Revista de Ciencias Tecnológicas (RECIT). Universidad Autónoma de Baja California ISSN 2594-1925
Volumen 3 (2):106-119. Abril-Junio 2020 https://doi.org/10.37636/recit.v32106119
106
ISSN: 2594-1925
Instrumental system to estimate the turbuce ratio of
the air flow in a rigid grid, based on its reduced
dynamic order transfer functions matrix
Sistema instrumental para estimar la relación de turbulencia del flujo de aire
en una cuadrícula rígida, en función de su matriz de funciones de
transferencia de orden dinámico reducido
Ana Marell Arteaga Martínez
1,2
, Eloy Edmundo Rodríguez Vázquez
1,3
,
María Elizabeth Rodríguez Ibarra
1,2
, Helen Janeth Zúñiga Osorio
3
,
Luis Álvaro Montoya Santiyanes
2,4
1
Engineering Center for Industrial Development (CIDESI), National Laboratory for Cooling
Technology Research (LaNITeF), Av. Pie de la Cuesta 207, Desarrollo San Pablo, Querétaro, 76250
México.
2
Universidad TecMilenio, Fudamental Science Department, Camino Real a Humilpan, Corregidora,
Querétaro.
3
Universidad Anáhuac Querétaro, School of Engineering, Quantitative Methods and Fundamental
Science, Circuito Universidades, El Marques, Querétaro.
4
Universidad Politécnica de Querétaro, School of Engineering, Carretera a los Cues, El Marques,
Querétaro.
Corresponding author: Dr. Eloy Edmundo Rodríguez Vázquez, Engineering Center for Industrial
Development (CIDESI), National Laboratory for Cooling Technology Research (LaNITeF), Av. Pie de
la Cuesta 207, Desarrollo San Pablo, Querétaro, 76250 México. E-mail: eloy.rodriguez@cidesi.edu.mx
Recibido: 30 de Junio del 2019 Aceptado: 15 de Mayo del 2020 Publicado: 30 de Junio del 2020
Abstract. – In words of the cooling technology experts, there is at least a 20-year gap between
the nowadays vapor compression based technology for refrigeration, cooling and HVAC, and
what we have defined as alternatives technologies. There is also a big amount of scientific effort
to endow this vapor compression technology with more degrees of freedom to implement more
accurate energy optimization algorithms. In this way, as a first step to get more robust control
algorithms in heat interchangers of condenser and evaporators units, authors have developed
some instrumentation systems to analyze the behavior of the air flowing through the rigid blades
of this kind of devices. This previous effort has been before reported as a complete vibrational
modal model for the concerned rigid grid, however; due to its 16 spatially degrees of freedom
and its 16th dynamic order, its model re-solution on line while the heat interchanger unit is
working is almost impossible with a normal computer. Therefore, to get an algorithm with less
computational resource consumption and with the same accuracy than the complete modal
model, authors have reported in this document, the implementation of a reduced dynamical
order transfer function matrix model. Reduction that as well as it is described is based on the
poles averaging and zeros selection, from the set experimental graphs of the frequency spectral
magnitude from a set of impact tests (experimental modal testing) performed at LaNITeF-
CIDESI. Numerical prediction of the transfer function matrix from the dynamic reduced order
Revista de Ciencias Tecnológicas. Volumen 3 (2): 106-119.
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ISSN: 2594-1925
model have been validated with the experimental spectral. Based on the hypothesis, that due to
the incident angle, the resonance spectral vibration is excited by the laminar air flow, while the
air flow turbulence does not excite the resonance vibrational spectral, the turbulence ration
from the incident air flow has been analyzed from a wind tunnel test. As the main conclusion,
authors have developed and validated a new instrumentation system to analyze the turbulence
ratio of the air flow incident in a rigid grid, which can be part of a condenser or evaporator
unit from a conventional cooling system, by implementing the concerned transfer functions
matrix model with reduced dynamic order.
Keywords: Vibrational modal model; Laminar and turbulent air flow; Reduce order transfer
functions matrix.
Resumen. - En palabras de los expertos en tecnología de enfriamiento, hay al menos una brecha
de 20 años entre la tecnología actual basada en compresión de vapor para refrigeración,
enfriamiento y HVAC, y lo que hemos definido como tecnologías alternativas. También hay
una gran cantidad de esfuerzo científico para dotar a esta tecnología de compresión de vapor
con más grados de libertad para implementar algoritmos de optimización de energía más
precisos. De esta manera, como primer paso para obtener algoritmos de control más robustos en
intercambiadores de calor de unidades de condensadores y evaporadores, los autores han
desarrollado algunos sistemas de instrumentación para analizar el comportamiento del aire que
fluye a través de las cuchillas rígidas de este tipo de dispositivos. Sin embargo, este esfuerzo
anterior se informó anteriormente como un modelo modal vibracional completo para la grilla
rígida en cuestión; Debido a sus 16 grados de libertad espacial y su 16 ° orden dinámico, su
redisolución de modelo en línea mientras la unidad de intercambiador de calor está funcionando
es casi imposible con una computadora normal. Por lo tanto, para obtener un algoritmo con
menos consumo de recursos computacionales y con la misma precisión que el modelo modal
completo, los autores han informado en este documento, la implementación de un modelo de
matriz de función de transferencia de orden dinámico reducido. Reducción que, como se
describe, se basa en el promedio de los polos y la selección de ceros, a partir de los gráficos
experimentales establecidos de la magnitud espectral de frecuencia de un conjunto de pruebas
de impacto (prueba modal experimental) realizadas en LaNITeF-CIDESI. La predicción
numérica de la matriz de la función de transferencia del modelo dinámico de orden reducido se
ha validado con el espectro experimental. Según la hipótesis, que debido al ángulo incidente, la
vibración espectral de resonancia es excitada por el flujo de aire laminar, mientras que la
turbulencia del flujo de aire no excita la espectral vibracional de resonancia, la relación de
turbulencia del flujo de aire incidente se ha analizado desde un prueba de túnel de viento. Como
conclusión principal, los autores han desarrollado y validado un nuevo sistema de
instrumentación para analizar la relación de turbulencia del flujo de aire incidente en una red
rígida, que puede ser parte de una unidad de condensador o evaporador de un sistema de
enfriamiento convencional, mediante la implementación de la transferencia correspondiente.
modelo matricial de funciones con orden dinámico reducido.
Palabras clave: Modelo modal vibracional; Flujo de aire laminar y turbulento; Reduzca la
matriz de funciones de transferencia de orden.
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Revista de Ciencias Tecnológicas. Volumen 3 (2): 106-119.
1. Introduction
Several international engineer organizations
and company clusters like ASHRAE
(American Society for Heating,
Refrigeration and Air Conditioning
Engineers) and ANFIR (National
Association for the Refrigeration Industry
Manufactures in Mexico) have reported that
the perishable product preservation
consumes almost 25% of electric energy [1],
therefore; based on the average efficiency
reported from the equipment use for the cold
chain conservation, in 2016 almost 1 TWh
was wasted, magnitude that represents
1,300.00 Million of USD per hour [2].
The cooling technology expert’s predictions
say that there is at least a 20 years’ gap for
the commercial consolidation of a new
alternative technology for the perishables
preservation. Based on this scenario, there is
still a big importance to perform several
researching efforts focused on the
optimization of the conventional technology
for refrigeration and air conditioning based
on vapor compression [3 – 5].
In this point, several scientific and
technological works have taken place to
increase the energetic performance of these
conventional cooling systems. Some of
them are concentrated on the development
and implementation of new materials for the
thermal isolation of cooling chambers [6, 7].
Important improvements have also been
reported in the alternative cooling
technology development field. These
developments include the regulation of
different physical phenomena, as well as:
thermo-acoustics [8], magneto-caloric
properties [9] or arrangements of electro-
thermal devices [10]. However, as it has
been reported and as the experts have
predicted, these alternative technologies
have not achieved the same thermal load
and time response capacity than the actual
systems based on the vapor compression
refrigeration cycle do [11, 12].
In the same way, to improve the energetic
performance of the conventional cooling
technology, the control engineering has
been involved by trying several strategies,
such as: neural networks [13], fuzzy logic
[14], or adaptive linear controllers [15 - 18].
All these control algorithms are based on the
compressor activation regulation, since
there is only one degree of freedom that the
conventional cooling technology has for the
regulation of its energetic performance.
In order to get more accurate energetic
optimization strategies for the conventional
cooling systems, heat interchange from the
condenser and evaporator units takes
importance [17 - 21]. Here is where the
scientific proposal of this work is grounded,
because it represents the first stage to
develop a control algorithm to regulate the
heat interchange by monitoring the
waveform magnitude from the air flowing
in between of the heat interchangers blades
with not affection to its thermodynamic
performance.
In the next section the fundamentals of the
scientific proposal are described by showing
the mathematical model hypothesis and its
structure. The third section shows the
experimental details and the test results for
the dynamic characterization of the
experimental setup. Finally, in sections four
and five the experimental results are
analyzed and the conclusions are supported
based on these results.
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2. Dynamic model fundamentals
The proposal for the waveform magnitude
estimation for the air flowing through a rigid
grid of a heat interchanger unit is based on
the vibrational modal model from the set of
blades shown on Fig. 1 which is grounded
on the lumped mass structure illustrated on
Fig. 2. This model has been structured based
on the lumped mass hypothesis, and its
coefficients come from an experimental
modal test, performed at the LaNITeF
facilities at CIDESI Querétaro.
The main hypothesis of this proposal is
grounded on the strong correlation between
the dynamic performance of the air flow in
the blades and their vibrational behavior.
The purpose of this effort is to know how
this correlation can be monitored with an
acceptable certainty.
Authors have reported the concerned model
for this vibrational structure in its complete
version with a recursive adjustment of its
damping coefficients [17]. That version has
been considered complete because its
dynamical order (16th) is the same than the
spatial degrees of freedom [16].
Figure 1. Set of blades used to get the vibrational modal
model.
Figure 2. Structural hypothesis for the vibrational modal model.
Due to the computational resources needed
to perform this model solution on line while
the heat interchanger are working, the 16
degrees of freedom with their 16th
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dynamical order is not technologically
feasible without a supercomputer behind.
Then, authors propose the reduction of the
16 complete dynamical orders to the ones
needed depending on the frequency spectral
magnitude from their corresponded transfer
function. Effort that is documented here.
At the end, the fundamental mathematical
structure based on the lumped mass
hypothesis gives the dynamic relationship
between the forces
and the output
displacements
defined by a transfer
matrix, given by:
(1)
where:
is the polynomial of Eigenvalues
(poles) of the entire system, and
is the polynomial of
zeros that links the output variable
with
the input variable
.
For the reduced dynamical order model, the
zeros polynomial order are less than 16,
which again it is the most important
difference between this reduced model and
the complete model, and which avoids over
consumption of computational resources for
the model solution on line.
3. Experimental characterization of
the vibrational model
Both, poles confirmation and zeros location
for each transfer function between the
output variables
versus the input
variables
, given by
(2)
were graphically identified from the
experimental plot of the concerned variables
behavior, while a set of impact tests were
performed as the fundamental part of the
experimental modal test. Fig. 3 shows the
impact test setup where the accelerometers
and instrumented hammer used are
identified.
Figure 3. Experimental setup for the impact test.
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Table 1 list the technical characteristics of
the equipment used for the impact test
experimentation.
Table 1. Technical characteristics of the equipment used.
Description
Accuracy
Model
Manufactured
Accelerometer
10.5 mV/g
M353B17
PCB
Instrumented Hammer
2.25 mV/N
086C03
Data Acquisition System
NI cDAQ 9178
National Instruments
Signal Conditioning
NI 9234
The spectral responses from some transfer
functions from their 256 set of them, are
shown on Figs. 4 to 7.
Figure 4. Spectral response of the transfer function magnitude “
”.
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Figure 5. Spectral response of the transfer function magnitude “
”.
Figure 6. Spectral response of the transfer function magnitude “
”.
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Figure 7. Spectral response of the transfer function magnitude “
”.
From the spectral response graphs the poles
polynomial was gotten by analyzing the
magnitude spectral peaks as well as Fig. 8
shows; therefore based on an average
criteria from the 256 impact experiments,
this 16th order polynomial was defined as:
, (3)
In the same graphical criteria, but by
analyzing the spectral minimum magnitude
as well as it is shown on Fig. 9, in this
experimental case for each transfer function
the concerned zeros were defined as well as
they are listed on Table 2.
Table 2. Model zeros list.
Z1
Z2
Z3
Z4
Z5
Z6
Z7
Z8
Z9
Z10
Z11
Z12
Z
(1,1)(1,1)
950
2500
3600
5300
7200
8300
9000
9600
10400
11300
12100
12600
Z
(1,1)(1,2)
850
1950
3100
3800
5000
9300
99000
10000
Z
(1,1)(1,3)
1000
2000
3400
4400
7100
8900
10100
11800
Z
(1,1)(1,4)
850
2100
3500
5900
7300
10100
11400
Z
(1,1)(2,1)
750
2600
3700
5300
6600
7500
8300
9200
10500
Z
(1,1)(2,2)
800
2100
5300
6700
8600
9200
10400
11500
Z
(1,1)(2,3)
900
3100
5000
7200
8400
10200
Z
(1,1)(2,4)
900
2000
3100
5200
6900
8300
9700
Z
(1,1)(3,1)
800
4100
6300
7200
9300
10500
Z
(1,1)(3,2)
900
4300
7000
8300
10100
Z
(1,1)(3,3)
850
2900
5200
7300
10000
11300
Z
(1,1)(3,4)
3800
6500
7100
9800
11300
12100
Z
(1,1)(4,1)
4000
6200
7300
8400
9200
12000
Z
(1,1)(4,2)
900
3900
5500
7100
9800
Z
(1,1)(4,3)
3900
5300
7100
10100
Z
(1,1)(4,4)
4200
7000
9300
12100
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Figure 8. Graphical identification of the transfer function poles.
Figure 9. Graphical identification of the transfer fuction zeros.
The poles and zeros values estimation
reported on Ec. 3 and Table 2 are similar
than the ones estimated by the authors
before, by applying others experimental
techniques [17]. The bandwidth of the
spectral range starts at 800 Hz and goes to
12600 Hz, because of the accelerometers
limitations.
The transfer function response from an
impulse input vector was simulated to
compare the experimental data from the
modal test with the numerical prediction in
the frequency dominium. Based on the
results plotted on Fig. 10 to 13, the
simulation results are strongly accepted.
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4. Air flow correlation and the
model tuning
After the transfer function validation
through its simulation and comparison with
the experimental results, the set of blades
shown on Fig. 1, was tested on a wind tunnel
as it is illustrated on Fig. 14, with a set of air
flow profiles with different turbulence ratio.
The experimental results from the wind
tunnel test are reported on Table 3.
Figure 10. Spectral comparison between transfer function simulation and experimental results from
“
”.
Figure 11. Spectral comparison between transfer function simulation and experimental results from “
”.
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Figure 12. Spectral comparison between transfer function simulation and experimental results from
“
”.
Figure 13. Spectral comparison between transfer function simulation and experimental results from
“
”.
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Figure 14. Experimental setup from the wind tunnel test”.
Table 3. Summary of results from the wind tunnel test.
Turbulence Ratio
Resonance Vibrations RMS
Not Resonance Vibrations RMS
10 %
30.7 m/s
2
5.0 m/s
2
30 %
24.2 m/s
2
7.8 m/s
2
70 %
19.6 m/s
2
10.4 m/s
2
Resonance vibrations RMS and not
resonance vibrations RMS values have been
reported, because the hypothesis to analyze
the turbulence ratio is based on the fact that
due to the incident angle of the laminar air
flow, it excites the resonance vibrations,
while the not resonance vibrations are
excited by the air flow turbulence.
5. Conclusions
By analyzing the plots from Figs. 10 to 13,
the transfer function matrix from Ec. 1 has
been experimentally validated, therefore;
the dynamic order reduction from the
complete model with 16 spatial degrees of
freedom and 16th dynamic order, to the
reduced model with the dynamic order
defined by the zeros listed on Table 2, works
correctly. Another fact that can be added to
the last paragraph statement is that the
transfer function matrix predicts the poles
from Ec. 3 and zeros from Table 2, so that
the spectral peaks that were not considered
and taken out from the numerical prediction
of Ec 1, are taken in account as not-
resonance response of the vibrational
model. Table 3 shows in certain level, the
validation of the hypothesis which is based
on the fact that due to the incident angle of
the laminar air flow, it excites the resonance
spectra from the set of blades, and the air
flow turbulence excites the corresponded
not resonance spectra. At the end, authors
have developed and validated an
instrumentation system that can predict the
relationship between the laminar and
turbulence air flow, incident in a set of
blades. Specifically, in this case from a
turbo-compressor stator, but than can be
also implemented in heat interchangers
grids from condenser or evaporators units
from cooling systems, which works based
on the vapor compression cooling cycle.
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Acknowledgment
Authors thank CONACYT for the support
through the Scholarships No. 906807 and
903766 and by the National Laboratories
Program Project No. 299090 from the
National Laboratory for Cooling
Technology Research (LaNITeF). Thanks,
are extended to the School of Engineering
of the Anahuac University of Querétaro and
to the LaNITeF from the Engineering
Center of Industrial Development
(CIDESI).
Part of the result reported in this paper
comes from the project
VINCULACIÓN/2018/02 developed by
CIDESI and WALWORTH México with
the support of COMECYT by the
PROGRAMA PARA LA VINCULACIÓN
DE EMPRESAS DEL ESTADO DE
MÉXICO CON INSTITUCIONES DE
EDUCACIÓN SUPERIOR Y CENTROS
DE INVESTIGACIÓN.
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cambios. Puede hacerlo en cualquier forma razonable, pero no de forma tal que sugiera que tiene el apoyo del licenciante o lo recibe por el uso
que hace de la obra.
Resumen de licencia - Texto completo de la licencia
