.out.sup.h, T.sub.out.sup.c); [0149] static pressure drop (dP.sub.h, dP.sub.c); [0150] outlet velocity (v.sub.out.sup.h, v.sub.out.sup.c).

[0151] In particular, these interpolating functions have been implemented in Python.

[0152] FIG. 3 shows the single layer that will be computed with cells schematically representing the elemental volume seen in a direction perpendicular to the heat exchanging wall (1.6).

[0153] The method iterates over all the elemental volumes (EV) having available values at the inlet regions, at each iteration updating the values at the outlet regions by using the estimation module, iterating until a predetermined norm evaluated over the increments of updated values is below a predetermined threshold value.

[0154] As seen in FIG. 3, the elemental volume (EV) at the upper left corner is the first one computing column by column (as shown in the table).

[0155] At each elemental volume (EV), for instance cell (1,1), the temperature (T.sub.w) of the portion of heat exchanging wall (1.6.1) located in the elemental volume (EV) is assumed as is (T.sub.in.sup.h+T.sub.in.sup.c), wherein T.sub.in.sup.h is the temperature of the first fluid (f.sub.h) at the inlet boundary region (EVIh) and T.sub.in.sup.c is the temperature of the second fluid (f.sub.c) at the inlet boundary region (EVIc).

[0156] At a next step, density (.sub.in.sup.h, .sub.in.sup.c) form ambient pressure (P.sub.amb) and inlet static pressure is calculated since the velocity and the inlet boundary region (EVIh, EVIc) is known from mass flow rate.

[00002]${}_{\mathrm{in}}^h=\frac{P_{\mathrm{amb}}+P_{\mathrm{in}}^h}{R.Math.T_{\mathrm{in}}^h}{}_{\mathrm{in}}^c=\frac{P_{\mathrm{amb}}+P_{\mathrm{in}}^c}{R.Math.T_{\mathrm{in}}^c}$

where R=287 J/kg K.

[0157] The mass flow rate ({dot over (m)}.sub.h, {dot over (m)}.sub.c) for the first fluid (f.sub.h) and the second fluid (f.sub.c) respectively is then calculated as:

[00003]$\stackrel{.}{m_h}={}_{\mathrm{in}}^h.Math.A_h.Math.v_{\mathrm{in}}^h\stackrel{.}{m_c}={}_{\mathrm{in}}^c.Math.A_h.Math.v_{\mathrm{in}}^c$

wherein A.sub.h and A.sub.c are the trasversal area crossed by the first fluid (f.sub.h) and the second fluid (f.sub.c) respectively. Inlet velocity is only required as initial guess to calculate total pressure and total temperature from mass flow values known as input boundary conditions.

[0158] Now, using predictive values using first and the second interpolation module (IM1, IM2) static temperature at outlet boundary region (EVOh, EVOc) are determined, T.sub.out.sup.h and T.sub.out.sup.c.

[0159] Now, iteratively the heat transfer balance at the portion of the heat exchanging wall (1.6.1) is achieved for cell (1.1) by updating the wall temperature T.sub.w.

[0160] In a first step, total temperature is determined from the static temperature:

[00004]${\mathrm{Ttot}}_{\mathrm{in}}^h=T_{\mathrm{in}}^h+\frac{{\left(v_{\mathrm{in}}^h\right)}^2}{2.Math.C_p^h}{\mathrm{Ttot}}_{\mathrm{in}}^c=T_{\mathrm{in}}^c+\frac{{\left(v_{\mathrm{in}}^c\right)}^2}{2.Math.C_p^c}$

wherein tot identification in the temperature variable identifies the total temperature, as previously used indexes h, c stand for the hot/cold fluid, that is, the first fluid (f.sub.h) and the second fluid (f.sub.c), and C, is the heat capacity at constant pressure.

[0161] From these variables, it is calculated the heat transferred from the first fluid (f.sub.h) to the portion of the heat exchanging wall (1.6.1), Q.sub.h, and the heat transferred from the portion of the heat exchanging wall (1.6.1) to the second fluid (f.sub.c), i.e. Q.sub.c:

[00005]$Q_h=\stackrel{.}{m_h}{C}_p^h\left({\mathrm{Ttot}}_{\mathrm{in}}^h-{\mathrm{Ttot}}_{\mathrm{out}}^h\right)Q_c=\stackrel{.}{m_c}{C}_p^c\left({\mathrm{Ttot}}_{\mathrm{out}}^c-{\mathrm{Ttot}}_{\mathrm{in}}^c\right)$

wherein as already identified: [0162] {dot over (m)}.sub.h and {dot over (m)}.sub.c the mass flow of the first fluid (f.sub.h) and the second fluid (f.sub.c) respectively; C.sub.p.sup.h and C.sub.p.sup.c the heat capacity at constant pressure of the first fluid (f.sub.h) and the second fluid (f.sub.c) respectively; and, [0163] Ttot denotes the total temperature of the fluid wherein h, c indexes denotes the first fluid (f.sub.h) and the second fluid (f.sub.c) respectively and in, out denotes at the inlet boundary region and the outlet boundary region respectively.

[0164] Since the heat exchanging wall (1.6) does not store heat, and less so under the stationary flow hypothesis, once convergence has occurred the two quantities Q.sub.h and Q.sub.c are equal. However, if convergence has not been reached they are distinct and therefore the difference is non-zero.

[0165] The correction during the iterative process is applied on the heat exchanging wall temperature T.sub.w (1.6.1).

[0166] In this example embodiment the correction is proportional to the difference and follows the following criterion: if Q.sub.h>Q.sub.c the value of the temperature (T.sub.w) of the portion (1.6.1) of the heat exchanging wall (1.6) is updated incrementing a value e and, if Q.sub.h<Q.sub.c the value of the temperature (T.sub.w) of the portion (1.6.1) of the heat exchanging wall (1.6) is updated decrementing said value e, wherein e is the ratio between the heat transfer according to the values of the current iteration and, the maximum heat transfer; said ratio being preferably estimated as:

[00006]$e=\stackrel{.}{m_h}{C}_p^h\left({\mathrm{Ttot}}_{\mathrm{in}}^h-{\mathrm{Ttot}}_{\mathrm{out}}^h\right)/C_{\min }\left({\mathrm{Ttot}}_{\mathrm{in}}^h-{\mathrm{Ttot}}_{\mathrm{out}}^c\right)$

wherein C.sub.min=min({dot over (m)}.sub.hC.sub.p.sup.h,{dot over (m)}.sub.cC.sub.P.sup.c).

[0167] In a general case C.sub.p.sup.h and C.sub.p.sup.c depend on temperature.

[0168] Once the heat balance is achieved for cell (1.1) then T.sub.out.sup.h, T.sub.out.sup.c, dP.sub.h, dP.sub.c and v.sub.out.sup.h, v.sub.out.sup.c are predicted using the first and the second interpolation modules (IM1, IM2) at the hot and cold side.

[0169] The static pressure at the outlet of the elemental volume (EV) is calculated using the pressure drop at the output:

[00007]$P_{\mathrm{out}}^h=P_{\mathrm{in}}^h-{\mathrm{dP}}_h{P}_{\mathrm{out}}^c=P_{\mathrm{in}}^c-{\mathrm{dP}}_c$

and also the density:

[00008]${}_{\mathrm{out}}^h=\frac{P_{\mathrm{amb}}+P_{\mathrm{out}}^h}{R.Math.T_{\mathrm{out}}^h}{}_{\mathrm{out}}^c=\frac{P_{\mathrm{amb}}+P_{\mathrm{out}}^c}{R.Math.T_{\mathrm{out}}^c}$

[0170] The same applies to the total pressure at the output:

[00009]${\mathrm{Ptot}}_{\mathrm{out}}^h=P_{\mathrm{out}}^h+\frac{\left({}_{\mathrm{out}}^h.Math.{\left(v_{\mathrm{out}}^h\right)}^2\right)}{2}{\mathrm{Ptot}}_{\mathrm{out}}^c=P_{\mathrm{out}}^c+\frac{\left({}_{\mathrm{out}}^2.Math.{\left(v_{\mathrm{out}}^c\right)}^2\right)}{2}$

[0171] Once convergence is achieved, it is assumed that the mass is conserved so that the output values of cell (1.1) now become the input values of cell (1.2), the adjacent cell. Specifically,

[00010]$\stackrel{.}{m_h}\left(1,2\right)=\stackrel{.}{m_h}\left(1,1\right){\mathrm{Ptot}}_{\mathrm{in}}^h\left(1,2\right)={\mathrm{Ptot}}_{\mathrm{out}}^h\left(1,1\right)T_{\mathrm{in}}^h\left(1,2\right)=T_{\mathrm{out}}^h\left(1,1\right)T_{w\left(1,2\right)}=\frac{T_{\mathrm{in}}^{h\left(1,1\right)}+T_{\mathrm{in}}^{c\left(1,1\right)}}{2}$

[0172] Similarly for the cold side:

[00011]$\stackrel{.}{m_c}\left(1,2\right)=\stackrel{.}{m_c}\left(1,1\right){\mathrm{Ptot}}_{\mathrm{in}}^c\left(1,2\right)={\mathrm{Ptot}}_{\mathrm{out}}^c\left(1,1\right)T_{\mathrm{in}}^c\left(1,2\right)=T_{\mathrm{out}}^c\left(1,1\right).$

[0173] Once the first row is completely solved then the method moves on to the second and subsequent rows until completing the layer.

[0174] The process repeats for other layers if no homogeneous conditions are at the inlet of the heat exchanger (1) and at the end the mass flow averages are taken for outlet temperature and pressure of full heat exchanger.

[0175] It has been checked that the method, only requires CFD simulations for building the interpolation modules (IM1, IM2) wherein in this case about 500 simulations have been used. This is only a small amount of computation compared to the huge amount of cpu resources deeded for a full simulation of the entire heat exchanger (1) in view of the small size of the element volume (EM) represented in FIG. 1. This method has been checked to be very accurate even while consuming a minimal amount of computational resources.

[0176] The systems and devices described herein may include a controller or a computing device comprising a processing and a memory which has stored therein computer-executable instructions for implementing the processes described herein. The processing unit may comprise any suitable devices configured to cause a series of steps to be performed so as to implement the method such that instructions, when executed by the computing device or other programmable apparatus, may cause the functions/acts/steps specified in the methods described herein to be executed. The processing unit may comprise, for example, any type of general-purpose microprocessor or microcontroller, a digital signal processing (DSP) processor, a central processing unit (CPU), an integrated circuit, a field programmable gate array (FPGA), a reconfigurable processor, other suitably programmed or programmable logic circuits, or any combination thereof.

[0177] The memory may be any suitable known or other machine-readable storage medium. The memory may comprise non-transitory computer readable storage medium such as, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. The memory may include a suitable combination of any type of computer memory that is located either internally or externally to the device such as, for example, random-access memory (RAM), read-only memory (ROM), compact disc read-only memory (CDROM), electro-optical memory, magneto-optical memory, erasable programmable read-only memory (EPROM), and electrically-erasable programmable read-only memory (EEPROM), Ferroelectric RAM (FRAM) or the like. The memory may comprise any storage means (e.g., devices) suitable for retrievably storing the computer-executable instructions executable by processing unit.

[0178] The methods and systems described herein may be implemented in a high-level procedural or object-oriented programming or scripting language, or a combination thereof, to communicate with or assist in the operation of the controller or computing device. Alternatively, the methods and systems described herein may be implemented in assembly or machine language. The language may be a compiled or interpreted language. Program code for implementing the methods and systems described herein may be stored on the storage media or the device, for example a ROM, a magnetic disk, an optical disc, a flash drive, or any other suitable storage media or device. The program code may be readable by a general or special-purpose programmable computer for configuring and operating the computer when the storage media or device is read by the computer to perform the procedures described herein.

[0179] Computer-executable instructions may be in many forms, including modules, executed by one or more computers or other devices. Generally, modules include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Typically, the functionality of the modules may be combined or distributed as desired in various embodiments.

[0180] It will be appreciated that the systems and devices and components thereof may utilize communication through any of various network protocols such as TCP/IP, Ethernet, FTP, HTTP and the like, and/or through various wireless communication technologies such as GSM, CDMA, Wi-Fi, and WiMAX, is and the various computing devices described herein may be configured to communicate using any of these network protocols or technologies.

[0181] While at least one exemplary embodiment of the present invention(s) is disclosed herein, it should be understood that modifications, substitutions and alternatives may be apparent to one of ordinary skill in the art and can be made without departing from the scope of this disclosure. This disclosure is intended to cover any adaptations or variations of the exemplary embodiment(s). In addition, in this disclosure, the terms comprise or comprising do not exclude other elements or steps, the terms a or one do not exclude a plural number, and the term or means either or both. Furthermore, characteristics or steps which have been described may also be used in combination with other characteristics or steps and in any order unless the disclosure or context suggests otherwise. This disclosure hereby incorporates by reference the complete disclosure of any patent or application from which it claims benefit or priority.