A new model framework is proposed to describe the expansion of extrudates with extruder operating conditions based on dimensional analysis principle. The Buckingham pi dimensional analysis method is applied to form the basic structure of the model from extrusion process operational parameters. Using the Central Composite Design (CCD) method, whole wheat flour was processed in a twin-screw extruder with 16 trials. The proposed model can well correlate the expansion of the 16 trials using 3 regression parameters. The average deviation of the correlation is 5.9%

Cheng, Hongyuan

Friis, Alan

English

Organic Eprints

EXPANSION OF THE WHOLE WHEAT FLOUR EXTRUSION  Hongyuan Cheng and Alan Friis Food Production Engineering, National Food Institute Technical University of Denmark Søltofts Plads, Building 227, DK-2800, Lyngby, Denmark E-mail: hyc[a]bio.dtu.dk    KEYWORDS Expansion, Extrusion, whole wheat flour, modelling.  ABSTRACT  A new model framework is proposed to describe the expansion of extrudates with extruder operating conditions based on dimensional analysis principle. The Buckingham pi dimensional  analysis  method  is  applied  to  form  the  basic structure  of  the  model  from  extrusion  process  operational parameters.  Using  the  Central  Composite  Design  (CCD) method,  whole  wheat  flour  was  processed  in a twin-screw extruder  with  16  trials.  The  proposed  model  can  well correlate  the  expansion  of  the  16  trials  using 3 regression parameters. The average deviation of the correlation is 5.9%.    INTRODUCTION  Diets with high amounts of whole grains may help achieve significant weight loss, and also reduce the risk of chronic diseases such as diabetes and cardiovascular disease. Epidemiological studies have shown that increased intakes of whole  grain  products  are  associated  with  reduced  risks  of diabetes  mellitus,  hypertension,  and  cardiovascular  disease (Jones, 2000, Slavin, 2004, Katcher et al. 2008). However, most  cereal  products  available  in  Europe  and  the  United States are produced from highly refined grains, which lead to the  loss  of  many  potentially  beneficial  micronutrients, antioxidants,  minerals,  phytochemicals,  and  fiber. Subsequently, the consumption of whole grain is far less than the three servings on a daily basis as suggested by the food pyramid  of  the  United  States  Department  of  Agriculture (Slavin,  2004).  Whole  grain  breakfast  cereals  might contribute  to  satisfy  the  recommended  daily  intake,  since they  fit  to  the  increasingly  fast-paced  nature  of  consumer lifestyles.  Breakfast  cereals  are  convenient  to  prepare  and easily consumed. In addition, they appeal to consumers of all income levels (Jones, 2000)  Extrusion  cooking  has  become  a  well-established industrial  technology  by  offering  continuous  and  flexible processes  which  allow  producing  breakfast  cereals  with diverse textures and shapes and ultimately reducing the costs of the final products. The extrusion cooking process can be analyzed  in  terms  of  operational  parameters,  system  and product  characteristics.  By  changing  the  operational parameters it is possible to influence the time-temperature-shear  history  of  the  grain  flour  in  the  extruder.  System parameters  such  as  specific  mechanical  energy  (SME)  are generally used to describe the time-temperature-shear history, which  affects  the  extent  of  biopolymer  modification  and finally  the  expansion  and  texture  of  extruded  products. Although  starch  is  known  to  be  the  key  biopolymer  in extrusion  cooking,  other  ingredients  of  cereal-based  food systems  such  as  proteins,  fat  or  fiber  also  influence  the system and product characteristics, e.g. by competing with starch for water (Moraru and Kokini, 2003). Due to these compositional and structural complexities of the raw material as  well  as  the  large  number  of  operational  parameters involved  in  the  extrusion  process,  obtaining  the  desired extrudate properties, e.g. optimal expansion and texture, is a challenging  task  and  often  depends  on  trial  and  error experience. The empirical experience is often valid only for the  specific  extrusion  equipment  that  has  been  used  to generate the good operation conditions.  In practical food industrial applications, one often needs to run some trials in a pilot extrusion process in a new food product development stage. Through the trials, a set of specific operating parameters can be established for the new recipe material extrusion. The procedure sometimes is out of control in the time or raw materials cost frame. In this work, we present an engineering procedure to find out the suitable process  parameters  to  reach  correct  expansion  for  whole wheat  flour  extrusion  in  a  pilot  plant,  which  includes experimental design and process parameter correlation.    EXTRUSION EXPERIMENTS DESIGN  The  extrusion  experiments  design  was  setup  by  a traditional way. With considering the extruder limitation, a Central Composite Design (CCD) (Esbensen, 2000) was used in  the  study,  which  was  based  on  five  levels  of  three variables  (Table  1).  The  independent  extrusion  variables considered were barrel temperature in different zones, feed water  content  and  screw  speed. All other parameters were kept constant. Operating ranges and five standardized levels were  established  by  preliminary  study  of  each  variable. According to the CCD, the experimental plan comprised 15 trials (8 factorial points, 6 axial points and 1 central point).  Table 1 Coded levels for the central composite design Variables  Levels -α α α α  -1  0  1  +α α α α T5, °C  101  111  125  139  149 Xw, %  9.2  10.5  12.5  14.5  15.8 Ns, rpm  208  245  300  355  393 In Table 1, T5 is the temperature of zone 5 (closest zone to die), °C, Xw is the water content, weight percent, %, Ns is the screw speed, rpm, α equals to 1.682.   In the investigation, the extrudate expansion was set as the objective of the extrusion process operation. Through the  experiments,  it was expected to develop a quantitative correlation for extrudate expansion and extrusion operating conditions.  With  the  help  of  the  correlation  model,  the number of runs could be reduced for a similar recipe food extrusion using the whole wheat flour.   EXTRUSION EXPERIMENTS  Whole  wheat  grain  was  milled  to  obtain  the  whole  wheat flour. The whole wheat flour was processed in a Werner & Pfleiderer Continua 37 co-rotating twin-screw extruder. The CCD table, i.e. Table 1, was used to set up 15 experimental runs. First, 15 trials were carried out to search the optimal extrusion conditions for maximum expansion. After the 15 trials, one more run was carried out to obtain the maximum expansion. The last trial conditions were estimated from the response surface methodology. The trial capacity was in 22-27kg/hr  levels.  In  the  experimental  work,  the  wheat  flour, water and additives are directly fed into extruder without pre-mixing.  The  extrudates  were  dried  at  110°C  for  about  10 minutes in a continuous processing oven. The extrudate bulk density was measured during the extrusion operations using weight method for 1 liter extrudates.   MODEL CONSTRUCTION   In decades, many investigations have been carried out  for  the  relationship  between  extrudate  expansion  and operating conditions (Alvarez-Martinez, et al. 1988, Cai and Diosady,  1993,  Moraru  and  Kokini,  2003).  As  the  food market is very volatile, food producers have to change their recipe all the time. Sometimes the maximum expansion is the target. In other cases, mild extrusion conditions are expected in order to improve the nutritional quality of products (Singh et  al.  2007).  A  quantitative  correlation  for  the  extrudate expansion and operating condition will significant benefit the food extrusion applications.  In these correlations and models, some are based on empirical regression from operating conditions (Ding, et al. 2006).  Others  use  the  models  from  a  sort  of  theories  or mechanisms  (Fan  and  Mitchell,  1994).  In  the  empirical regressions,  a  model  is  often  constructed  with  linear  and quadratic  terms  according  the  statistical  significant  for  a specific extrusion process. This kind of model construction normally  results  in  many  regression  coefficients  to  be determined from experimental data. No doubt, the empirical equation has played an important role in extrusion product development.  However,  sometimes  the  empirical  models contain many operating parameters and product properties. The uncertainty of the measurement of the product properties could be very diverse. Thus, the uncertainty can transfer into the empirical correlation model. The mechanism model has a solid theoretic background and is the direction to develop a model to describe the extrusion process operation. However, the mechanism-based model often needs accurate food fluids physical property correlations to support its prediction and estimation for the extrusion process behaviors. Because the food  fluids  belong  to  non-Newtonian  fluid  and  have  very complicated behaviors, the development of a precise physical property  calculation  model  for  such  food  fluid  is  very difficult.   In this work, a dimensional analysis based model is proposed to correlate the extrudate expansion and extruder operating  conditions.  Dimensional  analysis  method  is  a classical way in industrial applications to setup a model. In the applications of fluid mechanics and fluid heat transfer, the  dimensional  analysis  method  has  obtained  tremendous successful  achievements.  However,  this  method  is  seldom used  to  setup  the  correlation  between  extrudate  expansion and extrusion operating parameters.   Extrudate  expansion  is  a  reflection  of  extrusion equipment  design  and  process  operation  conditions.  The equipment design may include different pre-mixing methods, various screw structures, die design, etc. Because the process operation  conditions  are  the  adjustable  process  control parameters for an existing production line, we will only study the  correlation  between  process  operation  conditions  and extrudate  expansion  in  this  work.  In  an  extrusion  process, many  process  parameters  have  influence  on  the  extrudate expansion, e.g. different zone temperatures, die temperature and  pressure,  process  capacity,  screw  speed,  torque, water content,  fluid  viscosity,  specific  mechanical  energy,  etc. Many researchers have used different methods to correlate the  process  parameters  with  extrudate  expansion  (bulk density)  and  achieved  their  successes.  In  this  work,  the dimensional analysis method will be applied to analysis and correlate these parameters.    Historically,  the  dimensional  analysis  methods include the Rayleigh method and the Buckingham pi method (Buckingham,  1914,  Rayleigh,  1915,  Perry  and  Green, 1999). In this work, the Buckingham pi method is applied to construct a model. For an extrusion process, we can find out a set of key variables and their dimensions in the engineering system as below: T0, Td=temperature, T FT, Fw=flowrate, mass/time, M/t Ns=screw speed, 1/time, 1/t τ =torque, force⋅length F⋅L Pd =die pressure, force/length2 F/L2 B ρ =density, mass/volume, M/L3 Here,  the  units  T,  M,  t,  F  and  L  respectively  represent temperature,  mass,  time,  force  and  length.  Among  the variables,  B ρ is the bulk density of extrudates, g/liter, Fw is the water flowrate added into the extruder, kg/hr, FT is the total flowrate of all feed materials (wheat flour, water and additives), kg/hr, Td is the die temperature, °C, T0 is the room temperature  (25°C),  which  is  also  the  raw  material  initial temperature, Pd is the die pressure, bar, τ is the torque, Nm, Ns is the screw speed, rpm. From  the  key  extrusion  process  parameters,  a variable and units matrix is formed as shown in Table 2.   Table 2 Selected variables and units matrix  Unit   T0  Td   FT  Fw  Ns  Pd  τ   B ρ  T  1  1  0  0  0  0  0  0 M   0  0  1  1  0  0  0  1 t   0  0  -1  -1  -1  0  0  0 F  0  0  0  0  0  1  1  0 L  0  0  0  0  0  -2  1  -3  In the formation of Table 2, we assume that the fluid density just before flash-out from die linearly proportions to the bulk density.      Through  calculation,  it  can  be  found  out  that  the rank  of  the  matrix  shown  in  Table  2  is  5.  The  physical variables in Table 2 are 8. From the Buckingham pi theorem, three  dimensionless  groups  can  be  established  from  the matrix, which are given as follows:  s BT dNF P⋅ ⋅⋅τ ρ,   TwFF,    0 TTd  In the studied extrusions process, the term Fw/FT represents the water content of processing materials. The term Td/T0 is the  temperature  changes  of  processing  materials  from  its initial  condition  to  the  vicinity of flash-out from extruder. The  term s BT dNF P⋅ ⋅⋅τ ρ  represents  the  energy  added into the processing  materials.  In  fact,  the  term  τ⋅Ns/FT  reflects  the widely  used  specific  mechanical  energy  (SME).  From  the three dimensionless groups, different model expressions can be constructed. In this work, a model is obtained as    ( ) (1)             0W B   ⋅⋅  =sT d dNF PTTX Kτρβα where  B ρ is the bulk density of extrudates, g/liter, Xw is the water content of feed material and equals to Fw/FT, weight fraction. K, α and β are the model coefficients, which need to be determined from experimental data.   From  the  equation  (1),  it  can  be  seen  that  the equation lacks of physical properties of food fluids. Thus it is only  suitable  to  the  specific  whole  wheat  flour  extrusion. However,  the  equation  is  simple  and  contains  only  correlation coefficients. The simple format model meets the engineering applications.   Using the data from the 16 runs for whole wheat flour  extrusion,  the  model  coefficients  are  determined  as shown in Table 3. The average absolute deviation (AAD) of the model correlation with experimental bulk density data is 5.9%, where AAD is calculated as.  %1AAD expcal exp∑ −=n BB Bn ρρ ρ    (2) In  equation  (2),  n  is  the  number  of  experimental runs.  The  model  correlation  results  for  the  extrudate  bulk density  are  shown  in  Figure  1.  The  estimation  error distribution of the model for extrudate bulk density is shown in  Figure  2.  As  shown  in  Figure  2,  the  bulk  density estimation errors are evenly distributed.   Table 3 Coefficients of equation (1) Coefficient  K  α  β Value  13508  0.7774  -0.2882   Figure 1: Correlation results of bulk density at different runs   Figure 2: Relative deviations of equation (1) in correlation with bulk density and extusion operating conditions   In Figure 2, the relative deviation (Rd) is calculated as % expcal expBB Bd Rρρ ρ −=     (3)  DISCUSSIONS AND CONCLUSIONS  In  engineering  applications,  a  simple  and  reliable model often can help engineers to reach an optimal solution through  observing  the  interactions  of  different  operational parameters. In this work, the model construction is based on the engineering principle. A dimensional analysis method is used to build a model with the key process parameters. From the model one can quantitatively estimate the extrudate bulk density  changes  with  different  control  parameters  and  the interactions of these parameters.  The model estimation results show that the proposed can  successfully  represent  the  extrudate  bulk  density  in different extruder operating conditions. The average absolute deviation in the estimation of extrudate bulk density is 5.9%.       ACKNOWLEDGMENTS We acknowledge Hanne T. Pedersen, Jørgen Busk from Danish Technological Institute and Danish Technological Institute for providing its pilot plant, raw materials and technical support in this research work.   REFERENCES Alvarez-Martinez, L.; K. P. Kndury and J. M. Harper 1988. “A general model for expansion of extruded products.” Journal of Food Science, 53, 609-615 Cai, W. and L. L. Diosady. 1993. “Modeling of expansion and water solubility index of wheat starch during extrusion  cooking” Acta Alimentaria, 22, 181-92.  Buckingham, E. 1914. “On physically similar systems; illustrations of the use of dimensional equations". Phys. Rev. 4: 345-376. Ding, Q.-B.; P. Ainsworth; A. Plunkett; G. Tucker and H. 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Kokini. 2003 “Nucleation and expansion during extrusion and microwave heating of cereal foods”. Comprehensive Reviews in Food Science and Food Safety, 2, 120-138. Perry, R.H and D. W. Green. 1999. Perry’s Chemical Engineers Handbook, 7th Ed. McGraw-Hill, New York, p.3-89 to 3-90 Rayleigh, 1915. “The principle of similitude”. Nature, 95, 66-68. Singh, S.; S. Gamlath and L. Wakeling. 2007. “Nutritional Aspects of Food Extrusion: a Review” International Journal of Food Science and Technology, 42, 916-929.  Slavin, J. 2004. “Whole grains and human health”. Nutrition Research Review, 17, 99-110.   

Expansion of the whole wheat flour extrusion

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