Module: EngineeringCalculator::GasDynamics

Defined in:
lib/engineering_calculator/gas_dynamics.rb

Class Method Summary collapse

Class Method Details

.fanno(m, gamma) ⇒ Object 



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# File 'lib/engineering_calculator/gas_dynamics.rb', line 6

def self.fanno(m,gamma)
  m = m.to_f
  gamma = gamma.to_f

  p_ratio     = 1/m * 1/Math.sqrt((2/(gamma+1)*(1+(gamma-1)/2*pow(m, 2))))
  rho_ratio   = 1/m * Math.sqrt((2/(gamma+1)) * (1+(gamma-1)/2*pow(m, 2)))
  t_ratio     = 1/(2/(gamma+1)*(1+(gamma-1)/2*pow(m, 2)))
  u_ratio     = m * 1/Math.sqrt(2/(gamma+1) * (1 + (gamma-1)/2*pow(m, 2)))
  po_ratio    = 1/m * pow(2/(gamma+1) * (1+(gamma-1)/2*pow(m, 2)),(gamma+1)/(gamma-1)/2)
  fanno_param = (1-pow(m, 2))/(gamma*pow(m, 2)) + (gamma+1)/(gamma*2)*Math.log(pow(m, 2)/(2/(gamma+1)*(1+(gamma-1)/2*pow(m, 2))))

  result = {
    p_ratio:      p_ratio,
    rho_ratio:    rho_ratio,
    t_ratio:      t_ratio,
    u_ratio:      u_ratio,
    po_ratio:     po_ratio,
    fanno_param:  fanno_param
  }
end

.isentropic(m, gamma) ⇒ Object 



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# File 'lib/engineering_calculator/gas_dynamics.rb', line 27

def self.isentropic(m,gamma)
  m = m.to_f
  gamma = gamma.to_f
  
  ratio_t   = pow(1 + (gamma - 1)/2 * pow(m, 2), -1)
  ratio_p   = pow(1 + (gamma - 1)/2 * pow(m, 2), -gamma/(gamma-1))
  ratio_rho = pow(1 + (gamma - 1)/2 * pow(m, 2), -1/(gamma-1))
  ratio_a   = pow((gamma + 1)/2, -((gamma + 1)/(gamma - 1)/2))/m * pow(1 + (gamma - 1)/2 * pow(m, 2), ((gamma + 1)/(gamma - 1))/2)
  
  result = {
    ratio_t:    ratio_t,
    ratio_p:    ratio_p,
    ratio_rho:  ratio_rho,
    ratio_a:    ratio_a
  }
end

.normal_shock(mx, gamma) ⇒ Object 



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# File 'lib/engineering_calculator/gas_dynamics.rb', line 44

def self.normal_shock(mx,gamma)
  my        = Math.sqrt((pow(mx,2)*(gamma-1)+2)/(2*gamma*pow(mx,2)-(gamma-1)))
  py_px     = 2*gamma* pow(mx,2) /(gamma+1)-(gamma-1)/(gamma+1)
  rhoy_rhox = (gamma+1)*pow(mx,2)/((gamma-1)*pow(mx,2)+2)
  ty_tx     = (1 + (gamma - 1)/2 * pow(mx, 2))*(2*gamma/(gamma - 1) * pow(mx, 2) - 1)/(pow(mx, 2)*(2*gamma/(gamma - 1) + (gamma - 1)/2))
  poy_pox   = pow((gamma + 1)/2 * pow(mx, 2)/(1 + (gamma - 1)/2 * pow(mx, 2)), gamma/(gamma - 1)) * pow(1/(2 * gamma/(gamma+1) * pow(mx,2) - (gamma-1)/(gamma+1)), 1/(gamma - 1));
  
  result = {
    my:         my,
    py_px:      py_px,
    rhoy_rhox:  rhoy_rhox,
    ty_tx:      ty_tx,
    poy_pox:    poy_pox
  }
end

.oblique(mx, gamma, delta) ⇒ Object 



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# File 'lib/engineering_calculator/gas_dynamics.rb', line 60

def self.oblique(mx,gamma,delta)
  pi    = Math::PI
  beta  = delta*pi/180 # Initial guess that beta and delta coincide.
  e     = 1
  rhs   = Math.tan(delta*pi/180)

  while (e >= 1*10**(-5))
    lhs   = 2*(1/Math.tan(beta))*(pow(mx,2)*pow(Math.sin(beta),2)-1)/(pow(mx,2)*(gamma+Math.cos(2*beta))+2)
    e     = rhs - lhs
    beta  = beta + 0.00001
  end

  ratio_rho = (gamma+1) * pow(mx, 2)*pow(Math.sin(beta), 2) / ((gamma-1)*pow(mx, 2)*pow(Math.sin(beta), 2)+2)
  beta      = beta*180/pi;
  ratio_p   = 1+2*gamma/(gamma+1)*(pow(mx,2)*pow(Math.sin(beta*pi/180),2)-1);
  ratio_t   = ratio_p*pow((gamma+1)*pow(mx,2)*pow(Math.sin(beta*pi/180),2)/((gamma-1)*pow(mx,2)*pow(Math.sin(beta*pi/180),2)+2),-1);
  my        = (1/Math.sin((beta-delta)*pi/180))*pow((1+0.5*(gamma-1)*pow(mx,2)*pow(Math.sin(beta*pi/180),2))/(gamma*pow(mx,2)*pow(Math.sin(beta*pi/180),2)-0.5*(gamma-1)),0.5);
  ratio_px  = pow(1 + (gamma - 1)/2 * pow(mx, 2), -gamma/(gamma-1));
  ratio_py  = pow(1 + (gamma - 1)/2 * pow(my, 2), -gamma/(gamma-1));
  ratio_po  = ratio_px/ratio_py*ratio_p;
  
  result = {
    my: my,
    ratio_rho: ratio_rho,
    beta: beta,
    ratio_p: ratio_p,
    ratio_t: ratio_t,
    ratio_po: ratio_po
  }
end

.prandtl_compression(mx, gamma, turning_angle) ⇒ Object 



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# File 'lib/engineering_calculator/gas_dynamics.rb', line 91

def self.prandtl_compression(mx,gamma,turning_angle)

  pi            = Math::PI
  nux           = Math.sqrt((gamma+1)/(gamma-1)) * Math.atan(Math.sqrt((gamma-1)/(gamma+1)*(pow(mx, 2)-1))) - Math.atan(Math.sqrt(pow(mx, 2)-1))
  turningAngle  = turning_angle*pi/180
  nuy           = nux - turningAngle
  my            = 1
  e             = 1

  while (e >= 0.00001)
    nuy_test  = Math.sqrt((gamma+1)/(gamma-1)) * Math.atan(Math.sqrt((gamma-1)/(gamma+1)*(pow(my, 2)-1))) - Math.atan(Math.sqrt(pow(my, 2)-1))
    e         = nuy - nuy_test
    my        = my+0.00001
  end

  my        = my-0.00001
  ty_tx     = (1+(gamma-1)/2*pow(mx, 2))/(1+(gamma-1)/2*pow(my, 2))
  py_px     = pow((1+(gamma-1)/2*pow(mx, 2))/(1+(gamma-1)/2*pow(my, 2)), gamma/(gamma-1))
  rhoy_rhox = pow((1+(gamma-1)/2*pow(mx, 2))/(1+(gamma-1)/2*pow(my, 2)), 1/(gamma-1))
  mux       = Math.asin(1/mx)
  muy       = Math.asin(1/my)

  result = {
    ty_tx:      ty_tx,
    py_px:      py_px,
    rhoy_rhox:  rhoy_rhox,
    my:         my,
    nux:        nux*180/pi,
    nuy:        nuy*180/pi,
    mux:        mux*180/pi,
    muy:        muy*180/pi,
  }
end

.prandtl_expansion(mx, gamma, turning_angle) ⇒ Object 



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# File 'lib/engineering_calculator/gas_dynamics.rb', line 125

def self.prandtl_expansion(mx,gamma,turning_angle)

  pi            = Math::PI
  nux           = Math.sqrt((gamma+1)/(gamma-1)) * Math.atan(Math.sqrt((gamma-1)/(gamma+1)*(pow(mx, 2)-1))) - Math.atan(Math.sqrt(pow(mx, 2)-1))
  turningAngle  = turning_angle*pi/180
  nuy           = nux + turningAngle
  my            = 1
  e             = 1

  while (e >= 0.00001)
    nuy_test  = Math.sqrt((gamma+1)/(gamma-1)) * Math.atan(Math.sqrt((gamma-1)/(gamma+1)*(pow(my, 2)-1))) - Math.atan(Math.sqrt(pow(my, 2)-1))
    e         = nuy - nuy_test
    my        = my+0.00001
  end

  my        = my-0.00001
  ty_tx     = (1+(gamma-1)/2*pow(mx, 2))/(1+(gamma-1)/2*pow(my, 2))
  py_px     = pow((1+(gamma-1)/2*pow(mx, 2))/(1+(gamma-1)/2*pow(my, 2)), gamma/(gamma-1))
  rhoy_rhox = pow((1+(gamma-1)/2*pow(mx, 2))/(1+(gamma-1)/2*pow(my, 2)), 1/(gamma-1))
  mux       = Math.asin(1/mx)
  muy       = Math.asin(1/my)

  result = {
    ty_tx:      ty_tx,
    py_px:      py_px,
    rhoy_rhox:  rhoy_rhox,
    my:         my,
    nux:        nux*180/pi,
    nuy:        nuy*180/pi,
    mux:        mux*180/pi,
    muy:        muy*180/pi,
  }
end

.rayleigh(m, gamma) ⇒ Object 



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# File 'lib/engineering_calculator/gas_dynamics.rb', line 159

def self.rayleigh(m,gamma)
  p_ratio   = (gamma+1)/(1+gamma*pow(m, 2));
  rho_ratio = (1+gamma*pow(m,2))/((1+gamma)*pow(m,2));
  t_ratio   = pow(gamma+1, 2)*pow(m, 2)/pow(1+gamma*pow(m, 2), 2);
  u_ratio   = (gamma+1)*pow(m, 2)/(1+gamma*pow(m, 2));
  po_ratio  = (gamma+1)/(1+gamma*pow(m, 2)) * pow(2/(gamma+1)*(1+(gamma-1)/2*pow(m, 2)), gamma/(gamma-1));
  to_ratio  = 2*(gamma+1)*pow(m, 2)/pow(1+gamma*pow(m, 2),2) * (1+(gamma-1)/2*pow(m, 2));

  result = {
    p_ratio:    p_ratio,
    rho_ratio:  rho_ratio,
    t_ratio:    t_ratio,
    u_ratio:    u_ratio,
    po_ratio:   po_ratio,
    to_ratio:   to_ratio
  }
end